diff --git a/.gitattributes b/.gitattributes
index 5efb3ef53711355c806e9f61b856e197a2d9d507..3fa8738dc0f95eadcdf7d3be86a4b1c14100699a 100644
--- a/.gitattributes
+++ b/.gitattributes
@@ -15422,3 +15422,71 @@ jNFJT4oBgHgl3EQfXSyN/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -tex
 0tFRT4oBgHgl3EQfkzf9/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
 INAzT4oBgHgl3EQfjf2_/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
 89AzT4oBgHgl3EQfgvxw/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+ndE3T4oBgHgl3EQf7Asa/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+SNE2T4oBgHgl3EQfCAY8/content/2301.03608v1.pdf filter=lfs diff=lfs merge=lfs -text
+5NAzT4oBgHgl3EQf9v7Q/content/2301.01925v1.pdf filter=lfs diff=lfs merge=lfs -text
+htAyT4oBgHgl3EQfXvc6/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+5NE6T4oBgHgl3EQflhFb/content/2301.06150v1.pdf filter=lfs diff=lfs merge=lfs -text
+SNE2T4oBgHgl3EQfCAY8/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+5tAyT4oBgHgl3EQf2fk_/content/2301.00751v1.pdf filter=lfs diff=lfs merge=lfs -text
+idFJT4oBgHgl3EQfWizT/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+uNE5T4oBgHgl3EQfLQ6L/content/2301.05472v1.pdf filter=lfs diff=lfs merge=lfs -text
+gdE0T4oBgHgl3EQfXgBN/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+adFAT4oBgHgl3EQf4h70/content/2301.08727v1.pdf filter=lfs diff=lfs merge=lfs -text
+b9AyT4oBgHgl3EQf-PqC/content/2301.00889v1.pdf filter=lfs diff=lfs merge=lfs -text
+LNE3T4oBgHgl3EQfYAr5/content/2301.04485v1.pdf filter=lfs diff=lfs merge=lfs -text
+RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf filter=lfs diff=lfs merge=lfs -text
+VtE4T4oBgHgl3EQfng0j/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+gdE0T4oBgHgl3EQfXgBN/content/2301.02293v1.pdf filter=lfs diff=lfs merge=lfs -text
+39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf filter=lfs diff=lfs merge=lfs -text
+dNFAT4oBgHgl3EQfYx1Q/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+ddFST4oBgHgl3EQfEzgN/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+b9AyT4oBgHgl3EQfi_hp/content/2301.00406v1.pdf filter=lfs diff=lfs merge=lfs -text
+dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf filter=lfs diff=lfs merge=lfs -text
+_tA0T4oBgHgl3EQfPf_J/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+nNFIT4oBgHgl3EQfuCsf/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+nNFIT4oBgHgl3EQfuCsf/content/2301.11341v1.pdf filter=lfs diff=lfs merge=lfs -text
+b9E2T4oBgHgl3EQfFgZ2/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+XdE3T4oBgHgl3EQfbwqk/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+5NAzT4oBgHgl3EQf9v7Q/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+uNE5T4oBgHgl3EQfLQ6L/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+zNAyT4oBgHgl3EQf0vni/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+n9E_T4oBgHgl3EQf8Byb/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+0dE0T4oBgHgl3EQfdQAz/content/2301.02373v1.pdf filter=lfs diff=lfs merge=lfs -text
+2dAyT4oBgHgl3EQfPvZl/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+RtFJT4oBgHgl3EQfKyxj/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+39AzT4oBgHgl3EQf9f54/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+m9E5T4oBgHgl3EQfHw6d/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf filter=lfs diff=lfs merge=lfs -text
+J9FIT4oBgHgl3EQfZytY/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+BNE4T4oBgHgl3EQfFAx2/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+xdE5T4oBgHgl3EQfMw71/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+5NE6T4oBgHgl3EQflhFb/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+39AyT4oBgHgl3EQfP_aH/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf filter=lfs diff=lfs merge=lfs -text
+JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf filter=lfs diff=lfs merge=lfs -text
+8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf filter=lfs diff=lfs merge=lfs -text
+O9AzT4oBgHgl3EQfIfuL/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+eNE1T4oBgHgl3EQfeQRR/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+eNE2T4oBgHgl3EQfbQcn/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+8tE0T4oBgHgl3EQfwgFY/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf filter=lfs diff=lfs merge=lfs -text
+p9AzT4oBgHgl3EQfAvo4/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+5dFJT4oBgHgl3EQfkywG/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf filter=lfs diff=lfs merge=lfs -text
+JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf filter=lfs diff=lfs merge=lfs -text
+cNAzT4oBgHgl3EQfnf3Z/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+stE1T4oBgHgl3EQfjgQE/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf filter=lfs diff=lfs merge=lfs -text
+ndE1T4oBgHgl3EQfhgRQ/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+GNAzT4oBgHgl3EQfi_3N/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+StA0T4oBgHgl3EQfD_-h/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+bdFRT4oBgHgl3EQfRzcI/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf filter=lfs diff=lfs merge=lfs -text
+rtAyT4oBgHgl3EQfz_l6/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+zjlab/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+adFAT4oBgHgl3EQf4h70/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf filter=lfs diff=lfs merge=lfs -text
+zjlab/vector_store/index_kw.faiss filter=lfs diff=lfs merge=lfs -text
+F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf filter=lfs diff=lfs merge=lfs -text
+QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf filter=lfs diff=lfs merge=lfs -text
diff --git a/09FPT4oBgHgl3EQfTzT7/content/tmp_files/2301.13055v1.pdf.txt b/09FPT4oBgHgl3EQfTzT7/content/tmp_files/2301.13055v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b0049cd52911a8aefb3b812c340867aedfd63a61
--- /dev/null
+++ b/09FPT4oBgHgl3EQfTzT7/content/tmp_files/2301.13055v1.pdf.txt
@@ -0,0 +1,1308 @@
+Theoretical model of membrane protrusions driven by curved active proteins
+Yoav Ravid 1,∗, Samo Peniˇc 2, Yuko Mimori-Kiyosue,3, Shiro Suetsugu,4,5,6, Aleˇs Igliˇc 2, and Nir S. Gov 1,∗
+1Department of Chemical and Biological Physics, Weizmann Institute of Science, Rehovot, Israel
+2Laboratory of Physics, Faculty of Electrical Engineering, University of Ljubljana, Ljubljana, Slovenia
+3Laboratory for Molecular and Cellular Dynamics,
+RIKEN Center for Biosystems Dynamics Research,
+Minatojima-minaminachi, Chuo-ku, Kobe, Hyogo 650-0047, Japan
+4Division of Biological Science, Graduate School of Science and Technology,
+Nara Institute of Science and Technology 8916-5, Takayama, Ikoma, Nara, 630-0192, Japan
+5 Data Science Center, Nara Institute of Science and Technology, Ikoma 630-0192, Japan
+6 Center for Digital Green-innovation, Nara Institute of Science and Technology, Ikoma 630-0192, Japan
+Eukaryotic cells intrinsically change their shape, by changing the composition of their membrane
+and by restructuring their underlying cytoskeleton. We present here further studies and extensions
+of a minimal physical model, describing a closed vesicle with mobile curved membrane protein
+complexes. The cytoskeletal forces describe the protrusive force due to actin polymerization which is
+recruited to the membrane by the curved protein complexes. We characterize the phase diagrams of
+this model, as function of the magnitude of the active forces, nearest-neighbor protein interactions
+and the proteins’ spontaneous curvature. It was previously shown that this model can explain the
+formation of lamellipodia-like flat protrusions, and here we explore the regimes where the model can
+also give rise to filopodia-like tubular protrusions. We extend the simulation with curved components
+of both convex and concave species, where we find the formation of complex ruffled clusters, as well
+as internalized invaginations that resemble the process of endocytosis and macropinocytosis. We
+alter the force model representing the cytoskeleton to simulate the effects of bundled instead of
+branched structure, resulting in shapes which resemble filopodia.
+Keywords: Cell membrane, Curved inclusions, Monte-Carlo simulations, Closed vesicle shapes, Cell motility, Filopodia
+I.
+INTRODUCTION
+Cells in our body have different shapes depending on their function, and they control their shapes by exerting
+forces on the flexible plasma membrane [1]. These forces are mostly due to the underlying cytoskeleton, dominated
+by the cortical actin network. The actin polymerization near the membrane exerts protrusive forces that can give
+rise to cellular protrusions, such as filopodia and lamellipodia [2]. The control of the actin polymerization in space
+and time is provided by a host of proteins that nucleate actin polymerization where and when it is needed, and
+are in turn controlled by different signalling cascades. One mechanism for controlling the spatial pattern of actin
+polymerization on the membrane, is to couple the actin nucleation to curved membrane components (CMCs), that are
+both bending locally the membrane and are sensitive to the local membrane curvature (such as BAR domain proteins
+[3]). This coupling was shown theoretically to give rise to positive and negative feedbacks [4], that can result in pattern
+formation in both the spatial distribution of the actin nucleators (recruited by the CMCs) and the membrane shape.
+This coupling between curvature and active protrusive forces was explored for a limited regime of parameters in [5].
+Experimental evidence for this coupling between CMC and protrusive forces has been accumulated in the context of
+lamellipodia [6, 7] and filopodia [8–14] formation.
+A summary of the vesicle shapes that we found in [5] are shown in Fig.1, explored as function of temperature and
+CMC density (Fig.1A). The main phases which were identified are [15]:
+• Diffused CMC-gas phase, where CMC are dispersed as entropy dominates over bending and binding energies.
+• Budded phase, where binding and bending leads to CMC forming hemispherical clusters at the CMC spontaneous
+curvature.
+• Flattened ”pancake” phase, where the active forces push the CMC outwards, leading to a large CMC cluster along
+the rim, with two flat bare membrane disc regions. Low temperature is required to prevent lateral membrane
+fluctuations and thermal diffusion of the CMC from breaking up the rim cluster.
+The pancake phase is quite dynamic, and tends to form ”ruffles” along the edges. With insufficient density of CMC,
+there is a ”two-arc” phase with multiple flat edges connected by elongated membrane (Fig.1B). If the CMC density if
+high, the excess CMC form pearled structures along the rim of the pancake (Fig.1C).
+arXiv:2301.13055v1  [cond-mat.soft]  30 Jan 2023
+
+2
+When the active force is weak or zero (passive CMC), at low temperatures the system is phase-separated into
+energy-minimizing ”pearled necklace” of CMC clusters, each at the CMC spontaneous curvature (Fig.1D). When the
+force is strong and the CMC have low spontaneous curvature (flat), there is a phase of highly elongated ”tubular”
+vesicles, where CMC caps apply large forces that pull membrane tethers (tubular protrusions) (fig.1E).
+Here we expand the analysis of the coupling between the spontaneous curvature of the CMC and protrusive forces,
+by exploring the patterns that form as function of the natural parameters that the cell can manipulate, such as the
+strength of the actin-driven force, the binding strength between the CMCs and the spontaneous curvature of the
+CMCs. By gaining a fuller understanding of the space of shapes that this coupling can produce, we are able to explore
+two more complex configurations: a mixture of two CMCs of different intrinsic curvatures, and CMCs that induce
+aligned active forces which model the effects of actin bundling[16]. These more complex systems, can be compared to
+important biological phenomena, such as endocytosis[17] and filopodia.
+II.
+THE MODEL
+We follow the same coarse-grained continuum model used previously [5] and [18], where the physics of the cell shape
+is described by differential geometry and very few energy components [1, 19]. The lipid bilayer membrane is modeled
+as a 2D flexible sheet, with zero spontaneous curvature, except where there are CMCs. Each CMC on the membrane
+surface represents a complex of proteins that have a specific spontaneous curvature. The energy of the surface is
+modeled by the Helfrich hamiltonian
+Hbending =
+��
+κ
+2 (C1 + C2 − C0φ)2
+(1)
+which penalizes deviation of the shape, given by the local curvatures C1 and C2, from a preferred local shape, determined
+by the CMC relative lateral density φ and the CMC’s preferred membrane curvature C0. To simulate, we discretize
+the system as a closed vesicle described by a graph V, E (vertices and edges respectively) with vertices representing
+small area patches of either bare lipid bilayer or CMC. Note that the simulation does not have an intrinsic length
+scale, however the edge length has to represent lengths larger than tens of nanometers for the coarse-grained model to
+be physically valid. We therefore obtain the following discretized energy
+E =
+�
+i∈V
+κ
+2 (2h(i) − ρiC0)2 A(i) +
+�
+⟨i,j⟩∈E
+−wρiρj +
+�
+i∈V
+wad θ (zi − z0)
+(2)
+where ρi = 1 for a CMC vertex and ρi = 0 for a bare vertex, such that the overall density of CMC is given by
+ρ = �
+i∈V ρi/N, where N = 4502 is the total number of vertices in our simulations. The first term is a discretized
+version of the bending energy (Eq.1), κ is the bending modulus, h(i) is the mean curvature calculated at each vertex
+h = (C1 + C2)/2, C0 is the spontaneous curvature of a CMC, and A(i) is the area assigned to the vertex. The second
+term is the CMC-CMC nearest-neighbor binding energy, going over the edges ⟨i, j⟩, where w is the binding energy per
+bond. The third term is adhesion energy of the membrane to a flat rigid surface located at z = z0, which applies to
+all the nodes that are within a distance of ℓmin from this surface. The membrane is prevented from moving below
+z0 − ℓmin.
+This energy model is used in a Monte-Carlo (MC) simulation Trisurf-ng, described in [5], where random movement
+of vertices and bond flips of edges are accepted if they lower the energy or according to a Boltzmann probability:
+P = exp (−∆E − Wi) where Wi represents the work done by the active forces on each node that contains a CMC, as
+follows
+Wi = −f ˆn(i) · δ⃗xi
+(3)
+where ˆn(i) is the local outwards normal unit vector, and δ⃗xi is the vertex displacement.
+The shift in the locations of the vertices are limited such that the length of each edge remains within this range:
+ℓmin < ℓ < ℓmax. The edge length and adhesion surface constraints are enforced by rejecting any MC moves which
+violate them. In a passive system this would lead to thermal equilibrium, but the active work term is unbounded
+from below, so the system is out of equilibrium. The MC simulation does not have time-scale, as it does not include
+the hydrodynamic flows and dissipative processes that determine the relaxation time-scales of the membrane shape
+changes. It does allow us to follow the shape dynamics by evolving the system along decreasing energy gradients, so
+the trajectory in shape space is correctly described.
+The parameters in the model, used in this paper, are given in table I. All the energies in the model are in units of
+kBT (κ, w), while the external force f is in units of kBT/ℓmin.
+
+3
+In addition, we implement optional models of inhibition of the force on the CMC by neighbors, based on [20] which
+shows different protein species can inhibit the activity of polymerization, inhibiting the actin recruitment and thus
+force on the CMCs. We implement a proportional inhibition, where an active (1) and inhibiting (2) CMC species exist
+f prop
+i
+= f
+1
+Nneighbors
+�
+⟨i,j⟩
+�
+1 − ρ(2)
+j
+�
+(4)
+We also implement a disabling inhibition, where any inhibiting CMC species completely disables the force on it’s
+neighbors.
+f dis
+i
+= f
+�
+⟨i,j⟩
+�
+1 − ρ(2)
+j
+�
+(5)
+In biological filopodia, the actin filament are known to bundle by cross-lining proteins [21]. Our model does not
+have a true representation of the cytoskeleton structure, but we can simulate this bundling by adding an alignment to
+the force on the active CMCs, since the shared internal actin bundle would apply a force in the same direction. This is
+added as an Vicsek-like interaction [22]
+ˆf = ˆni + s �
+r ˆnj
+|ˆni + s �
+r ˆnj|
+(6)
+The direction of force on CMC vertex i ˆfi is a weighted average of the normal direction plus a contribution from all the
+vertices j a distance r from the vertex i with a weight of s, normalized. This replaces the ˆn(i) term in the work term
+i.e. the unmediated local normal. This is superficially similar to the normal Vicsek model [22], where self-propelled
+particles similarly align their direction with neighbors, producing flocking behavior, but here the CMCs/particles are
+connected to each other and embedded in a 2D flexible sheet, and we use force in a MC simulation instead of velocity
+in a Langevin simulation.
+III.
+MATERIALS AND METHODS
+A.
+Computational Methods
+The simulations were run using trisurf-ng [5] version fb86a41 (”Modeled trisurf” branch) (see X) with a tape file
+modified from the available default with the different physical parameters (see I), and additional simulation running
+parameters of nshell=30, mcsweeps=50,000-200,000, iterations=100-1,000 (depending on the desired time resolution).
+Each simulation with a set of parameters was ran independently (”embarrassingly parallel”), which took about two
+weeks to finish, with occasional restarts and expansion of the space limits (nxmax). The resulting VTU files were
+viewed and colored in ParaView, but further analysis and graph generation were done by separate python scripts.
+B.
+Experimental Methods
+The cell culture and lattice light sheet microscopic observation U-251 cells were obtained from the Japanese Collection
+of Research Bioresources Cell Bank. The IRSp53 knockout (KO) cells were generated by the CRISPR/Cas9 system, as
+described previously [23]. The guide RNA targeting the first exon of IRSp53 (CCATGGCGATGAAGTTCCGG) was
+designed using the server http://crispr.mit.edu and inserted into the pX330 vector [23]. After transfection, the cells
+were cloned by monitoring the GFP fluorescence from the reporter plasmid pCAG-EGxxFP with the IRSp53 genome
+fragment using a fluorescence-activated cell sorter [FACSAria (BD)] [24]. The expression of GFP or GFP-IRSp53
+in the IRSp53 knockout cells was performed by the retrovirus-mediated gene transfer, as described previously [24].
+All cell lines were cultured in high glucose DMEM (Thermo Fisher Scientific) supplemented with 10% bovine calf
+serum (Thermo Fischer Scientific) and 1% penicillin-streptomycin solution (Thermo Fischer Scientific) and stored in
+an incubator at 37oC in 5% CO2 and humidified conditions. The cells were seeded on coverslips and then imaged with
+the Lattice light-sheet microscope built in the Mimori-Kiyosue laboratory at RIKEN Center for Biosystems Dynamics
+Research following the design of the Betzig laboratory [25] as described previously [26].
+
+4
+IV.
+FORCE-BINDING STRENGTH PHASE DIAGRAM
+In [5] the phases of the vesicle with active CMC, were mostly explored as function of temperature and global density
+of CMC. However, the cell can more easily modify other parameters, such as the strength of the protrusive forces
+produced by actin polymerization and the binding strength between neighboring CMC. The rate of actin polymerization
+recruited to the CMC can be controlled by the cell through various proteins [27–29]. The effective binding strength
+between the neighboring CMC can similarly depend on the lateral concentration and character of the proteins that
+form the CMC [7], as well as on the type of lipids between the CMC [30]. The cell can modify these internal parameters
+spontaneously or in response to external signals.
+We scan over the force f and binding strength w parameters plane (Fig.2A), with the other parameters of the model
+having the following constant values: The bending modulus is taken to be κ = 20KBT, which is a typical value for
+lipid bilayers. The spontaneous curvature of the CMC is taken to be C0 = 1ℓ−1
+min, representing highly curved objects on
+the membrane. The CMC density is ρ = 10%, which is sufficient to form the pancake shapes that require a complete
+circular cluster of CMC along the vesicle rim [5].
+We find that the simulated vesicles can be divided into several distinct phases: gas phase, budded phase, pancake
+phase, and pearling phase. In addition there are more ambiguous, and possibly transient, elongated and mixed phases
+(Fig.2A). In order to distinguish between these phases, we use four measures that characterize the vesicle shape and
+the CMC cluster organization:
+• Mean cluster size ⟨N⟩
+• 1st eigenvalue of the Gyration tensor λ2
+1
+• 2nd eigenvalue of the Gyration tensor λ2
+2
+• Length of CMC-bare membrane boundary ℓp
+The mean cluster size is averaged over all the CMC clusters, each cluster i having a size Ni of vertices
+⟨N⟩ =
+�
+i Ni
+�
+i 1 = Nvertex
+Nclusters
+We plot this measure (Fig.2B), extracted after the simulation reaches its steady-state regime, where the measures do
+not change on average (see SI). we see that it allows to clearly distinguish the gas phase, which has small cluster sizes
+(yellow line in Fig.2A denotes ⟨N⟩ = 1.5). However, it is rather poor at separating the condensed phases, which all
+have large clusters but differ greatly in their morphology and cluster organization. This is due to the dependence
+of this measure on the number of clusters, which gives large weight to small single-vertex clusters. This makes this
+measure too noisy to distinguish between the other phases, except for the gas phase which mostly contains single-vertex
+clusters.
+We therefore use morphological measures in order to clearly distinguish between the different phases where the
+CMCs are condensed in large clusters. The morphology of the vesicle is quantified by the eigenvalues of the gyration
+tensor λ2
+i . The gyration tensor [31] is defined as the average over all the vertices, with respect to the center of mass
+(similar to the moment of inertia tensor for equal-mass vertices)
+RG ij = ⟨rirj⟩ = 1
+N
+�
+vertices
+�
+�
+x2 xy xz
+xy y2 yz
+zx yz z2
+�
+�
+This can be visualized by a unique ellipsoid which has the same gyration tensor
+xT R−1
+G x = (x · e1)2
+λ2
+1
++ (x · e2)2
+λ2
+2
++ (x · e3)2
+λ2
+1
+= 3
+The eigenvectors ei of the gyration tensor are the directions of the semi-axes of the equivalent ellipsoid and the
+eigenvalues are their length squared divided by 3, ordered by their size: λ2
+1 ≤ λ2
+2 ≤ λ2
+3. The first eigenvalue λ1
+essentially gives how thin is the ellipsoid, and is low for both pancake and highly elongated (linear) shapes. The
+second eigenvalue λ2 is large for the pancake shape (as it is roughly equal to the largest eigenvalue λ2 ∼ λ3), but is
+minimized for elongated shapes, where it similar to the value of the smallest eigenvalue, λ2 ∼ λ1. In Fig.2C,d we plot
+the eigenvalues λ2
+1, λ2
+2, respectively. We find that the phase of pancake shapes is distinguished by the lowest λ2
+1 (green
+and dashed green-light blue lines in Fig.2A), indicating its flatness.
+
+5
+We identify a new phase of elongated shapes, which is distinguished by the lowest values of λ2
+2 (between the light
+blue and dashed green-light blue lines in Fig.2A). These elongated phases are somewhat similar to the ”two-arc” phase
+found in [5], which appeared when there are not enough CMCs to form a complete circular cluster along the flat vesicle
+rim. However, here we do have enough CMC to form a complete circular cluster, as shown in the ”flat” regime. The
+origin of the elongated shapes as w increases beyond the ”flat” phase is due to the formation of transient or stable
+pearling clusters. These cluster effectively sequester enough CMC to prevent the formation of the complete circular
+cluster, leading to two curved regions that collect the CMC and stretch the vesicle due to the active forces. The CMC
+clusters have the shape of flat arcs near the boundary with the ”flat” phase, while closer to the ”pearling” phase the
+clusters are pearled and localized near the curved tips of the vesicle.
+While the ”core” of the phases distinguished by λ2
+1,2 is clear, the edges are much less sharp, due to lack of statistics,
+long evolution time, and the fact that intermediate shapes do exist. There is also no obvious normalization: The
+volume changes greatly, and the area is only approximately conserved. For our Nvertex = 4,502 The flat phase is found
+around λ2
+1 < 50, and the elongated phases is found around 80 < λ2
+2 < 150.
+Finally, we wish to distinguish the phases where the CMCs form pearled clusters. The most outstanding property of
+the pearled clusters is that they phase-separate between the CMC and the bare membrane, as also predicted within
+the theory of self-assembly [5]. We therefore measure the average length of the CMC-bare membrane boundary ¯ℓp, per
+CMC, for all clusters larger than 1 (see SI section 1, Fig.S1)
+¯ℓp =
+�ℓpi
+Ni
+�
+Ni>1
+The phase with pearling clusters is distinguished by having very low ¯ℓp < 0.375 (Fig.2E). We find that this measure
+identifies the pearled clusters both in the pearling and in the elongated phases (red dotted line in Fig.2A). In addition,
+a contour of this measure allows us to separate the mixed phase, where the CMC are in both buds and pearled clusters,
+from the phase that contains only buds (red solid line ¯ℓp <= 1.875 in Fig.2A,E).
+Note that we do not know if these phases are necessarily the absolute steady-states of the system in the limit of
+infinite time. The system might be trapped in a local meta-stable configuration due to dynamical barriers that would
+require unreasonably long simulations for them to escape. For example, in the regime of low force f and large binding
+strength w, the global minimum energy configuration should have all the CMC in a single pearled cluster, but during
+the merging of the pearled clusters into a single cluster they have to overcome bending energy barriers that hinder this
+process [32]. In other regimes, such as the elongated phase, we do not know if a stationary steady-state even exists,
+since the presence of active forces may induce a constantly changing configurations. In the SI section 2 we give a
+simple analytic calculation that gives reasonably well the transition line between the pearled and flat phases, which
+are the main stable condensed phases in this phase diagram (Figs.S2,S3).
+The evolution of a handful of chosen simulations are shown in Fig.3, showing flat, elongated-flat, elongated-pearling,
+and pearling phases. All the simulations begin in a disordered uniform distribution of the CMC on the spherical vesicle,
+but in all of them we find that buds form rather quickly (Fig.3B(i)-E(i)). In the budded phase this configuration
+simply remains stable and does not evolve significantly. It takes longer time for the larger clusters of the flat rim, arcs
+and pearls to form. The transition lines separating two different vesicle phases, obtained from our simulations, are not
+precise, and one can obtain either one of the vesicle shapes close to these lines (Fig.3A).
+To conclude, by exploring the f − w phase diagram, we demonstrate the competition between the protein binding
+which drives the formation of pearled clusters, and the active force that drives the formation of arc-like clusters at
+the edge of flat protrusion. This competition is highlighted in the new phases of vesicle morphologies that we found,
+namely the elongated two-arcs and the elongated-pearled phases. The pearling phase appears for large enough values
+of w, as follows also from the theory of self-assembly [5].
+V.
+FORCE-SPONTANEOUS CURVATURE PHASE DIAGRAM
+We now proceed to explore the interplay between the active force and the spontaneous curvature of the CMC in
+determining the morphology of the vesicle. We chose the parameters for a new set of simulations such that we are in
+the flat phase when the CMC are highly curved: ρ = 20%, κ = 28.5, w = 2. The resulting phase diagram is shown in
+Fig4A.
+We find several phases: budded phase, flat phase, elongated (arcs) phase and highly-elongated (tubes) phase. Here
+the boundaries between the different phases were drawn by eye, due to relative sparse scan over the parameters, and the
+self-evident boundaries (Fig.4A). In this parameter regime, we do not find any pearled phase, with the budded phase
+remaining stable due to the bending energy barrier that prevents buds merging (note that the bending modulus is
+larger here), and lower relative w. Similar to the force-binding strength system (Fig.2A), where the budded and pearled
+
+6
+phases exist for low active force, we also find that as the active force is increased the budded phase is destabilized to
+form the flat phase (Fig.4A).
+The flat phase is destabilized as the spontaneous curvature decreases due to the following mechanism: as C0 decreases
+the thickness of the rim cluster increases, which means that there are not enough CMC to complete a circular cluster
+around the edge of the flat shape. The morphology then changes into local arc-like clusters that pull the vesicle into
+elongated shapes. The elongation of these vesicles depends on the magnitude of the active force.
+The main feature of this phase diagram is the appearance of the highly-elongated tubular phase, where the entire
+vesicle is stretch into a several tubes that are pulled by CMC clusters at their tips. We can theoretically estimate
+the location of the phase transition line, above which a vesicle will become highly-elongated, by comparing the force
+exerted by the active CMC cluster and the restoring force of the emerging membrane tube due to bending (Fig.4B).
+A hemispherical CMC cap with radius r = 2/C0 minimizes the bending energy (Eq.1): E ∝
+�
+1
+r1 + 1
+r2 − C0
+�2
+, and
+maximizes the pulling force (since adding any more CMCs to the cluster, beyond the hemisphere, adds force in the
+opposite direction). The total pulling force of this hemispherical cluster is given by
+Fpull = f ·
+1
+2
+����
+geometry
+· 2π(2/C0)2
+s0
+�
+��
+�
+#vertices
+(7)
+where s0 is the area per vertex, and 2πr2/s0 is the number of CMC in the cluster. This hemispherical cap pulls a tube
+with the same radius from the main vesicle body. Note the extra factor of 1/2 due to the hemispherical shape of the
+cup, compared to the calculation done for a flat cluster of active proteins in [5].
+Assuming the restoring force is dominated by the bending energy of the membrane tube, it is given by (Eq.1) [5]
+Frestore = κ
+2
+2π
+(2/C0)
+(8)
+The highly elongated shape is initiated when the pulling force is greater than this restoring force, so the critical value
+is given by equating Eqs.7,8, which gives
+f = AC3
+0
+(9)
+where A is a constant determined by the constant parameters of the simulation (bending modulus and average area
+per vertex). Plotting this simple cubic relation in Fig.4A (blue solid line, where we fit the value of A), shows a good
+agreement with the observed boundary of the regime of the highly-elongated tubular shapes on the phase diagram.
+Note however that the shapes of the vesicles at the transition to the tubular phase are not always simple cylindrical
+tubes with hemispherical clusters at their tips (Fig.4A), as the analytic model assumes (Fig.4B).
+To conclude this section, we have shown that active CMC give rise to flat protrusions when they are highly curved.
+Tubular protrusions can form for weakly curved active CMC, while for highly curved CMC the active force needed
+to produce such slender protrusions increases extremely fast. In the next sections we explore how slender tubular
+protrusions can be produced with highly curved active proteins, by either changing the effective curvature of the CMC
+cluster, or by increasing the effective pulling force of the cluster.
+VI.
+MULTIPLE CURVATURE
+Real cells have many species of membrane protein of both convex and concave intrinsic curvature. While these
+membrane proteins have distinct curvatures, the effective curvature of a cluster of CMC may depend on the composition
+of the cluster, if it contains CMC of different spontaneous curvatures. In order to form clusters of mixed curvatures,
+we explore vesicles that contain CMC of different curvatures (concave and convex), that bind to each other equally. If
+the two CMC types bind only to their own kind, they form separate clusters on the vesicle, and their coupling with
+each other due to curvature alone is rather weak (see SI). The convex CMC maintain their activity, as in the previous
+sections, while the concave CMC is passive.
+In Fig.4C(i) we show snapshots of the steady-state shapes of the vesicles that contain 10% passive concave CMC, i.e.
+a CMC species with C−
+0 < 0 and f − = 0, in addition to convex CMCs (ρ+ = 10%, f = 0.5, and C+
+0 = 0.8). Both
+types of CMC have the same binding strength w = 2, which binds both types equally, leading to strong mixing of the
+two CMC types. For weakly curved concave CMC (C−
+0 = −0.001) the flat phase remains stable (Fig.4C(i6)), driven by
+the convex active CMC. As the concave CMC become more curved (Fig.4C(i) from right to left) the circular cluster at
+the rim of the flat shape breaks up, and highly elongated shapes appear (Fig.4C(i2,i3)).
+
+7
+These shapes can be explained by mapping the vesicles in Fig.4C(i) on the phase diagram (Fig.4A). For each
+simulation, we calculate the average spontaneous curvature of the CMC clusters: C0,eff =
+�
+C+
+0 + C−
+0
+�
+/2, as well as
+the average pulling force per CMC: feff = f/2. In Fig.4D we plot the typical dashed outline of the vesicles from
+Fig.4C(i) on the phase diagram according to these effective parameters C0,eff, feff. Most vesicles match the shape
+of the phase to which they are mapped in this way. The only exception is the vesicle with the most concave CMCs
+(and effective C0,eff = 0), which is not in the shape of highly-elongated tubes, as suggested by the calculated average
+parameters, but fits better the arcs phase. This phenomena is due to the concave CMCs phase-separating into internal
+”sacks” of concave-enriched clusters (Fig. 5Ai), which results in an effective removal of these concave CMC from
+determining the outer shape of the vesicle. To take this into account, we calculate the effective mean curvature of the
+CMCs while removing the concave CMC that are contained in the internalized sacks. This is done by including in the
+calculation of the average curvature only concave CMCs which are connected to at least one convex CMC. Using this
+revised average spontaneous curvature, we plot the locations of the vesicles on the phase diagram (full snapshots),
+and find that except for the most curved concave CMC (A1), the locations of the other vesicles is minimally affected.
+For the case A1, we find that indeed the formations of large sacks of concave CMC, push the vesicle into the arcs
+regime, compatible with its revised location on the phase diagram. The phase separation of the passive concave CMC
+into sacks is driven by the minimization of the total bending energy. The highly elongated tubes cost a high bending
+energy of the bare membrane: in Fig.4C(i2) the average bending energy of the bare membrane is ∼ 25KBT, while in
+the flatter shapes after the phase separation (Fig.4C(i1)) the average bending energy of the bare membrane drops to
+∼ 17KBT.
+In addition to the overall vesicle shape in the system of mixed curvatures, we are interested in the character of the
+CMC clusters. We find that concave and convex CMCs create complex mixed clusters with a ”coral”- or ”sponge”-like
+texture (Fig.4C and close up in Fig. 5Aii). The texture of these clusters seems similar to the membrane ruffles observed
+in [20] behind the leading edge of motile cells. In this work, the ruffles were attributed to the interaction between
+concave and convex membrane proteins, that are also involved in the recruitment of the actin polymerization. It was
+furthermore proposed in [20] that the pattern of ruffles observed in these cells is determined by the interaction between
+a concave membrane protein that inhibits the actin polymerization, which is recruited by the convex CMC. Motivated
+by this proposed mechanism, we explored the resulting shapes of the vesicle and CMC clusters when the concave
+CMCs inhibit the active force exerted by the convex CMCs. We tested two possibilities: inhibition that is proportional
+to the number of concave neighbors (Eq.4, Fig. 4C(ii)), and full inhibition with even one concave neighbor (Eq.5, Fig.
+4C(iii)). In both cases we find that the effective force is reduced, and that the resulting shapes correspond very well to
+their locations on the phase diagram (Fig.4D). The shapes obtained for full inhibition (Fig. 4C(iii)) are very similar
+to those for a vesicle with a mixture of passive CMC (see SI section 3, Fig.S4). Regarding the comparison with the
+experiments [20], we conclude from the model that the ruffle texture of the CMC clusters does not crucially depend
+on the inhibitory interaction between the two CMC types, but rather on their spontaneous curvatures and binding
+interaction.
+Let us now focus on the phase-separated sacks of highly curved concave CMC, which form within the mixed clusters
+(Fig.5). We observed that the neck that connects the sacks to the outer part of the cluster is much narrower when
+the convex CMC exert outwards protrusive forces (compare Fig.5(Aii) and (Cii)). We quantified the area of the
+narrowest part of the neck in Fig.5B,D for the active and passive convex CMC, respectively. The necks are naturally
+narrower for more highly curved concave CMC. The active convex CMC, which push the membrane outwards, exert
+an effective pressure force that squeezes the neck into a narrower radius. Note that for the narrowest necks, we are
+clearly at the limit of the spatial resolution of the simulation. We do not allow membrane fission, and therefore can
+not describe the process of detachment of such sacks as internalized vesicles [33], as occurs in cells during endocytosis
+and macropinocytosis [34].
+In Fig.5E,F we show the dynamics of the cluster formation, whereby a patch of passive concave CMC (blues) increase
+in size, while its rim is populated by active convex CMC (red). In these images the surrounding bare membrane is
+rendered to be invisible. These simulated dynamics resemble those calculated by another model of macropinocytic
+cups [35], which was based on reaction-diffusion dynamics coupled to active forces.
+Finally, when the two CMC types bind exclusively to their own kind, they form separate clusters, with very limited
+coupling between them (see SI section 4, Fig.S5).
+VII.
+FORCE ALIGNMENT
+As we show in Fig.4A, when the highly curved CMC induce a protrusive force that is directed at the outwards
+normal, we require an extremely large force in order for the highly elongated tubes to form. However, cells initiate
+slender, tube-like filopodia protrusions using highly curved membrane proteins, such as IRsp53 [8–10, 12–14], in
+agreement with theoretical calculations [36]. Within the slender filopodia in cells, the actin filaments are organized into
+
+8
+a cross-linked bundle, which efficiently directs the forces of all the polymerizing actin filaments along the protrusion’s
+axis. The actin nucleators at the tip of the filopodia are different from those at the leading edge of the flat lamellipodia
+[14, 21, 37], and initiate the growth of parallel actin filaments that form the bundle at the filopodia core. In our model,
+since we do not explicitly describe the actin filaments organization, we can only describe the effects of the bundling on
+the forces exerted on the membrane. To simulate this kind of bundling, we add an alignment term of a Vicsek-like
+interaction [22], which aligns the forces exerted on the membrane by each CMC that is bound in a cluster
+ˆfi = ˆni + s �
+r ˆnj
+|ˆni + s �
+r ˆnj|
+(10)
+The direction of the active force exerted on each CMC vertex i, ˆfi, is a weighted average of the local outwards normal
+direction (ˆni) and a contribution from all the vertices j within a distance r from the vertex i (and in the same connected
+cluster), with a weight of s.
+In Fig.6A we plot typical steady-state snapshots of the vesicle shape and CMC clusters, as function of the strength
+and range of the alignment interaction of Eq.10. We observe a rather sharp transition from flat shapes for short-range
+alignment (r < 10) to shapes containing thin tube-like protrusions for long-range alignment. As function of the
+parameter s we find only weak dependence: at very small values of s and r = 10, we find that the weak alignment
+is sufficient to increase the net pulling force of the CMC clusters, such that they break the circular rim of the flat
+shape (Fig.4B(iii)). The resulting shape, with ”paddle”-like protrusions, resembles the ”arcs” phase we found in Fig.4
+between the flat and tubes phases. At higher values of s this paddles phase changes to tubes, due to the stronger
+alignment leading to a larger net pulling force.
+At these larger interaction strength the vesicle produces thin, finger-like clusters with a small bulbous ”head” and an
+elongated ”sleeve” (Fig.6B(ii)). This shape allows the CMC to satisfy their spontaneous curvature, with a spherical tip
+that has a radius of rtip = 2/C0, while the sleeve has a thinner radius of rsleeve = 1/C0. Such a cluster configuration
+is stable due to the alignment of the active forces along the tube axis (perpendicular to the membrane along the
+sleeve, Fig.6B(ii)). Once these elongated clusters form, they exert a large pulling force on the remaining membrane,
+thereby pulling elongated bare-membrane tubes behind them. The membrane tube can have a larger radius than the
+radius of the tubular CMC cluster, as it balances the pulling force with the restoring force due to bending energy. The
+alignment of the forces means that the entire CMC cluster pulls along the protrusion axis (Fig.6B(ii)), exerting a
+much larger total force than was possible using purely normal forces at the tip, thereby forming tubes at values of
+the force per protein that are much lower than predicted by Eq.9 and Fig.4A. Smaller clusters that only contain the
+hemispherical tip (such as Fig.6B(i)), do not grow tube-like protrusions, even though their net pulling force is larger
+by up to a factor of 2 compared to normal-force CMC, due to alignment (compare Fig.6B(i) to Fig.4B and Eq.7).
+In Fig.7A we plot the time progression of a vesicle with aligned-force CMC. We observe that initially localized
+hemispherical buds form rapidly. These buds then coalesce to form larger clusters that grow into the typical shape
+of bulbous tip with a thinner tubular part behind it. The size and total force of each of the clusters are plotted as
+function of time, with each point size indicating the cluster size, and its y-axis coordinate giving its total active force,
+respectively. Note that clusters that contain patches of ”trapped” bare membrane undergo large force fluctuations
+(blue and yellow points, largest two clusters shown on the right of Fig.7A). These fluctuations arise from loss of global
+alignment over the entire CMC cluster, due to the bare membrane patch that allows the alignment to change, especially
+between the protrusion tip and the tubular part.
+In Fig.7B we compare the finger-like protrusions that form due to highly curved aligned-force CMC, with the tubular
+shapes that form due to weakly curved normal-force CMC (Fig.4A). The main difference is that the aligned-force
+protrusions are much more stable compared to the tubes formed by the much smaller clusters of normal-force CMC.
+The normal-force CMC undergo frequent fission and coalescence events, that correspond to tubes shrinking and
+regrowing. These differences in dynamics can be seen in the SI movies S1,S2.
+VIII.
+VESICLES WITH BOTH NORMAL AND ALIGNED-FORCE CMC, ADHERED TO A FLAT
+SUBSTRATE
+We simulate a vesicle with a mixture of CMCs (ρ = 5% of each type), both highly curved and convex, one type with
+normal force and the other with strongly aligned force (r = 15, s = 1). Our initial state of the vesicle is obtained by
+letting the vesicle spread over a flat adhesive substrate, while it contains only normal-force CMC. Then, at a time
+where the vesicle is partially spread (time 0 in Fig.8A), we convert randomly half of the CMC to aligned-force behavior.
+We chose an adhesion strength wad = 0.25 (Eq.2), which gives a well-spread vesicle when containing only normal-force
+CMC [18].
+In Fig.8A we show two simulations: one with universal binding between the normal and aligned-force CMCs, and
+the other with exclusive binding, such that normal-normal and aligned-aligned CMC bind to their own type exclusively.
+
+9
+In these examples we see that the rim cluster forms and drives strong spreading of the vesicle, as expected [18]. The
+aligned-force CMC (labeled in yellow) aggregate to form a single filopodia-like protrusion, which is able to recruit into
+it also normal-force CMC (labeled in red). This filopodia is highly dynamic, undergoing periods of attachment to the
+rim cluster, and to the adhesive substrate, as well as detachments from the substrate. The filopodia is observed to
+attach and detach from the rim cluster, leading to meandering motion. When the two types bind exclusively, they
+form segregated clusters along the rim, with the aligned-force clusters protruding slightly more outwards compared to
+the normal-force clusters. The dynamics of this system can be seen in SI movie S3.
+In Fig.8B we show the evolution of the segregation factor in the simulations, which is defined as
+S = 2 · Prob (CMC neighbor is of the same type) − 1
+(11)
+This segregation factor is equal to 0 for well-mixed clusters (where the probability to have a neighbor CMC of the
+same type is equal to 1/2), and it is equal to 1 for complete phase-separation of the types. In the main panels we give
+the segregation factor per cluster for the simulations shown in Fig.8A. The insets show the average of 4 independent
+simulations, which converge to a value of about S = 0.25 for the universal binding and S = 0.9 for the exclusive
+binding. In the universal case, we can see that the segregation is strongest in the filopodia, so the segergation factor
+for the large rim cluster jumps up or down, when the filopodia protrusion cluster attaches or detaches respectively.
+The protrusion cluster is more segregated (S ≈ 0.25), since its tip is enriched with aligned-force CMCs that drive its
+formation, while the rim cluster is nearly perfectly mixed (S ≈ 0). For the exclusive binding, the segregation is high
+both in the filopodia protrusion and in the rim cluster, so it does not change when the filopodia attach or detach from
+the rim.
+Note that along the adhered vesicle rim, the regions of aligned-force CMC protrude slightly more than the normal-
+force regions (Fig.8A, exclusive). This is enhanced when the normal-force CMC are disabled, so that they do not exert
+any active force, as shown in Fig.S6.
+IX.
+COMPARISON WITH EXPERIMENTS
+We can now compare some of our theoretical results to experimental observations, published and new.
+A.
+Membrane shapes driven by branched actin polymerization
+The active protrusive forces in our model are representative of actin polymerization activity near the cell membrane.
+When the actin polymerization is nucleated by proteins that induce branched actin networks (such as WASP, WAVE
+[38–40]), it is more natural to describe the force as a local pressure on the membrane, which therefore acts towards the
+outwards normal.
+The variety of shapes we obtained in our model (Figs.2,3), range from flat lamellipodia-like shapes, to cylindrical
+filopodia, to pearling-like protrusions. Some of these new elongated shapes can be compared with elongated global cell
+shapes, observed in living cells [41].
+B.
+Membrane shapes driven by bundled actin polymerization
+The introduction of alignment in the forces exerted by the CMC represents in our model the case of proteins that
+nucleate parallel actin bundles, such as VASP and Formins [10, 12, 21]. Our model has demonstrated previously that
+curved proteins that apply normal forces, induce the formation of flattened, lamellipodia-like protrusions [5, 18]. Here
+we show that curved proteins that induce polymerization of bundled actin (aligned-force in our model), naturally give
+rise to filopodia-like protrusions (Figs.6,7). This result fits the observation of highly curved convex-shaped proteins
+such as IRSp53 in both the leading edge of lamellipodia [7, 42] and in filopodia [2], where the actin organization is
+very different due to the different type of actin nucleators [38, 43]. Note that the combination of convex curvature, and
+nucleators of bundled actin, can form filopodia even without the explicit presence of I-BAR proteins (such as IRSp53)
+[44, 45].
+Note that protrusions of similar shapes to our aligned-force protrusions, which have a bulbous tip and a slender
+neck (Figs.6,7), were theoretically predicted to form by anisotropic CMC, even without force [46]. Similar thin tubes
+with bulbous tips are observed in cellular nanotubes [47] and in filopodia [48]. Since many curved proteins, such as
+IRSp53 are anisotropic in their intrinsic shape, it will be interesting to extend our work in the future to include such
+anisotropy.
+
+10
+Finally, our simulations of an adhered vesicle (Fig.8) indicate that the filopodia protrusions can undergo attachment
+and detachment from the substrate, resembling such motion observed in experiments [14]. In addition, when we
+mixed the aligned-force and normal-force CMC with exclusive binding between them, we obtained their segregated
+organization along the rim of the adhered vesicle. This is reminiscent of the observations of segregated regions of
+bundled actin and branched actin nucleators along the rim of cellular protrusions extending on adhered substrates
+[37, 49–51]. As in the experiments, the clusters of aligned-force CMC along the rim slightly protrude, as they exert
+a higher local force on the membrane rim, compared to the normal-force CMC. These small protrusions have been
+termed ”spikes” and ”microspikes” along the edge of lamellipodia in cells [45, 50, 52].
+In Fig.9 we show images illustrating the dynamics of filopodia in cells, using lattice light-sheet microscopy, which is
+capable of the high spatial and temporal resolution necessary to view the dynamics of the thin filopodia [53]. The
+curved membrane protein IRSp53 is fluorescently labeled in green (GFP-IRSp53), while the actin filaments are labeled
+in red (mCherry-lifeact). We observe in the experiments several features that are captured by the theoretical model:
+The filopodia are highly dynamic, both at the cell rim and along its dorsal surface (Fig.9A-D), as we also see in the
+model (Fig.8). The filopodia in the experiments migrate on the cell surface, merge with other filopodia, and undergo
+attachments and detachments from the surface (see SI movies 5-8), as we also see in the simulations (SI movies 3 and
+4). Our assumption in the model of uniform adhesion along the membrane, and along the filopodia, agrees with some
+observations [48, 54], and we can add more complex adhesion models in the future if needed. Note that in the cells we
+observe an additional retraction motion that is driven by myosin-II contractile forces, which we do not have in our
+current model.
+The highly curved IRSp53 is observed to aggregate strongly at the tips of the filopodia, while along the lower parts
+of the protrusion its aggregation is more fragmented (Fig.9E,F). This fits with the shapes that we obtained in the
+model (Fig.6B,8A). Furthermore, our simulations of mixtures of aligned-force and normal-force CMC indicate that
+while the aligned-force CMC are essential for forming the filopodia protrusions and occupy its tip region, there can be
+significant amount of normal-force CMC along the lower part of the filpodia. Since the normal-force CMC correspond
+to branched-actin nucleators, this result suggests that along the lower part of filopodia we may expect to find proteins
+such as WAVE, which are usually associated with the leading edge of the lamellipodia. This prediction is supported by
+some experimental observations of WAVE proteins [55], Arp2/3 complexes [56], and small lamellipodia-like protrusions,
+along filopodia shafts [57].
+C.
+Membrane shapes driven by mixtures of passive concave and active convex CMC
+Our mixtures of CMC of opposite curvatures (Figs.4C,5) gives rise to membrane shapes that resemble in their
+texture the ruffles observed in cells [20]. In addition, we find that when the passive concave component is highly
+curved, we observe a phase separation within the CMC clusters, whereby the concave CMC forms an internalized
+spherical invagination. These invaginations are then squeezed at their base by the active forces induced by the convex
+CMC, and the calculated membrane shape dynamics resembles the process of actin-dependent endycytosis [17, 58–60]
+and macropinocytosis [34, 61–63].
+Note that there is some experimental evidence that the internalized membrane, corresponding to our concave CMC
+region, do indeed contain concave membrane components, such as BAR proteins [64]. In addition, there are examples
+where the internalized region contains membrane components that interact with the convex proteins that recruit actin
+and form the squeezing at the narrow neck. In [59] the internalized activated integrins and associated proteins, bind to
+the actin which is nucleated at the neck, recruited there by IRSp53 (convex) proteins. In our model we show that such
+a direct interaction is necessary for robust formation of the internalized sacks with the recruited convex proteins at the
+neck.
+X.
+DISCUSSION
+In this study we greatly extend our theoretical understanding of the space of membrane shapes that are produced
+by curved membrane protein complexes (CMC) that exert active protrusive forces on the membrane [15]. We started
+by mapping the phases as function of the magnitude of the active force and attractive nearest-neighbor interaction
+strength of CMCs (Fig.2A), demonstrating the competition between these two terms: systems dominated by the
+binding interactions tend to have the equilibrium (pearled) shapes of the CMC clusters. The active forces tend to
+break-up the pearled clusters, and induce the formation of either elongated or flat pancake-like membrane shapes.
+Similarly we exposed the phase diagram in terms of the active force and the CMC spontaneous curvature (Fig.4A),
+whereby highly curved CMC induce flattened vesicle shapes, while less curved CMC induce elongated tubular shapes.
+Note that in these studies the protrusive force applied by each CMC is towards the local outwards normal.
+
+11
+Based on these results we further explored systems where highly curved active CMC could induce tubular protrusions.
+We tested two possible scenarios: In the first one, the effective curvature of the CMC cluster is reduced by mixing
+two types of CMC of opposite curvatures, such that a tubular protrusion forms with a rather flat CMC cluster at its
+tip (Fig.4C,D). In the second, the net protrusive force of the CMC cluster is increased by introducing an alignment
+interaction that tends to align the forces exerted by CMC that are bound within the same cluster (Fig.6). This
+alignment is found to stabilize long tubular CMC clusters, since the aligned active forces act along the tube axis and
+do not act to expand the tube, unlike the case of normal protrusive forces.
+We found that that mixtures of CMC of opposite curvatures, specifically passive concave and active convex, lead
+to formation of clusters with complex textures that resemble ruffles on cell membranes (Figs.4C,5). In addition, we
+found in these systems the formation of internalized invaginations, where the convex active CMC form a narrow neck,
+resembling endocytosis and macropinocytosis in cells.
+To conclude, the results presented in this work expand out theoretical understanding of membrane shapes and
+dynamics driven by intrinsic (spontaneous) curvature of membrane components and cytoskeletal active forces. Some
+of these shapes resemble observed membrane dynamics in living cells, suggesting that this coupling between curved
+membrane proteins and cytoskeleton forces gives rise to these biological phenomena. Many of the features that we
+found, such as the ruffles and the internalized invaginations by mixing CMC of different curvatures, remain to be
+further explored in future theoretical studies. In addition, future studies will explore the dynamics of the membranes
+when the CMC have anisotropic spontaneous curvature, and also in the presence of contractile forces.
+Conflict of Interest Statement
+The authors declare that the research was conducted in the absence of any commercial or financial relationships
+that could be construed as a potential conflict of interest.
+Author Contributions
+YR and NG developed the theoretical model; SP and AI developed the software; YR and NG conceived, designed
+and implemented the analysis of the model, and prepared the manuscript. YK and SS cultured and imaged the cells.
+The manuscript was edited by all the authors.
+Funding
+NG is the incumbent of the Lee and William Abramowitz Professorial Chair of Biophysics, and acknowledges support
+by the Ben May Center for Theory and Computation, and the Israel Science Foundation (Grant No. 207/22). AI and
+SM were supported by the Slovenian Research Agency (ARRS) through the Grants No. J3-3066 and J2-4447 and
+Programme No. P2-0232. YK and SS was supported by grants from the JSPS (KAKENHI JP20H03252, JP20KK0341,
+and JP21H05047) and JST CREST (JPMJCR1863) to SS and Takeda Science Foundation, a Grant-in-Aid for
+Challenging Exploratory Research (KAKENHI No. 20K20379), and JST CREST (JPMJCR1863) to YK.
+Acknowledgments
+NG is the incumbent of the Lee and William Abramowitz Professorial Chair of Biophysics. This research is made
+possible in part by the historic generosity of the Harold Perlman Family.
+Supplemental Data
+The SI text, figures, and movies are also available from the Box drive.
+Data Availability Statement
+The code for generating the simulations of this study can be found in the GitHub repository of YR, which is taken
+and modified off the GitBlit repository of SP. Reconstruction of the initial simulation folders are also available from
+
+12
+the Box drive. Further data or code requests will be happily fulfilled by YR.
+[1] F. Frey and T. Idema, Soft matter 17, 3533 (2021), ISSN 1744-6848.
+[2] P. K. Mattila and P. Lappalainen, Nature Reviews Molecular Cell Biology 9, 446 (2008), ISSN 14710072.
+[3] M. Simunovic, G. A. Voth, A. Callan-Jones, and P. Bassereau, Trends Cell Biol. 2015 (2015).
+[4] N. Gov, Philosophical Transactions of the Royal Society B: Biological Sciences 373, 20170115 (2018).
+[5] M. Foˇsnariˇc, S. Peniˇc, A. Igliˇc, V. Kralj-Igliˇc, M. Drab, and N. S. Gov, Soft Matter 15, 5319 (2019), ISSN 17446848,
+1812.01460.
+[6] I. Begemann, T. Saha, L. Lamparter, I. Rathmann, D. Grill, L. Golbach, C. Rasch, U. Keller, B. Trappmann, M. Matis,
+et al., Nature Physics 15, 848 (2019).
+[7] A. Pipathsouk, R. M. Brunetti, J. P. Town, B. R. Graziano, A. Breuer, P. A. Pellett, K. Marchuk, N.-H. T. Tran, M. F.
+Krummel, D. Stamou, et al., Journal of Cell Biology 220, e202003086 (2021).
+[8] G. Scita, S. Confalonieri, P. Lappalainen, and S. Suetsugu, Trends in cell biology 18, 52 (2008).
+[9] S. Ahmed, W. I. Goh, and W. Bu, in Seminars in cell & developmental biology (Elsevier, 2010), vol. 21, pp. 350–356.
+[10] F. Vaggi, A. Disanza, F. Milanesi, P. P. Di Fiore, E. Menna, M. Matteoli, N. S. Gov, G. Scita, and A. Ciliberto, PLoS
+computational biology 7, e1002088 (2011).
+[11] G. Mancinelli, L. Lamparter, G. Nosov, T. Saha, A. Pawluchin, R. Kurre, C. Rasch, M. Ebrahimkutty, J. Klingauf, and
+M. Galic, Proceedings of the National Academy of Sciences 118, e2106921118 (2021).
+[12] F.-C. Tsai, J. M. Henderson, Z. Jarin, E. Kremneva, Y. Senju, J. Pernier, O. Mikhajlov, J. Manzi, K. Kogan, C. L.
+Clainche, et al., Science Advances 8, eabp8677 (2022), https://www.science.org/doi/pdf/10.1126/sciadv.abp8677, URL
+https://www.science.org/doi/abs/10.1126/sciadv.abp8677.
+[13] S. Fox, A. Tran, L. Trinkle-Mulcahy, and J. W. Copeland, Journal of Biological Chemistry 298 (2022).
+[14] S. Y. Lee, T. Fujioka, M. Osuga, T. Nishimura, and S. Suetsugu, in Plasma Membrane Shaping (Elsevier, 2023), pp.
+245–263.
+[15] M. Drab, R. K. Sadhu, Y. Ravid, A. Igliˇc, V. Kralj-Igliˇc, and N. S. Gov, Plasma Membrane Shaping pp. 415–429 (2023).
+[16] H. Mellor, Biochimica et Biophysica Acta (BBA)-Molecular Cell Research 1803, 191 (2010).
+[17] G. J. Doherty and H. T. McMahon, Annual review of biochemistry 78, 857 (2009).
+[18] R. K. Sadhu, S. Peniˇc, A. Igliˇc, and N. S. Gov, European Physical Journal Plus 136, 495 (2021), ISSN 21905444, 2101.00313.
+[19] N. S. Gov, V. Kralj-Igliˇc, R. K. Sadhu, L. Mesarec, and A. Igliˇc, in Plasma Membrane Shaping (Elsevier, 2023), pp. 393–413.
+[20] E. Sitarska, S. D. Almeida, M. S. Beckwith, J. Stopp, Y. Schwab, M. Sixt, A. Kreshuk, A. Erzberger, and A. Diz-Mu˜noz,
+bioRxiv p. 2021.03.26.437199 (2021).
+[21] J. Faix and K. Rottner, Current Opinion in Cell Biology 18, 18 (2006), ISSN 09550674.
+[22] T. Vicsek and A. Zafeiris, Physics reports 517, 71 (2012).
+[23] D. Mashiko, Y. Fujihara, Y. Satouh, H. Miyata, A. Isotani, and M. Ikawa, Scientific reports 3, 1 (2013).
+[24] K. Hanawa-Suetsugu, Y. Itoh, M. Ab Fatah, T. Nishimura, K. Takemura, K. Takeshita, S. Kubota, N. Miyazaki, W. N. I.
+Wan Mohamad Noor, T. Inaba, et al., Nature communications 10, 1 (2019).
+[25] B.-C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer III,
+Z. Liu, et al., Science 346, 1257998 (2014).
+[26] T. Nishimura, T. Oyama, H. T. Hu, T. Fujioka, K. Hanawa-Suetsugu, K. Ikeda, S. Yamada, H. Kawana, D. Saigusa,
+H. Ikeda, et al., Developmental cell 56, 842 (2021).
+[27] M. D. Welch and R. D. Mullins, Annual review of cell and developmental biology 18, 247 (2002).
+[28] M.-F. Carlier and D. Pantaloni, Journal of Biological Chemistry 282, 23005 (2007).
+[29] K. G. Campellone and M. D. Welch, Nature reviews Molecular cell biology 11, 237 (2010).
+[30] K. Bohinc, V. Kralj-Igliˇc, and S. May, The Journal of chemical physics 119, 7435 (2003).
+[31] D. N. Theodorou and U. W. Suter, Macromolecules 18, 1206 (1985).
+[32] G. Golani, N. Ariotti, R. G. Parton, and M. M. Kozlov, Developmental Cell 48, 523 (2019), ISSN 15345807.
+[33] S. Peniˇc, L. Mesarec, M. Foˇsnariˇc, L. Mr´owczy´nska, H. H¨agerstrand, V. Kralj-Igliˇc, and A. Igliˇc, Frontiers in Physics 8, 342
+(2020).
+[34] R. R. Kay, Cells & Development 168, 203713 (2021).
+[35] N. Saito and S. Sawai, Iscience 24, 103087 (2021).
+[36] L. Mesarec, W. G´o´zd´z, V. K. Igliˇc, S. Kralj, and A. Igliˇc, Colloids and Surfaces B: Biointerfaces 141, 132 (2016).
+[37] J. Faix and K. Rottner, Journal of Cell Science 135, jcs259226 (2022).
+[38] J. V. Small, T. Stradal, E. Vignal, and K. Rottner, Trends in cell biology 12, 112 (2002).
+[39] T. Takenawa and S. Suetsugu, Nature reviews Molecular cell biology 8, 37 (2007).
+[40] K. Rottner and M. Schaks, Current opinion in cell biology 56, 53 (2019).
+[41] S. Suetsugu, K. Murayama, A. Sakamoto, K. Hanawa-Suetsugu, A. Seto, T. Oikawa, C. Mishima, M. Shirouzu, T. Takenawa,
+and S. Yokoyama, Journal of Biological Chemistry 281, 35347 (2006).
+[42] A. Pawluchin and M. Galic, Frontiers in Cell and Developmental Biology 10 (2022), ISSN 2296-634X, URL https:
+//www.frontiersin.org/articles/10.3389/fcell.2022.1080995.
+[43] M. Krause and A. Gautreau, Nature reviews Molecular cell biology 15, 577 (2014).
+
+13
+parameter
+units
+Fig.1,[5]
+Fig.2
+Fig.4A
+Fig.4C
+Fig.6
+Fig.7
+Fig.8
+f
+KBT/ℓmin
+1
+0 − 1.2 0 − 0.5
+0.5
+0.2
+0.2, 0.5
+0.5
+w
+KBT
+1
+0 − 4.8
+2
+2
+2
+2
+2
+κ
+KBT
+20*
+20
+28.5
+28.5
+28.5
+28.5
+28.5
+ρ
+1
+0%-20%
+10%
+20%
+10%, 10%
+20%
+20%,
+10%, 10%
+C0
+1/ℓmin
+1(0)
+1
+0.8
+-0.75 − 0, 0.8
+0.4
+0.4, 0.1
+0.8
+TABLE I: The values of the model parameters used in the simulations, in the different figures. The energy units are KBT = 1,
+which define the scale of f, w, κ, and the length units are ℓmin = 1, which define the scale of the vertex lattice, the force, and
+spontaneous curvature.
+[44] S. K¨uhn, C. Erdmann, F. Kage, J. Block, L. Schwenkmezger, A. Steffen, K. Rottner, and M. Geyer, Nature communications
+6, 1 (2015).
+[45] T. Pokrant, J. I. Hein, S. K¨orber, A. Disanza, A. Pich, G. Scita, K. Rottner, and J. Faix, Proceedings of the National
+Academy of Sciences 120, e2217437120 (2023).
+[46] N. Bobrovska, W. G´o´zd´z, V. Kralj-Igliˇc, and A. Igliˇc, PloS one 8, e73941 (2013).
+[47] K. Schara, V. Janˇsa, V. ˇSuˇstar, D. Dolinar, J. I. Pavliˇc, M. Lokar, V. Kralj-Igliˇc, P. Veraniˇc, and A. Igliˇc, Cellular &
+molecular biology letters 14, 636 (2009).
+[48] M. Miihkinen, M. L. Gr¨onloh, A. Popovi´c, H. Vihinen, E. Jokitalo, B. T. Goult, J. Ivaska, and G. Jacquemet, Cell reports
+36, 109716 (2021).
+[49] C. S. Cohan, E. A. Welnhofer, L. Zhao, F. Matsumura, and S. Yamashiro, Cell motility and the cytoskeleton 48, 109 (2001).
+[50] J. Damiano-Guercio, L. Kurzawa, J. Mueller, G. Dimchev, M. Schaks, M. Nemethova, T. Pokrant, S. Br¨uhmann, J. Linkner,
+L. Blanchoin, et al., Elife 9 (2020).
+[51] F. Kage, H. D¨oring, M. Mietkowska, M. Schaks, F. Gr¨uner, S. Stahnke, A. Steffen, M. M¨usken, T. E. Stradal, and K. Rottner,
+Journal of Cell Science 135, jcs260364 (2022).
+[52] S. A. Koestler, S. Auinger, M. Vinzenz, K. Rottner, and J. V. Small, Nature cell biology 10, 306 (2008).
+[53] Y. Mimori-Kiyosue, in Plasma Membrane Shaping (Elsevier, 2023), pp. 357–374.
+[54] Y. Tu, K. Pal, J. Austin, and X. Wang, Current Biology 32, 4386 (2022).
+[55] M. Nozumi, H. Nakagawa, H. Miki, T. Takenawa, and S. Miyamoto, Journal of cell science 116, 239 (2003).
+[56] S. A. Johnston, J. P. Bramble, C. L. Yeung, P. M. Mendes, and L. M. Machesky, BMC cell biology 9, 1 (2008).
+[57] C. Lebrand, E. W. Dent, G. A. Strasser, L. M. Lanier, M. Krause, T. M. Svitkina, G. G. Borisy, and F. B. Gertler, Neuron
+42, 37 (2004).
+[58] O. L. Mooren, B. J. Galletta, and J. A. Cooper, Annual review of biochemistry 81, 661 (2012).
+[59] P. Moreno-Layseca, N. Z. J¨antti, R. Godbole, C. Sommer, G. Jacquemet, H. Al-Akhrass, J. R. Conway, P. Kronqvist, R. E.
+Kallionp¨a¨a, L. Oliveira-Ferrer, et al., Nature cell biology 23, 1073 (2021).
+[60] C. Kaplan, S. J. Kenny, X. Chen, J. Sch¨oneberg, E. Sitarska, A. Diz-Mu˜noz, M. Akamatsu, K. Xu, and D. G. Drubin,
+Molecular Biology of the Cell 33, ar50 (2022).
+[61] S. L. Sønder, S. C. H¨ager, A. S. B. Heitmann, L. B. Frankel, C. Dias, A. C. Simonsen, and J. Nylandsted, Science Advances
+7, eabg1969 (2021).
+[62] S. Mylvaganam, S. A. Freeman, and S. Grinstein, Current Biology 31, R619 (2021).
+[63] J. Lutton, P. Paschke, C. Munn, J. S. King, R. Kay, T. Bretschneider, et al., bioRxiv (2022).
+[64] M. V. Baranov, R. A. Olea, and G. van den Bogaart, Trends in cell biology 29, 727 (2019).
+
+14
+FIG. 1: Phases of vesicle shapes driven by curved active CMC, as obtained in [5]. (A) Phase diagram in the temperature-density
+plane: mixed (gas), budded, and flattened (pancake). The gas phase is dominated by entropy, hence appears at either high
+temperatures or low densities. The pancake phase is dominated by having favorable binding and bending energy, where the
+active forces are all radial and stabilize the flat shape. This phase requires large stable CMC cluster, and so can only appear at
+low temperatures. The budded phase appears between the two other phases. At a CMC density that is lower than the minimal
+value needed for a closed circular rim, the pancake shape changes to B) a two-arcs phase, while when the CMC concentration is
+very high the pancake forms pearled extensions that contain the surplus CMC (C). There are two other phases in different
+regimes: (D) The pearling phase appears at higher CMC density, where most of the CMC aggregate into long necklace-like
+clusters that minimize the protein-protein binding energy (phase-separation of CMC), and (E) highly-elongated (tubular) phase
+for flat CMCs, where large CMC caps can exert a strong force that pulls out elongated tubes. Pictures taken from [5] Figs.4c,7d,
+and SI.
+
+(A)
+2
+1.5
+Mixed
+I
+Budded
+0.5
+Pancake
+4
+6
+8
+10
+12
+14
+16
+p[%]15
+FIG. 2: Force-binding strength plane. (A) Phase diagram as function of f and w, with: κ = 20, C0 = 1, and ρ = 10%. The
+different phases are indicated by their names, and a typical snapshot of the vesicle after a long simulation is shown. The
+transition lines between the phases were drawn according to the measures shown in the bottom panels. The gas and buds phase
+is separated by mean cluster size ⟨N⟩ = 1.5 (yellow solid line), as obtained from (B). The green line denotes the boundary of the
+flat phase, obtained approximately from a contour of the first (small) gyration eigenvalue λ2
+1, which is minimal for flat shapes
+(C). The light blue line denotes the boundary of the elongated shapes, roughly following a contour of the second (intermediate)
+gyration eigenvalue λ2
+2 (D). The transition line between the buds and mixed phases is given by a contour of CMC perimeter
+length (¯ℓp = 1.875, red solid line), extracted from (E). Finally, the pearling phase transition line (red dotted line) is drawn along
+the contour of small CMC perimeter length (¯ℓp = 0.375), from (E). In panels (B-E) we plot heatmaps of the following quantities:
+(B) Mean cluster size for clusters smaller than 10, ⟨N⟩ > 10 (C) first (small) gyration eigenvalue λ2
+1, (D) second (intermediate)
+gyration eigenvalue λ2
+2, (E) Mean CMC cluster perimeter length (excluding isolated CMC) ¯ℓ.
+
+Elongated
+Mixed16
+FIG. 3: Evolution of the MC simulation at four different points (B-E) denoted on the phase diagram (A) (Fig.2A). (B): f=0.8,
+w=1.6, (C): f=0.8, w=2.88, (D): f=0.8, w=3.20, and (E): f=0.4, w=4.16. The MC time-steps shown in the snapshots are: (i) 10,
+(ii) 50 (ii) and (iii) 200, and the final time-step (299) is shown on the phase diagram (A). At time (i), all simulations are in the
+budded state. At time (ii), arc and pearling clusters begin to form, favoring arcs for large forces and pearling for large binding
+strength. At time (iii), the vesicles are close to their final steady-state shapes. The flat simulation (B) generates several arcs
+in stage (ii), which coalesce to form a circular stable rim. The pearling simulation (E) generates pearling clusters (ii) which
+coalesce into a few larger clusters (coarsening). In contrast, the elongated simulations generate both arcs and pearled clusters at
+the intermediate stage (ii). These arc-like clusters are sufficient stretch the vesicle, even in (D), to give rise to the final elongated
+phase.
+
+Ci
+D i
+11
+Bi
+ili
+Ei
+ili17
+FIG. 4: (A) Phase diagram in the force-spontaneous curvature plane, using the parameters: ρ = 20%, κ = 28.5, w = 2. The
+different phases are denoted by their typical shapes, and the thin colored transition lines were drawn by hand (yellow, red and
+green). With no or weak force, we find a budded phase. As the force is increased, we find for the high spontaneous curvature
+the flat phase. As the spontaneous curvature is reduced, the flat phase is observed to give way to an ”arcs” phase, which is
+finally replaced by a highly-elongated tubular phase. The thick blue line denotes the theoretical calculation for the transition
+line that bounds the tubes phase, which is a cubic equation: f = AC3
+0 (Eq.9), where we use: A ≈ 10.6. This equation is derived
+from the force balance shown schematically in (B). (C) Typical steady-state snapshots of simulations with a mixture of CMC:
+active convex CMC (C0 = 0.8, f = 0.5, ρ = 10%), and passive concave CMCs (ρ = 10%) with different concave curvatures
+C−
+0 (along the x-axis). We show here three cases: i) no inhibition of the active convex CMC, ii) proportional inhibition, where
+the force exerted by a convex CMC is proportional to number of non-concave neighbors, and iii) disabling interaction, where
+the convex CMC do not exert any force if they have a concave neighbor. (D) Mapping of the vesicles shown in (C) to their
+respective locations in the force-spontaneous curvature phase diagram (A), using the average force and spontaneous curvature of
+the mixture (dashed outlines). The snapshots are shown at shifted locations, according to the effective curvature when we take
+into account the phase-separation of the concave CMC, into internalized sacks. These shifts in locations are most dramatic for
+1i,1ii,2ii,1iii,2iii (indicated by arrows), which places the vesicles in a phase which is appropriate for their shapes.
+
+2
+Flat
+SO
+ubes
+Arcs
+Buds
+Flat
+5i
+61
+2ii
+Tubes
+3ii
+4ii
+511
+61l
+1ili
+Arcs
+2ili
+5ili.
+Buds
+6ili
+3ill18
+FIG. 5: Mixed clusters can precipitate internal sacks, which are composed almost entirely of the concave (passive) CMC, when
+the concave CMCs are highly curved C0 = −0.75, −0.6. This is shown in A(i,ii),C(i,ii) for a system with and without active
+force, respectively. This internal sack is connected to the outside by a thin neck, or ”hole”, shown in A(iii) and C(iii). The
+cross-sectional area of the hole was measured by computing the area of the polygon made from the hole edge, which was picked
+by hand (vertices). A histogram of the simulated hole sizes is shown for the system with and without active force respectively
+(B,D). It is clear that the hole size is smaller in systems with force (B), such that it is in the limit of the simulation resolution.
+The holes are also larger as the spontaneous curvature of the passive concave CMC is smaller. The insets of B,D show typical
+examples of sacks (light blue nodes) connected to the outer part of the cluster (blue nodes) through the neck region (grey
+shading). (E) and (F): Snapshots showing the formation of a sack for the system with active force (A), from the initial random
+state. In (E) we show the cluster viewed from outside of the vesicle (where the bare membrane is rendered invisible), looking
+down on the patch that forms the sack, while in (F) we show the same process viewed from within the vesicle, where we see
+clearly the final invagination.
+
+Aii
+A ili
+curvature: -0.75
+curvature: -0.6
+Ai
+B
+10
+5
+20
+25C
+10
+15
+20
+25
+c i
+c ii
+cili
+LO
+15
+20
+25 0
+10
+15
+20
+50
+Hole area
+Hole area
+0219
+FIG. 6: (A) Vesicle steady-state shapes as function of the strength (s) and range (r) of the Vicsek-like alignment interaction
+(Eq.10)(ρ = 20%,κ = 28.5,C0 = 0.4,w = 2,f = 0.2). Interaction radius smaller than 10 leads to a flat phase. Above an interaction
+radius of 10, the system transitions from a flat to a tubes phase. In between the flat and elongated tubes phases, we find a phase
+with ”paddle”-like clusters. The tubular phase is characterized by CMC clusters that are mostly finger-like with a bulbous tip
+and a tubular sleeve, which often stretch a membrane tube behind them. (B) Snapshots of CMC clusters, with the active forces
+indicated by the arrows, and the colormap indicating the dot product of the local force and local outwards normal. In the tubes
+phase (s = 0.75, r = 15) we show in (i) an example of a hemispherical cluster, which is not able to pull an elongated protrusion.
+In (ii) (top) we show an example of a CMC cluster that contains a tubular sleeve, which increases the net pulling force above
+the threshold to pull a membrane tube. Note that at the sleeve base the alignment is weak due to the bare membrane boundary.
+This effect is also shown in (iii) (bottom), where a small patch of bare membrane is trapped between the cluster tip and the
+sleeve, leading to formation of two different alignment domains within the same cluster. Finally, in (iv) we show an example of
+the paddle cluster (s = 0.1, r = 10), where the weak alignment interaction gives rise to shapes similar to the regular arc-like
+clusters (Fig.4A), elongated by the non-normal force.
+
+Tube
+Paddle
+Flat
+iv
+120
+FIG. 7: (A) Dynamics of the formation of the tubular phase, driven by strong alignment interactions (ρ = 20%, κ = 28.5, C0 =
+0.4, w = 2, f = 0.2, s = 0.75, r = 15). Each circle represents a CMC-cluster at different MC time (x axis), the y axis represents
+the total force exerted by the cluster. The circle size represents the size of the CMC cluster (see sidebar). Color gives a persistent
+”identity” to each cluster, which last until fusion or fission. On the top right is a snapshot of the vesicle in the last time step.
+The four largest cluster are highlighted, and also shown on the right of the panel. Below the x-axis, we give snapshots of the
+vesicle. The rapid initial formation of buds is seen followed by slower fusion of clusters to form elongated protrusions. Two
+of the final large clusters, the bud and one of the elongated tube, are relatively stable, while the other two elongated clusters
+have wildly oscillating force. We can see on the right that the fluctuating cluster incorporates a few bare membrane vertices
+(Fig. 6B,iii). (B) The dynamics of tube formation due to aligned force with highly curved CMCs (top, s = 0.5, r = 30, f = 0.2,
+C0 = 0.4) compared to formation due to shallow (weakly curved) CMCs with normal force (bottom, f = 0.5, C0 = 0.1). The
+tubes of the latter are more dynamic and less stable than clusters of the former. This is also seen on the right panel, which
+shows the total force on the largest clusters, which is far less noisy for the former.
+
+50
+Sizes
+40
+2
+30
+4
+8
+20
+16
+32
+10
+64
+128
+256
+20
+40
+60
+80
+100
+120
+140
+timestep
+75
+50
+25
+0
+200
+400
+75
+50
+25
+0
+200
+40021
+FIG. 8: A: Initial progress of simulation with normal-force CMCs (red) and aligned-force CMCs (yellow), in universal binding
+(top) and type-exclusive binding (bottom), from the side and above (ρalign = 10%, ρnormal = 10%, κ = 28.5, C0 = 0.8, w = 2,
+f = 0.5, s = 0, 1, r = 15, wad = 0.25). CMCs in the rim drive the spreading of the vesicle on the surface, while some aligned-force
+CMCs aggregate into a bulb-and-sleeve cluster which drives the formation of a filopodia-like protrusion. This protrusion can
+attach to the rim cluster and then adhere to the substrate, while it can also detach from the substrate, and consequently also from
+the rim cluster. B: Evolution of the segregation factor in the simulations (Eq.11). The colored lines give the segregation factor
+for each cluster, with the cluster size indicated by the line thickness. In the inset we give the average of the total segregation
+factor for 4 independent simulations. In the universal binding simulation we can see the fliopodia-like cluster repeatedly attach
+and detach from the rim cluster. The rim cluster is mostly mixed for this case, while the protrusion is much more segregated, as
+its tip is enriched with aligned-force CMCs.
+
+0.4
+1.00
+1.00
+0.2
+0.75
+0.75
+factor
+0.0
+0.8
+0.50
+time 0
+50
+100　150　200　250
+0.50
+segregation t
+0.6 
+detachments -
+0.25
+0.25
+0.4
+0
+50
+100
+150
+200
+250
+time
+0.00
+0.00
+Rim cluster
+0.25
+-0.25
+-0.50
+-0.50
+0
+50
+100
+150
+200
+250
+0
+50
+100
+150
+200
+250
+time
+time22
+FIG. 9: Movements of IRSp53-localized cellular protrusions. (A, B) The adhesion (A) and apical (B) plane section of the
+three-dimensional images of an IRSp53-knockout U251 glioblastoma cell expressing GFP-IRSp53 (green) and mCherry-lifeact
+(red). In (A) and (B), the region for the ∼ 2 µm thick xz section projection is indicated by the cyan dotted rectangle. (C) The
+xz section of the region of (A). The white lines indicate the plane in (A,B). The yellow line, which was set in the proximity
+of the surface plane of the cell, indicates the line for the kymograph. (D) The kymograph of the cell surface as indicated in
+the yellow line in (C), along with the annotation of the representative motion of the IRSp53. (E-F) The xy and xz sections at
+the regions that are marked in (A,B), from the periphery (E), the middle (F), and the center (G). The plane parallel to the
+plasma membrane was sectioned and the regions that were projected xy and xz sections each others were marked in cyan dotted
+rectangles. Arrows indicate the protrusions. The scale bar, 10 µm (A-D), 2 µm (E-G), and 50 sec (D).
+
+xz section
+apical plane
+moving to
+the center (E)
+moving to
+the periphery (F)
+adhesion plane
+apical plane
+merging (G)Supplementary Material
+S-1.
+CALCULATION OF THE PERIMETER OF CMC CLUSTERS
+The CMC-bare membrane boundary is measured by summing the dual of the edges between the cluster and bare
+membrane. These are the edges in the voronoi lattice, connecting the mid-section of each edge to the circumcenter of
+the adjacent triangles i.e. the center of the inscribing circle (see figure S-1). Partitioning each triangle between its
+vertices is already used in the calculation of the curvature [1].
+S-2.
+ANALYTICAL CALCULATION OF THE FLAT-PEARLING PHASE TRANSITION LINE
+We can make a rough analytical estimation for the flat-pearling transition by equating the active work and energy of
+the flat phase from a mixed phase to the energy of the pearling phase (Fig. S-2). In the flat phase, moving the active
+CMCs outwards from the radius of the sphere rp to the larger radius of the flattened disc rf results in work. The
+pearling phase has binding advantage because all CMC vertices are connected, with −w per edge, while the flat rim
+has large interface (boundary perimeter length) where CMCs vertices neighbor bare membrane vertices, whose edge
+does not contribute. The pearling phase has a bending disadvantage due to the bare membrane body, which is roughly
+spherical with an energy of 8πκ, compare to the flat phase where the bare membrane is in two flat discs with no
+bending energy (both the pearling and rim clusters are curved to fit the CMCs, so they do not have bending energy).
+− (rf − rp) F = −w (χp − χf) + 8πκ
+(S-1)
+The radius difference ∆r = rf − rp (Fig. S-2), and the number of CMC-CMC bonds χp, χf in the pearling and
+flat phases respectively, are dependant on the geometry of the phases, so they should be very weakly dependant on
+the specific model parameters. Therefore ∆r and χp − χf do not depend on w, f, κ, and we end up having a linear
+relation between f and w along the transition line in the f, w phase diagram. In the force-binding strength (f − w)
+system, we take the values for these geometric quantities from simulations and draw the resulting line on the phase
+diagram (Fig. S-3, green line), which qualitatively matches the behavior of the transition observed in the simulations.
+S-3.
+MIXED CURVATURE CMC CLUSTERS
+The concave and convex CMCs generate a wavelike pattern, but analyzing it in terms of wavenumber is difficult,
+since the clusters are part of an irregular, triangulated surface. The undulations of the CMCs in the mixed clusters are
+essentially independent of C0, and f, as shown in Fig.S-4. Note that we are at the limit of the mesh resolution for
+these undulations. We have yet to be able to compare this to the experimental results in [2].
+S-4.
+MIXED CURVATURE WITH EXCLUSIVE BINDING
+The mixed curvature system (Fig. 4c in the main text) was also simulated using exclusive binding, i.e. only
+same-curvature CMCs bind together (Fig.S-5). The result is that the two CMCs types form separated aggregates,
+with the active convex CMCs aggregating along the rim and forming the flat phase. The passive concave CMC form
+separated clusters of different shapes, depending on their spontaneous curvature. Highly concave CMCs (C−
+0 ≤ −0.45)
+aggregate into internal pearling clusters, that do not affect the flat global phase. The shallower concave CMCs
+(C−
+0 ≥ −0.3) aggregate into large, shallow bowl-like patches.
+In some cases, these concave aggregates are able to form with convex CMC along their rim, since their curvatures
+complement each other (see for example at C−
+0 = −0.3). Since the convex active CMC along the rim of the concave
+cluster apply protrusive forces, they end up forming together a ”cup”-like protrusion. When the force is inhibited,
+this aggregation occurs, but it is not elongated as a protrusion (compare ”None” with ”Disable” at C−
+0 = −0.3 in
+Fig.S-5). Other than that, inhibition doesn’t appear to significantly affect the results in Fig.S-5, since there is no
+significant contact between the two CMC types. These shapes, in the form of open bowls, resemble early stages of
+macropinocytosis [3, 4], but do not evolve to induce closure of the ”mouth”, as we observed when the convex and
+concave CMC had direct interactions (Fig.5 in the main text).
+arXiv:2301.13055v1  [cond-mat.soft]  30 Jan 2023
+
+2
+parameter
+units
+Fig.S-3
+Fig.S-4
+Fig.S-5
+Fig.S-6
+movie 1,2 movie 3,4
+f
+KBT/ℓmin 0 − 1.2
+0.5, 0
+0.5
+0.5
+0.2, 0.5
+0.5
+w
+KBT
+0 − 0.48
+2
+2
+2
+2
+2
+κ
+KBT
+20
+28.5
+28.5
+28.5
+28.5
+28.5
+ρ
+1
+10%
+10%, 10%
+10%, 10%
+10%, 10%
+20%
+10%, 10%
+C0
+1/ℓmin
+1
+-0.6 − 0, 0.8 -0.75 − 0, 0.8
+0.8
+0.4,0.1
+0.8
+TABLE I: The values of the model parameters used in the simulations in the different figures. The energy units are KBT = 1,
+which define the scale of f, w, κ, and the length units are ℓmin = 1, which define the scale of the vertex lattice, the force, and
+spontaneous curvature.
+S-5.
+VESICLES WITH BOTH NORMAL AND ALIGNED-FORCE CMC, ADHERED TO A FLAT
+SUBSTRATE
+In Fig.S-6 we show the dynamics of the vesicle that contains the mixture of aligned-force (yellow) and normal-force
+(red) CMC, which have exclusive binding interactions between them (see Fig.8 in the main text). At time t = 250
+we turned off the normal-force CMC, keeping only the aligned-force CMC active. We find that the adhered area
+shape changes, with the rim regions that contain the curved passive (red) CMC retract into the vesicle, while the
+aligned-force regions protrude more prominently along the adhered rim.
+Movies
+• Movie-S1 Aligned-force simulation of the formation of filopodia-like tubular protrusions (corresponding to
+Fig.7B), with parameters κ = 28.5, f = 0.2, w = 2, C0 = 0.4, ρ = 20%, s = 0.5, r = 30
+• Movie-S2 Normal force simulation, in the regime of tubes shapes (corresponding to Fig.7B), with parameters
+κ = 28.5, f = 0.5, w = 2, C0 = 0.1, ρ = 20%
+• Movie-S3 Adhered, universal-binding between normal-force CMCs (red) and aligned-force CMCs (yellow),
+corresponding to Fig.8A. Parameters used: κ = 28.5, f = 0.5, w = 2, wad = 0.25, C0 = 0.8, ρn = 10%, ρa =
+10%, s = 1, r = 15
+• Movie-S4 Adhered, exclusive-binding between normal-force CMCs (red) and aligned-force CMCs (yellow),
+corresponding to Fig.8A. Parameters used: κ = 28.5, f = 0.5, w = 2, wad = 0.25, C0 = 0.8, ρn = 10%, ρa =
+10%, s = 1, r = 15
+• Movie-S5. The 3D movie of the cell in Figure 9A
+• Movie-S6. The movie of the XY and XZ section for Figure 9E
+• Movie-S7. The movie of the XY and XZ section for Figure 9F
+• Movie-S8. The movie of the XY and XZ section for Figure 9G
+[1] G. Gompper and D. M. Kroll, in Statistical Mechanics of Membranes and Surfaces (WORLD SCIENTIFIC, 2004), pp.
+359–426.
+[2] E. Sitarska, S. D. Almeida, M. S. Beckwith, J. Stopp, Y. Schwab, M. Sixt, A. Kreshuk, A. Erzberger, and A. Diz-Mu˜noz,
+bioRxiv p. 2021.03.26.437199 (2021).
+[3] D. M. Veltman, T. D. Williams, G. Bloomfield, B.-C. Chen, E. Betzig, R. H. Insall, and R. R. Kay, Elife 5, e20085 (2016).
+[4] R. R. Kay, Cells & Development 168, 203713 (2021).
+
+3
+FIG. S-1: Sketch of the boundary of connected clusters: for each edge between the cluster and the outside, a line is drawn from
+the middle to the center each of the adjacent triangles. We ignore the single-clusters (dashed line)
+FIG. S-2: Schematic description of the transition between flat and pearling phases, from an initially mixed, spherical phase (at
+the center). Bare membrane is in white, and CMCs in red, and mixed composition in pink. The flat transition result in all
+CMCs moving from the surface of the sphere to the rim of a flat disc, which has a larger radius ∆r. Due to active force f,
+this generates work W = −f∆r. The bending energy of the CMCs on the rim and in the pearling clusters is assumed to be
+approximately 0, but the spherical body of bare membrane in the pearling phase has a bending energy of a closed sphere: 8πκ,
+while it is zero for the flat discs of bare membrane in the flat phase (since they are flat). Finally, the number of CMC-CMC
+bonds in the pearling phase χp is larger than in the flat phase χf, since in the flat phase it is reduced due to the large boundary
+between the rim cluster the the flat bare membrane discs.
+
+f△r
+8πK4
+FIG. S-3: Phase diagram of the force-binding strength system, with an analytically-derived transition line for the pearling-flat
+transition (green line, Eq.S-1).
+FIG. S-4: The undulation of a CMC cluster with (A) highly concave (−0.6) active CMC (B) with shallow concave (−0.001)
+CMC and disabled force. The size and shape of the clusters is very different, but the peaks and troughs patterning due to CMC
+shape is at the limit of the mesh resolution for both.
+
+20 
+12 
+longai
+04
+96
+88
+Buds
+80
+72
+64 
+56
+48
+earlino
+40
+32
+24
+16
+08(A)
+(B)5
+FIG. S-5: Active convex and passive concave system (red and blue, respectively), with binding between same type only. As in
+the universal binding case, the suppressive and disabling inhibition do not have any strong effects, since the types are separated.
+Simulations with C−
+0 ≤ −0.3 are draw semi-transparent. In all cases, the convex CMCs aggregate in a rim, making the vesicle
+flat, and concave CMCs aggregate in pearling for C−
+0 < −0.3, bowl-like patches for C−
+0 > −0.3, and both for C−
+0 = −0.3.
+
+6
+FIG. S-6: Overview of an adhered vesicle with a mixture of aligned-force (yellow) and normal-force (red) CMC, which have
+exclusive binding interactions between them (see Fig.8 in the main text). At time t = 250 the force is disabled for the
+normal-force CMCs, leaving only the aligned-force CMCs active. The original simulation is given on the top (times 0 − 100),
+and the simulation after the normal-force has been disabled is at the bottom.
+
diff --git a/09FPT4oBgHgl3EQfTzT7/content/tmp_files/load_file.txt b/09FPT4oBgHgl3EQfTzT7/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d48b4cd685127d19e8b5c059636245e98d8808fb
--- /dev/null
+++ b/09FPT4oBgHgl3EQfTzT7/content/tmp_files/load_file.txt
@@ -0,0 +1,1378 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf,len=1377
+page_content='Theoretical model of membrane protrusions driven by curved active proteins  Yoav Ravid 1,∗, Samo Peniˇc 2, Yuko Mimori-Kiyosue,3, Shiro Suetsugu,4,5,6, Aleˇs Igliˇc 2, and Nir S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Gov 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='∗  1Department of Chemical and Biological Physics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Weizmann Institute of Science,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Rehovot,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Israel  2Laboratory of Physics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Faculty of Electrical Engineering,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' University of Ljubljana,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Ljubljana,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Slovenia  3Laboratory for Molecular and Cellular Dynamics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  RIKEN Center for Biosystems Dynamics Research,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  Minatojima-minaminachi,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Chuo-ku,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Kobe,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Hyogo 650-0047,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Japan  4Division of Biological Science,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Graduate School of Science and Technology,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  Nara Institute of Science and Technology 8916-5,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Takayama,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Ikoma,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Nara,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' 630-0192,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Japan  5 Data Science Center,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Nara Institute of Science and Technology,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Ikoma 630-0192,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Japan  6 Center for Digital Green-innovation,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Nara Institute of Science and Technology,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Ikoma 630-0192,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Japan  Eukaryotic cells intrinsically change their shape,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' by changing the composition of their membrane  and by restructuring their underlying cytoskeleton.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' We present here further studies and extensions  of a minimal physical model, describing a closed vesicle with mobile curved membrane protein  complexes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The cytoskeletal forces describe the protrusive force due to actin polymerization which is  recruited to the membrane by the curved protein complexes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' We characterize the phase diagrams of  this model, as function of the magnitude of the active forces, nearest-neighbor protein interactions  and the proteins’ spontaneous curvature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' It was previously shown that this model can explain the  formation of lamellipodia-like flat protrusions, and here we explore the regimes where the model can  also give rise to filopodia-like tubular protrusions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' We extend the simulation with curved components  of both convex and concave species, where we find the formation of complex ruffled clusters, as well  as internalized invaginations that resemble the process of endocytosis and macropinocytosis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' We  alter the force model representing the cytoskeleton to simulate the effects of bundled instead of  branched structure, resulting in shapes which resemble filopodia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  Keywords: Cell membrane, Curved inclusions, Monte-Carlo simulations, Closed vesicle shapes, Cell motility, Filopodia  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  INTRODUCTION  Cells in our body have different shapes depending on their function, and they control their shapes by exerting  forces on the flexible plasma membrane [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' These forces are mostly due to the underlying cytoskeleton, dominated  by the cortical actin network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The actin polymerization near the membrane exerts protrusive forces that can give  rise to cellular protrusions, such as filopodia and lamellipodia [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The control of the actin polymerization in space  and time is provided by a host of proteins that nucleate actin polymerization where and when it is needed, and  are in turn controlled by different signalling cascades.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' One mechanism for controlling the spatial pattern of actin  polymerization on the membrane, is to couple the actin nucleation to curved membrane components (CMCs), that are  both bending locally the membrane and are sensitive to the local membrane curvature (such as BAR domain proteins  [3]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' This coupling was shown theoretically to give rise to positive and negative feedbacks [4], that can result in pattern  formation in both the spatial distribution of the actin nucleators (recruited by the CMCs) and the membrane shape.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  This coupling between curvature and active protrusive forces was explored for a limited regime of parameters in [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  Experimental evidence for this coupling between CMC and protrusive forces has been accumulated in the context of  lamellipodia [6, 7] and filopodia [8–14] formation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  A summary of the vesicle shapes that we found in [5] are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='1, explored as function of temperature and  CMC density (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='1A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The main phases which were identified are [15]:  Diffused CMC-gas phase, where CMC are dispersed as entropy dominates over bending and binding energies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  Budded phase, where binding and bending leads to CMC forming hemispherical clusters at the CMC spontaneous  curvature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  Flattened ”pancake” phase, where the active forces push the CMC outwards, leading to a large CMC cluster along  the rim, with two flat bare membrane disc regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Low temperature is required to prevent lateral membrane  fluctuations and thermal diffusion of the CMC from breaking up the rim cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  The pancake phase is quite dynamic, and tends to form ”ruffles” along the edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' With insufficient density of CMC,  there is a ”two-arc” phase with multiple flat edges connected by elongated membrane (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='1B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' If the CMC density if  high, the excess CMC form pearled structures along the rim of the pancake (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='1C).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='13055v1  [cond-mat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='soft]  30 Jan 2023  2  When the active force is weak or zero (passive CMC), at low temperatures the system is phase-separated into  energy-minimizing ”pearled necklace” of CMC clusters, each at the CMC spontaneous curvature (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='1D).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' When the  force is strong and the CMC have low spontaneous curvature (flat), there is a phase of highly elongated ”tubular”  vesicles, where CMC caps apply large forces that pull membrane tethers (tubular protrusions) (fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='1E).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  Here we expand the analysis of the coupling between the spontaneous curvature of the CMC and protrusive forces,  by exploring the patterns that form as function of the natural parameters that the cell can manipulate, such as the  strength of the actin-driven force, the binding strength between the CMCs and the spontaneous curvature of the  CMCs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' By gaining a fuller understanding of the space of shapes that this coupling can produce, we are able to explore  two more complex configurations: a mixture of two CMCs of different intrinsic curvatures, and CMCs that induce  aligned active forces which model the effects of actin bundling[16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' These more complex systems, can be compared to  important biological phenomena, such as endocytosis[17] and filopodia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  THE MODEL  We follow the same coarse-grained continuum model used previously [5] and [18], where the physics of the cell shape  is described by differential geometry and very few energy components [1, 19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The lipid bilayer membrane is modeled  as a 2D flexible sheet, with zero spontaneous curvature, except where there are CMCs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Each CMC on the membrane  surface represents a complex of proteins that have a specific spontaneous curvature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The energy of the surface is  modeled by the Helfrich hamiltonian  Hbending =  ��  κ  2 (C1 + C2 − C0φ)2  (1)  which penalizes deviation of the shape, given by the local curvatures C1 and C2, from a preferred local shape, determined  by the CMC relative lateral density φ and the CMC’s preferred membrane curvature C0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' To simulate, we discretize  the system as a closed vesicle described by a graph V, E (vertices and edges respectively) with vertices representing  small area patches of either bare lipid bilayer or CMC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Note that the simulation does not have an intrinsic length  scale, however the edge length has to represent lengths larger than tens of nanometers for the coarse-grained model to  be physically valid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' We therefore obtain the following discretized energy  E =  �  i∈V  κ  2 (2h(i) − ρiC0)2 A(i) +  �  ⟨i,j⟩∈E  −wρiρj +  �  i∈V  wad θ (zi − z0)  (2)  where ρi = 1 for a CMC vertex and ρi = 0 for a bare vertex, such that the overall density of CMC is given by  ρ = �  i∈V ρi/N, where N = 4502 is the total number of vertices in our simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The first term is a discretized  version of the bending energy (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='1), κ is the bending modulus, h(i) is the mean curvature calculated at each vertex  h = (C1 + C2)/2, C0 is the spontaneous curvature of a CMC, and A(i) is the area assigned to the vertex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The second  term is the CMC-CMC nearest-neighbor binding energy, going over the edges ⟨i, j⟩, where w is the binding energy per  bond.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The third term is adhesion energy of the membrane to a flat rigid surface located at z = z0, which applies to  all the nodes that are within a distance of ℓmin from this surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The membrane is prevented from moving below  z0 − ℓmin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  This energy model is used in a Monte-Carlo (MC) simulation Trisurf-ng, described in [5], where random movement  of vertices and bond flips of edges are accepted if they lower the energy or according to a Boltzmann probability:  P = exp (−∆E − Wi) where Wi represents the work done by the active forces on each node that contains a CMC, as  follows  Wi = −f ˆn(i) · δ⃗xi  (3)  where ˆn(i) is the local outwards normal unit vector, and δ⃗xi is the vertex displacement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  The shift in the locations of the vertices are limited such that the length of each edge remains within this range:  ℓmin < ℓ < ℓmax.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The edge length and adhesion surface constraints are enforced by rejecting any MC moves which  violate them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' In a passive system this would lead to thermal equilibrium, but the active work term is unbounded  from below, so the system is out of equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The MC simulation does not have time-scale, as it does not include  the hydrodynamic flows and dissipative processes that determine the relaxation time-scales of the membrane shape  changes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' It does allow us to follow the shape dynamics by evolving the system along decreasing energy gradients, so  the trajectory in shape space is correctly described.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  The parameters in the model, used in this paper, are given in table I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' All the energies in the model are in units of  kBT (κ, w), while the external force f is in units of kBT/ℓmin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  3  In addition, we implement optional models of inhibition of the force on the CMC by neighbors, based on [20] which  shows different protein species can inhibit the activity of polymerization, inhibiting the actin recruitment and thus  force on the CMCs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' We implement a proportional inhibition, where an active (1) and inhibiting (2) CMC species exist  f prop  i  = f  1  Nneighbors  �  ⟨i,j⟩  �  1 − ρ(2)  j  �  (4)  We also implement a disabling inhibition, where any inhibiting CMC species completely disables the force on it’s  neighbors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  f dis  i  = f  �  ⟨i,j⟩  �  1 − ρ(2)  j  �  (5)  In biological filopodia, the actin filament are known to bundle by cross-lining proteins [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Our model does not  have a true representation of the cytoskeleton structure, but we can simulate this bundling by adding an alignment to  the force on the active CMCs, since the shared internal actin bundle would apply a force in the same direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' This is  added as an Vicsek-like interaction [22]  ˆf = ˆni + s �  r ˆnj  |ˆni + s �  r ˆnj|  (6)  The direction of force on CMC vertex i ˆfi is a weighted average of the normal direction plus a contribution from all the  vertices j a distance r from the vertex i with a weight of s, normalized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' This replaces the ˆn(i) term in the work term  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' the unmediated local normal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' This is superficially similar to the normal Vicsek model [22], where self-propelled  particles similarly align their direction with neighbors, producing flocking behavior, but here the CMCs/particles are  connected to each other and embedded in a 2D flexible sheet, and we use force in a MC simulation instead of velocity  in a Langevin simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  MATERIALS AND METHODS  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  Computational Methods  The simulations were run using trisurf-ng [5] version fb86a41 (”Modeled trisurf” branch) (see X) with a tape file  modified from the available default with the different physical parameters (see I), and additional simulation running  parameters of nshell=30, mcsweeps=50,000-200,000, iterations=100-1,000 (depending on the desired time resolution).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  Each simulation with a set of parameters was ran independently (”embarrassingly parallel”), which took about two  weeks to finish, with occasional restarts and expansion of the space limits (nxmax).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The resulting VTU files were  viewed and colored in ParaView, but further analysis and graph generation were done by separate python scripts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  Experimental Methods  The cell culture and lattice light sheet microscopic observation U-251 cells were obtained from the Japanese Collection  of Research Bioresources Cell Bank.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The IRSp53 knockout (KO) cells were generated by the CRISPR/Cas9 system, as  described previously [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The guide RNA targeting the first exon of IRSp53 (CCATGGCGATGAAGTTCCGG) was  designed using the server http://crispr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='mit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='edu and inserted into the pX330 vector [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' After transfection, the cells  were cloned by monitoring the GFP fluorescence from the reporter plasmid pCAG-EGxxFP with the IRSp53 genome  fragment using a fluorescence-activated cell sorter [FACSAria (BD)] [24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The expression of GFP or GFP-IRSp53  in the IRSp53 knockout cells was performed by the retrovirus-mediated gene transfer, as described previously [24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  All cell lines were cultured in high glucose DMEM (Thermo Fisher Scientific) supplemented with 10% bovine calf  serum (Thermo Fischer Scientific) and 1% penicillin-streptomycin solution (Thermo Fischer Scientific) and stored in  an incubator at 37oC in 5% CO2 and humidified conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The cells were seeded on coverslips and then imaged with  the Lattice light-sheet microscope built in the Mimori-Kiyosue laboratory at RIKEN Center for Biosystems Dynamics  Research following the design of the Betzig laboratory [25] as described previously [26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  4  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  FORCE-BINDING STRENGTH PHASE DIAGRAM  In [5] the phases of the vesicle with active CMC, were mostly explored as function of temperature and global density  of CMC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' However, the cell can more easily modify other parameters, such as the strength of the protrusive forces  produced by actin polymerization and the binding strength between neighboring CMC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The rate of actin polymerization  recruited to the CMC can be controlled by the cell through various proteins [27–29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The effective binding strength  between the neighboring CMC can similarly depend on the lateral concentration and character of the proteins that  form the CMC [7], as well as on the type of lipids between the CMC [30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The cell can modify these internal parameters  spontaneously or in response to external signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  We scan over the force f and binding strength w parameters plane (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='2A), with the other parameters of the model  having the following constant values: The bending modulus is taken to be κ = 20KBT, which is a typical value for  lipid bilayers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The spontaneous curvature of the CMC is taken to be C0 = 1ℓ−1  min, representing highly curved objects on  the membrane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The CMC density is ρ = 10%, which is sufficient to form the pancake shapes that require a complete  circular cluster of CMC along the vesicle rim [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  We find that the simulated vesicles can be divided into several distinct phases: gas phase, budded phase, pancake  phase, and pearling phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' In addition there are more ambiguous, and possibly transient, elongated and mixed phases  (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='2A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' In order to distinguish between these phases, we use four measures that characterize the vesicle shape and  the CMC cluster organization:  Mean cluster size ⟨N⟩  1st eigenvalue of the Gyration tensor λ2  1  2nd eigenvalue of the Gyration tensor λ2  2  Length of CMC-bare membrane boundary ℓp  The mean cluster size is averaged over all the CMC clusters, each cluster i having a size Ni of vertices  ⟨N⟩ =  �  i Ni  �  i 1 = Nvertex  Nclusters  We plot this measure (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='2B), extracted after the simulation reaches its steady-state regime, where the measures do  not change on average (see SI).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' we see that it allows to clearly distinguish the gas phase, which has small cluster sizes  (yellow line in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='2A denotes ⟨N⟩ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' However, it is rather poor at separating the condensed phases, which all  have large clusters but differ greatly in their morphology and cluster organization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' This is due to the dependence  of this measure on the number of clusters, which gives large weight to small single-vertex clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' This makes this  measure too noisy to distinguish between the other phases, except for the gas phase which mostly contains single-vertex  clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  We therefore use morphological measures in order to clearly distinguish between the different phases where the  CMCs are condensed in large clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The morphology of the vesicle is quantified by the eigenvalues of the gyration  tensor λ2  i .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The gyration tensor [31] is defined as the average over all the vertices,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' with respect to the center of mass  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='(similar to the moment of inertia tensor for equal-mass vertices)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='RG ij = ⟨rirj⟩ = 1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='N  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='vertices  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='x2 xy xz  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='xy y2 yz  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='zx yz z2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='This can be visualized by a unique ellipsoid which has the same gyration tensor  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='xT R−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='G x = (x · e1)2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='λ2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='+ (x · e2)2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='λ2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='+ (x · e3)2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='λ2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='= 3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='The eigenvectors ei of the gyration tensor are the directions of the semi-axes of the equivalent ellipsoid and the  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='eigenvalues are their length squared divided by 3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' ordered by their size: λ2  1 ≤ λ2  2 ≤ λ2  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The first eigenvalue λ1  essentially gives how thin is the ellipsoid, and is low for both pancake and highly elongated (linear) shapes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The  second eigenvalue λ2 is large for the pancake shape (as it is roughly equal to the largest eigenvalue λ2 ∼ λ3), but is  minimized for elongated shapes, where it similar to the value of the smallest eigenvalue, λ2 ∼ λ1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='2C,d we plot  the eigenvalues λ2  1, λ2  2, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' We find that the phase of pancake shapes is distinguished by the lowest λ2  1 (green  and dashed green-light blue lines in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='2A), indicating its flatness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  5  We identify a new phase of elongated shapes, which is distinguished by the lowest values of λ2  2 (between the light  blue and dashed green-light blue lines in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='2A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' These elongated phases are somewhat similar to the ”two-arc” phase  found in [5], which appeared when there are not enough CMCs to form a complete circular cluster along the flat vesicle  rim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' However, here we do have enough CMC to form a complete circular cluster, as shown in the ”flat” regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The  origin of the elongated shapes as w increases beyond the ”flat” phase is due to the formation of transient or stable  pearling clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' These cluster effectively sequester enough CMC to prevent the formation of the complete circular  cluster, leading to two curved regions that collect the CMC and stretch the vesicle due to the active forces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The CMC  clusters have the shape of flat arcs near the boundary with the ”flat” phase, while closer to the ”pearling” phase the  clusters are pearled and localized near the curved tips of the vesicle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  While the ”core” of the phases distinguished by λ2  1,2 is clear, the edges are much less sharp, due to lack of statistics,  long evolution time, and the fact that intermediate shapes do exist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' There is also no obvious normalization: The  volume changes greatly, and the area is only approximately conserved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' For our Nvertex = 4,502 The flat phase is found  around λ2  1 < 50, and the elongated phases is found around 80 < λ2  2 < 150.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  Finally, we wish to distinguish the phases where the CMCs form pearled clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The most outstanding property of  the pearled clusters is that they phase-separate between the CMC and the bare membrane, as also predicted within  the theory of self-assembly [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' We therefore measure the average length of the CMC-bare membrane boundary ¯ℓp, per  CMC, for all clusters larger than 1 (see SI section 1, Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='S1)  ¯ℓp =  �ℓpi  Ni  �  Ni>1  The phase with pearling clusters is distinguished by having very low ¯ℓp < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='375 (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='2E).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' We find that this measure  identifies the pearled clusters both in the pearling and in the elongated phases (red dotted line in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='2A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' In addition,  a contour of this measure allows us to separate the mixed phase, where the CMC are in both buds and pearled clusters,  from the phase that contains only buds (red solid line ¯ℓp <= 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='875 in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='2A,E).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  Note that we do not know if these phases are necessarily the absolute steady-states of the system in the limit of  infinite time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The system might be trapped in a local meta-stable configuration due to dynamical barriers that would  require unreasonably long simulations for them to escape.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' For example, in the regime of low force f and large binding  strength w, the global minimum energy configuration should have all the CMC in a single pearled cluster, but during  the merging of the pearled clusters into a single cluster they have to overcome bending energy barriers that hinder this  process [32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' In other regimes, such as the elongated phase, we do not know if a stationary steady-state even exists,  since the presence of active forces may induce a constantly changing configurations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' In the SI section 2 we give a  simple analytic calculation that gives reasonably well the transition line between the pearled and flat phases, which  are the main stable condensed phases in this phase diagram (Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='S2,S3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  The evolution of a handful of chosen simulations are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='3, showing flat, elongated-flat, elongated-pearling,  and pearling phases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' All the simulations begin in a disordered uniform distribution of the CMC on the spherical vesicle,  but in all of them we find that buds form rather quickly (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='3B(i)-E(i)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' In the budded phase this configuration  simply remains stable and does not evolve significantly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' It takes longer time for the larger clusters of the flat rim, arcs  and pearls to form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The transition lines separating two different vesicle phases, obtained from our simulations, are not  precise, and one can obtain either one of the vesicle shapes close to these lines (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='3A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  To conclude, by exploring the f − w phase diagram, we demonstrate the competition between the protein binding  which drives the formation of pearled clusters, and the active force that drives the formation of arc-like clusters at  the edge of flat protrusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' This competition is highlighted in the new phases of vesicle morphologies that we found,  namely the elongated two-arcs and the elongated-pearled phases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The pearling phase appears for large enough values  of w, as follows also from the theory of self-assembly [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  FORCE-SPONTANEOUS CURVATURE PHASE DIAGRAM  We now proceed to explore the interplay between the active force and the spontaneous curvature of the CMC in  determining the morphology of the vesicle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' We chose the parameters for a new set of simulations such that we are in  the flat phase when the CMC are highly curved: ρ = 20%, κ = 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='5, w = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The resulting phase diagram is shown in  Fig4A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  We find several phases: budded phase, flat phase, elongated (arcs) phase and highly-elongated (tubes) phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Here  the boundaries between the different phases were drawn by eye, due to relative sparse scan over the parameters, and the  self-evident boundaries (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='4A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' In this parameter regime, we do not find any pearled phase, with the budded phase  remaining stable due to the bending energy barrier that prevents buds merging (note that the bending modulus is  larger here), and lower relative w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Similar to the force-binding strength system (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='2A), where the budded and pearled  6  phases exist for low active force, we also find that as the active force is increased the budded phase is destabilized to  form the flat phase (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='4A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  The flat phase is destabilized as the spontaneous curvature decreases due to the following mechanism: as C0 decreases  the thickness of the rim cluster increases, which means that there are not enough CMC to complete a circular cluster  around the edge of the flat shape.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The morphology then changes into local arc-like clusters that pull the vesicle into  elongated shapes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The elongation of these vesicles depends on the magnitude of the active force.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  The main feature of this phase diagram is the appearance of the highly-elongated tubular phase, where the entire  vesicle is stretch into a several tubes that are pulled by CMC clusters at their tips.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' We can theoretically estimate  the location of the phase transition line, above which a vesicle will become highly-elongated, by comparing the force  exerted by the active CMC cluster and the restoring force of the emerging membrane tube due to bending (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='4B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  A hemispherical CMC cap with radius r = 2/C0 minimizes the bending energy (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='1): E ∝  �  1  r1 + 1  r2 − C0  �2  , and  maximizes the pulling force (since adding any more CMCs to the cluster, beyond the hemisphere, adds force in the  opposite direction).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The total pulling force of this hemispherical cluster is given by  Fpull = f ·  1  2  ����  geometry  2π(2/C0)2  s0  �  ��  �  #vertices  (7)  where s0 is the area per vertex, and 2πr2/s0 is the number of CMC in the cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' This hemispherical cap pulls a tube  with the same radius from the main vesicle body.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Note the extra factor of 1/2 due to the hemispherical shape of the  cup, compared to the calculation done for a flat cluster of active proteins in [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  Assuming the restoring force is dominated by the bending energy of the membrane tube, it is given by (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='1) [5]  Frestore = κ  2  2π  (2/C0)  (8)  The highly elongated shape is initiated when the pulling force is greater than this restoring force, so the critical value  is given by equating Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='7,8, which gives  f = AC3  0  (9)  where A is a constant determined by the constant parameters of the simulation (bending modulus and average area  per vertex).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Plotting this simple cubic relation in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='4A (blue solid line, where we fit the value of A), shows a good  agreement with the observed boundary of the regime of the highly-elongated tubular shapes on the phase diagram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  Note however that the shapes of the vesicles at the transition to the tubular phase are not always simple cylindrical  tubes with hemispherical clusters at their tips (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='4A), as the analytic model assumes (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='4B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  To conclude this section, we have shown that active CMC give rise to flat protrusions when they are highly curved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  Tubular protrusions can form for weakly curved active CMC, while for highly curved CMC the active force needed  to produce such slender protrusions increases extremely fast.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' In the next sections we explore how slender tubular  protrusions can be produced with highly curved active proteins, by either changing the effective curvature of the CMC  cluster, or by increasing the effective pulling force of the cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  MULTIPLE CURVATURE  Real cells have many species of membrane protein of both convex and concave intrinsic curvature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' While these  membrane proteins have distinct curvatures, the effective curvature of a cluster of CMC may depend on the composition  of the cluster, if it contains CMC of different spontaneous curvatures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' In order to form clusters of mixed curvatures,  we explore vesicles that contain CMC of different curvatures (concave and convex), that bind to each other equally.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' If  the two CMC types bind only to their own kind, they form separate clusters on the vesicle, and their coupling with  each other due to curvature alone is rather weak (see SI).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The convex CMC maintain their activity, as in the previous  sections, while the concave CMC is passive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='4C(i) we show snapshots of the steady-state shapes of the vesicles that contain 10% passive concave CMC, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  a CMC species with C−  0 < 0 and f − = 0, in addition to convex CMCs (ρ+ = 10%, f = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='5, and C+  0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Both  types of CMC have the same binding strength w = 2, which binds both types equally, leading to strong mixing of the  two CMC types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' For weakly curved concave CMC (C−  0 = −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='001) the flat phase remains stable (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='4C(i6)), driven by  the convex active CMC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' As the concave CMC become more curved (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='4C(i) from right to left) the circular cluster at  the rim of the flat shape breaks up, and highly elongated shapes appear (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='4C(i2,i3)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  7  These shapes can be explained by mapping the vesicles in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='4C(i) on the phase diagram (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='4A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' For each  simulation, we calculate the average spontaneous curvature of the CMC clusters: C0,eff =  �  C+  0 + C−  0  �  /2, as well as  the average pulling force per CMC: feff = f/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='4D we plot the typical dashed outline of the vesicles from  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='4C(i) on the phase diagram according to these effective parameters C0,eff, feff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Most vesicles match the shape  of the phase to which they are mapped in this way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The only exception is the vesicle with the most concave CMCs  (and effective C0,eff = 0), which is not in the shape of highly-elongated tubes, as suggested by the calculated average  parameters, but fits better the arcs phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' This phenomena is due to the concave CMCs phase-separating into internal  ”sacks” of concave-enriched clusters (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' 5Ai), which results in an effective removal of these concave CMC from  determining the outer shape of the vesicle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' To take this into account, we calculate the effective mean curvature of the  CMCs while removing the concave CMC that are contained in the internalized sacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' This is done by including in the  calculation of the average curvature only concave CMCs which are connected to at least one convex CMC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Using this  revised average spontaneous curvature, we plot the locations of the vesicles on the phase diagram (full snapshots),  and find that except for the most curved concave CMC (A1), the locations of the other vesicles is minimally affected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  For the case A1, we find that indeed the formations of large sacks of concave CMC, push the vesicle into the arcs  regime, compatible with its revised location on the phase diagram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The phase separation of the passive concave CMC  into sacks is driven by the minimization of the total bending energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The highly elongated tubes cost a high bending  energy of the bare membrane: in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='4C(i2) the average bending energy of the bare membrane is ∼ 25KBT, while in  the flatter shapes after the phase separation (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='4C(i1)) the average bending energy of the bare membrane drops to  ∼ 17KBT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  In addition to the overall vesicle shape in the system of mixed curvatures, we are interested in the character of the  CMC clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' We find that concave and convex CMCs create complex mixed clusters with a ”coral”- or ”sponge”-like  texture (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='4C and close up in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' 5Aii).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The texture of these clusters seems similar to the membrane ruffles observed  in [20] behind the leading edge of motile cells.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' In this work, the ruffles were attributed to the interaction between  concave and convex membrane proteins, that are also involved in the recruitment of the actin polymerization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' It was  furthermore proposed in [20] that the pattern of ruffles observed in these cells is determined by the interaction between  a concave membrane protein that inhibits the actin polymerization, which is recruited by the convex CMC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Motivated  by this proposed mechanism, we explored the resulting shapes of the vesicle and CMC clusters when the concave  CMCs inhibit the active force exerted by the convex CMCs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' We tested two possibilities: inhibition that is proportional  to the number of concave neighbors (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='4, Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' 4C(ii)), and full inhibition with even one concave neighbor (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='5, Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  4C(iii)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' In both cases we find that the effective force is reduced, and that the resulting shapes correspond very well to  their locations on the phase diagram (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='4D).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The shapes obtained for full inhibition (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' 4C(iii)) are very similar  to those for a vesicle with a mixture of passive CMC (see SI section 3, Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='S4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Regarding the comparison with the  experiments [20], we conclude from the model that the ruffle texture of the CMC clusters does not crucially depend  on the inhibitory interaction between the two CMC types, but rather on their spontaneous curvatures and binding  interaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  Let us now focus on the phase-separated sacks of highly curved concave CMC, which form within the mixed clusters  (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' We observed that the neck that connects the sacks to the outer part of the cluster is much narrower when  the convex CMC exert outwards protrusive forces (compare Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='5(Aii) and (Cii)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' We quantified the area of the  narrowest part of the neck in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='5B,D for the active and passive convex CMC, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The necks are naturally  narrower for more highly curved concave CMC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The active convex CMC, which push the membrane outwards, exert  an effective pressure force that squeezes the neck into a narrower radius.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Note that for the narrowest necks, we are  clearly at the limit of the spatial resolution of the simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' We do not allow membrane fission, and therefore can  not describe the process of detachment of such sacks as internalized vesicles [33], as occurs in cells during endocytosis  and macropinocytosis [34].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='5E,F we show the dynamics of the cluster formation, whereby a patch of passive concave CMC (blues) increase  in size, while its rim is populated by active convex CMC (red).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' In these images the surrounding bare membrane is  rendered to be invisible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' These simulated dynamics resemble those calculated by another model of macropinocytic  cups [35], which was based on reaction-diffusion dynamics coupled to active forces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  Finally, when the two CMC types bind exclusively to their own kind, they form separate clusters, with very limited  coupling between them (see SI section 4, Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='S5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  VII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  FORCE ALIGNMENT  As we show in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='4A, when the highly curved CMC induce a protrusive force that is directed at the outwards  normal, we require an extremely large force in order for the highly elongated tubes to form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' However, cells initiate  slender, tube-like filopodia protrusions using highly curved membrane proteins, such as IRsp53 [8–10, 12–14], in  agreement with theoretical calculations [36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Within the slender filopodia in cells, the actin filaments are organized into  8  a cross-linked bundle, which efficiently directs the forces of all the polymerizing actin filaments along the protrusion’s  axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The actin nucleators at the tip of the filopodia are different from those at the leading edge of the flat lamellipodia  [14, 21, 37], and initiate the growth of parallel actin filaments that form the bundle at the filopodia core.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' In our model,  since we do not explicitly describe the actin filaments organization, we can only describe the effects of the bundling on  the forces exerted on the membrane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' To simulate this kind of bundling,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' we add an alignment term of a Vicsek-like  interaction [22],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' which aligns the forces exerted on the membrane by each CMC that is bound in a cluster  ˆfi = ˆni + s �  r ˆnj  |ˆni + s �  r ˆnj|  (10)  The direction of the active force exerted on each CMC vertex i,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' ˆfi,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' is a weighted average of the local outwards normal  direction (ˆni) and a contribution from all the vertices j within a distance r from the vertex i (and in the same connected  cluster),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' with a weight of s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='6A we plot typical steady-state snapshots of the vesicle shape and CMC clusters, as function of the strength  and range of the alignment interaction of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' We observe a rather sharp transition from flat shapes for short-range  alignment (r < 10) to shapes containing thin tube-like protrusions for long-range alignment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' As function of the  parameter s we find only weak dependence: at very small values of s and r = 10, we find that the weak alignment  is sufficient to increase the net pulling force of the CMC clusters, such that they break the circular rim of the flat  shape (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='4B(iii)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The resulting shape, with ”paddle”-like protrusions, resembles the ”arcs” phase we found in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='4  between the flat and tubes phases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' At higher values of s this paddles phase changes to tubes, due to the stronger  alignment leading to a larger net pulling force.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  At these larger interaction strength the vesicle produces thin, finger-like clusters with a small bulbous ”head” and an  elongated ”sleeve” (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='6B(ii)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' This shape allows the CMC to satisfy their spontaneous curvature, with a spherical tip  that has a radius of rtip = 2/C0, while the sleeve has a thinner radius of rsleeve = 1/C0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Such a cluster configuration  is stable due to the alignment of the active forces along the tube axis (perpendicular to the membrane along the  sleeve, Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='6B(ii)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Once these elongated clusters form, they exert a large pulling force on the remaining membrane,  thereby pulling elongated bare-membrane tubes behind them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The membrane tube can have a larger radius than the  radius of the tubular CMC cluster, as it balances the pulling force with the restoring force due to bending energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The  alignment of the forces means that the entire CMC cluster pulls along the protrusion axis (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='6B(ii)), exerting a  much larger total force than was possible using purely normal forces at the tip, thereby forming tubes at values of  the force per protein that are much lower than predicted by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='9 and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='4A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Smaller clusters that only contain the  hemispherical tip (such as Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='6B(i)), do not grow tube-like protrusions, even though their net pulling force is larger  by up to a factor of 2 compared to normal-force CMC, due to alignment (compare Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='6B(i) to Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='4B and Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='7A we plot the time progression of a vesicle with aligned-force CMC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' We observe that initially localized  hemispherical buds form rapidly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' These buds then coalesce to form larger clusters that grow into the typical shape  of bulbous tip with a thinner tubular part behind it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The size and total force of each of the clusters are plotted as  function of time, with each point size indicating the cluster size, and its y-axis coordinate giving its total active force,  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Note that clusters that contain patches of ”trapped” bare membrane undergo large force fluctuations  (blue and yellow points, largest two clusters shown on the right of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='7A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' These fluctuations arise from loss of global  alignment over the entire CMC cluster, due to the bare membrane patch that allows the alignment to change, especially  between the protrusion tip and the tubular part.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='7B we compare the finger-like protrusions that form due to highly curved aligned-force CMC, with the tubular  shapes that form due to weakly curved normal-force CMC (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='4A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The main difference is that the aligned-force  protrusions are much more stable compared to the tubes formed by the much smaller clusters of normal-force CMC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  The normal-force CMC undergo frequent fission and coalescence events, that correspond to tubes shrinking and  regrowing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' These differences in dynamics can be seen in the SI movies S1,S2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  VIII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  VESICLES WITH BOTH NORMAL AND ALIGNED-FORCE CMC, ADHERED TO A FLAT  SUBSTRATE  We simulate a vesicle with a mixture of CMCs (ρ = 5% of each type), both highly curved and convex, one type with  normal force and the other with strongly aligned force (r = 15, s = 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Our initial state of the vesicle is obtained by  letting the vesicle spread over a flat adhesive substrate, while it contains only normal-force CMC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Then, at a time  where the vesicle is partially spread (time 0 in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='8A), we convert randomly half of the CMC to aligned-force behavior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  We chose an adhesion strength wad = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='25 (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='2), which gives a well-spread vesicle when containing only normal-force  CMC [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='8A we show two simulations: one with universal binding between the normal and aligned-force CMCs, and  the other with exclusive binding, such that normal-normal and aligned-aligned CMC bind to their own type exclusively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  9  In these examples we see that the rim cluster forms and drives strong spreading of the vesicle, as expected [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The  aligned-force CMC (labeled in yellow) aggregate to form a single filopodia-like protrusion, which is able to recruit into  it also normal-force CMC (labeled in red).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' This filopodia is highly dynamic, undergoing periods of attachment to the  rim cluster, and to the adhesive substrate, as well as detachments from the substrate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The filopodia is observed to  attach and detach from the rim cluster, leading to meandering motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' When the two types bind exclusively, they  form segregated clusters along the rim, with the aligned-force clusters protruding slightly more outwards compared to  the normal-force clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The dynamics of this system can be seen in SI movie S3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='8B we show the evolution of the segregation factor in the simulations, which is defined as  S = 2 · Prob (CMC neighbor is of the same type) − 1  (11)  This segregation factor is equal to 0 for well-mixed clusters (where the probability to have a neighbor CMC of the  same type is equal to 1/2), and it is equal to 1 for complete phase-separation of the types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' In the main panels we give  the segregation factor per cluster for the simulations shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='8A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The insets show the average of 4 independent  simulations, which converge to a value of about S = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='25 for the universal binding and S = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='9 for the exclusive  binding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' In the universal case, we can see that the segregation is strongest in the filopodia, so the segergation factor  for the large rim cluster jumps up or down, when the filopodia protrusion cluster attaches or detaches respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  The protrusion cluster is more segregated (S ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='25), since its tip is enriched with aligned-force CMCs that drive its  formation, while the rim cluster is nearly perfectly mixed (S ≈ 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' For the exclusive binding, the segregation is high  both in the filopodia protrusion and in the rim cluster, so it does not change when the filopodia attach or detach from  the rim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  Note that along the adhered vesicle rim, the regions of aligned-force CMC protrude slightly more than the normal-  force regions (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='8A, exclusive).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' This is enhanced when the normal-force CMC are disabled, so that they do not exert  any active force, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='S6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  IX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  COMPARISON WITH EXPERIMENTS  We can now compare some of our theoretical results to experimental observations, published and new.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  Membrane shapes driven by branched actin polymerization  The active protrusive forces in our model are representative of actin polymerization activity near the cell membrane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  When the actin polymerization is nucleated by proteins that induce branched actin networks (such as WASP, WAVE  [38–40]), it is more natural to describe the force as a local pressure on the membrane, which therefore acts towards the  outwards normal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  The variety of shapes we obtained in our model (Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='2,3), range from flat lamellipodia-like shapes, to cylindrical  filopodia, to pearling-like protrusions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Some of these new elongated shapes can be compared with elongated global cell  shapes, observed in living cells [41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  Membrane shapes driven by bundled actin polymerization  The introduction of alignment in the forces exerted by the CMC represents in our model the case of proteins that  nucleate parallel actin bundles, such as VASP and Formins [10, 12, 21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Our model has demonstrated previously that  curved proteins that apply normal forces, induce the formation of flattened, lamellipodia-like protrusions [5, 18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Here  we show that curved proteins that induce polymerization of bundled actin (aligned-force in our model), naturally give  rise to filopodia-like protrusions (Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='6,7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' This result fits the observation of highly curved convex-shaped proteins  such as IRSp53 in both the leading edge of lamellipodia [7, 42] and in filopodia [2], where the actin organization is  very different due to the different type of actin nucleators [38, 43].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Note that the combination of convex curvature, and  nucleators of bundled actin, can form filopodia even without the explicit presence of I-BAR proteins (such as IRSp53)  [44, 45].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  Note that protrusions of similar shapes to our aligned-force protrusions, which have a bulbous tip and a slender  neck (Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='6,7), were theoretically predicted to form by anisotropic CMC, even without force [46].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Similar thin tubes  with bulbous tips are observed in cellular nanotubes [47] and in filopodia [48].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Since many curved proteins, such as  IRSp53 are anisotropic in their intrinsic shape, it will be interesting to extend our work in the future to include such  anisotropy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  10  Finally, our simulations of an adhered vesicle (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='8) indicate that the filopodia protrusions can undergo attachment  and detachment from the substrate, resembling such motion observed in experiments [14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' In addition, when we  mixed the aligned-force and normal-force CMC with exclusive binding between them, we obtained their segregated  organization along the rim of the adhered vesicle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' This is reminiscent of the observations of segregated regions of  bundled actin and branched actin nucleators along the rim of cellular protrusions extending on adhered substrates  [37, 49–51].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' As in the experiments, the clusters of aligned-force CMC along the rim slightly protrude, as they exert  a higher local force on the membrane rim, compared to the normal-force CMC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' These small protrusions have been  termed ”spikes” and ”microspikes” along the edge of lamellipodia in cells [45, 50, 52].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='9 we show images illustrating the dynamics of filopodia in cells, using lattice light-sheet microscopy, which is  capable of the high spatial and temporal resolution necessary to view the dynamics of the thin filopodia [53].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The  curved membrane protein IRSp53 is fluorescently labeled in green (GFP-IRSp53), while the actin filaments are labeled  in red (mCherry-lifeact).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' We observe in the experiments several features that are captured by the theoretical model:  The filopodia are highly dynamic, both at the cell rim and along its dorsal surface (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='9A-D), as we also see in the  model (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The filopodia in the experiments migrate on the cell surface, merge with other filopodia, and undergo  attachments and detachments from the surface (see SI movies 5-8), as we also see in the simulations (SI movies 3 and  4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Our assumption in the model of uniform adhesion along the membrane, and along the filopodia, agrees with some  observations [48, 54], and we can add more complex adhesion models in the future if needed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Note that in the cells we  observe an additional retraction motion that is driven by myosin-II contractile forces, which we do not have in our  current model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  The highly curved IRSp53 is observed to aggregate strongly at the tips of the filopodia, while along the lower parts  of the protrusion its aggregation is more fragmented (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='9E,F).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' This fits with the shapes that we obtained in the  model (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='6B,8A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Furthermore, our simulations of mixtures of aligned-force and normal-force CMC indicate that  while the aligned-force CMC are essential for forming the filopodia protrusions and occupy its tip region, there can be  significant amount of normal-force CMC along the lower part of the filpodia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Since the normal-force CMC correspond  to branched-actin nucleators, this result suggests that along the lower part of filopodia we may expect to find proteins  such as WAVE, which are usually associated with the leading edge of the lamellipodia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' This prediction is supported by  some experimental observations of WAVE proteins [55], Arp2/3 complexes [56], and small lamellipodia-like protrusions,  along filopodia shafts [57].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  Membrane shapes driven by mixtures of passive concave and active convex CMC  Our mixtures of CMC of opposite curvatures (Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='4C,5) gives rise to membrane shapes that resemble in their  texture the ruffles observed in cells [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' In addition, we find that when the passive concave component is highly  curved, we observe a phase separation within the CMC clusters, whereby the concave CMC forms an internalized  spherical invagination.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' These invaginations are then squeezed at their base by the active forces induced by the convex  CMC, and the calculated membrane shape dynamics resembles the process of actin-dependent endycytosis [17, 58–60]  and macropinocytosis [34, 61–63].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  Note that there is some experimental evidence that the internalized membrane, corresponding to our concave CMC  region, do indeed contain concave membrane components, such as BAR proteins [64].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' In addition, there are examples  where the internalized region contains membrane components that interact with the convex proteins that recruit actin  and form the squeezing at the narrow neck.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' In [59] the internalized activated integrins and associated proteins, bind to  the actin which is nucleated at the neck, recruited there by IRSp53 (convex) proteins.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' In our model we show that such  a direct interaction is necessary for robust formation of the internalized sacks with the recruited convex proteins at the  neck.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  DISCUSSION  In this study we greatly extend our theoretical understanding of the space of membrane shapes that are produced  by curved membrane protein complexes (CMC) that exert active protrusive forces on the membrane [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' We started  by mapping the phases as function of the magnitude of the active force and attractive nearest-neighbor interaction  strength of CMCs (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='2A), demonstrating the competition between these two terms: systems dominated by the  binding interactions tend to have the equilibrium (pearled) shapes of the CMC clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The active forces tend to  break-up the pearled clusters, and induce the formation of either elongated or flat pancake-like membrane shapes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  Similarly we exposed the phase diagram in terms of the active force and the CMC spontaneous curvature (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='4A),  whereby highly curved CMC induce flattened vesicle shapes, while less curved CMC induce elongated tubular shapes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  Note that in these studies the protrusive force applied by each CMC is towards the local outwards normal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  11  Based on these results we further explored systems where highly curved active CMC could induce tubular protrusions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  We tested two possible scenarios: In the first one, the effective curvature of the CMC cluster is reduced by mixing  two types of CMC of opposite curvatures, such that a tubular protrusion forms with a rather flat CMC cluster at its  tip (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='4C,D).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' In the second, the net protrusive force of the CMC cluster is increased by introducing an alignment  interaction that tends to align the forces exerted by CMC that are bound within the same cluster (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' This  alignment is found to stabilize long tubular CMC clusters, since the aligned active forces act along the tube axis and  do not act to expand the tube, unlike the case of normal protrusive forces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  We found that that mixtures of CMC of opposite curvatures, specifically passive concave and active convex, lead  to formation of clusters with complex textures that resemble ruffles on cell membranes (Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='4C,5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' In addition, we  found in these systems the formation of internalized invaginations, where the convex active CMC form a narrow neck,  resembling endocytosis and macropinocytosis in cells.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  To conclude, the results presented in this work expand out theoretical understanding of membrane shapes and  dynamics driven by intrinsic (spontaneous) curvature of membrane components and cytoskeletal active forces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Some  of these shapes resemble observed membrane dynamics in living cells, suggesting that this coupling between curved  membrane proteins and cytoskeleton forces gives rise to these biological phenomena.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Many of the features that we  found, such as the ruffles and the internalized invaginations by mixing CMC of different curvatures, remain to be  further explored in future theoretical studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' In addition, future studies will explore the dynamics of the membranes  when the CMC have anisotropic spontaneous curvature, and also in the presence of contractile forces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  Conflict of Interest Statement  The authors declare that the research was conducted in the absence of any commercial or financial relationships  that could be construed as a potential conflict of interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  Author Contributions  YR and NG developed the theoretical model;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' SP and AI developed the software;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' YR and NG conceived, designed  and implemented the analysis of the model, and prepared the manuscript.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' YK and SS cultured and imaged the cells.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  The manuscript was edited by all the authors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  Funding  NG is the incumbent of the Lee and William Abramowitz Professorial Chair of Biophysics, and acknowledges support  by the Ben May Center for Theory and Computation, and the Israel Science Foundation (Grant No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' 207/22).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' AI and  SM were supported by the Slovenian Research Agency (ARRS) through the Grants No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' J3-3066 and J2-4447 and  Programme No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' P2-0232.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' YK and SS was supported by grants from the JSPS (KAKENHI JP20H03252, JP20KK0341,  and JP21H05047) and JST CREST (JPMJCR1863) to SS and Takeda Science Foundation, a Grant-in-Aid for  Challenging Exploratory Research (KAKENHI No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' 20K20379), and JST CREST (JPMJCR1863) to YK.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  Acknowledgments  NG is the incumbent of the Lee and William Abramowitz Professorial Chair of Biophysics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' This research is made  possible in part by the historic generosity of the Harold Perlman Family.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  Supplemental Data  The SI text, figures, and movies are also available from the Box drive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  Data Availability Statement  The code for generating the simulations of this study can be found in the GitHub repository of YR, which is taken  and modified off the GitBlit repository of SP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Reconstruction of the initial simulation folders are also available from  12  the Box drive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Further data or code requests will be happily fulfilled by YR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [1] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Frey and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Idema, Soft matter 17, 3533 (2021), ISSN 1744-6848.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [2] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Mattila and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Lappalainen, Nature Reviews Molecular Cell Biology 9, 446 (2008), ISSN 14710072.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [3] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Simunovic, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Voth, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Callan-Jones, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Bassereau, Trends Cell Biol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' 2015 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [4] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Gov, Philosophical Transactions of the Royal Society B: Biological Sciences 373, 20170115 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [5] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Foˇsnariˇc, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Peniˇc, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Igliˇc, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Kralj-Igliˇc, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Drab, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Gov, Soft Matter 15, 5319 (2019), ISSN 17446848,  1812.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='01460.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [6] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Begemann, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Saha, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Lamparter, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Rathmann, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Grill, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Golbach, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Rasch, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Keller, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Trappmann, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Matis,  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=', Nature Physics 15, 848 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [7] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Pipathsouk, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Brunetti, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Town, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Graziano, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Breuer, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Pellett, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Marchuk, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Tran, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  Krummel, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Stamou, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=', Journal of Cell Biology 220, e202003086 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [8] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Scita, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Confalonieri, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Lappalainen, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Suetsugu, Trends in cell biology 18, 52 (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [9] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Ahmed, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Goh, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Bu, in Seminars in cell & developmental biology (Elsevier, 2010), vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' 21, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' 350–356.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [10] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Vaggi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Disanza, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Milanesi, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Di Fiore, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Menna, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Matteoli, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Gov, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Scita, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Ciliberto, PLoS  computational biology 7, e1002088 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [11] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Mancinelli, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Lamparter, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Nosov, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Saha, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Pawluchin, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Kurre, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Rasch, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Ebrahimkutty, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Klingauf, and  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Galic, Proceedings of the National Academy of Sciences 118, e2106921118 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [12] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Tsai, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Henderson, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Jarin, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Kremneva, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Senju, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Pernier, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Mikhajlov, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Manzi, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Kogan, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  Clainche, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=', Science Advances 8, eabp8677 (2022), https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='org/doi/pdf/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='1126/sciadv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='abp8677, URL  https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='org/doi/abs/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='1126/sciadv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='abp8677.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [13] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Fox, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Tran, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Trinkle-Mulcahy, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Copeland, Journal of Biological Chemistry 298 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [14] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Lee, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Fujioka, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Osuga, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Nishimura, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Suetsugu, in Plasma Membrane Shaping (Elsevier, 2023), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  245–263.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [15] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Drab, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Sadhu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Ravid, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Igliˇc, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Kralj-Igliˇc, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Gov, Plasma Membrane Shaping pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' 415–429 (2023).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [16] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Mellor, Biochimica et Biophysica Acta (BBA)-Molecular Cell Research 1803, 191 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [17] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Doherty and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' McMahon, Annual review of biochemistry 78, 857 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [18] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Sadhu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Peniˇc, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Igliˇc, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Gov, European Physical Journal Plus 136, 495 (2021), ISSN 21905444, 2101.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='00313.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [19] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Gov, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Kralj-Igliˇc, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Sadhu, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Mesarec, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Igliˇc, in Plasma Membrane Shaping (Elsevier, 2023), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' 393–413.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [20] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Sitarska, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Almeida, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Beckwith, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Stopp, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Schwab, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Sixt, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Kreshuk, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Erzberger, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Diz-Mu˜noz,  bioRxiv p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='03.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='437199 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [21] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Faix and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Rottner, Current Opinion in Cell Biology 18, 18 (2006), ISSN 09550674.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [22] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Vicsek and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Zafeiris, Physics reports 517, 71 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [23] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Mashiko, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Fujihara, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Satouh, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Miyata, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Isotani, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Ikawa, Scientific reports 3, 1 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [24] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Hanawa-Suetsugu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Itoh, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Ab Fatah, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Nishimura, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Takemura, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Takeshita, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Kubota, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Miyazaki, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  Wan Mohamad Noor, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Inaba, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=', Nature communications 10, 1 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [25] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Chen, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Legant, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Wang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Shao, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Milkie, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Davidson, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Janetopoulos, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Wu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Hammer III,  Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Liu, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=', Science 346, 1257998 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [26] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Nishimura, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Oyama, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Hu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Fujioka, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Hanawa-Suetsugu, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Ikeda, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Yamada, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Kawana, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Saigusa,  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Ikeda, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=', Developmental cell 56, 842 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [27] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Welch and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Mullins, Annual review of cell and developmental biology 18, 247 (2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [28] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='-F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Carlier and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Pantaloni, Journal of Biological Chemistry 282, 23005 (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [29] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Campellone and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Welch, Nature reviews Molecular cell biology 11, 237 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [30] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Bohinc, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Kralj-Igliˇc, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' May, The Journal of chemical physics 119, 7435 (2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [31] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Theodorou and U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Suter, Macromolecules 18, 1206 (1985).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [32] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Golani, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Ariotti, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Parton, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Kozlov, Developmental Cell 48, 523 (2019), ISSN 15345807.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [33] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Peniˇc, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Mesarec, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Foˇsnariˇc, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Mr´owczy´nska, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' H¨agerstrand, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Kralj-Igliˇc, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Igliˇc, Frontiers in Physics 8, 342  (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [34] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Kay, Cells & Development 168, 203713 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [35] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Saito and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Sawai, Iscience 24, 103087 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [36] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Mesarec, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' G´o´zd´z, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Igliˇc, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Kralj, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Igliˇc, Colloids and Surfaces B: Biointerfaces 141, 132 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [37] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Faix and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Rottner, Journal of Cell Science 135, jcs259226 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [38] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Small, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Stradal, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Vignal, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Rottner, Trends in cell biology 12, 112 (2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [39] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Takenawa and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Suetsugu, Nature reviews Molecular cell biology 8, 37 (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [40] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Rottner and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Schaks, Current opinion in cell biology 56, 53 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [41] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Suetsugu, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Murayama, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Sakamoto, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Hanawa-Suetsugu, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Seto, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Oikawa, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Mishima, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Shirouzu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Takenawa,  and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Yokoyama, Journal of Biological Chemistry 281, 35347 (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [42] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Pawluchin and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Galic, Frontiers in Cell and Developmental Biology 10 (2022), ISSN 2296-634X, URL https:  //www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='frontiersin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='org/articles/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='3389/fcell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='1080995.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [43] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Krause and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Gautreau, Nature reviews Molecular cell biology 15, 577 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  13  parameter  units  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='1,[5]  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='2  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='4A  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='4C  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='6  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='7  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='8  f  KBT/ℓmin  1  0 − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='2 0 − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='2, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='5  w  KBT  1  0 − 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='8  2  2  2  2  2  κ  KBT  20*  20  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='5  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='5  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='5  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='5  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='5  ρ  1  0%-20%  10%  20%  10%, 10%  20%  20%,  10%, 10%  C0  1/ℓmin  1(0)  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='75 − 0, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='4, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='8  TABLE I: The values of the model parameters used in the simulations, in the different figures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The energy units are KBT = 1,  which define the scale of f, w, κ, and the length units are ℓmin = 1, which define the scale of the vertex lattice, the force, and  spontaneous curvature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [44] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' K¨uhn, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Erdmann, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Kage, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Block, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Schwenkmezger, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Steffen, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Rottner, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Geyer, Nature communications  6, 1 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [45] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Pokrant, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Hein, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' K¨orber, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Disanza, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Pich, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Scita, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Rottner, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Faix, Proceedings of the National  Academy of Sciences 120, e2217437120 (2023).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [46] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Bobrovska, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' G´o´zd´z, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Kralj-Igliˇc, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Igliˇc, PloS one 8, e73941 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [47] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Schara, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Janˇsa, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' ˇSuˇstar, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Dolinar, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Pavliˇc, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Lokar, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Kralj-Igliˇc, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Veraniˇc, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Igliˇc, Cellular &  molecular biology letters 14, 636 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [48] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Miihkinen, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Gr¨onloh, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Popovi´c, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Vihinen, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Jokitalo, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Goult, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Ivaska, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Jacquemet, Cell reports  36, 109716 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [49] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Cohan, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Welnhofer, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Zhao, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Matsumura, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Yamashiro, Cell motility and the cytoskeleton 48, 109 (2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [50] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Damiano-Guercio, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Kurzawa, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Mueller, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Dimchev, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Schaks, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Nemethova, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Pokrant, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Br¨uhmann, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Linkner,  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Blanchoin, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=', Elife 9 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [51] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Kage, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' D¨oring, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Mietkowska, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Schaks, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Gr¨uner, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Stahnke, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Steffen, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' M¨usken, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Stradal, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Rottner,  Journal of Cell Science 135, jcs260364 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [52] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Koestler, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Auinger, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Vinzenz, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Rottner, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Small, Nature cell biology 10, 306 (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [53] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Mimori-Kiyosue, in Plasma Membrane Shaping (Elsevier, 2023), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' 357–374.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [54] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Tu, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Pal, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Austin, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Wang, Current Biology 32, 4386 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [55] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Nozumi, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Nakagawa, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Miki, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Takenawa, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Miyamoto, Journal of cell science 116, 239 (2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [56] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Johnston, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Bramble, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Yeung, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Mendes, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Machesky, BMC cell biology 9, 1 (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [57] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Lebrand, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Dent, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Strasser, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Lanier, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Krause, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Svitkina, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Borisy, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Gertler, Neuron  42, 37 (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [58] O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Mooren, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Galletta, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Cooper, Annual review of biochemistry 81, 661 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [59] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Moreno-Layseca, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' J¨antti, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Godbole, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Sommer, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Jacquemet, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Al-Akhrass, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Conway, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Kronqvist, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  Kallionp¨a¨a, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Oliveira-Ferrer, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=', Nature cell biology 23, 1073 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [60] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Kaplan, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Kenny, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Chen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Sch¨oneberg, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Sitarska, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Diz-Mu˜noz, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Akamatsu, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Xu, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Drubin,  Molecular Biology of the Cell 33, ar50 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [61] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Sønder, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' H¨ager, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Heitmann, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Frankel, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Dias, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Simonsen, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Nylandsted, Science Advances  7, eabg1969 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [62] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Mylvaganam, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Freeman, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Grinstein, Current Biology 31, R619 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [63] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Lutton, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Paschke, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Munn, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' King, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Kay, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Bretschneider, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=', bioRxiv (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [64] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Baranov, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Olea, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' van den Bogaart, Trends in cell biology 29, 727 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  14  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' 1: Phases of vesicle shapes driven by curved active CMC, as obtained in [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' (A) Phase diagram in the temperature-density  plane: mixed (gas), budded, and flattened (pancake).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The gas phase is dominated by entropy, hence appears at either high  temperatures or low densities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The pancake phase is dominated by having favorable binding and bending energy, where the  active forces are all radial and stabilize the flat shape.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' This phase requires large stable CMC cluster, and so can only appear at  low temperatures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The budded phase appears between the two other phases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' At a CMC density that is lower than the minimal  value needed for a closed circular rim, the pancake shape changes to B) a two-arcs phase, while when the CMC concentration is  very high the pancake forms pearled extensions that contain the surplus CMC (C).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' There are two other phases in different  regimes: (D) The pearling phase appears at higher CMC density, where most of the CMC aggregate into long necklace-like  clusters that minimize the protein-protein binding energy (phase-separation of CMC), and (E) highly-elongated (tubular) phase  for flat CMCs, where large CMC caps can exert a strong force that pulls out elongated tubes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Pictures taken from [5] Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='4c,7d,  and SI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  (A)  2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='5  Mixed  I  Budded  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='5  Pancake  4  6  8  10  12  14  16  p[%]15  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' 2: Force-binding strength plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' (A) Phase diagram as function of f and w, with: κ = 20, C0 = 1, and ρ = 10%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The  different phases are indicated by their names, and a typical snapshot of the vesicle after a long simulation is shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The  transition lines between the phases were drawn according to the measures shown in the bottom panels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The gas and buds phase  is separated by mean cluster size ⟨N⟩ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='5 (yellow solid line), as obtained from (B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The green line denotes the boundary of the  flat phase, obtained approximately from a contour of the first (small) gyration eigenvalue λ2  1, which is minimal for flat shapes  (C).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The light blue line denotes the boundary of the elongated shapes, roughly following a contour of the second (intermediate)  gyration eigenvalue λ2  2 (D).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The transition line between the buds and mixed phases is given by a contour of CMC perimeter  length (¯ℓp = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='875, red solid line), extracted from (E).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Finally, the pearling phase transition line (red dotted line) is drawn along  the contour of small CMC perimeter length (¯ℓp = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='375), from (E).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' In panels (B-E) we plot heatmaps of the following quantities:  (B) Mean cluster size for clusters smaller than 10, ⟨N⟩ > 10 (C) first (small) gyration eigenvalue λ2  1, (D) second (intermediate)  gyration eigenvalue λ2  2, (E) Mean CMC cluster perimeter length (excluding isolated CMC) ¯ℓ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  Elongated  Mixed16  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' 3: Evolution of the MC simulation at four different points (B-E) denoted on the phase diagram (A) (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='2A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' (B): f=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='8,  w=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='6, (C): f=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='8, w=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='88, (D): f=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='8, w=3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='20, and (E): f=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='4, w=4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The MC time-steps shown in the snapshots are: (i) 10,  (ii) 50 (ii) and (iii) 200, and the final time-step (299) is shown on the phase diagram (A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' At time (i), all simulations are in the  budded state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' At time (ii), arc and pearling clusters begin to form, favoring arcs for large forces and pearling for large binding  strength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' At time (iii), the vesicles are close to their final steady-state shapes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The flat simulation (B) generates several arcs  in stage (ii), which coalesce to form a circular stable rim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The pearling simulation (E) generates pearling clusters (ii) which  coalesce into a few larger clusters (coarsening).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' In contrast, the elongated simulations generate both arcs and pearled clusters at  the intermediate stage (ii).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' These arc-like clusters are sufficient stretch the vesicle, even in (D), to give rise to the final elongated  phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  Ci  D i  11  Bi  ili  Ei  ili17  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' 4: (A) Phase diagram in the force-spontaneous curvature plane, using the parameters: ρ = 20%, κ = 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='5, w = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The  different phases are denoted by their typical shapes, and the thin colored transition lines were drawn by hand (yellow, red and  green).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' With no or weak force, we find a budded phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' As the force is increased, we find for the high spontaneous curvature  the flat phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' As the spontaneous curvature is reduced, the flat phase is observed to give way to an ”arcs” phase, which is  finally replaced by a highly-elongated tubular phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The thick blue line denotes the theoretical calculation for the transition  line that bounds the tubes phase, which is a cubic equation: f = AC3  0 (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='9), where we use: A ≈ 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' This equation is derived  from the force balance shown schematically in (B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' (C) Typical steady-state snapshots of simulations with a mixture of CMC:  active convex CMC (C0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='8, f = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='5, ρ = 10%), and passive concave CMCs (ρ = 10%) with different concave curvatures  C−  0 (along the x-axis).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' We show here three cases: i) no inhibition of the active convex CMC, ii) proportional inhibition, where  the force exerted by a convex CMC is proportional to number of non-concave neighbors, and iii) disabling interaction, where  the convex CMC do not exert any force if they have a concave neighbor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' (D) Mapping of the vesicles shown in (C) to their  respective locations in the force-spontaneous curvature phase diagram (A), using the average force and spontaneous curvature of  the mixture (dashed outlines).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The snapshots are shown at shifted locations, according to the effective curvature when we take  into account the phase-separation of the concave CMC, into internalized sacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' These shifts in locations are most dramatic for  1i,1ii,2ii,1iii,2iii (indicated by arrows), which places the vesicles in a phase which is appropriate for their shapes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  2  Flat  SO  ubes  Arcs  Buds  Flat  5i  61  2ii  Tubes  3ii  4ii  511  61l  1ili  Arcs  2ili  5ili.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  Buds  6ili  3ill18  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' 5: Mixed clusters can precipitate internal sacks, which are composed almost entirely of the concave (passive) CMC, when  the concave CMCs are highly curved C0 = −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='75, −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' This is shown in A(i,ii),C(i,ii) for a system with and without active  force, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' This internal sack is connected to the outside by a thin neck, or ”hole”, shown in A(iii) and C(iii).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The  cross-sectional area of the hole was measured by computing the area of the polygon made from the hole edge, which was picked  by hand (vertices).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' A histogram of the simulated hole sizes is shown for the system with and without active force respectively  (B,D).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' It is clear that the hole size is smaller in systems with force (B), such that it is in the limit of the simulation resolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  The holes are also larger as the spontaneous curvature of the passive concave CMC is smaller.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The insets of B,D show typical  examples of sacks (light blue nodes) connected to the outer part of the cluster (blue nodes) through the neck region (grey  shading).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' (E) and (F): Snapshots showing the formation of a sack for the system with active force (A), from the initial random  state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' In (E) we show the cluster viewed from outside of the vesicle (where the bare membrane is rendered invisible), looking  down on the patch that forms the sack, while in (F) we show the same process viewed from within the vesicle, where we see  clearly the final invagination.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  Aii  A ili  curvature: -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='75  curvature: -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='6  Ai  B  10  5  20  25C  10  15  20  25  c i  c ii  cili  LO  15  20  25 0  10  15  20  50  Hole area  Hole area  0219  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' 6: (A) Vesicle steady-state shapes as function of the strength (s) and range (r) of the Vicsek-like alignment interaction  (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='10)(ρ = 20%,κ = 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='5,C0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='4,w = 2,f = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Interaction radius smaller than 10 leads to a flat phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Above an interaction  radius of 10, the system transitions from a flat to a tubes phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' In between the flat and elongated tubes phases, we find a phase  with ”paddle”-like clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The tubular phase is characterized by CMC clusters that are mostly finger-like with a bulbous tip  and a tubular sleeve, which often stretch a membrane tube behind them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' (B) Snapshots of CMC clusters, with the active forces  indicated by the arrows, and the colormap indicating the dot product of the local force and local outwards normal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' In the tubes  phase (s = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='75, r = 15) we show in (i) an example of a hemispherical cluster, which is not able to pull an elongated protrusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  In (ii) (top) we show an example of a CMC cluster that contains a tubular sleeve, which increases the net pulling force above  the threshold to pull a membrane tube.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Note that at the sleeve base the alignment is weak due to the bare membrane boundary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  This effect is also shown in (iii) (bottom), where a small patch of bare membrane is trapped between the cluster tip and the  sleeve, leading to formation of two different alignment domains within the same cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Finally, in (iv) we show an example of  the paddle cluster (s = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='1, r = 10), where the weak alignment interaction gives rise to shapes similar to the regular arc-like  clusters (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='4A), elongated by the non-normal force.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  Tube  Paddle  Flat  iv  120  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' 7: (A) Dynamics of the formation of the tubular phase, driven by strong alignment interactions (ρ = 20%, κ = 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='5, C0 =  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='4, w = 2, f = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='2, s = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='75, r = 15).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Each circle represents a CMC-cluster at different MC time (x axis), the y axis represents  the total force exerted by the cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The circle size represents the size of the CMC cluster (see sidebar).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Color gives a persistent  ”identity” to each cluster, which last until fusion or fission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' On the top right is a snapshot of the vesicle in the last time step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  The four largest cluster are highlighted, and also shown on the right of the panel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Below the x-axis, we give snapshots of the  vesicle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The rapid initial formation of buds is seen followed by slower fusion of clusters to form elongated protrusions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Two  of the final large clusters, the bud and one of the elongated tube, are relatively stable, while the other two elongated clusters  have wildly oscillating force.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' We can see on the right that the fluctuating cluster incorporates a few bare membrane vertices  (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' 6B,iii).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' (B) The dynamics of tube formation due to aligned force with highly curved CMCs (top, s = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='5, r = 30, f = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='2,  C0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='4) compared to formation due to shallow (weakly curved) CMCs with normal force (bottom, f = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='5, C0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The  tubes of the latter are more dynamic and less stable than clusters of the former.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' This is also seen on the right panel, which  shows the total force on the largest clusters, which is far less noisy for the former.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  50  Sizes  40  2  30  4  8  20  16  32  10  64  128  256  20  40  60  80  100  120  140  timestep  75  50  25  0  200  400  75  50  25  0  200  40021  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' 8: A: Initial progress of simulation with normal-force CMCs (red) and aligned-force CMCs (yellow), in universal binding  (top) and type-exclusive binding (bottom), from the side and above (ρalign = 10%, ρnormal = 10%, κ = 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='5, C0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='8, w = 2,  f = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='5, s = 0, 1, r = 15, wad = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='25).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' CMCs in the rim drive the spreading of the vesicle on the surface, while some aligned-force  CMCs aggregate into a bulb-and-sleeve cluster which drives the formation of a filopodia-like protrusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' This protrusion can  attach to the rim cluster and then adhere to the substrate, while it can also detach from the substrate, and consequently also from  the rim cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' B: Evolution of the segregation factor in the simulations (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='11).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The colored lines give the segregation factor  for each cluster, with the cluster size indicated by the line thickness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' In the inset we give the average of the total segregation  factor for 4 independent simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' In the universal binding simulation we can see the fliopodia-like cluster repeatedly attach  and detach from the rim cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The rim cluster is mostly mixed for this case, while the protrusion is much more segregated, as  its tip is enriched with aligned-force CMCs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='00  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='75  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='75  factor  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='50  time 0  50  100 150 200 250  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='50  segregation t  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='6  detachments -  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='4  0  50  100  150  200  250  time  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='00  Rim cluster  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='50  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='50  0  50  100  150  200  250  0  50  100  150  200  250  time  time22  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' 9: Movements of IRSp53-localized cellular protrusions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' (A, B) The adhesion (A) and apical (B) plane section of the  three-dimensional images of an IRSp53-knockout U251 glioblastoma cell expressing GFP-IRSp53 (green) and mCherry-lifeact  (red).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' In (A) and (B), the region for the ∼ 2 µm thick xz section projection is indicated by the cyan dotted rectangle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' (C) The  xz section of the region of (A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The white lines indicate the plane in (A,B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The yellow line, which was set in the proximity  of the surface plane of the cell, indicates the line for the kymograph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' (D) The kymograph of the cell surface as indicated in  the yellow line in (C), along with the annotation of the representative motion of the IRSp53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' (E-F) The xy and xz sections at  the regions that are marked in (A,B), from the periphery (E), the middle (F), and the center (G).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The plane parallel to the  plasma membrane was sectioned and the regions that were projected xy and xz sections each others were marked in cyan dotted  rectangles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Arrows indicate the protrusions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The scale bar, 10 µm (A-D), 2 µm (E-G), and 50 sec (D).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  xz section  apical plane  moving to  the center (E)  moving to  the periphery (F)  adhesion plane  apical plane  merging (G)Supplementary Material  S-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  CALCULATION OF THE PERIMETER OF CMC CLUSTERS  The CMC-bare membrane boundary is measured by summing the dual of the edges between the cluster and bare  membrane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' These are the edges in the voronoi lattice, connecting the mid-section of each edge to the circumcenter of  the adjacent triangles i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' the center of the inscribing circle (see figure S-1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Partitioning each triangle between its  vertices is already used in the calculation of the curvature [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  S-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  ANALYTICAL CALCULATION OF THE FLAT-PEARLING PHASE TRANSITION LINE  We can make a rough analytical estimation for the flat-pearling transition by equating the active work and energy of  the flat phase from a mixed phase to the energy of the pearling phase (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' S-2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' In the flat phase, moving the active  CMCs outwards from the radius of the sphere rp to the larger radius of the flattened disc rf results in work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The  pearling phase has binding advantage because all CMC vertices are connected, with −w per edge, while the flat rim  has large interface (boundary perimeter length) where CMCs vertices neighbor bare membrane vertices, whose edge  does not contribute.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The pearling phase has a bending disadvantage due to the bare membrane body, which is roughly  spherical with an energy of 8πκ, compare to the flat phase where the bare membrane is in two flat discs with no  bending energy (both the pearling and rim clusters are curved to fit the CMCs, so they do not have bending energy).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  − (rf − rp) F = −w (χp − χf) + 8πκ  (S-1)  The radius difference ∆r = rf − rp (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' S-2), and the number of CMC-CMC bonds χp, χf in the pearling and  flat phases respectively, are dependant on the geometry of the phases, so they should be very weakly dependant on  the specific model parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Therefore ∆r and χp − χf do not depend on w, f, κ, and we end up having a linear  relation between f and w along the transition line in the f, w phase diagram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' In the force-binding strength (f − w)  system, we take the values for these geometric quantities from simulations and draw the resulting line on the phase  diagram (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' S-3, green line), which qualitatively matches the behavior of the transition observed in the simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  S-3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  MIXED CURVATURE CMC CLUSTERS  The concave and convex CMCs generate a wavelike pattern, but analyzing it in terms of wavenumber is difficult,  since the clusters are part of an irregular, triangulated surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The undulations of the CMCs in the mixed clusters are  essentially independent of C0, and f, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='S-4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Note that we are at the limit of the mesh resolution for  these undulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' We have yet to be able to compare this to the experimental results in [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  S-4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  MIXED CURVATURE WITH EXCLUSIVE BINDING  The mixed curvature system (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' 4c in the main text) was also simulated using exclusive binding, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' only  same-curvature CMCs bind together (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='S-5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The result is that the two CMCs types form separated aggregates,  with the active convex CMCs aggregating along the rim and forming the flat phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The passive concave CMC form  separated clusters of different shapes, depending on their spontaneous curvature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Highly concave CMCs (C−  0 ≤ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='45)  aggregate into internal pearling clusters, that do not affect the flat global phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The shallower concave CMCs  (C−  0 ≥ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='3) aggregate into large, shallow bowl-like patches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  In some cases, these concave aggregates are able to form with convex CMC along their rim, since their curvatures  complement each other (see for example at C−  0 = −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Since the convex active CMC along the rim of the concave  cluster apply protrusive forces, they end up forming together a ”cup”-like protrusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' When the force is inhibited,  this aggregation occurs, but it is not elongated as a protrusion (compare ”None” with ”Disable” at C−  0 = −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='3 in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='S-5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Other than that, inhibition doesn’t appear to significantly affect the results in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='S-5, since there is no  significant contact between the two CMC types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' These shapes, in the form of open bowls, resemble early stages of  macropinocytosis [3, 4], but do not evolve to induce closure of the ”mouth”, as we observed when the convex and  concave CMC had direct interactions (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='5 in the main text).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='13055v1  [cond-mat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='soft]  30 Jan 2023  2  parameter  units  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='S-3  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='S-4  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='S-5  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='S-6  movie 1,2 movie 3,4  f  KBT/ℓmin 0 − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='5, 0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='2, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='5  w  KBT  0 − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='48  2  2  2  2  2  κ  KBT  20  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='5  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='5  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='5  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='5  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='5  ρ  1  10%  10%, 10%  10%, 10%  10%, 10%  20%  10%, 10%  C0  1/ℓmin  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='6 − 0, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='8 -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='75 − 0, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='4,0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='8  TABLE I: The values of the model parameters used in the simulations in the different figures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The energy units are KBT = 1,  which define the scale of f, w, κ, and the length units are ℓmin = 1, which define the scale of the vertex lattice, the force, and  spontaneous curvature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  S-5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  VESICLES WITH BOTH NORMAL AND ALIGNED-FORCE CMC, ADHERED TO A FLAT  SUBSTRATE  In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='S-6 we show the dynamics of the vesicle that contains the mixture of aligned-force (yellow) and normal-force  (red) CMC, which have exclusive binding interactions between them (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='8 in the main text).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' At time t = 250  we turned off the normal-force CMC, keeping only the aligned-force CMC active.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' We find that the adhered area  shape changes, with the rim regions that contain the curved passive (red) CMC retract into the vesicle, while the  aligned-force regions protrude more prominently along the adhered rim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  Movies  Movie-S1 Aligned-force simulation of the formation of filopodia-like tubular protrusions (corresponding to  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='7B), with parameters κ = 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='5, f = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='2, w = 2, C0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='4, ρ = 20%, s = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='5, r = 30  Movie-S2 Normal force simulation, in the regime of tubes shapes (corresponding to Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='7B), with parameters  κ = 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='5, f = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='5, w = 2, C0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='1, ρ = 20%  Movie-S3 Adhered, universal-binding between normal-force CMCs (red) and aligned-force CMCs (yellow),  corresponding to Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='8A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Parameters used: κ = 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='5, f = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='5, w = 2, wad = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='25, C0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='8, ρn = 10%, ρa =  10%, s = 1, r = 15  Movie-S4 Adhered, exclusive-binding between normal-force CMCs (red) and aligned-force CMCs (yellow),  corresponding to Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='8A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Parameters used: κ = 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='5, f = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='5, w = 2, wad = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='25, C0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='8, ρn = 10%, ρa =  10%, s = 1, r = 15  Movie-S5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The 3D movie of the cell in Figure 9A  Movie-S6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The movie of the XY and XZ section for Figure 9E  Movie-S7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The movie of the XY and XZ section for Figure 9F  Movie-S8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The movie of the XY and XZ section for Figure 9G  [1] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Gompper and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Kroll, in Statistical Mechanics of Membranes and Surfaces (WORLD SCIENTIFIC, 2004), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  359–426.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [2] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Sitarska, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Almeida, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Beckwith, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Stopp, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Schwab, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Sixt, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Kreshuk, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Erzberger, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Diz-Mu˜noz,  bioRxiv p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='03.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='437199 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [3] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Veltman, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Williams, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Bloomfield, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Chen, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Betzig, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Insall, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Kay, Elife 5, e20085 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  [4] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Kay, Cells & Development 168, 203713 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  3  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' S-1: Sketch of the boundary of connected clusters: for each edge between the cluster and the outside, a line is drawn from  the middle to the center each of the adjacent triangles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' We ignore the single-clusters (dashed line)  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' S-2: Schematic description of the transition between flat and pearling phases, from an initially mixed, spherical phase (at  the center).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Bare membrane is in white, and CMCs in red, and mixed composition in pink.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The flat transition result in all  CMCs moving from the surface of the sphere to the rim of a flat disc, which has a larger radius ∆r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Due to active force f,  this generates work W = −f∆r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The bending energy of the CMCs on the rim and in the pearling clusters is assumed to be  approximately 0, but the spherical body of bare membrane in the pearling phase has a bending energy of a closed sphere: 8πκ,  while it is zero for the flat discs of bare membrane in the flat phase (since they are flat).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' Finally, the number of CMC-CMC  bonds in the pearling phase χp is larger than in the flat phase χf, since in the flat phase it is reduced due to the large boundary  between the rim cluster the the flat bare membrane discs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  f△r  8πK4  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' S-3: Phase diagram of the force-binding strength system, with an analytically-derived transition line for the pearling-flat  transition (green line, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='S-1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' S-4: The undulation of a CMC cluster with (A) highly concave (−0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='6) active CMC (B) with shallow concave (−0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='001)  CMC and disabled force.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The size and shape of the clusters is very different, but the peaks and troughs patterning due to CMC  shape is at the limit of the mesh resolution for both.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  20  12  longai  04  96  88  Buds  80  72  64  56  48  earlino  40  32  24  16  08(A)  (B)5  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' S-5: Active convex and passive concave system (red and blue, respectively), with binding between same type only.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' As in  the universal binding case, the suppressive and disabling inhibition do not have any strong effects, since the types are separated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  Simulations with C−  0 ≤ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='3 are draw semi-transparent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' In all cases, the convex CMCs aggregate in a rim, making the vesicle  flat, and concave CMCs aggregate in pearling for C−  0 < −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='3, bowl-like patches for C−  0 > −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='3, and both for C−  0 = −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='  6  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' S-6: Overview of an adhered vesicle with a mixture of aligned-force (yellow) and normal-force (red) CMC, which have  exclusive binding interactions between them (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content='8 in the main text).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' At time t = 250 the force is disabled for the  normal-force CMCs, leaving only the aligned-force CMCs active.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
+page_content=' The original simulation is given on the top (times 0 − 100),  and the simulation after the normal-force has been disabled is at the bottom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/09FPT4oBgHgl3EQfTzT7/content/2301.13055v1.pdf'}
diff --git a/0NE0T4oBgHgl3EQfuAEL/vector_store/index.pkl b/0NE0T4oBgHgl3EQfuAEL/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..1b35cb09d7fb4842816be64c837900221e87bc35
--- /dev/null
+++ b/0NE0T4oBgHgl3EQfuAEL/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:beabefade3125d84a32d15e2b9fc837cb1044190f5b318f594916eb9fa231501
+size 214946
diff --git a/0dE0T4oBgHgl3EQfdQAz/content/2301.02373v1.pdf b/0dE0T4oBgHgl3EQfdQAz/content/2301.02373v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..31f042d82eb3d35dd889d05206c8fe2f08b124bc
--- /dev/null
+++ b/0dE0T4oBgHgl3EQfdQAz/content/2301.02373v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:db72da4bbfb9f0d8a3d0ae04393ab17426d2817636ab4f29e318013574f4cabc
+size 1149364
diff --git a/0dE0T4oBgHgl3EQfdQAz/vector_store/index.pkl b/0dE0T4oBgHgl3EQfdQAz/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..afb12fcee645fa04b855b3447f5d73b955093d88
--- /dev/null
+++ b/0dE0T4oBgHgl3EQfdQAz/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:54741b01aec35316ade50059c52a02816abc01076ae445bf14328db55c400663
+size 186207
diff --git a/2dAyT4oBgHgl3EQfPvZl/vector_store/index.faiss b/2dAyT4oBgHgl3EQfPvZl/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..f34cd7fe53e041a5c0dc1c28b47d2d1c0d870a36
--- /dev/null
+++ b/2dAyT4oBgHgl3EQfPvZl/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:5b0691c3b4953c66d1153295e3811421d5c59f50bb7589729f0aae8e3bc30def
+size 1900589
diff --git a/39AyT4oBgHgl3EQfP_aH/vector_store/index.faiss b/39AyT4oBgHgl3EQfP_aH/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..78f910c4c605889d96e84ababb4355d58b6e3973
--- /dev/null
+++ b/39AyT4oBgHgl3EQfP_aH/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:ea35ba6b678140d8ebeb07e626c992184d5014c7127e80d24683d4cb2f2e5e14
+size 3604525
diff --git a/39AyT4oBgHgl3EQfP_aH/vector_store/index.pkl b/39AyT4oBgHgl3EQfP_aH/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..567abf0c644a297aa24cef651e822e8481996de7
--- /dev/null
+++ b/39AyT4oBgHgl3EQfP_aH/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:1e30d6c9669d24faaa686d7924d702a60b89aa8667c1ed57a2a07a9f980e6db8
+size 132178
diff --git a/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf b/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..518b382fb30a082de95d996ab610e4bf6ee50c5a
--- /dev/null
+++ b/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:8cf47c369078df06d4e69d5ccae0231442a4bca44db6fcb9e71c6716e95d2904
+size 306215
diff --git a/39AzT4oBgHgl3EQf9f54/vector_store/index.faiss b/39AzT4oBgHgl3EQf9f54/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..4fa928ce9ed27c39e620ff63ba88110afdb5662b
--- /dev/null
+++ b/39AzT4oBgHgl3EQf9f54/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:65a05b1787ac794377798a8398327e570abdf122146c6cfc697677275d864ab7
+size 1572909
diff --git a/39AzT4oBgHgl3EQf9f54/vector_store/index.pkl b/39AzT4oBgHgl3EQf9f54/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..ac65d5b34f8de5471b094a30acee99ee1666a5c9
--- /dev/null
+++ b/39AzT4oBgHgl3EQf9f54/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:4ccd548c9d9e059c261856e6078b911bae8fd472fb363334bada74058cd639b9
+size 57417
diff --git a/4dE2T4oBgHgl3EQf6Qjc/vector_store/index.pkl b/4dE2T4oBgHgl3EQf6Qjc/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..97342d8d73322cead7c66d5f9861d91829415088
--- /dev/null
+++ b/4dE2T4oBgHgl3EQf6Qjc/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:f6fb507d0f141987111733433b7e6747d0e0675b2a45e16b9128e49ae06d4fa2
+size 239529
diff --git a/5NAzT4oBgHgl3EQf9v7Q/content/2301.01925v1.pdf b/5NAzT4oBgHgl3EQf9v7Q/content/2301.01925v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..3b2220b32730c24b89662316d5a5db46bbe6e10f
--- /dev/null
+++ b/5NAzT4oBgHgl3EQf9v7Q/content/2301.01925v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:a542b4fb2a66e02de76930b25c0d209f9b56fb0c2f29b337130c787dfa33b75b
+size 234699
diff --git a/5NAzT4oBgHgl3EQf9v7Q/vector_store/index.faiss b/5NAzT4oBgHgl3EQf9v7Q/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..7233558f529dac82b94a0c603272598f14e7cccb
--- /dev/null
+++ b/5NAzT4oBgHgl3EQf9v7Q/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:63b5bbe9606650596034fcd5c3eea9182790f9b45bc85d99a97d59b367b393ef
+size 2555949
diff --git a/5NAzT4oBgHgl3EQf9v7Q/vector_store/index.pkl b/5NAzT4oBgHgl3EQf9v7Q/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..41b68b40315205cbc83673dafe0bebf975ad60f3
--- /dev/null
+++ b/5NAzT4oBgHgl3EQf9v7Q/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:50c45b4aef8cdf65eadf09d716eca6cace1ad2f136b5343af77a4b174311c815
+size 85246
diff --git a/5NAzT4oBgHgl3EQffvy-/content/tmp_files/2301.01458v1.pdf.txt b/5NAzT4oBgHgl3EQffvy-/content/tmp_files/2301.01458v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..066a03ed07929edbf63ef5e2dbd5e88ed3748ac2
--- /dev/null
+++ b/5NAzT4oBgHgl3EQffvy-/content/tmp_files/2301.01458v1.pdf.txt
@@ -0,0 +1,1303 @@
+An improved hybrid regularization approach for extreme
+learning machine
+Liangjuan Zhou
+School of Mathematics, Hunan University
+Changsha, China
+Wei Miao∗
+miaow@hnu.edu.cn
+School of Mathematics, Hunan University
+Changsha, China
+ABSTRACT
+Extreme learning machine (ELM) is a network model that arbitrarily
+initializes the first hidden layer and can be computed speedily.
+In order to improve the classification performance of ELM, a ℓ2
+and ℓ0.5 regularization ELM model (ℓ2-ℓ0.5-ELM) is proposed in
+this paper. An iterative optimization algorithm of the fixed point
+contraction mapping is applied to solve the ℓ2-ℓ0.5-ELM model. The
+convergence and sparsity of the proposed method are discussed
+and analyzed under reasonable assumptions. The performance of
+the proposed ℓ2-ℓ0.5-ELM method is compared with BP, SVM, ELM,
+ℓ0.5-ELM, ℓ1-ELM, ℓ2-ELM and ℓ2-ℓ1ELM, the results show that the
+prediction accuracy, sparsity, and stability of the ℓ2-ℓ0.5-ELM are
+better than the other 7 models.
+CCS CONCEPTS
+• Mathematics of computing → Convex optimization; • Com-
+puting methodologies → Regularization.
+KEYWORDS
+High-dimensional data, Sparsity, Hybird regularization, Dimension-
+ality reduction
+ACM Reference Format:
+Liangjuan Zhou and Wei Miao. 2022. An improved hybrid regularization
+approach for extreme learning machine. In 2022 4th International Conference
+on Advanced Information Science and System (AISS 2022), November 25–27,
+2022, Sanya, China. ACM, New York, NY, USA, 7 pages. https://doi.org/10.
+1145/3573834.3574501
+1
+INTRODUCTION
+Feedforward neural networks(FNNs), as one of the most frequently
+used neural networks which can be defined mathematically as:
+𝐺𝑁 (𝑥𝑖) =
+𝑁
+∑︁
+𝑖=1
+𝛽𝑖𝑔(⟨𝜔𝑖,𝑥𝑖⟩ + 𝑏𝑖),
+where 𝑥𝑖 = (𝑥𝑖1,𝑥𝑖2, . . . ,𝑥𝑖𝑝) ∈ R𝑝 is the input, 𝑏𝑖 is the bias and 𝑔
+is the activation function. ⟨𝜔𝑖,𝑥𝑖⟩ = �𝑝
+𝑗=1 𝜔𝑖𝑗𝑥𝑖𝑗 is the euclidean
+∗Both authors contributed equally to this research.
+Permission to make digital or hard copies of all or part of this work for personal or
+classroom use is granted without fee provided that copies are not made or distributed
+for profit or commercial advantage and that copies bear this notice and the full citation
+on the first page. Copyrights for components of this work owned by others than ACM
+must be honored. Abstracting with credit is permitted. To copy otherwise, or republish,
+to post on servers or to redistribute to lists, requires prior specific permission and/or a
+fee. Request permissions from permissions@acm.org.
+AISS 2022, November 25–27, 2022, Sanya, China
+© 2022 Association for Computing Machinery.
+ACM ISBN 978-1-4503-9793-3/22/11...$15.00
+https://doi.org/10.1145/3573834.3574501
+inner product, 𝜔𝑖 = (𝜔𝑖1,𝜔𝑖2, . . . ,𝜔𝑖𝑝) ∈ R𝑝 are the weights con-
+necting the input and the 𝑖-th hidden node, and 𝛽𝑖 ∈ R are the
+weights connecting the 𝑖-th hidden and output node. In terms of
+the traditional learning algorithm of FNNs, all parameters in the
+network need to be adjusted based on specific tasks. A classical
+learning method is the backpropagation (BP) algorithm, which is
+mainly solved by gradient descent:
+min
+𝜔𝑖,𝛽𝑖,𝑏𝑖
+𝑛
+∑︁
+𝑖=1
+∥𝑡𝑖 − 𝐺𝑁 (𝑥𝑖)∥2
+2,
+where (𝑥𝑖,𝑡𝑖)(𝑖 = 1, 2, . . . ,𝑛) denotes the training samples. How-
+ever, a randomized learner model, different to the traditional learn-
+ing of FNNs, called as Extreme learning machine(ELM) and related
+algorithms were proposed by Huang[10]. In the ELM model, 𝜔𝑖 and
+𝑏𝑖 are randomly assigned without training, so only 𝛽𝑖 needs to be
+trained. Set T = [𝑡1,𝑡2, . . . ,𝑡𝑛] and
+H =
+
+𝑔(⟨𝜔1,𝑥1⟩ + 𝑏1)
+. . .
+𝑔(⟨𝜔𝑁,𝑥1⟩ + 𝑏𝑁 )
+...
+. . .
+...
+𝑔(⟨𝜔1,𝑥𝑛⟩ + 𝑏1)
+. . .
+𝑔(⟨𝜔𝑁,𝑥𝑛⟩ + 𝑏𝑁 )
+
+,
+(1)
+once the input weights and biases are specified randomly with uni-
+form distribution in [−𝑐,𝑐], the hidden output matrix remains un-
+changed during the training phase. Accordingly, the output weights
+could be written by utilizing the least squares method:
+min
+𝛽 ∈R𝑁
+�
+∥H𝛽 − T∥2
+2
+�
+,
+(2)
+the solution to model (2) could be written as 𝛽 = H†T, where H†
+is the Moore–Penrose generalized inverse of hidden output matrix
+H[14].
+The theoretical basis for the general approximation capability of
+ELM networks has been proposed and established by Igelnik[11] ,
+where the range of randomly allocated input weights and biases
+are data related and assigned in a constructive mode. Consequently,
+the scope of parameters in the algorithm implementation should
+be carefully estimated for diverse datasets. On the other hand,
+considering the sparsity of the output parameter 𝛽 for many high-
+dimensional data, Cao et al.[4] proposed a ℓ1 regular ELM model
+based on the sparsity of the ℓ1 regularization term, which takes the
+following form:
+min
+𝛽 ∈R𝑁
+� 1
+2 ∥H𝛽 − T∥2
+2 + 𝜆∥𝛽∥1
+�
+,
+(3)
+where 𝜆 > 0 is a regularization parameter and 𝛽 is the output
+coefficient calculated by iteration. This model is called the Lasso
+model, and has been studied by many scholars in recent years [15].
+arXiv:2301.01458v1  [math.OC]  4 Jan 2023
+
+AISS 2022, November 25–27, 2022, Sanya, China
+Zhou and Miao.
+For the model (2), Fan et al. [8] added a ℓ0.5 regularization term
+to the ELM model, based on the solution generated by ℓ0.5 is sparser
+than the ℓ1 regularization term [16], and the model is defined as
+follows:
+min
+𝛽 ∈R𝑁
+� 1
+2 ∥H𝛽 − T∥2
+2 + 𝜆∥𝛽∥0.5
+�
+,
+(4)
+where 𝜆 > 0 is a regularization parameter, the model can be solved
+by the iterative semi-threshold algorithm [16].
+The other regularization model for model (2) was about the ℓ2
+regularization term (ℓ2-ELM) [5]:
+min
+𝛽 ∈R𝑁
+� 1
+2 ∥H𝛽 − T∥2
+2 + 𝜇∥𝛽∥2
+2
+�
+,
+(5)
+where 𝜇 is a regularization parameter, and when the expression
+H𝑇 H+𝜇I is invertible after choosing the parameter 𝜇, then the solu-
+tion of the model (5) can be written as 𝛽 = (H𝑇 H + 𝜇I)−1I)−1H𝑇 T.
+Hai et al.[9] proposed a ℓ2-ℓ1-ELM hybrid model by integrating
+the sparsity of the ℓ1 regularization term and the stability of the ℓ2
+regularization term as follows:
+min
+𝛽 ∈R𝑁
+� 1
+2 ∥H𝛽 − T∥2
+2 + 𝜆(𝛾∥𝛽∥1 + 𝜀∥𝛽∥2
+2)
+�
+,
+(6)
+where 𝜆 ≥ 0, 𝛾 ≥ 0 and 𝜀 ≥ 0 are regularization parameters. In-
+spired by the ℓ2-ℓ1-ELM model, according to Xu et al.[17], they
+found that the sparsity of the solution of the ℓ𝑝 (𝑝 ∈ (0, 1)) regular-
+ization term: when 0 < 𝑝 < 0.5, there is no significant difference in
+the sparse effect of ℓ𝑝; when 0.5 < 𝑝 < 1, the smaller 𝑝, the better
+the sparse effect, so the ℓ0.5 regularization term can be used as a
+representative element of ℓ𝑝 (𝑝 ∈ (0, 1)); Therefore, we propose the
+ℓ2-ℓ0.5-ELM model by combining the stability of ℓ2 regularization
+term and the sparsity of ℓ0.5 which is sparser than ℓ1, the new
+model is described as:
+min
+𝛽 ∈R𝑁
+� 1
+2 ∥H𝛽 − T∥2
+2 + 𝜆(𝛾∥𝛽∥0.5 + 𝜀∥𝛽∥2
+2)
+�
+,
+(7)
+where the parameters have the same meaning as the expression
+of (6). The thought of adding ℓ0.5 and ℓ2 penalties simultaneously in
+the optimization model could be found in classification [2, 6]. This
+study mainly establishes an iterative algorithm and studies some
+properties of randomized learner model as Hai[9]. In particular, we
+integrate the features of ELM and propose an iterative strategy for
+solving the hybrid model (7). The main contributions of this paper
+can be summarized as follows:
+(i) The whole model is a non-convex, non-smooth and non-
+Lipschitz optimization problem due to the existence of ℓ0.5 norm.
+We propose a new algorithm called as an ℓ2-ℓ0.5-ELM algorithm.
+This algorithm is proved to be effective by analyzing the sum mini-
+mization problem of two convex functions with certain characteris-
+tics.
+(ii) The key theoretical properties such as convergence, sparsity
+are derived to guarantee the feasibility of the proposed method.
+(iii) Numerous experiments were carried out, including some
+UCI datasets collected from experts and intelligent systems fields,
+gene datasets and ORL face image datasets. Experimental results
+show that the better performance of the proposed ℓ2- ℓ0.5-ELM
+algorithm.
+The rest of this paper is organized as follows. Section 2 reviews
+some basic concepts and theories. Section 3 demonstrates the itera-
+tive method by a fixed point equation and proposes a algorithm for
+ℓ2 - ℓ0.5-ELM model. In Section 4, some theoretical results about
+convergence and sparsity are analyzed. In Section 5, experimental
+results on UCI datasets, gene datasets and ORL face image datasets
+are shown. The conclusion is drawn in Section 6.
+2
+PRELIMINARIES
+In this section, we present some fundamental concepts and con-
+vex optimization theorems primarily. Initially, it is about the half-
+thresholding function[16]. 𝒫(𝜆,𝑡) : R → R, 𝜆 > 0, which can be
+written as:
+𝒫(𝜆,𝑡) =
+� 2
+3𝑡
+�
+1 + cos
+� 2(𝜋−𝜙 (𝑡))
+3
+��
+|𝑡| > 3
+4𝜆
+2
+3
+0
+|𝑡| ≤ 3
+4𝜆
+2
+3
+,
+(8)
+where 𝜙(𝑡) = arccos
+�
+𝜆
+8 ( |𝑡 |
+3 )− 3
+2
+�
+, 𝜋 = 3.14, and then the corre-
+sponding half-thresholding operator half(𝜆, 𝛽) : R𝑁 → R𝑁 acts
+component-wise as:
+[half(𝜆, 𝛽)]𝑖 = 𝒫(𝜆, 𝛽𝑖).
+(9)
+Next, we introduce one key characteristic of the half-thresholding
+operator [7, 16]:
+∥half(𝜆,𝑡) − half(𝜆,𝑡 ′)∥ ≤ ∥𝑡 − 𝑡 ′∥.
+(10)
+Another crucial notion of convex optimization is the proximity
+operator [12]:
+prox𝜑𝛽 = arg min
+�
+∥𝑢 − 𝛽∥2
+2 + 𝜑(𝑢)
+�
+,
+where𝜙 is a real-valued convex function on R𝑁 . A primary property
+of the proximity operator is drawn in Proposition 1[7], which will
+be utilized to prove our major result.
+Proposition 1. Let 𝜑 be a real-valued convex function on R𝑁 .
+Suppose 𝜓 (·) = 𝜑 + 𝜌
+2 ∥ · ∥2
+2 + ⟨·,𝑢⟩ + 𝜎, where 𝑢 ∈ R𝑁 , 𝜌 ∈ [0, ∞),
+𝜎 ∈ R, then
+prox𝜓 𝛽 = prox𝜑/(1+𝜌) ((𝛽 − 𝑢)/(1 + 𝜌)).
+(11)
+3
+SOLUTION: FIXED POINT ITERATIVE
+ALGORITHM FOR THE MODEL
+For the ELM, the output matrix H is a bounded linear operator from
+R𝑁 to R𝑚 owing to the activation function 𝑔(·) ∈ (0, 1), which is
+finite. In order to further improve the accuracy and sparsity, we
+employ the regularization model (7) to estimate the output weights
+of the network. We define concisely as:
+𝑝𝛾,𝜀 = 𝛾∥𝛽∥0.5 + 𝜀∥𝛽∥2
+2,
+where 𝜀, 𝛾 ≥ 0, 𝑝𝛾,𝜀 : R𝑁 → [0, ∞). Then the model (7) can be
+redefined as
+min
+𝛽 ∈R𝑁
+� 1
+2 ∥H𝛽 − T∥2
+2 + 𝜆𝑝𝛾,𝜀
+�
+.
+(12)
+Furthermore, we introduce the following Lemma and Theorem
+which will be utilized to solve our model:
+
+An improved hybrid regularization approach for extreme learning machine
+AISS 2022, November 25–27, 2022, Sanya, China
+Lemma 1. For all 𝜆 > 0 and 𝛽 ∈ R𝑁 ,the half-thresholding operator
+(8) can be described as:
+half(𝜆, 𝛽) = arg min
+𝑢
+� 1
+2 ∥𝑢 − 𝛽∥2
+2 + 𝜆∥𝑢∥0.5
+�
+.
+Lemma 2. For all 𝜆
+>
+0,𝛾
+≥
+0,𝜀
+≥
+0 and 𝛽
+∈
+R𝑁 ,
+half(
+𝜆𝛾
+1+2𝜀𝜆,
+𝛽
+1+2𝜀𝜆 ) is the proximity operator of 𝜆𝑝𝛾,𝜀 (𝛽).
+Theorem 1. Let 𝜆 > 0, 𝛾 ≥ 0, 𝜀 ≥ 0 and 𝛿 ∈ (0, ∞). Then 𝛽 is
+a minimizer of function (12) if and only if it meets the fixed point
+equation:
+𝛽 = half
+�
+𝛿𝜆𝛾
+1 + 2𝜀𝜆𝛿 , (I − 𝛿H𝑇 H)𝛽 − 𝛿H𝑇 T
+1 + 2𝜀𝜆𝛿
+�
+,
+(13)
+where the unit operator I : R𝑁 → R𝑁 , the definition of H is shown
+in (1), and H𝑇 represents the adjoint of H.
+Moreover, from the property of the proximity operator, we can
+drive a precise statement for the Lipschitz constant of a contractive
+map and the corresponding theorem as follows.
+Theorem 2. Set 𝜆 > 0,𝛾 ≥ 0,𝜀 ≥ 0 and 𝛿 ∈ (0, ∞). Suppose that
+there exist two positive constants 𝜅0 and 𝜅, such that the norm of the
+output matrix H shown in (1) of the hidden layer is finite by them,
+namely 𝜅0 ≤ ∥H𝑇 H∥2 ≤ 𝜅, Thus 𝛽 is a minimizer of (12) if and
+only if it is a fixed point of the Lipchitz map Γ : R𝑁 → R𝑁 , that is,
+𝛽 = Γ𝛽 where
+Γ𝛽 = half
+�
+𝛿𝜆𝛾
+1 + 2𝜀𝜆𝛿 , (I − 𝛿H𝑇 H)𝛽 + 𝛿H𝑇 T
+1 + 2𝜀𝜆𝛿
+�
+.
+(14)
+Selecting𝛿 =
+2
+𝜅0+𝜅 , the Lipschitz constant is finite by𝑞 = 1− 2𝜅0
+𝜅 + 𝜅0
+≤
+1. In particular, if 𝜅0 > 0, we can get Γ is a contractive map.
+Theorem 1 and Theorem 2 illustrate that the problem of ℓ2-ℓ0.5-
+ELM can be described as a fixed point algorithm. Furthermore, the
+next theorem will introduce the iterative procedure of the ℓ2-ℓ0.5-
+ELM.
+Theorem 3. Suppose that 𝜅0 and 𝜅 are positive constants, such
+that the norm of the output matrix H shown in (1) of the hidden
+layer is finite by them, namely, 𝜅0 ≤ ∥H𝑇 H∥2 ≤ 𝜅, and the sequence
+{𝛽}∞
+𝑙=0 ⊆ R𝑁 is described iteratively as
+𝛽𝑙 = half
+�
+𝛿𝜆𝛾
+1 + 2𝜀𝜆𝛿 , (I − 𝛿H𝑁 H)𝛽𝑙−1 − 𝛿H𝑇 T
+1 + 2𝜀𝜆𝛿
+�
+,
+(15)
+where 𝑙 = 1, 2, 3, . . . , 𝜆 > 0,𝜀 > 0,𝛾 ≥ 0 and 𝛿 =
+2
+𝜅+𝜅0 . Thus {𝛽𝑙 }∞
+𝑙=0
+strongly converges the minimizer of model (10) in spite of the choice
+of 𝛽0.
+Remark 1. It is not difficult to obtain from the proof of Theorem 3.
+∥𝛽𝑙 − 𝛽∗∥2 ≤
+𝜅 + 𝜅0
+𝜅0(𝜅 + 𝜅0 + 4𝜀𝜆)
+�𝜅 − 𝜅0
+𝜅 + 𝜅0
+�𝑙
+∥H𝑇 T∥2.
+Therefore, for each 𝜉 > 0, if
+𝜅 + 𝜅0
+𝜅0(𝜅 + 𝜅0 + 4𝜀𝜆)
+�𝜅 − 𝜅0
+𝜅 + 𝜅0
+�𝑙
+∥𝛽1 − 𝛽0∥2 < 𝜉.
+namely,
+𝑙 >
+log
+� ∥𝛽1−𝛽0 ∥2(𝜅+𝜅0)
+𝜉𝜅0(𝜅+𝜅0+4𝜀𝜆)
+�
+log
+� 𝜅+𝜅0
+𝜅−𝜅0
+�
+,
+thus
+∥𝛽𝑙 − 𝛽∗∥2 < 𝜉.
+As a conclusion, the complete ℓ2-ℓ0.5-ELM algorithm is given in
+Algorithm 1 which integrates the result of Theorem 3 and Remark
+1. Next section, we want give some properties of our proposed
+algorithm.
+Algorithm 1: the algorithm for ℓ2-ℓ0.5-ELM model
+Input:Given
+a
+set
+of
+training
+samples
+𝒻
+=
+�
+(𝑥𝑗,𝑡𝑗) : 𝑥𝑗 ∈ R𝑝,𝑡𝑗 ∈ R𝑚, 𝑗 = 1, 2, . . . ,𝑛
+�,
+activation
+func-
+tion 𝑔, hidden node number 𝑁, the related regularization
+parameters 𝜆 > 0, 𝛾 ≥ 0, 𝜀 ≥ 0, the corresponding parameter 𝛿,
+and an acceptable error 𝜉.
+Step 1: Randomly assign a proper scope for input weight 𝜔𝑖 and
+bias 𝑏𝑖 (𝑖 = 1, 2, . . . , 𝑁)
+Step 2: Compute the hidden layer output matrix H;
+Step
+3:
+Set
+𝛽0
+=
+(0, 0, . . . , 0),
+𝛽1
+=
+half(
+𝛿𝜆𝛾
+1 + 2𝜀𝜆𝛿 , (I − 𝛿H𝑇 H)𝛽0 + 𝛿H𝑇 T
+1 + 2𝜀𝜆𝛿
+), and 𝑙𝑚𝑎𝑥 be a minimal
+positive integer but larger than
+log
+� ∥𝛽1 − 𝛽0∥2(𝜅 + 𝜅0)
+𝜉𝜅0(𝜅 + 𝜅0 + 4𝜀𝜆)
+�
+log
+� 𝜅+𝜅0
+𝜅−𝜅0
+�
+.
+Step 4: For 𝑙 = 1 : 𝑙𝑚𝑎𝑥
+if 𝑙 ≥ 𝑙𝑚𝑎𝑥, stop;
+else 𝑙 := 𝑙 + 1 and update the 𝛽 as follows: 𝛽𝑙+1 =
+half(
+𝛿𝜆𝛾
+1 + 2𝜀𝜆𝛿 , (I − 𝛿H𝑇 H)𝛽𝑙 + 𝛿H𝑇 T
+1 + 2𝜀𝜆𝛿
+).
+repeat Step 4, until that the desired output weight is ^𝛽 = 𝛽𝑚𝑎𝑥.
+Output: Return the output weights ^𝛽;
+4
+SOME CHARACTERISTICS FOR ℓ2-ℓ0.5-ELM
+For the new section, we want to discuss and analyze some key
+characteristics of the estimator regarding ℓ2-ℓ0.5-ELM, such as the
+convergence and sparsity.
+Theorem 4. 𝛽𝑙 strongly converges to the minimum value 𝛽∗ of
+the minimization problem
+min
+𝛽 ∈R𝑁
+� 1
+2 ∥H𝛽 − T∥2
+2 + 𝜆𝑝𝛾𝜀 (𝛽)
+�
+as 𝑙 → ∞.
+𝛽0.5 in the ℓ2-ℓ0.5-ELM is a highly significant part of the sparsity
+of the solution. Thus, we set the Theorem 5 as follows.
+Theorem 5. Suppose 𝜆
+>
+0,𝛾
+>
+0, then the support of
+half(
+𝜆𝛾
+1+2𝜀𝜆,
+𝛽
+1+2𝜀𝜆 ) is finite for any 𝛽 ∈ R𝑁 . Particularly, 𝛽∗ and 𝛽𝑙
+are all finitely supported.
+If the regularization parameters 𝜆 and 𝛾 are fixed as some con-
+stant values, then 𝛽∗ and 𝛽𝑙 have only a few finite nonzero coeffi-
+cients, and hence the solution to (12) is sparse.
+
+AISS 2022, November 25–27, 2022, Sanya, China
+Zhou and Miao.
+Table 1: Details of the 6 datasets
+Dataset
+Type
+Sapmple
+Feature
+Catagory
+Austrian
+UCI
+690
+14
+2
+Ionosphere
+UCI
+151
+34
+2
+Balance
+UCL
+625
+4
+3
+colon
+gene
+62
+2000
+2
+DLBCL
+gene
+77
+7129
+2
+ORL
+image
+400
+10304
+40
+5
+PERFORMANCE EVALUATION
+In the new section, a succession of experiments, containing some
+UCI benchmark datasets[9] and gene data, are carried out to demon-
+strate the performance of the proposed ℓ2-ℓ0.5-ELM method. All
+the experiments are performed in the Mac Pycharm environment
+running on Quad-Core Intel Core i5, CPU (8 GB 2133 MHz LPDDR3)
+processor with the speed of 1.40GHz. The activation function of
+networks used in the experiments is taken as sigmoid function
+𝑔(𝑥) = 1/(1 + 𝑒−𝑥).
+The ℓ2-ℓ0.5-ELM model is compared with seven other models:
+BP, SVM, ELM, ℓ2-ℓ1-ELM, ℓ2-ELM, ℓ1-ELM, ℓ0.5-ELM. BP includes
+only one hidden layer and output layer, and all parameters are
+trained by back-propagation algorithm; ℓ1-ELM and ℓ0.5-ELM are
+the simplified forms of ℓ2-ℓ1-ELM and ℓ2-ℓ0.5-ELM, respectively.
+The activation function is defined as: 𝑔(𝑥) = 1/(1 + 𝑒−𝑥).
+In order to check the algorithm for ℓ2-ℓ0.5-ELM model, three real
+classification datasets from the UCI machine learning repository
+are considered. The basic information of each dataset is shown in
+Table 1. The average of 30 experimental validations was used as
+the final result. For these datasets, the sample size is fixed, but each
+sample is randomly assigned as training or testing data.
+5.1
+Performance for UCI datasets
+To validate the performance of the proposed ℓ2-ℓ0.5-ELM model,
+three types of real classification datasets were used for the experi-
+ments, including UCI[3], gene expression, and ORL face datasets.
+The UCI machine learning repository (2013UCI) contains three
+datasets: Austrian Credit Approval(Austrian), Ionosphere, and Bal-
+ance Scale(Balance). The gene expression datasets contain colon[1]
+and DLBCL[13], both of which are binary datasets. Moreover, the
+ORL face dataset includes 400 images divided into 40 categories.
+Each category contains 10 images with different facial details and
+each image size is 112 × 92. The detail information of all datasets
+are summarized in Table 1. In addition, these data were obtained
+from different application fields, and it is hoped that the ℓ2-ℓ0.5-
+ELM model can be analyzed from multiple perspectives by using
+these data from different backgrounds.
+We repeat 30 trials and take the averages as the final results
+on account of reducing the random error. And the regularization
+parameters are used to control the trade-off between the error and
+the penalty. For Austrian dataset, take the parameters ( ℓ2-ℓ0.5-ELM,
+ℓ2-ℓ1-ELM : 𝜆 = 0.8,𝛾 = 0.1,𝜀 = 0.9) and for Ionosphere dataset,
+take ( ℓ2-ℓ0.5-ELM, ℓ2-ℓ1-ELM : 𝜆 = 0.9,𝛾 = 0.05,𝜀 = 0.9) and
+Balance Scale dataset, ( ℓ2-ℓ0.5-ELM : 𝜆 = 0.8,𝛾 = 1,𝜀 = 1, for ℓ2-ℓ1-
+ELM : 𝜆 = 0.005,𝛾 = 0.5,𝜀 = 0.5), we set the acceptable error 𝜉 =
+Table 2: Performance comparison of 8 models on 3 different
+datasets
+Datasets
+Methods
+Times(s)
+Remaining Nodes
+Accuracy(% ± %)
+Austrain
+BP
+2.1751
+600
+72.58 ± 13.57
+SVM
+0.0448
+—
+79.14 ± 1.98
+ELM
+0.0588
+600
+65.37 ± 3.08
+ℓ0.5-ELM
+5.8542
+48.5
+82.76 ± 0.00
+ℓ1-ELM
+8.1648
+118.5
+81.38 ± 0.00
+ℓ2-ELM
+8.2735
+600
+80.36 ± 0.00
+ℓ2-ℓ1-ELM
+10.041
+492.5
+81.38 ± 0.00
+ℓ2-ℓ0.5-ELM
+7.5875
+118.5
+82.76 ± 0.00
+Ionosphere
+BP
+2.1751
+600
+72.58 ± 13.57
+SVM
+0.0108
+–
+86.51 ± 2.09
+ELM
+0.0003
+600
+91.55 ± 2.78
+ℓ0.5-ELM
+0.0487
+29.5
+96.96 ± 0.00
+ℓ1-ELM
+5.4755
+115.9
+97.24 ± 1.06
+ℓ2-ELM
+0.0520
+600
+96.05 ± 1.57
+ℓ2-ℓ1-ELM
+4.4093
+437.5
+96.84 ± 0.98
+ℓ2-ℓ0.5-ELM
+0.0569
+193
+98.01 ± 0.00
+Balance
+BP
+4.3814
+600
+59.99 ± 25.26
+SVM
+0.0215
+–
+88.63 ± 1.86
+EL,M
+0.0008
+600
+50.72 ± 6.66
+ℓ0.5-ELM
+0.1285
+23.3
+90.55 ± 0.00
+ℓ1-ELM
+6.5074
+42.9
+90.47 ± 1.66
+ℓ2-ELM
+0.1579
+600
+90.55 ± 0.00
+ℓ2-ℓ1-ELM
+6.8678
+246.4
+90.10 ± 1.35
+ℓ2-ℓ0.5-ELM
+0.0974
+52.7
+90.91 ± 0.00
+0.0001, 0.001, 0.0001 respectively. The number of hidden nodes in
+the experiments is 600. Table 2 shows the running time, the number
+of nodes retained, and the accuracy of the test for each dataset for
+the eight models (the standard deviation is kept to 4 significant
+digits, 0.00 in the table indicates a standard deviation of less than
+10−4). These indices are used to measure the sparsity, stability and
+effectiveness of the proposed method. The corresponding figures
+on testing are shown as follows.
+From the results of 1-3, we can see that the accuracy of the ELM
+model is lower than all the regularized ELM models. The standard
+deviation of the ELM model is higher than that of other regularized
+ELM models, which indicates that the stability of the ELM model is
+lower. The accuracy of the ℓ2-ℓ0.5-ELM model at all nodes can be
+compared with other regularized ELM models, and the accuracy at
+most hidden nodes is higher than other comparable regularized ELM
+models. This indicates that the ℓ2-ℓ0.5-ELM model has consistently
+good classification prediction. In terms of the standard deviation
+of different nodes, the ℓ2-ℓ0.5-ELM model is lower than the other
+compared models, indicating that the classification accuracy of this
+method is more stable.
+We can see the performance of ℓ2-ℓ0.5-ELM in detail and draw
+the following conclusions:
+(i) In 3 datasets, the classification accuracy of the regularized
+ELM methods (ℓ2-ℓ0.5-ELM, ℓ0.5-ELM, ℓ2-ℓ1-ELM, ℓ1-ELM, ℓ2-ELM)
+are significantly higher than that of the BP, SVM and ELM methods,
+indicating that the regularized ELM methods have better general-
+ization performance, and the classification accuracy of ℓ2-ℓ0.5-ELM
+methods is higher than that of other compared regularized ELM
+methods.
+(ii) From the perspective of the number of remaining hidden
+nodes, ℓ0.5-ELM has the lowest number of hidden nodes. It is shown
+
+An improved hybrid regularization approach for extreme learning machine
+AISS 2022, November 25–27, 2022, Sanya, China
+200
+300
+400
+500
+600
+700
+800
+900
+1000 1100 1200
+Number of Hidden Nodes
+0.50
+0.55
+0.60
+0.65
+0.70
+0.75
+0.80
+0.85
+0.90
+0.95
+1.00
+Testing accuracy
+ELM
+l0.5
+l1
+l2
+l2l1
+l2l0.5
+200
+300
+400
+500
+600
+700
+800
+900
+1000 1100 1200
+Number of Hidden Nodes
+0.000
+0.002
+0.004
+0.006
+0.008
+0.010
+0.012
+0.014
+0.016
+0.018
+0.020
+0.022
+0.024
+0.026
+0.028
+0.030
+SDs of Testing
+ELM
+l0.5
+l1
+l2
+l2l1
+l2l0.5
+Figure 1: Performance comparison of 6 models in the Austrian dataset
+200
+300
+400
+500
+600
+700
+800
+900
+1000 1100 1200
+Number of Hidden Nodes
+0.60
+0.62
+0.64
+0.66
+0.68
+0.70
+0.72
+0.74
+0.76
+0.78
+0.80
+0.82
+0.84
+0.86
+0.88
+0.90
+0.92
+0.94
+0.96
+0.98
+1.00
+Testing accuracy
+ELM
+l0.5
+l1
+l2
+l2l1
+l2l0.5
+200
+300
+400
+500
+600
+700
+800
+900
+1000 1100 1200
+Number of Hidden Nodes
+-0.01
+0.00
+0.01
+0.02
+0.03
+0.04
+0.05
+0.06
+SDs of Testing
+ELM
+l0.5
+l1
+l2
+l2l1
+l2l0.5
+Figure 2: Performance comparison of 6 models in the Ionosphere dataset
+200
+300
+400
+500
+600
+700
+800
+900
+1000 1100 1200
+Number of Hidden Nodes
+0.35
+0.40
+0.45
+0.50
+0.55
+0.60
+0.65
+0.70
+0.75
+0.80
+0.85
+0.90
+0.95
+1.00
+Testing accuracy
+ELM
+l0.5
+l1
+l2
+l2l1
+l2l0.5
+200
+300
+400
+500
+600
+700
+800
+900
+1000 1100 1200
+Number of Hidden Nodes
+-0.005
+0.000
+0.005
+0.010
+0.015
+0.020
+0.025
+0.030
+0.035
+0.040
+0.045
+0.050
+0.055
+0.060
+0.065
+0.070
+0.075
+0.080
+0.085
+0.090
+0.095
+0.100
+SDs of Testing
+ELM
+l0.5
+l1
+l2
+l2l1
+l2l0.5
+Figure 3: Performance comparison of 6 models in the Balance dataset
+that the ℓ0.5 or ℓ1-regularization term is beneficial to enhance the
+sparsity of the hidden nodes of the model. Compared with the ℓ2-
+ℓ1-ELM model, the ℓ2-ℓ0.5-ELM model adds the ℓ0.5 regularization
+term to the model, which has a sparser solution and thus a better
+generalization ability.
+(iii) From the perspective of algorithm running time, the ELM
+model runs in the shortest time (the ELM model can obtain the
+analytic solution directly without iterative computation). In com-
+parison, the SVM model runs faster than all ELM methods with
+regularity. Secondly, for the 5 regularized ELM models, the models
+with ℓ0.5 regularization terms (ℓ0.5-ELM, ℓ2-ℓ0.5-ELM) are faster
+than the models with ℓ1 regularization terms (ℓ1-ELM, ℓ2- ℓ1-ELM).
+5.2
+Performance for gene datasets
+In this section, the performance of the ℓ2-ℓ0.5-ELM model is vali-
+dated using the colon and DLBCL data. The training and testing sets
+of each dataset were experimented in the ratio of 1 : 1. The regular-
+ization parameters are set as follows, colon data: (ℓ2-ℓ0.5-ELM and
+ℓ2-ℓ1-ELM : 𝜆 = 0.09,𝛾 = 0.9,𝜀 = 0.9), DLBCL data: (ℓ2-ℓ0.5-ELM
+and ℓ2-ℓ1-ELM : 𝜆 = 0.005,𝛾 = 0.5,𝜀 = 0.5); and 𝜉 = 0.001. Each
+dataset was repeatedly run 30 times, and the average was taken as
+the final result. As shown in Table 3.
+It can be demonstrated that the prediction accuracy of the single-
+layer BP network is very low and does not capture the features of
+
+AISS 2022, November 25–27, 2022, Sanya, China
+Zhou and Miao.
+200
+300
+400
+500
+600
+700
+800
+900
+1000 1100 1200
+Number of Hidden Nodes
+0.72
+0.73
+0.74
+0.75
+0.76
+0.77
+0.78
+0.79
+0.80
+0.81
+0.82
+0.83
+0.84
+0.85
+0.86
+0.87
+0.88
+0.89
+Testing accuracy
+ELM
+l0.5
+l1
+l2
+l2l1
+l2l0.5
+200
+300
+400
+500
+600
+700
+800
+900
+1000 1100 1200
+Number of Hidden Nodes
+0.000
+0.005
+0.010
+0.015
+0.020
+0.025
+0.030
+SDs of Testing
+ELM
+l0.5
+l1
+l2
+l2l1
+l2l0.5
+Figure 4: Performance comparison of 6 models in colon dataset
+Table 3: Performance comparison of 8 models in 2 gene
+datasets
+Datasets
+Methods
+Times(s)
+Remaining Nodes
+Accuracy(% ± %)
+colon
+BP
+22.2641
+1000.0
+55.52 ± 9.15
+SVM
+0.0358
+–
+77.5 ± 7.28
+ELM
+0.0056
+1000.0
+83.02 ± 1.92
+ℓ0.5-ELM
+0.0829
+370.5
+75.00 ± 0.00
+ℓ1-ELM
+0.0488
+974.5
+84.79 ± 2.22
+ℓ2-ELM
+0.0815
+1000.0
+84.17 ± 2.20
+ℓ2-ℓ1-ELM
+0.0401
+1000.0
+83.96 ± 2.24
+ℓ2-ℓ0.5-ELM
+0.0879
+877.0
+87.50 ± 0.00
+DLBCL
+BP
+122.3174
+1000.0
+57.24 ± 12.55
+SVM
+0.0968
+–
+87.24 ± 5.98
+ELM
+0.0060
+786.0
+89.90 ± 5.98
+ℓ0.5-ELM
+5.2214
+242.0
+91.43 ± 0.00
+ℓ1-ELM
+18.2957
+188.5
+89.05 ± 5.12
+ℓ2-ELM
+5.2324
+764.0
+89.51 ± 5.48
+ℓ2-ℓ1-ELM
+15.5286
+431.5
+89.62 ± 6.10
+ℓ2-ℓ0.5-ELM
+5.4519
+575.5
+91.43 ± 0.00
+the data very well. It can also be found that the prediction accu-
+racy of the ℓ2-ℓ0.5-ELM model is slightly higher than that of the
+other methods. The standard deviations of the accuracy of the ELM
+methods with ℓ0.5 regularization are much smaller than those of
+BP, SVM, and ELM, indicating that the ELM model variants with
+ℓ0.5 regularization terms can improve the stability of the solutions;
+The number of hidden nodes in the ℓ0.5-ELM and ℓ1-ELM models
+is smaller, that is, the sparsity of these two regularization terms is
+the strongest, indicating that the addition of ℓ0.5 or ℓ1 regularization
+terms in the ELM model enhances the sparsity of the model, while
+the number of hidden nodes in the ℓ2-ELM model is 1000. The
+number of nodes in the ℓ2-ELM model is 1000, indicating that the
+ℓ2-regularization term has no sparse effect on the model. The ℓ2
+norm is used to increase the stability of the model by penalizing
+oversized regularization parameters. This makes the ℓ2-ℓ0.5-ELM
+sparser and model stable, and thus obtains better generalization
+ability.
+From the perspective of algorithm running time, it can be seen
+that the ELM model has the shortest running time (the ELM model
+can obtain the analytical solution directly without iterative solving).
+In contrast, the SVM model runs faster than all ELM methods with
+regularization.
+Further, we use the colon data to verify the effect of different
+number of hidden nodes (200, 400, 600, 800, 1000, 1200) on the sta-
+bility of the ELM correlation model. We perform 30 experiments
+for each hidden node and calculate the ELM, ℓ2-ℓ0.5-ELM, ℓ0.5-ELM,
+ℓ2-ℓ1-ELM, ℓ1-ELM, ℓ2-ELM for the test set accuracy and standard
+deviation as shown in Figure 4. The test accuracy of ℓ2-ℓ0.5-ELM at
+all nodes can be compared with all regularized ELM models, while
+the accuracy at most hidden nodes is higher than other models.
+The standard deviation of ℓ2-ℓ0.5-ELM model is lower than other
+regularized ELM models.
+5.3
+Performance for ORL face dataset
+The ORL face dataset is used for experimental validation. The num-
+ber of hidden nodes for the experiment is 1000. The average of
+30 experiments is used as the final result. Since the original im-
+age has high dimensionality, we preprocess each image by using
+the (2𝐷)2PCA[18] dimensionality reduction technique. And the
+training set and test set are in the ratio of 7 : 3. The values of the
+regular parameters set in the experiment are as follows: ℓ0.5-ELM
+and ℓ1-ELM (𝛾 = 0.05,𝜀 = 0), ℓ2-ELM (𝛾 = 0,𝜀 = 0.5), ℓ2 -ℓ1-ELM,
+ℓ2-ℓ0.5-ELM(𝛾 = 0.05,𝜀 = 0.5); 𝜆 = 0.001 and 𝜀 = 0.0001 are cho-
+sen in all experiments. This experiment validates the performance
+of the model in terms of accuracy and standard deviation. The re-
+sults are shown in Table 4. From the table, it can be seen that the
+Table 4: Performance comparison of 8 models in ORL face
+dataset
+Methods
+Accuracy(%)
+BP
+31.00 ± 4.90
+SVM
+71.53 ± 2.12
+ELM
+70.58 ± 2.95
+ℓ0.5-ELM
+71.00 ± 2.34
+ℓ1-ELM
+70.85 ± 2.86
+ℓ2-ELM
+71.17 ± 2.47
+ℓ2-ℓ1-ELM
+70.58 ± 2.87
+ℓ2-ℓ0.5-ELM
+71.67 ± 2.34
+
+An improved hybrid regularization approach for extreme learning machine
+AISS 2022, November 25–27, 2022, Sanya, China
+Table 5: Performance comparison of 6 models in ORL face dataset
+Nodes
+ELM
+ℓ0.5-ELM
+ℓ1-ELM
+ℓ2-ELM
+ℓ2-ℓ1-ELM
+ℓ2-ℓ0.5-ELM
+500
+52.92±3.04
+66.10±2.55
+60.00 ±1.77
+62.63± 2.38
+59.25 ±2.32
+65.83 ± 2.46
+1500
+76.08±0.73
+77.00±0.93
+76.33 ±0.67
+76.75± 0.75
+76.33 ±0.76
+77.20 ±0.93
+2000
+78.25±2.00
+78.73±2.45
+78.33 ±2.08
+78.63± 2.18
+78.33 ±2.08
+78.83 ±2.45
+2500
+79.58±3.49
+79.74±3.36
+79.67 ±3.44
+79.21±3.29
+79.63 ±3.44
+79.76 ± 3.26
+3000
+81.50±1.98
+81.55±2.69
+81.42 ±2.07
+81.45±2.39
+81.42 ±2.07
+81.58 ± 2.68
+3500
+81.17±1.81
+81.13±2.22
+81.17 ±1.87
+81.17±1.89
+81.17 ±1.87
+81.25 ± 2.12
+4000
+82.00±1.81
+82.00±1.67
+81.92 ±1.74
+81.96±1.64
+81.92 ±1.74
+82.08 ± 1.65
+mean
+75.22±9.12
+77.16±5.33
+76.21 ±7.00
+76.62±6.21
+76.08 ±7.24
+77.26 ± 5.32
+accuracy of the ℓ2-ℓ0.5-ELM model (which is slightly higher than
+the SVM model) is slightly higher than all other models tested.
+Further, we verify the effect of different values of hidden nodes
+on the prediction accuracy. The number of hidden nodes chosen in
+the experiment is 500, 1000, 1500, 2000, 2500, 3000, 3500, 4000.
+The results are shown in Table 5, which show that the test accu-
+racy of ℓ2-ℓ0.5-ELM model is higher than the other comparative
+ELM models. The test accuracy of the ELM model fluctuates the
+most with the changing of the number of hidden nodes, i.e., the
+selection of different nodes has the greatest impact on it, indicating
+that the ELM model is less stable in high-dimensional data. In con-
+trast, the standard deviations of all the regularized ELM methods
+(5.33, 7.00, 6.21, 7.24, 5.32) are lower than those of the ELM meth-
+ods, indicating that the stability of the ELM model is improved by
+adding the regularization term. ELM methods, indicating that the
+stability of the proposed method is better than the other 5 compared
+to ELM methods.
+6
+CONCLUSION
+In order to further improve the stability and generalization of the
+ELM model, this paper proposes a ℓ2-ℓ0.5-ELM model by combin-
+ing the ℓ0.5 and the ℓ2 regularization term. The iterative algorithm
+is applied to solve the model with a fixed points algorithm. The
+convergence and sparsity of this algorithm are proved. Moreover,
+the proposed ℓ2-ℓ0.5-ELM model is compared with BP, SVM, ELM,
+ℓ0.5-ELM, ℓ1-ELM, ℓ2-ELM and ℓ2-ELM. ℓ2-ℓ1-ELM models. Experi-
+mental comparisons on several datasets (UCI dataset, gene dataset,
+ORL face dataset) show that the ℓ2-ℓ0.5-ELM method outperforms
+the other 7 models in terms of prediction accuracy and stability
+on these data. Therefore, the model can be improved as follows:
+the information of previously computed nodes is not used in the
+computation of different hidden nodes, and it can be learned from
+the incremental learning point of view, which can reduce the com-
+putation time to a certain extent.
+REFERENCES
+[1] U. Alon, N. Barkai, D. A. Notterman, K. Gish, S. Ybarra, D. Mack, and A. J. Levine.
+1999. Broad patterns of gene expression revealed by clustering analysis of tumor
+and normal colon tissues probed by oligonucleotide arrays. 96, 12 (1999), 6745–
+6750.
+[2] Hai Hui Huang A B and Yong Liang C. 2018. Hybrid 𝐿1/2+2 method for gene
+selection in the Cox proportional hazards model. Computer Methods and Programs
+in Biomedicine 164 (2018), 65–73.
+[3] K. Bache and M. Lichman. 2013. UCI machine learning repository. (2013).
+[4] Feilong Cao, Yuanpeng Tan, and Miaomiao Cai. 2014. Sparse algorithms of
+random weight networks and applications. Expert Systems with Applications 41,
+5 (2014), 2457–2462.
+[5] Feilong Cao, Dianhui Wang, Houying Zhu, and Yuguang Wang. 2016. An itera-
+tive learning algorithm for feedforward neural networks with random weights.
+Information Sciences 328 (2016), 546–557.
+[6] G. C. Cawley and Nlc Talbot. 2006. Gene selection in cancer classification using
+sparse logistic regression with Bayesian regularization. Oxford University Press
+(2006).
+[7] Patrick L. Combettes and Valérie R. Wajs. 2005. Signal recovery by proximal
+forward-backward splitting. Multiscale Model. Simul. 4 (2005), 1168–1200.
+[8] Qinwei Fan, Lei Niu, and Qian Kang. 2020. Regression and multiclass classification
+using sparse extreme learning machine via smoothing group 𝐿1/2 regularizer.
+IEEE Access 8 (2020), 191482–191494.
+[9] Hailiang, Ye, Feilong, Cao, Dianhui, and Wang. [n. d.]. A hybrid regularization
+approach for random vector functional-link networks - ScienceDirect. Expert
+Systems with Applications 140 ([n. d.]), 112912–112912.
+[10] Guang-Bin Huang, Qin-Yu Zhu, and Chee-Kheong Siew. 2006. Extreme learning
+machine: theory and applications. Neurocomputing 70, 1 (2006), 489–501.
+[11] B. Igelnik and Y. H. Pao. 1995. Stochastic choice of basis functions in adaptive
+function approximation and the functional-link net. IEEE Trans Neural Netw 6, 6
+(1995), 1320–1329.
+[12] Charles Micchelli, Lixin Shen, and Yuesheng Xu. 2011. Proximity algorithms for
+image models: denoising. Inverse Problems 27 (03 2011), 045009.
+[13] A. Rosenwald, G. Wright, W. C. Chan, J. M. Connors, E. Campo, R. I. Fisher, R. D.
+Gascoyne, H. K. Muller-Hermelink, E. B. Smeland, and J. M. Giltnane. 2011. The
+use of molecular profiling to predict survival after chemotherapy for diffuse
+large-B-cell lymphoma. New England Journal of Medicine 346, 25 (2011), 1937.
+[14] W.F. Schmidt, M.A. Kraaijveld, and R.P.W. Duin. 1992.
+Feedforward neural
+networks with random weights. (1992), 1–4.
+[15] Robert Tibshirani. 2011. Regression shrinkage and selection via the lasso: a retro-
+spective. Journal of the Royal Statistical Society: Series B (Statistical Methodology)
+73, 3 (2011), 267–288.
+[16] Zongben Xu, Xiangyu Chang, Fengmin Xu, and Hai Zhang. 2012. 𝐿1/2 regular-
+ization: a thresholding representation theory and a fast solver. IEEE Transac-
+tions on Neural Networks and Learning Systems 23, 7 (2012), 1013–1027. https:
+//doi.org/10.1109/TNNLS.2012.2197412
+[17] Zong-Ben Xu, Hai-Liang Guo, Yao Wang, and Hai Zhang. 2012. Representative
+of 𝐿1/2 regularization among 𝐿𝑞 (0 < 𝑞 ≤ 1) regularizations: an experimental
+study based on phase diagram. Acta Automatica Sinica 38, 7 (2012), 1225–1228.
+[18] Daoqiang Zhang and Zhi-Hua Zhou. 2005. (2D)2PCA: Two-directional two-
+dimensional PCA for efficient face representation and recognition. Neurocom-
+puting 69, 1 (2005), 224–231.
+
diff --git a/5NAzT4oBgHgl3EQffvy-/content/tmp_files/load_file.txt b/5NAzT4oBgHgl3EQffvy-/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..de8a9535686029c84d23fb14af9ed4fdea64a262
--- /dev/null
+++ b/5NAzT4oBgHgl3EQffvy-/content/tmp_files/load_file.txt
@@ -0,0 +1,888 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf,len=887
+page_content='An improved hybrid regularization approach for extreme  learning machine  Liangjuan Zhou  School of Mathematics, Hunan University  Changsha, China  Wei Miao∗  miaow@hnu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='cn  School of Mathematics, Hunan University  Changsha, China  ABSTRACT  Extreme learning machine (ELM) is a network model that arbitrarily  initializes the first hidden layer and can be computed speedily.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  In order to improve the classification performance of ELM, a ℓ2  and ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5 regularization ELM model (ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM) is proposed in  this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' An iterative optimization algorithm of the fixed point  contraction mapping is applied to solve the ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' The  convergence and sparsity of the proposed method are discussed  and analyzed under reasonable assumptions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' The performance of  the proposed ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM method is compared with BP, SVM, ELM,  ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM, ℓ1-ELM, ℓ2-ELM and ℓ2-ℓ1ELM, the results show that the  prediction accuracy, sparsity, and stability of the ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM are  better than the other 7 models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  CCS CONCEPTS  Mathematics of computing → Convex optimization;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' • Com-  puting methodologies → Regularization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  KEYWORDS  High-dimensional data, Sparsity, Hybird regularization, Dimension-  ality reduction  ACM Reference Format:  Liangjuan Zhou and Wei Miao.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' An improved hybrid regularization  approach for extreme learning machine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' In 2022 4th International Conference  on Advanced Information Science and System (AISS 2022), November 25–27,  2022, Sanya, China.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' ACM, New York, NY, USA, 7 pages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  1145/3573834.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='3574501  1  INTRODUCTION  Feedforward neural networks(FNNs), as one of the most frequently  used neural networks which can be defined mathematically as:  𝐺𝑁 (𝑥𝑖) =  𝑁  ∑︁  𝑖=1  𝛽𝑖𝑔(⟨𝜔𝑖,𝑥𝑖⟩ + 𝑏𝑖),  where 𝑥𝑖 = (𝑥𝑖1,𝑥𝑖2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' ,𝑥𝑖𝑝) ∈ R𝑝 is the input, 𝑏𝑖 is the bias and 𝑔  is the activation function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' ⟨𝜔𝑖,𝑥𝑖⟩ = �𝑝  𝑗=1 𝜔𝑖𝑗𝑥𝑖𝑗 is the euclidean  ∗Both authors contributed equally to this research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  Permission to make digital or hard copies of all or part of this work for personal or  classroom use is granted without fee provided that copies are not made or distributed  for profit or commercial advantage and that copies bear this notice and the full citation  on the first page.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Copyrights for components of this work owned by others than ACM  must be honored.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Abstracting with credit is permitted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' To copy otherwise, or republish,  to post on servers or to redistribute to lists, requires prior specific permission and/or a  fee.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Request permissions from permissions@acm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='org.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  AISS 2022, November 25–27, 2022, Sanya, China  © 2022 Association for Computing Machinery.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  ACM ISBN 978-1-4503-9793-3/22/11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='$15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='00  https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='1145/3573834.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='3574501  inner product, 𝜔𝑖 = (𝜔𝑖1,𝜔𝑖2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' ,𝜔𝑖𝑝) ∈ R𝑝 are the weights con-  necting the input and the 𝑖-th hidden node, and 𝛽𝑖 ∈ R are the  weights connecting the 𝑖-th hidden and output node.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' In terms of  the traditional learning algorithm of FNNs, all parameters in the  network need to be adjusted based on specific tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' A classical  learning method is the backpropagation (BP) algorithm, which is  mainly solved by gradient descent:  min  𝜔𝑖,𝛽𝑖,𝑏𝑖  𝑛  ∑︁  𝑖=1  ∥𝑡𝑖 − 𝐺𝑁 (𝑥𝑖)∥2  2,  where (𝑥𝑖,𝑡𝑖)(𝑖 = 1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' ,𝑛) denotes the training samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' How-  ever, a randomized learner model, different to the traditional learn-  ing of FNNs, called as Extreme learning machine(ELM) and related  algorithms were proposed by Huang[10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' In the ELM model, 𝜔𝑖 and  𝑏𝑖 are randomly assigned without training, so only 𝛽𝑖 needs to be  trained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Set T = [𝑡1,𝑡2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' ,𝑡𝑛] and  H =  \uf8ee\uf8ef\uf8ef\uf8ef\uf8ef\uf8ef\uf8f0  𝑔(⟨𝜔1,𝑥1⟩ + 𝑏1)  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  𝑔(⟨𝜔𝑁,𝑥1⟩ + 𝑏𝑁 )  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  𝑔(⟨𝜔1,𝑥𝑛⟩ + 𝑏1)  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  𝑔(⟨𝜔𝑁,𝑥𝑛⟩ + 𝑏𝑁 )  \uf8f9\uf8fa\uf8fa\uf8fa\uf8fa\uf8fa\uf8fb  ,  (1)  once the input weights and biases are specified randomly with uni-  form distribution in [−𝑐,𝑐], the hidden output matrix remains un-  changed during the training phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Accordingly, the output weights  could be written by utilizing the least squares method:  min  𝛽 ∈R𝑁  �  ∥H𝛽 − T∥2  2  �  ,  (2)  the solution to model (2) could be written as 𝛽 = H†T, where H†  is the Moore–Penrose generalized inverse of hidden output matrix  H[14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  The theoretical basis for the general approximation capability of  ELM networks has been proposed and established by Igelnik[11] ,  where the range of randomly allocated input weights and biases  are data related and assigned in a constructive mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Consequently,  the scope of parameters in the algorithm implementation should  be carefully estimated for diverse datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' On the other hand,  considering the sparsity of the output parameter 𝛽 for many high-  dimensional data, Cao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' [4] proposed a ℓ1 regular ELM model  based on the sparsity of the ℓ1 regularization term, which takes the  following form:  min  𝛽 ∈R𝑁  � 1  2 ∥H𝛽 − T∥2  2 + 𝜆∥𝛽∥1  �  ,  (3)  where 𝜆 > 0 is a regularization parameter and 𝛽 is the output  coefficient calculated by iteration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' This model is called the Lasso  model, and has been studied by many scholars in recent years [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='01458v1  [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='OC]  4 Jan 2023  AISS 2022, November 25–27, 2022, Sanya, China  Zhou and Miao.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  For the model (2), Fan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' [8] added a ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5 regularization term  to the ELM model, based on the solution generated by ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5 is sparser  than the ℓ1 regularization term [16], and the model is defined as  follows:  min  𝛽 ∈R𝑁  � 1  2 ∥H𝛽 − T∥2  2 + 𝜆∥𝛽∥0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5  �  ,  (4)  where 𝜆 > 0 is a regularization parameter, the model can be solved  by the iterative semi-threshold algorithm [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  The other regularization model for model (2) was about the ℓ2  regularization term (ℓ2-ELM) [5]:  min  𝛽 ∈R𝑁  � 1  2 ∥H𝛽 − T∥2  2 + 𝜇∥𝛽∥2  2  �  ,  (5)  where 𝜇 is a regularization parameter, and when the expression  H𝑇 H+𝜇I is invertible after choosing the parameter 𝜇, then the solu-  tion of the model (5) can be written as 𝛽 = (H𝑇 H + 𝜇I)−1I)−1H𝑇 T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  Hai et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' [9] proposed a ℓ2-ℓ1-ELM hybrid model by integrating  the sparsity of the ℓ1 regularization term and the stability of the ℓ2  regularization term as follows:  min  𝛽 ∈R𝑁  � 1  2 ∥H𝛽 − T∥2  2 + 𝜆(𝛾∥𝛽∥1 + 𝜀∥𝛽∥2  2)  �  ,  (6)  where 𝜆 ≥ 0, 𝛾 ≥ 0 and 𝜀 ≥ 0 are regularization parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' In-  spired by the ℓ2-ℓ1-ELM model, according to Xu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' [17], they  found that the sparsity of the solution of the ℓ𝑝 (𝑝 ∈ (0, 1)) regular-  ization term: when 0 < 𝑝 < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5, there is no significant difference in  the sparse effect of ℓ𝑝;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' when 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5 < 𝑝 < 1, the smaller 𝑝, the better  the sparse effect, so the ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5 regularization term can be used as a  representative element of ℓ𝑝 (𝑝 ∈ (0, 1));' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Therefore, we propose the  ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM model by combining the stability of ℓ2 regularization  term and the sparsity of ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5 which is sparser than ℓ1, the new  model is described as:  min  𝛽 ∈R𝑁  � 1  2 ∥H𝛽 − T∥2  2 + 𝜆(𝛾∥𝛽∥0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5 + 𝜀∥𝛽∥2  2)  �  ,  (7)  where the parameters have the same meaning as the expression  of (6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' The thought of adding ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5 and ℓ2 penalties simultaneously in  the optimization model could be found in classification [2, 6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' This  study mainly establishes an iterative algorithm and studies some  properties of randomized learner model as Hai[9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' In particular, we  integrate the features of ELM and propose an iterative strategy for  solving the hybrid model (7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' The main contributions of this paper  can be summarized as follows:  (i) The whole model is a non-convex, non-smooth and non-  Lipschitz optimization problem due to the existence of ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5 norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  We propose a new algorithm called as an ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  This algorithm is proved to be effective by analyzing the sum mini-  mization problem of two convex functions with certain characteris-  tics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  (ii) The key theoretical properties such as convergence, sparsity  are derived to guarantee the feasibility of the proposed method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  (iii) Numerous experiments were carried out, including some  UCI datasets collected from experts and intelligent systems fields,  gene datasets and ORL face image datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Experimental results  show that the better performance of the proposed ℓ2- ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM  algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  The rest of this paper is organized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Section 2 reviews  some basic concepts and theories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Section 3 demonstrates the itera-  tive method by a fixed point equation and proposes a algorithm for  ℓ2 - ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' In Section 4, some theoretical results about  convergence and sparsity are analyzed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' In Section 5, experimental  results on UCI datasets, gene datasets and ORL face image datasets  are shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' The conclusion is drawn in Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  2  PRELIMINARIES  In this section, we present some fundamental concepts and con-  vex optimization theorems primarily.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Initially, it is about the half-  thresholding function[16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' 𝒫(𝜆,𝑡) : R → R, 𝜆 > 0, which can be  written as:  𝒫(𝜆,𝑡) =  � 2  3𝑡  �  1 + cos  � 2(𝜋−𝜙 (𝑡))  3  ��  |𝑡| > 3  4𝜆  2  3  0  |𝑡| ≤ 3  4𝜆  2  3  ,  (8)  where 𝜙(𝑡) = arccos  �  𝜆  8 ( |𝑡 |  3 )− 3  2  �  , 𝜋 = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='14, and then the corre-  sponding half-thresholding operator half(𝜆, 𝛽) : R𝑁 → R𝑁 acts  component-wise as:  [half(𝜆, 𝛽)]𝑖 = 𝒫(𝜆, 𝛽𝑖).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  (9)  Next, we introduce one key characteristic of the half-thresholding  operator [7, 16]:  ∥half(𝜆,𝑡) − half(𝜆,𝑡 ′)∥ ≤ ∥𝑡 − 𝑡 ′∥.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  (10)  Another crucial notion of convex optimization is the proximity  operator [12]:  prox𝜑𝛽 = arg min  �  ∥𝑢 − 𝛽∥2  2 + 𝜑(𝑢)  �  ,  where𝜙 is a real-valued convex function on R𝑁 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' A primary property  of the proximity operator is drawn in Proposition 1[7], which will  be utilized to prove our major result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  Proposition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Let 𝜑 be a real-valued convex function on R𝑁 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  Suppose 𝜓 (·) = 𝜑 + 𝜌  2 ∥ · ∥2  2 + ⟨·,𝑢⟩ + 𝜎, where 𝑢 ∈ R𝑁 , 𝜌 ∈ [0, ∞),  𝜎 ∈ R, then  prox𝜓 𝛽 = prox𝜑/(1+𝜌) ((𝛽 − 𝑢)/(1 + 𝜌)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  (11)  3  SOLUTION: FIXED POINT ITERATIVE  ALGORITHM FOR THE MODEL  For the ELM, the output matrix H is a bounded linear operator from  R𝑁 to R𝑚 owing to the activation function 𝑔(·) ∈ (0, 1), which is  finite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' In order to further improve the accuracy and sparsity, we  employ the regularization model (7) to estimate the output weights  of the network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' We define concisely as:  𝑝𝛾,𝜀 = 𝛾∥𝛽∥0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5 + 𝜀∥𝛽∥2  2,  where 𝜀, 𝛾 ≥ 0, 𝑝𝛾,𝜀 : R𝑁 → [0, ∞).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Then the model (7) can be  redefined as  min  𝛽 ∈R𝑁  � 1  2 ∥H𝛽 − T∥2  2 + 𝜆𝑝𝛾,𝜀  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  (12)  Furthermore, we introduce the following Lemma and Theorem  which will be utilized to solve our model:  An improved hybrid regularization approach for extreme learning machine  AISS 2022, November 25–27, 2022, Sanya, China  Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' For all 𝜆 > 0 and 𝛽 ∈ R𝑁 ,the half-thresholding operator  (8) can be described as:  half(𝜆, 𝛽) = arg min  𝑢  � 1  2 ∥𝑢 − 𝛽∥2  2 + 𝜆∥𝑢∥0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' For all 𝜆  >  0,𝛾  ≥  0,𝜀  ≥  0 and 𝛽  ∈  R𝑁 ,  half(  𝜆𝛾  1+2𝜀𝜆,  𝛽  1+2𝜀𝜆 ) is the proximity operator of 𝜆𝑝𝛾,𝜀 (𝛽).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Let 𝜆 > 0, 𝛾 ≥ 0, 𝜀 ≥ 0 and 𝛿 ∈ (0, ∞).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Then 𝛽 is  a minimizer of function (12) if and only if it meets the fixed point  equation:  𝛽 = half  �  𝛿𝜆𝛾  1 + 2𝜀𝜆𝛿 , (I − 𝛿H𝑇 H)𝛽 − 𝛿H𝑇 T  1 + 2𝜀𝜆𝛿  �  ,  (13)  where the unit operator I : R𝑁 → R𝑁 , the definition of H is shown  in (1), and H𝑇 represents the adjoint of H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  Moreover, from the property of the proximity operator, we can  drive a precise statement for the Lipschitz constant of a contractive  map and the corresponding theorem as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Set 𝜆 > 0,𝛾 ≥ 0,𝜀 ≥ 0 and 𝛿 ∈ (0, ∞).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Suppose that  there exist two positive constants 𝜅0 and 𝜅, such that the norm of the  output matrix H shown in (1) of the hidden layer is finite by them,  namely 𝜅0 ≤ ∥H𝑇 H∥2 ≤ 𝜅, Thus 𝛽 is a minimizer of (12) if and  only if it is a fixed point of the Lipchitz map Γ : R𝑁 → R𝑁 , that is,  𝛽 = Γ𝛽 where  Γ𝛽 = half  �  𝛿𝜆𝛾  1 + 2𝜀𝜆𝛿 , (I − 𝛿H𝑇 H)𝛽 + 𝛿H𝑇 T  1 + 2𝜀𝜆𝛿  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  (14)  Selecting𝛿 =  2  𝜅0+𝜅 , the Lipschitz constant is finite by𝑞 = 1− 2𝜅0  𝜅 + 𝜅0  ≤  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' In particular, if 𝜅0 > 0, we can get Γ is a contractive map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  Theorem 1 and Theorem 2 illustrate that the problem of ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-  ELM can be described as a fixed point algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Furthermore, the  next theorem will introduce the iterative procedure of the ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-  ELM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Suppose that 𝜅0 and 𝜅 are positive constants, such  that the norm of the output matrix H shown in (1) of the hidden  layer is finite by them, namely, 𝜅0 ≤ ∥H𝑇 H∥2 ≤ 𝜅, and the sequence  {𝛽}∞  𝑙=0 ⊆ R𝑁 is described iteratively as  𝛽𝑙 = half  �  𝛿𝜆𝛾  1 + 2𝜀𝜆𝛿 , (I − 𝛿H𝑁 H)𝛽𝑙−1 − 𝛿H𝑇 T  1 + 2𝜀𝜆𝛿  �  ,  (15)  where 𝑙 = 1, 2, 3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' , 𝜆 > 0,𝜀 > 0,𝛾 ≥ 0 and 𝛿 =  2  𝜅+𝜅0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Thus {𝛽𝑙 }∞  𝑙=0  strongly converges the minimizer of model (10) in spite of the choice  of 𝛽0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  Remark 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' It is not difficult to obtain from the proof of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  ∥𝛽𝑙 − 𝛽∗∥2 ≤  𝜅 + 𝜅0  𝜅0(𝜅 + 𝜅0 + 4𝜀𝜆)  �𝜅 − 𝜅0  𝜅 + 𝜅0  �𝑙  ∥H𝑇 T∥2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  Therefore, for each 𝜉 > 0, if  𝜅 + 𝜅0  𝜅0(𝜅 + 𝜅0 + 4𝜀𝜆)  �𝜅 − 𝜅0  𝜅 + 𝜅0  �𝑙  ∥𝛽1 − 𝛽0∥2 < 𝜉.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  namely,  𝑙 >  log  � ∥𝛽1−𝛽0 ∥2(𝜅+𝜅0)  𝜉𝜅0(𝜅+𝜅0+4𝜀𝜆)  �  log  � 𝜅+𝜅0  𝜅−𝜅0  �  ,  thus  ∥𝛽𝑙 − 𝛽∗∥2 < 𝜉.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  As a conclusion, the complete ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM algorithm is given in  Algorithm 1 which integrates the result of Theorem 3 and Remark  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Next section, we want give some properties of our proposed  algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  Algorithm 1: the algorithm for ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM model  Input:Given  a  set  of  training  samples  𝒻  =  �  (𝑥𝑗,𝑡𝑗) : 𝑥𝑗 ∈ R𝑝,𝑡𝑗 ∈ R𝑚, 𝑗 = 1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' ,𝑛  �,  activation  func-  tion 𝑔, hidden node number 𝑁, the related regularization  parameters 𝜆 > 0, 𝛾 ≥ 0, 𝜀 ≥ 0, the corresponding parameter 𝛿,  and an acceptable error 𝜉.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  Step 1: Randomly assign a proper scope for input weight 𝜔𝑖 and  bias 𝑏𝑖 (𝑖 = 1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' , 𝑁)  Step 2: Compute the hidden layer output matrix H;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  Step  3:  Set  𝛽0  =  (0, 0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' , 0),  𝛽1  =  half(  𝛿𝜆𝛾  1 + 2𝜀𝜆𝛿 , (I − 𝛿H𝑇 H)𝛽0 + 𝛿H𝑇 T  1 + 2𝜀𝜆𝛿  ), and 𝑙𝑚𝑎𝑥 be a minimal  positive integer but larger than  log  � ∥𝛽1 − 𝛽0∥2(𝜅 + 𝜅0)  𝜉𝜅0(𝜅 + 𝜅0 + 4𝜀𝜆)  �  log  � 𝜅+𝜅0  𝜅−𝜅0  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  Step 4: For 𝑙 = 1 : 𝑙𝑚𝑎𝑥  if 𝑙 ≥ 𝑙𝑚𝑎𝑥, stop;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  else 𝑙 := 𝑙 + 1 and update the 𝛽 as follows: 𝛽𝑙+1 =  half(  𝛿𝜆𝛾  1 + 2𝜀𝜆𝛿 , (I − 𝛿H𝑇 H)𝛽𝑙 + 𝛿H𝑇 T  1 + 2𝜀𝜆𝛿  ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  repeat Step 4, until that the desired output weight is ^𝛽 = 𝛽𝑚𝑎𝑥.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  Output: Return the output weights ^𝛽;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  4  SOME CHARACTERISTICS FOR ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM  For the new section, we want to discuss and analyze some key  characteristics of the estimator regarding ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM, such as the  convergence and sparsity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' 𝛽𝑙 strongly converges to the minimum value 𝛽∗ of  the minimization problem  min  𝛽 ∈R𝑁  � 1  2 ∥H𝛽 − T∥2  2 + 𝜆𝑝𝛾𝜀 (𝛽)  �  as 𝑙 → ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  𝛽0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5 in the ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM is a highly significant part of the sparsity  of the solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Thus, we set the Theorem 5 as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Suppose 𝜆  >  0,𝛾  >  0, then the support of  half(  𝜆𝛾  1+2𝜀𝜆,  𝛽  1+2𝜀𝜆 ) is finite for any 𝛽 ∈ R𝑁 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Particularly, 𝛽∗ and 𝛽𝑙  are all finitely supported.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  If the regularization parameters 𝜆 and 𝛾 are fixed as some con-  stant values, then 𝛽∗ and 𝛽𝑙 have only a few finite nonzero coeffi-  cients, and hence the solution to (12) is sparse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  AISS 2022, November 25–27, 2022, Sanya, China  Zhou and Miao.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  Table 1: Details of the 6 datasets  Dataset  Type  Sapmple  Feature  Catagory  Austrian  UCI  690  14  2  Ionosphere  UCI  151  34  2  Balance  UCL  625  4  3  colon  gene  62  2000  2  DLBCL  gene  77  7129  2  ORL  image  400  10304  40  5  PERFORMANCE EVALUATION  In the new section, a succession of experiments, containing some  UCI benchmark datasets[9] and gene data, are carried out to demon-  strate the performance of the proposed ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' All  the experiments are performed in the Mac Pycharm environment  running on Quad-Core Intel Core i5, CPU (8 GB 2133 MHz LPDDR3)  processor with the speed of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='40GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' The activation function of  networks used in the experiments is taken as sigmoid function  𝑔(𝑥) = 1/(1 + 𝑒−𝑥).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  The ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM model is compared with seven other models:  BP, SVM, ELM, ℓ2-ℓ1-ELM, ℓ2-ELM, ℓ1-ELM, ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' BP includes  only one hidden layer and output layer, and all parameters are  trained by back-propagation algorithm;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' ℓ1-ELM and ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM are  the simplified forms of ℓ2-ℓ1-ELM and ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  The activation function is defined as: 𝑔(𝑥) = 1/(1 + 𝑒−𝑥).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  In order to check the algorithm for ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM model, three real  classification datasets from the UCI machine learning repository  are considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' The basic information of each dataset is shown in  Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' The average of 30 experimental validations was used as  the final result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' For these datasets, the sample size is fixed, but each  sample is randomly assigned as training or testing data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='1  Performance for UCI datasets  To validate the performance of the proposed ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM model,  three types of real classification datasets were used for the experi-  ments, including UCI[3], gene expression, and ORL face datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  The UCI machine learning repository (2013UCI) contains three  datasets: Austrian Credit Approval(Austrian), Ionosphere, and Bal-  ance Scale(Balance).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' The gene expression datasets contain colon[1]  and DLBCL[13], both of which are binary datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Moreover, the  ORL face dataset includes 400 images divided into 40 categories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  Each category contains 10 images with different facial details and  each image size is 112 × 92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' The detail information of all datasets  are summarized in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' In addition, these data were obtained  from different application fields, and it is hoped that the ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-  ELM model can be analyzed from multiple perspectives by using  these data from different backgrounds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  We repeat 30 trials and take the averages as the final results  on account of reducing the random error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' And the regularization  parameters are used to control the trade-off between the error and  the penalty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' For Austrian dataset, take the parameters ( ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM,  ℓ2-ℓ1-ELM : 𝜆 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='8,𝛾 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='1,𝜀 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='9) and for Ionosphere dataset,  take ( ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM, ℓ2-ℓ1-ELM : 𝜆 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='9,𝛾 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='05,𝜀 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='9) and  Balance Scale dataset, ( ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM : 𝜆 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='8,𝛾 = 1,𝜀 = 1, for ℓ2-ℓ1-  ELM : 𝜆 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='005,𝛾 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5,𝜀 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5), we set the acceptable error 𝜉 =  Table 2: Performance comparison of 8 models on 3 different  datasets  Datasets  Methods  Times(s)  Remaining Nodes  Accuracy(% ± %)  Austrain  BP  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='1751  600  72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='58 ± 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='57  SVM  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='0448  —  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='14 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='98  ELM  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='0588  600  65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='37 ± 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='08  ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='8542  48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5  82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='76 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='00  ℓ1-ELM  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='1648  118.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='38 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='00  ℓ2-ELM  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='2735  600  80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='36 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='00  ℓ2-ℓ1-ELM  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='041  492.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='38 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='00  ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5875  118.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5  82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='76 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='00  Ionosphere  BP  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='1751  600  72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='58 ± 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='57  SVM  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='0108  –  86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='51 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='09  ELM  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='0003  600  91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='55 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='78  ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='0487  29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5  96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='96 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='00  ℓ1-ELM  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='4755  115.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='9  97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='24 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='06  ℓ2-ELM  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='0520  600  96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='05 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='57  ℓ2-ℓ1-ELM  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='4093  437.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5  96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='84 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='98  ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='0569  193  98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='01 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='00  Balance  BP  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='3814  600  59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='99 ± 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='26  SVM  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='0215  –  88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='63 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='86  EL,M  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='0008  600  50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='72 ± 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='66  ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='1285  23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='3  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='55 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='00  ℓ1-ELM  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5074  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='9  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='47 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='66  ℓ2-ELM  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='1579  600  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='55 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='00  ℓ2-ℓ1-ELM  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='8678  246.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='4  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='10 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='35  ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='0974  52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='7  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='91 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='0001, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='001, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='0001 respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' The number of hidden nodes in  the experiments is 600.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Table 2 shows the running time, the number  of nodes retained, and the accuracy of the test for each dataset for  the eight models (the standard deviation is kept to 4 significant  digits, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='00 in the table indicates a standard deviation of less than  10−4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' These indices are used to measure the sparsity, stability and  effectiveness of the proposed method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' The corresponding figures  on testing are shown as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  From the results of 1-3, we can see that the accuracy of the ELM  model is lower than all the regularized ELM models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' The standard  deviation of the ELM model is higher than that of other regularized  ELM models, which indicates that the stability of the ELM model is  lower.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' The accuracy of the ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM model at all nodes can be  compared with other regularized ELM models, and the accuracy at  most hidden nodes is higher than other comparable regularized ELM  models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' This indicates that the ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM model has consistently  good classification prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' In terms of the standard deviation  of different nodes, the ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM model is lower than the other  compared models, indicating that the classification accuracy of this  method is more stable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  We can see the performance of ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM in detail and draw  the following conclusions:  (i) In 3 datasets, the classification accuracy of the regularized  ELM methods (ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM, ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM, ℓ2-ℓ1-ELM, ℓ1-ELM, ℓ2-ELM)  are significantly higher than that of the BP, SVM and ELM methods,  indicating that the regularized ELM methods have better general-  ization performance, and the classification accuracy of ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM  methods is higher than that of other compared regularized ELM  methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  (ii) From the perspective of the number of remaining hidden  nodes, ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM has the lowest number of hidden nodes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' It is shown  An improved hybrid regularization approach for extreme learning machine  AISS 2022, November 25–27, 2022, Sanya, China  200  300  400  500  600  700  800  900  1000 1100 1200  Number of Hidden Nodes  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='50  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='55  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='60  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='65  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='70  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='75  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='80  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='85  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='90  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='95  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='00  Testing accuracy  ELM  l0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5  l1  l2  l2l1  l2l0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5  200  300  400  500  600  700  800  900  1000 1100 1200  Number of Hidden Nodes  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='000  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='002  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='004  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='006  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='008  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='010  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='012  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='014  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='016  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='018  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='020  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='022  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='024  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='026  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='028  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='030  SDs of Testing  ELM  l0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5  l1  l2  l2l1  l2l0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5  Figure 1: Performance comparison of 6 models in the Austrian dataset  200  300  400  500  600  700  800  900  1000 1100 1200  Number of Hidden Nodes  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='60  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='62  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='64  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='66  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='68  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='70  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='72  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='74  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='76  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='78  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='80  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='82  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='84  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='86  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='88  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='90  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='92  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='94  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='96  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='98  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='00  Testing accuracy  ELM  l0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5  l1  l2  l2l1  l2l0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5  200  300  400  500  600  700  800  900  1000 1100 1200  Number of Hidden Nodes  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='03  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='06  SDs of Testing  ELM  l0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5  l1  l2  l2l1  l2l0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5  Figure 2: Performance comparison of 6 models in the Ionosphere dataset  200  300  400  500  600  700  800  900  1000 1100 1200  Number of Hidden Nodes  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='35  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='40  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='45  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='50  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='55  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='60  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='65  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='70  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='75  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='80  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='85  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='90  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='95  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='00  Testing accuracy  ELM  l0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5  l1  l2  l2l1  l2l0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5  200  300  400  500  600  700  800  900  1000 1100 1200  Number of Hidden Nodes  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='005  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='000  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='005  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='010  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='015  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='020  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='025  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='030  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='035  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='040  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='045  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='050  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='055  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='060  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='065  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='070  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='075  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='080  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='085  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='090  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='095  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='100  SDs of Testing  ELM  l0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5  l1  l2  l2l1  l2l0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5  Figure 3: Performance comparison of 6 models in the Balance dataset  that the ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5 or ℓ1-regularization term is beneficial to enhance the  sparsity of the hidden nodes of the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Compared with the ℓ2-  ℓ1-ELM model, the ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM model adds the ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5 regularization  term to the model, which has a sparser solution and thus a better  generalization ability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  (iii) From the perspective of algorithm running time, the ELM  model runs in the shortest time (the ELM model can obtain the  analytic solution directly without iterative computation).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' In com-  parison, the SVM model runs faster than all ELM methods with  regularity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Secondly, for the 5 regularized ELM models, the models  with ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5 regularization terms (ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM, ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM) are faster  than the models with ℓ1 regularization terms (ℓ1-ELM, ℓ2- ℓ1-ELM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='2  Performance for gene datasets  In this section, the performance of the ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM model is vali-  dated using the colon and DLBCL data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' The training and testing sets  of each dataset were experimented in the ratio of 1 : 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' The regular-  ization parameters are set as follows, colon data: (ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM and  ℓ2-ℓ1-ELM : 𝜆 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='09,𝛾 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='9,𝜀 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='9), DLBCL data: (ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM  and ℓ2-ℓ1-ELM : 𝜆 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='005,𝛾 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5,𝜀 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' and 𝜉 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Each  dataset was repeatedly run 30 times, and the average was taken as  the final result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' As shown in Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  It can be demonstrated that the prediction accuracy of the single-  layer BP network is very low and does not capture the features of  AISS 2022, November 25–27, 2022, Sanya, China  Zhou and Miao.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  200  300  400  500  600  700  800  900  1000 1100 1200  Number of Hidden Nodes  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='72  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='73  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='74  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='75  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='76  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='77  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='78  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='79  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='80  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='81  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='82  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='83  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='84  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='85  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='86  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='87  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='88  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='89  Testing accuracy  ELM  l0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5  l1  l2  l2l1  l2l0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5  200  300  400  500  600  700  800  900  1000 1100 1200  Number of Hidden Nodes  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='000  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='005  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='010  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='015  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='020  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='025  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='030  SDs of Testing  ELM  l0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5  l1  l2  l2l1  l2l0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5  Figure 4: Performance comparison of 6 models in colon dataset  Table 3: Performance comparison of 8 models in 2 gene  datasets  Datasets  Methods  Times(s)  Remaining Nodes  Accuracy(% ± %)  colon  BP  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='2641  1000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='0  55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='52 ± 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='15  SVM  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='0358  –  77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5 ± 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='28  ELM  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='0056  1000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='0  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='02 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='92  ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='0829  370.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='00 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='00  ℓ1-ELM  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='0488  974.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='79 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='22  ℓ2-ELM  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='0815  1000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='0  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='17 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='20  ℓ2-ℓ1-ELM  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='0401  1000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='0  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='96 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='24  ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='0879  877.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='0  87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='50 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='00  DLBCL  BP  122.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='3174  1000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='0  57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='24 ± 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='55  SVM  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='0968  –  87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='24 ± 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='98  ELM  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='0060  786.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='0  89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='90 ± 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='98  ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='2214  242.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='0  91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='43 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='00  ℓ1-ELM  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='2957  188.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5  89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='05 ± 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='12  ℓ2-ELM  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='2324  764.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='0  89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='51 ± 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='48  ℓ2-ℓ1-ELM  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5286  431.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5  89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='62 ± 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='10  ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='4519  575.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5  91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='43 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='00  the data very well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' It can also be found that the prediction accu-  racy of the ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM model is slightly higher than that of the  other methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' The standard deviations of the accuracy of the ELM  methods with ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5 regularization are much smaller than those of  BP, SVM, and ELM, indicating that the ELM model variants with  ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5 regularization terms can improve the stability of the solutions;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  The number of hidden nodes in the ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM and ℓ1-ELM models  is smaller, that is, the sparsity of these two regularization terms is  the strongest, indicating that the addition of ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5 or ℓ1 regularization  terms in the ELM model enhances the sparsity of the model, while  the number of hidden nodes in the ℓ2-ELM model is 1000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' The  number of nodes in the ℓ2-ELM model is 1000, indicating that the  ℓ2-regularization term has no sparse effect on the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' The ℓ2  norm is used to increase the stability of the model by penalizing  oversized regularization parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' This makes the ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM  sparser and model stable, and thus obtains better generalization  ability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  From the perspective of algorithm running time, it can be seen  that the ELM model has the shortest running time (the ELM model  can obtain the analytical solution directly without iterative solving).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  In contrast, the SVM model runs faster than all ELM methods with  regularization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  Further, we use the colon data to verify the effect of different  number of hidden nodes (200, 400, 600, 800, 1000, 1200) on the sta-  bility of the ELM correlation model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' We perform 30 experiments  for each hidden node and calculate the ELM, ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM, ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM,  ℓ2-ℓ1-ELM, ℓ1-ELM, ℓ2-ELM for the test set accuracy and standard  deviation as shown in Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' The test accuracy of ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM at  all nodes can be compared with all regularized ELM models, while  the accuracy at most hidden nodes is higher than other models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  The standard deviation of ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM model is lower than other  regularized ELM models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='3  Performance for ORL face dataset  The ORL face dataset is used for experimental validation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' The num-  ber of hidden nodes for the experiment is 1000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' The average of  30 experiments is used as the final result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Since the original im-  age has high dimensionality, we preprocess each image by using  the (2𝐷)2PCA[18] dimensionality reduction technique.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' And the  training set and test set are in the ratio of 7 : 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' The values of the  regular parameters set in the experiment are as follows: ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM  and ℓ1-ELM (𝛾 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='05,𝜀 = 0), ℓ2-ELM (𝛾 = 0,𝜀 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5), ℓ2 -ℓ1-ELM,  ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM(𝛾 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='05,𝜀 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' 𝜆 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='001 and 𝜀 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='0001 are cho-  sen in all experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' This experiment validates the performance  of the model in terms of accuracy and standard deviation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' The re-  sults are shown in Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' From the table, it can be seen that the  Table 4: Performance comparison of 8 models in ORL face  dataset  Methods  Accuracy(%)  BP  31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='00 ± 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='90  SVM  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='53 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='12  ELM  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='58 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='95  ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='00 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='34  ℓ1-ELM  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='85 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='86  ℓ2-ELM  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='17 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='47  ℓ2-ℓ1-ELM  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='58 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='87  ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='67 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='34  An improved hybrid regularization approach for extreme learning machine  AISS 2022, November 25–27, 2022, Sanya, China  Table 5: Performance comparison of 6 models in ORL face dataset  Nodes  ELM  ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM  ℓ1-ELM  ℓ2-ELM  ℓ2-ℓ1-ELM  ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM  500  52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='92±3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='04  66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='10±2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='55  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='00 ±1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='77  62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='63± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='38  59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='25 ±2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='32  65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='83 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='46  1500  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='08±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='73  77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='00±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='93  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='33 ±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='67  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='75± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='75  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='33 ±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='76  77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='20 ±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='93  2000  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='25±2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='00  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='73±2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='45  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='33 ±2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='08  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='63± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='18  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='33 ±2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='08  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='83 ±2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='45  2500  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='58±3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='49  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='74±3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='36  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='67 ±3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='44  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='21±3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='29  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='63 ±3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='44  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='76 ± 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='26  3000  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='50±1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='98  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='55±2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='69  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='42 ±2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='07  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='45±2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='39  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='42 ±2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='07  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='58 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='68  3500  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='17±1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='81  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='13±2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='22  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='17 ±1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='87  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='17±1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='89  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='17 ±1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='87  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='25 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='12  4000  82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='00±1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='81  82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='00±1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='67  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='92 ±1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='74  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='96±1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='64  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='92 ±1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='74  82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='08 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='65  mean  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='22±9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='12  77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='16±5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='33  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='21 ±7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='00  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='62±6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='21  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='08 ±7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='24  77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='26 ± 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='32  accuracy of the ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM model (which is slightly higher than  the SVM model) is slightly higher than all other models tested.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  Further, we verify the effect of different values of hidden nodes  on the prediction accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' The number of hidden nodes chosen in  the experiment is 500, 1000, 1500, 2000, 2500, 3000, 3500, 4000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  The results are shown in Table 5, which show that the test accu-  racy of ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM model is higher than the other comparative  ELM models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' The test accuracy of the ELM model fluctuates the  most with the changing of the number of hidden nodes, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=', the  selection of different nodes has the greatest impact on it, indicating  that the ELM model is less stable in high-dimensional data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' In con-  trast, the standard deviations of all the regularized ELM methods  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='33, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='00, 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='21, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='24, 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='32) are lower than those of the ELM meth-  ods, indicating that the stability of the ELM model is improved by  adding the regularization term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' ELM methods, indicating that the  stability of the proposed method is better than the other 5 compared  to ELM methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  6  CONCLUSION  In order to further improve the stability and generalization of the  ELM model, this paper proposes a ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM model by combin-  ing the ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5 and the ℓ2 regularization term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' The iterative algorithm  is applied to solve the model with a fixed points algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' The  convergence and sparsity of this algorithm are proved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Moreover,  the proposed ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM model is compared with BP, SVM, ELM,  ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM, ℓ1-ELM, ℓ2-ELM and ℓ2-ELM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' ℓ2-ℓ1-ELM models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Experi-  mental comparisons on several datasets (UCI dataset, gene dataset,  ORL face dataset) show that the ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM method outperforms  the other 7 models in terms of prediction accuracy and stability  on these data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Therefore, the model can be improved as follows:  the information of previously computed nodes is not used in the  computation of different hidden nodes, and it can be learned from  the incremental learning point of view, which can reduce the com-  putation time to a certain extent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  REFERENCES  [1] U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Alon, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Barkai, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Notterman, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Gish, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Ybarra, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Mack, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Levine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  1999.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Broad patterns of gene expression revealed by clustering analysis of tumor  and normal colon tissues probed by oligonucleotide arrays.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' 96, 12 (1999), 6745–  6750.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  [2] Hai Hui Huang A B and Yong Liang C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Hybrid 𝐿1/2+2 method for gene  selection in the Cox proportional hazards model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Computer Methods and Programs  in Biomedicine 164 (2018), 65–73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  [3] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Bache and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Lichman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' UCI machine learning repository.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  [4] Feilong Cao, Yuanpeng Tan, and Miaomiao Cai.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Sparse algorithms of  random weight networks and applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Expert Systems with Applications 41,  5 (2014), 2457–2462.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  [5] Feilong Cao, Dianhui Wang, Houying Zhu, and Yuguang Wang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' An itera-  tive learning algorithm for feedforward neural networks with random weights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  Information Sciences 328 (2016), 546–557.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  [6] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Cawley and Nlc Talbot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Gene selection in cancer classification using  sparse logistic regression with Bayesian regularization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Oxford University Press  (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  [7] Patrick L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Combettes and Valérie R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Wajs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Signal recovery by proximal  forward-backward splitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Multiscale Model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Simul.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' 4 (2005), 1168–1200.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  [8] Qinwei Fan, Lei Niu, and Qian Kang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Regression and multiclass classification  using sparse extreme learning machine via smoothing group 𝐿1/2 regularizer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  IEEE Access 8 (2020), 191482–191494.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  [9] Hailiang, Ye, Feilong, Cao, Dianhui, and Wang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' [n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' A hybrid regularization  approach for random vector functional-link networks - ScienceDirect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Expert  Systems with Applications 140 ([n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=']), 112912–112912.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  [10] Guang-Bin Huang, Qin-Yu Zhu, and Chee-Kheong Siew.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Extreme learning  machine: theory and applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Neurocomputing 70, 1 (2006), 489–501.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  [11] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Igelnik and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Pao.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' 1995.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Stochastic choice of basis functions in adaptive  function approximation and the functional-link net.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' IEEE Trans Neural Netw 6, 6  (1995), 1320–1329.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  [12] Charles Micchelli, Lixin Shen, and Yuesheng Xu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Proximity algorithms for  image models: denoising.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Inverse Problems 27 (03 2011), 045009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  [13] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Rosenwald, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Wright, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Chan, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Connors, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Campo, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Fisher, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  Gascoyne, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Muller-Hermelink, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Smeland, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Giltnane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' The  use of molecular profiling to predict survival after chemotherapy for diffuse  large-B-cell lymphoma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' New England Journal of Medicine 346, 25 (2011), 1937.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  [14] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Schmidt, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Kraaijveld, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Duin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' 1992.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  Feedforward neural  networks with random weights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' (1992), 1–4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  [15] Robert Tibshirani.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Regression shrinkage and selection via the lasso: a retro-  spective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Journal of the Royal Statistical Society: Series B (Statistical Methodology)  73, 3 (2011), 267–288.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  [16] Zongben Xu, Xiangyu Chang, Fengmin Xu, and Hai Zhang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' 𝐿1/2 regular-  ization: a thresholding representation theory and a fast solver.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' IEEE Transac-  tions on Neural Networks and Learning Systems 23, 7 (2012), 1013–1027.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' https:  //doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='1109/TNNLS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='2197412  [17] Zong-Ben Xu, Hai-Liang Guo, Yao Wang, and Hai Zhang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Representative  of 𝐿1/2 regularization among 𝐿𝑞 (0 < 𝑞 ≤ 1) regularizations: an experimental  study based on phase diagram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Acta Automatica Sinica 38, 7 (2012), 1225–1228.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  [18] Daoqiang Zhang and Zhi-Hua Zhou.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' (2D)2PCA: Two-directional two-  dimensional PCA for efficient face representation and recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Neurocom-  puting 69, 1 (2005), 224–231.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
diff --git a/5NE6T4oBgHgl3EQflhFb/content/2301.06150v1.pdf b/5NE6T4oBgHgl3EQflhFb/content/2301.06150v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..399bd9cde58dc5f0c81fbfdac1ecfb64822b042c
--- /dev/null
+++ b/5NE6T4oBgHgl3EQflhFb/content/2301.06150v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:9fef1677046b2a312a589bbd35c6fc0da21781ecf895dec3b75925919ea719b2
+size 594263
diff --git a/5NE6T4oBgHgl3EQflhFb/vector_store/index.faiss b/5NE6T4oBgHgl3EQflhFb/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..a6b1a8c4c64fe121790068e7185ec5ac777e6877
--- /dev/null
+++ b/5NE6T4oBgHgl3EQflhFb/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:f94e60c2e2f56c51918a1d062847d72e7a3c8aba635b37f6336375c0f16a29b3
+size 6029357
diff --git a/5dFJT4oBgHgl3EQfkywG/vector_store/index.faiss b/5dFJT4oBgHgl3EQfkywG/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..9826038d7fb8496f15e5737474f87963d6da80cb
--- /dev/null
+++ b/5dFJT4oBgHgl3EQfkywG/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:47514ca2a9094ee84929f023419aa2bd8efbc03778eb575718fc7e4f76792f3a
+size 3211309
diff --git a/5tAyT4oBgHgl3EQf2fk_/content/2301.00751v1.pdf b/5tAyT4oBgHgl3EQf2fk_/content/2301.00751v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..68c9da676377f5e0064e9d65ef6f8ea88b1e209b
--- /dev/null
+++ b/5tAyT4oBgHgl3EQf2fk_/content/2301.00751v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:e99a11bddf86ddb786e4970140d61a2679534619ab775198e163795faf6ca217
+size 637742
diff --git a/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf b/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..1c2a8c2bd8f94c1f3764ef016679688237ea13e8
--- /dev/null
+++ b/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:626ddf71600516aecb5cff64488791940c9fea908b757c2613b351ec3386d909
+size 152485
diff --git a/8tE0T4oBgHgl3EQfwgFY/vector_store/index.faiss b/8tE0T4oBgHgl3EQfwgFY/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..01ca4f1b157a720bc7e3f05c3eba447fdf38e027
--- /dev/null
+++ b/8tE0T4oBgHgl3EQfwgFY/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:d42d133246a5f7d86810f1ceecb695928f46472e1980dc713d385237fda50338
+size 1376301
diff --git a/8tE0T4oBgHgl3EQfwgFY/vector_store/index.pkl b/8tE0T4oBgHgl3EQfwgFY/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..8b7d439cb0bd5802e33417a47c717d3e355f20d5
--- /dev/null
+++ b/8tE0T4oBgHgl3EQfwgFY/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:d0e5fcad3f379b480c30d1c3441bee0f4b0fc7c90d2812ff4ff8845e7009766c
+size 54415
diff --git a/BNE4T4oBgHgl3EQfFAx2/vector_store/index.faiss b/BNE4T4oBgHgl3EQfFAx2/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..0776d1d78b9200011e100cf254438df8c5864778
--- /dev/null
+++ b/BNE4T4oBgHgl3EQfFAx2/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:f594e20c913eb693a3dc18a16ca0d4d7c97c347a29adb8d88d13d489fe27aaa9
+size 7864365
diff --git a/BNE4T4oBgHgl3EQfFAx2/vector_store/index.pkl b/BNE4T4oBgHgl3EQfFAx2/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..a7d83e332194040d42bcd90ef2a9903ee79940f4
--- /dev/null
+++ b/BNE4T4oBgHgl3EQfFAx2/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:870b6012fd477f4dcaffe50173e55a6a5d311410b36cd36edeb30f3335655cb8
+size 260496
diff --git a/D9E2T4oBgHgl3EQfogh1/content/tmp_files/2301.04019v1.pdf.txt b/D9E2T4oBgHgl3EQfogh1/content/tmp_files/2301.04019v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..bf540fb28fab39f2f66c23c1989f9fa5fe9af512
--- /dev/null
+++ b/D9E2T4oBgHgl3EQfogh1/content/tmp_files/2301.04019v1.pdf.txt
@@ -0,0 +1,2460 @@
+JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 10, JANUARY 2023
+1
+FGAHOI: Fine-Grained Anchors for
+Human-Object Interaction Detection
+Shuailei Ma, Yuefeng Wang, Shanze Wang, and Ying Wei
+Abstract—Human-Object Interaction (HOI), as an important problem in computer vision, requires locating the human-object pair and
+identifying the interactive relationships between them. The HOI instance has a greater span in spatial, scale, and task than the
+individual object instance, making its detection more susceptible to noisy backgrounds. To alleviate the disturbance of noisy
+backgrounds on HOI detection, it is necessary to consider the input image information to generate fine-grained anchors which are then
+leveraged to guide the detection of HOI instances. However, it is challenging for the following reasons. 𝑖) how to extract pivotal features
+from the images with complex background information is still an open question. 𝑖𝑖) how to semantically align the extracted features and
+query embeddings is also a difficult issue. In this paper, a novel end-to-end transformer-based framework (FGAHOI) is proposed to
+alleviate the above problems. FGAHOI comprises three dedicated components namely, multi-scale sampling (MSS), hierarchical
+spatial-aware merging (HSAM) and task-aware merging mechanism (TAM). MSS extracts features of humans, objects and
+interaction areas from noisy backgrounds for HOI instances of various scales. HSAM and TAM semantically align and merge the
+extracted features and query embeddings in the hierarchical spatial and task perspectives in turn. In the meanwhile, a novel training
+strategy Stage-wise Training Strategy is designed to reduce the training pressure caused by overly complex tasks done by FGAHOI.
+In addition, we propose two ways to measure the difficulty of HOI detection and a novel dataset, 𝑖.𝑒., HOI-SDC for the two challenges
+(Uneven Distributed Area in Human-Object Pairs and Long Distance Visual Modeling of Human-Object Pairs) of HOI instances
+detection. Experiments are conducted on three benchmarks: HICO-DET, HOI-SDC and V-COCO. Our model outperforms the
+state-of-the-art HOI detection methods, and the extensive ablations reveal the merits of our proposed contribution. The code is
+available at https://github.com/xiaomabufei/FGAHOI.
+Index Terms—Human-Object Interaction, FGAHOI, Fine-Grained Anchors, Noisy Background, Semantically Aligning.
+!
+1
+INTRODUCTION
+H
+UMAN-Object
+interaction
+(HOI)
+detection,
+as
+a
+downstream task of object detection [1], [2], [3], [4],
+[5], has recently received increasing attention due to its
+great application potential. For successful HOI detection, it
+needs to have the ability to understand human activities
+which are abstracted as a set of <human, object, action>
+triplets in this task, requiring a much deeper understanding
+for the semantic information of visual scenes. Without HOI
+detection, machines can only interpret images as collections
+of object bounding boxes, i.e., AI systems can only pick up
+information such as ’A man is on the bike’ or ’A bike is in
+the corner’, but not ’A man rides a bike’.
+Spanning the past and the present, the existing HOI
+detection approaches [6], [7], [8], [9], [10], [11], [12], [13],
+[14], [15], [16], [17], [18], [19], [20], [21] tend to fall into
+two categories, namely two-stage and one-stage methods.
+Conventional two-stage methods [7], [8], [10], [12], [13],
+[14], [18], [20], [22], [23], [24], [25], as an intuitive approach,
+detect human and object instances by leveraging the off-the-
+•
+Shuailei Ma, Yuefeng Wang are with College of Information Science and
+Engineering, Northeastern University, Shenyang, China, 110819.
+E-mail: {xiaomabufei, wangyuefeng0203} @gmail.com
+•
+Shanze Wang is with Changsha Hisense Intelligent System Research
+Institute Co., Ltd. and Information Technology R&D Innovation Center of
+Peking University, Shaoxing, China.
+E-mail: szgg0099@gmail.com
+•
+Ying Wei is the corresponding author, with College of Information Science
+and Engineering, Northeastern University, Shenyang, China, 110819.
+E-mail: weiying@ise.neu.edu.cn
+Manuscript received October 26, 2022; revised January 10, 2023.
+FGAHOI
+Low Level
+Middle Level
+High Level
+Fine-Grained 
+Anchors
+Attention Weights
+Fig. 1: FGAHOI leverages the query embeddings and multi-
+scale features to generate fine-grained anchors and the
+corresponding weights for HOI instances of diverse scales.
+Then, they guide the decoder to aid key semantic infor-
+mation of HOI instances to the content embeddings and
+translate the content embeddings to HOI embeddings for
+predicting all elements of the HOI instances.
+shelf object detector [1], [3], [4], utilizing the visual features
+extracted from the located areas to recognize action classes.
+To fully leverage the visual features, several methods [7],
+[10], [14], [20], [22], [23], [24], [25] separately extract vi-
+sual features of human-object pairs and spatial information
+from the located area in a multi-stream architecture, fusing
+them in a post-fusion strategy. In the meanwhile, several
+approaches [8], [10], [20], [23], [24] employ the existing pose
+arXiv:2301.04019v1  [cs.CV]  8 Jan 2023
+
+JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 10, JANUARY 2023
+2
+estimation methods, such as [26], [27], [28] to extract pose
+information and fuse it with other features to predict the
+action class. In addition, some works [8], [12], [13], [18],
+[29] leverage the graph neural network to extract complex
+semantic relationship between humans and objects. How-
+ever, the difficulties encountered in the two-stage approach
+lie mainly in the effective fusion of human-object pairs and
+complex semantic information. Besides, owing to the limita-
+tions of the fixed detector and some other components (pose
+estimation etc.), the two-stage method can only achieve a
+sub-optimal solution.
+To achieve high efficiency, one-stage approaches [6], [9],
+[11], [15], [17], [21], [30], [31] which utilize interaction points
+between the human-object pairs to simultaneously predict
+human and object offset vectors and action classes, are
+proposed to detect human-object pairs and recognize inter-
+active relationships in parallel. However, when the human
+and object in the image are far apart from each other, these
+methods are disturbed by ambiguous semantic features.
+The one-stage methods do not achieve much attention until
+the appearance of the Detection Transformer (DETR) [32]
+and QPIC [19] applies it for HOI detection. Then, plenty
+of transformer-based works [6], [9], [16], [17], [33] attempt
+to solve the HOI detection with different encoder-decoder
+structures and backbone models.
+In comparison to object instances, HOI instances have
+a greater span of spatial, scale and task. In most HOI
+instances, there is a certain distance between human and
+objects and their scale varies enormously. Compared with
+simple object classification, it is necessary to consider more
+information between human-object pairs rather than the
+features of humans and objects for interaction classification.
+Therefore, the detection is more susceptible to distractions
+from noisy backgrounds. However, most recent works [19],
+[33] use object detection frameworks [32], [34] directly for
+HOI detection by simply adding the interaction classifica-
+tion head, ignoring these problems. Inspired by [34] which
+leverages the reference points to guide the decoding pro-
+cess, we propose to leverage fine-grained anchors to guide
+the detection of HOI instances and protect it from noisy
+backgrounds. To generate fine-grained anchors for kinds
+of HOI instances, it is obviously necessary to consider the
+input image features. There are, however, two inevitable
+challenges that arise as a result of this. 𝑖) it is difficult to
+extract pivotal features from the images which contain noisy
+background information. 𝑖𝑖) how to semantically align and
+merge the extracted features with query embeddings is also
+an open question.
+In this paper, we propose a novel transformer-based
+model for HOI detection, i.e., FGAHOI: Fine-Grained An-
+chors for Human-Object Interaction Detection (as shown in
+Fig.1). FGAHOI leverages the multi-scale sampling mech-
+anism (MSS) to extract pivotal features from images with
+noisy background information for variable HOI instances.
+Based on the sampling strategy and initial anchor gener-
+ated by the corresponding query embedding, MSS could
+extract hierarchical spatial features of human, object and the
+interaction region for each HOI instance. Besides, the hi-
+erarchical spatial-aware (HSAM) and task-aware merging
+mechanism (TAM) are utilized to semantically align and
+merge the extracted features with the query embeddings.
+HSAM merges the extracted features in the hierarchical
+spatial perspective according to the cross-attention between
+the features and the query embeddings. Meanwhile, the
+extracted features are aligned towards the query embed-
+dings, according to the cross-attention weights of the merg-
+ing process. Thereafter, TAM leverages the switches which
+dynamically switch ON and OFF to merge the input features
+and query embeddings in the task perspective.
+According to experiment results, we investigate that it
+is difficult of the end-to-end training approach to allow the
+transformer-based models to achieve optimal performance
+when more complex task requirements are required. In-
+spired by the stage-wise training [35], [36] for LTR [37], we
+propose a novel stage-wise training strategy for FGAHOI.
+During the training process, we add the important compo-
+nents of the model in turn to clarify the training direction
+of the model at each stage, so as to maximize the savings in
+the training cost of the model.
+To the best of our knowledge, there are no measurements
+for the difficulty of detecting HOI instances. We investigate
+that two difficulties lie in the detection of human-object
+pairs, 𝑖.𝑒., Uneven Distributed Area in Human-Object
+Pairs and Long Distance Visual Modeling of Human-
+Object Pairs. In this paper, we propose two measurements
+and a novel dataset (HOI-SDC) for these two challenges.
+HOI-SDC eliminates the influence of other factors (Too few
+training samples of some HOI categories, too tricky interac-
+tion actions, et.al.) on the model training and focuses on the
+model for these two difficult challenges. Our contributions
+can be summarized fourfold:
+•
+We propose a novel transformer-based human-object
+interaction detector (FGAHOI) which leverages input
+features to generate fine-grained anchors for pro-
+tecting the detection of HOI instances from noisy
+backgrounds.
+•
+We propose a novel training strategy where each
+component of the model is trained in turn to clar-
+ify the training direction at each stage, in order to
+maximize the training cost savings.
+•
+We propose two ways to measure the difficulty of
+HOI detection and a dataset, 𝑖.𝑒., HOI-SDC for the
+two challenges (Uneven Distributed Area in Human-
+Object Pairs and Long Distance Visual Modeling of
+Human-Object Pairs) of detecting HOI instances.
+•
+Our extensive experiments on three benchmarks:
+HICO-DET
+[38],
+HOI-SDC
+and
+V-COCO
+[39],
+demonstrate the effectiveness of the proposed FGA-
+HOI. Specifically, FGAHOI outperforms all existing
+state-of-the-art methods by a large margin.
+2
+RELATED WORKS
+Two-stage HOI Detection Approaches: The two-stage HOI
+detection approaches [7], [8], [10], [12], [13], [14], [18], [20],
+[22], [23], [24], [25], [29] employ the off-the-shelf object de-
+tector [1], [3], [4] to localize humans and objects. Afterwards,
+the features of backbone networks inside the human and
+objects regions are cropped. Part of the two-stage meth-
+ods [8], [12], [13], [18], [29] treat the human and objects
+feature as nodes and employ graph neural networks [40]
+
+JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 10, JANUARY 2023
+3
+Encoder
+Content Embeddings
+…
+Initial Anchor
+…
+Positional Encoding
+Human Box
+Object box/Class
+Human Box
+Object box/Class
+Verb Class
+Verb Class
+HOI
+Detection
+Head
+Decoder
+Task-Aware
+Merging 
+Dynamic
+Switch On/Off
+…
+Positional 
+Embeddings
+Multi-Scale 
+Sampling Strategy
+Multi-Scale 
+Features 
+Hierarchical Spatial-Aware 
+Merging 
+Fig. 2: This figure illustrates the overall structure of FGAHOI. FGAHOI utilizes a hierarchical backbone and a deformable
+encoder to extract the semantic features in a multi-scale approach. In the decoding phrase, FGAHOI leverages the multi-
+scale sampling, hierarchical spatial-aware merging and task-aware merging mechanism to align input features with
+query embeddings and assist the generation of fine-grained anchors for the translation of HOI embeddings. At the back
+end of the pipeline, HOI detector leverages the HOI embeddings and initial anchor to predict all elements of the HOI
+instances.
+to predict action classes. The other part of the two-stage
+approach [7], [10], [14], [20], [22], [23], [24], [25] leverages
+multi-stream networks to extract diverse information from
+cropped regions, such as human features, object features,
+spatial information and human pose information. Then,
+the information is fused to predict the action in a post-
+fusion strategy. Two-stage methods mainly concentrate on
+predicting the action class in the second stage. Nevertheless,
+the quality of cropped features from the first stage cannot
+be guaranteed in most cases, so the method cannot achieve
+an optimal solution. More importantly, integrating semantic
+information of human-object pairs requires massive time
+and computing resources.
+One-stage HOI Detection Approaches: The traditional one-
+stage approaches [9], [11], [15], [31] use interaction points
+or union regions to detect human-object pairs and identify
+interactive action classes in parallel. However, these meth-
+ods which and are hampered by distant human-object pairs,
+require a gathering and pairing process. With the creation of
+DETR [32], one-stage approaches have become the current
+mainstream. QPIC [19] converts the object detection head
+of DETR into an interaction detection head to predict HOI
+instance directly. HOITrans [17] combines transformer [41]
+and CNN [42] to straightly predict HOI instances from the
+query embeddings. AS-Net [6] and HOTR [9] each propose a
+two-branch transformer method that consists of an instance
+decoder and an interaction decoder to predict the boxes
+and action classes in parallel. CDN [16] proposes a cascade
+disentangling decoder to decode action classes. QAHOI [33]
+directly combines Swin Transformer [43] and deformable
+DETR [34] to predict HOI instances.
+Anchor-Based Object Detection Transformer: Deformable
+DETR [34] first introduces the reference point concept,
+where the sampling offset is predicted by each reference
+point to perform deformable cross-attention. To facilitate
+extreme region discrimination, Conditional DETR [44] re-
+formulates the attention operation and rebuilt positional
+queries based on reference points. Anchor DETR [45] pro-
+poses to explicitly capitalize on the spatial prior during
+cross-attention and box regression by utilizing a predefined
+2D anchor point [𝑐𝑥, 𝑐𝑦]. DAB-DETR [46] extends such a
+2D concept to a 4D anchor box [𝑐𝑥, 𝑐𝑦, 𝑤, ℎ] and proposed
+to refine it layer-by-layer. SAM-DETR [47] proposes directly
+updating content embeddings by extracting salient points
+from image features. In this paper, we propose a novel
+decoding process for HOI detection. The alignment and fine-
+grained anchor generation is proposed to align the multi-
+scale features with HOI query embeddings and generate
+fine-grained anchors for the diverse HOI instances with
+variable spatial distribution, scales and tasks. Then, the fine-
+grained anchors guide the deformable attention process in
+aiding key information to query embeddings from noisy
+backgrounds.
+3
+PROPOSED METHOD
+In Sec.3.1, we show the overall architecture of FGAHOI.
+Then, we describe the multi-scale feature extractor in Sec.3.2.
+We introduce the multi-scale sampling strategy in Sec.3.3.1.
+The hierarchical spatial-aware, task-aware merging mech-
+anism and the decoding process is proposed in Sec.3.3.2,
+Sec.3.3.3 and Sec.3.3.4, respectively. In Sec.3.4, we present
+the architecture of the HOI detection head. In Sec.3.5, the
+stage-wise training strategy, loss calculation and inference
+process is illustrated.
+3.1
+Overall Architecture
+The overall architecture of our proposed FGAHOI is illus-
+trated in Fig 2. For a given image 𝑥 ∈ R𝐻×𝑊 ×3, FGAHOI
+firstly uses a hierarchical backbone network to extract the
+multi-scale features Z𝑖
+∈ R
+𝐻
+4×2𝑖 × 𝑊
+4×2𝑖 ×2𝑖𝐶𝑠, 𝑖
+= 1, 2, 3. The
+multi-scale features are then projected from dimension C𝑠
+to dimension C𝑑 by using 1×1 convolution. After being
+flattened out, the multi-scale features are concatenated to
+N𝑠 vectors with C𝑑 dimensions. Afterwards, along with
+
+JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 10, JANUARY 2023
+4
+supplementary positional encoding 𝑝 ∈ R𝑁𝑠×𝐶𝑑, the multi-
+scale features are sent into the deformable transformer en-
+coder which consists of a set of stacked deformable encoder
+layers to encode semantic features. The encoded semantic
+features 𝑀 ∈ R𝑁𝑠×𝐶𝑑 are then acquired. In the decoding
+process, the content 𝐶 and positional 𝑃 embeddings are both
+a set of learnable vectors {𝑣𝑖 | 𝑣𝑖 ∈ R𝑐𝑑}𝑁𝑞
+𝑖=1. The positional
+embeddings 𝑃 first generate the initial anchor 𝐴 ∈ R𝑁𝑞×2
+according to a linear layer. The positional 𝑃, content 𝐶
+embeddings, inital anchor 𝐴 and encoded features 𝑀 are
+simultaneously sent into the decoder 𝐹𝑑𝑒𝑐𝑜𝑑𝑒𝑟 (·, ·, ·, ·) which
+is a set of stacked decoder layers. In every decoder layer,
+the initial anchor first leverages the multi-scale sampling
+strategy to sample the multi-scale features corresponding
+to the content embeddings. The sampled features assist
+the generation of fine-grained anchors and corresponding
+attention weights through the hierarchical spatial-aware
+and task-aware merging mechanism. The HOI embeddings
+𝐻 = {ℎ𝑖 | ℎ𝑖 ∈ R𝑐𝑑}𝑁𝑞
+𝑖=1 are translated from the query embed-
+dings 𝑄 through the fine-grained anchors, attention weights
+and the deformable attention. The HOI embeddings 𝐻 are
+acquired as 𝐻 = 𝐹𝑑𝑒𝑐𝑜𝑑𝑒𝑟 (𝑀, 𝑃, 𝐶, 𝐴). Eventually, the HOI
+detector leverages the HOI embeddings 𝐻 and initial anchor
+to predict the HOI instances < 𝑏ℎ, 𝑏𝑜, 𝑐𝑜, 𝑐𝑣 >, where 𝑏ℎ, 𝑏𝑜,
+𝑐𝑜 and 𝑐𝑣 stands for the human box coordinate (𝑥, 𝑦, 𝑤, ℎ),
+object box coordinate, object class and verb class, respec-
+tively.
+3.2
+Multi-Scale Features Extractor
+High-quality visual features are a prerequisite for successful
+HOI detection. For extracting the multi-scale features with
+long-range semantic information, FGAHOI leverages the
+multi-scale feature extractor which consists of a hierarchical
+backbone network and a deformable transformer encoder to
+extract features, the folumation is as Equation.1:
+𝑀 = 𝐹𝑒𝑛𝑐𝑜𝑑𝑒𝑟 (𝐹𝑓 𝑙𝑎𝑡𝑡𝑒𝑛(𝜙(𝑥)), 𝑝, 𝑠, 𝑟, 𝑙)
+∈ R𝑁𝑠×𝐶𝑑,
+(1)
+where 𝐹𝑒𝑛𝑐𝑜𝑑𝑒𝑟 (·), 𝐹𝑓 𝑙𝑎𝑡𝑡𝑒𝑛(·) and 𝜙(·) denotes the encoder,
+flatten operation and backbone network, respectively. 𝑝 is
+the position encoding, 𝑠 is the spatial shape of the multi-
+scale features, 𝑟 stands for the valid ratios and 𝑙 represents
+the level index corresponding the multi-scale features. The
+hierarchical backbone network is flexible and can be com-
+posed of any convolutional neural network [42], [48], [49],
+[50] and transformer backbone network [43], [51], [52], [53],
+[54], [55], [56], [57]. However, CNN is poor at capturing
+non-local semantic features like the relationships between
+humans and objects. In this paper, we mainly use Swin
+Transformer tiny and large version [43] to enhance the
+ability of feature extractor for extracting long-range features.
+3.3
+Why FGAHOI Decodes Better?
+During the decoding process, the fine-grained anchors can
+be regarded as a positional prior to let decoder focus on
+the region of interest, directly guiding the decoder to aid
+semantic information to the content embeddings which are
+used to predict all elements of the HOI instances. Therefore,
+fine-grained anchors play the following two crucial roles in
+HOI detection. 𝑖) Fine-grained anchors directly determine
+whether the information gained from input features to
+content embeddings is instance-critical or noisy background
+information. 𝑖𝑖) Fine-grained anchors determine the quality
+of alignment between the query embeddings and multi-
+scale features of input scenarios. Both are crucial factors for
+the quality of decoding results. The existing methods [33],
+[34] directly utilize the query embedding to generate fine-
+grained anchors based on the initial anchor, without consid-
+ering the multi-scale features of the input scenarios and the
+semantic alignment between the query embedding and the
+input features at all. Our FGAHOI proposes a novel fine-
+grained anchors generator which consists of multi-scale
+sampling, hierarchical spatial-aware merging and task-
+aware merging mechanism (as shown in Fig.3). The gen-
+erator adequately leverages the initial anchor, multi-scale
+features and query embeddings for generating suitable fine-
+grained anchors for diverse input scenarios and aligning
+semantic information between different input scenarios and
+query embeddings. The formulation of FGAHOI decoding
+process is as follows:
+𝐻 = Defattn(Task(Hier Spatial({𝑥𝑖
+𝑠}, 𝐶𝑢), 𝐶𝑢), 𝑀, 𝐶𝑢),
+(2)
+where 𝐶𝑢 is the content embeddings updated by the po-
+sitional embeddings, Defattn represents the deformable at-
+tention, 𝑥𝑖
+𝑠 represents the sampled features of the 𝑖-th level
+features. 𝑀 is the encoded input features.
+3.3.1
+Multi-Scale Sampling Mechanism
+The HOI instances contained in the input scenarios usually
+vary in size, where some instances taking up most of the
+area in the input scenarios and others occupying perhaps
+only a few pixels. Our FGAHOI aims at detecting all in-
+stances in the scene, regardless of the size. Therefore, when
+using the initial anchor to sample the multi-scale features,
+for shallow features mainly used to detect instances of small
+size, the sampling strategy only samples a small range of
+features around the initial anchor. In contrast, for deep
+features mainly used to detect instances of large size, the
+sampling strategy samples a large range of features around
+the initial anchor. As shown in Fig.3 (b), in the generator, the
+encoded features are first reshaped to the original shape.
+Based on the initial anchor, generator leverages the sam-
+pling strategy to sample multi-scale features as follows:
+𝑥𝑖
+𝑠 =𝐹𝑠𝑎𝑚𝑝𝑙𝑒( 𝑟𝑒𝑠ℎ𝑎𝑝𝑒(𝑀)𝑖, 𝐴, 𝑠𝑖𝑧𝑒𝑖, 𝑏𝑖𝑙𝑖𝑛𝑒𝑎𝑟 ),
+(3)
+where 𝑠𝑖𝑧𝑒𝑖 (𝑖 = 0, 1, 2) denotes the sampling size of the 𝑖-th
+level features. 𝑀 is the encoded input features. 𝐴 is the ini-
+tial anchor. Inspired by [58], we utilize bilinear interpolation
+in the sampling strategy.
+3.3.2
+Hierarchical Spatial-Aware Merging Mechanism
+In order to better utilize the hierarchical spatial informa-
+tion of sampled features for aligning content embeddings
+with the sampled features, we propose a novel hierarchical
+spatial-aware merging mechanism (HSAM) which utilizes
+the content embeddings to extract hierarchical spatial in-
+formation and merge the sampled features, as shown in
+Fig.3 (c). The content embeddings are first updated by the
+positional embeddings and multi-head self-attention mech-
+anism as follows:
+𝐶𝑢 = 𝐶 + 𝐹MHA
+�
+(𝐶 + 𝑃)𝑊𝑞, (𝐶 + 𝑃)𝑊 𝑘, 𝐶𝑊 𝑣�
+,
+(4)
+
+JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 10, JANUARY 2023
+5
+Multi-Scale Sampling Strategy
+Src Shape
+Anchor
+Sampling
+Low
+High 
+Middle
+Positional 
+Embeddings
+Multi-Head
+Self-Attention
+Add & Norm
+Deformable
+Multi-Head
+Cross-Attention
+FFN
+Add & Norm
+Add & Norm
+Encoded Multi-Scale Features
+Alignment &
+Fine-Grained
+Anchor Generation
+Query
+Embeddings
+(������������ , ������������ )
+V
+K
+Q
+V
+Fined-grained 
+Anchors
+Initial Anchor
+Attention
+Weights
+0
+Updated
+Content 
+Embeddings
+Fine-grained 
+Anchors
+Corresponding
+Attention Weights
+Linear
+Linear
+SoftMax
+Generation of Fine-Grained Anchors
+Reshape
+Reshape
+（b）
+（a）
+（d）
+（e）
+Hierarchical Spatial-Aware 
+Merging Mechanism
+Middle
+Multi-Head 
+Attention
+Flatten
+Low
+High 
+Multi-Head Attention
+CAT
+Positional 
+Embeddings
+Content
+Embeddings
+…
+Task-Aware Merging Mechanism
+Dynamic
+Switch On/Off
+Cross-Attn[(
+,
+]
+Linear
+Linear
+RELU
+Normalize
+Updated
+Content 
+Embeddings
+,
+)
+（c）
+Middle
+Low
+High 
+Merge 
+Features
+Fig. 3: The architecture of FGAHOI’s decoder. (a) Illustration of FGAHOI’s decoding process. (b) Illustration of Multi-
+scale sampling mechanism. (c) Illustration of Hierarchical spatial-aware merging mechanism. (d) Illustration of Task-aware
+merging mechanism. (e) Generation process of fine-grained anchors and the corresponding attention weights.
+where 𝑊𝑞, 𝑊 𝑘 and 𝑊 𝑣 denotes the parameter matrices
+for query, key and value in the self-attention mechanism,
+respectively. 𝐹MHA(·) is the multi-head attention mechanism.
+𝐶 and 𝑃 represents the content and position embeddings,
+respectively. Then, the updated content embeddings are
+leveraged to merge the sampled features, the formulation
+is as follows:
+𝑥𝑖
+𝑚 = 𝐹concat
+�head1, . . . , headNH
+� 𝑊𝑂,
+where headn = Softmax
+�
+(𝐶𝑢𝑊𝑞
+n ) · (𝑥𝑖
+𝑠𝑊 𝑘
+n )𝑇
+√𝑑𝑘
+�
+(𝑥𝑖
+𝑠𝑊 𝑣
+n ).
+(5)
+Where 𝑥𝑖
+𝑚 represents the merged features of the 𝑖-th level
+sampled features. 𝐶𝑢 is the content embeddings updated
+by the positional embeddings. 𝑊𝑂 denotes the parameter
+matrices for multi-head concatenation. 𝑊𝑞
+𝑛 , 𝑊 𝑘
+𝑛 and 𝑊 𝑣
+𝑛
+denote the parameter matrices for query, key and value of
+n-th attention head. 𝐹concat is the concatenating operation.
+𝑑𝑘 =
+𝑁ℎ𝑑
+𝑁𝐻 , 𝑁ℎ𝑑 is the hidden dimensions, and 𝑁𝐻 is the
+number of attention head.
+Following the merging of the sampled features at each
+scale based on spatial information, the merged features at
+each scale are first concatenated together as follows:
+𝑋𝑚 = 𝐹concat({𝑥𝑖
+𝑚}𝑖=0,1,2) ∈ R𝐵×𝑁𝑞×𝑁𝐿×𝑁ℎ𝑑,
+(6)
+where 𝑁𝐿 is the number of multi-scale, 𝑥𝑖
+𝑚 represents the
+merged features of the 𝑖-th level sampled features, 𝑋𝑚 is the
+concatenated multi-scale features and merged by the scale-
+aware merging mechanism as follows:
+𝑋𝑢 = 𝐹concat (head1, . . . , headh) 𝑊𝑂,
+where headn = Softmax
+�
+(𝐶𝑢𝑊𝑞
+n ) · (𝑋𝑚𝑊 𝑘
+n )𝑇
+√𝑑𝑘
+�
+(𝑋𝑚𝑊 𝑣
+n ).
+(7)
+Where 𝑋𝑢 is the merged multi-scale features for updating
+the content embeddings.
+3.3.3
+Task-Aware Merging Mechanism
+Considering diverse HOI instances, the task-aware merging
+mechanism is proposed to fuse the merged multi-scale
+features and content embeddings and align the content
+embeddings with the merged feature in the task-aware
+perspective, as shown in Fig.3 (e). It leverages the merged
+multi-scale features and content embeddings to generate
+dynamic switch for selecting suitable channel in the merging
+process. Content embedding and multi-scale information
+after fusion are first stitched together, the formulation is as
+follows:
+𝑋 = 𝐹𝑠𝑡𝑎𝑐𝑘 (𝐶𝑢, 𝑋𝑢) ∈ R𝐵×𝑁𝑞×(2×𝑁ℎ𝑑).
+(8)
+Where 𝐶𝑢 is the content embeddings updated by the posi-
+tional embeddings, 𝑋𝑢 is the merged multi-scale features.
+Thereafter, we use cross-attention mechanism to update
+these as follows:
+𝑋𝑠𝑤𝑖𝑡𝑐ℎ = 𝐹concat (head1, . . . , headh) 𝑊𝑂,
+where headn = Softmax
+�
+(𝐶𝑢𝑊𝑞
+n ) · (𝑋𝑊 𝑘
+n )𝑇
+√𝑑𝑘
+�
+(𝑋𝑊 𝑣
+n ).
+(9)
+
+JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 10, JANUARY 2023
+6
+TABLE 1: Instance statistics of two difficulties. We quantify all the instances in the HAKE-HOI [20] dataset according to
+two newly proposed metrics and divide them into ten intervals.
+Dataset
+IMI
+IMI0
+IMI1
+IMI2
+IMI3
+IMI4
+IMI5
+IMI6
+IMI7
+IMI8
+IMI9
+HAKE-HOI
+num𝐴𝑅
+104243
+65499
+44303
+31241
+21982
+11888
+4670
+1818
+598
+168
+num𝐿𝑅
+424
+1243
+1784
+3043
+8668
+70191
+83314
+79427
+34017
+4299
+SDC Train
+num𝐴𝑅
+62526
+30235
+16346
+12013
+10269
+11189
+4223
+1540
+423
+139
+num𝐿𝑅
+177
+515
+874
+1656
+5208
+48798
+38517
+29544
+20265
+3349
+SDC Test
+num𝐴𝑅
+24737
+0
+0
+0
+0
+0
+0
+0
+0
+0
+num𝐿𝑅
+153
+415
+464
+834
+2704
+20167
+0
+0
+0
+0
+Then, the generated information is utilized to gain the
+dynamic switch for merging, the formulation is as follows:
+𝑆𝑤𝑖𝑡𝑐ℎ𝛾 = 𝐹𝑛𝑜𝑟𝑚𝑎𝑙𝑖𝑧𝑒(𝐹𝑚𝑙𝑝(𝑋𝑠𝑤𝑖𝑡𝑐ℎ))𝛾 ∈ R𝐵×𝑁𝑞×2×2,
+(10)
+where 𝑆𝑤𝑖𝑡𝑐ℎ𝛾 is the dynamic switch for 𝛾-th dimension
+of the merged features. 𝐹ℎ𝑠𝑖𝑔𝑚𝑜𝑖𝑑(·) and 𝐹𝑚𝑙𝑝(·) denote the
+hard sigmoid and feed forward network which consists of
+two linear layers and one Relu activation layer, respectively.
+Inspired by [59], the merging mechanism is designed as
+follows:
+𝑈𝛾 = 𝐹𝑀 𝑎𝑥{𝑆𝑤𝑖𝑡𝑐ℎ𝛾
+𝑖,0 ⊙ 𝑋𝛾
+𝑢 + 𝑆𝑤𝑖𝑡𝑐ℎ𝛾
+𝑖,1}𝑖=0,1 + 𝐶𝛾
+𝑢 ,
+(11)
+where 𝑈𝛾 is 𝛾-th features of content embeddings updated by
+the merged multi-scale features. 𝐹𝑀 𝑎𝑥 is the max operation.
+…
+Linear
+Linear
+MLP
+MLP
+Object Class
+Action Class
+Human Box
+Object Box
+HOI Instances
+<Human/Object Boxes, Object 
+Class, Action Class>
+Initial Anchor
+HOI
+Embeddings
+Fig. 4: The prediction process of the HOI detection head. See
+sec 3.4 for more details.
+3.3.4
+Decoding with Fine-Grained Anchor
+As shown in Fig.3 (e), the updated content embeddings
+are used to generate fine-grained anchors and attention
+weights. According to the linear layer, reshape operation
+and softmax function, the formulation is as follows:
+A = 𝐹𝑙𝑖𝑛&𝑟𝑒𝑠(𝑈) ∈ R𝐵×𝑁𝑞×𝑁𝐻 ×𝑁𝐿×𝑁A×2,
+(12)
+W = 𝐹𝑙𝑖𝑛&𝑟𝑒𝑠&𝑠𝑜 𝑓 𝑡 (𝑈) ∈ R𝐵×𝑁𝑞×𝑁𝐻 ×𝑁𝐿×𝑁A,
+(13)
+As shown in Fig.3 (a), the fine-grained anchors and at-
+tention weights are utilized to aid semantic features from
+the encoded features of the input scenarios to the content
+embeddings, the formulation is as follows:
+P𝑞 =
+𝑁𝐻
+∑︁
+𝑛=1
+𝑾𝑛
+� 𝑁𝐿
+∑︁
+𝑙=1
+𝑁A
+∑︁
+𝑘=1
+W𝑙
+𝑛𝑞𝑘 · 𝑾′
+𝑛𝒙𝒍 �
+A𝑙
+𝑛𝑞𝑘
+��
+,
+(14)
+where P𝑞 is the extracted semantic information used for
+translating 𝑞-th content to HOI embeddings. A𝑙
+𝑛𝑞𝑘 and
+W𝑙
+𝑛𝑞𝑘 represent the 𝑘-th fine-grained anchors and corre-
+sponding attention weights of the 𝑛-th attention head for
+the 𝑞-th query embedding. Both 𝑊𝑛 and 𝑊 ′
+𝑛 are parameter
+matrices of the 𝑛-th attention head. 𝑁A is the number of
+fine-grained anchors of each scale in one attention head.
+3.4
+HOI Detection Head
+FGAHOI leverages a simple HOI detection head to predict
+all elements of HOI instances. As shown in Fig.4, the detec-
+tion head utilizes the HOI embeddings and the initial anchor
+to localize the human and object boxes. In this process, each
+initial anchor acts as the base point for the bounding boxes
+of the corresponding pair of a human and an object, the
+formulation is as follows:
+𝑏ℎ = 𝐹𝑚𝑙𝑝(𝐻)[· · · , : 2] + 𝑖𝑛𝑖𝑡𝑖𝑎𝑙 𝑎𝑛𝑐ℎ𝑜𝑟
+∈ R𝑁𝑞×4,
+(15)
+𝑏𝑜 = 𝐹𝑚𝑙𝑝(𝐻)[· · · , : 2] + 𝑖𝑛𝑖𝑡𝑖𝑎𝑙 𝑎𝑛𝑐ℎ𝑜𝑟
+∈ R𝑁𝑞×4,
+(16)
+𝑐𝑜 = 𝐹𝑙𝑖𝑛𝑒𝑎𝑟 (𝐻)
+∈ R𝑁𝑞×𝑛𝑢𝑚𝑜,
+(17)
+𝑐𝑣 = 𝐹𝑙𝑖𝑛𝑒𝑎𝑟 (𝐻)
+∈ R𝑁𝑞×𝑛𝑢𝑚𝑣,
+(18)
+where 𝐹𝑚𝑙𝑝 denotes the feed forward network consists of
+three linear layers and three relu activation layers. 𝐹𝑙𝑖𝑛𝑒𝑎𝑟
+stands for the linear layer. 𝑛𝑢𝑚𝑜 and 𝑛𝑢𝑚𝑣 are the number
+of object and action classes, respectively. 𝐻 denotes the HOI
+embeddings.
+3.5
+Training and Inference
+3.5.1
+Stage-wise Training
+Inspired by the stage-wise training approach [35], [36] which
+decouples feature learning and classifier learning into two
+independent stages for LTR [37], we propose a novel stage-
+wise training strategy for FGAHOI. We start by training
+the base network (FGAHOI without any merging mecha-
+nism) in an end-to-end manner. We then add the merging
+mechanism in turn to the trained base network for another
+short period of training. In this phrase, the parameters
+of the trained base network are leveraged as pretrained
+parameters and no parameters are fixed during the training
+process.
+
+JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 10, JANUARY 2023
+7
+ ride, fly, sit_on, exit, 
+direct airplane
+ride, straddle, run, 
+hold,  race horse 
+lasso cow
+carry handbag
+ wear  backpack
+hold, stand_under umbrella 
+ ride, race, run
+straddle, hold horse
+fly, pull 
+kite 
+sail, ride, sit_on, 
+stand_on, drive boat
+race, turn, ride, sit on, 
+straddle, hold motorcycle
+wear tie 
+scratch, walk, 
+pet, train  dog      
+ride, sit on,
+drive, board bus
+carry, wear, hold  
+backpack        
+serve, hit sports_ball 
+swing tennis_racket  
+direct, inspect, ride, 
+sit on, fly  airplane
+type on, read, 
+hold laptop
+ sit on  couch
+brush_with, hold 
+toothbrush 
+kick, block, hit, 
+inspect, dribble  
+sports_ball 
+stand_on, ride, jump,  
+hold skateboard
+ ride, fly, sit_on, exit, 
+direct airplane
+ride, straddle, run, 
+hold,  race horse 
+lasso cow
+carry handbag
+ wear  backpack
+hold, stand_under umbrella 
+ ride, race, run
+straddle, hold horse
+fly, pull 
+kite 
+sail, ride, sit_on, 
+stand_on, drive boat
+race, turn, ride, sit on, 
+straddle, hold motorcycle
+wear tie 
+scratch, walk, 
+pet, train  dog      
+ride, sit on,
+drive, board bus
+carry, wear, hold  
+backpack        
+serve, hit sports_ball 
+swing tennis_racket  
+direct, inspect, ride, 
+sit on, fly  airplane
+type on, read, 
+hold laptop
+ sit on  couch
+brush_with, hold 
+toothbrush 
+kick, block, hit, 
+inspect, dribble  
+sports_ball 
+stand_on, ride, jump,  
+hold skateboard
+Fig. 5: Visualization of HOI detection. Humans and objects are represented by pink and blue bounding boxes respectively,
+and interactions are marked by grey lines linking the box centers. Kindly refer to Sec. 5.6.1 for more details.
+(a)
+(b)
+(c)
+catch sport ball
+watch 
+bird
+kick 
+sports ball
+hit sport 
+ball
+fly kite
+hit sport 
+ball
+wear tie
+swing 
+tennis_racket   
+sit_on 
+toilet
+hold 
+surfboard
+ride skateboard
+ride skateboard
+carry surfboard
+ride surfboard
+ride surfboard
+ride surfboard
+ride surfboard
+ride surfboard
+flip 
+skateboard
+catch sport ball
+watch 
+bird
+kick 
+sports ball
+hit sport 
+ball
+fly kite
+hit sport 
+ball
+wear tie
+swing 
+tennis_racket   
+sit_on 
+toilet
+hold 
+surfboard
+ride skateboard
+carry surfboard
+ride surfboard
+ride surfboard
+flip 
+skateboard
+(a)
+(b)
+(c)
+catch sport ball
+watch 
+bird
+kick 
+sports ball
+hit sport 
+ball
+fly kite
+hit sport 
+ball
+wear tie
+swing 
+tennis_racket   
+sit_on 
+toilet
+hold 
+surfboard
+ride skateboard
+carry surfboard
+ride surfboard
+ride surfboard
+flip 
+skateboard
+Fig. 6: (a) illustrates the excellent long-range visual mod-
+elling capabilities. (b) demonstrates remarkable robustness.
+(c) shows the superior capabilities for identifying small HOI
+instances. Kindly refer to Sec. 5.6.1 for more details.
+3.5.2
+Loss Calculation
+Inspired by the set-based training process of HOI-Trans
+[17], QPIC [19], CDN [16] and QAHOI [33], we first use
+the bipartite matching with the Hungarian algorithm to
+match each ground truth with its best-matching prediction.
+For subsequent back-propagation, a loss is then established
+between the matched predictions and the matching ground
+truths. The folumation is as follows:
+𝐿 = 𝜆𝑜𝐿𝑜
+𝑐 + 𝜆𝑣 𝐿𝑣
+𝑐 +
+∑︁
+𝑘 ∈(ℎ,𝑜)
+�
+𝜆𝑏𝐿𝑘
+𝑏 + 𝜆𝐺𝐼𝑜𝑈 𝐿𝑘
+𝐺𝐼𝑜𝑈
+�
+,
+(19)
+where 𝐿𝑜
+𝑐 and 𝐿𝑣
+𝑐 represent the object class and action class
+loss, respectively. We utilize the modified focal loss function
+[60] and sigmoid focal loss function [61] for 𝐿𝑣
+𝑐 and 𝐿𝑜
+𝑐,
+respectively. 𝐿𝑏 is the box regression loss and consists of the
+𝐿1 Loss. 𝐿𝐺𝐼𝑂𝑈 denotes the intersection-over-union loss, the
+same as the function in QPIC [19]. 𝜆𝑜, 𝜆𝑣, 𝜆𝑏 and 𝜆𝐺𝐼𝑜𝑈 are
+the hyper parameters for adjusting the weights of each loss.
+3.5.3
+Inference
+The inference process is to composite the output of the HOI
+detection head to form HOI triplets. Formally, the 𝑖-th out-
+put prediction is generated as < 𝑏ℎ
+𝑖 , 𝑏𝑜
+𝑖 , 𝑎𝑟𝑔𝑚𝑎𝑥𝑘𝑐ℎ𝑜𝑖
+𝑖
+(𝑘) >.
+The HOI triplet score 𝑐ℎ𝑜𝑖
+𝑖
+combined by the scores of action
+𝑐𝑣
+𝑖 and object 𝑐𝑜
+𝑖 classification, formularized as 𝑐ℎ𝑜𝑖
+𝑖
+= 𝑐𝑣
+𝑖 · 𝑐𝑜
+𝑖 .
+4
+PROPOSED DATASET
+There are two main difficulties existing with human-object
+pairs. 𝑖) Uneven size distribution of human and objects in
+human-object pairs. 𝑖𝑖) Excessive distance between person
+and object in human-object pairs. To the best of our knowl-
+edge, there are no relevant metrics to measure these two
+difficulties. In this paper, we propose two metrics 𝐴𝑅 and
+𝐿𝑅 for measuring these two difficulties. Then two novel
+challenges corresponding to these two difficulties are pro-
+posed. In addition, we propose a novel Set for these Double
+Challenges (HOI-SDC). The data is selected from HAKE-
+HOI [20] which is re-split from HAKE [62] and provides
+110K+ images. HAKE-HOI has 117 action classes, 80 object
+classes and 520 HOI categories.
+
+CB福CREERSBK2
+M
+WITDBWEJOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 10, JANUARY 2023
+8
+FGAHOI
+QAHOI
+FGAHOI
+QAHOI
+FGAHOI
+QAHOI
+Fine-Grained
+Anchors #1
+Fine-Grained
+Anchors #2
+Fine-Grained
+Anchors #3
+Fine-Grained
+Anchors #4
+Fine-Grained
+Anchors #5
+Fine-Grained
+Anchors #6
+Fine-Grained
+Anchors #7
+Fine-Grained
+Anchors #8
+HOI
+Instance
+Hold 
+Sport Ball
+Ride 
+Motorcycle
+Fly Kite
+Fig. 7: Comparison of fine-grained anchors between FGAHOI and QAHOI. We visualize the fine-grained anchors
+corresponding to all attention heads and the corresponding attention weights, where the shades of colors correspond
+to the magnitude of the weights. Obviously, FGAHOI is more accurate in focusing on humans, objects and interaction
+areas. Kindly refer to Sec. 5.6.2 for more details.
+4.1
+HOI-UDA
+We propose a novel measurement for the challenge of
+Uneven Distributed Area in Human-Object Pairs, the
+formulation is as follow:
+𝐴𝑅 = 𝐴𝑟𝑒𝑎ℎ · 𝐴𝑟𝑒𝑎𝑜
+𝐴𝑟𝑒𝑎2
+ℎ𝑜𝑖
+,
+(20)
+where 𝐴𝑟𝑒𝑎ℎ, 𝐴𝑟𝑒𝑎𝑜 and 𝐴𝑟𝑒𝑎ℎ𝑜𝑖 denote the area of human,
+object and HOI instances, respectively (as shown in Fig.8
+(a)). We quantify all the instances in the HAKE-HOI into ten
+intervals and count the number of instances of each interval
+in the second and fifth row of Table.1. To better evaluate the
+ability of the model to detect HOI for human-object pairs
+with uneven distributed areas, we specially select 24737
+HOI instances of IMIUDA
+0
+in testing set.
+4.2
+HOI-LDVM
+A novel measurement for the challenge of Long Distance
+Visual Modeling of Human-Object Pairs is proposed in
+Eq.21.
+𝐿𝑅 = 𝐿ℎ + 𝐿𝑜
+𝐿ℎ𝑜𝑖
+,
+(21)
+where 𝐿ℎ, 𝐿𝑜 and 𝐿ℎ𝑜𝑖 denote the size we define of human,
+object and HOI instances, respectively (as shown in Fig.8
+(b)). The instances are quantified in the third and sixth row
+of Table.1. To better evaluate the ability of the model to de-
+tect HOI for human-object pairs with with long distance, we
+specially select 24737 HOI instances of IMILDVM
+0
+∼ IMILDVM
+6
+in testing set.
+4.3
+HOI-SDC
+In order to avoid the training process of the model being
+influenced by a portion of HOI classes with a very small
+number of instances, we remove some of the HOI classes
+containing a very small number of instances and HOI
+classes with no interaction from the training Set for the
+Double Challenge. Finally, there are total 321 HOI classes,
+
+JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 10, JANUARY 2023
+9
+TABLE 2: Performance comparison with the state-of-the-art methods on the HICO-DET dataset. ’V’, ’S’, ’P’ and ’L’ represent
+the visual feature, spatial feature, human pose feature and language feature respectively. Fine-tuned Detection means the
+parameter of the model is pre-trained on the MS-COCO dataset. Backbone with ’*’ and ’+’ means that they are pre-trained
+on ImageNet-22K with 384×384 input resolution. QAHOI(R) represents that the results are reproduced on the same machine
+with our model. Kindly refer to Sec. 5.4.1 for more details.
+Architecture
+Method
+Backbone
+Fine-tuned
+Feature
+Default (↑)
+Known Object (↑)
+Full
+Rare
+Non-Rare
+Full
+Rare
+Non-Rare
+Two-Stage Methods
+Multi-stream
+No-Frill [23]
+ResNet-152
+
+A+S+P
+17.18
+12.17
+18.08
+-
+-
+-
+PMFNet [24]
+ResNet-50-FPN
+
+A+S
+17.46
+15.65
+18.00
+20.34
+17.47
+21.20
+ACP [25]
+ResNet-101
+
+A+S+L
+21.96
+16.43
+23.62
+-
+-
+-
+PD-Net [10]
+ResNet-152
+
+A+S+P+L
+22.37
+17.61
+23.79
+26.86
+21.70
+28.44
+VCL [7]
+ResNet-50
+
+A+S
+23.63
+17.21
+25.55
+25.98
+19.12
+28.03
+Graph-Based
+RPNN [8]
+ResNet-50
+
+A+P
+17.35
+12.78
+18.71
+-
+-
+-
+VSGNet [13]
+ResNet-152
+
+A+S
+19.80
+16.05
+20.91
+-
+-
+-
+DRG [12]
+ResNet-50-FPN
+
+A+S+L
+24.53
+19.47
+26.04
+27.98
+23.14
+29.43
+SCG [18]
+ResNet-50-FPN
+
+A+S
+31.33
+24.72
+33.31
+34.37
+27.18
+36.50
+One-Stage Methods
+Interaction points
+IP-Net [15]
+ResNet-50-FPN
+
+A
+19.56
+12.79
+21.58
+22.05
+15.77
+23.92
+PPDM [31]
+Hourglass-104
+
+A
+21.73
+13.78
+24.10
+24.58
+16.65
+26.84
+GGNet [11]
+Hourglass-104
+
+A
+23.47
+16.48
+25.60
+27.36
+20.23
+29.48
+Transformer-Based
+HOITrans [17]
+ResNet-101
+
+A
+26.60
+19.15
+28.54
+29.1
+20.98
+31.57
+HOTR [9]
+ResNet-50
+
+A
+23.46
+16.21
+25.65
+-
+-
+-
+ResNet-50
+
+A
+25.10
+17.34
+27.42
+-
+-
+-
+AS-Net [6]
+ResNet-50
+
+A
+24.40
+22.39
+25.01
+27.41
+25.44
+28.00
+ResNet-50
+
+A
+28.87
+24.25
+30.25
+31.74
+27.07
+33.14
+QPIC [19]
+ResNet-50
+
+A
+29.07
+21.85
+31.23
+31.68
+24.14
+33.93
+ResNet-50
+
+A
+24.21
+17.51
+26.21
+-
+-
+-
+QAHOI [33]
+Swin-Tiny
+
+A
+28.47
+22.44
+30.27
+30.99
+24.83
+32.84
+Swin-Large∗
++
+
+A
+35.78
+29.80
+37.56
+37.59
+31.66
+39.36
+QAHOI (R)
+Swin-Tiny
+
+A
+27.67
+20.22
+29.69
+30.06
+22.95
+32.18
+Swin-Large∗
++
+
+A
+35.43
+29.22
+37.29
+37.23
+31.01
+39.09
+FGAHOI
+Swin-Tiny
+
+A
+29.94
+22.24
+32.24
+32.48
+24.16
+34.97
+Swin-Large∗
++
+
+A
+37.18
+30.71
+39.11
+38.93
+31.93
+41.02
+74 object classes and 93 action classes. The training and
+testing set contain 37,155 and 9,666 images, respectively. The
+detailed distribution of HOI instances is shown in Table.1.
+(b)
+(a)
+������������������������������������������������������������
+������������������������������������������������������������
+������������������������������������������������������������������������������������
+������������������������
+������������������������
+������������������������������������������������
+Fig. 8: Proposed metrics for the difficulties existing with HOI
+instances. (a) Metric for uneven size distribution of humans
+and objects. (b) Metric for excessive distance between person
+and object. Kindly refer to Sec. 4.1 and 4.2 for more details.
+5
+EXPERIMENTS
+5.1
+Dataset
+Experiments are conducted on three HOI datasets: HICO-
+DET [38], V-COCO [39] and HOI-SDC dataset
+HICO-DET [38] has 80 object classes, 117 action classes
+and 600 HOI classes. HICO-DET offers 47,776 images with
+TABLE 3: Performance comparison with the state-of-the-art
+methods on the HOI-SDC dataset. Kindly refer to Sec. 5.4.2
+for more details.
+Dataset
+Backbone
+Method
+mAProle (↑)
+HOI-SDC
+Swin-Tiny
+QAHOI
+19.55
+Swin-Tiny
+Baseline
+21.18
+Swin-Tiny
++HSAM
+21.91
+Swin-Tiny
++TAM
+21.84
+Swin-Tiny
+FGAHOI
+22.25
+151,276 HOI instances, including 38,118 images with 117,871
+annotated instances of human-object pairs in the training set
+and 9658 images with 33,405 annotated instances of human-
+object pairs in the testing set. According to the number
+of these HOI classes, the 600 HOI classes in the dataset
+are grouped into three categories: Full (all HOI classes),
+Rare (138 classes with fewer than ten instances) and Non-
+Rare (462 classes with more than ten instances). Following
+HICO [63], we consider two different evaluation settings
+(the results are shown in Table.2: (1) Known object settings:
+For each HOI category (such as ’flying a kite’), the detection
+is only evaluated on the images that contain the target object
+category (such as ’kite’). The difficulty lies in the local-
+
+JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 10, JANUARY 2023
+10
+TABLE 4: Performance comparison with the state-of-the-art
+methods on the V-COCO dataset. Kindly refer to Sec. 5.4.3
+for more details.
+Method
+AP𝑆1
+role (↑)
+AP𝑆2
+role (↑)
+Two-stage Method
+VSG-Net
+51.8
+57.0
+PD-Net
+52.0
+-
+ACP
+53.2
+-
+One-stage Method
+HOITrans
+52.9
+-
+AS-Net
+53.9
+-
+HOTR
+55.2
+64.4
+DIRV
+56.1
+-
+QAHOI(R-50)
+58.2
+58.7
+FGAHOI(R-50)
+59.0
+59.3
+FGAHOI(Swin-T)
+60.5
+61.2
+ization of HOI (e.g. human-kite pairs) and distinguishing
+the interaction (e.g. ’flying’). (2) Default setting: For each
+HOI category, the detection is evaluated on the whole test
+set, including images containing and without target object
+categories. This is a more challenging setting because we
+also need to distinguish background images (such as images
+without ’kite’).
+V-COCO [39] contains 80 different object classes and
+29 action categories and is developed from the MS-COCO
+dataset, which includes 4,946 images for the test subset,
+2,533 images for the train subset and 2,867 images for the
+validation subset. The objects are divided into two types:
+“object” and “instrument”.
+5.2
+Metric
+Following the standard evaluation [21], [39], we use role
+mean average precious to evaluate the predicted HOI in-
+stances. A detected bounding box is considered a true
+positive for object detection if it overlaps with a ground
+truth bounding box of the same class with an intersection
+greater than union (𝐼𝑂𝑈) greater than 0.5. In HOI detection,
+we need to predict human-object pairs. The human-object
+pairs whose human overlap 𝐼𝑂𝑈ℎ and object overlap 𝐼𝑂𝑈𝑜
+both exceed 0.5, i.e., min (𝐼𝑂𝑈ℎ, 𝐼𝑂𝑈𝑜) > 0.5 are declared
+a true positive (as shown in Fig 9). Specifically, for HICO-
+DET, besides the full set of 600 HOI classes, the role mAP
+over a rare set of 138 HOI classes that have less than 10
+training instances and a non-rare set of the other 462 HOI
+classes are also reported. Furthermore, we report the role
+mAP of two scenarios for V-COCO: scenario 1 includes the
+cases even without any objects (for the four action categories
+of body motions), while scenario 2 ignores these cases. For
+HOI-SDC, we report the role mean average precision for the
+full set of 321 HOI classes.
+5.3
+Implementation Details
+The Visual Feature Extractor consists of Swin Transformer
+and a deformable transformer encoder. For Swin-Tiny and
+Swin-Large, the dimensions of the feature maps in the first
+stage are set to 𝐶𝑠 = 96 and 𝐶𝑠 = 192, respectively. We pre-
+train Swin-Tiny on the ImageNet-1k dataset. Swin-Large is
+first pre-trained on the ImageNet-22k dataset and finetuned
+Fig. 9: The human-object pairs with human overlap 𝐼𝑂𝑈ℎ
+and object overlap 𝐼𝑂𝑈𝑜 both exceeding 0.5 are declared as
+true positives. Kindly refer to Sec. 5.2 for more details.
+on the ImageNet-1k dataset. Then the weights are used
+to fine-tune the FGAHOI for the HOI detection task. The
+number of both encoder and decoder layers are set to 6
+(𝑁𝐿𝑎𝑦𝑒𝑟 = 6). The number of query embeddings is set to 300
+(𝑁𝑞 = 300), and the hidden dimension of embeddings in the
+transformer is set to 256 (𝐶𝑑 = 256). In the post-processing
+phase, the first 100 HOI instances are selected according
+to object confidence, and we use 𝛿=0.5 to filter the HOI
+instances by the combined 𝐼𝑂𝑈. Following Deformable-
+DETR [34], the AdamW [64] optimizer is used. The learning
+rates of the extractor and the other components are set to
+10−5 and 10−4, respectively. We use 8 RTX 3090 to train the
+model (QAHOI & FGAHOI) with Swin-Tiny. For the model
+with Swin-Large∗
++, we use 16 RTX 3090 to train them. For
+HICO-DET and HOI-SDC, we train the base network for
+150 epochs and carry out the learning rate drop from the
+120th epoch at the first stage of training. For subsequent
+training, we trained the model for 40 epochs, with a learning
+rate drop at the 15th epoch. For V-COCO dataset, we train
+the base network for 90 epochs and drop the learning rate
+from 60th epoch at the first stage of training. For subsequent
+training, we trained the model for 30 epochs, with a learning
+rate drop at the 10th epoch.
+5.4
+Comparison with State-of-the-Arts
+5.4.1
+HICO-DET
+We compare FGAHOI with the state-of-the-art two-stage
+and one-stage methods on the HICO-DET dataset and
+report the results in Table.1. FGAHOI outperforms both
+state-of-the-art methods. In contrast to the state-of-the-art
+two-stage method SCG [18], FGAHOI with Swin-Large*+
+backbone exceeds an especially significant gain of 5.85 mAP
+in default full setting, 5.99 mAP in default rare setting, 5.8
+mAP in default non-rare setting, 4.56 mAP in known object
+full setting, 4.75 mAP in known rare settings and 4.52 mAP
+in known object non-rare setting. For a fair comparison, we
+used the same machine for the reproduction of the QAHOI
+(as shown in Table.2 QAHOI(R)). In comparison to the state-
+of-the-art one-stage method QAHOI, FGAHOI exceeds it
+in all settings for all backbone networks. For Swin-Tiny
+backbone network, FGAHOI exceeds an especially signifi-
+cant gain of 2.27 mAP in default full setting, 2.02 mAP in
+default rare setting, 2.55 mAP in default non-rare setting,
+2.42 mAP in known object full setting, 1.11 mAP in known
+rare settings and 2.79 mAP in known object non-rare setting.
+In addition, FGAHOI with Swin-Large*+ backbone exceeds
+an especially significant gain of 1.75 mAP in default full
+
+OU
+IOU.
+Ground-truth label
+Prediction boxesJOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 10, JANUARY 2023
+11
+TABLE 5: Comparison on ten intervals of the two proposed challenges. We divide the HICO-DET dataset into ten intervals
+based on each of the two challenges and compare the performance of QAHOI and FGAHOI on each interval. Kindly refer
+to Sec. 5.5 for more details.
+Challenge
+Method
+Backbone
+mAProle (↑)
+IMI0
+IMI1
+IMI2
+IMI3
+IMI4
+IMI5
+IMI6
+IMI7
+IMI8
+IMI9
+UDA
+QAHOI
+Swin-Tiny
+16.35
+24.72
+29.24
+34.79
+38.70
+46.21
+53.13
+47.60
+58.66
+60.19
+Swin-Large∗
++
+20.53
+33.58
+41.11
+45.41
+45.44
+56.43
+56.25
+63.53
+71.12
+75.08
+FGAHOI
+Swin-Tiny
+19.74
+29.85
+32.20
+39.46
+40.54
+48.55
+51.32
+46.50
+66.44
+78.17
+Swin-Large∗
++
+23.69
+35.85
+42.51
+50.50
+46.89
+56.95
+56.33
+63.04
+75.70
+79.42
+LDVM
+QAHOI
+Swin-Tiny
+1.33
+4.43
+2.57
+5.00
+8.06
+17.87
+22.81
+29.25
+34.03
+42.29
+Swin-Large∗
++
+0.82
+4.08
+2.56
+7.53
+11.42
+22.87
+30.94
+41.38
+45.31
+60.15
+FGAHOI
+Swin-Tiny
+2.50
+4.15
+3.34
+7.58
+9.83
+21.61
+27.64
+33.07
+38.31
+45.07
+Swin-Large∗
++
+1.44
+4.32
+4.57
+7.81
+11.82
+24.92
+32.50
+43.66
+47.26
+60.55
+TABLE 6: We carefully ablate each of the constituent component of FGAHOI. The middle results denote the role mAP. The
+results in the top right corner represent the performance improvement compared to QAHOI. The results in the bottom
+right corner represent the performance improvement compared to the baseline. Kindly refer to Sec. 5.7.1 for more details.
+Method
+Merging Mechanism
+Default
+Known Object
+Hierarchical Spatial-Aware
+Task-Aware
+Full ↑
+Rare ↑
+Non-Rare ↑
+Full ↑
+Rare ↑
+Non-Rare ↑
+QAHOI
+-
+-
+27.67
+20.22
+29.69
+30.06
+22.95
+32.18
+FGAHOI
+
+
+28.45( +0.78 )
+(
+-
+)
+21.07( +0.85 )
+(
+-
+)
+30.66( +0.97 )
+(
+-
+)
+31.08( +1.02 )
+(
+-
+)
+24.02( +1.01 )
+(
+-
+)
+33.19( +1.07 )
+(
+-
+)
+
+
+29.60( +1.93 )
+( +1.15 )
+22.39( +2.17 )
+( +1.32 )
+31.76( +2.07 )
+( +1.10 )
+32.07( +2.01 )
+( +0.99 )
+24.48( +1.53 )
+( +0.46 )
+34.34( +2.16 )
+( +1.15 )
+
+
+29.32( +1.65 )
+( +0.87 )
+22.34( +2.12 )
+( +1.27 )
+31.41( +1.72 )
+( +0.75)
+31.81( +1.75 )
+( +0.73)
+24.30( +1.35 )
+( +0.28)
+34.05( +1.87 )
+( +0.86)
+
+
+29.94( +2.27 )
+( +1.49 )
+22.24( +2.02 )
+( +1.17 )
+32.24( +2.55 )
+( +1.58 )
+32.48( +2.42 )
+( +1.40 )
+24.16( +1.21 )
+( +0.14 )
+34.97( +2.79 )
+( +1.78 )
+setting, 1.49 mAP in default rare setting, 1.82 mAP in default
+non-rare setting, 1.7 mAP in known object full setting, 0.92
+mAP in known rare settings and 1.93 mAP in known object
+non-rare setting.
+5.4.2
+HOI-SDC
+On the dataset we propose, 𝑖.𝑒., HOI-SDC, we compare
+FGAHOI with QAHOI and ablate each component of FGA-
+HOI (As shown in Table.3). The backbone is set to Swin-Tiny.
+The baseline exceeds QAHOI an especially significant gain
+of 1.63 mAP. HSAM and TAM improve a significant gain
+of 0.73 and 0.66 mAP, respectively. Benefit from the MSS,
+HSAM and TAM, FGAHOI achieve 22.25 mAP on HOI-
+SDC.
+5.4.3
+V-COCO
+We compare FGAHOI with the state-of-the-art methods
+on V-COCO dataset and report the results in Table.4. In
+comparison to QAHOI, FGAHOI only exceeds a small
+margin. This phenomenon is mainly caused by too little
+training data in the dataset. We investigate that FGAHOI
+cannot adequately perform when the training data is not
+sufficient due to the complex task requirements. In addition,
+we investigate the transformer backbone is still superior to
+CNN backbone in this case.
+5.5
+Sensitivity Analysis for UDA and LDVM
+According to the two proposed challenges, we divide the
+HICO-DET into ten intervals. At each intervals, we compare
+FGAHOI and QAHOI with Swin-Tiny, Large∗
++ backbone,
+respectively (As shown in Table.5). When compared be-
+tween each interval of UDA and LDVM, we investigate
+that the difficulty of HOI detection decreases as the interval
+level increases. This justifies the original design. Thus, it
+is imperative to consider ability of the model to address
+these two challenges when proposing novel frameworks for
+HOI detection. In the comparison between FGAHOI and
+QAHOI, the results demonstrate that FGAHOI has better
+capability for uneven distributed area and long distance
+visual modeling of human-object pairs.
+5.6
+Qualitative Analysis
+5.6.1
+Visualized Results
+In order to demonstrate our model, several representative
+HOI predictions are visualized. As shown in Fig.5, our
+model can pinpoint HOI instances from noisy backgrounds
+and excels at detecting various complicated HOIs, including
+one object interacting with different humans, one human
+engaging in multiple interactions with various objects, mul-
+tiple interactions within a single pair, and multiple humans
+engaging in various interactions with various objects. In
+addition, our model is good at long-range visual modelling,
+withstanding the impacts of hostile environments and small
+target identification. Fig.6 (a) illustrates that FGAHOI has
+excellent long-range visual modelling capabilities and can
+accurately identify interactions between human-object pairs
+far from each other. As Fig.6 (b) shows, our model has
+
+JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 10, JANUARY 2023
+12
+text_on cell_phone
+talk_on cell_phone
+eat orange
+open book
+cut with knife
+repair hair_drier
+hold hotdog
+hop_on elephant
+kick sports_ball
+hold cup
+carry handbag
+jump skateboard
+hold cup
+drink with cup
+text_on cell_phone
+talk_on cell_phone
+eat orange
+open book
+cut with knife
+repair hair_drier
+hold hotdog
+hop_on elephant
+kick sports_ball
+hold cup
+carry handbag
+jump skateboard
+hold cup
+drink with cup
+(a)
+(b)
+(c)
+Level_0
+Level_0
+Level_1
+Level_1
+Level_2
+Level_2
+Low
+High 
+Read
+Laptop
+Read
+Laptop
+Low
+High 
+Read
+Laptop
+Exit
+Airplane
+Sit on
+Airplane
+Hold
+Horse
+Ride
+Horse
+Fly Kite
+(a)
+(b)
+(c)
+Level_0
+Level_1
+Level_2
+Low
+High 
+Read
+Laptop
+Exit
+Airplane
+Sit on
+Airplane
+Hold
+Horse
+Ride
+Horse
+Fly Kite
+Fig. 10: Visualization of fine-grained anchors in the decoding phase, Level 0, Level 1 and Level 2 represent the features
+at different scales respectively, the color of the blue dots from light to dark represents the degrees of attention of the fine-
+grained anchors and red dots represent the positions of interest of fine-grained anchors in current scale features. Kindly
+refer to Sec. 5.6.2 for more details.
+outstanding robustness and can effectively resist disruption
+from harsh environmental factors, including blurring, block-
+ing and glare. Fig.6 (c) demonstrates the superior capabili-
+ties of FGAHOI to identify small HOI instances.
+5.6.2
+What do the fine-grained anchors look at?
+As shown in Fig.7, we compare the fine-grained anchors of
+FGAHOI and QAHOI. First two HOI instances (𝑖.𝑒, hold
+sport ball and ride motorcycles) exhibit that FGAHOI could
+better focus on humans, objects and the interaction areas
+rather than noisy backgrounds. The fourth head of FGAHOI
+still focuses on the HOI instance, while QAHOI focuses
+on the background. When detecting instance with a long
+distance between human and object, FGAHOI could focus
+on the right position, while QAHOI is like a chicken with its
+head cut off (As shown in the last HOI instance).
+To exhibit the effectiveness of the fine-grained anchors
+for identifying HOI instances and demonstrate the working
+mechanism of fine-grained anchors, we visualize the fine-
+grained anchors of the feature maps at different scales in
+the decoding phase. In Fig.10 (a), we visualize the instances
+of two different humans and one object. As shown in Fig.10
+(b), even for exactly the same human-object pair, the areas
+of focus vary from one interaction to another. In Fig.10 (c),
+
+IS人
+D2MVAD2MVAD2MVAD2MVAJOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 10, JANUARY 2023
+13
+text_on cell_phone
+talk_on cell_phone
+eat orange
+ride bicycle
+cut with knife
+repair hair_drier
+hold hotdog
+hop_on elephant
+kick sports_ball
+hold cup
+carry handbag
+jump skateboard
+hold cup
+drink with cup
+text_on cell_phone
+talk_on cell_phone
+eat orange
+ride bicycle
+cut with knife
+repair hair_drier
+hold hotdog
+hop_on elephant
+kick sports_ball
+hold cup
+carry handbag
+jump skateboard
+hold cup
+drink with cup
+Fig. 11: Visualization of several representative interactive actions and the corresponding fine-grained anchors. We only
+visualize a single representative interactive action for one human-object pair. Kindly refer to Sec. 5.6.2 for more details.
+we show two instances contain short and long distance
+between humans and objects, respectively. We investigate
+that the fine-grained anchors of low level feature map focus
+on small and fine-grained areas. They play a major role in
+detecting close range and small HOI instances. The fine-
+grained anchors of high level feature maps focus on large
+and coarse-grained areas. It is necessary for detecting long
+distance and large HOI instances.
+In order to explore what the fine-grained anchors focus
+on, we visualize several representative actions in Fig.11.
+Visualization shows that fine-grained anchors could con-
+centrate attention precisely on the location where the in-
+teractive action is generated. For example, the fine-grained
+anchors mainly focus on the hand for ’text on cell phone’,
+the mouth for ’eat orange’ and the ear and the mouth
+for ’talk on cell phone’. For ’kick sports ball’, ’jump skate-
+board’ and ’hop on elephant’, central areas of interest are
+around legs and feet, while fine-grained anchors primarily
+focuses on hands for ’carry handbag’, ’repair hair drier’,
+’hold cup’, ’hold hotdog’ and ’cut with kinfe’.
+5.7
+Ablation Study
+In this subsection, a set of experiments are designed to
+clearly understand the contribution of each of the con-
+stituent components of the proposed methodology: Merg-
+ing mechanism, Multi-Scale Sampling Strategy and Stage-
+wise Training Strategy. We conducted all experiments on
+the HICO-DET dataset.
+5.7.1
+Ablating FGAHOI Components
+To study the contribution of each of the merging mecha-
+nisms in FGAHOI, we design careful ablation experiments
+in Table.6. To ensure a fair comparison, the sampling sizes
+are all set to [1, 3, 5]. For the baseline which does not lever-
+ages the hierarchical spatial-aware and task-aware merging
+mechanism, we use the average and direct summation op-
+eration to merge the sampled features and connect embed-
+dings. For the results in the table, the middle results denote
+the role mAP, the results in the top right corner represent
+the performance improvement compared to QAHOI and the
+results in the bottom right corner represent the performance
+improvement compared to the baseline. In comparison to
+row 1 (QAHOI), row 2 adds the multi-scale sampling
+strategy. The results demonstrate that adding the sampling
+strategy improves the ability of the model to detect HOI
+instances. The row 3 and 4 show that both hierarchical
+spatial-aware and task-aware merging mechanism make
+an essential contribution to the success of FGAHOI. The
+hierarchical spatial-aware merging mechanism, combined
+with the task-aware merging mechanism performs better
+together (row 5) than using either of them separately (row 3
+and 4). Thus, each component in FGAHOI has a critical role
+to play in HOI detection.
+5.7.2
+Sensitivity Analysis On Multi-Scale Sampling Sizes
+Our multi-scale sampling strategy samples multi-scale fea-
+tures according to the pre-determined sampling sizes. We
+vary different sampling sizes to conduct the sensitivity
+
+EJOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 10, JANUARY 2023
+14
+analysis for the sampling strategy and report the results
+in Table.7. We find that the sampling strategy is relatively
+stable. Changes in sampling sizes do not have a significant
+impact on the performance of FGAHOI. However, there is
+still a slight degradation in the performance of FGAHOI as
+the sample size increases. We investigate that as the sample
+size increases, too many background features around the
+fine-grained anchors are sampled, resulting in contamina-
+tion of the sampled features and thus the performance of
+the model suffers. Hence, for validation, we set the sampling
+sizes to [1, 3, 5] in all our experiments, which is a sweet spot
+that balances performance.
+TABLE 7: Comparison between different sampling sizes.
+Smpling Size
+Default
+Known Object
+Full
+Rare
+Non-Rare
+Full
+Rare
+Non-Rare
+[ 1, 3, 5 ]
+29.94
+22.24
+32.24
+32.48
+24.16
+34.97
+[ 3, 5, 7 ]
+29.72
+23.03
+31.72
+32.33
+25.67
+34.30
+[ 5, 7, 9 ]
+29.65
+22.64
+31.74
+32.55
+25.64
+34.62
+5.7.3
+Training Strategies
+As shown in Table.8, we leverage the stage-wise and end-
+to-end training strategy to train FGAHOI, respectively. In
+the end-to-end training strategy, we train FGAHOI for 150
+epochs and the learning rate drop is carried out at the
+120th epoch. The stage-wise training strategy promotes 5.96
+mAP for default full setting, 4.61 for default rare, 6.36 for
+default non-rare, 6.04 for known object full, 4.65 for known
+object rare and 6.46 mAP for known object non-rare setting.
+In comparison to the end-to-end training strategy, we in-
+vestigate that the stage-wise training strategy reduces the
+learning difficulty of the FGAHOI and clarify the learning
+direction of the model by emphasizing it to learn what it
+needs at each stage.
+TABLE 8: Comparison between Stage-Wise and End-to-End
+training approach.
+Training Strategy
+Default
+Known Object
+Full
+Rare
+Non-Rare
+Full
+Rare
+Non-Rare
+Stage-Wise
+29.94
+22.24
+32.24
+32.48
+24.16
+34.97
+End-to-End
+23.98
+17.63
+25.88
+26.44
+19.51
+28.51
+6
+CONCLUSION
+In this paper, we propose a novel transformer-based human-
+object interaction detector (FGAHOI) which leverages the
+input features to generate fine-grained anchors for protect-
+ing the detection of HOI instances from noisy backgrounds.
+We propose a novel training strategy where each component
+of the model is trained sequentially to clarify the training
+direction at each stage, for maximizing the savings of the
+training cost. We propose two novel metrics and a novel
+dataset, 𝑖.𝑒., HOI-SDC for the two challenges (Uneven Dis-
+tributed Area in Human-Object Pairs and Long Distance
+Visual Modeling of Human-Object Pairs) of detecting HOI
+instances. Our extensive experiments on three benchmarks:
+HICO-DET, HOI-SDC and V-COCO, demonstrate the effec-
+tiveness of the proposed FGAHOI. Specifically, FGAHOI
+outperforms all existing state-of-the-art methods by a large
+margin.
+ACKNOWLEDGMENTS
+This work is supported by National Natural Science Foun-
+dation of China (grant No.61871106 and No.61370152),
+Key R&D projects of Liaoning Province, China (grant
+No.2020JH2/10100029), and the Open Project Program
+Foundation of the Key Laboratory of Opto-Electronics In-
+formation Processing, Chinese Academy of Sciences (OEIP-
+O-202002).
+REFERENCES
+[1]
+R. Girshick, “Fast r-cnn,” in Proceedings of the IEEE international
+conference on computer vision, pp. 1440–1448, 2015.
+[2]
+Z. Li and F. Zhou, “Fssd: feature fusion single shot multibox
+detector,” arXiv preprint arXiv:1712.00960, 2017.
+[3]
+S. Ren, K. He, R. Girshick, and J. Sun, “Faster r-cnn: Towards real-
+time object detection with region proposal networks,” Advances in
+neural information processing systems, vol. 28, 2015.
+[4]
+R. Girshick, J. Donahue, T. Darrell, and J. Malik, “Rich feature hier-
+archies for accurate object detection and semantic segmentation,”
+in Proceedings of the IEEE conference on computer vision and pattern
+recognition, pp. 580–587, 2014.
+[5]
+J. Redmon, S. Divvala, R. Girshick, and A. Farhadi, “You only look
+once: Unified, real-time object detection,” in Proceedings of the IEEE
+conference on computer vision and pattern recognition, pp. 779–788,
+2016.
+[6]
+M. Chen, Y. Liao, S. Liu, Z. Chen, F. Wang, and C. Qian, “Refor-
+mulating hoi detection as adaptive set prediction,” in Proceedings of
+the IEEE/CVF Conference on Computer Vision and Pattern Recognition,
+pp. 9004–9013, 2021.
+[7]
+Z. Hou, X. Peng, Y. Qiao, and D. Tao, “Visual compositional learn-
+ing for human-object interaction detection,” in European Conference
+on Computer Vision, pp. 584–600, Springer, 2020.
+[8]
+P. Zhou and M. Chi, “Relation parsing neural network for human-
+object interaction detection,” in Proceedings of the IEEE/CVF Inter-
+national Conference on Computer Vision, pp. 843–851, 2019.
+[9]
+B. Kim, J. Lee, J. Kang, E.-S. Kim, and H. J. Kim, “Hotr: End-
+to-end human-object interaction detection with transformers,” in
+Proceedings of the IEEE/CVF Conference on Computer Vision and
+Pattern Recognition, pp. 74–83, 2021.
+[10] X. Zhong, C. Ding, X. Qu, and D. Tao, “Polysemy deciphering net-
+work for robust human–object interaction detection,” International
+Journal of Computer Vision, vol. 129, no. 6, pp. 1910–1929, 2021.
+[11] X. Zhong, X. Qu, C. Ding, and D. Tao, “Glance and gaze: Inferring
+action-aware points for one-stage human-object interaction detec-
+tion,” in Proceedings of the IEEE/CVF Conference on Computer Vision
+and Pattern Recognition, pp. 13234–13243, 2021.
+[12] C. Gao, J. Xu, Y. Zou, and J.-B. Huang, “Drg: Dual relation graph
+for human-object interaction detection,” in European Conference on
+Computer Vision, pp. 696–712, Springer, 2020.
+[13] O. Ulutan, A. Iftekhar, and B. S. Manjunath, “Vsgnet: Spatial
+attention network for detecting human object interactions using
+graph convolutions,” in Proceedings of the IEEE/CVF conference on
+computer vision and pattern recognition, pp. 13617–13626, 2020.
+[14] C. Gao, Y. Zou, and J.-B. Huang, “ican: Instance-centric attention
+network for human-object interaction detection,” arXiv preprint
+arXiv:1808.10437, 2018.
+[15] T. Wang, T. Yang, M. Danelljan, F. S. Khan, X. Zhang, and J. Sun,
+“Learning human-object interaction detection using interaction
+points,” in Proceedings of the IEEE/CVF Conference on Computer
+Vision and Pattern Recognition, pp. 4116–4125, 2020.
+[16] A. Zhang, Y. Liao, S. Liu, M. Lu, Y. Wang, C. Gao, and X. Li, “Min-
+ing the benefits of two-stage and one-stage hoi detection,” Ad-
+vances in Neural Information Processing Systems, vol. 34, pp. 17209–
+17220, 2021.
+[17] C. Zou, B. Wang, Y. Hu, J. Liu, Q. Wu, Y. Zhao, B. Li, C. Zhang,
+C. Zhang, Y. Wei, et al., “End-to-end human object interaction
+detection with hoi transformer,” in Proceedings of the IEEE/CVF
+conference on computer vision and pattern recognition, pp. 11825–
+11834, 2021.
+
+JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 10, JANUARY 2023
+15
+[18] F. Z. Zhang, D. Campbell, and S. Gould, “Spatially condi-
+tioned graphs for detecting human-object interactions,” in Proceed-
+ings of the IEEE/CVF International Conference on Computer Vision,
+pp. 13319–13327, 2021.
+[19] M. Tamura, H. Ohashi, and T. Yoshinaga, “Qpic: Query-based
+pairwise human-object interaction detection with image-wide con-
+textual information,” in Proceedings of the IEEE/CVF Conference on
+Computer Vision and Pattern Recognition, pp. 10410–10419, 2021.
+[20] Y.-L. Li, S. Zhou, X. Huang, L. Xu, Z. Ma, H.-S. Fang, Y. Wang, and
+C. Lu, “Transferable interactiveness knowledge for human-object
+interaction detection,” in Proceedings of the IEEE/CVF Conference on
+Computer Vision and Pattern Recognition, pp. 3585–3594, 2019.
+[21] G. Gkioxari, R. Girshick, P. Doll´ar, and K. He, “Detecting and
+recognizing human-object interactions,” in Proceedings of the IEEE
+conference on computer vision and pattern recognition, pp. 8359–8367,
+2018.
+[22] Y.-W. Chao, Y. Liu, X. Liu, H. Zeng, and J. Deng, “Learning to
+detect human-object interactions,” in 2018 ieee winter conference on
+applications of computer vision (wacv), pp. 381–389, IEEE, 2018.
+[23] T. Gupta, A. Schwing, and D. Hoiem, “No-frills human-object
+interaction detection: Factorization, layout encodings, and training
+techniques,” in Proceedings of the IEEE/CVF International Conference
+on Computer Vision, pp. 9677–9685, 2019.
+[24] B. Wan, D. Zhou, Y. Liu, R. Li, and X. He, “Pose-aware multi-
+level feature network for human object interaction detection,” in
+Proceedings of the IEEE/CVF International Conference on Computer
+Vision, pp. 9469–9478, 2019.
+[25] A. Bansal, S. S. Rambhatla, A. Shrivastava, and R. Chellappa, “De-
+tecting human-object interactions via functional generalization,”
+in Proceedings of the AAAI Conference on Artificial Intelligence, vol. 34,
+pp. 10460–10469, 2020.
+[26] H.-S. Fang, Y. Xu, W. Wang, X. Liu, and S.-C. Zhu, “Learning pose
+grammar to encode human body configuration for 3d pose estima-
+tion,” in Proceedings of the AAAI conference on artificial intelligence,
+vol. 32, 2018.
+[27] H.-S. Fang, G. Lu, X. Fang, J. Xie, Y.-W. Tai, and C. Lu, “Weakly
+and semi supervised human body part parsing via pose-guided
+knowledge transfer,” arXiv preprint arXiv:1805.04310, 2018.
+[28] Y. Xiu, J. Li, H. Wang, Y. Fang, and C. Lu, “Pose flow: Efficient
+online pose tracking,” arXiv preprint arXiv:1802.00977, 2018.
+[29] S. Qi, W. Wang, B. Jia, J. Shen, and S.-C. Zhu, “Learning human-
+object interactions by graph parsing neural networks,” in Proceed-
+ings of the European conference on computer vision (ECCV), pp. 401–
+417, 2018.
+[30] B. Kim, T. Choi, J. Kang, and H. J. Kim, “Uniondet: Union-level
+detector towards real-time human-object interaction detection,”
+in European Conference on Computer Vision, pp. 498–514, Springer,
+2020.
+[31] Y. Liao, S. Liu, F. Wang, Y. Chen, C. Qian, and J. Feng, “Ppdm:
+Parallel point detection and matching for real-time human-object
+interaction detection,” in Proceedings of the IEEE/CVF Conference on
+Computer Vision and Pattern Recognition, pp. 482–490, 2020.
+[32] N. Carion, F. Massa, G. Synnaeve, N. Usunier, A. Kirillov, and
+S. Zagoruyko, “End-to-end object detection with transformers,” in
+European conference on computer vision, pp. 213–229, Springer, 2020.
+[33] J. Chen and K. Yanai, “Qahoi: Query-based anchors for human-
+object interaction detection,” arXiv preprint arXiv:2112.08647, 2021.
+[34] X. Zhu, W. Su, L. Lu, B. Li, X. Wang, and J. Dai, “Deformable detr:
+Deformable transformers for end-to-end object detection,” arXiv
+preprint arXiv:2010.04159, 2020.
+[35] Y. Bengio, P. Lamblin, D. Popovici, and H. Larochelle, “Greedy
+layer-wise training of deep networks,” Advances in neural informa-
+tion processing systems, vol. 19, 2006.
+[36] G. E. Hinton, S. Osindero, and Y.-W. Teh, “A fast learning al-
+gorithm for deep belief nets,” Neural computation, vol. 18, no. 7,
+pp. 1527–1554, 2006.
+[37] B. Kang, S. Xie, M. Rohrbach, Z. Yan, A. Gordo, J. Feng, and
+Y. Kalantidis, “Decoupling representation and classifier for long-
+tailed recognition,” arXiv preprint arXiv:1910.09217, 2019.
+[38] Y.-W. Chao, Y. Liu, X. Liu, H. Zeng, and J. Deng, “Learning to
+detect human-object interactions,” in 2018 ieee winter conference on
+applications of computer vision (wacv), pp. 381–389, IEEE, 2018.
+[39] S. Gupta and J. Malik, “Visual semantic role labeling,” arXiv e-
+prints, 2015.
+[40] F. Scarselli, M. Gori, A. C. Tsoi, M. Hagenbuchner, and G. Mon-
+fardini, “The graph neural network model,” IEEE transactions on
+neural networks, vol. 20, no. 1, pp. 61–80, 2008.
+[41] A. Vaswani, N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A. N.
+Gomez, Ł. Kaiser, and I. Polosukhin, “Attention is all you need,”
+Advances in neural information processing systems, vol. 30, 2017.
+[42] Y. LeCun, Y. Bengio, et al., “Convolutional networks for images,
+speech, and time series,” The handbook of brain theory and neural
+networks, vol. 3361, no. 10, p. 1995, 1995.
+[43] Z. Liu, Y. Lin, Y. Cao, H. Hu, Y. Wei, Z. Zhang, S. Lin, and B. Guo,
+“Swin transformer: Hierarchical vision transformer using shifted
+windows,” in Proceedings of the IEEE/CVF International Conference
+on Computer Vision, pp. 10012–10022, 2021.
+[44] X. Chen, F. Wei, G. Zeng, and J. Wang, “Conditional detr v2:
+Efficient detection transformer with box queries,” arXiv preprint
+arXiv:2207.08914, 2022.
+[45] Y. Wang, X. Zhang, T. Yang, and J. Sun, “Anchor detr: Query
+design for transformer-based detector,” in Proceedings of the AAAI
+conference on artificial intelligence, vol. 36, pp. 2567–2575, 2022.
+[46] S. Liu, F. Li, H. Zhang, X. Yang, X. Qi, H. Su, J. Zhu, and L. Zhang,
+“Dab-detr: Dynamic anchor boxes are better queries for detr,”
+arXiv preprint arXiv:2201.12329, 2022.
+[47] G. Zhang, Z. Luo, Y. Yu, K. Cui, and S. Lu, “Accelerating detr
+convergence via semantic-aligned matching,” in Proceedings of the
+IEEE/CVF Conference on Computer Vision and Pattern Recognition,
+pp. 949–958, 2022.
+[48] K. He, X. Zhang, S. Ren, and J. Sun, “Deep residual learning for
+image recognition,” in Proceedings of the IEEE conference on computer
+vision and pattern recognition, pp. 770–778, 2016.
+[49] F. Iandola, M. Moskewicz, S. Karayev, R. Girshick, T. Darrell, and
+K. Keutzer, “Densenet: Implementing efficient convnet descriptor
+pyramids,” arXiv preprint arXiv:1404.1869, 2014.
+[50] A. Newell, K. Yang, and J. Deng, “Stacked hourglass networks for
+human pose estimation,” in European conference on computer vision,
+pp. 483–499, Springer, 2016.
+[51] X. Dong, J. Bao, D. Chen, W. Zhang, N. Yu, L. Yuan, D. Chen, and
+B. Guo, “Cswin transformer: A general vision transformer back-
+bone with cross-shaped windows,” in Proceedings of the IEEE/CVF
+Conference on Computer Vision and Pattern Recognition, pp. 12124–
+12134, 2022.
+[52] J. Yang, C. Li, P. Zhang, X. Dai, B. Xiao, L. Yuan, and J. Gao, “Focal
+self-attention for local-global interactions in vision transformers,”
+arXiv preprint arXiv:2107.00641, 2021.
+[53] Z. Xia, X. Pan, S. Song, L. E. Li, and G. Huang, “Vision transformer
+with deformable attention,” in Proceedings of the IEEE/CVF Con-
+ference on Computer Vision and Pattern Recognition, pp. 4794–4803,
+2022.
+[54] H. Wu, B. Xiao, N. Codella, M. Liu, X. Dai, L. Yuan, and L. Zhang,
+“Cvt: Introducing convolutions to vision transformers,” in Proceed-
+ings of the IEEE/CVF International Conference on Computer Vision,
+pp. 22–31, 2021.
+[55] A. Dosovitskiy, L. Beyer, A. Kolesnikov, D. Weissenborn, X. Zhai,
+T. Unterthiner, M. Dehghani, M. Minderer, G. Heigold, S. Gelly,
+et al., “An image is worth 16x16 words: Transformers for image
+recognition at scale,” arXiv preprint arXiv:2010.11929, 2020.
+[56] C.-F. Chen, R. Panda, and Q. Fan, “Regionvit: Regional-to-local
+attention for vision transformers,” arXiv preprint arXiv:2106.02689,
+2021.
+[57] Y. Wang, R. Huang, S. Song, Z. Huang, and G. Huang, “Not all
+images are worth 16x16 words: Dynamic transformers for efficient
+image recognition,” Advances in Neural Information Processing Sys-
+tems, vol. 34, pp. 11960–11973, 2021.
+[58] K. He, G. Gkioxari, P. Doll´ar, and R. Girshick, “Mask r-cnn,” in
+Proceedings of the IEEE international conference on computer vision,
+pp. 2961–2969, 2017.
+[59] X. Dai, Y. Chen, B. Xiao, D. Chen, M. Liu, L. Yuan, and L. Zhang,
+“Dynamic head: Unifying object detection heads with attentions,”
+in Proceedings of the IEEE/CVF conference on computer vision and
+pattern recognition, pp. 7373–7382, 2021.
+[60] H. Law and J. Deng, “Cornernet: Detecting objects as paired
+keypoints,” in Proceedings of the European conference on computer
+vision (ECCV), pp. 734–750, 2018.
+[61] T.-Y. Lin, P. Goyal, R. Girshick, K. He, and P. Doll´ar, “Focal loss
+for dense object detection,” in Proceedings of the IEEE international
+conference on computer vision, pp. 2980–2988, 2017.
+[62] Y.-L. Li, L. Xu, X. Liu, X. Huang, Y. Xu, S. Wang, H.-S. Fang,
+Z. Ma, M. Chen, and C. Lu, “Pastanet: Toward human activity
+knowledge engine,” in Proceedings of the IEEE/CVF Conference on
+Computer Vision and Pattern Recognition, pp. 382–391, 2020.
+
+JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 10, JANUARY 2023
+16
+[63] Y.-W. Chao, Z. Wang, Y. He, J. Wang, and J. Deng, “Hico: A
+benchmark for recognizing human-object interactions in images,”
+in Proceedings of the IEEE international conference on computer vision,
+pp. 1017–1025, 2015.
+[64] I. Loshchilov and F. Hutter, “Decoupled weight decay regulariza-
+tion,” arXiv preprint arXiv:1711.05101, 2017.
+
diff --git a/D9E2T4oBgHgl3EQfogh1/content/tmp_files/load_file.txt b/D9E2T4oBgHgl3EQfogh1/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..15cd115b4eeb545e7939cc4cf021ce90d04ec444
--- /dev/null
+++ b/D9E2T4oBgHgl3EQfogh1/content/tmp_files/load_file.txt
@@ -0,0 +1,1738 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf,len=1737
+page_content='JOURNAL OF LATEX CLASS FILES, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 14, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 10, JANUARY 2023  1  FGAHOI: Fine-Grained Anchors for  Human-Object Interaction Detection  Shuailei Ma, Yuefeng Wang, Shanze Wang, and Ying Wei  Abstract—Human-Object Interaction (HOI), as an important problem in computer vision, requires locating the human-object pair and  identifying the interactive relationships between them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' The HOI instance has a greater span in spatial, scale, and task than the  individual object instance, making its detection more susceptible to noisy backgrounds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' To alleviate the disturbance of noisy  backgrounds on HOI detection, it is necessary to consider the input image information to generate fine-grained anchors which are then  leveraged to guide the detection of HOI instances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' However, it is challenging for the following reasons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 𝑖) how to extract pivotal features  from the images with complex background information is still an open question.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 𝑖𝑖) how to semantically align the extracted features and  query embeddings is also a difficult issue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' In this paper, a novel end-to-end transformer-based framework (FGAHOI) is proposed to  alleviate the above problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' FGAHOI comprises three dedicated components namely, multi-scale sampling (MSS), hierarchical  spatial-aware merging (HSAM) and task-aware merging mechanism (TAM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' MSS extracts features of humans, objects and  interaction areas from noisy backgrounds for HOI instances of various scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' HSAM and TAM semantically align and merge the  extracted features and query embeddings in the hierarchical spatial and task perspectives in turn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' In the meanwhile, a novel training  strategy Stage-wise Training Strategy is designed to reduce the training pressure caused by overly complex tasks done by FGAHOI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  In addition, we propose two ways to measure the difficulty of HOI detection and a novel dataset, 𝑖.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='𝑒.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=', HOI-SDC for the two challenges  (Uneven Distributed Area in Human-Object Pairs and Long Distance Visual Modeling of Human-Object Pairs) of HOI instances  detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Experiments are conducted on three benchmarks: HICO-DET, HOI-SDC and V-COCO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Our model outperforms the  state-of-the-art HOI detection methods, and the extensive ablations reveal the merits of our proposed contribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' The code is  available at https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='com/xiaomabufei/FGAHOI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  Index Terms—Human-Object Interaction, FGAHOI, Fine-Grained Anchors, Noisy Background, Semantically Aligning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  1  INTRODUCTION  H  UMAN-Object  interaction  (HOI)  detection,  as  a  downstream task of object detection [1], [2], [3], [4],  [5], has recently received increasing attention due to its  great application potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' For successful HOI detection, it  needs to have the ability to understand human activities  which are abstracted as a set of <human, object, action>  triplets in this task, requiring a much deeper understanding  for the semantic information of visual scenes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Without HOI  detection, machines can only interpret images as collections  of object bounding boxes, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=', AI systems can only pick up  information such as ’A man is on the bike’ or ’A bike is in  the corner’, but not ’A man rides a bike’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  Spanning the past and the present, the existing HOI  detection approaches [6], [7], [8], [9], [10], [11], [12], [13],  [14], [15], [16], [17], [18], [19], [20], [21] tend to fall into  two categories, namely two-stage and one-stage methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  Conventional two-stage methods [7], [8], [10], [12], [13],  [14], [18], [20], [22], [23], [24], [25], as an intuitive approach,  detect human and object instances by leveraging the off-the- Shuailei Ma, Yuefeng Wang are with College of Information Science and  Engineering, Northeastern University, Shenyang, China, 110819.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  E-mail: {xiaomabufei, wangyuefeng0203} @gmail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='com Shanze Wang is with Changsha Hisense Intelligent System Research  Institute Co.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=', Ltd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' and Information Technology R&D Innovation Center of  Peking University, Shaoxing, China.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  E-mail: szgg0099@gmail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='com Ying Wei is the corresponding author, with College of Information Science  and Engineering, Northeastern University, Shenyang, China, 110819.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  E-mail: weiying@ise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='neu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='cn  Manuscript received October 26, 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' revised January 10, 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  FGAHOI  Low Level  Middle Level  High Level  Fine-Grained  Anchors  Attention Weights  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 1: FGAHOI leverages the query embeddings and multi-  scale features to generate fine-grained anchors and the  corresponding weights for HOI instances of diverse scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  Then, they guide the decoder to aid key semantic infor-  mation of HOI instances to the content embeddings and  translate the content embeddings to HOI embeddings for  predicting all elements of the HOI instances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  shelf object detector [1], [3], [4], utilizing the visual features  extracted from the located areas to recognize action classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  To fully leverage the visual features, several methods [7],  [10], [14], [20], [22], [23], [24], [25] separately extract vi-  sual features of human-object pairs and spatial information  from the located area in a multi-stream architecture, fusing  them in a post-fusion strategy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' In the meanwhile, several  approaches [8], [10], [20], [23], [24] employ the existing pose  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='04019v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='CV]  8 Jan 2023  JOURNAL OF LATEX CLASS FILES, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 14, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 10, JANUARY 2023  2  estimation methods, such as [26], [27], [28] to extract pose  information and fuse it with other features to predict the  action class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' In addition, some works [8], [12], [13], [18],  [29] leverage the graph neural network to extract complex  semantic relationship between humans and objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' How-  ever, the difficulties encountered in the two-stage approach  lie mainly in the effective fusion of human-object pairs and  complex semantic information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Besides, owing to the limita-  tions of the fixed detector and some other components (pose  estimation etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' ), the two-stage method can only achieve a  sub-optimal solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  To achieve high efficiency, one-stage approaches [6], [9],  [11], [15], [17], [21], [30], [31] which utilize interaction points  between the human-object pairs to simultaneously predict  human and object offset vectors and action classes, are  proposed to detect human-object pairs and recognize inter-  active relationships in parallel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' However, when the human  and object in the image are far apart from each other, these  methods are disturbed by ambiguous semantic features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  The one-stage methods do not achieve much attention until  the appearance of the Detection Transformer (DETR) [32]  and QPIC [19] applies it for HOI detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Then, plenty  of transformer-based works [6], [9], [16], [17], [33] attempt  to solve the HOI detection with different encoder-decoder  structures and backbone models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  In comparison to object instances, HOI instances have  a greater span of spatial, scale and task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' In most HOI  instances, there is a certain distance between human and  objects and their scale varies enormously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Compared with  simple object classification, it is necessary to consider more  information between human-object pairs rather than the  features of humans and objects for interaction classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  Therefore, the detection is more susceptible to distractions  from noisy backgrounds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' However, most recent works [19],  [33] use object detection frameworks [32], [34] directly for  HOI detection by simply adding the interaction classifica-  tion head, ignoring these problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Inspired by [34] which  leverages the reference points to guide the decoding pro-  cess, we propose to leverage fine-grained anchors to guide  the detection of HOI instances and protect it from noisy  backgrounds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' To generate fine-grained anchors for kinds  of HOI instances, it is obviously necessary to consider the  input image features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' There are, however, two inevitable  challenges that arise as a result of this.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 𝑖) it is difficult to  extract pivotal features from the images which contain noisy  background information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 𝑖𝑖) how to semantically align and  merge the extracted features with query embeddings is also  an open question.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  In this paper, we propose a novel transformer-based  model for HOI detection, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=', FGAHOI: Fine-Grained An-  chors for Human-Object Interaction Detection (as shown in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' FGAHOI leverages the multi-scale sampling mech-  anism (MSS) to extract pivotal features from images with  noisy background information for variable HOI instances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  Based on the sampling strategy and initial anchor gener-  ated by the corresponding query embedding, MSS could  extract hierarchical spatial features of human, object and the  interaction region for each HOI instance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Besides, the hi-  erarchical spatial-aware (HSAM) and task-aware merging  mechanism (TAM) are utilized to semantically align and  merge the extracted features with the query embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  HSAM merges the extracted features in the hierarchical  spatial perspective according to the cross-attention between  the features and the query embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Meanwhile, the  extracted features are aligned towards the query embed-  dings, according to the cross-attention weights of the merg-  ing process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Thereafter, TAM leverages the switches which  dynamically switch ON and OFF to merge the input features  and query embeddings in the task perspective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  According to experiment results, we investigate that it  is difficult of the end-to-end training approach to allow the  transformer-based models to achieve optimal performance  when more complex task requirements are required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' In-  spired by the stage-wise training [35], [36] for LTR [37], we  propose a novel stage-wise training strategy for FGAHOI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  During the training process, we add the important compo-  nents of the model in turn to clarify the training direction  of the model at each stage, so as to maximize the savings in  the training cost of the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  To the best of our knowledge, there are no measurements  for the difficulty of detecting HOI instances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' We investigate  that two difficulties lie in the detection of human-object  pairs, 𝑖.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='𝑒.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=', Uneven Distributed Area in Human-Object  Pairs and Long Distance Visual Modeling of Human-  Object Pairs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' In this paper, we propose two measurements  and a novel dataset (HOI-SDC) for these two challenges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  HOI-SDC eliminates the influence of other factors (Too few  training samples of some HOI categories, too tricky interac-  tion actions, et.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=') on the model training and focuses on the  model for these two difficult challenges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Our contributions  can be summarized fourfold: We propose a novel transformer-based human-object  interaction detector (FGAHOI) which leverages input  features to generate fine-grained anchors for pro-  tecting the detection of HOI instances from noisy  backgrounds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' We propose a novel training strategy where each  component of the model is trained in turn to clar-  ify the training direction at each stage, in order to  maximize the training cost savings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' We propose two ways to measure the difficulty of  HOI detection and a dataset, 𝑖.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='𝑒.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=', HOI-SDC for the  two challenges (Uneven Distributed Area in Human-  Object Pairs and Long Distance Visual Modeling of  Human-Object Pairs) of detecting HOI instances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Our extensive experiments on three benchmarks:  HICO-DET  [38],  HOI-SDC  and  V-COCO  [39],  demonstrate the effectiveness of the proposed FGA-  HOI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Specifically, FGAHOI outperforms all existing  state-of-the-art methods by a large margin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  2  RELATED WORKS  Two-stage HOI Detection Approaches: The two-stage HOI  detection approaches [7], [8], [10], [12], [13], [14], [18], [20],  [22], [23], [24], [25], [29] employ the off-the-shelf object de-  tector [1], [3], [4] to localize humans and objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Afterwards,  the features of backbone networks inside the human and  objects regions are cropped.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Part of the two-stage meth-  ods [8], [12], [13], [18], [29] treat the human and objects  feature as nodes and employ graph neural networks [40]  JOURNAL OF LATEX CLASS FILES, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 14, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 10, JANUARY 2023  3  Encoder  Content Embeddings  …  Initial Anchor  …  Positional Encoding  Human Box  Object box/Class  Human Box  Object box/Class  Verb Class  Verb Class  HOI  Detection  Head  Decoder  Task-Aware  Merging  Dynamic  Switch On/Off  …  Positional  Embeddings  Multi-Scale  Sampling Strategy  Multi-Scale  Features  Hierarchical Spatial-Aware  Merging  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 2: This figure illustrates the overall structure of FGAHOI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' FGAHOI utilizes a hierarchical backbone and a deformable  encoder to extract the semantic features in a multi-scale approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' In the decoding phrase, FGAHOI leverages the multi-  scale sampling, hierarchical spatial-aware merging and task-aware merging mechanism to align input features with  query embeddings and assist the generation of fine-grained anchors for the translation of HOI embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' At the back  end of the pipeline, HOI detector leverages the HOI embeddings and initial anchor to predict all elements of the HOI  instances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  to predict action classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' The other part of the two-stage  approach [7], [10], [14], [20], [22], [23], [24], [25] leverages  multi-stream networks to extract diverse information from  cropped regions, such as human features, object features,  spatial information and human pose information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Then,  the information is fused to predict the action in a post-  fusion strategy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Two-stage methods mainly concentrate on  predicting the action class in the second stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Nevertheless,  the quality of cropped features from the first stage cannot  be guaranteed in most cases, so the method cannot achieve  an optimal solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' More importantly, integrating semantic  information of human-object pairs requires massive time  and computing resources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  One-stage HOI Detection Approaches: The traditional one-  stage approaches [9], [11], [15], [31] use interaction points  or union regions to detect human-object pairs and identify  interactive action classes in parallel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' However, these meth-  ods which and are hampered by distant human-object pairs,  require a gathering and pairing process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' With the creation of  DETR [32], one-stage approaches have become the current  mainstream.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' QPIC [19] converts the object detection head  of DETR into an interaction detection head to predict HOI  instance directly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' HOITrans [17] combines transformer [41]  and CNN [42] to straightly predict HOI instances from the  query embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' AS-Net [6] and HOTR [9] each propose a  two-branch transformer method that consists of an instance  decoder and an interaction decoder to predict the boxes  and action classes in parallel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' CDN [16] proposes a cascade  disentangling decoder to decode action classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' QAHOI [33]  directly combines Swin Transformer [43] and deformable  DETR [34] to predict HOI instances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  Anchor-Based Object Detection Transformer: Deformable  DETR [34] first introduces the reference point concept,  where the sampling offset is predicted by each reference  point to perform deformable cross-attention.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' To facilitate  extreme region discrimination, Conditional DETR [44] re-  formulates the attention operation and rebuilt positional  queries based on reference points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Anchor DETR [45] pro-  poses to explicitly capitalize on the spatial prior during  cross-attention and box regression by utilizing a predefined  2D anchor point [𝑐𝑥, 𝑐𝑦].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' DAB-DETR [46] extends such a  2D concept to a 4D anchor box [𝑐𝑥, 𝑐𝑦, 𝑤, ℎ] and proposed  to refine it layer-by-layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' SAM-DETR [47] proposes directly  updating content embeddings by extracting salient points  from image features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' In this paper, we propose a novel  decoding process for HOI detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' The alignment and fine-  grained anchor generation is proposed to align the multi-  scale features with HOI query embeddings and generate  fine-grained anchors for the diverse HOI instances with  variable spatial distribution, scales and tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Then, the fine-  grained anchors guide the deformable attention process in  aiding key information to query embeddings from noisy  backgrounds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  3  PROPOSED METHOD  In Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='1, we show the overall architecture of FGAHOI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  Then, we describe the multi-scale feature extractor in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  We introduce the multi-scale sampling strategy in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  The hierarchical spatial-aware, task-aware merging mech-  anism and the decoding process is proposed in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='2,  Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='3 and Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='4, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' In Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='4, we present  the architecture of the HOI detection head.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' In Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='5, the  stage-wise training strategy, loss calculation and inference  process is illustrated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='1  Overall Architecture  The overall architecture of our proposed FGAHOI is illus-  trated in Fig 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' For a given image 𝑥 ∈ R𝐻×𝑊 ×3, FGAHOI  firstly uses a hierarchical backbone network to extract the  multi-scale features Z𝑖  ∈ R  𝐻  4×2𝑖 × 𝑊  4×2𝑖 ×2𝑖𝐶𝑠, 𝑖  = 1, 2, 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' The  multi-scale features are then projected from dimension C𝑠  to dimension C𝑑 by using 1×1 convolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' After being  flattened out, the multi-scale features are concatenated to  N𝑠 vectors with C𝑑 dimensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Afterwards, along with  JOURNAL OF LATEX CLASS FILES, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 14, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 10, JANUARY 2023  4  supplementary positional encoding 𝑝 ∈ R𝑁𝑠×𝐶𝑑, the multi-  scale features are sent into the deformable transformer en-  coder which consists of a set of stacked deformable encoder  layers to encode semantic features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' The encoded semantic  features 𝑀 ∈ R𝑁𝑠×𝐶𝑑 are then acquired.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' In the decoding  process, the content 𝐶 and positional 𝑃 embeddings are both  a set of learnable vectors {𝑣𝑖 | 𝑣𝑖 ∈ R𝑐𝑑}𝑁𝑞  𝑖=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' The positional  embeddings 𝑃 first generate the initial anchor 𝐴 ∈ R𝑁𝑞×2  according to a linear layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' The positional 𝑃, content 𝐶  embeddings, inital anchor 𝐴 and encoded features 𝑀 are  simultaneously sent into the decoder 𝐹𝑑𝑒𝑐𝑜𝑑𝑒𝑟 (·, ·, ·, ·) which  is a set of stacked decoder layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' In every decoder layer,  the initial anchor first leverages the multi-scale sampling  strategy to sample the multi-scale features corresponding  to the content embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' The sampled features assist  the generation of fine-grained anchors and corresponding  attention weights through the hierarchical spatial-aware  and task-aware merging mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' The HOI embeddings  𝐻 = {ℎ𝑖 | ℎ𝑖 ∈ R𝑐𝑑}𝑁𝑞  𝑖=1 are translated from the query embed-  dings 𝑄 through the fine-grained anchors, attention weights  and the deformable attention.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' The HOI embeddings 𝐻 are  acquired as 𝐻 = 𝐹𝑑𝑒𝑐𝑜𝑑𝑒𝑟 (𝑀, 𝑃, 𝐶, 𝐴).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Eventually, the HOI  detector leverages the HOI embeddings 𝐻 and initial anchor  to predict the HOI instances < 𝑏ℎ, 𝑏𝑜, 𝑐𝑜, 𝑐𝑣 >, where 𝑏ℎ, 𝑏𝑜,  𝑐𝑜 and 𝑐𝑣 stands for the human box coordinate (𝑥, 𝑦, 𝑤, ℎ),  object box coordinate, object class and verb class, respec-  tively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='2  Multi-Scale Features Extractor  High-quality visual features are a prerequisite for successful  HOI detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' For extracting the multi-scale features with  long-range semantic information, FGAHOI leverages the  multi-scale feature extractor which consists of a hierarchical  backbone network and a deformable transformer encoder to  extract features, the folumation is as Equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='1:  𝑀 = 𝐹𝑒𝑛𝑐𝑜𝑑𝑒𝑟 (𝐹𝑓 𝑙𝑎𝑡𝑡𝑒𝑛(𝜙(𝑥)), 𝑝, 𝑠, 𝑟, 𝑙)  ∈ R𝑁𝑠×𝐶𝑑,  (1)  where 𝐹𝑒𝑛𝑐𝑜𝑑𝑒𝑟 (·), 𝐹𝑓 𝑙𝑎𝑡𝑡𝑒𝑛(·) and 𝜙(·) denotes the encoder,  flatten operation and backbone network, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 𝑝 is  the position encoding, 𝑠 is the spatial shape of the multi-  scale features, 𝑟 stands for the valid ratios and 𝑙 represents  the level index corresponding the multi-scale features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' The  hierarchical backbone network is flexible and can be com-  posed of any convolutional neural network [42], [48], [49],  [50] and transformer backbone network [43], [51], [52], [53],  [54], [55], [56], [57].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' However, CNN is poor at capturing  non-local semantic features like the relationships between  humans and objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' In this paper, we mainly use Swin  Transformer tiny and large version [43] to enhance the  ability of feature extractor for extracting long-range features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='3  Why FGAHOI Decodes Better?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  During the decoding process, the fine-grained anchors can  be regarded as a positional prior to let decoder focus on  the region of interest, directly guiding the decoder to aid  semantic information to the content embeddings which are  used to predict all elements of the HOI instances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Therefore,  fine-grained anchors play the following two crucial roles in  HOI detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 𝑖) Fine-grained anchors directly determine  whether the information gained from input features to  content embeddings is instance-critical or noisy background  information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 𝑖𝑖) Fine-grained anchors determine the quality  of alignment between the query embeddings and multi-  scale features of input scenarios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Both are crucial factors for  the quality of decoding results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' The existing methods [33],  [34] directly utilize the query embedding to generate fine-  grained anchors based on the initial anchor, without consid-  ering the multi-scale features of the input scenarios and the  semantic alignment between the query embedding and the  input features at all.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Our FGAHOI proposes a novel fine-  grained anchors generator which consists of multi-scale  sampling, hierarchical spatial-aware merging and task-  aware merging mechanism (as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' The gen-  erator adequately leverages the initial anchor, multi-scale  features and query embeddings for generating suitable fine-  grained anchors for diverse input scenarios and aligning  semantic information between different input scenarios and  query embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' The formulation of FGAHOI decoding  process is as follows:  𝐻 = Defattn(Task(Hier Spatial({𝑥𝑖  𝑠}, 𝐶𝑢), 𝐶𝑢), 𝑀, 𝐶𝑢),  (2)  where 𝐶𝑢 is the content embeddings updated by the po-  sitional embeddings, Defattn represents the deformable at-  tention, 𝑥𝑖  𝑠 represents the sampled features of the 𝑖-th level  features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 𝑀 is the encoded input features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='1  Multi-Scale Sampling Mechanism  The HOI instances contained in the input scenarios usually  vary in size, where some instances taking up most of the  area in the input scenarios and others occupying perhaps  only a few pixels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Our FGAHOI aims at detecting all in-  stances in the scene, regardless of the size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Therefore, when  using the initial anchor to sample the multi-scale features,  for shallow features mainly used to detect instances of small  size, the sampling strategy only samples a small range of  features around the initial anchor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' In contrast, for deep  features mainly used to detect instances of large size, the  sampling strategy samples a large range of features around  the initial anchor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='3 (b), in the generator, the  encoded features are first reshaped to the original shape.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  Based on the initial anchor, generator leverages the sam-  pling strategy to sample multi-scale features as follows:  𝑥𝑖  𝑠 =𝐹𝑠𝑎𝑚𝑝𝑙𝑒( 𝑟𝑒𝑠ℎ𝑎𝑝𝑒(𝑀)𝑖, 𝐴, 𝑠𝑖𝑧𝑒𝑖, 𝑏𝑖𝑙𝑖𝑛𝑒𝑎𝑟 ),  (3)  where 𝑠𝑖𝑧𝑒𝑖 (𝑖 = 0, 1, 2) denotes the sampling size of the 𝑖-th  level features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 𝑀 is the encoded input features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 𝐴 is the ini-  tial anchor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Inspired by [58], we utilize bilinear interpolation  in the sampling strategy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='2  Hierarchical Spatial-Aware Merging Mechanism  In order to better utilize the hierarchical spatial informa-  tion of sampled features for aligning content embeddings  with the sampled features, we propose a novel hierarchical  spatial-aware merging mechanism (HSAM) which utilizes  the content embeddings to extract hierarchical spatial in-  formation and merge the sampled features, as shown in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='3 (c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' The content embeddings are first updated by the  positional embeddings and multi-head self-attention mech-  anism as follows:  𝐶𝑢 = 𝐶 + 𝐹MHA  �  (𝐶 + 𝑃)𝑊𝑞, (𝐶 + 𝑃)𝑊 𝑘, 𝐶𝑊 𝑣�  ,  (4)  JOURNAL OF LATEX CLASS FILES, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 14, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 10,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' JANUARY 2023  5  Multi-Scale Sampling Strategy  Src Shape  Anchor  Sampling  Low  High  Middle  Positional  Embeddings  Multi-Head  Self-Attention  Add & Norm  Deformable  Multi-Head  Cross-Attention  FFN  Add & Norm  Add & Norm  Encoded Multi-Scale Features  Alignment &  Fine-Grained  Anchor Generation  Query  Embeddings  (������������ ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' ������������ )  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='V  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='K  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Q  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='V  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Fined-grained  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Anchors  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Initial Anchor  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Attention  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Weights  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Updated  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Content  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Embeddings  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Fine-grained  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Anchors  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Corresponding  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Attention Weights  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Linear  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Linear  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='SoftMax  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Generation of Fine-Grained Anchors  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Reshape  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Reshape  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='（b）  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='（a）  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='（d）  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='（e）  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Hierarchical Spatial-Aware  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Merging Mechanism  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Middle  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Multi-Head  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Attention  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Flatten  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Low  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='High  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Multi-Head Attention  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='CAT  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Positional  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Embeddings  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Content  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Embeddings  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='…  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Task-Aware Merging Mechanism  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Dynamic  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Switch On/Off  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Cross-Attn[(  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=',' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  ]  Linear  Linear  RELU  Normalize  Updated  Content  Embeddings  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  )  （c）  Middle  Low  High  Merge  Features  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 3: The architecture of FGAHOI’s decoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' (a) Illustration of FGAHOI’s decoding process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' (b) Illustration of Multi-  scale sampling mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' (c) Illustration of Hierarchical spatial-aware merging mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' (d) Illustration of Task-aware  merging mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' (e) Generation process of fine-grained anchors and the corresponding attention weights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  where 𝑊𝑞, 𝑊 𝑘 and 𝑊 𝑣 denotes the parameter matrices  for query, key and value in the self-attention mechanism,  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 𝐹MHA(·) is the multi-head attention mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  𝐶 and 𝑃 represents the content and position embeddings,  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Then, the updated content embeddings are  leveraged to merge the sampled features, the formulation  is as follows:  𝑥𝑖  𝑚 = 𝐹concat  �head1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' , headNH  � 𝑊𝑂,  where headn = Softmax  �  (𝐶𝑢𝑊𝑞  n ) · (𝑥𝑖  𝑠𝑊 𝑘  n )𝑇  √𝑑𝑘  �  (𝑥𝑖  𝑠𝑊 𝑣  n ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  (5)  Where 𝑥𝑖  𝑚 represents the merged features of the 𝑖-th level  sampled features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 𝐶𝑢 is the content embeddings updated  by the positional embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 𝑊𝑂 denotes the parameter  matrices for multi-head concatenation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 𝑊𝑞  𝑛 , 𝑊 𝑘  𝑛 and 𝑊 𝑣  𝑛  denote the parameter matrices for query, key and value of  n-th attention head.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 𝐹concat is the concatenating operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  𝑑𝑘 =  𝑁ℎ𝑑  𝑁𝐻 , 𝑁ℎ𝑑 is the hidden dimensions, and 𝑁𝐻 is the  number of attention head.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  Following the merging of the sampled features at each  scale based on spatial information, the merged features at  each scale are first concatenated together as follows:  𝑋𝑚 = 𝐹concat({𝑥𝑖  𝑚}𝑖=0,1,2) ∈ R𝐵×𝑁𝑞×𝑁𝐿×𝑁ℎ𝑑,  (6)  where 𝑁𝐿 is the number of multi-scale, 𝑥𝑖  𝑚 represents the  merged features of the 𝑖-th level sampled features, 𝑋𝑚 is the  concatenated multi-scale features and merged by the scale-  aware merging mechanism as follows:  𝑋𝑢 = 𝐹concat (head1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' , headh) 𝑊𝑂,  where headn = Softmax  �  (𝐶𝑢𝑊𝑞  n ) · (𝑋𝑚𝑊 𝑘  n )𝑇  √𝑑𝑘  �  (𝑋𝑚𝑊 𝑣  n ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  (7)  Where 𝑋𝑢 is the merged multi-scale features for updating  the content embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='3  Task-Aware Merging Mechanism  Considering diverse HOI instances, the task-aware merging  mechanism is proposed to fuse the merged multi-scale  features and content embeddings and align the content  embeddings with the merged feature in the task-aware  perspective, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='3 (e).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' It leverages the merged  multi-scale features and content embeddings to generate  dynamic switch for selecting suitable channel in the merging  process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Content embedding and multi-scale information  after fusion are first stitched together, the formulation is as  follows:  𝑋 = 𝐹𝑠𝑡𝑎𝑐𝑘 (𝐶𝑢, 𝑋𝑢) ∈ R𝐵×𝑁𝑞×(2×𝑁ℎ𝑑).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  (8)  Where 𝐶𝑢 is the content embeddings updated by the posi-  tional embeddings, 𝑋𝑢 is the merged multi-scale features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  Thereafter, we use cross-attention mechanism to update  these as follows:  𝑋𝑠𝑤𝑖𝑡𝑐ℎ = 𝐹concat (head1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' , headh) 𝑊𝑂,  where headn = Softmax  �  (𝐶𝑢𝑊𝑞  n ) · (𝑋𝑊 𝑘  n )𝑇  √𝑑𝑘  �  (𝑋𝑊 𝑣  n ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  (9)  JOURNAL OF LATEX CLASS FILES, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 14, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 10, JANUARY 2023  6  TABLE 1: Instance statistics of two difficulties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' We quantify all the instances in the HAKE-HOI [20] dataset according to  two newly proposed metrics and divide them into ten intervals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  Dataset  IMI  IMI0  IMI1  IMI2  IMI3  IMI4  IMI5  IMI6  IMI7  IMI8  IMI9  HAKE-HOI  num𝐴𝑅  104243  65499  44303  31241  21982  11888  4670  1818  598  168  num𝐿𝑅  424  1243  1784  3043  8668  70191  83314  79427  34017  4299  SDC Train  num𝐴𝑅  62526  30235  16346  12013  10269  11189  4223  1540  423  139  num𝐿𝑅  177  515  874  1656  5208  48798  38517  29544  20265  3349  SDC Test  num𝐴𝑅  24737  0  0  0  0  0  0  0  0  0  num𝐿𝑅  153  415  464  834  2704  20167  0  0  0  0  Then,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' the generated information is utilized to gain the  dynamic switch for merging,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' the formulation is as follows:  𝑆𝑤𝑖𝑡𝑐ℎ𝛾 = 𝐹𝑛𝑜𝑟𝑚𝑎𝑙𝑖𝑧𝑒(𝐹𝑚𝑙𝑝(𝑋𝑠𝑤𝑖𝑡𝑐ℎ))𝛾 ∈ R𝐵×𝑁𝑞×2×2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  (10)  where 𝑆𝑤𝑖𝑡𝑐ℎ𝛾 is the dynamic switch for 𝛾-th dimension  of the merged features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 𝐹ℎ𝑠𝑖𝑔𝑚𝑜𝑖𝑑(·) and 𝐹𝑚𝑙𝑝(·) denote the  hard sigmoid and feed forward network which consists of  two linear layers and one Relu activation layer, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  Inspired by [59], the merging mechanism is designed as  follows:  𝑈𝛾 = 𝐹𝑀 𝑎𝑥{𝑆𝑤𝑖𝑡𝑐ℎ𝛾  𝑖,0 ⊙ 𝑋𝛾  𝑢 + 𝑆𝑤𝑖𝑡𝑐ℎ𝛾  𝑖,1}𝑖=0,1 + 𝐶𝛾  𝑢 ,  (11)  where 𝑈𝛾 is 𝛾-th features of content embeddings updated by  the merged multi-scale features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 𝐹𝑀 𝑎𝑥 is the max operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  …  Linear  Linear  MLP  MLP  Object Class  Action Class  Human Box  Object Box  HOI Instances  <Human/Object Boxes, Object  Class, Action Class>  Initial Anchor  HOI  Embeddings  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 4: The prediction process of the HOI detection head.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' See  sec 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='4 for more details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='4  Decoding with Fine-Grained Anchor  As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='3 (e), the updated content embeddings  are used to generate fine-grained anchors and attention  weights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' According to the linear layer, reshape operation  and softmax function, the formulation is as follows:  A = 𝐹𝑙𝑖𝑛&𝑟𝑒𝑠(𝑈) ∈ R𝐵×𝑁𝑞×𝑁𝐻 ×𝑁𝐿×𝑁A×2,  (12)  W = 𝐹𝑙𝑖𝑛&𝑟𝑒𝑠&𝑠𝑜 𝑓 𝑡 (𝑈) ∈ R𝐵×𝑁𝑞×𝑁𝐻 ×𝑁𝐿×𝑁A,  (13)  As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='3 (a), the fine-grained anchors and at-  tention weights are utilized to aid semantic features from  the encoded features of the input scenarios to the content  embeddings, the formulation is as follows:  P𝑞 =  𝑁𝐻  ∑︁  𝑛=1  𝑾𝑛  � 𝑁𝐿  ∑︁  𝑙=1  𝑁A  ∑︁  𝑘=1  W𝑙  𝑛𝑞𝑘 · 𝑾′  𝑛𝒙𝒍 �  A𝑙  𝑛𝑞𝑘  ��  ,  (14)  where P𝑞 is the extracted semantic information used for  translating 𝑞-th content to HOI embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' A𝑙  𝑛𝑞𝑘 and  W𝑙  𝑛𝑞𝑘 represent the 𝑘-th fine-grained anchors and corre-  sponding attention weights of the 𝑛-th attention head for  the 𝑞-th query embedding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Both 𝑊𝑛 and 𝑊 ′  𝑛 are parameter  matrices of the 𝑛-th attention head.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 𝑁A is the number of  fine-grained anchors of each scale in one attention head.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='4  HOI Detection Head  FGAHOI leverages a simple HOI detection head to predict  all elements of HOI instances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='4, the detec-  tion head utilizes the HOI embeddings and the initial anchor  to localize the human and object boxes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' In this process, each  initial anchor acts as the base point for the bounding boxes  of the corresponding pair of a human and an object, the  formulation is as follows:  𝑏ℎ = 𝐹𝑚𝑙𝑝(𝐻)[· · · , : 2] + 𝑖𝑛𝑖𝑡𝑖𝑎𝑙 𝑎𝑛𝑐ℎ𝑜𝑟  ∈ R𝑁𝑞×4,  (15)  𝑏𝑜 = 𝐹𝑚𝑙𝑝(𝐻)[· · · , : 2] + 𝑖𝑛𝑖𝑡𝑖𝑎𝑙 𝑎𝑛𝑐ℎ𝑜𝑟  ∈ R𝑁𝑞×4,  (16)  𝑐𝑜 = 𝐹𝑙𝑖𝑛𝑒𝑎𝑟 (𝐻)  ∈ R𝑁𝑞×𝑛𝑢𝑚𝑜,  (17)  𝑐𝑣 = 𝐹𝑙𝑖𝑛𝑒𝑎𝑟 (𝐻)  ∈ R𝑁𝑞×𝑛𝑢𝑚𝑣,  (18)  where 𝐹𝑚𝑙𝑝 denotes the feed forward network consists of  three linear layers and three relu activation layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 𝐹𝑙𝑖𝑛𝑒𝑎𝑟  stands for the linear layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 𝑛𝑢𝑚𝑜 and 𝑛𝑢𝑚𝑣 are the number  of object and action classes, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 𝐻 denotes the HOI  embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='5  Training and Inference  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='1  Stage-wise Training  Inspired by the stage-wise training approach [35], [36] which  decouples feature learning and classifier learning into two  independent stages for LTR [37], we propose a novel stage-  wise training strategy for FGAHOI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' We start by training  the base network (FGAHOI without any merging mecha-  nism) in an end-to-end manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' We then add the merging  mechanism in turn to the trained base network for another  short period of training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' In this phrase, the parameters  of the trained base network are leveraged as pretrained  parameters and no parameters are fixed during the training  process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  JOURNAL OF LATEX CLASS FILES, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 14, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 10,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' JANUARY 2023  7  ride,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' fly,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' sit_on,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' exit,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  direct airplane  ride,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' straddle,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' run,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  hold,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  race horse  lasso cow  carry handbag  wear  backpack  hold,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' stand_under umbrella  ride,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' race,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' run  straddle,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' hold horse  fly,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' pull  kite  sail,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' ride,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' sit_on,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  stand_on,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' drive boat  race,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' turn,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' ride,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' sit on,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  straddle,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' hold motorcycle  wear tie  scratch,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' walk,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  pet,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' train  dog  ride,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' sit on,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  drive,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' board bus  carry,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' wear,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' hold  backpack  serve,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' hit sports_ball  swing tennis_racket  direct,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' inspect,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' ride,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  sit on,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' fly  airplane  type on,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' read,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  hold laptop  sit on  couch  brush_with,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' hold  toothbrush  kick,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' block,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' hit,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  inspect,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' dribble  sports_ball  stand_on,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' ride,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' jump,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  hold skateboard  ride,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' fly,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' sit_on,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' exit,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  direct airplane  ride,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' straddle,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' run,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  hold,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  race horse  lasso cow  carry handbag  wear  backpack  hold,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' stand_under umbrella  ride,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' race,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' run  straddle,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' hold horse  fly,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' pull  kite  sail,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' ride,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' sit_on,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  stand_on,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' drive boat  race,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' turn,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' ride,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' sit on,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  straddle,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' hold motorcycle  wear tie  scratch,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' walk,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  pet,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' train  dog  ride,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' sit on,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  drive,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' board bus  carry,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' wear,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' hold  backpack  serve,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' hit sports_ball  swing tennis_racket  direct,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' inspect,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' ride,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  sit on,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' fly  airplane  type on,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' read,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  hold laptop  sit on  couch  brush_with,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' hold  toothbrush  kick,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' block,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' hit,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  inspect,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' dribble  sports_ball  stand_on,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' ride,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' jump,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  hold skateboard  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 5: Visualization of HOI detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Humans and objects are represented by pink and blue bounding boxes respectively,  and interactions are marked by grey lines linking the box centers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Kindly refer to Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='1 for more details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='(a)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='(b)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='(c)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='catch sport ball  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='watch  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='bird  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='kick  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='sports ball  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='hit sport  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='ball  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='fly kite  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='hit sport  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='ball  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='wear tie  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='swing  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='tennis_racket  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='sit_on  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='toilet  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='hold  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='surfboard  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='ride skateboard  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='ride skateboard  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='carry surfboard  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='ride surfboard  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='ride surfboard  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='ride surfboard  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='ride surfboard  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='ride surfboard  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='flip  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='skateboard  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='catch sport ball  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='watch  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='bird  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='kick  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='sports ball  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='hit sport  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='ball  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='fly kite  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='hit sport  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='ball  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='wear tie  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='swing  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='tennis_racket  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='sit_on  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='toilet  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='hold  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='surfboard  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='ride skateboard  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='carry surfboard  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='ride surfboard  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='ride surfboard  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='flip  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='skateboard  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='(a)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='(b)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='(c)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='catch sport ball  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='watch  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='bird  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='kick  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='sports ball  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='hit sport  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='ball  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='fly kite  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='hit sport  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='ball  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='wear tie  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='swing  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='tennis_racket  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='sit_on  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='toilet  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='hold  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='surfboard  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='ride skateboard  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='carry surfboard  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='ride surfboard  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='ride surfboard  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='flip  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='skateboard  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 6: (a) illustrates the excellent long-range visual mod-  elling capabilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' (b) demonstrates remarkable robustness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  (c) shows the superior capabilities for identifying small HOI  instances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Kindly refer to Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='1 for more details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='2  Loss Calculation  Inspired by the set-based training process of HOI-Trans  [17], QPIC [19], CDN [16] and QAHOI [33], we first use  the bipartite matching with the Hungarian algorithm to  match each ground truth with its best-matching prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  For subsequent back-propagation, a loss is then established  between the matched predictions and the matching ground  truths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' The folumation is as follows:  𝐿 = 𝜆𝑜𝐿𝑜  𝑐 + 𝜆𝑣 𝐿𝑣  𝑐 +  ∑︁  𝑘 ∈(ℎ,𝑜)  �  𝜆𝑏𝐿𝑘  𝑏 + 𝜆𝐺𝐼𝑜𝑈 𝐿𝑘  𝐺𝐼𝑜𝑈  �  ,  (19)  where 𝐿𝑜  𝑐 and 𝐿𝑣  𝑐 represent the object class and action class  loss, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' We utilize the modified focal loss function  [60] and sigmoid focal loss function [61] for 𝐿𝑣  𝑐 and 𝐿𝑜  𝑐,  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 𝐿𝑏 is the box regression loss and consists of the  𝐿1 Loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 𝐿𝐺𝐼𝑂𝑈 denotes the intersection-over-union loss, the  same as the function in QPIC [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 𝜆𝑜, 𝜆𝑣, 𝜆𝑏 and 𝜆𝐺𝐼𝑜𝑈 are  the hyper parameters for adjusting the weights of each loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='3  Inference  The inference process is to composite the output of the HOI  detection head to form HOI triplets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Formally, the 𝑖-th out-  put prediction is generated as < 𝑏ℎ  𝑖 , 𝑏𝑜  𝑖 , 𝑎𝑟𝑔𝑚𝑎𝑥𝑘𝑐ℎ𝑜𝑖  𝑖  (𝑘) >.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  The HOI triplet score 𝑐ℎ𝑜𝑖  𝑖  combined by the scores of action  𝑐𝑣  𝑖 and object 𝑐𝑜  𝑖 classification, formularized as 𝑐ℎ𝑜𝑖  𝑖  = 𝑐𝑣  𝑖 · 𝑐𝑜  𝑖 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  4  PROPOSED DATASET  There are two main difficulties existing with human-object  pairs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 𝑖) Uneven size distribution of human and objects in  human-object pairs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 𝑖𝑖) Excessive distance between person  and object in human-object pairs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' To the best of our knowl-  edge, there are no relevant metrics to measure these two  difficulties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' In this paper, we propose two metrics 𝐴𝑅 and  𝐿𝑅 for measuring these two difficulties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Then two novel  challenges corresponding to these two difficulties are pro-  posed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' In addition, we propose a novel Set for these Double  Challenges (HOI-SDC).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' The data is selected from HAKE-  HOI [20] which is re-split from HAKE [62] and provides  110K+ images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' HAKE-HOI has 117 action classes, 80 object  classes and 520 HOI categories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  CB福CREERSBK2  M  WITDBWEJOURNAL OF LATEX CLASS FILES, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 14, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 10, JANUARY 2023  8  FGAHOI  QAHOI  FGAHOI  QAHOI  FGAHOI  QAHOI  Fine-Grained  Anchors #1  Fine-Grained  Anchors #2  Fine-Grained  Anchors #3  Fine-Grained  Anchors #4  Fine-Grained  Anchors #5  Fine-Grained  Anchors #6  Fine-Grained  Anchors #7  Fine-Grained  Anchors #8  HOI  Instance  Hold  Sport Ball  Ride  Motorcycle  Fly Kite  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 7: Comparison of fine-grained anchors between FGAHOI and QAHOI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' We visualize the fine-grained anchors  corresponding to all attention heads and the corresponding attention weights, where the shades of colors correspond  to the magnitude of the weights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Obviously, FGAHOI is more accurate in focusing on humans, objects and interaction  areas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Kindly refer to Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='2 for more details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='1  HOI-UDA  We propose a novel measurement for the challenge of  Uneven Distributed Area in Human-Object Pairs, the  formulation is as follow:  𝐴𝑅 = 𝐴𝑟𝑒𝑎ℎ · 𝐴𝑟𝑒𝑎𝑜  𝐴𝑟𝑒𝑎2  ℎ𝑜𝑖  ,  (20)  where 𝐴𝑟𝑒𝑎ℎ, 𝐴𝑟𝑒𝑎𝑜 and 𝐴𝑟𝑒𝑎ℎ𝑜𝑖 denote the area of human,  object and HOI instances, respectively (as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='8  (a)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' We quantify all the instances in the HAKE-HOI into ten  intervals and count the number of instances of each interval  in the second and fifth row of Table.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' To better evaluate the  ability of the model to detect HOI for human-object pairs  with uneven distributed areas, we specially select 24737  HOI instances of IMIUDA  0  in testing set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='2  HOI-LDVM  A novel measurement for the challenge of Long Distance  Visual Modeling of Human-Object Pairs is proposed in  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  𝐿𝑅 = 𝐿ℎ + 𝐿𝑜  𝐿ℎ𝑜𝑖  ,  (21)  where 𝐿ℎ, 𝐿𝑜 and 𝐿ℎ𝑜𝑖 denote the size we define of human,  object and HOI instances, respectively (as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='8  (b)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' The instances are quantified in the third and sixth row  of Table.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' To better evaluate the ability of the model to de-  tect HOI for human-object pairs with with long distance, we  specially select 24737 HOI instances of IMILDVM  0  ∼ IMILDVM  6  in testing set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='3  HOI-SDC  In order to avoid the training process of the model being  influenced by a portion of HOI classes with a very small  number of instances, we remove some of the HOI classes  containing a very small number of instances and HOI  classes with no interaction from the training Set for the  Double Challenge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Finally, there are total 321 HOI classes,  JOURNAL OF LATEX CLASS FILES, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 14, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 10, JANUARY 2023  9  TABLE 2: Performance comparison with the state-of-the-art methods on the HICO-DET dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' ’V’, ’S’, ’P’ and ’L’ represent  the visual feature, spatial feature, human pose feature and language feature respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Fine-tuned Detection means the  parameter of the model is pre-trained on the MS-COCO dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Backbone with ’*’ and ’+’ means that they are pre-trained  on ImageNet-22K with 384×384 input resolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' QAHOI(R) represents that the results are reproduced on the same machine  with our model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Kindly refer to Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='1 for more details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  Architecture  Method  Backbone  Fine-tuned  Feature  Default (↑)  Known Object (↑)  Full  Rare  Non-Rare  Full  Rare  Non-Rare  Two-Stage Methods  Multi-stream  No-Frill [23]  ResNet-152  \x17  A+S+P  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='18  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='17  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='08 PMFNet [24]  ResNet-50-FPN  \x17  A+S  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='46  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='65  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='00  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='34  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='47  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='20  ACP [25]  ResNet-101  \x14  A+S+L  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='96  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='43  23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='62 PD-Net [10]  ResNet-152  \x17  A+S+P+L  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='37  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='61  23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='79  26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='86  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='70  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='44  VCL [7]  ResNet-50  \x14  A+S  23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='63  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='21  25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='55  25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='98  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='12  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='03  Graph-Based  RPNN [8]  ResNet-50  \x17  A+P  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='35  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='78  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='71 VSGNet [13]  ResNet-152  \x17  A+S  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='80  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='05  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='91 DRG [12]  ResNet-50-FPN  \x14  A+S+L  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='53  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='47  26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='04  27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='98  23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='14  29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='43  SCG [18]  ResNet-50-FPN  \x14  A+S  31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='33  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='72  33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='31  34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='37  27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='18  36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='50  One-Stage Methods  Interaction points  IP-Net [15]  ResNet-50-FPN  \x17  A  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='56  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='79  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='58  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='05  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='77  23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='92  PPDM [31]  Hourglass-104  \x14  A  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='73  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='78  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='10  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='58  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='65  26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='84  GGNet [11]  Hourglass-104  \x14  A  23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='47  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='48  25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='60  27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='36  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='23  29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='48  Transformer-Based  HOITrans [17]  ResNet-101  \x14  A  26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='60  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='15  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='54  29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='1  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='98  31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='57  HOTR [9]  ResNet-50  \x17  A  23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='46  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='21  25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='65 ResNet-50  \x14  A  25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='10  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='34  27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='42 AS-Net [6]  ResNet-50  \x17  A  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='40  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='39  25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='01  27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='41  25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='44  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='00  ResNet-50  \x14  A  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='87  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='25  30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='25  31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='74  27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='07  33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='14  QPIC [19]  ResNet-50  \x14  A  29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='07  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='85  31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='23  31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='68  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='14  33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='93  ResNet-50  \x17  A  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='21  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='51  26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='21 QAHOI [33]  Swin-Tiny  \x17  A  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='47  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='44  30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='27  30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='99  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='83  32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='84  Swin-Large∗  +  \x17  A  35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='78  29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='80  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='56  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='59  31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='66  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='36  QAHOI (R)  Swin-Tiny  \x17  A  27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='67  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='22  29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='69  30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='06  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='95  32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='18  Swin-Large∗  +  \x17  A  35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='43  29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='22  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='29  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='23  31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='01  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='09  FGAHOI  Swin-Tiny  \x17  A  29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='94  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='24  32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='24  32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='48  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='16  34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='97  Swin-Large∗  +  \x17  A  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='18  30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='71  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='11  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='93  31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='93  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='02  74 object classes and 93 action classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' The training and  testing set contain 37,155 and 9,666 images, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' The  detailed distribution of HOI instances is shown in Table.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  (b)  (a)  ������������������������������������������������������������  ������������������������������������������������������������  ������������������������������������������������������������������������������������  ������������������������  ������������������������  ������������������������������������������������  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 8: Proposed metrics for the difficulties existing with HOI  instances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' (a) Metric for uneven size distribution of humans  and objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' (b) Metric for excessive distance between person  and object.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Kindly refer to Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='1 and 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='2 for more details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  5  EXPERIMENTS  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='1  Dataset  Experiments are conducted on three HOI datasets: HICO-  DET [38], V-COCO [39] and HOI-SDC dataset  HICO-DET [38] has 80 object classes, 117 action classes  and 600 HOI classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' HICO-DET offers 47,776 images with  TABLE 3: Performance comparison with the state-of-the-art  methods on the HOI-SDC dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Kindly refer to Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='2  for more details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  Dataset  Backbone  Method  mAProle (↑)  HOI-SDC  Swin-Tiny  QAHOI  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='55  Swin-Tiny  Baseline  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='18  Swin-Tiny  +HSAM  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='91  Swin-Tiny  +TAM  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='84  Swin-Tiny  FGAHOI  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='25  151,276 HOI instances, including 38,118 images with 117,871  annotated instances of human-object pairs in the training set  and 9658 images with 33,405 annotated instances of human-  object pairs in the testing set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' According to the number  of these HOI classes, the 600 HOI classes in the dataset  are grouped into three categories: Full (all HOI classes),  Rare (138 classes with fewer than ten instances) and Non-  Rare (462 classes with more than ten instances).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Following  HICO [63], we consider two different evaluation settings  (the results are shown in Table.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='2: (1) Known object settings:  For each HOI category (such as ’flying a kite’), the detection  is only evaluated on the images that contain the target object  category (such as ’kite’).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' The difficulty lies in the local-  JOURNAL OF LATEX CLASS FILES, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 14, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 10, JANUARY 2023  10  TABLE 4: Performance comparison with the state-of-the-art  methods on the V-COCO dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Kindly refer to Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='3  for more details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  Method  AP𝑆1  role (↑)  AP𝑆2  role (↑)  Two-stage Method  VSG-Net  51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='8  57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='0  PD-Net  52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='0 ACP  53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='2 One-stage Method  HOITrans  52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='9 AS-Net  53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='9 HOTR  55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='2  64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='4  DIRV  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='1 QAHOI(R-50)  58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='2  58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='7  FGAHOI(R-50)  59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='0  59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='3  FGAHOI(Swin-T)  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='5  61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='2  ization of HOI (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' human-kite pairs) and distinguishing  the interaction (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' ’flying’).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' (2) Default setting: For each  HOI category, the detection is evaluated on the whole test  set, including images containing and without target object  categories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' This is a more challenging setting because we  also need to distinguish background images (such as images  without ’kite’).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  V-COCO [39] contains 80 different object classes and  29 action categories and is developed from the MS-COCO  dataset, which includes 4,946 images for the test subset,  2,533 images for the train subset and 2,867 images for the  validation subset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' The objects are divided into two types:  “object” and “instrument”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='2  Metric  Following the standard evaluation [21], [39], we use role  mean average precious to evaluate the predicted HOI in-  stances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' A detected bounding box is considered a true  positive for object detection if it overlaps with a ground  truth bounding box of the same class with an intersection  greater than union (𝐼𝑂𝑈) greater than 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' In HOI detection,  we need to predict human-object pairs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' The human-object  pairs whose human overlap 𝐼𝑂𝑈ℎ and object overlap 𝐼𝑂𝑈𝑜  both exceed 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='5, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=', min (𝐼𝑂𝑈ℎ, 𝐼𝑂𝑈𝑜) > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='5 are declared  a true positive (as shown in Fig 9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Specifically, for HICO-  DET, besides the full set of 600 HOI classes, the role mAP  over a rare set of 138 HOI classes that have less than 10  training instances and a non-rare set of the other 462 HOI  classes are also reported.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Furthermore, we report the role  mAP of two scenarios for V-COCO: scenario 1 includes the  cases even without any objects (for the four action categories  of body motions), while scenario 2 ignores these cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' For  HOI-SDC, we report the role mean average precision for the  full set of 321 HOI classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='3  Implementation Details  The Visual Feature Extractor consists of Swin Transformer  and a deformable transformer encoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' For Swin-Tiny and  Swin-Large, the dimensions of the feature maps in the first  stage are set to 𝐶𝑠 = 96 and 𝐶𝑠 = 192, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' We pre-  train Swin-Tiny on the ImageNet-1k dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Swin-Large is  first pre-trained on the ImageNet-22k dataset and finetuned  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 9: The human-object pairs with human overlap 𝐼𝑂𝑈ℎ  and object overlap 𝐼𝑂𝑈𝑜 both exceeding 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='5 are declared as  true positives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Kindly refer to Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='2 for more details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  on the ImageNet-1k dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Then the weights are used  to fine-tune the FGAHOI for the HOI detection task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' The  number of both encoder and decoder layers are set to 6  (𝑁𝐿𝑎𝑦𝑒𝑟 = 6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' The number of query embeddings is set to 300  (𝑁𝑞 = 300), and the hidden dimension of embeddings in the  transformer is set to 256 (𝐶𝑑 = 256).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' In the post-processing  phase, the first 100 HOI instances are selected according  to object confidence, and we use 𝛿=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='5 to filter the HOI  instances by the combined 𝐼𝑂𝑈.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Following Deformable-  DETR [34], the AdamW [64] optimizer is used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' The learning  rates of the extractor and the other components are set to  10−5 and 10−4, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' We use 8 RTX 3090 to train the  model (QAHOI & FGAHOI) with Swin-Tiny.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' For the model  with Swin-Large∗  +, we use 16 RTX 3090 to train them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' For  HICO-DET and HOI-SDC, we train the base network for  150 epochs and carry out the learning rate drop from the  120th epoch at the first stage of training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' For subsequent  training, we trained the model for 40 epochs, with a learning  rate drop at the 15th epoch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' For V-COCO dataset, we train  the base network for 90 epochs and drop the learning rate  from 60th epoch at the first stage of training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' For subsequent  training, we trained the model for 30 epochs, with a learning  rate drop at the 10th epoch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='4  Comparison with State-of-the-Arts  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='1  HICO-DET  We compare FGAHOI with the state-of-the-art two-stage  and one-stage methods on the HICO-DET dataset and  report the results in Table.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' FGAHOI outperforms both  state-of-the-art methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' In contrast to the state-of-the-art  two-stage method SCG [18], FGAHOI with Swin-Large*+  backbone exceeds an especially significant gain of 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='85 mAP  in default full setting, 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='99 mAP in default rare setting, 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='8  mAP in default non-rare setting, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='56 mAP in known object  full setting, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='75 mAP in known rare settings and 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='52 mAP  in known object non-rare setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' For a fair comparison, we  used the same machine for the reproduction of the QAHOI  (as shown in Table.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='2 QAHOI(R)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' In comparison to the state-  of-the-art one-stage method QAHOI, FGAHOI exceeds it  in all settings for all backbone networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' For Swin-Tiny  backbone network, FGAHOI exceeds an especially signifi-  cant gain of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='27 mAP in default full setting, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='02 mAP in  default rare setting, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='55 mAP in default non-rare setting,  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='42 mAP in known object full setting, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='11 mAP in known  rare settings and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='79 mAP in known object non-rare setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  In addition, FGAHOI with Swin-Large*+ backbone exceeds  an especially significant gain of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='75 mAP in default full  OU  IOU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  Ground-truth label  Prediction boxesJOURNAL OF LATEX CLASS FILES, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 14, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 10, JANUARY 2023  11  TABLE 5: Comparison on ten intervals of the two proposed challenges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' We divide the HICO-DET dataset into ten intervals  based on each of the two challenges and compare the performance of QAHOI and FGAHOI on each interval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Kindly refer  to Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='5 for more details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  Challenge  Method  Backbone  mAProle (↑)  IMI0  IMI1  IMI2  IMI3  IMI4  IMI5  IMI6  IMI7  IMI8  IMI9  UDA  QAHOI  Swin-Tiny  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='35  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='72  29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='24  34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='79  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='70  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='21  53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='13  47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='60  58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='66  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='19  Swin-Large∗  +  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='53  33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='58  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='11  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='41  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='44  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='43  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='25  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='53  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='12  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='08  FGAHOI  Swin-Tiny  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='74  29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='85  32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='20  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='46  40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='54  48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='55  51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='32  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='50  66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='44  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='17  Swin-Large∗  +  23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='69  35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='85  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='51  50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='50  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='89  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='95  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='33  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='04  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='70  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='42  LDVM  QAHOI  Swin-Tiny  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='33  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='43  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='57  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='00  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='06  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='87  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='81  29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='25  34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='03  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='29  Swin-Large∗  +  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='82  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='08  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='56  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='53  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='42  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='87  30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='94  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='38  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='31  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='15  FGAHOI  Swin-Tiny  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='50  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='15  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='34  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='58  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='83  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='61  27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='64  33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='07  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='31  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='07  Swin-Large∗  +  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='44  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='32  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='57  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='81  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='82  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='92  32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='50  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='66  47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='26  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='55  TABLE 6: We carefully ablate each of the constituent component of FGAHOI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' The middle results denote the role mAP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' The  results in the top right corner represent the performance improvement compared to QAHOI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' The results in the bottom  right corner represent the performance improvement compared to the baseline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Kindly refer to Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='1 for more details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  Method  Merging Mechanism  Default  Known Object  Hierarchical Spatial-Aware  Task-Aware  Full ↑  Rare ↑  Non-Rare ↑  Full ↑  Rare ↑  Non-Rare ↑  QAHOI 27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='67  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='22  29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='69  30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='06  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='95  32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='18  FGAHOI  \x17  \x17  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='45( +0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='78 )  ( )  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='07( +0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='85 )  ( )  30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='66( +0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='97 )  ( )  31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='08( +1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='02 )  ( )  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='02( +1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='01 )  ( )  33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='19( +1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='07 )  ( )  \x14  \x17  29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='60( +1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='93 )  ( +1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='15 )  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='39( +2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='17 )  ( +1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='32 )  31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='76( +2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='07 )  ( +1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='10 )  32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='07( +2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='01 )  ( +0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='99 )  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='48( +1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='53 )  ( +0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='46 )  34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='34( +2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='16 )  ( +1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='15 )  \x17  \x14  29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='32( +1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='65 )  ( +0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='87 )  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='34( +2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='12 )  ( +1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='27 )  31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='41( +1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='72 )  ( +0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='75)  31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='81( +1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='75 )  ( +0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='73)  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='30( +1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='35 )  ( +0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='28)  34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='05( +1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='87 )  ( +0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='86)  \x14  \x14  29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='94( +2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='27 )  ( +1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='49 )  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='24( +2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='02 )  ( +1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='17 )  32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='24( +2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='55 )  ( +1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='58 )  32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='48( +2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='42 )  ( +1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='40 )  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='16( +1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='21 )  ( +0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='14 )  34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='97( +2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='79 )  ( +1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='78 )  setting, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='49 mAP in default rare setting, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='82 mAP in default  non-rare setting, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='7 mAP in known object full setting, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='92  mAP in known rare settings and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='93 mAP in known object  non-rare setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='2  HOI-SDC  On the dataset we propose, 𝑖.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='𝑒.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=', HOI-SDC, we compare  FGAHOI with QAHOI and ablate each component of FGA-  HOI (As shown in Table.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' The backbone is set to Swin-Tiny.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  The baseline exceeds QAHOI an especially significant gain  of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='63 mAP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' HSAM and TAM improve a significant gain  of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='73 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='66 mAP, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Benefit from the MSS,  HSAM and TAM, FGAHOI achieve 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='25 mAP on HOI-  SDC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='3  V-COCO  We compare FGAHOI with the state-of-the-art methods  on V-COCO dataset and report the results in Table.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' In  comparison to QAHOI, FGAHOI only exceeds a small  margin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' This phenomenon is mainly caused by too little  training data in the dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' We investigate that FGAHOI  cannot adequately perform when the training data is not  sufficient due to the complex task requirements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' In addition,  we investigate the transformer backbone is still superior to  CNN backbone in this case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='5  Sensitivity Analysis for UDA and LDVM  According to the two proposed challenges, we divide the  HICO-DET into ten intervals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' At each intervals, we compare  FGAHOI and QAHOI with Swin-Tiny, Large∗  + backbone,  respectively (As shown in Table.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' When compared be-  tween each interval of UDA and LDVM, we investigate  that the difficulty of HOI detection decreases as the interval  level increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' This justifies the original design.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Thus, it  is imperative to consider ability of the model to address  these two challenges when proposing novel frameworks for  HOI detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' In the comparison between FGAHOI and  QAHOI, the results demonstrate that FGAHOI has better  capability for uneven distributed area and long distance  visual modeling of human-object pairs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='6  Qualitative Analysis  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='1  Visualized Results  In order to demonstrate our model, several representative  HOI predictions are visualized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='5, our  model can pinpoint HOI instances from noisy backgrounds  and excels at detecting various complicated HOIs, including  one object interacting with different humans, one human  engaging in multiple interactions with various objects, mul-  tiple interactions within a single pair, and multiple humans  engaging in various interactions with various objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' In  addition, our model is good at long-range visual modelling,  withstanding the impacts of hostile environments and small  target identification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='6 (a) illustrates that FGAHOI has  excellent long-range visual modelling capabilities and can  accurately identify interactions between human-object pairs  far from each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' As Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='6 (b) shows, our model has  JOURNAL OF LATEX CLASS FILES, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 14, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 10,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' JANUARY 2023  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='text_on cell_phone  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='talk_on cell_phone  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='eat orange  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='open book  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='cut with knife  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='repair hair_drier  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='hold hotdog  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='hop_on elephant  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='kick sports_ball  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='hold cup  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='carry handbag  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='jump skateboard  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='hold cup  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='drink with cup  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='text_on cell_phone  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='talk_on cell_phone  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='eat orange  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='open book  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='cut with knife  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='repair hair_drier  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='hold hotdog  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='hop_on elephant  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='kick sports_ball  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='hold cup  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='carry handbag  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='jump skateboard  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='hold cup  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='drink with cup  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='(a)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='(b)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='(c)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Level_0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Level_0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Level_1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Level_1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Level_2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Level_2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Low  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='High  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Read  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Laptop  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Read  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Laptop  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Low  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='High  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Read  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Laptop  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Exit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Airplane  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Sit on  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Airplane  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Hold  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Horse  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Ride  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Horse  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Fly Kite  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='(a)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='(b)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='(c)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Level_0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Level_1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Level_2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Low  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='High  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Read  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Laptop  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Exit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Airplane  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Sit on  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Airplane  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Hold  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Horse  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Ride  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Horse  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Fly Kite  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 10: Visualization of fine-grained anchors in the decoding phase, Level 0, Level 1 and Level 2 represent the features  at different scales respectively, the color of the blue dots from light to dark represents the degrees of attention of the fine-  grained anchors and red dots represent the positions of interest of fine-grained anchors in current scale features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Kindly  refer to Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='2 for more details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  outstanding robustness and can effectively resist disruption  from harsh environmental factors, including blurring, block-  ing and glare.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='6 (c) demonstrates the superior capabili-  ties of FGAHOI to identify small HOI instances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='2  What do the fine-grained anchors look at?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='7, we compare the fine-grained anchors of  FGAHOI and QAHOI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' First two HOI instances (𝑖.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='𝑒, hold  sport ball and ride motorcycles) exhibit that FGAHOI could  better focus on humans, objects and the interaction areas  rather than noisy backgrounds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' The fourth head of FGAHOI  still focuses on the HOI instance, while QAHOI focuses  on the background.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' When detecting instance with a long  distance between human and object, FGAHOI could focus  on the right position, while QAHOI is like a chicken with its  head cut off (As shown in the last HOI instance).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  To exhibit the effectiveness of the fine-grained anchors  for identifying HOI instances and demonstrate the working  mechanism of fine-grained anchors, we visualize the fine-  grained anchors of the feature maps at different scales in  the decoding phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='10 (a), we visualize the instances  of two different humans and one object.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='10  (b), even for exactly the same human-object pair, the areas  of focus vary from one interaction to another.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='10 (c),  IS人  D2MVAD2MVAD2MVAD2MVAJOURNAL OF LATEX CLASS FILES, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 14, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 10, JANUARY 2023  13  text_on cell_phone  talk_on cell_phone  eat orange  ride bicycle  cut with knife  repair hair_drier  hold hotdog  hop_on elephant  kick sports_ball  hold cup  carry handbag  jump skateboard  hold cup  drink with cup  text_on cell_phone  talk_on cell_phone  eat orange  ride bicycle  cut with knife  repair hair_drier  hold hotdog  hop_on elephant  kick sports_ball  hold cup  carry handbag  jump skateboard  hold cup  drink with cup  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 11: Visualization of several representative interactive actions and the corresponding fine-grained anchors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' We only  visualize a single representative interactive action for one human-object pair.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Kindly refer to Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='2 for more details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  we show two instances contain short and long distance  between humans and objects, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' We investigate  that the fine-grained anchors of low level feature map focus  on small and fine-grained areas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' They play a major role in  detecting close range and small HOI instances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' The fine-  grained anchors of high level feature maps focus on large  and coarse-grained areas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' It is necessary for detecting long  distance and large HOI instances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  In order to explore what the fine-grained anchors focus  on, we visualize several representative actions in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  Visualization shows that fine-grained anchors could con-  centrate attention precisely on the location where the in-  teractive action is generated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' For example, the fine-grained  anchors mainly focus on the hand for ’text on cell phone’,  the mouth for ’eat orange’ and the ear and the mouth  for ’talk on cell phone’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' For ’kick sports ball’, ’jump skate-  board’ and ’hop on elephant’, central areas of interest are  around legs and feet, while fine-grained anchors primarily  focuses on hands for ’carry handbag’, ’repair hair drier’,  ’hold cup’, ’hold hotdog’ and ’cut with kinfe’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='7  Ablation Study  In this subsection, a set of experiments are designed to  clearly understand the contribution of each of the con-  stituent components of the proposed methodology: Merg-  ing mechanism, Multi-Scale Sampling Strategy and Stage-  wise Training Strategy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' We conducted all experiments on  the HICO-DET dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='1  Ablating FGAHOI Components  To study the contribution of each of the merging mecha-  nisms in FGAHOI, we design careful ablation experiments  in Table.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' To ensure a fair comparison, the sampling sizes  are all set to [1, 3, 5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' For the baseline which does not lever-  ages the hierarchical spatial-aware and task-aware merging  mechanism, we use the average and direct summation op-  eration to merge the sampled features and connect embed-  dings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' For the results in the table, the middle results denote  the role mAP, the results in the top right corner represent  the performance improvement compared to QAHOI and the  results in the bottom right corner represent the performance  improvement compared to the baseline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' In comparison to  row 1 (QAHOI), row 2 adds the multi-scale sampling  strategy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' The results demonstrate that adding the sampling  strategy improves the ability of the model to detect HOI  instances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' The row 3 and 4 show that both hierarchical  spatial-aware and task-aware merging mechanism make  an essential contribution to the success of FGAHOI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' The  hierarchical spatial-aware merging mechanism, combined  with the task-aware merging mechanism performs better  together (row 5) than using either of them separately (row 3  and 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Thus, each component in FGAHOI has a critical role  to play in HOI detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='2  Sensitivity Analysis On Multi-Scale Sampling Sizes  Our multi-scale sampling strategy samples multi-scale fea-  tures according to the pre-determined sampling sizes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' We  vary different sampling sizes to conduct the sensitivity  EJOURNAL OF LATEX CLASS FILES, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 14, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 10, JANUARY 2023  14  analysis for the sampling strategy and report the results  in Table.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' We find that the sampling strategy is relatively  stable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Changes in sampling sizes do not have a significant  impact on the performance of FGAHOI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' However, there is  still a slight degradation in the performance of FGAHOI as  the sample size increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' We investigate that as the sample  size increases, too many background features around the  fine-grained anchors are sampled, resulting in contamina-  tion of the sampled features and thus the performance of  the model suffers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Hence, for validation, we set the sampling  sizes to [1, 3, 5] in all our experiments, which is a sweet spot  that balances performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  TABLE 7: Comparison between different sampling sizes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  Smpling Size  Default  Known Object  Full  Rare  Non-Rare  Full  Rare  Non-Rare  [ 1, 3, 5 ]  29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='94  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='24  32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='24  32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='48  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='16  34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='97  [ 3, 5, 7 ]  29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='72  23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='03  31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='72  32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='33  25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='67  34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='30  [ 5, 7, 9 ]  29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='65  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='64  31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='74  32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='55  25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='64  34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='62  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='3  Training Strategies  As shown in Table.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='8, we leverage the stage-wise and end-  to-end training strategy to train FGAHOI, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' In  the end-to-end training strategy, we train FGAHOI for 150  epochs and the learning rate drop is carried out at the  120th epoch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' The stage-wise training strategy promotes 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='96  mAP for default full setting, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='61 for default rare, 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='36 for  default non-rare, 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='04 for known object full, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='65 for known  object rare and 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='46 mAP for known object non-rare setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  In comparison to the end-to-end training strategy, we in-  vestigate that the stage-wise training strategy reduces the  learning difficulty of the FGAHOI and clarify the learning  direction of the model by emphasizing it to learn what it  needs at each stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  TABLE 8: Comparison between Stage-Wise and End-to-End  training approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  Training Strategy  Default  Known Object  Full  Rare  Non-Rare  Full  Rare  Non-Rare  Stage-Wise  29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='94  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='24  32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='24  32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='48  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='16  34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='97  End-to-End  23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='98  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='63  25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='88  26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='44  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='51  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='51  6  CONCLUSION  In this paper, we propose a novel transformer-based human-  object interaction detector (FGAHOI) which leverages the  input features to generate fine-grained anchors for protect-  ing the detection of HOI instances from noisy backgrounds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  We propose a novel training strategy where each component  of the model is trained sequentially to clarify the training  direction at each stage, for maximizing the savings of the  training cost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' We propose two novel metrics and a novel  dataset, 𝑖.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='𝑒.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=', HOI-SDC for the two challenges (Uneven Dis-  tributed Area in Human-Object Pairs and Long Distance  Visual Modeling of Human-Object Pairs) of detecting HOI  instances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Our extensive experiments on three benchmarks:  HICO-DET, HOI-SDC and V-COCO, demonstrate the effec-  tiveness of the proposed FGAHOI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Specifically, FGAHOI  outperforms all existing state-of-the-art methods by a large  margin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  ACKNOWLEDGMENTS  This work is supported by National Natural Science Foun-  dation of China (grant No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='61871106 and No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='61370152),  Key R&D projects of Liaoning Province, China (grant  No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='2020JH2/10100029), and the Open Project Program  Foundation of the Key Laboratory of Opto-Electronics In-  formation Processing, Chinese Academy of Sciences (OEIP-  O-202002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  REFERENCES  [1]  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Girshick, “Fast r-cnn,” in Proceedings of the IEEE international  conference on computer vision, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 1440–1448, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  [2]  Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Li and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Zhou, “Fssd: feature fusion single shot multibox  detector,” arXiv preprint arXiv:1712.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='00960, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  [3]  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Ren, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' He, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Girshick, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Sun, “Faster r-cnn: Towards real-  time object detection with region proposal networks,” Advances in  neural information processing systems, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 28, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  [4]  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Girshick, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Donahue, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Darrell, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Malik, “Rich feature hier-  archies for accurate object detection and semantic segmentation,”  in Proceedings of the IEEE conference on computer vision and pattern  recognition, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 580–587, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  [5]  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Redmon, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Divvala, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Girshick, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Farhadi, “You only look  once: Unified, real-time object detection,” in Proceedings of the IEEE  conference on computer vision and pattern recognition, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 779–788,  2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  [6]  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Chen, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Liao, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Liu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Chen, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Wang, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Qian, “Refor-  mulating hoi detection as adaptive set prediction,” in Proceedings of  the IEEE/CVF Conference on Computer Vision and Pattern Recognition,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 9004–9013, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  [7]  Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Hou, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Peng, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Qiao, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Tao, “Visual compositional learn-  ing for human-object interaction detection,” in European Conference  on Computer Vision, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 584–600, Springer, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  [8]  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Zhou and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Chi, “Relation parsing neural network for human-  object interaction detection,” in Proceedings of the IEEE/CVF Inter-  national Conference on Computer Vision, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 843–851, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  [9]  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Kim, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Lee, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Kang, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Kim, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Kim, “Hotr: End-  to-end human-object interaction detection with transformers,” in  Proceedings of the IEEE/CVF Conference on Computer Vision and  Pattern Recognition, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 74–83, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  [10] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Zhong, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Ding, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Qu, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Tao, “Polysemy deciphering net-  work for robust human–object interaction detection,” International  Journal of Computer Vision, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 129, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 6, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 1910–1929, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  [11] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Zhong, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Qu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Ding, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Tao, “Glance and gaze: Inferring  action-aware points for one-stage human-object interaction detec-  tion,” in Proceedings of the IEEE/CVF Conference on Computer Vision  and Pattern Recognition, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 13234–13243, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  [12] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Gao, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Xu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Zou, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='-B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Huang, “Drg: Dual relation graph  for human-object interaction detection,” in European Conference on  Computer Vision, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 696–712, Springer, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  [13] O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Ulutan, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Iftekhar, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Manjunath, “Vsgnet: Spatial  attention network for detecting human object interactions using  graph convolutions,” in Proceedings of the IEEE/CVF conference on  computer vision and pattern recognition, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 13617–13626, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  [14] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Gao, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Zou, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='-B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Huang, “ican: Instance-centric attention  network for human-object interaction detection,” arXiv preprint  arXiv:1808.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='10437, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  [15] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Wang, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Yang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Danelljan, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Khan, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Zhang, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Sun,  “Learning human-object interaction detection using interaction  points,” in Proceedings of the IEEE/CVF Conference on Computer  Vision and Pattern Recognition, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 4116–4125, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  [16] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Zhang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Liao, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Liu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Lu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Wang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Gao, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Li, “Min-  ing the benefits of two-stage and one-stage hoi detection,” Ad-  vances in Neural Information Processing Systems, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 34, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 17209–  17220, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  [17] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Zou, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Wang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Hu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Liu, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Wu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Zhao, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Li, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Zhang,  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Zhang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Wei, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=', “End-to-end human object interaction  detection with hoi transformer,” in Proceedings of the IEEE/CVF  conference on computer vision and pattern recognition, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 11825–  11834, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  JOURNAL OF LATEX CLASS FILES, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 14, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 10, JANUARY 2023  15  [18] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Zhang, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Campbell, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Gould, “Spatially condi-  tioned graphs for detecting human-object interactions,” in Proceed-  ings of the IEEE/CVF International Conference on Computer Vision,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 13319–13327, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  [19] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Tamura, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Ohashi, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Yoshinaga, “Qpic: Query-based  pairwise human-object interaction detection with image-wide con-  textual information,” in Proceedings of the IEEE/CVF Conference on  Computer Vision and Pattern Recognition, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 10410–10419, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  [20] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Li, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Zhou, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Huang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Xu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Ma, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Fang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Wang, and  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Lu, “Transferable interactiveness knowledge for human-object  interaction detection,” in Proceedings of the IEEE/CVF Conference on  Computer Vision and Pattern Recognition, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 3585–3594, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  [21] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Gkioxari, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Girshick, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Doll´ar, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' He, “Detecting and  recognizing human-object interactions,” in Proceedings of the IEEE  conference on computer vision and pattern recognition, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 8359–8367,  2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  [22] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='-W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Chao, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Liu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Liu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Zeng, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Deng, “Learning to  detect human-object interactions,” in 2018 ieee winter conference on  applications of computer vision (wacv), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 381–389, IEEE, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  [23] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Gupta, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Schwing, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Hoiem, “No-frills human-object  interaction detection: Factorization, layout encodings, and training  techniques,” in Proceedings of the IEEE/CVF International Conference  on Computer Vision, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 9677–9685, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  [24] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Wan, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Zhou, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Liu, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Li, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' He, “Pose-aware multi-  level feature network for human object interaction detection,” in  Proceedings of the IEEE/CVF International Conference on Computer  Vision, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 9469–9478, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  [25] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Bansal, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Rambhatla, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Shrivastava, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Chellappa, “De-  tecting human-object interactions via functional generalization,”  in Proceedings of the AAAI Conference on Artificial Intelligence, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 34,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 10460–10469, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  [26] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Fang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Xu, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Wang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Liu, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Zhu, “Learning pose  grammar to encode human body configuration for 3d pose estima-  tion,” in Proceedings of the AAAI conference on artificial intelligence,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 32, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  [27] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Fang, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Lu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Fang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Xie, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='-W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Tai, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Lu, “Weakly  and semi supervised human body part parsing via pose-guided  knowledge transfer,” arXiv preprint arXiv:1805.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='04310, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  [28] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Xiu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Li, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Wang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Fang, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Lu, “Pose flow: Efficient  online pose tracking,” arXiv preprint arXiv:1802.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='00977, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  [29] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Qi, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Wang, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Jia, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Shen, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Zhu, “Learning human-  object interactions by graph parsing neural networks,” in Proceed-  ings of the European conference on computer vision (ECCV), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 401–  417, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  [30] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Kim, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Choi, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Kang, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Kim, “Uniondet: Union-level  detector towards real-time human-object interaction detection,”  in European Conference on Computer Vision, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 498–514, Springer,  2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  [31] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Liao, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Liu, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Wang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Chen, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Qian, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Feng, “Ppdm:  Parallel point detection and matching for real-time human-object  interaction detection,” in Proceedings of the IEEE/CVF Conference on  Computer Vision and Pattern Recognition, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 482–490, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  [32] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Carion, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Massa, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Synnaeve, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Usunier, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Kirillov, and  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Zagoruyko, “End-to-end object detection with transformers,” in  European conference on computer vision, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 213–229, Springer, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  [33] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Chen and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Yanai, “Qahoi: Query-based anchors for human-  object interaction detection,” arXiv preprint arXiv:2112.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='08647, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  [34] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Zhu, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Su, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Lu, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Li, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Wang, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Dai, “Deformable detr:  Deformable transformers for end-to-end object detection,” arXiv  preprint arXiv:2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='04159, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  [35] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Bengio, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Lamblin, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Popovici, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Larochelle, “Greedy  layer-wise training of deep networks,” Advances in neural informa-  tion processing systems, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 19, 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  [36] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Hinton, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Osindero, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='-W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Teh, “A fast learning al-  gorithm for deep belief nets,” Neural computation, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 18, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 7,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 1527–1554, 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  [37] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Kang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Xie, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Rohrbach, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Yan, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Gordo, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Feng, and  Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Kalantidis, “Decoupling representation and classifier for long-  tailed recognition,” arXiv preprint arXiv:1910.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='09217, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  [38] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='-W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Chao, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Liu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Liu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Zeng, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Deng, “Learning to  detect human-object interactions,” in 2018 ieee winter conference on  applications of computer vision (wacv), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 381–389, IEEE, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  [39] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Gupta and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Malik, “Visual semantic role labeling,” arXiv e-  prints, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  [40] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Scarselli, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Gori, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Tsoi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Hagenbuchner, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Mon-  fardini, “The graph neural network model,” IEEE transactions on  neural networks, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 20, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 61–80, 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  [41] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Vaswani, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Shazeer, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Parmar, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Uszkoreit, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Jones, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  Gomez, Ł.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Kaiser, and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Polosukhin, “Attention is all you need,”  Advances in neural information processing systems, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 30, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  [42] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' LeCun, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Bengio, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=', “Convolutional networks for images,  speech, and time series,” The handbook of brain theory and neural  networks, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 3361, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 10, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 1995, 1995.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  [43] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Liu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Lin, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Cao, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Hu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Wei, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Zhang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Lin, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Guo,  “Swin transformer: Hierarchical vision transformer using shifted  windows,” in Proceedings of the IEEE/CVF International Conference  on Computer Vision, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 10012–10022, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  [44] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Chen, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Wei, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Zeng, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Wang, “Conditional detr v2:  Efficient detection transformer with box queries,” arXiv preprint  arXiv:2207.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='08914, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  [45] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Wang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Zhang, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Yang, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Sun, “Anchor detr: Query  design for transformer-based detector,” in Proceedings of the AAAI  conference on artificial intelligence, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 36, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 2567–2575, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  [46] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Liu, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Li, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Zhang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Yang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Qi, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Su, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Zhu, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Zhang,  “Dab-detr: Dynamic anchor boxes are better queries for detr,”  arXiv preprint arXiv:2201.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='12329, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  [47] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Zhang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Luo, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Yu, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Cui, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Lu, “Accelerating detr  convergence via semantic-aligned matching,” in Proceedings of the  IEEE/CVF Conference on Computer Vision and Pattern Recognition,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 949–958, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  [48] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' He, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Zhang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Ren, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Sun, “Deep residual learning for  image recognition,” in Proceedings of the IEEE conference on computer  vision and pattern recognition, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 770–778, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  [49] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Iandola, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Moskewicz, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Karayev, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Girshick, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Darrell, and  K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Keutzer, “Densenet: Implementing efficient convnet descriptor  pyramids,” arXiv preprint arXiv:1404.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='1869, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  [50] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Newell, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Yang, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Deng, “Stacked hourglass networks for  human pose estimation,” in European conference on computer vision,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 483–499, Springer, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  [51] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Dong, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Bao, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Chen, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Zhang, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Yu, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Yuan, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Chen, and  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Guo, “Cswin transformer: A general vision transformer back-  bone with cross-shaped windows,” in Proceedings of the IEEE/CVF  Conference on Computer Vision and Pattern Recognition, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 12124–  12134, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  [52] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Yang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Li, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Zhang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Dai, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Xiao, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Yuan, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Gao, “Focal  self-attention for local-global interactions in vision transformers,”  arXiv preprint arXiv:2107.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='00641, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  [53] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Xia, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Pan, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Song, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Li, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Huang, “Vision transformer  with deformable attention,” in Proceedings of the IEEE/CVF Con-  ference on Computer Vision and Pattern Recognition, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 4794–4803,  2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  [54] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Wu, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Xiao, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Codella, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Liu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Dai, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Yuan, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Zhang,  “Cvt: Introducing convolutions to vision transformers,” in Proceed-  ings of the IEEE/CVF International Conference on Computer Vision,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 22–31, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  [55] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Dosovitskiy, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Beyer, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Kolesnikov, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Weissenborn, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Zhai,  T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Unterthiner, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Dehghani, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Minderer, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Heigold, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Gelly,  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=', “An image is worth 16x16 words: Transformers for image  recognition at scale,” arXiv preprint arXiv:2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='11929, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  [56] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='-F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Chen, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Panda, and Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Fan, “Regionvit: Regional-to-local  attention for vision transformers,” arXiv preprint arXiv:2106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='02689,  2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  [57] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Wang, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Huang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Song, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Huang, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Huang, “Not all  images are worth 16x16 words: Dynamic transformers for efficient  image recognition,” Advances in Neural Information Processing Sys-  tems, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 34, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 11960–11973, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  [58] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' He, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Gkioxari, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Doll´ar, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Girshick, “Mask r-cnn,” in  Proceedings of the IEEE international conference on computer vision,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 2961–2969, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  [59] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Dai, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Chen, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Xiao, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Chen, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Liu, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Yuan, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Zhang,  “Dynamic head: Unifying object detection heads with attentions,”  in Proceedings of the IEEE/CVF conference on computer vision and  pattern recognition, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 7373–7382, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  [60] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Law and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Deng, “Cornernet: Detecting objects as paired  keypoints,” in Proceedings of the European conference on computer  vision (ECCV), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 734–750, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  [61] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Lin, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Goyal, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Girshick, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' He, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Doll´ar, “Focal loss  for dense object detection,” in Proceedings of the IEEE international  conference on computer vision, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 2980–2988, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  [62] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Li, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Xu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Liu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Huang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Xu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Wang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Fang,  Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Ma, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Chen, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Lu, “Pastanet: Toward human activity  knowledge engine,” in Proceedings of the IEEE/CVF Conference on  Computer Vision and Pattern Recognition, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 382–391, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  JOURNAL OF LATEX CLASS FILES, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 14, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 10, JANUARY 2023  16  [63] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='-W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Chao, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Wang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' He, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Wang, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Deng, “Hico: A  benchmark for recognizing human-object interactions in images,”  in Proceedings of the IEEE international conference on computer vision,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' 1017–1025, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='  [64] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Loshchilov and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content=' Hutter, “Decoupled weight decay regulariza-  tion,” arXiv preprint arXiv:1711.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
+page_content='05101, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E2T4oBgHgl3EQfogh1/content/2301.04019v1.pdf'}
diff --git a/D9FKT4oBgHgl3EQfZi4o/content/tmp_files/2301.11803v1.pdf.txt b/D9FKT4oBgHgl3EQfZi4o/content/tmp_files/2301.11803v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..47716c9f7a03a6cc3baa35ee978e9e7dd106bd09
--- /dev/null
+++ b/D9FKT4oBgHgl3EQfZi4o/content/tmp_files/2301.11803v1.pdf.txt
@@ -0,0 +1,2097 @@
+Asymptotics in an Asymptotic CFT
+Lucas Schepersa1 and Daniel C. Thompsona,b2
+a Department of Physics, Swansea University,
+Swansea SA2 8PP, United Kingdom
+b Theoretische Natuurkunde, Vrije Universiteit Brussel,
+& The International Solvay Institutes, Pleinlaan 2, B-1050 Brussels, Belgium
+Abstract
+In this work we illustrate the resurgent structure of the λ-deformation; a two-
+dimensional integrable quantum field theory that has an RG flow with an SU(N)k
+Wess-Zumino-Witten conformal fixed point in the UV. To do so we use modern
+matched asymptotic techniques applied to the thermodynamic Bethe ansatz formu-
+lation to compute the free energy to 38 perturbative orders in an expansion of large
+applied chemical potential. We find numerical evidence for factorial asymptotic be-
+haviour with both alternating and non-alternating character which we match to
+an analytic expression. A curiosity of the system is that it exhibits the Cheshire
+Cat phenomenon with the leading non-alternating factorial growth vanishing when
+k divides N. The ambiguities associated to Borel resummation of this series are
+suggestive of non-perturbative contributions.
+This is verified with an analytic
+study of the TBA system demonstrating a cancellation between perturbative and
+non-perturbative ambiguities.
+1lucas.schepers@swansea.ac.uk
+2daniel.c.thompson@swansea.ac.uk
+arXiv:2301.11803v1  [hep-th]  27 Jan 2023
+
+1
+Introduction
+A complete understanding of the strong coupling dynamics of four dimensional asymp-
+totically free (AF) non-supersymmetric gauge theory, i.e. QCD, remains elusive. To
+gain a foothold we may turn to simplified toy models. One strategy is to reduce the
+dimensionality of the problem considering instead two dimensional quantum field the-
+ories with similar RG behaviour. In the special case of integrable QFTs, an infinite set
+of symmetries completely determine the exact S-matrix [1] providing a powerful toolkit
+that can be used to tackle non-perturbative questions. An early success of this approach
+was the calculation of the exact ratio of the mass gap to cut-off of AF integrable QFTs
+theories [2–5].
+More recently, techniques in integrable models have been used to elucidate even
+deeper questions of the nature of perturbation theory. Typically, perturbation theory is
+asymptotic in nature with perturbative coefficients growing factorially. The programme
+of resurgence asserts that this breakdown of convergence signals the need to include
+non-perturbative physics. Even more strongly, ambiguities inherent in resummations of
+asymptotic perturbative expansions should be cancelled by compensating ambiguities
+in a non-perturbative sector. For a modern overview of resurgence from a physics view
+point see e.g. [6]. Again, integrable two-dimensional models provide an ideal test bed
+for resurgence.
+In semi-classical approaches [7–12], an adiabatic compactification of two-dimension
+models is used to obtain a quantum mechanics which can be probed to large perturbative
+orders. In these cases, two-dimensional finite Euclidean action configurations, known as
+unitons1 are shown to precisely resolve the semi-classical ambiguities of the perturbative
+sector. Whilst intriguing, such approaches intrinsically disregard degrees of freedom in
+compactification restricting to the lowest KK sector. Alongside this features of renorm-
+alisation group are disregarded in the truncation to Quantum Mechanics. Given these
+limitations, one thus prompted to ask if the resurgence paradigm can be established in
+a fully two-dimensional setting.
+A breakthrough was the work of Volin [13, 14], recently refined in [15, 16] (see also the
+recent papers [17–25]), in addressing the Thermodynamic Bethe Ansatz (TBA) system
+that determines free energy in a large chemical potential. By comparing two scaling
+limits, it is possible to reduce the complicated integral TBA equation to a (complicated)
+set of algebraic equations that fix unknown coefficients in an ansatz for a perturbative
+expansion (in the chemical potential or other more refined coupling). This allows access
+to sufficient order in perturbation theory to reveal factorial divergence of perturbative
+coefficients.
+Although we cannot identify an instanton or other semi-classical non-perturbative
+saddle in the TBA approach, we can find a matching ambiguity using a different method.
+[26] showed that it is possible to solve the TBA equations using a transseries. A critical
+step in their solution is an arbitrary choice of branch cut which introduces an ambiguity
+of the transseries. Although this approach, due to its computational difficulty, cannot
+be executed to large orders, it does exhibit a non-perturbative ambiguity that matches
+the ambiguity of the large-order behaviour found in the perturbative sector.
+In this note we will adopt this toolbox to study the resurgent structure of a theory
+that exhibits a different renormalisation group dynamic. We consider a theory in which
+the UV is not Gaussian but instead is described by a non-trivial interacting conformal
+fixed point. The theory we will consider, known as the λ-model [27, 28], is realised as a
+flow away from an SU(N)k Wess-Zumino-Witten (WZW) model driven at leading order
+by a certain current-current bilinear. The IR of the theory is the principal chiral model,
+expressed in non-Abelian T-dual coordinates, and accordingly is gapped. Whilst this
+1Unlike instantons, unitons are not topologically protected.
+1
+
+marginally relevant deformation breaks conformality and the full affine symmetry of the
+WZW current algebra, it does preserve an infinite symmetry associated to integrablity.
+At the quantum level the exact S-matrix is known (based on symmetry grounds pre-
+dating the Lagrangian description) [29, 30] and has been shown to match the λ-model
+Lagrangian using a light cone lattice discretisation and Quantum Inverse Scattering [31].
+The goal of this note is to match the perturbative ambiguity to that of the transseries
+the new context of a λ-model. The outline is as follows: Section 2 provides a more in-
+depth discussion of the λ-model as we consider its RG flow in more detail and present
+its exact S-matrix. In Section 3, we review the recent techniques to perturbatively solve
+TBA equation [13–16] that determine free energy.
+Introducing a special coupling γ
+in Section 3.4 results in a clean (i.e. log-free) series for the λ-model. We analyse its
+asymptotic behaviour in Section 4 and compute the leading ambiguity. This ambiguity
+is matched by a transseries calculation in Section 5. A particularly eye-catching result
+is that the leading UV ambiguity disappears when N divides k. We wrap up with ideas
+for future research in Section 6.
+2
+The λ-Model
+In this section we outline the salient properties of the two-dimensional integrable QFT
+that we are considering: the λ-deformed model. Classically, the λ-model provides a
+Lagrangian interpolation between the conformal Wess-Zumino-Witten (WZW) model
+for a Lie-group G [32] and the principal chiral model (PCM) (written in non-Abelian
+T-dual variables). Remarkably this theory is integrable for all values of the eponymous
+interpolating parameter λ related to the level, k, of WZW and the radius, r, of the PCM
+by
+λ =
+k
+k + r2 .
+(1)
+Whilst the λ-model for the restricted case of G = SU(2) was first proposed long ago
+[29, 33, 34], the pioneering work of Sfetsos [27] in constructing the general theory has
+prompted extensive recent development (for reviews see [35, 36]). The λ-model has been
+extended to Z2 graded symmetric spaces [27, 37] where it constitutes an interpolation
+between a G/H gauged WZW (representing the coset CFT) and the (non-abelian T-dual
+of) the principal chiral model on G/H and even to Z4 graded super-cosets relevant to
+the construction of the AdS5 × S5 superstring [38] underpinned by an elegant quantum
+group at root-of-unity symmetry structure. In this string theory context, λ-deformation
+is in fact marginal, and the world sheet theory can be viewed as a σ-model in some
+target space super-gravity background [39–41]. Here however we will be considering the
+simpler bosonic case for which the λ-deformation does not define a CFT but rather a
+relevant RG flow from a WZW fixed point in the UV to the dualised PCM the IR [28,
+42, 43]. A series of papers [44–48] have shown how the λ-model is actually part of a wide
+tapestry of integrable deformed models linked by (analytically continued) Poisson-Lie
+T-duality transformations.
+2.1
+Lagrangian Construction
+First we sketch the construction of the non-abelian T-dual of the PCM using the Buscher
+procedure [49] as it informs the construction of the λ-model. We start with the action
+2
+
+of the PCM for a group valued field ˜g 2
+SPCM[˜g] = − r2
+4π
+�
+d2σ Tr
+�
+˜g−1∂+˜g˜g−1∂−˜g
+�
+,
+(2)
+and downgrade the left symmetry ˜g → h−1˜g to a gauge symmetry by introducing a
+gauge connection transforming as A → h−1dh + h−1Ah and replacing derivatives to
+covariant derivatives d → D = d + A. This yields the gauged PCM action which we
+denote as SgPCM[˜g, A]. To ensure that the gauged theory is actually equivalent to the
+ungauged theory (at least in trivial topology which we assume throughout) we enforce
+that the connection is flat (i.e. the gauge field is pure gauge). This is implemented by
+introducing a Lagrange-multiplier term, − Tr(νF+−), to the Lagrangian. Integrating
+out the field ν enforces that the field strength F+− vanishes and we recover the original
+PCM after gauge-fixing ˜g = 1. However, if instead we integrate out the gauge fields A,
+after gauge fixing ˜g = 1, we obtain the non-abelian T-dual model in which the field ν
+becomes the fundamental field.
+The construction of the λ-model by Sfetsos [27] is achieved through a modification of
+this Buscher procedure. Instead of adding a Lagrange multiplier term, we add a gauged
+WZW term. Recall that the WZW model is given by
+SWZW,k[g] = − k
+2π
+�
+Σ
+d2σ Tr
+�
+g−1∂µgg−1∂µg
+�
+− ik
+6π
+�
+M3
+Tr
+�
+g−1dg
+�3 ,
+(3)
+in which g is extended to a 3-manifold M3 with boundary ∂(M3) = Σ.
+Standard
+arguments [32] ensure that the path integral is well-defined (independent of choice of
+extension) provided that k is appropriately quantised, and in particular for G = SU(N)
+which we assume henceforth, k ∈ Z. In this sector we gauge the diagonal symmetry
+g → h−1gh leading to a gauged WZW model action SgWZW,k[g, A] [50, 51].
+To construct the λ-model we combine a gauged PCM and a gauged WZW model:
+Sλ,k[g, ˜g, A] = SgPCM[˜g, A] + SgWZW[g, A] .
+(4)
+Notice that the two models are coupled through the fact that they are gauged by the
+same gauge field. The Sfetsos procedure is concluded by gauge fixing ˜g = 1 and integ-
+rating out the gauge field A using its on-shell value
+A+ = λ(1 − λAdg)−1R+ ,
+A− = −λ(1 − λAdg−1)−1L− ,
+(5)
+where we defined R± = ∂±gg−1 and L± = g−1∂±g and the adjoint action AdgX =
+gXg−1. Integrating out the gauge field then yields the action
+Sλ,k[g] = SWZW,k[g] + kλ
+π
+�
+Σ
+d2σ Tr
+�
+R+(1 − λAdg)−1L−
+�
+.
+(6)
+Though not vital for what follows we note that the equation of motion can be understood
+as a zero-curvature condition on the Lax connection [27, 52]
+L±(z) = −
+2
+1 + λ
+A±
+1 ∓ z ,
+(7)
+in which A± are evaluated with the on-shell values eq. (5) and z ∈ C is a spectral
+parameter. This is the starting point of establishing the classical integrability of the
+theory. Further to this one requires strong integrability i.e. that the conserved charges
+built from the monodromy of this Lax are in involution. This is ensured provided that
+the Poisson algebra of the spatial component of the Lax has a particular r-s Maillet form
+as was demonstrated for the λ-model, and its generalisations, in [47, 53, 54].
+2We use light cone coordinates σ± = 1
+2 (t ± x). Derivatives with respect to light cone coordinates
+are denoted by ∂±.
+3
+
+2.2
+Renormalisation
+The parameter λ given by eq. (1) varies from 0 to 1 and we shall now discuss what
+happens in each of those limits. At a quantum level the parameter λ undergoes an RG
+flow [28, 42, 43] given by (to all orders in λ and leading in 1
+k)
+µdλ
+dµ = β(λ) = −2N
+k
+�
+λ
+1 + λ
+�2
+= −β1λ2 − β2λ3 + O(λ4) .
+(8)
+The leading order behaviour, which shall be relevant later, is given by
+β1 = 2N
+k ,
+β2 = −4N
+k .
+(9)
+There is an evident UV fixed point at λ = 0, corresponding to the undeformed WZW
+model. In the vicinity of this λ ≈ 0, or k ≪ r2, we obtain a current-current deformation
+of the WZW model:
+Sλ,k[g] = SWZW,k[g] + λ
+�
+Σ
+d2σ Tr (R+L−) + O(λ2) ,
+(10)
+This, however, is not a marginal deformation (cf. marginal ones [55]), but relevant as it
+moves away from the WZW theory located in the UV.
+To understand the IR regime as λ → 1, we can force k → ∞. If the group element
+is expanded as g = 1 + i
+kνata, the action SgWZW,k reduces to the Lagrange multiplier
+term − Tr(νF+−). Thus in this limit the Sfetsos procedure reduces to the non-Abelian
+T-dualisation Buscher procedure described above. Hence, in this IR limit, we recover the
+non-abelian T-dual of the PCM. Further into the deep IR, one thus anticipates (as with
+the PCM) that the dimensionless parameter λ is transmuted into a mass gap mediated
+through a cut-off Λ.
+2.3
+Quantum Integrability
+Not only is the theory classical integrable, it remains so at the quantum level. The
+existence of higher spin conserved currents ensure that the scattering matrix of the
+theory factorises, and can be fully determined with the 2-to-2 particle scattering matrix
+the fundamental building block. The S-matrix for the SU(N) λ-model was constructed
+many years ago [56] from an algebraic perspective, and was related directly to the
+Lagrangian description for the SU(2) case in [29] by matching the free energy obtained
+by Lagrangian perturbation theory and by S-matrix TBA techniques. Following the
+introduction of the Lagrangian description λ-model by Sfetsos [27] for SU(N) the exact
+S-matrix was conjectured [52] for general ranks. This conjecture was substantiated by
+Appadu et al. [31] in which the form of the S-matrix was ‘derived’ by the Quantum
+Inverse Scattering Method (i.e. a latticed version of the theory that takes the form of a
+spin chain such from the QFT particle states are obtained as excitations over the ground
+state in a continuum limit)3. Rather than present the full details of the S-matrix (for
+which see [52]) we can give a schematic understanding somewhat mirroring the Sfetsos
+procedure.
+3This QISM is in fact rather non-trivial as the δ′(σ) non-ultra-local terms in the fundamental Poisson
+bracket preclude a simple application of QISM. Instead what is proposed is a modification of the
+λ-model, that lies in the same universality class, to which QISM can be applied.
+This provides a
+description as a spin-k XXX spin chain with alternating inhomogeneities.
+This idea was expanded
+to a two-parameter integrable λ-type model [57] realised as a spin-k XXZ spin chain with alternating
+inhomogeneities.
+4
+
+We start with the SU(N) principal chiral model which has in particular an SU(N)L×
+SU(N)R global symmetry. The fundamental particles are massive and transform in fun-
+damental antisymmetric tensor representations of the global symmetry. The scattering
+depends kinematically only on the rapidity difference θ of the particles4. Reflecting this
+global symmetry, the S-matrix of these fundamental excitations has a schematic tensor
+form (suppressing explicit representation labels)
+SPCM(θ) = X(θ)S(θ) ⊗ S(θ) ,
+(11)
+where X(θ) is an overall scalar dressing factor to ensure all S-matrix axioms are obeyed,
+and the S(θ) factors are separately SU(N) invariant (in fact invariant under a larger
+Yangian symmetry). Recalling that in the Sfetsos procedure the left acting SU(N)L
+symmetry was gauged, it is natural that the left hand block of the tensor product of eq.
+(11) is modified in the λ-theory and indeed this is the case with
+Sλ(θ) = Xk(θ)Sk(θ) ⊗ S(θ) .
+(12)
+Here Sk(θ) is a block [56] that furnishes a quantum group symmetry at the q2(k+N) = 1
+root of unity taken in Restricted-Solid-On-Solid (RSOS) picture representing the scat-
+tering of kink degrees of freedom.
+Given knowledge of the exact S-matrix, the Thermodynamic Bethe Ansatz yields
+a set of rather complicated coupled-integral equations can be used to determine the
+free-energy of the theory. Solving these is quite formidable especially as the S-matrix is
+non-diagonal. A powerful simplification is achieved by exposing the system to a chemical
+potential h for a U(1) charge such that only certain particles condense and contribute
+to the ground state. When the charge is chosen appropriately (as the one defined by
+a highest weight of a rank N/2 antisymmetric representation [31]) then only a single
+particle of maximal charge contributes and the TBA system simplifies to a single integral
+equation determined by the identical scattering of this particle.
+In this case, the scattering “matrix” reduces to a simple phase factor S(θ) that
+governs transmission and reflection.
+It shall prove useful in this case to define the
+scattering kernel of this reduced S-matrix by
+K(θ) =
+1
+2πi
+d
+dθ log S(θ) ,
+(13)
+and its Fourier transform
+K(ω) =
+� ∞
+−∞
+dθ eiωθK(θ) .
+(14)
+As a consequence of Hermitian analyticity on the reduced S-matrix, both K(θ) and its
+Fourier transform are symmetric functions. Explicitly we have that the relevant kernel
+is given by [57]
+1 − K(ω) =
+sinh2(πω/2)
+sinh(πω) sinh(πκω) exp(πκω) ,
+(15)
+where κ =
+k
+N . In what follows, it shall prove useful to write the Fourier transform of
+the scattering kernel as a Wiener-Hopf (WH) decomposition
+1 − K(ω) =
+1
+G+(ω)G−(ω) ,
+(16)
+where G−(ω) = G+(−ω), and G+(ω) is analytic in the Upper Half Plane (UHP) and
+normalised such that G+(2is) = 1 + O
+�
+1
+s
+�
+. Explicitly G+(ω) is given by
+G+(ω) =
+√
+4κ
+Γ(1 − iω/2)2
+Γ(1 − iω)Γ(1 − iκω) exp (ibω − iκω log(−iω)) ,
+(17)
+4The mass shell is related to rapidity by p0 = m cosh θ and p1 = m sinh θ.
+5
+
+with
+b = κ(1 − log(κ)) − log(2) .
+(18)
+3
+TBA Techniques
+Polyakov and Wiegmann [58–60] showed in the 80s that it is possible to compute the free
+energy of an integrable system with a chemical potential h turned on using a thermody-
+namic Bethe ansatz (TBA) technique. Using these techniques, Hasenfratz, Niedermayer
+and Maggiore [2, 3] showed in 19905 that it is possible to calculate the mass gap in
+integrable models by comparing the result from TBA with conventional Lagrangian
+pertubation theory. Building from this we will will apply, in section 3.4, the techniques
+pioneered by [13–16] to extract an expansion for the free energy of λ-model in
+1
+h the
+large order behaviour of which we will study extensively in section 4.
+3.1
+Free Energy
+To present the TBA equations we will specialise to the case described above in which we
+introduce a chemical potential h such that only a single particle dominates the ensemble
+at large h.6 With K(θ) the appropriate scattering kernel, the TBA equations determine
+the density distribution of states, χ(θ), via
+m cosh(θ) = χ(θ) −
+� B
+−B
+K(θ − θ′)χ(θ′)dθ′ ,
+θ2 < B2 ,
+(19)
+from which the charge and energy density follow
+e = m
+� −B
+B
+χ(θ) cosh(θ) dθ
+2π ,
+ρ =
+� −B
+B
+χ(θ) dθ
+2π .
+(20)
+A critical complexity of this system is that the occupied states lie within a Fermi surface
+specified by B, which is however a function of h (with large B corresponding to large
+h). Supposing that we have calculated the energy density, thought of as a function of
+the charge density e = e(ρ), then we can reconstruct a free energy density, F(h), from
+a Legendre transform:
+ρ = −F′(h) ,
+F(h) − F(0) = e(ρ) − ρh .
+(21)
+3.2
+Resolvent Approach
+It will prove useful to recast the integral equation that determines χ(θ) in terms of a
+resolvent function defined by
+R(θ) =
+� B
+−B
+χ(θ′)
+θ − θ′ dθ′.
+(22)
+5This computation was intially performed for the O(N) model, but was later also completed for
+Gross-Neveu models [4, 5] and PCM models [61, 62].
+6That we can reduce the TBA system to involve just one species of particle from the fundamental
+representation singled out by the applied chemical potential is of course an assumption that makes the
+problem readily tractable. One anticipates that states of higher mass and higher charge are energetically
+disfavoured, but properly speaking this assumption ought to be proven starting from a complete nested
+TBA system (which we do not attempt here).
+6
+
+The resolvent is analytical everywhere except around the interval [−B, B] where it has
+an ambiguity given by
+χ(θ) = − 1
+2πi
+�
+R+(θ) − R−(θ)
+�
+,
+(23)
+where we use the short hand notation R±(θ) = R(θ ± iϵ). Suppose that the kernel can
+be cast in terms of some operator O as K(θ) =
+1
+2πiO 1
+θ, then the eq. (19) is equivalent
+to a Riemann-Hilbert problem
+R+(θ) − R−(θ) + OR(θ) = −2πim cosh θ .
+(24)
+A determination of R(θ) is then equivalent to solving the TBA system and once known
+the charge density is immediately extracted as
+ρ = − 1
+2π Resθ=∞R(θ) .
+(25)
+We briefly now review the approach of [13–15] which does so by considering ansatz
+solutions for the resolvent in two limits (the edge and bulk) and matching them to fix
+all undetermined coefficients.
+3.2.1
+Edge Ansatz
+We begin first with the edge limit in which the weak coupling limit B → ∞ is taken
+whilst keeping an edge coordinate z = 2(θ −B) fixed and small. This evidently scales to
+large θ and hence probes the properties of χ(θ) around the vicinity of the Fermi energy,
+B. This limit is best studied by considering the Laplace transform of the resolvent (22)
+given by
+R(z) =
+� ∞
+0
+�R(s)e−szds ,
+�R(s) =
+1
+2πi
+� i∞+δ
+−i∞+δ
+eszR(z)dz .
+(26)
+Note at large B the energy density is related to this Laplace transformation by
+e = meB
+4π
+�R(1/2) .
+(27)
+The key result of [15, 16] is that in the edge limit the Laplace transformed resolvent
+has the following form
+�R(s) = meBΦ(s)Φ
+� 1
+2
+�
+2
+�
+1
+s + 1/2 + Q(s)
+�
+,
+Φ(s) = G+(2is) ,
+(28)
+where G+(s) is the WH decomposition (16) of the (Fourier transformed) scattering
+kernel and Q(s) is a series in large s and a perturbative expansion in
+1
+B of the form
+Q(s) = 1
+Bs
+∞
+�
+m,n=0
+Qn,m
+Bm+nsn .
+(29)
+It should be noted that the coefficients Qn,m may still depend on log B.
+3.2.2
+Bulk Ansatz
+In the bulk limit we let B → ∞ and θ → ∞ but we keep u = θ/B fixed, we are hence
+studying the regime where θ is in the bulk, between 0 and B. The precise form of the
+7
+
+Bulk ansatz depends on the model. For the λ-model, we shall take the same bulk ansatz
+for the Gross-Neveu model [15], which is given by
+R(u) =
+∞
+�
+n=1
+∞
+�
+m=0
+n+m
+�
+k=0
+cn,m,k
+ue(k+1)
+Bm+n(u2 − 1)n
+�
+log u − 1
+1 + u
+�k
+,
+(30)
+where e(k) is 0 if k is even and 1 if k is odd.The bulk ansatz can be motivated by
+constructing it using functions that are analytic outside the interval [−B, B], where
+they have a logarithmic branch cut.7 This is precisely the analytic structure demanded
+by eqs. (22) and (23).
+3.3
+Matching
+If we re-expand the bulk ansatz (30) in an edge regime where z = 2(θ − B) is fixed, we
+should recover the expansion in the edge regime given by (28). Here a miraculous feature
+occurs: upon comparing expansions order by order in large B, then order by order in
+large z (which is small s) and then in log(z), we can solve for all the coefficients cn,m,k
+and Qn,m. One peculiarity of the procedure is that we perform this matching only for
+the regular terms of the expansion z−n (n ≥ 0), while we disregard all divergent terms
+zn (n > 0). Using a desktop PC, over the course of a week, we solved the system up
+to 38 orders. Once this calculation is completed, we compute e and ρ. Using equations
+(28) and (25) we can express ρ and e in terms of the coefficients by
+e = m2e2BΦ(1/2)2
+8π
+�
+1 +
+∞
+�
+m=1
+1
+Bm
+m−1
+�
+n=0
+2n+1Qn,m−1−n
+�
+,
+ρ = 2π
+∞
+�
+m=0
+c1,m,0
+Bm .
+(31)
+Explicitly the first few coefficients required to determine up to order B−2 are given by
+c1,0,0 = 4√κ ,
+c1,1,0 = −2κ3/2 ,
+c1,2,0 = 1
+2κ3/2(2 − κ − 4 log 2 + 4κ log(2B/κ)) ,
+Q0,0 = 0 ,
+Q1,0 = 0 ,
+Q0,1 = κ
+4 .
+(32)
+The last step is to calculate the quantity
+e
+ρ2 as an expansion in B the first terms of
+which are
+8κ
+π
+e
+ρ2 = 1 + κ
+B + κ
+B2
+�
+1 − log(2) + κ
+2 + κ log(2B/κ)
+�
++ O(B−3) .
+(33)
+As this result depends on log(B), it is convenient to define a new effective coupling γ in
+terms of which the perturbative expansion is free from logarithms as we shall do in the
+next section.
+3.4
+Perturbative result
+Before introducing the log-free coupling, we show our results are consistent with those
+of [31], which determines the mass gap of this theory. Using standard TBA techniques,
+7This is different from the PCM bulk ansatz which also has a square root branch cut along the
+interval [−B, B].
+8
+
+they find an expansion for the free energy given by
+F(h) − F(0) = −2h2κ
+π
+�
+1 − 2κα + 2κα2�
+2 + κ + log 4 + +2κ log κ + 2κ log α
+�
+− 8κ2α3 log(α)
+�
+(−2 + 2κ + log 4 + 2κ log(κ) + κ log(α)
+�
++ O(α3)
+�
+.
+(34)
+The coupling α is here defined by
+1
+α = 2 log
+�
+2h
+m
+�
+8κ
+π
+�
+.
+(35)
+By using the Legendre transformation (21) we can compute the total energy e from eq.
+(34). Doing so, we obtain the expression
+8κ
+π
+e
+ρ2 =1 + 2ακ − 2κα2(2κ log(ακ) − κ − 2 + log(4))+
+8κ2α3�
+κ log2(α) + (log(α) − 1)(−2 log(4) + 2κ log(κ))
+�
++ O
+�
+α4�
+.
+(36)
+From eq. (33), it follows that
+e
+ρ2 = χ0 + O(α) where χ0 =
+π
+8κ. Therefore to leading
+order we have h = ∂e
+∂ρ = 2χ0ρ, which leads to ρ = 4hκ
+π . Looking at eq. (35), we should
+thus define a coupling by
+1
+α = 2 log
+�
+ρ
+m
+�
+2π
+κ
+�
+.
+(37)
+This defines α in terms of B. Inverting the relation and substituting into the series (33)
+recovers precisely the expansion (36), providing an important consistency check for our
+programme.
+We now take inspiration from the Gross-Neveu treatment of [15] to create a series
+expansions for
+e
+ρ2 that is log-free. This is appropriate because we have that to leading
+order ∆F ∼ −h2 + O(α), which leads to a coupling defined by8
+1
+γ + ξ log γ = log 2πρ
+m/c ,
+ξ = β2
+β2
+1
+= − k
+N = −κ .
+(38)
+One could demand that the right hand side be log 2πρ
+ΛMS , where ΛMS is the cut-off in
+the minimal subtraction scheme. To achieve this one has to tune the constant c = cMS
+such that cMSΛMS = m. A key outcome of [31] determines that cMS = e3/2N −1/2.
+However, we shall exercise the freedom to pick a c of our own choosing,
+c = 2−κΓ(κ)
+π
+,
+(39)
+such that resulting expressions appear considerably simplified. This leads to an expan-
+sion that is log-free in the coupling, given by
+8κ
+π
+e
+ρ2 =
+∞
+�
+n=0
+anγn = 1 + κγ + κ
+2 [2 − κ]γ2+
+κ
+2
+�
+3 − 5κ + 2κ2�
+γ3 + κ
+8
+�
+3(8 − ζ(3)) − 61κ + 52κ2 − 15κ3�
+γ4+
+κ
+12
+�
+90 − 18ζ(3) + κ(33ζ(3) − 288) + 355κ2 − 203κ3 + 46κ4�
+γ5+
+κ
+32
+�
+45(16 − 4ζ(3) − ζ(5)) + 2κ(259ζ(3) − 1338) + 1
+3κ2(12274 − 1329ζ(3))
+− 3285κ3 + 1412κ4 − 787κ5
+3
+�
+γ6 + O(γ7) .
+(40)
+8This is in contrast to the PCM calculation where the free energy has a structure ∆F ∼ − h2
+α +O(α0),
+which leads to a coupling 1
+γ + (ξ − 1) log γ ∝ log ρ.
+9
+
+Figure 1: Left to right, for κ = 0.98, 1 and 1.02, the Borel-Pad´e-poles in the ζ-plane.
+Evident are singularities at ζ = ±2, with the positive pole removed for κ = 1.
+In the next Section we shall explore this perturbative expansion further.
+4
+Asymptotic Analysis
+In this Section, we will quantitatively analyse the 38 orders of the perturbative series
+obtained in the previous Section. The goal shall be to compute an asymptotic formula
+for the growth of the coefficients as a function of κ. After obtaining such a formula, we
+can compute its Borel ambiguity, which can later be compared against an ambiguity of
+a transseries.
+As the perturbative series can readily be seen to exhibit factorial growth, as a first
+step to resummation we introduce the Borel transform
+B
+�8κ
+π
+e
+ρ
+2�
+≡
+∞
+�
+n=0
+an
+n! ζn .
+(41)
+This series has a finite radius of convergence but typically has either, or both, poles
+and branch cuts. The pole/branch point closest to the origin in the ζ plane is governed
+by the leading asymptotic behaviour.
+Of course, numerically one does not have all
+orders with which to establish this Borel transformation, rather only a finite number
+of coefficients an for n < N say. Here the Borel-Pad´e method can be employed: we
+compute BN[ 8κ
+π
+e
+ρ
+2] = �N
+n=0
+an
+n! ζn = P (ζ)
+Q(ζ) + O(ζ)N+1 in which P and Q are polynomials
+in ζ of degree N/2. This results in a picture in which an accumulation of poles (i.e.
+zeros of Q) is indicative of a branch point. We perform this numerically for various
+values of κ and generically we find evidence of branch points at ζ = ±2 whose location
+is independent of κ except that for κ ∈ Z>0 the pole in the positive axis is removed -
+see Figure 1. Pole/ branch points in the negative real axis of the Borel plane indicate
+contributions to an of alternating sign whereas the contributions to an that result in
+poles on the positive axis would have the same sign. Here the analysis indicates that we
+have both. With 38 perturbative coefficients this analysis should only be regarded as
+indicative but is sufficient to inform an educated guess as to the asymptotic behaviour
+of the an which we will robustly verify below.
+Motivated by the Borel-Pad´e analysis we assume the coefficients grow, to leading
+approximation, as
+an ≈ A+Γ(n + 1)/Sn + A−Γ(n + 1)/(−S)n + O(n−1) .
+(42)
+A first verification is to establish the factor S which can be done noting that
+g+,n :=
+a2n
+2n(2n − 1)a2n−2
+≈ 1
+S2 ,
+g−,n :=
+a2n+1
+2n(2n − 1)a2n−1
+≈ 1
+S2 .
+(43)
+10
+
+4
+2
+-2
+2
+4
+.4
+-24
+2
+-2
+2
+4
+4
+.24
+2
+-2
+2
+4
+.4
+-2Figure 2: The series g+,n (left) and g−,n (right) given by eq. (43) displayed for κ = 0.6.
+Circle markers indicate the raw data, square markers the second Richardson transform-
+ation with accelerated convergence. The final values of the second Richardson transform
+differ by 0.11% and 0.05% respectively from the expected value 1
+4.
+We find, see Figure 2, that the series g±,n converge to 1
+4, independent of κ thus estab-
+lishing S = 2 in accordance with the expectation from the Borel-Pad´e analysis.
+Having established the factorially growing character of the perturbative series, we
+now propose a more refined ansatz for the an. Our central claim can be summarised
+by stating that the perturbative series has coefficients that have a leading large order
+behaviour as
+an ≈ A+
+2n
+∞
+�
+l=0
+β+
+l Γ(n + a+ − l) +
+A−
+(−2)n
+∞
+�
+l=0
+β−
+l Γ(n + a− − l) ,
+(44)
+where we normalise β±
+0 = 1 and the first few coefficients are
+a± = ∓2κ ,
+A± = 8±1
+π
+sin(∓κ)Γ(±κ)
+Γ(∓κ) = −
+8±1
+Γ(∓κ)Γ(1 ∓ κ) ,
+β−
+1 = −β−
+2 = −4κ .
+(45)
+To support these claims, we shall define the auxiliary series
+cn =
+2n
+Γ(n + 1)an ,
+(46)
+to take care of the leading factorial and geometric growth. We project to the alternating
+and non-alternating parts of the series by considering
+f ±
+k = c2k ± c2k−1 ,
+(47)
+which have asymptotics
+f ±
+n = 2A±(2n)a±−1�
+1 + O
+� 1
+n
+��
+,
+(48)
+such that the sequences
+σ±
+n = 1 + n log f ±
+n+1
+f ±
+n
+,
+(49)
+converge to a±. With a± determined one can then directly consider the asymptotics of
+f ± to establish A±. Figure 3 illustrates the convergence of this procedure for a fixed
+11
+
++.n
+0.30r
+0.28
+O
+0.26
+boo
+0.24
+0.22
+0.20
+5
+10
+15
+0
+20g-,n
+0.30r
+0.28
+0.26
+0000000
+口
+0.24
+口
+0.22
+口
+0.20
+5
+10
+15
+0Figure 3: The series σ−
+n (left) converges to a− using (49). Using eq. (48) we display
+(right) the sequence that converges to A−. Circle markers indicate the raw data, square
+markers the second Richardson transformation. For both, we display results for κ = 0.9.
+The second Richardson transform converge to the expected results given by eq (45) up
+to errors of 0.011% and 0.00068% respectively.
+Figure 4: The second Richardson transformation of the sequences (49) (left) and (48)
+(right) to determine a± and A± as functions of κ. a+, A+ are indicated by red crosses
+and a−, A+ by blue points with solid lines showing the analytic formula of eq. (45).
+value of κ, and Figure 4 establishes the functional form of these coefficients for various
+values of κ.
+A methodological subtlety is that, from empirical observation, the contributions from
+the alternating sector, i.e.
+A− (and associated subleading terms), are dominant for
+κ > 0 over those of the non-alternating A+ sector. Thus to extract the non-alternating
+contributions we first establish the leading alternating contribution as described above
+and then repeat the process working instead with a new series in which the leading
+alternating contribution has been subtracted. However, when κ becomes sufficiently
+large, the sub-leading alternating contribution becomes comparable to that of the leading
+non-alternating contribution. This limits the reliability of determination numerically of
+the A+, a+ coefficients to small values of κ. However, these coefficients can be more
+readily verified by continuing to the κ < 0 regime where they are more dominant.
+Having determined in this fashion the leading contributions to an, these can then be
+subtracted from the data, the analysis repeated mutatis mutandis, to determine the sub-
+leading βk coefficients (and again for similar reasons to the above the β−
+k coefficients are
+more readily extracted). Figure 5 gives the numerical form of β−
+1 and β−
+2 as a function
+of κ indicating a linear relationship.
+It becomes somewhat challenging to extract further subleading contributions from
+the data available. However, one can consider defining a new series, ˜an, comprised by
+taking the data set and subtracting the already established asymptotic form of eq. (45).
+12
+
+n
+2.00
+1.95
+1.90
+O
+1.85
+1.80
+666660
+口
+1.75
+口
+口
+1.70
+1.65
+1.60
+0
+5
+10
+15A.
+-0.08r
+-0.10
+-0.12
+-0.14
+-0.16
+5
+10
+15
+20
+0a at
+4
+2
+K
+.3
+-2
+2
+3
+-264A- A+
+-2
+2
+-6
+8Figure 5: The sub-leading coefficient β−
+1 (left) and β−
+2 (right) for various values of κ.
+Shown is the terminal value of the second Richardson Transformation of the sequence
+that gives β−
+n constructed from fn after subtraction of leading alternating and non-
+alternating asymptotics.
+Grey lines correspond to β−
+1
+= −4κ and β−
+2
+= +4κ.
+A
+noticeable drift in β−
+2 for larger values of κ suggests pollution from further sub-dominant
+terms contributing at this order of perturbation theory.
+Figure 6: After subtracting the leading alternating and non-alternating contributions,
+we again perform a Borel-Pad´e computation for κ = −0.75 (left) and κ = 0.4 (right).
+This seems to suggest that there is no longer a Borel singularity at ζ = 2, but instead
+finding one at ζ = 4.
+Using the Borel-Pad´e again to this subtracted series produces some evidence, see Figure
+6, of a compelling feature. Instead of poles at ζ = ±2, as would be anticipated should
+the ansatz (44), one finds that leading positive pole appears to be at ζ = +4. The
+interpretation here is that the subtraction has removed the entire non-alternating terms
+with behaviour 2−n, suggesting that all fluctuations β+
+n>0 = 0 and the next contribution
+comes with twice the “action” 4−n.
+This behaviour is in accordance with the Parisi-’t Hooft conjecture [63–65]; the
+leading poles in the Borel plane at ζ = ±2 lie at integer values and the values of
+a± = ∓2κ = ±2ξ are as expected (see [15]).9
+The pole at ζ = +2 is accordingly
+interpreted as an IR renormalon.
+A similar procedure of subtraction (removing the
+IR renormalon) used above (in Figure 6) was performed in [26] to expose new Borel
+renormalon poles that were not in accordance with Parisi-’t Hooft in cases including e.g.
+the Gross-Neveu model. Here however, Figure 6 indicates that the next most proximate
+IR renormalon pole is found in a location that are consistent with Parisi-’t Hooft.
+9We thank M Mari˜no and T Reis for illuminating us on this point.
+13
+
+β1-
+K
+0.5
+1.0
+1.5
+2.0
+2.5
+3.0
+-2
+-4
+-6
+-8
+-10
+.12β2
+12
+10
+8
+6
+4
+2
+0.5
+1.0
+1.5
+2.0
+2.5
+3.02
+.2
+2
+6
+22
+2
+65
+Transseries and Ambiguity Cancellation
+In this section we compute the leading ambiguity of
+e
+ρ2 in two different ways. First,
+we calculate the Borel ambiguity of the large order behaviour of the perturbative sector
+established in 4. This is compared against an approach which solves the TBA system
+in terms of a transseries.
+5.1
+Borel resummation and Large Order Perturbative Ambigu-
+ity
+Naively, one could try to resum the original asymptotic series by performing a Laplace
+transform on the Borel transform (41)
+1
+γ
+� ∞
+0
+B
+�8κ
+π
+e
+ρ2
+�
+e−ζ/γdζ = 1
+γ
+� ∞
+0
+∞
+�
+n=0
+an
+n! ζne−ζ/γ ≃
+∞
+�
+n=0
+anγn = 8κ
+π
+e
+ρ2 .
+(50)
+However, as we have seen, the Borel transform B
+�
+8κ
+π
+e
+ρ2
+�
+generically has singularities
+along the positive real axis obstructing the contour of this integral. Therefore, we shall
+introduce a directional Borel resummation given by
+Sθ
+�8κ
+π
+e
+ρ2
+�
+= 1
+γ
+� eiθ∞
+0
+B
+�8κ
+π
+e
+ρ2
+�
+e−ζ/γdζ .
+(51)
+This procedure results, when integrating along a line without singularities, in a finite
+answer, which however, depends on the sign of θ, i.e.
+there is an ambiguity in the
+resummation of the perturbative series. This ambiguity, which is a Stokes phenomenon,
+is studied by considering S+ϵ − S−ϵ. This can be done analytically by using, instead of
+the numerically obtained results, a series whose coefficients are exactly the asymptotic
+form an given by eq. (44) for all values of n:
+(S+ϵ − S−ϵ)
+�8κ
+π
+e
+ρ2
+�
+(γ) = 2πiA+
+� 2
+γ
+�a+
+e−2/γ
+∞
+�
+k=0
+β+
+k
+�γ
+2
+�k
+= −
+16πi
+Γ(−κ)Γ(1 − κ)
+�γ
+2
+�2κ
+e−2/γ[1 + O(γ)] .
+(52)
+Similarly, across the negative real axis we find a leading ambiguity given by
+(Sπ+ϵ − Sπ−ϵ)
+�8κ
+π
+e
+ρ2
+�
+(γ) = 2πiA−
+�
+− 2
+γ
+�a−
+e2/γ
+∞
+�
+k=0
+β−
+k
+�
+− z
+2
+�k
+= −
+πi
+4Γ(κ)Γ(1 + κ)
+�
+−γ
+2
+�−2κ
+e2/γ[1 + O(γ)] .
+(53)
+In these expressions we note the presence of an exponentially small parameter, √qγ =
+�
+2
+γ
+�2κ
+e−2/κ (the square root is for convenience later) characteristic of non-perturbative
+physics. The main thrust of the modern resurgence paradigm is that physical quantities,
+here e/ρ2, should be understood as a transseries, i.e. an expansion in √qγ whose terms
+are each formal (asymptotic) series in γ. It is critical that whilst resummation may
+be ambiguous when applied to any individual term in this (here the perturbative √qγ0
+sector), taken altogether the final result is non-ambiguous. In particular, and this goes
+back to the pioneering work of Bogomol’nyi and Zinn-Justin [66–69], the ambiguity
+of this perturbative sector should be compensated by a leading order ambiguity in an
+appropriate non-perturbative sector. In the next section we shall verify that such an
+ambiguity cancellation does take place.
+14
+
+5.2
+Transseries and Leading Non-Perturbative Ambiguity
+In this series we shall apply a different type of analysis to the TBA equations which
+results in a transseries solution. The starting point shall be a reformulation of the TBA
+system as an integral equation for an auxiliary function u(ω),
+u(ω) = i
+ω +
+1
+2πi
+� ∞
+−∞
+dω′ e2iBω′ϱ(ω′)u(ω′)
+ω′ + ω + iδ
+,
+(54)
+where
+ϱ(ω) = 1 − iω
+1 + iω
+G−(ω)
+G+(ω) ,
+(55)
+together with the boundary condition
+u(i) = m
+2heB G+(i)
+G+(0) .
+(56)
+Having established the function u, the free energy is given by
+∆F(h) = − 1
+2π h2u(i)G−(0)2
+�
+1 −
+1
+2πi
+� ∞
+−∞
+dω e2iωBu(ω)ϱ(ω)
+ω − i
+�
+.
+(57)
+We will now apply to the λ-model the techniques pioneered by [26] to solve this re-
+cursively order by order in a perturbative parameter and a non-perturbative parameter.
+The idea is to move the integration contour of the integral equation (54) into the UHP
+so that it envelops all the branch cuts and poles in the UHP. The Sine-Gordon model is
+special as it only has poles but no branch cut. This was studied in [70] and gives rise to
+a convergent rather than asymptotic expansion. However, in the case of the λ-deformed
+model, we are dealing with both poles and a branch cut along the imagine axis of ρ(ω).
+To separate it from the poles, we slightly move the cut away from the imaginary axis
+to the ray C± = {ξeiθ|θ = π
+2 ± δ}. By deforming the integration contour we isolate the
+contributions coming from the discontinuity over the cut and the residues at the poles
+(see Figure 7). As explained in [26] the choice of moving the branch cut to C+ or C− is
+arbitrary and and gives rise to a leading non-perturbative ambiguity. Letting ϱn,± be
+the residues at x = xn with the cut moved to C±, after this contour pulling eq. (54)
+becomes
+u(ix) = 1
+x +
+1
+2πi
+� ∞e±iϵ
+0
+dx′ e−2Bx′u(ix′)δϱ(ix′)
+x′ + x
++
+�
+n
+e−2Bxnunϱn,±
+xn + x
+,
+(58)
+where un ≡ u(ixn) and δϱ is the discontinuity over the cut10.
+From the WH-decomposition (17), we evaluate ϱ(ω) using (55) as
+ϱ(ω) = −ω + i
+ω − i
+Γ
+� iω
+2 + 1
+�2 Γ(1 − iω)Γ(1 − iκω)
+Γ
+�
+1 − iω
+2
+�2 Γ(iω + 1)Γ(iκω + 1)
+e−2ibωeiκω(log(iω)+log(−iω)) .
+(59)
+For generic values of κ, this has poles on the positive real axis at ω = ixn = iµn with
+µ = 2 with residues given by
+ϱn,± =
+Res
+x=xn±iϵ ϱ(ix) = −2ie2n(2b±iπκ−2κ log(2n))n2n + 1
+2n − 1
+((2n)!)2
+(n!)4
+Γ(1 + 2nκ)
+Γ(1 − 2nκ) .
+(60)
+However, when κ is rational some of these poles are removed.
+Suppose we express
+κ ≡
+k
+N = p/q as a reduced fraction with p, q coprime integers (i.e. q = N/gcd(N, k)),
+10For the discontinuity function, we use the convention δρ(ω) = ρ(ω(1 − iϵ) − ρ(ω(1 + iϵ)).
+15
+
+ω
+C−
+C
+ϱ−
+1
+ϱ−
+2
+ϱ−
+3
+ω
+C+
+C
+ϱ+
+1
+ϱ+
+2
+ϱ+
+3
+Figure 7: The contour C = (−∞, ∞) is deformed into either of two ways. The branch
+cut, represented by the curvy line is moved to either the ray C+ or C−. In those cases
+respectively, the contour is deformed into C+ or C−. In both cases we pick up residues
+ϱ±
+n , but their values differ by the branch cut discontinuity.
+then the set of poles are located at x ∈ 2N\qN (rather than x ∈ 2N). Hence, the residue
+ϱn,± evaluates to zero if 2n ∈ 2N ∩ qN, i.e. 2n is a multiple of q. In particular, when
+k is an integer multiple of a half, i.e. q = 1 or q = 2, all poles are removed entirely.
+If ϱ1 = 0, then ϱn = 0 for all n; in what follows we shall consider only the case where
+ϱ1 ̸= 0 which is most relevant to our discussion.
+The discontinuity function is given by
+δϱ(ix) = 2ix + 1
+x − 1e2bxe−2κx log x sin(κπx)Γ(1 − x/2)2Γ(1 + x)Γ(1 + κx)
+Γ(1 + x/2)2Γ(1 − x)Γ(1 − κx) .
+(61)
+Notice this has simple poles at x = 2n, which have residues that vanish for κ half-integer.
+Lastly we shall need11
+ϱ(i ± 0) = 8e2b∓iπκ Γ(1 + κ)
+Γ(1 − κ) = 8
+πκe2b∓iπκΓ(1 + κ)2 sin(πκ) .
+(62)
+Following again [26], the integral equation (58) is simplified by the introduction of
+P(η, v) given by
+e−2Bxδϱ(ix) = −2ive−ηP(η, v) ,
+(63)
+with a change of variables (x, B) → (η, v):
+1
+v + a log v = 2B ,
+x = vη .
+(64)
+Here, a is a constant determined by demanding that P(η, v) is regular in v with, in
+particular, no log(v) terms. From eq. (61), we have that δϱ(ix) ∝ e˜ax log x � dnxn,
+where ˜a = −2κ, therefore this determines ˜a = a. This yields an expansion of P(η, v)
+given by
+P(η, v) = d1,0η + vη2(d2,0 + d2,1 log(η)) + O(v2) ,
+d1,0 = πκ ,
+d2,0 = 2πκ(1 + (1 − γE − log(κ))κ − log(2)) ,
+d2,1 = −2πκ2 .
+(65)
+With the introduction of an integral operator
+I[f](η) = − v
+π
+� ∞
+0
+dη′ e−η′P(η′, v)f(η′)
+η + η′
+,
+(66)
+11Because we are assuming that κ is not integer, ϱ(i±0) is non-zero. If κ < 0, then ϱ(i±0) generically
+has a finite ambiguity.
+16
+
+after this change of variables, eq. (58) can be written as
+u(η) = u(η) + I[u](η) ,
+(67)
+in which the ‘seed’ solution is given as
+u(η) = 1
+vη + 1
+v
+�
+n
+e−2Bvηnunϱn,±
+ηn + η
+.
+(68)
+The formal solution obtained by iteration is thus presented as
+u(η) =
+∞
+�
+l=0
+Il[u](η) ≡ J [u](η) .
+(69)
+To determine the unknown coefficients un = u(ηn) we evaluate eq.(67) at η = ηn =
+µn/v and define In[f] ≡ I[f](η = ηn) to obtain
+un = 1
+µn + In[u] + 1
+µ
+�
+m
+e−2Bvηnumϱm,±
+m + n
+.
+(70)
+Here we have made a slight adaptation compared to [26] to suit the locations of the poles
+at xn = µn (with µ = 2) (cf. the Gross-Neveu model for which xn = 2n+1
+Υ
+for some
+constant Υ). To treat the exponentially small contributions coming from the residue
+term we introduce the small parameter
+q = e−2Bµ = e−µ/vv−µa .
+(71)
+Both the seed and formal solution, and the unkown values un, admit expansion in q
+u(η) =
+�
+s=1
+u(s)(η)qs ,
+u(η) =
+�
+u(s)(η)qs ,
+un =
+�
+s=0
+u(s)
+n qs .
+(72)
+As the operator J does not introduce factors of q we can construct the full solution
+order by order in q noting u(s)(η) = J [u(s)](η). Using (68) one finds that the first few
+terms12 of the seed solution are given by
+u(0) = 1
+vη ,
+u(1) = ϱ1,±u(0)
+1
+vη + µ ,
+u(2) = ϱ1,±u(1)
+1
+vη + µ + ϱ2,±u(0)
+2
+vη + 2µ .
+(74)
+Applying the q-expansion to eq. (70) we have that
+u(0)
+n
+= J [u(0)](ηn) = 1
+µn + In[J [ 1
+vη ]] ,
+u(1)
+n
+= In[J [u(1)]] + 1
+µ
+ϱ1,±u(0)
+1
+1 + n
+.
+(75)
+Let us assume that ϱ1,± ̸= 0 (i.e. κ is not half-integer), such that these two expressions
+are governing the leading behaviour. Suppose now we work formally13 to leading order
+12For n ≥ 1, we have in general
+u(n)(η) =
+n
+�
+m=1
+ϱm,±u(n−m)
+m
+vη + µm
+.
+(73)
+13i.e. ignoring that q is exponentially smaller than higher order polynomial terms in v.
+17
+
+in v and leading order in q . Because each application of I carries a factor v, to leading
+order it is sufficient to consider only the identity operator J = 1+. . . which results in14
+u(0)
+n
+= 1
+µn −
+v
+nπµd1,0 + O(v2) ,
+u(1)
+n
+=
+ϱ1,±
+µ2(n + 1) −
+d1,0ϱ1,±
+µ2π(n + 1)v + O(v2) .
+(76)
+The leading orders of u(η) are obtained by
+u(η) =
+�
+u(0) + I[u(0)] + O(v)
+�
++ q
+�
+u(1) + I[u(1)] + O(v2)
+�
++ O(q2) .
+(77)
+To implement the boundary condition that relates the chemical potential h to q, v,
+we will need
+u(i) = u
+�
+η = 1
+v
+�
+=
+�
+1 − d1,0
+π v + O(v2)
+�
++
+qϱ1,±
+µ(1 + µ)
+�
+1 − d1,0v
+π
++ O(v2)
+�
++ O(q2) .
+(78)
+The next step is to do the Legendre transform and calculate
+e
+ρ2 from ∆F. This can
+then be used to compare against the perturbative calculation. The same procedure of
+resolving the cut away from the poles of ρ and deforming the contour appropriately
+yields
+∆F(h) = − h2
+2π u(i)G+(0)2
+�
+1 + v2
+π
+� e−ηP(η, v)u(η)
+ηv − 1
+dη
+− e−2Bϱ(i ± ϵ)u(i) −
+�
+n≥1
+qnϱn,±un
+µn − 1
+�
+.
+(79)
+The leading orders of eq. (79) are given by
+∆F(h) = − G+(0)2h
+2π
+�
+1 − 2d10
+π v + O(v2)
+�
+×
+�
+1 − ρ(i ± ϵ)q1/µ +
+2ρ1,±
+µ(1 − µ2)q − 2ρ1,±ρ(i ± ϵ)
+µ(1 + µ)
+q1+1/µ + O(q2)
+�
+.
+(80)
+The first step of the Legendre transform is to relate h to the parameters q and v. This
+is done by substituting the expansion (78) for u(i) into the boundary condition (56)
+which, for µ = 2, gives
+h =
+mG+(i)
+12πG+(0)q−1/4�
+π + d1,0v + O(v2)
+��
+6 − ρ1,±q + O(q2)
+�
+.
+(81)
+As a consequence ρ = − d∆F
+dh
+is given by
+ρ = G+(i)G+(0)m
+12π2
+�
+π − d1,0v + O(v2)
+��
+6q−1/4 + ρ1,±q3/4 + O(q7/4)
+�
+,
+(82)
+from which we obtain
+e
+ρ2 as a series in v and q:
+e
+ρ2 =
+1
+6G+(0)2
+�
+π + 2d1,0v + O(v2)
+��
+3 + 3ρ(i + ±ϵ)q1/2 + ρ1,±q + O(q3/2)
+�
+.
+(83)
+14The small v limit can be taken also in the integral:
+I
+� 1
+vη
+�
+(ηn) = − v
+π
+� ∞
+0
+eη′d1,0η
+vη′ + nµ = − v
+π
+� ∞
+0
+�
+eη′d1,0
+nµ
++ O(v)
+�
+= − vd1,0
+nπµ + O(v2) .
+18
+
+We will now write this expansion in terms of the coupling (38) used in the previous
+Sections. Let us introduce a parameter exponentially small in γ, analogous to q being
+exponentially small in v, given by qγ = e−4/γ(γ/2)4κ. We use (38) to write v as a series
+in γ and qγ. Substituting this series for v (and q = q(v)) into (83), we arrive at
+8κ
+π
+e
+ρ2 =
+�
+1 + κγ + O(γ2)
+�
+− 8e∓iπκ Γ(κ)
+Γ(−κ)q1/2
+γ
+(1 + O(γ))
++ 23−4κe∓2iπκ Γ(2κ)
+Γ(−2κ)qγ(1 + O(γ)) .
+(84)
+We see that the first two coefficient of the perturbative series match precisely with eq.
+(40). The presence of transseries parameters qγ = e−4/γ(γ/2)4κ provides concrete pre-
+dictions of the resurgent structure of the perturbative series. In particular, we compute
+the ambiguity of the transseries (84) due to the difference in result if the branch cut is
+left or right of the poles. To leading order in qγ and γ, it is given by
+8κ
+π
+�� e
+ρ2
+�
+−
+−
+� e
+ρ2
+�
++
+�
+=
+16πi
+Γ(−κ)Γ(1 − κ)
+�γ
+2
+�2κ
+e−2/γ .
+(85)
+This is exactly the same ambiguity as obtained through the asymptotic analysis of our
+perturbative calculation - see eq. (52). We thus observe that the Borel-ambiguity of
+the perturbative series can be cancelled precisely by an ambiguity of a transmonomial.
+Therefore, the large order non-perturbative behaviour is unambiguous up to the order
+considered. This mirrors the fabled BZJJ ambiguity cancellation [66–69] in a field theory
+context.
+The analysis above only finds a source of the leading ambiguity on the positive
+real axis of the Borel plane. However, we can do a similar analysis to recover the Borel
+branch singularity on the negative real axis. The critical modification of the programme,
+as realised by [15], is to deform the contour of the integral equation (54) into the lower
+half plane, instead of the upper half plan. The critical analytic data is then given by the
+branch cut and residues at the negative imaginary axis. In the lower half plane, ϱ(−ix)
+has residues at xn = 2n + 1 and at ˜xn := n
+κ. However, as the latter set of residues is
+unambiguous with respect to the branch cut, they do not contribute15. One subtlety
+when using this approach arises when computing u(i). Deforming the contour of eq.
+(54) to an envelopment of the negative imaginary axis picks up a residue at ω = −i,
+which introduces a contribution of u(−i)ρ(−i ± ϵ)q not present in the analysis above.
+We will not present a detailed derivation as it is similar to the one above. Rather, we
+can report that the final result is a transseries with a leading ambiguity given by
+8κ
+π
+�� e
+ρ2
+�
+−
+−
+� e
+ρ2
+�
++
+�
+= −
+πi
+4Γ(κ)Γ(1 + κ)
+�
+−γ
+2
+�−2κ
+e2/γ .
+(86)
+This precisely matches the ambiguity of the perturbative sector around the negative real
+axis found in eq. (53).
+6
+Discussion
+In this note, we have studied the λ-model and brought it into the fold of resurgent
+analysis of [13–15, 26]. The model is particularly interesting, because, distinct from
+previously considered models, it has a interacting CFT fixed point in the UV.
+15They would be part of a transseries solution, but as they are unambiguous, they are not of interest
+to us currently. As a further side remark, when choosing κ < 0, along the positive imaginary axis ϱ(ix)
+also has such unambiguous residues at x = n
+κ .
+19
+
+We have found a perturbative series for the energy density at finite chemical poten-
+tial of the λ-model in Section 3.4 and identified with numerical techniques its asymp-
+totic form in Section 4.
+A key feature is that the Borel resummation of the large
+order behaviour is ambiguous when taken along either the positive or negative real axis.
+These ambiguities are exactly compensated/cancelled by a further ambiguity in a non-
+perturbative sector of a transseries solution in Section 5. These cancellations provide the
+λ-model with a robustly defined foundation which may serve as a paradigmatic example
+for other theories with asymptotic CFT behaviour.
+Of particular note is that the leading ambiguity on the positive axis (and associated
+features in the Borel plane) vanishes for κ ∈ Z>0, i.e. when the WZW level k divides
+the rank N of the gauge group SU(N). This is reminiscent of Cheshire-cat resurgence
+[71–74] in which the full glory of resurgence only becomes apparent as you deform away
+from certain special points at which it truncates.
+Let us finish with some broader questions to ponder following the analysis of the
+λ-model that we hope might stimulate further investigations on the topic:
+• An interesting feature of the WZW CFT that defines the UV of the λ model is
+that it exhibits level-rank duality [75]. It would be valuable to understand the
+extent to which this property constrains, or is encapsulated, in the form of the
+transseries that defines the λ-model.
+• In a QFT it is sometimes possible to directly link poles/branch points in the
+Borel plane to finite action non-pertubative saddle configurations. Remarkably,
+this can be done even in theories without instantons. In a series of paper [9, 11,
+12] finite action ‘uniton’ configurations of 1+1d integrable QFTs were matched
+to Borel poles of a quantum mechanics that followed by dimensional reduction
+with twisted boundary conditions (akin to a chemical potential as deployed here).
+This poses a natural question: can the features of the Borel plane we have found
+here via TBA methods be related to some finite action saddles? Conversely, given
+the knowledge of such uniton configurations, what do they imply for the TBA
+method? Achieving this would serve to put the semi-classical approaches of [9, 11,
+12] on a surer-footing in quantum field theory.
+• On the other hand there are a class of ambiguities which don’t (yet at least) have an
+interpretation as semi-classical saddles. Instead they are renormalon ambiguities
+associated to certain classes of Feynman diagrams. In [18, 76] it was shown how
+to construct such a series of diagrams which source the renormalon ambiguities in
+1/N expansion of the O(N) vector model, the Gross-Neveu and the SU(N) PCM.
+It would be interesting to investigate if there are diagrams that are responsible for
+the ambiguities in the λ-models.
+• The landscape of integrable models in two dimensions has been vastly expanded
+in recent years through variants of this λ-model, and the related Yang-Baxter σ-
+models. It could be rewarding to deploy similar technique across this landscape
+included e.g. to models with multiple deformation parameters or theories based
+on cosets rather than group manifolds.
+• In [57] the Quantum Inverse Scattering Method was applied to give a direct quant-
+isation of the λ-models as a continuum limit of a spin k Heisenberg spin-chain with
+inhomogeneities. The parameter that governs the in-homogeneity becomes a mass.
+Although the ground state of the system is quite a complicated Fermi sea, one can
+identify holes as certain particle excitations. After taking the continuum limit,
+one can obtain a TBA system for these excitations matching that of the QFT.
+An exciting question is if the above resurgent structure can be given a similar ab
+initio derivation within the QISM framework.
+20
+
+Acknowledgements
+DCT is supported by The Royal Society through a University Research FellowshipGen-
+eralised Dualities in String Theory and Holography URF 150185 and in part by STFC
+grant ST/P00055X/1 as well as by the FWO-Vlaanderen through the project G006119N
+and Vrije Universiteit Brussel through the Strategic Research Program “High-Energy
+Physics”. LS is supported by a PhD studentship from The Royal Society and the grant
+RF\ERE\210269. For the purpose of open access, the authors have applied a Creative
+Commons Attribution (CC BY) licence to any Author Accepted Manuscript version
+arising. We thank M Mari˜no and T Reis for helpful comments on a draft and I Aniceto
+for comments relating to this project.
+References
+[1]
+Al B Zamolodchikov. ‘Exact two-particle S-matrix of quantum sine-Gordon solitons’.
+Communications in Mathematical Physics 55.2 (1977), pp. 183–186.
+[2]
+Peter Hasenfratz, Michele Maggiore and Ferenc Niedermayer. ‘The exact mass gap
+of the O(3) and O(4) non-linear σ-models in d = 2’. Physics Letters B 245.3-4
+(1990), pp. 522–528.
+[3]
+Peter Hasenfratz and Ferenc Niedermayer. ‘The exact mass gap of the O(N) σ-
+model for arbitrary N ≥ 3 in d = 2’. Physics Letters B 245.3-4 (1990), pp. 529–
+532.
+[4]
+P. Forgacs, F. Niedermayer and P. Weisz. ‘The Exact mass gap of the Gross-Neveu
+model. 1. The Thermodynamic Bethe ansatz’. Nucl. Phys. B 367 (1991), pp. 123–
+143. doi: 10.1016/0550-3213(91)90044-X.
+[5]
+P. Forgacs, F. Niedermayer and P. Weisz. ‘The Exact mass gap of the Gross-
+Neveu model. 2. The 1/N expansion’. Nucl. Phys. B 367 (1991), pp. 144–157. doi:
+10.1016/0550-3213(91)90045-Y.
+[6]
+Inˆes Aniceto, Gok¸ce Ba¸sar and Ricardo Schiappa. ‘A Primer on Resurgent Trans-
+series and Their Asymptotics’. Phys. Rept. 809 (2019), pp. 1–135. doi: 10.1016/
+j.physrep.2019.02.003. arXiv: 1802.10441 [hep-th].
+[7]
+Gerald V Dunne and Mithat ¨Unsal. ‘Resurgence and trans-series in Quantum Field
+Theory: the CPN−1 model’. JHEP 11 (2012), p. 170. doi: 10.1007/JHEP11(2012)
+170. arXiv: 1210.2423 [hep-th].
+[8]
+Aleksey Cherman, Daniele Dorigoni, Gerald V. Dunne and Mithat ¨Unsal. ‘Resur-
+gence in Quantum Field Theory: Nonperturbative Effects in the Principal Chiral
+Model’. Phys. Rev. Lett. 112 (2014), p. 021601. doi: 10.1103/PhysRevLett.112.
+021601. arXiv: 1308.0127 [hep-th].
+[9]
+Aleksey Cherman, Daniele Dorigoni and Mithat Unsal. ‘Decoding perturbation
+theory using resurgence: Stokes phenomena, new saddle points and Lefschetz
+thimbles’. JHEP 10 (2015), p. 056. doi: 10 . 1007 / JHEP10(2015 ) 056. arXiv:
+1403.1277 [hep-th].
+[10]
+Gerald V. Dunne and Mithat Unsal. ‘Resurgence and Dynamics of O(N) and
+Grassmannian Sigma Models’. JHEP 09 (2015), p. 199. doi: 10.1007/JHEP09(2015)
+199. arXiv: 1505.07803 [hep-th].
+[11]
+Saskia Demulder, Daniele Dorigoni and Daniel C. Thompson. ‘Resurgence in η-
+deformed Principal Chiral Models’. JHEP 07 (2016), p. 088. doi: 10 . 1007 /
+JHEP07(2016)088. arXiv: 1604.07851 [hep-th].
+21
+
+[12]
+Lucas Schepers and Daniel C. Thompson. ‘Resurgence in the bi-Yang-Baxter
+model’. Nucl. Phys. B 964 (2021), p. 115308. doi: 10.1016/j.nuclphysb.2021.
+115308. arXiv: 2007.03683 [hep-th].
+[13]
+Dmytro Volin. ‘From the mass gap in O(N) to the non-Borel-summability in
+O(3) and O(4) sigma-models’. Phys. Rev. D 81 (2010), p. 105008. doi: 10.1103/
+PhysRevD.81.105008. arXiv: 0904.2744 [hep-th].
+[14]
+Dmytro Volin. ‘Quantum integrability and functional equations: Applications to
+the spectral problem of AdS/CFT and two-dimensional sigma models’. Journal of
+Physics A: Mathematical and Theoretical 44.12 (2011), p. 124003. arXiv: 1003.
+4725 [hep-th].
+[15]
+Marcos Mari˜no and Tom´as Reis. ‘Renormalons in integrable field theories’. JHEP
+04 (2020), p. 160. doi: 10.1007/JHEP04(2020)160. arXiv: 1909.12134 [hep-th].
+[16]
+Marcos Mari˜no and Tom´as Reis. ‘Resurgence for superconductors’ (May 2019).
+doi: 10.1088/1742-5468/ab4802. arXiv: 1905.09569 [hep-th].
+[17]
+Marcos Mari˜no and Tom´as Reis. ‘A new renormalon in two dimensions’. JHEP 07
+(2020), p. 216. doi: 10.1007/JHEP07(2020)216. arXiv: 1912.06228 [hep-th].
+[18]
+Marcos Marino, Ramon Miravitllas and Tomas Reis. ‘Testing the Bethe ansatz
+with large N renormalons’. Eur. Phys. J. ST 230.12-13 (2021), pp. 2641–2666.
+doi: 10.1140/epjs/s11734-021-00252-4. arXiv: 2102.03078 [hep-th].
+[19]
+Zoltan Bajnok, Janos Balog, Arpad Hegedus and Istvan Vona. ‘Instanton effects
+vs resurgence in the O(3) sigma model’. Phys. Lett. B 829 (2022), p. 137073. doi:
+10.1016/j.physletb.2022.137073. arXiv: 2112.11741 [hep-th].
+[20]
+Zoltan Bajnok and Romuald A. Janik. ‘OPE coefficients and the mass-gap from
+the integrable scattering description of 2D CFT’s’. JHEP 11 (2022), p. 128. doi:
+10.1007/JHEP11(2022)128. arXiv: 2209.10393 [hep-th].
+[21]
+Zoltan Bajnok, Janos Balog, Arpad Hegedus and Istvan Vona. ‘Running coupling
+and non-perturbative corrections for O(N) free energy and for disk capacitor’.
+JHEP 09 (2022), p. 001. doi: 10.1007/JHEP09(2022)001. arXiv: 2204.13365
+[hep-th].
+[22]
+Zolt´an Bajnok, J´anos Balog and Istv´an Vona. ‘Analytic resurgence in the O(4)
+model’. JHEP 04 (2022), p. 043. doi: 10.1007/JHEP04(2022)043. arXiv: 2111.
+15390 [hep-th].
+[23]
+Michael C. Abbott, Zolt´an Bajnok, J´anos Balog, ´Arp´ad Heged´us and Saeedeh
+Sadeghian. ‘Resurgence in the O(4) sigma model’. JHEP 05 (2021), p. 253. doi:
+10.1007/JHEP05(2021)253. arXiv: 2011.12254 [hep-th].
+[24]
+Michael C. Abbott, Zolt´an Bajnok, J´anos Balog and ´Arp´ad Heged´us. ‘From per-
+turbative to non-perturbative in the O (4) sigma model’. Phys. Lett. B 818 (2021),
+p. 136369. doi: 10.1016/j.physletb.2021.136369. arXiv: 2011.09897 [hep-th].
+[25]
+Zoltan Bajnok, Janos Balog and Istvan Vona. ‘The full analytic trans-series in
+integrable field theories’ (Dec. 2022). arXiv: 2212.09416 [hep-th].
+[26]
+Marcos Marino, Ramon Miravitllas and Tomas Reis. ‘New renormalons from ana-
+lytic trans-series’ (Nov. 2021). arXiv: 2111.11951 [hep-th].
+[27]
+Konstadinos Sfetsos. ‘Integrable interpolations: From exact CFTs to non-Abelian
+T-duals’. Nucl. Phys. B 880 (2014), pp. 225–246. doi: 10.1016/j.nuclphysb.
+2014.01.004. arXiv: 1312.4560 [hep-th].
+22
+
+[28]
+Konstadinos Sfetsos and Konstadinos Siampos. ‘Gauged WZW-type theories and
+the all-loop anisotropic non-Abelian Thirring model’. Nucl. Phys. B 885 (2014),
+pp. 583–599. doi: 10.1016/j.nuclphysb.2014.06.012. arXiv: 1405.7803
+[hep-th].
+[29]
+Jonathan M. Evans and Timothy J. Hollowood. ‘Integrable theories that are
+asymptotically CFT’. Nucl. Phys. B 438 (1995), pp. 469–490. doi: 10.1016/0550-
+3213(94)00473-R. arXiv: hep-th/9407113.
+[30]
+Jonathan M. Evans and Timothy J. Hollowood. ‘Exact results for integrable
+asymptotically - free field theories’. Nucl. Phys. B Proc. Suppl. 45.1 (1996). Ed. by
+G. Mussardo, S. Randjbar-Daemi and H. Saleur, pp. 130–139. doi: 10.1016/0920-
+5632(95)00622-2. arXiv: hep-th/9508141.
+[31]
+Calan Appadu, Timothy J. Hollowood and Dafydd Price. ‘Quantum Inverse Scat-
+tering and the Lambda Deformed Principal Chiral Model’. J. Phys. A 50.30 (2017),
+p. 305401. doi: 10.1088/1751-8121/aa7958. arXiv: 1703.06699 [hep-th].
+[32]
+Edward Witten. ‘Non-abelian bosonization in two dimensions’. Bosonization. World
+Scientific, 1994, pp. 201–218.
+[33]
+J. Balog, P. Forgacs, Z. Horvath and L. Palla. ‘A New family of SU(2) symmetric
+integrable sigma models’. Phys. Lett. B 324 (1994). Ed. by D. Lust and G. Weigt,
+pp. 403–408. doi: 10.1016/0370-2693(94)90213-5. arXiv: hep-th/9307030.
+[34]
+Konstadinos Sfetsos. ‘Gauged WZW models and nonAbelian duality’. Phys. Rev.
+D 50 (1994), pp. 2784–2798. doi: 10.1103/PhysRevD.50.2784. arXiv: hep-
+th/9402031.
+[35]
+Daniel C. Thompson. ‘An Introduction to Generalised Dualities and their Applic-
+ations to Holography and Integrability’. PoS CORFU2018 (2019). Ed. by Kon-
+stantinos Anagnostopoulos et al., p. 099. doi: 10.22323/1.347.0099. arXiv:
+1904.11561 [hep-th].
+[36]
+Ben Hoare. ‘Integrable deformations of sigma models’. J. Phys. A 55.9 (2022),
+p. 093001. doi: 10.1088/1751-8121/ac4a1e. arXiv: 2109.14284 [hep-th].
+[37]
+Timothy J. Hollowood, J. Luis Miramontes and David M. Schmidtt. ‘Integrable
+Deformations of Strings on Symmetric Spaces’. JHEP 11 (2014), p. 009. doi:
+10.1007/JHEP11(2014)009. arXiv: 1407.2840 [hep-th].
+[38]
+Timothy J. Hollowood, J.Luis Miramontes and David M. Schmidtt. ‘An Integrable
+Deformation of the AdS5 × S5 Superstring’. J. Phys. A 47.49 (2014), p. 495402.
+doi: 10.1088/1751-8113/47/49/495402. arXiv: 1409.1538 [hep-th].
+[39]
+Konstantinos Sfetsos and Daniel C. Thompson. ‘Spacetimes for λ-deformations’.
+JHEP 12 (2014), p. 164. doi: 10.1007/JHEP12(2014)164. arXiv: 1410.1886
+[hep-th].
+[40]
+Saskia Demulder, Konstantinos Sfetsos and Daniel C. Thompson. ‘Integrable λ-
+deformations: Squashing Coset CFTs and AdS5 × S5’. JHEP 07 (2015), p. 019.
+doi: 10.1007/JHEP07(2015)019. arXiv: 1504.02781 [hep-th].
+[41]
+Riccardo Borsato and Linus Wulff. ‘Target space supergeometry of η and λ-
+deformed strings’. JHEP 10 (2016), p. 045. doi: 10.1007/JHEP10(2016)045.
+arXiv: 1608.03570 [hep-th].
+[42]
+Arkady A. Tseytlin. ‘On A ’Universal’ class of WZW type conformal models’.
+Nucl. Phys. B 418 (1994), pp. 173–194. doi: 10.1016/0550-3213(94)90243-7.
+arXiv: hep-th/9311062.
+23
+
+[43]
+Calan Appadu and Timothy J. Hollowood. ‘Beta function of k deformed AdS5
+× S5 string theory’. JHEP 11 (2015), p. 095. doi: 10.1007/JHEP11(2015)095.
+arXiv: 1507.05420 [hep-th].
+[44]
+Ctirad Klimˇc´ık. ‘Poisson–Lie T-duals of the bi-Yang–Baxter models’. Phys. Lett.
+B 760 (2016), pp. 345–349. doi: 10.1016/j.physletb.2016.06.077. arXiv:
+1606.03016 [hep-th].
+[45]
+B. Hoare and A. A. Tseytlin. ‘On integrable deformations of superstring sigma
+models related to AdSn ×Sn supercosets’. Nucl. Phys. B 897 (2015), pp. 448–478.
+doi: 10.1016/j.nuclphysb.2015.06.001. arXiv: 1504.07213 [hep-th].
+[46]
+Konstantinos Sfetsos, Konstantinos Siampos and Daniel C. Thompson. ‘Gener-
+alised integrable λ - and η-deformations and their relation’. Nucl. Phys. B 899
+(2015), pp. 489–512. doi: 10.1016/j.nuclphysb.2015.08.015. arXiv: 1506.
+05784 [hep-th].
+[47]
+Benoit Vicedo. ‘Deformed integrable σ-models, classical R-matrices and classical
+exchange algebra on Drinfel’d doubles’. J. Phys. A 48.35 (2015), p. 355203. doi:
+10.1088/1751-8113/48/35/355203. arXiv: 1504.06303 [hep-th].
+[48]
+Ctirad Klimˇc´ık. ‘η and λ deformations as E -models’. Nucl. Phys. B 900 (2015),
+pp. 259–272. doi: 10.1016/j.nuclphysb.2015.09.011. arXiv: 1508.05832
+[hep-th].
+[49]
+T. H. Buscher. ‘Path Integral Derivation of Quantum Duality in Nonlinear Sigma
+Models’. Phys. Lett. B 201 (1988), pp. 466–472. doi: 10.1016/0370-2693(88)
+90602-8.
+[50]
+K. Gawedzki and A. Kupiainen. ‘G/h Conformal Field Theory from Gauged WZW
+Model’. Phys. Lett. B 215 (1988), pp. 119–123. doi: 10.1016/0370-2693(88)
+91081-7.
+[51]
+Edward Witten. ‘On Holomorphic factorization of WZW and coset models’. Com-
+mun. Math. Phys. 144 (1992), pp. 189–212. doi: 10.1007/BF02099196.
+[52]
+Timothy J. Hollowood, J. Luis Miramontes and David M. Schmidtt. ‘S-Matrices
+and Quantum Group Symmetry of k-Deformed Sigma Models’. J. Phys. A 49.46
+(2016), p. 465201. doi: 10.1088/1751-8113/49/46/465201. arXiv: 1506.06601
+[hep-th].
+[53]
+Georgios Itsios, Konstantinos Sfetsos, Konstantinos Siampos and Alessandro Tor-
+rielli. ‘The classical Yang–Baxter equation and the associated Yangian symmetry
+of gauged WZW-type theories’. Nucl. Phys. B 889 (2014), pp. 64–86. doi: 10.
+1016/j.nuclphysb.2014.10.004. arXiv: 1409.0554 [hep-th].
+[54]
+George Georgiou, Konstantinos Sfetsos and Konstantinos Siampos. ‘Strong in-
+tegrability of λ-deformed models’. Nucl. Phys. B 952 (2020), p. 114923. doi:
+10.1016/j.nuclphysb.2020.114923. arXiv: 1911.07859 [hep-th].
+[55]
+S. F. Hassan and Ashoke Sen. ‘Marginal deformations of WZNW and coset models
+from O(d,d) transformation’. Nucl. Phys. B 405 (1993), pp. 143–165. doi: 10.
+1016/0550-3213(93)90429-S. arXiv: hep-th/9210121.
+[56]
+C Ahn, D Bernard and A LeClair. ‘Fractional supersymmetries in perturbed coset
+CFTs and integrable soliton theory’. Nuclear Physics B 346.2-3 (1990), pp. 409–
+439.
+[57]
+Calan Appadu, Timothy J. Hollowood, Dafydd Price and Daniel C. Thompson.
+‘Quantum Anisotropic Sigma and Lambda Models as Spin Chains’. J. Phys. A
+51.40 (2018), p. 405401. doi: 10.1088/1751-8121/aadc6d. arXiv: 1802.06016
+[hep-th].
+24
+
+[58]
+A Polyakov and Paul B Wiegmann. ‘Theory of nonabelian Goldstone bosons in
+two dimensions’. Physics Letters B 131.1-3 (1983), pp. 121–126.
+[59]
+Alexander M Polyakov and PB Wiegmann. ‘Goldstone fields in two dimensions
+with multivalued actions’. Physics Letters B 141.3-4 (1984), pp. 223–228.
+[60]
+PB Wiegmann. ‘Exact solution of the O(3) nonlinear two-dimensional sigma-
+model’. JETP Letters 41.2 (1985), pp. 95–100.
+[61]
+J. Balog, S. Naik, F. Niedermayer and P. Weisz. ‘Exact mass gap of the chiral
+SU(n) x SU(n) model’. Phys. Rev. Lett. 69 (1992), pp. 873–876. doi: 10.1103/
+PhysRevLett.69.873.
+[62]
+Timothy J. Hollowood. ‘The Exact mass gaps of the principal chiral models’. Phys.
+Lett. B 329 (1994), pp. 450–456. doi: 10.1016/0370-2693(94)91089-8. arXiv:
+hep-th/9402084.
+[63]
+G. Parisi. ‘On Infrared Divergences’. Nucl. Phys. B 150 (1979), pp. 163–172. doi:
+10.1016/0550-3213(79)90298-0.
+[64]
+G. Parisi. ‘Singularities of the Borel Transform in Renormalizable Theories’. Phys.
+Lett. B 76 (1978), pp. 65–66. doi: 10.1016/0370-2693(78)90101-6.
+[65]
+Gerard ’t Hooft. ‘Can We Make Sense Out of Quantum Chromodynamics?’ Sub-
+nucl. Ser. 15 (1979). Ed. by Antonino Zichichi, p. 943.
+[66]
+EB Bogomolny. ‘Calculation of instanton-anti-instanton contributions in quantum
+mechanics’. Physics Letters B 91.3-4 (1980), pp. 431–435.
+[67]
+J. Zinn-Justin and U.D. Jentschura. ‘Multi-instantons and exact results I: Con-
+jectures, WKB expansions, and instanton interactions’. Annals Phys. 313 (2004),
+pp. 197–267. doi: 10.1016/j.aop.2004.04.004. arXiv: quant-ph/0501136.
+[68]
+J. Zinn-Justin and U.D. Jentschura. ‘Multi-instantons and exact results II: Specific
+cases, higher-order effects, and numerical calculations’. Annals Phys. 313 (2004),
+pp. 269–325. doi: 10.1016/j.aop.2004.04.003. arXiv: quant-ph/0501137.
+[69]
+Jean Zinn-Justin. ‘Perturbation Series at Large Orders in Quantum Mechanics
+and Field Theories: Application to the Problem of Resummation’. Phys. Rept. 70
+(1981), p. 109. doi: 10.1016/0370-1573(81)90016-8.
+[70]
+Alexei B. Zamolodchikov. ‘Mass scale in the sine-Gordon model and its reductions’.
+Int. J. Mod. Phys. A 10 (1995), pp. 1125–1150. doi: 10.1142/S0217751X9500053X.
+[71]
+Daniele Dorigoni and Philip Glass. ‘The grin of Cheshire cat resurgence from
+supersymmetric localization’. SciPost Physics 4.2 (2018), p. 012.
+[72]
+Daniele Dorigoni and Philip Glass. ‘Picard-Lefschetz decomposition and Cheshire
+Cat resurgence in 3D N = 2 field theories’. Journal of High Energy Physics 2019.12
+(2019), pp. 1–40.
+[73]
+Can Koz¸caz, Tin Sulejmanpasic, Yuya Tanizaki and Mithat ¨Unsal. ‘Cheshire Cat
+resurgence, Self-resurgence and Quasi-Exact Solvable Systems’. Commun. Math.
+Phys. 364.3 (2018), pp. 835–878. doi: 10.1007/s00220- 018- 3281- y. arXiv:
+1609.06198 [hep-th].
+[74]
+Syo Kamata, Tatsuhiro Misumi, Naohisa Sueishi and Mithat ¨Unsal. ‘Exact-WKB
+analysis for SUSY and quantum deformed potentials: Quantum mechanics with
+Grassmann fields and Wess-Zumino terms’ (Nov. 2021). arXiv: 2111.05922 [hep-th].
+[75]
+Stephen G. Naculich and Howard J. Schnitzer. ‘Duality Between SU(N)k and
+SU(k)N WZW Models’. Nucl. Phys. B 347 (1990), pp. 687–742. doi: 10.1016/
+0550-3213(90)90380-V.
+25
+
+[76]
+Lorenzo Di Pietro, Marcos Mari˜no, Giacomo Sberveglieri and Marco Serone. ‘Re-
+surgence and 1/N Expansion in Integrable Field Theories’. JHEP 10 (2021), p. 166.
+doi: 10.1007/JHEP10(2021)166. arXiv: 2108.02647 [hep-th].
+26
+
diff --git a/D9FKT4oBgHgl3EQfZi4o/content/tmp_files/load_file.txt b/D9FKT4oBgHgl3EQfZi4o/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..2765cf4cd2b786d5caf9a09c8185b2d70f1f50b4
--- /dev/null
+++ b/D9FKT4oBgHgl3EQfZi4o/content/tmp_files/load_file.txt
@@ -0,0 +1,1281 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf,len=1280
+page_content='Asymptotics in an Asymptotic CFT  Lucas Schepersa1 and Daniel C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Thompsona,b2  a Department of Physics, Swansea University,  Swansea SA2 8PP, United Kingdom  b Theoretische Natuurkunde, Vrije Universiteit Brussel,  & The International Solvay Institutes, Pleinlaan 2, B-1050 Brussels, Belgium  Abstract  In this work we illustrate the resurgent structure of the λ-deformation;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' a two-  dimensional integrable quantum field theory that has an RG flow with an SU(N)k  Wess-Zumino-Witten conformal fixed point in the UV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' To do so we use modern  matched asymptotic techniques applied to the thermodynamic Bethe ansatz formu-  lation to compute the free energy to 38 perturbative orders in an expansion of large  applied chemical potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' We find numerical evidence for factorial asymptotic be-  haviour with both alternating and non-alternating character which we match to  an analytic expression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' A curiosity of the system is that it exhibits the Cheshire  Cat phenomenon with the leading non-alternating factorial growth vanishing when  k divides N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' The ambiguities associated to Borel resummation of this series are  suggestive of non-perturbative contributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  This is verified with an analytic  study of the TBA system demonstrating a cancellation between perturbative and  non-perturbative ambiguities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  1lucas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='schepers@swansea.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='uk  2daniel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='thompson@swansea.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='uk  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='11803v1  [hep-th]  27 Jan 2023  1  Introduction  A complete understanding of the strong coupling dynamics of four dimensional asymp-  totically free (AF) non-supersymmetric gauge theory, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' QCD, remains elusive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' To  gain a foothold we may turn to simplified toy models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' One strategy is to reduce the  dimensionality of the problem considering instead two dimensional quantum field the-  ories with similar RG behaviour.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' In the special case of integrable QFTs, an infinite set  of symmetries completely determine the exact S-matrix [1] providing a powerful toolkit  that can be used to tackle non-perturbative questions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' An early success of this approach  was the calculation of the exact ratio of the mass gap to cut-off of AF integrable QFTs  theories [2–5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  More recently, techniques in integrable models have been used to elucidate even  deeper questions of the nature of perturbation theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Typically, perturbation theory is  asymptotic in nature with perturbative coefficients growing factorially.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' The programme  of resurgence asserts that this breakdown of convergence signals the need to include  non-perturbative physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Even more strongly, ambiguities inherent in resummations of  asymptotic perturbative expansions should be cancelled by compensating ambiguities  in a non-perturbative sector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' For a modern overview of resurgence from a physics view  point see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Again, integrable two-dimensional models provide an ideal test bed  for resurgence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  In semi-classical approaches [7–12], an adiabatic compactification of two-dimension  models is used to obtain a quantum mechanics which can be probed to large perturbative  orders.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' In these cases, two-dimensional finite Euclidean action configurations, known as  unitons1 are shown to precisely resolve the semi-classical ambiguities of the perturbative  sector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Whilst intriguing, such approaches intrinsically disregard degrees of freedom in  compactification restricting to the lowest KK sector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Alongside this features of renorm-  alisation group are disregarded in the truncation to Quantum Mechanics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Given these  limitations, one thus prompted to ask if the resurgence paradigm can be established in  a fully two-dimensional setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  A breakthrough was the work of Volin [13, 14], recently refined in [15, 16] (see also the  recent papers [17–25]), in addressing the Thermodynamic Bethe Ansatz (TBA) system  that determines free energy in a large chemical potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' By comparing two scaling  limits, it is possible to reduce the complicated integral TBA equation to a (complicated)  set of algebraic equations that fix unknown coefficients in an ansatz for a perturbative  expansion (in the chemical potential or other more refined coupling).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' This allows access  to sufficient order in perturbation theory to reveal factorial divergence of perturbative  coefficients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  Although we cannot identify an instanton or other semi-classical non-perturbative  saddle in the TBA approach, we can find a matching ambiguity using a different method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [26] showed that it is possible to solve the TBA equations using a transseries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' A critical  step in their solution is an arbitrary choice of branch cut which introduces an ambiguity  of the transseries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Although this approach, due to its computational difficulty, cannot  be executed to large orders, it does exhibit a non-perturbative ambiguity that matches  the ambiguity of the large-order behaviour found in the perturbative sector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  In this note we will adopt this toolbox to study the resurgent structure of a theory  that exhibits a different renormalisation group dynamic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' We consider a theory in which  the UV is not Gaussian but instead is described by a non-trivial interacting conformal  fixed point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' The theory we will consider, known as the λ-model [27, 28], is realised as a  flow away from an SU(N)k Wess-Zumino-Witten (WZW) model driven at leading order  by a certain current-current bilinear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' The IR of the theory is the principal chiral model,  expressed in non-Abelian T-dual coordinates, and accordingly is gapped.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Whilst this  1Unlike instantons, unitons are not topologically protected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  1  marginally relevant deformation breaks conformality and the full affine symmetry of the  WZW current algebra, it does preserve an infinite symmetry associated to integrablity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  At the quantum level the exact S-matrix is known (based on symmetry grounds pre-  dating the Lagrangian description) [29, 30] and has been shown to match the λ-model  Lagrangian using a light cone lattice discretisation and Quantum Inverse Scattering [31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  The goal of this note is to match the perturbative ambiguity to that of the transseries  the new context of a λ-model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' The outline is as follows: Section 2 provides a more in-  depth discussion of the λ-model as we consider its RG flow in more detail and present  its exact S-matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' In Section 3, we review the recent techniques to perturbatively solve  TBA equation [13–16] that determine free energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  Introducing a special coupling γ  in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='4 results in a clean (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' log-free) series for the λ-model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' We analyse its  asymptotic behaviour in Section 4 and compute the leading ambiguity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' This ambiguity  is matched by a transseries calculation in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' A particularly eye-catching result  is that the leading UV ambiguity disappears when N divides k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' We wrap up with ideas  for future research in Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  2  The λ-Model  In this section we outline the salient properties of the two-dimensional integrable QFT  that we are considering: the λ-deformed model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Classically, the λ-model provides a  Lagrangian interpolation between the conformal Wess-Zumino-Witten (WZW) model  for a Lie-group G [32] and the principal chiral model (PCM) (written in non-Abelian  T-dual variables).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Remarkably this theory is integrable for all values of the eponymous  interpolating parameter λ related to the level, k, of WZW and the radius, r, of the PCM  by  λ =  k  k + r2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  (1)  Whilst the λ-model for the restricted case of G = SU(2) was first proposed long ago  [29, 33, 34], the pioneering work of Sfetsos [27] in constructing the general theory has  prompted extensive recent development (for reviews see [35, 36]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' The λ-model has been  extended to Z2 graded symmetric spaces [27, 37] where it constitutes an interpolation  between a G/H gauged WZW (representing the coset CFT) and the (non-abelian T-dual  of) the principal chiral model on G/H and even to Z4 graded super-cosets relevant to  the construction of the AdS5 × S5 superstring [38] underpinned by an elegant quantum  group at root-of-unity symmetry structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' In this string theory context, λ-deformation  is in fact marginal, and the world sheet theory can be viewed as a σ-model in some  target space super-gravity background [39–41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Here however we will be considering the  simpler bosonic case for which the λ-deformation does not define a CFT but rather a  relevant RG flow from a WZW fixed point in the UV to the dualised PCM the IR [28,  42, 43].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' A series of papers [44–48] have shown how the λ-model is actually part of a wide  tapestry of integrable deformed models linked by (analytically continued) Poisson-Lie  T-duality transformations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='1  Lagrangian Construction  First we sketch the construction of the non-abelian T-dual of the PCM using the Buscher  procedure [49] as it informs the construction of the λ-model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' We start with the action  2  of the PCM for a group valued field ˜g 2  SPCM[˜g] = − r2  4π  �  d2σ Tr  �  ˜g−1∂+˜g˜g−1∂−˜g  �  ,  (2)  and downgrade the left symmetry ˜g → h−1˜g to a gauge symmetry by introducing a  gauge connection transforming as A → h−1dh + h−1Ah and replacing derivatives to  covariant derivatives d → D = d + A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' This yields the gauged PCM action which we  denote as SgPCM[˜g, A].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' To ensure that the gauged theory is actually equivalent to the  ungauged theory (at least in trivial topology which we assume throughout) we enforce  that the connection is flat (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' the gauge field is pure gauge).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' This is implemented by  introducing a Lagrange-multiplier term, − Tr(νF+−), to the Lagrangian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Integrating  out the field ν enforces that the field strength F+− vanishes and we recover the original  PCM after gauge-fixing ˜g = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' However, if instead we integrate out the gauge fields A,  after gauge fixing ˜g = 1, we obtain the non-abelian T-dual model in which the field ν  becomes the fundamental field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  The construction of the λ-model by Sfetsos [27] is achieved through a modification of  this Buscher procedure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Instead of adding a Lagrange multiplier term, we add a gauged  WZW term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Recall that the WZW model is given by  SWZW,k[g] = − k  2π  �  Σ  d2σ Tr  �  g−1∂µgg−1∂µg  �  − ik  6π  �  M3  Tr  �  g−1dg  �3 ,  (3)  in which g is extended to a 3-manifold M3 with boundary ∂(M3) = Σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  Standard  arguments [32] ensure that the path integral is well-defined (independent of choice of  extension) provided that k is appropriately quantised, and in particular for G = SU(N)  which we assume henceforth, k ∈ Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' In this sector we gauge the diagonal symmetry  g → h−1gh leading to a gauged WZW model action SgWZW,k[g, A] [50, 51].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  To construct the λ-model we combine a gauged PCM and a gauged WZW model:  Sλ,k[g, ˜g, A] = SgPCM[˜g, A] + SgWZW[g, A] .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  (4)  Notice that the two models are coupled through the fact that they are gauged by the  same gauge field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' The Sfetsos procedure is concluded by gauge fixing ˜g = 1 and integ-  rating out the gauge field A using its on-shell value  A+ = λ(1 − λAdg)−1R+ ,  A− = −λ(1 − λAdg−1)−1L− ,  (5)  where we defined R± = ∂±gg−1 and L± = g−1∂±g and the adjoint action AdgX =  gXg−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Integrating out the gauge field then yields the action  Sλ,k[g] = SWZW,k[g] + kλ  π  �  Σ  d2σ Tr  �  R+(1 − λAdg)−1L−  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  (6)  Though not vital for what follows we note that the equation of motion can be understood  as a zero-curvature condition on the Lax connection [27, 52]  L±(z) = −  2  1 + λ  A±  1 ∓ z ,  (7)  in which A± are evaluated with the on-shell values eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' (5) and z ∈ C is a spectral  parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' This is the starting point of establishing the classical integrability of the  theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Further to this one requires strong integrability i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' that the conserved charges  built from the monodromy of this Lax are in involution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' This is ensured provided that  the Poisson algebra of the spatial component of the Lax has a particular r-s Maillet form  as was demonstrated for the λ-model, and its generalisations, in [47, 53, 54].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  2We use light cone coordinates σ± = 1  2 (t ± x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Derivatives with respect to light cone coordinates  are denoted by ∂±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  3  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='2  Renormalisation  The parameter λ given by eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' (1) varies from 0 to 1 and we shall now discuss what  happens in each of those limits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' At a quantum level the parameter λ undergoes an RG  flow [28, 42, 43] given by (to all orders in λ and leading in 1  k)  µdλ  dµ = β(λ) = −2N  k  �  λ  1 + λ  �2  = −β1λ2 − β2λ3 + O(λ4) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  (8)  The leading order behaviour, which shall be relevant later, is given by  β1 = 2N  k ,  β2 = −4N  k .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  (9)  There is an evident UV fixed point at λ = 0, corresponding to the undeformed WZW  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' In the vicinity of this λ ≈ 0, or k ≪ r2, we obtain a current-current deformation  of the WZW model:  Sλ,k[g] = SWZW,k[g] + λ  �  Σ  d2σ Tr (R+L−) + O(λ2) ,  (10)  This, however, is not a marginal deformation (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' marginal ones [55]), but relevant as it  moves away from the WZW theory located in the UV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  To understand the IR regime as λ → 1, we can force k → ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' If the group element  is expanded as g = 1 + i  kνata, the action SgWZW,k reduces to the Lagrange multiplier  term − Tr(νF+−).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Thus in this limit the Sfetsos procedure reduces to the non-Abelian  T-dualisation Buscher procedure described above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Hence, in this IR limit, we recover the  non-abelian T-dual of the PCM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Further into the deep IR, one thus anticipates (as with  the PCM) that the dimensionless parameter λ is transmuted into a mass gap mediated  through a cut-off Λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='3  Quantum Integrability  Not only is the theory classical integrable, it remains so at the quantum level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' The  existence of higher spin conserved currents ensure that the scattering matrix of the  theory factorises, and can be fully determined with the 2-to-2 particle scattering matrix  the fundamental building block.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' The S-matrix for the SU(N) λ-model was constructed  many years ago [56] from an algebraic perspective, and was related directly to the  Lagrangian description for the SU(2) case in [29] by matching the free energy obtained  by Lagrangian perturbation theory and by S-matrix TBA techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Following the  introduction of the Lagrangian description λ-model by Sfetsos [27] for SU(N) the exact  S-matrix was conjectured [52] for general ranks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' This conjecture was substantiated by  Appadu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' [31] in which the form of the S-matrix was ‘derived’ by the Quantum  Inverse Scattering Method (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' a latticed version of the theory that takes the form of a  spin chain such from the QFT particle states are obtained as excitations over the ground  state in a continuum limit)3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Rather than present the full details of the S-matrix (for  which see [52]) we can give a schematic understanding somewhat mirroring the Sfetsos  procedure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  3This QISM is in fact rather non-trivial as the δ′(σ) non-ultra-local terms in the fundamental Poisson  bracket preclude a simple application of QISM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Instead what is proposed is a modification of the  λ-model, that lies in the same universality class, to which QISM can be applied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  This provides a  description as a spin-k XXX spin chain with alternating inhomogeneities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  This idea was expanded  to a two-parameter integrable λ-type model [57] realised as a spin-k XXZ spin chain with alternating  inhomogeneities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  4  We start with the SU(N) principal chiral model which has in particular an SU(N)L×  SU(N)R global symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' The fundamental particles are massive and transform in fun-  damental antisymmetric tensor representations of the global symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' The scattering  depends kinematically only on the rapidity difference θ of the particles4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Reflecting this  global symmetry, the S-matrix of these fundamental excitations has a schematic tensor  form (suppressing explicit representation labels)  SPCM(θ) = X(θ)S(θ) ⊗ S(θ) ,  (11)  where X(θ) is an overall scalar dressing factor to ensure all S-matrix axioms are obeyed,  and the S(θ) factors are separately SU(N) invariant (in fact invariant under a larger  Yangian symmetry).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Recalling that in the Sfetsos procedure the left acting SU(N)L  symmetry was gauged, it is natural that the left hand block of the tensor product of eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  (11) is modified in the λ-theory and indeed this is the case with  Sλ(θ) = Xk(θ)Sk(θ) ⊗ S(θ) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  (12)  Here Sk(θ) is a block [56] that furnishes a quantum group symmetry at the q2(k+N) = 1  root of unity taken in Restricted-Solid-On-Solid (RSOS) picture representing the scat-  tering of kink degrees of freedom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  Given knowledge of the exact S-matrix, the Thermodynamic Bethe Ansatz yields  a set of rather complicated coupled-integral equations can be used to determine the  free-energy of the theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Solving these is quite formidable especially as the S-matrix is  non-diagonal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' A powerful simplification is achieved by exposing the system to a chemical  potential h for a U(1) charge such that only certain particles condense and contribute  to the ground state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' When the charge is chosen appropriately (as the one defined by  a highest weight of a rank N/2 antisymmetric representation [31]) then only a single  particle of maximal charge contributes and the TBA system simplifies to a single integral  equation determined by the identical scattering of this particle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  In this case, the scattering “matrix” reduces to a simple phase factor S(θ) that  governs transmission and reflection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  It shall prove useful in this case to define the  scattering kernel of this reduced S-matrix by  K(θ) =  1  2πi  d  dθ log S(θ) ,  (13)  and its Fourier transform  K(ω) =  � ∞  −∞  dθ eiωθK(θ) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  (14)  As a consequence of Hermitian analyticity on the reduced S-matrix, both K(θ) and its  Fourier transform are symmetric functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Explicitly we have that the relevant kernel  is given by [57]  1 − K(ω) =  sinh2(πω/2)  sinh(πω) sinh(πκω) exp(πκω) ,  (15)  where κ =  k  N .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' In what follows, it shall prove useful to write the Fourier transform of  the scattering kernel as a Wiener-Hopf (WH) decomposition  1 − K(ω) =  1  G+(ω)G−(ω) ,  (16)  where G−(ω) = G+(−ω), and G+(ω) is analytic in the Upper Half Plane (UHP) and  normalised such that G+(2is) = 1 + O  �  1  s  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Explicitly G+(ω) is given by  G+(ω) =  √  4κ  Γ(1 − iω/2)2  Γ(1 − iω)Γ(1 − iκω) exp (ibω − iκω log(−iω)) ,  (17)  4The mass shell is related to rapidity by p0 = m cosh θ and p1 = m sinh θ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  5  with  b = κ(1 − log(κ)) − log(2) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  (18)  3  TBA Techniques  Polyakov and Wiegmann [58–60] showed in the 80s that it is possible to compute the free  energy of an integrable system with a chemical potential h turned on using a thermody-  namic Bethe ansatz (TBA) technique.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Using these techniques, Hasenfratz, Niedermayer  and Maggiore [2, 3] showed in 19905 that it is possible to calculate the mass gap in  integrable models by comparing the result from TBA with conventional Lagrangian  pertubation theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Building from this we will will apply, in section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='4, the techniques  pioneered by [13–16] to extract an expansion for the free energy of λ-model in  1  h the  large order behaviour of which we will study extensively in section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='1  Free Energy  To present the TBA equations we will specialise to the case described above in which we  introduce a chemical potential h such that only a single particle dominates the ensemble  at large h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='6 With K(θ) the appropriate scattering kernel, the TBA equations determine  the density distribution of states, χ(θ), via  m cosh(θ) = χ(θ) −  � B  −B  K(θ − θ′)χ(θ′)dθ′ ,  θ2 < B2 ,  (19)  from which the charge and energy density follow  e = m  � −B  B  χ(θ) cosh(θ) dθ  2π ,  ρ =  � −B  B  χ(θ) dθ  2π .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  (20)  A critical complexity of this system is that the occupied states lie within a Fermi surface  specified by B, which is however a function of h (with large B corresponding to large  h).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Supposing that we have calculated the energy density, thought of as a function of  the charge density e = e(ρ), then we can reconstruct a free energy density, F(h), from  a Legendre transform:  ρ = −F′(h) ,  F(h) − F(0) = e(ρ) − ρh .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  (21)  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='2  Resolvent Approach  It will prove useful to recast the integral equation that determines χ(θ) in terms of a  resolvent function defined by  R(θ) =  � B  −B  χ(θ′)  θ − θ′ dθ′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  (22)  5This computation was intially performed for the O(N) model, but was later also completed for  Gross-Neveu models [4, 5] and PCM models [61, 62].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  6That we can reduce the TBA system to involve just one species of particle from the fundamental  representation singled out by the applied chemical potential is of course an assumption that makes the  problem readily tractable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' One anticipates that states of higher mass and higher charge are energetically  disfavoured, but properly speaking this assumption ought to be proven starting from a complete nested  TBA system (which we do not attempt here).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  6  The resolvent is analytical everywhere except around the interval [−B, B] where it has  an ambiguity given by  χ(θ) = − 1  2πi  �  R+(θ) − R−(θ)  �  ,  (23)  where we use the short hand notation R±(θ) = R(θ ± iϵ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Suppose that the kernel can  be cast in terms of some operator O as K(θ) =  1  2πiO 1  θ, then the eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' (19) is equivalent  to a Riemann-Hilbert problem  R+(θ) − R−(θ) + OR(θ) = −2πim cosh θ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  (24)  A determination of R(θ) is then equivalent to solving the TBA system and once known  the charge density is immediately extracted as  ρ = − 1  2π Resθ=∞R(θ) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  (25)  We briefly now review the approach of [13–15] which does so by considering ansatz  solutions for the resolvent in two limits (the edge and bulk) and matching them to fix  all undetermined coefficients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='1  Edge Ansatz  We begin first with the edge limit in which the weak coupling limit B → ∞ is taken  whilst keeping an edge coordinate z = 2(θ −B) fixed and small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' This evidently scales to  large θ and hence probes the properties of χ(θ) around the vicinity of the Fermi energy,  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' This limit is best studied by considering the Laplace transform of the resolvent (22)  given by  R(z) =  � ∞  0  �R(s)e−szds ,  �R(s) =  1  2πi  � i∞+δ  −i∞+δ  eszR(z)dz .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  (26)  Note at large B the energy density is related to this Laplace transformation by  e = meB  4π  �R(1/2) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  (27)  The key result of [15, 16] is that in the edge limit the Laplace transformed resolvent  has the following form  �R(s) = meBΦ(s)Φ  � 1  2  �  2  �  1  s + 1/2 + Q(s)  �  ,  Φ(s) = G+(2is) ,  (28)  where G+(s) is the WH decomposition (16) of the (Fourier transformed) scattering  kernel and Q(s) is a series in large s and a perturbative expansion in  1  B of the form  Q(s) = 1  Bs  ∞  �  m,n=0  Qn,m  Bm+nsn .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  (29)  It should be noted that the coefficients Qn,m may still depend on log B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='2  Bulk Ansatz  In the bulk limit we let B → ∞ and θ → ∞ but we keep u = θ/B fixed, we are hence  studying the regime where θ is in the bulk, between 0 and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' The precise form of the  7  Bulk ansatz depends on the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' For the λ-model, we shall take the same bulk ansatz  for the Gross-Neveu model [15], which is given by  R(u) =  ∞  �  n=1  ∞  �  m=0  n+m  �  k=0  cn,m,k  ue(k+1)  Bm+n(u2 − 1)n  �  log u − 1  1 + u  �k  ,  (30)  where e(k) is 0 if k is even and 1 if k is odd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='The bulk ansatz can be motivated by  constructing it using functions that are analytic outside the interval [−B, B], where  they have a logarithmic branch cut.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='7 This is precisely the analytic structure demanded  by eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' (22) and (23).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='3  Matching  If we re-expand the bulk ansatz (30) in an edge regime where z = 2(θ − B) is fixed, we  should recover the expansion in the edge regime given by (28).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Here a miraculous feature  occurs: upon comparing expansions order by order in large B, then order by order in  large z (which is small s) and then in log(z), we can solve for all the coefficients cn,m,k  and Qn,m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' One peculiarity of the procedure is that we perform this matching only for  the regular terms of the expansion z−n (n ≥ 0), while we disregard all divergent terms  zn (n > 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Using a desktop PC, over the course of a week, we solved the system up  to 38 orders.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Once this calculation is completed, we compute e and ρ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Using equations  (28) and (25) we can express ρ and e in terms of the coefficients by  e = m2e2BΦ(1/2)2  8π  �  1 +  ∞  �  m=1  1  Bm  m−1  �  n=0  2n+1Qn,m−1−n  �  ,  ρ = 2π  ∞  �  m=0  c1,m,0  Bm .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  (31)  Explicitly the first few coefficients required to determine up to order B−2 are given by  c1,0,0 = 4√κ ,  c1,1,0 = −2κ3/2 ,  c1,2,0 = 1  2κ3/2(2 − κ − 4 log 2 + 4κ log(2B/κ)) ,  Q0,0 = 0 ,  Q1,0 = 0 ,  Q0,1 = κ  4 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  (32)  The last step is to calculate the quantity  e  ρ2 as an expansion in B the first terms of  which are  8κ  π  e  ρ2 = 1 + κ  B + κ  B2  �  1 − log(2) + κ  2 + κ log(2B/κ)  �  + O(B−3) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  (33)  As this result depends on log(B), it is convenient to define a new effective coupling γ in  terms of which the perturbative expansion is free from logarithms as we shall do in the  next section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='4  Perturbative result  Before introducing the log-free coupling, we show our results are consistent with those  of [31], which determines the mass gap of this theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Using standard TBA techniques,  7This is different from the PCM bulk ansatz which also has a square root branch cut along the  interval [−B, B].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  8  they find an expansion for the free energy given by  F(h) − F(0) = −2h2κ  π  �  1 − 2κα + 2κα2�  2 + κ + log 4 + +2κ log κ + 2κ log α  �  − 8κ2α3 log(α)  �  (−2 + 2κ + log 4 + 2κ log(κ) + κ log(α)  �  + O(α3)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  (34)  The coupling α is here defined by  1  α = 2 log  �  2h  m  �  8κ  π  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  (35)  By using the Legendre transformation (21) we can compute the total energy e from eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  (34).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Doing so, we obtain the expression  8κ  π  e  ρ2 =1 + 2ακ − 2κα2(2κ log(ακ) − κ − 2 + log(4))+  8κ2α3�  κ log2(α) + (log(α) − 1)(−2 log(4) + 2κ log(κ))  �  + O  �  α4�  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  (36)  From eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' (33), it follows that  e  ρ2 = χ0 + O(α) where χ0 =  π  8κ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Therefore to leading  order we have h = ∂e  ∂ρ = 2χ0ρ, which leads to ρ = 4hκ  π .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Looking at eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' (35), we should  thus define a coupling by  1  α = 2 log  �  ρ  m  �  2π  κ  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  (37)  This defines α in terms of B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Inverting the relation and substituting into the series (33)  recovers precisely the expansion (36), providing an important consistency check for our  programme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  We now take inspiration from the Gross-Neveu treatment of [15] to create a series  expansions for  e  ρ2 that is log-free.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' This is appropriate because we have that to leading  order ∆F ∼ −h2 + O(α), which leads to a coupling defined by8  1  γ + ξ log γ = log 2πρ  m/c ,  ξ = β2  β2  1  = − k  N = −κ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  (38)  One could demand that the right hand side be log 2πρ  ΛMS , where ΛMS is the cut-off in  the minimal subtraction scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' To achieve this one has to tune the constant c = cMS  such that cMSΛMS = m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' A key outcome of [31] determines that cMS = e3/2N −1/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  However, we shall exercise the freedom to pick a c of our own choosing,  c = 2−κΓ(κ)  π  ,  (39)  such that resulting expressions appear considerably simplified.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' This leads to an expan-  sion that is log-free in the coupling, given by  8κ  π  e  ρ2 =  ∞  �  n=0  anγn = 1 + κγ + κ  2 [2 − κ]γ2+  κ  2  �  3 − 5κ + 2κ2�  γ3 + κ  8  �  3(8 − ζ(3)) − 61κ + 52κ2 − 15κ3�  γ4+  κ  12  �  90 − 18ζ(3) + κ(33ζ(3) − 288) + 355κ2 − 203κ3 + 46κ4�  γ5+  κ  32  �  45(16 − 4ζ(3) − ζ(5)) + 2κ(259ζ(3) − 1338) + 1  3κ2(12274 − 1329ζ(3))  − 3285κ3 + 1412κ4 − 787κ5  3  �  γ6 + O(γ7) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  (40)  8This is in contrast to the PCM calculation where the free energy has a structure ∆F ∼ − h2  α +O(α0),  which leads to a coupling 1  γ + (ξ − 1) log γ ∝ log ρ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  9  Figure 1: Left to right, for κ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='98, 1 and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='02, the Borel-Pad´e-poles in the ζ-plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  Evident are singularities at ζ = ±2, with the positive pole removed for κ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  In the next Section we shall explore this perturbative expansion further.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  4  Asymptotic Analysis  In this Section, we will quantitatively analyse the 38 orders of the perturbative series  obtained in the previous Section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' The goal shall be to compute an asymptotic formula  for the growth of the coefficients as a function of κ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' After obtaining such a formula, we  can compute its Borel ambiguity, which can later be compared against an ambiguity of  a transseries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  As the perturbative series can readily be seen to exhibit factorial growth, as a first  step to resummation we introduce the Borel transform  B  �8κ  π  e  ρ  2�  ≡  ∞  �  n=0  an  n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ζn .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  (41)  This series has a finite radius of convergence but typically has either, or both, poles  and branch cuts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' The pole/branch point closest to the origin in the ζ plane is governed  by the leading asymptotic behaviour.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  Of course, numerically one does not have all  orders with which to establish this Borel transformation, rather only a finite number  of coefficients an for n < N say.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Here the Borel-Pad´e method can be employed: we  compute BN[ 8κ  π  e  ρ  2] = �N  n=0  an  n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ζn = P (ζ)  Q(ζ) + O(ζ)N+1 in which P and Q are polynomials  in ζ of degree N/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' This results in a picture in which an accumulation of poles (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  zeros of Q) is indicative of a branch point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' We perform this numerically for various  values of κ and generically we find evidence of branch points at ζ = ±2 whose location  is independent of κ except that for κ ∈ Z>0 the pole in the positive axis is removed -  see Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Pole/ branch points in the negative real axis of the Borel plane indicate  contributions to an of alternating sign whereas the contributions to an that result in  poles on the positive axis would have the same sign.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Here the analysis indicates that we  have both.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' With 38 perturbative coefficients this analysis should only be regarded as  indicative but is sufficient to inform an educated guess as to the asymptotic behaviour  of the an which we will robustly verify below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  Motivated by the Borel-Pad´e analysis we assume the coefficients grow, to leading  approximation, as  an ≈ A+Γ(n + 1)/Sn + A−Γ(n + 1)/(−S)n + O(n−1) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  (42)  A first verification is to establish the factor S which can be done noting that  g+,n :=  a2n  2n(2n − 1)a2n−2  ≈ 1  S2 ,  g−,n :=  a2n+1  2n(2n − 1)a2n−1  ≈ 1  S2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  (43)  10  4  2  2  2  4  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='4  24  2  2  2  4  4  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='24  2  2  2  4  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='4  2Figure 2: The series g+,n (left) and g−,n (right) given by eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' (43) displayed for κ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  Circle markers indicate the raw data, square markers the second Richardson transform-  ation with accelerated convergence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' The final values of the second Richardson transform  differ by 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='11% and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='05% respectively from the expected value 1  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  We find, see Figure 2, that the series g±,n converge to 1  4, independent of κ thus estab-  lishing S = 2 in accordance with the expectation from the Borel-Pad´e analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  Having established the factorially growing character of the perturbative series, we  now propose a more refined ansatz for the an.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Our central claim can be summarised  by stating that the perturbative series has coefficients that have a leading large order  behaviour as  an ≈ A+  2n  ∞  �  l=0  β+  l Γ(n + a+ − l) +  A−  (−2)n  ∞  �  l=0  β−  l Γ(n + a− − l) ,  (44)  where we normalise β±  0 = 1 and the first few coefficients are  a± = ∓2κ ,  A± = 8±1  π  sin(∓κ)Γ(±κ)  Γ(∓κ) = −  8±1  Γ(∓κ)Γ(1 ∓ κ) ,  β−  1 = −β−  2 = −4κ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  (45)  To support these claims, we shall define the auxiliary series  cn =  2n  Γ(n + 1)an ,  (46)  to take care of the leading factorial and geometric growth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' We project to the alternating  and non-alternating parts of the series by considering  f ±  k = c2k ± c2k−1 ,  (47)  which have asymptotics  f ±  n = 2A±(2n)a±−1�  1 + O  � 1  n  ��  ,  (48)  such that the sequences  σ±  n = 1 + n log f ±  n+1  f ±  n  ,  (49)  converge to a±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' With a± determined one can then directly consider the asymptotics of  f ± to establish A±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Figure 3 illustrates the convergence of this procedure for a fixed  11  +.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='n  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='30r  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='28  O  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='26  boo  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='24  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='22  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='20  5  10  15  0  20g-,n  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='30r  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='28  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='26  0000000  口  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='24  口  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='22  口  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='20  5  10  15  0Figure 3: The series σ−  n (left) converges to a− using (49).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Using eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' (48) we display  (right) the sequence that converges to A−.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Circle markers indicate the raw data, square  markers the second Richardson transformation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' For both, we display results for κ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  The second Richardson transform converge to the expected results given by eq (45) up  to errors of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='011% and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='00068% respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  Figure 4: The second Richardson transformation of the sequences (49) (left) and (48)  (right) to determine a± and A± as functions of κ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' a+, A+ are indicated by red crosses  and a−, A+ by blue points with solid lines showing the analytic formula of eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' (45).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  value of κ, and Figure 4 establishes the functional form of these coefficients for various  values of κ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  A methodological subtlety is that, from empirical observation, the contributions from  the alternating sector, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  A− (and associated subleading terms), are dominant for  κ > 0 over those of the non-alternating A+ sector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Thus to extract the non-alternating  contributions we first establish the leading alternating contribution as described above  and then repeat the process working instead with a new series in which the leading  alternating contribution has been subtracted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' However, when κ becomes sufficiently  large, the sub-leading alternating contribution becomes comparable to that of the leading  non-alternating contribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' This limits the reliability of determination numerically of  the A+, a+ coefficients to small values of κ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' However, these coefficients can be more  readily verified by continuing to the κ < 0 regime where they are more dominant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  Having determined in this fashion the leading contributions to an, these can then be  subtracted from the data, the analysis repeated mutatis mutandis, to determine the sub-  leading βk coefficients (and again for similar reasons to the above the β−  k coefficients are  more readily extracted).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Figure 5 gives the numerical form of β−  1 and β−  2 as a function  of κ indicating a linear relationship.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  It becomes somewhat challenging to extract further subleading contributions from  the data available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' However, one can consider defining a new series, ˜an, comprised by  taking the data set and subtracting the already established asymptotic form of eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' (45).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  12  n  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='00  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='95  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='90  O  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='85  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='80  666660  口  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='75  口  口  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='70  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='65  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='60  0  5  10  15A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='08r  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='12  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='14  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='16  5  10  15  20  0a at  4  2  K  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='3  2  2  3  264A- A+  2  2  6  8Figure 5: The sub-leading coefficient β−  1 (left) and β−  2 (right) for various values of κ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  Shown is the terminal value of the second Richardson Transformation of the sequence  that gives β−  n constructed from fn after subtraction of leading alternating and non-  alternating asymptotics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  Grey lines correspond to β−  1  = −4κ and β−  2  = +4κ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  A  noticeable drift in β−  2 for larger values of κ suggests pollution from further sub-dominant  terms contributing at this order of perturbation theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  Figure 6: After subtracting the leading alternating and non-alternating contributions,  we again perform a Borel-Pad´e computation for κ = −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='75 (left) and κ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='4 (right).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  This seems to suggest that there is no longer a Borel singularity at ζ = 2, but instead  finding one at ζ = 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  Using the Borel-Pad´e again to this subtracted series produces some evidence, see Figure  6, of a compelling feature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Instead of poles at ζ = ±2, as would be anticipated should  the ansatz (44), one finds that leading positive pole appears to be at ζ = +4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' The  interpretation here is that the subtraction has removed the entire non-alternating terms  with behaviour 2−n, suggesting that all fluctuations β+  n>0 = 0 and the next contribution  comes with twice the “action” 4−n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  This behaviour is in accordance with the Parisi-’t Hooft conjecture [63–65];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' the  leading poles in the Borel plane at ζ = ±2 lie at integer values and the values of  a± = ∓2κ = ±2ξ are as expected (see [15]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='9  The pole at ζ = +2 is accordingly  interpreted as an IR renormalon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  A similar procedure of subtraction (removing the  IR renormalon) used above (in Figure 6) was performed in [26] to expose new Borel  renormalon poles that were not in accordance with Parisi-’t Hooft in cases including e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  the Gross-Neveu model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Here however, Figure 6 indicates that the next most proximate  IR renormalon pole is found in a location that are consistent with Parisi-’t Hooft.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  9We thank M Mari˜no and T Reis for illuminating us on this point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  13  β1-  K  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='0  2  4  6  8  10  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='12β2  12  10  8  6  4  2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='02  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='2  2  6  22  2  65  Transseries and Ambiguity Cancellation  In this section we compute the leading ambiguity of  e  ρ2 in two different ways.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' First,  we calculate the Borel ambiguity of the large order behaviour of the perturbative sector  established in 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' This is compared against an approach which solves the TBA system  in terms of a transseries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='1  Borel resummation and Large Order Perturbative Ambigu-  ity  Naively, one could try to resum the original asymptotic series by performing a Laplace  transform on the Borel transform (41)  1  γ  � ∞  0  B  �8κ  π  e  ρ2  �  e−ζ/γdζ = 1  γ  � ∞  0  ∞  �  n=0  an  n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ζne−ζ/γ ≃  ∞  �  n=0  anγn = 8κ  π  e  ρ2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  (50)  However, as we have seen, the Borel transform B  �  8κ  π  e  ρ2  �  generically has singularities  along the positive real axis obstructing the contour of this integral.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Therefore, we shall  introduce a directional Borel resummation given by  Sθ  �8κ  π  e  ρ2  �  = 1  γ  � eiθ∞  0  B  �8κ  π  e  ρ2  �  e−ζ/γdζ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  (51)  This procedure results, when integrating along a line without singularities, in a finite  answer, which however, depends on the sign of θ, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  there is an ambiguity in the  resummation of the perturbative series.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' This ambiguity, which is a Stokes phenomenon,  is studied by considering S+ϵ − S−ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' This can be done analytically by using, instead of  the numerically obtained results, a series whose coefficients are exactly the asymptotic  form an given by eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' (44) for all values of n:  (S+ϵ − S−ϵ)  �8κ  π  e  ρ2  �  (γ) = 2πiA+  � 2  γ  �a+  e−2/γ  ∞  �  k=0  β+  k  �γ  2  �k  = −  16πi  Γ(−κ)Γ(1 − κ)  �γ  2  �2κ  e−2/γ[1 + O(γ)] .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  (52)  Similarly, across the negative real axis we find a leading ambiguity given by  (Sπ+ϵ − Sπ−ϵ)  �8κ  π  e  ρ2  �  (γ) = 2πiA−  �  − 2  γ  �a−  e2/γ  ∞  �  k=0  β−  k  �  − z  2  �k  = −  πi  4Γ(κ)Γ(1 + κ)  �  −γ  2  �−2κ  e2/γ[1 + O(γ)] .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  (53)  In these expressions we note the presence of an exponentially small parameter, √qγ =  �  2  γ  �2κ  e−2/κ (the square root is for convenience later) characteristic of non-perturbative  physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' The main thrust of the modern resurgence paradigm is that physical quantities,  here e/ρ2, should be understood as a transseries, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' an expansion in √qγ whose terms  are each formal (asymptotic) series in γ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' It is critical that whilst resummation may  be ambiguous when applied to any individual term in this (here the perturbative √qγ0  sector), taken altogether the final result is non-ambiguous.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' In particular, and this goes  back to the pioneering work of Bogomol’nyi and Zinn-Justin [66–69], the ambiguity  of this perturbative sector should be compensated by a leading order ambiguity in an  appropriate non-perturbative sector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' In the next section we shall verify that such an  ambiguity cancellation does take place.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  14  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='2  Transseries and Leading Non-Perturbative Ambiguity  In this series we shall apply a different type of analysis to the TBA equations which  results in a transseries solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' The starting point shall be a reformulation of the TBA  system as an integral equation for an auxiliary function u(ω),  u(ω) = i  ω +  1  2πi  � ∞  −∞  dω′ e2iBω′ϱ(ω′)u(ω′)  ω′ + ω + iδ  ,  (54)  where  ϱ(ω) = 1 − iω  1 + iω  G−(ω)  G+(ω) ,  (55)  together with the boundary condition  u(i) = m  2heB G+(i)  G+(0) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  (56)  Having established the function u, the free energy is given by  ∆F(h) = − 1  2π h2u(i)G−(0)2  �  1 −  1  2πi  � ∞  −∞  dω e2iωBu(ω)ϱ(ω)  ω − i  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  (57)  We will now apply to the λ-model the techniques pioneered by [26] to solve this re-  cursively order by order in a perturbative parameter and a non-perturbative parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  The idea is to move the integration contour of the integral equation (54) into the UHP  so that it envelops all the branch cuts and poles in the UHP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' The Sine-Gordon model is  special as it only has poles but no branch cut.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' This was studied in [70] and gives rise to  a convergent rather than asymptotic expansion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' However, in the case of the λ-deformed  model, we are dealing with both poles and a branch cut along the imagine axis of ρ(ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  To separate it from the poles, we slightly move the cut away from the imaginary axis  to the ray C± = {ξeiθ|θ = π  2 ± δ}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' By deforming the integration contour we isolate the  contributions coming from the discontinuity over the cut and the residues at the poles  (see Figure 7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' As explained in [26] the choice of moving the branch cut to C+ or C− is  arbitrary and and gives rise to a leading non-perturbative ambiguity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Letting ϱn,± be  the residues at x = xn with the cut moved to C±, after this contour pulling eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' (54)  becomes  u(ix) = 1  x +  1  2πi  � ∞e±iϵ  0  dx′ e−2Bx′u(ix′)δϱ(ix′)  x′ + x  +  �  n  e−2Bxnunϱn,±  xn + x  ,  (58)  where un ≡ u(ixn) and δϱ is the discontinuity over the cut10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  From the WH-decomposition (17), we evaluate ϱ(ω) using (55) as  ϱ(ω) = −ω + i  ω − i  Γ  � iω  2 + 1  �2 Γ(1 − iω)Γ(1 − iκω)  Γ  �  1 − iω  2  �2 Γ(iω + 1)Γ(iκω + 1)  e−2ibωeiκω(log(iω)+log(−iω)) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  (59)  For generic values of κ, this has poles on the positive real axis at ω = ixn = iµn with  µ = 2 with residues given by  ϱn,± =  Res  x=xn±iϵ ϱ(ix) = −2ie2n(2b±iπκ−2κ log(2n))n2n + 1  2n − 1  ((2n)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' )2  (n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' )4  Γ(1 + 2nκ)  Γ(1 − 2nκ) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  (60)  However, when κ is rational some of these poles are removed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  Suppose we express  κ ≡  k  N = p/q as a reduced fraction with p, q coprime integers (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' q = N/gcd(N, k)),  10For the discontinuity function, we use the convention δρ(ω) = ρ(ω(1 − iϵ) − ρ(ω(1 + iϵ)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  15  ω  C−  C  ϱ−  1  ϱ−  2  ϱ−  3  ω  C+  C  ϱ+  1  ϱ+  2  ϱ+  3  Figure 7: The contour C = (−∞, ∞) is deformed into either of two ways.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' The branch  cut, represented by the curvy line is moved to either the ray C+ or C−.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' In those cases  respectively, the contour is deformed into C+ or C−.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' In both cases we pick up residues  ϱ±  n , but their values differ by the branch cut discontinuity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  then the set of poles are located at x ∈ 2N\\qN (rather than x ∈ 2N).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Hence, the residue  ϱn,± evaluates to zero if 2n ∈ 2N ∩ qN, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 2n is a multiple of q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' In particular, when  k is an integer multiple of a half, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' q = 1 or q = 2, all poles are removed entirely.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  If ϱ1 = 0, then ϱn = 0 for all n;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' in what follows we shall consider only the case where  ϱ1 ̸= 0 which is most relevant to our discussion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  The discontinuity function is given by  δϱ(ix) = 2ix + 1  x − 1e2bxe−2κx log x sin(κπx)Γ(1 − x/2)2Γ(1 + x)Γ(1 + κx)  Γ(1 + x/2)2Γ(1 − x)Γ(1 − κx) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  (61)  Notice this has simple poles at x = 2n, which have residues that vanish for κ half-integer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  Lastly we shall need11  ϱ(i ± 0) = 8e2b∓iπκ Γ(1 + κ)  Γ(1 − κ) = 8  πκe2b∓iπκΓ(1 + κ)2 sin(πκ) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  (62)  Following again [26], the integral equation (58) is simplified by the introduction of  P(η, v) given by  e−2Bxδϱ(ix) = −2ive−ηP(η, v) ,  (63)  with a change of variables (x, B) → (η, v):  1  v + a log v = 2B ,  x = vη .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  (64)  Here, a is a constant determined by demanding that P(η, v) is regular in v with, in  particular, no log(v) terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' From eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' (61), we have that δϱ(ix) ∝ e˜ax log x � dnxn,  where ˜a = −2κ, therefore this determines ˜a = a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' This yields an expansion of P(η, v)  given by  P(η, v) = d1,0η + vη2(d2,0 + d2,1 log(η)) + O(v2) ,  d1,0 = πκ ,  d2,0 = 2πκ(1 + (1 − γE − log(κ))κ − log(2)) ,  d2,1 = −2πκ2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  (65)  With the introduction of an integral operator  I[f](η) = − v  π  � ∞  0  dη′ e−η′P(η′, v)f(η′)  η + η′  ,  (66)  11Because we are assuming that κ is not integer, ϱ(i±0) is non-zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' If κ < 0, then ϱ(i±0) generically  has a finite ambiguity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  16  after this change of variables, eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' (58) can be written as  u(η) = u(η) + I[u](η) ,  (67)  in which the ‘seed’ solution is given as  u(η) = 1  vη + 1  v  �  n  e−2Bvηnunϱn,±  ηn + η  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  (68)  The formal solution obtained by iteration is thus presented as  u(η) =  ∞  �  l=0  Il[u](η) ≡ J [u](η) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  (69)  To determine the unknown coefficients un = u(ηn) we evaluate eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' (67) at η = ηn =  µn/v and define In[f] ≡ I[f](η = ηn) to obtain  un = 1  µn + In[u] + 1  µ  �  m  e−2Bvηnumϱm,±  m + n  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  (70)  Here we have made a slight adaptation compared to [26] to suit the locations of the poles  at xn = µn (with µ = 2) (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' the Gross-Neveu model for which xn = 2n+1  Υ  for some  constant Υ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' To treat the exponentially small contributions coming from the residue  term we introduce the small parameter  q = e−2Bµ = e−µ/vv−µa .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  (71)  Both the seed and formal solution, and the unkown values un, admit expansion in q  u(η) =  �  s=1  u(s)(η)qs ,  u(η) =  �  u(s)(η)qs ,  un =  �  s=0  u(s)  n qs .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  (72)  As the operator J does not introduce factors of q we can construct the full solution  order by order in q noting u(s)(η) = J [u(s)](η).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Using (68) one finds that the first few  terms12 of the seed solution are given by  u(0) = 1  vη ,  u(1) = ϱ1,±u(0)  1  vη + µ ,  u(2) = ϱ1,±u(1)  1  vη + µ + ϱ2,±u(0)  2  vη + 2µ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  (74)  Applying the q-expansion to eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' (70) we have that  u(0)  n  = J [u(0)](ηn) = 1  µn + In[J [ 1  vη ]] ,  u(1)  n  = In[J [u(1)]] + 1  µ  ϱ1,±u(0)  1  1 + n  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  (75)  Let us assume that ϱ1,± ̸= 0 (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' κ is not half-integer), such that these two expressions  are governing the leading behaviour.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Suppose now we work formally13 to leading order  12For n ≥ 1, we have in general  u(n)(η) =  n  �  m=1  ϱm,±u(n−m)  m  vη + µm  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  (73)  13i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ignoring that q is exponentially smaller than higher order polynomial terms in v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  17  in v and leading order in q .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Because each application of I carries a factor v, to leading  order it is sufficient to consider only the identity operator J = 1+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' which results in14  u(0)  n  = 1  µn −  v  nπµd1,0 + O(v2) ,  u(1)  n  =  ϱ1,±  µ2(n + 1) −  d1,0ϱ1,±  µ2π(n + 1)v + O(v2) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  (76)  The leading orders of u(η) are obtained by  u(η) =  �  u(0) + I[u(0)] + O(v)  �  + q  �  u(1) + I[u(1)] + O(v2)  �  + O(q2) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  (77)  To implement the boundary condition that relates the chemical potential h to q, v,  we will need  u(i) = u  �  η = 1  v  �  =  �  1 − d1,0  π v + O(v2)  �  +  qϱ1,±  µ(1 + µ)  �  1 − d1,0v  π  + O(v2)  �  + O(q2) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  (78)  The next step is to do the Legendre transform and calculate  e  ρ2 from ∆F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' This can  then be used to compare against the perturbative calculation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' The same procedure of  resolving the cut away from the poles of ρ and deforming the contour appropriately  yields  ∆F(h) = − h2  2π u(i)G+(0)2  �  1 + v2  π  � e−ηP(η, v)u(η)  ηv − 1  dη  − e−2Bϱ(i ± ϵ)u(i) −  �  n≥1  qnϱn,±un  µn − 1  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  (79)  The leading orders of eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' (79) are given by  ∆F(h) = − G+(0)2h  2π  �  1 − 2d10  π v + O(v2)  �  ×  �  1 − ρ(i ± ϵ)q1/µ +  2ρ1,±  µ(1 − µ2)q − 2ρ1,±ρ(i ± ϵ)  µ(1 + µ)  q1+1/µ + O(q2)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  (80)  The first step of the Legendre transform is to relate h to the parameters q and v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' This  is done by substituting the expansion (78) for u(i) into the boundary condition (56)  which, for µ = 2, gives  h =  mG+(i)  12πG+(0)q−1/4�  π + d1,0v + O(v2)  ��  6 − ρ1,±q + O(q2)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  (81)  As a consequence ρ = − d∆F  dh  is given by  ρ = G+(i)G+(0)m  12π2  �  π − d1,0v + O(v2)  ��  6q−1/4 + ρ1,±q3/4 + O(q7/4)  �  ,  (82)  from which we obtain  e  ρ2 as a series in v and q:  e  ρ2 =  1  6G+(0)2  �  π + 2d1,0v + O(v2)  ��  3 + 3ρ(i + ±ϵ)q1/2 + ρ1,±q + O(q3/2)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  (83)  14The small v limit can be taken also in the integral:  I  � 1  vη  �  (ηn) = − v  π  � ∞  0  eη′d1,0η  vη′ + nµ = − v  π  � ∞  0  �  eη′d1,0  nµ  + O(v)  �  = − vd1,0  nπµ + O(v2) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  18  We will now write this expansion in terms of the coupling (38) used in the previous  Sections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Let us introduce a parameter exponentially small in γ, analogous to q being  exponentially small in v, given by qγ = e−4/γ(γ/2)4κ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' We use (38) to write v as a series  in γ and qγ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Substituting this series for v (and q = q(v)) into (83), we arrive at  8κ  π  e  ρ2 =  �  1 + κγ + O(γ2)  �  − 8e∓iπκ Γ(κ)  Γ(−κ)q1/2  γ  (1 + O(γ))  + 23−4κe∓2iπκ Γ(2κ)  Γ(−2κ)qγ(1 + O(γ)) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  (84)  We see that the first two coefficient of the perturbative series match precisely with eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  (40).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' The presence of transseries parameters qγ = e−4/γ(γ/2)4κ provides concrete pre-  dictions of the resurgent structure of the perturbative series.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' In particular, we compute  the ambiguity of the transseries (84) due to the difference in result if the branch cut is  left or right of the poles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' To leading order in qγ and γ, it is given by  8κ  π  �� e  ρ2  �  −  −  � e  ρ2  �  +  �  =  16πi  Γ(−κ)Γ(1 − κ)  �γ  2  �2κ  e−2/γ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  (85)  This is exactly the same ambiguity as obtained through the asymptotic analysis of our  perturbative calculation - see eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' (52).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' We thus observe that the Borel-ambiguity of  the perturbative series can be cancelled precisely by an ambiguity of a transmonomial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  Therefore, the large order non-perturbative behaviour is unambiguous up to the order  considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' This mirrors the fabled BZJJ ambiguity cancellation [66–69] in a field theory  context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  The analysis above only finds a source of the leading ambiguity on the positive  real axis of the Borel plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' However, we can do a similar analysis to recover the Borel  branch singularity on the negative real axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' The critical modification of the programme,  as realised by [15], is to deform the contour of the integral equation (54) into the lower  half plane, instead of the upper half plan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' The critical analytic data is then given by the  branch cut and residues at the negative imaginary axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' In the lower half plane, ϱ(−ix)  has residues at xn = 2n + 1 and at ˜xn := n  κ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' However, as the latter set of residues is  unambiguous with respect to the branch cut, they do not contribute15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' One subtlety  when using this approach arises when computing u(i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Deforming the contour of eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  (54) to an envelopment of the negative imaginary axis picks up a residue at ω = −i,  which introduces a contribution of u(−i)ρ(−i ± ϵ)q not present in the analysis above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  We will not present a detailed derivation as it is similar to the one above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Rather, we  can report that the final result is a transseries with a leading ambiguity given by  8κ  π  �� e  ρ2  �  −  −  � e  ρ2  �  +  �  = −  πi  4Γ(κ)Γ(1 + κ)  �  −γ  2  �−2κ  e2/γ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  (86)  This precisely matches the ambiguity of the perturbative sector around the negative real  axis found in eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' (53).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  6  Discussion  In this note, we have studied the λ-model and brought it into the fold of resurgent  analysis of [13–15, 26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' The model is particularly interesting, because, distinct from  previously considered models, it has a interacting CFT fixed point in the UV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  15They would be part of a transseries solution, but as they are unambiguous, they are not of interest  to us currently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' As a further side remark, when choosing κ < 0, along the positive imaginary axis ϱ(ix)  also has such unambiguous residues at x = n  κ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  19  We have found a perturbative series for the energy density at finite chemical poten-  tial of the λ-model in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='4 and identified with numerical techniques its asymp-  totic form in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  A key feature is that the Borel resummation of the large  order behaviour is ambiguous when taken along either the positive or negative real axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  These ambiguities are exactly compensated/cancelled by a further ambiguity in a non-  perturbative sector of a transseries solution in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' These cancellations provide the  λ-model with a robustly defined foundation which may serve as a paradigmatic example  for other theories with asymptotic CFT behaviour.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  Of particular note is that the leading ambiguity on the positive axis (and associated  features in the Borel plane) vanishes for κ ∈ Z>0, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' when the WZW level k divides  the rank N of the gauge group SU(N).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' This is reminiscent of Cheshire-cat resurgence  [71–74] in which the full glory of resurgence only becomes apparent as you deform away  from certain special points at which it truncates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  Let us finish with some broader questions to ponder following the analysis of the  λ-model that we hope might stimulate further investigations on the topic:  An interesting feature of the WZW CFT that defines the UV of the λ model is  that it exhibits level-rank duality [75].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' It would be valuable to understand the  extent to which this property constrains, or is encapsulated, in the form of the  transseries that defines the λ-model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  In a QFT it is sometimes possible to directly link poles/branch points in the  Borel plane to finite action non-pertubative saddle configurations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Remarkably,  this can be done even in theories without instantons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' In a series of paper [9, 11,  12] finite action ‘uniton’ configurations of 1+1d integrable QFTs were matched  to Borel poles of a quantum mechanics that followed by dimensional reduction  with twisted boundary conditions (akin to a chemical potential as deployed here).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  This poses a natural question: can the features of the Borel plane we have found  here via TBA methods be related to some finite action saddles?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Conversely, given  the knowledge of such uniton configurations, what do they imply for the TBA  method?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Achieving this would serve to put the semi-classical approaches of [9, 11,  12] on a surer-footing in quantum field theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  On the other hand there are a class of ambiguities which don’t (yet at least) have an  interpretation as semi-classical saddles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Instead they are renormalon ambiguities  associated to certain classes of Feynman diagrams.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' In [18, 76] it was shown how  to construct such a series of diagrams which source the renormalon ambiguities in  1/N expansion of the O(N) vector model, the Gross-Neveu and the SU(N) PCM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  It would be interesting to investigate if there are diagrams that are responsible for  the ambiguities in the λ-models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  The landscape of integrable models in two dimensions has been vastly expanded  in recent years through variants of this λ-model, and the related Yang-Baxter σ-  models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' It could be rewarding to deploy similar technique across this landscape  included e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' to models with multiple deformation parameters or theories based  on cosets rather than group manifolds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  In [57] the Quantum Inverse Scattering Method was applied to give a direct quant-  isation of the λ-models as a continuum limit of a spin k Heisenberg spin-chain with  inhomogeneities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' The parameter that governs the in-homogeneity becomes a mass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  Although the ground state of the system is quite a complicated Fermi sea, one can  identify holes as certain particle excitations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' After taking the continuum limit,  one can obtain a TBA system for these excitations matching that of the QFT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  An exciting question is if the above resurgent structure can be given a similar ab  initio derivation within the QISM framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  20  Acknowledgements  DCT is supported by The Royal Society through a University Research FellowshipGen-  eralised Dualities in String Theory and Holography URF 150185 and in part by STFC  grant ST/P00055X/1 as well as by the FWO-Vlaanderen through the project G006119N  and Vrije Universiteit Brussel through the Strategic Research Program “High-Energy  Physics”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' LS is supported by a PhD studentship from The Royal Society and the grant  RF\\ERE\\210269.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' For the purpose of open access, the authors have applied a Creative  Commons Attribution (CC BY) licence to any Author Accepted Manuscript version  arising.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' We thank M Mari˜no and T Reis for helpful comments on a draft and I Aniceto  for comments relating to this project.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  References  [1]  Al B Zamolodchikov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘Exact two-particle S-matrix of quantum sine-Gordon solitons’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  Communications in Mathematical Physics 55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='2 (1977), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 183–186.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [2]  Peter Hasenfratz, Michele Maggiore and Ferenc Niedermayer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘The exact mass gap  of the O(3) and O(4) non-linear σ-models in d = 2’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Physics Letters B 245.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='3-4  (1990), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 522–528.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [3]  Peter Hasenfratz and Ferenc Niedermayer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘The exact mass gap of the O(N) σ-  model for arbitrary N ≥ 3 in d = 2’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Physics Letters B 245.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='3-4 (1990), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 529–  532.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [4]  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Forgacs, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Niedermayer and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Weisz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘The Exact mass gap of the Gross-Neveu  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' The Thermodynamic Bethe ansatz’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' B 367 (1991), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 123–  143.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='1016/0550-3213(91)90044-X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [5]  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Forgacs, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Niedermayer and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Weisz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘The Exact mass gap of the Gross-  Neveu model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' The 1/N expansion’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' B 367 (1991), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 144–157.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' doi:  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='1016/0550-3213(91)90045-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [6]  Inˆes Aniceto, Gok¸ce Ba¸sar and Ricardo Schiappa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘A Primer on Resurgent Trans-  series and Their Asymptotics’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Rept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 809 (2019), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 1–135.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='1016/  j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='physrep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='02.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' arXiv: 1802.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='10441 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [7]  Gerald V Dunne and Mithat ¨Unsal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘Resurgence and trans-series in Quantum Field  Theory: the CPN−1 model’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' JHEP 11 (2012), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 170.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='1007/JHEP11(2012)  170.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' arXiv: 1210.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='2423 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [8]  Aleksey Cherman, Daniele Dorigoni, Gerald V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Dunne and Mithat ¨Unsal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘Resur-  gence in Quantum Field Theory: Nonperturbative Effects in the Principal Chiral  Model’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 112 (2014), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 021601.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='1103/PhysRevLett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='112.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  021601.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' arXiv: 1308.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='0127 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [9]  Aleksey Cherman, Daniele Dorigoni and Mithat Unsal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘Decoding perturbation  theory using resurgence: Stokes phenomena, new saddle points and Lefschetz  thimbles’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' JHEP 10 (2015), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 056.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' doi: 10 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 1007 / JHEP10(2015 ) 056.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' arXiv:  1403.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='1277 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [10]  Gerald V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Dunne and Mithat Unsal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘Resurgence and Dynamics of O(N) and  Grassmannian Sigma Models’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' JHEP 09 (2015), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 199.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='1007/JHEP09(2015)  199.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' arXiv: 1505.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='07803 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [11]  Saskia Demulder, Daniele Dorigoni and Daniel C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Thompson.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘Resurgence in η-  deformed Principal Chiral Models’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' JHEP 07 (2016), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 088.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' doi: 10 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 1007 /  JHEP07(2016)088.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' arXiv: 1604.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='07851 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  21  [12]  Lucas Schepers and Daniel C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Thompson.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘Resurgence in the bi-Yang-Baxter  model’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' B 964 (2021), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 115308.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='nuclphysb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  115308.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' arXiv: 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='03683 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [13]  Dmytro Volin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘From the mass gap in O(N) to the non-Borel-summability in  O(3) and O(4) sigma-models’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' D 81 (2010), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 105008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='1103/  PhysRevD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='105008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' arXiv: 0904.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='2744 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [14]  Dmytro Volin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘Quantum integrability and functional equations: Applications to  the spectral problem of AdS/CFT and two-dimensional sigma models’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Journal of  Physics A: Mathematical and Theoretical 44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='12 (2011), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 124003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' arXiv: 1003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  4725 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [15]  Marcos Mari˜no and Tom´as Reis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘Renormalons in integrable field theories’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' JHEP  04 (2020), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 160.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='1007/JHEP04(2020)160.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' arXiv: 1909.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='12134 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [16]  Marcos Mari˜no and Tom´as Reis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘Resurgence for superconductors’ (May 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='1088/1742-5468/ab4802.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' arXiv: 1905.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='09569 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [17]  Marcos Mari˜no and Tom´as Reis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘A new renormalon in two dimensions’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' JHEP 07  (2020), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 216.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='1007/JHEP07(2020)216.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' arXiv: 1912.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='06228 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [18]  Marcos Marino, Ramon Miravitllas and Tomas Reis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘Testing the Bethe ansatz  with large N renormalons’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ST 230.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='12-13 (2021), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 2641–2666.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='1140/epjs/s11734-021-00252-4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' arXiv: 2102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='03078 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [19]  Zoltan Bajnok, Janos Balog, Arpad Hegedus and Istvan Vona.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘Instanton effects  vs resurgence in the O(3) sigma model’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' B 829 (2022), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 137073.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' doi:  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='physletb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='137073.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' arXiv: 2112.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='11741 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [20]  Zoltan Bajnok and Romuald A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Janik.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘OPE coefficients and the mass-gap from  the integrable scattering description of 2D CFT’s’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' JHEP 11 (2022), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 128.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' doi:  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='1007/JHEP11(2022)128.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' arXiv: 2209.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='10393 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [21]  Zoltan Bajnok, Janos Balog, Arpad Hegedus and Istvan Vona.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘Running coupling  and non-perturbative corrections for O(N) free energy and for disk capacitor’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  JHEP 09 (2022), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='1007/JHEP09(2022)001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' arXiv: 2204.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='13365  [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [22]  Zolt´an Bajnok, J´anos Balog and Istv´an Vona.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘Analytic resurgence in the O(4)  model’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' JHEP 04 (2022), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 043.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='1007/JHEP04(2022)043.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' arXiv: 2111.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  15390 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [23]  Michael C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Abbott, Zolt´an Bajnok, J´anos Balog, ´Arp´ad Heged´us and Saeedeh  Sadeghian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘Resurgence in the O(4) sigma model’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' JHEP 05 (2021), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 253.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' doi:  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='1007/JHEP05(2021)253.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' arXiv: 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='12254 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [24]  Michael C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Abbott, Zolt´an Bajnok, J´anos Balog and ´Arp´ad Heged´us.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘From per-  turbative to non-perturbative in the O (4) sigma model’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' B 818 (2021),  p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 136369.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='physletb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='136369.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' arXiv: 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='09897 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [25]  Zoltan Bajnok, Janos Balog and Istvan Vona.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘The full analytic trans-series in  integrable field theories’ (Dec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' arXiv: 2212.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='09416 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [26]  Marcos Marino, Ramon Miravitllas and Tomas Reis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘New renormalons from ana-  lytic trans-series’ (Nov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' arXiv: 2111.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='11951 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [27]  Konstadinos Sfetsos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘Integrable interpolations: From exact CFTs to non-Abelian  T-duals’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' B 880 (2014), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 225–246.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='nuclphysb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='01.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' arXiv: 1312.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='4560 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  22  [28]  Konstadinos Sfetsos and Konstadinos Siampos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘Gauged WZW-type theories and  the all-loop anisotropic non-Abelian Thirring model’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' B 885 (2014),  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 583–599.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='nuclphysb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='06.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' arXiv: 1405.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='7803  [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [29]  Jonathan M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Evans and Timothy J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Hollowood.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘Integrable theories that are  asymptotically CFT’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' B 438 (1995), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 469–490.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='1016/0550-  3213(94)00473-R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' arXiv: hep-th/9407113.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [30]  Jonathan M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Evans and Timothy J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Hollowood.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘Exact results for integrable  asymptotically - free field theories’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' B Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Suppl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='1 (1996).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' by  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Mussardo, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Randjbar-Daemi and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Saleur, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 130–139.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='1016/0920-  5632(95)00622-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' arXiv: hep-th/9508141.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [31]  Calan Appadu, Timothy J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Hollowood and Dafydd Price.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘Quantum Inverse Scat-  tering and the Lambda Deformed Principal Chiral Model’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' A 50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='30 (2017),  p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 305401.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='1088/1751-8121/aa7958.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' arXiv: 1703.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='06699 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [32]  Edward Witten.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘Non-abelian bosonization in two dimensions’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Bosonization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' World  Scientific, 1994, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 201–218.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [33]  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Balog, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Forgacs, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Horvath and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Palla.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘A New family of SU(2) symmetric  integrable sigma models’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' B 324 (1994).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' by D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Lust and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Weigt,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 403–408.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='1016/0370-2693(94)90213-5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' arXiv: hep-th/9307030.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [34]  Konstadinos Sfetsos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘Gauged WZW models and nonAbelian duality’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  D 50 (1994), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 2784–2798.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='1103/PhysRevD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='2784.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' arXiv: hep-  th/9402031.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [35]  Daniel C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Thompson.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘An Introduction to Generalised Dualities and their Applic-  ations to Holography and Integrability’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' PoS CORFU2018 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' by Kon-  stantinos Anagnostopoulos et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=', p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 099.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='22323/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='347.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='0099.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' arXiv:  1904.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='11561 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [36]  Ben Hoare.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘Integrable deformations of sigma models’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' A 55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='9 (2022),  p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 093001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='1088/1751-8121/ac4a1e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' arXiv: 2109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='14284 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [37]  Timothy J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Hollowood, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Luis Miramontes and David M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Schmidtt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘Integrable  Deformations of Strings on Symmetric Spaces’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' JHEP 11 (2014), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' doi:  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='1007/JHEP11(2014)009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' arXiv: 1407.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='2840 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [38]  Timothy J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Hollowood, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='Luis Miramontes and David M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Schmidtt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘An Integrable  Deformation of the AdS5 × S5 Superstring’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' A 47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='49 (2014), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 495402.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='1088/1751-8113/47/49/495402.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' arXiv: 1409.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='1538 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [39]  Konstantinos Sfetsos and Daniel C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Thompson.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘Spacetimes for λ-deformations’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  JHEP 12 (2014), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 164.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='1007/JHEP12(2014)164.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' arXiv: 1410.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='1886  [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [40]  Saskia Demulder, Konstantinos Sfetsos and Daniel C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Thompson.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘Integrable λ-  deformations: Squashing Coset CFTs and AdS5 × S5’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' JHEP 07 (2015), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='1007/JHEP07(2015)019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' arXiv: 1504.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='02781 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [41]  Riccardo Borsato and Linus Wulff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘Target space supergeometry of η and λ-  deformed strings’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' JHEP 10 (2016), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 045.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='1007/JHEP10(2016)045.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  arXiv: 1608.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='03570 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [42]  Arkady A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Tseytlin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘On A ’Universal’ class of WZW type conformal models’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' B 418 (1994), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 173–194.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='1016/0550-3213(94)90243-7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  arXiv: hep-th/9311062.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  23  [43]  Calan Appadu and Timothy J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Hollowood.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘Beta function of k deformed AdS5  × S5 string theory’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' JHEP 11 (2015), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 095.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='1007/JHEP11(2015)095.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  arXiv: 1507.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='05420 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [44]  Ctirad Klimˇc´ık.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘Poisson–Lie T-duals of the bi-Yang–Baxter models’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  B 760 (2016), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 345–349.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='physletb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='06.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='077.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' arXiv:  1606.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='03016 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [45]  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Hoare and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Tseytlin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘On integrable deformations of superstring sigma  models related to AdSn ×Sn supercosets’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' B 897 (2015), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 448–478.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='nuclphysb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='06.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' arXiv: 1504.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='07213 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [46]  Konstantinos Sfetsos, Konstantinos Siampos and Daniel C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Thompson.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘Gener-  alised integrable λ - and η-deformations and their relation’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' B 899  (2015), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 489–512.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='nuclphysb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='08.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' arXiv: 1506.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  05784 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [47]  Benoit Vicedo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘Deformed integrable σ-models, classical R-matrices and classical  exchange algebra on Drinfel’d doubles’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' A 48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='35 (2015), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 355203.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' doi:  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='1088/1751-8113/48/35/355203.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' arXiv: 1504.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='06303 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [48]  Ctirad Klimˇc´ık.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘η and λ deformations as E -models’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' B 900 (2015),  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 259–272.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='nuclphysb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='09.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' arXiv: 1508.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='05832  [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [49]  T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Buscher.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘Path Integral Derivation of Quantum Duality in Nonlinear Sigma  Models’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' B 201 (1988), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 466–472.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='1016/0370-2693(88)  90602-8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [50]  K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Gawedzki and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Kupiainen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘G/h Conformal Field Theory from Gauged WZW  Model’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' B 215 (1988), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 119–123.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='1016/0370-2693(88)  91081-7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [51]  Edward Witten.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘On Holomorphic factorization of WZW and coset models’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Com-  mun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 144 (1992), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 189–212.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='1007/BF02099196.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [52]  Timothy J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Hollowood, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Luis Miramontes and David M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Schmidtt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘S-Matrices  and Quantum Group Symmetry of k-Deformed Sigma Models’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' A 49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='46  (2016), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 465201.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='1088/1751-8113/49/46/465201.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' arXiv: 1506.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='06601  [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [53]  Georgios Itsios, Konstantinos Sfetsos, Konstantinos Siampos and Alessandro Tor-  rielli.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘The classical Yang–Baxter equation and the associated Yangian symmetry  of gauged WZW-type theories’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' B 889 (2014), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 64–86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='nuclphysb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' arXiv: 1409.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='0554 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [54]  George Georgiou, Konstantinos Sfetsos and Konstantinos Siampos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘Strong in-  tegrability of λ-deformed models’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' B 952 (2020), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 114923.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' doi:  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='nuclphysb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='114923.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' arXiv: 1911.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='07859 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [55]  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Hassan and Ashoke Sen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘Marginal deformations of WZNW and coset models  from O(d,d) transformation’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' B 405 (1993), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 143–165.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  1016/0550-3213(93)90429-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' arXiv: hep-th/9210121.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [56]  C Ahn, D Bernard and A LeClair.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘Fractional supersymmetries in perturbed coset  CFTs and integrable soliton theory’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Nuclear Physics B 346.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='2-3 (1990), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 409–  439.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [57]  Calan Appadu, Timothy J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Hollowood, Dafydd Price and Daniel C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Thompson.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  ‘Quantum Anisotropic Sigma and Lambda Models as Spin Chains’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' A  51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='40 (2018), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 405401.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='1088/1751-8121/aadc6d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' arXiv: 1802.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='06016  [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  24  [58]  A Polyakov and Paul B Wiegmann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘Theory of nonabelian Goldstone bosons in  two dimensions’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Physics Letters B 131.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='1-3 (1983), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 121–126.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [59]  Alexander M Polyakov and PB Wiegmann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘Goldstone fields in two dimensions  with multivalued actions’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Physics Letters B 141.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='3-4 (1984), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 223–228.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [60]  PB Wiegmann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘Exact solution of the O(3) nonlinear two-dimensional sigma-  model’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' JETP Letters 41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='2 (1985), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 95–100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [61]  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Balog, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Naik, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Niedermayer and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Weisz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘Exact mass gap of the chiral  SU(n) x SU(n) model’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 69 (1992), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 873–876.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='1103/  PhysRevLett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='873.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [62]  Timothy J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Hollowood.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘The Exact mass gaps of the principal chiral models’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' B 329 (1994), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 450–456.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='1016/0370-2693(94)91089-8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' arXiv:  hep-th/9402084.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [63]  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Parisi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘On Infrared Divergences’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' B 150 (1979), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 163–172.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' doi:  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='1016/0550-3213(79)90298-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [64]  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Parisi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘Singularities of the Borel Transform in Renormalizable Theories’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' B 76 (1978), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 65–66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='1016/0370-2693(78)90101-6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [65]  Gerard ’t Hooft.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘Can We Make Sense Out of Quantum Chromodynamics?’' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Sub-  nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 15 (1979).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' by Antonino Zichichi, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 943.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [66]  EB Bogomolny.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘Calculation of instanton-anti-instanton contributions in quantum  mechanics’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Physics Letters B 91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='3-4 (1980), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 431–435.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [67]  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Zinn-Justin and U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Jentschura.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘Multi-instantons and exact results I: Con-  jectures, WKB expansions, and instanton interactions’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Annals Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 313 (2004),  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 197–267.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='aop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='04.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' arXiv: quant-ph/0501136.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [68]  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Zinn-Justin and U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Jentschura.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘Multi-instantons and exact results II: Specific  cases, higher-order effects, and numerical calculations’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Annals Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 313 (2004),  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 269–325.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='aop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='04.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' arXiv: quant-ph/0501137.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [69]  Jean Zinn-Justin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘Perturbation Series at Large Orders in Quantum Mechanics  and Field Theories: Application to the Problem of Resummation’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Rept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 70  (1981), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='1016/0370-1573(81)90016-8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [70]  Alexei B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Zamolodchikov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘Mass scale in the sine-Gordon model and its reductions’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' A 10 (1995), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 1125–1150.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='1142/S0217751X9500053X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [71]  Daniele Dorigoni and Philip Glass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘The grin of Cheshire cat resurgence from  supersymmetric localization’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' SciPost Physics 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='2 (2018), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [72]  Daniele Dorigoni and Philip Glass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘Picard-Lefschetz decomposition and Cheshire  Cat resurgence in 3D N = 2 field theories’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Journal of High Energy Physics 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='12  (2019), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 1–40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [73]  Can Koz¸caz, Tin Sulejmanpasic, Yuya Tanizaki and Mithat ¨Unsal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘Cheshire Cat  resurgence, Self-resurgence and Quasi-Exact Solvable Systems’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 364.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='3 (2018), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 835–878.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='1007/s00220- 018- 3281- y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' arXiv:  1609.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='06198 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [74]  Syo Kamata, Tatsuhiro Misumi, Naohisa Sueishi and Mithat ¨Unsal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘Exact-WKB  analysis for SUSY and quantum deformed potentials: Quantum mechanics with  Grassmann fields and Wess-Zumino terms’ (Nov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' arXiv: 2111.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='05922 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  [75]  Stephen G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Naculich and Howard J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Schnitzer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘Duality Between SU(N)k and  SU(k)N WZW Models’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' B 347 (1990), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 687–742.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='1016/  0550-3213(90)90380-V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  25  [76]  Lorenzo Di Pietro, Marcos Mari˜no, Giacomo Sberveglieri and Marco Serone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' ‘Re-  surgence and 1/N Expansion in Integrable Field Theories’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' JHEP 10 (2021), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' 166.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='1007/JHEP10(2021)166.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content=' arXiv: 2108.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='02647 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
+page_content='  26' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9FKT4oBgHgl3EQfZi4o/content/2301.11803v1.pdf'}
diff --git a/DdE1T4oBgHgl3EQf-Abs/vector_store/index.pkl b/DdE1T4oBgHgl3EQf-Abs/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..5362bfa7e87fd2e9b552c34a534af482a4c502af
--- /dev/null
+++ b/DdE1T4oBgHgl3EQf-Abs/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:c78210b91bd907702ac2071c284b7dd233aa36bb850ae753ae158d36975ea5f1
+size 167437
diff --git a/DdE5T4oBgHgl3EQfUQ9g/content/tmp_files/2301.05542v1.pdf.txt b/DdE5T4oBgHgl3EQfUQ9g/content/tmp_files/2301.05542v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..21e9db4d7504673b0804599d08903efaa4dedbec
--- /dev/null
+++ b/DdE5T4oBgHgl3EQfUQ9g/content/tmp_files/2301.05542v1.pdf.txt
@@ -0,0 +1,4006 @@
+arXiv:2301.05542v1  [math.CT]  13 Jan 2023
+Tangent categories as a bridge between
+differential geometry and algebraic geometry
+G.S.H. Cruttwell∗ and Jean-Simon Pacaud Lemay†
+January 16, 2023
+Abstract
+Discussions of tangent vectors, tangent spaces, and differentials are important in both differential
+geometry and algebraic geometry. In this paper, we use the abstract notion of a tangent category to
+make some of these commonalities precise. In particular, we focus on the idea of a differential bundle in
+a tangent category, which gives a new way to compare smooth vector bundles and modules. The results
+of this paper also give a new characterization of the opposite category of modules over a commutative
+ring and the opposite category of quasicoherent sheaves.
+Contents
+1
+Introduction
+2
+2
+Tangent Categories
+4
+2.1
+Basics of Tangent Categories
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+4
+2.2
+Commutative rings as a Tangent Category . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+11
+2.3
+Affine schemes as a Tangent Category . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+14
+3
+Differential Bundles
+18
+3.1
+Differential Bundles and Differential Objects
+. . . . . . . . . . . . . . . . . . . . . . . . . . .
+19
+3.2
+Differential Bundles as Pre-Differential Bundles . . . . . . . . . . . . . . . . . . . . . . . . . .
+22
+3.3
+Morphisms and Categories of Differential Bundles . . . . . . . . . . . . . . . . . . . . . . . . .
+24
+4
+Differential Bundles for Commutative Rings
+26
+4.1
+From Differential Bundles to Modules
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+26
+4.2
+From Modules to Differential Bundles
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+26
+4.3
+Equivalence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+29
+5
+Differential Bundles for (Affine) Schemes
+34
+5.1
+From Differential Bundles to Modules
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+34
+5.2
+From Modules to Differential Bundles
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+34
+5.3
+Equivalence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+37
+5.4
+Differential bundles in schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+42
+6
+Future work
+44
+∗Partially supported by an NSERC Discovery grant.
+†For this research, author was financially supported by NSERC Postdoctoral Fellowship - Award #: 456414649 and a JSPS
+Postdoctoral Fellowship, Award #: P21746
+1
+
+1
+Introduction
+What exactly is the relationship between differential geometry and algebraic geometry? While there are
+many differences between these two subjects, one common thread is the use of “differential” methods.
+Indeed, discussions of tangent vectors, tangent spaces, and differentials are important in both subjects. A
+natural question to ask then is: can we precisely relate and contrast how differential geometry and algebraic
+geometry use these ideas? This paper gives one way to approach this question, via the theory of tangent
+categories, and in particular through investigating differential bundles in tangent categories.
+Tangent categories were first introduced by Rosick´y in [25], and later generalized and further developed by
+Cockett and Cruttwell in [5]. A tangent category (Definition 2.1) is a category equipped with an endofunctor
+T which for every object A associates an object T(A) that “behaves like a tangent bundle” for A. More
+precisely, this behaviour is captured through various natural transformations related to the endofunctor T
+which encode basic properties such as linearity of the derivative and symmetry of mixed partial derivatives.
+The canonical example of a tangent category is the category of smooth manifolds, where the endofunctor
+is the tangent bundle functor (Example 2.6). But there are many other interesting examples of tangent
+categories. In fact, almost any category which has some form of “differentiation” for its morphisms can be
+given the structure of a tangent category. Examples of tangent categories include:
+• Most generalizations of smooth manifolds form tangent categories.
+The category of “convenient”
+manifolds [19], the category of C∞ rings [20], and any model of synthetic differential geometry (SDG)
+[18], all give tangent categories.
+• Any Cartesian differential category [3], which formalizes differential calculus over Euclidean spaces,
+gives a tangent category. In particular, there are many examples of Cartesian differential categories
+from computer science, such as models of the differential lambda-calculus [12].
+• The category of commutative rings and the category of commutative algebras are tangent categories,
+with a particularly simple tangent structure induced by dual numbers. This example will be discussed
+in more detail below (Section 2.2).
+• “Tangent infinity” categories model ideas in Goodwillie functor calculus [1].
+The theory of tangent categories is now well-established with a rich literature. There are also many things
+one can do in an arbitrary tangent category. In particular, one can discuss:
+• Vector fields (Definition 2.10), and prove important ideas such as the Jacobi identity [6].
+• The analogue of vector bundles, known as differential bundles [8], which is one of the main structures
+of focus in this paper (Section 3).
+• Connections on differential bundles and corresponding results such as the Bianchi identities and the
+existence of geodesics [7].
+• Solutions to differential equations and dynamical systems [9].
+• Differential forms and de Rham cohomology [11].
+It is worth noting that translating these ideas from the category of smooth manifolds to an arbitrary tangent
+category is not a trivial process. The definition of a tangent category involves various natural transformations
+which appear in the category of smooth manifolds, but are not generally seen as central to differential
+geometry. In a tangent category, these natural transformations are the core part of the structure, and so
+to translate a desired notion to an arbitrary tangent category, one must translate the definition to make
+appropriate use of those natural transformations. The fact that one can do so with many of the central
+notions of differential geometry provides evidence that the abstract notion of a tangent category is indeed
+a good categorical generalization of differential geometry. A central question of tangent category theory
+2
+
+is to understand what these notions look like in the various examples of tangent categories. In categories
+which generalize the category of smooth manifolds (such as convenient manifolds, or synthetic differential
+geometry), these generally reconstruct existing definitions in these subjects. But in other areas, what these
+notions give is less obvious.
+One particular focus of this paper is examples of tangent categories in algebra and algebraic geometry,
+and investigating what tangent structure definitions look like in these particular examples. In particular,
+categories of (affine) schemes (potentially over some fixed ring or scheme). All such categories are also tangent
+categories, with the endofunctor given by the Spec of the symmetric algebra of the Kahler differentials of a
+scheme, which is precisely what Grothendieck himself called the “tangent bundle” of a scheme [15, Definition
+16.5.12.I]. While this example was mentioned in [5], as a corollary to a more general result, the tangent
+structure was not explored explicitly. One of the contributions of this paper is an explicit description of the
+natural transformations for this tangent structure (Section 2.3). This is a necessary component to further
+understand how the theory of tangent categories applies to algebraic geometry. Given this, then, the next
+important question is: what do the concepts which can be applied to any tangent category give you when
+applied to the algebraic geometry examples?
+Do they recreate existing notions?
+Do they give us new
+perspectives on existing ideas?
+The main focus of this paper is on differential bundles (Definition 3.1) in the examples of tangent cate-
+gories in algebra and algebraic geometry. Differential bundles are a central structure in tangent categories,
+as they generalize smooth vector bundles in the category of smooth manifolds (Example 3.3). However,
+intriguingly, they are defined quite differently than vector bundles. The definition of a differential bundle
+contains no mention of either vector spaces, a base field, or local triviality. Instead, their central structure is
+the existence of a vertical lift, which is a map from the total space to its tangent bundle, which satisfies a key
+universal property. That such a structure, when looked at in the category of smooth manifolds, gives exactly
+smooth vector bundles [22], is already interesting enough, as structures like the vector spaces in each fibre,
+and the local triviality, all come “for free” from the universality of the vertical lift. But what are differential
+bundles in the tangent categories of (affine) schemes? It is not immediately obvious what they should be.
+The main objective of this paper is to answer this question, and in doing also providing new and interesting
+results which hopefully opens up the possibility for many future investigations in this area. In summary, the
+main results of this paper are that:
+• Proposition 4.5 and Theorem 4.7: In the tangent category of commutative rings, differential bundles
+over a commutative ring R correspond to modules over R, and the category of differential bundles over
+R is equivalent to the category of modules over R.
+• Proposition 5.5 and Theorem 5.7: In the tangent category of affine schemes (or equivalently the opposite
+category of commutative rings), differential bundles over a commutative ring R correspond to modules
+over R, and the category of differential bundles over R is equivalent to the opposite category of modules
+over R.
+• Theorem 5.17: In the tangent category of schemes, differential bundles over a scheme A correspond to
+quasicoherent sheaves of modules over A, and the category of differential bundles over A is equivalent
+to the opposite of the category of quasicoherent sheaves of modules over A.
+These results are fascinating for several reasons. For one, they show how diverse differential bundles can
+be. In the canonical tangent category example of smooth manifolds, differential bundles are exactly smooth
+vector bundles, which includes the strict condition of local triviality. However, for these algebra or algebraic
+geometry examples of tangent categories, differential bundles still give categories of central importance
+(modules) but in which the objects have no sort of local triviality condition. Independently, these results
+are also interesting as they give a new characterization of these categories. In particular, differential bundles
+provide a novel characterization of the opposite of the category of (quasicoherent sheaves of) modules over
+a commutative. To the best of the authors’ knowledge, there is no known previous characterization of the
+opposite of the category of modules for an arbitrary commutative ring (though there are some results in
+3
+
+special cases, like characterizations of the opposite category of Abelian groups).
+These results are thus
+interesting in and of themselves.
+Even more promising than the results themselves is what future results and ideas they can lead to. As
+described above, in any tangent category one can define and prove results about connections on such bundles;
+again, when applied to the tangent category of smooth manifolds, this recreates the usual notion. But now
+via tangent categories, we get a notion of connection on modules - what do these look like? What examples
+of them are there? Do they recreate existing notions of connections in algebraic geometry? We hope to
+explore these questions in future work (Section 6), and continue to use these ideas to bridge the gap between
+differential geometry and algebraic geometry.
+Outline:
+In section 2, we review the definition of tangent categories and explore some of their basic
+examples and theory. We also explicitly describe the tangent structure of the category of (affine) schemes,
+which as noted above, has not previously been given.
+In section 3, we recall the theory of differential
+bundles in tangent categories, and review MacAdam’s characterization of differential bundles in the tangent
+category of smooth manifolds [22].
+In Section 4, we give our first major result: a characterization of
+differential bundles in the tangent category of commutative rings. Section 5 contains our most important
+results: characterizations of differential bundles in the tangent categories of affine schemes and schemes. As
+mentioned above, as far as we know, these results provide new characterizations of the opposites of categories
+of (quasicoherent sheaves of) modules. Lastly, in Section 6, we describe future work that we hope to pursue
+that builds on the ideas presented in this paper.
+Conventions:
+We assume the reader is familiar with the basic notions of category theory such as categories,
+opposite categories, functors, natural transformations, and (co)limits like (co)products, pullbacks, pushouts,
+terminal/initial objects, etc. In an arbitrary category, we denote identity maps as 1A : A −→ A, and we use
+the classical notation for composition, g ◦ f, as opposed to diagrammatic order which was used in other
+papers on tangent categories (such as in [5, 8] for example). For pullbacks and products (which recall are
+specific kinds of pullbacks), we use πj for the projections and ⟨−, −⟩ for the pairing operation which is
+induced by the universal property.
+2
+Tangent Categories
+In this section, we review the basics of tangent categories and provide full detailed descriptions of the main
+tangent categories of interest for this paper. Tangent categories were first defined by Rosick´y [25], then later
+generalized by Cockett and Cruttwell [5]. We begin by providing the full definition of a tangent category, both
+the Cockett and Cruttwell version without negatives (Definition 2.1), and the Rosick´y version with negatives
+(Definition 2.2). Afterwards, we provide a detailed description of the tangent categories of commutative
+rings (Section 2.2) and (affine) schemes (Section 2.3), the latter of which has not been previously done in
+full. We also discuss some basic, but important, concepts in these tangent categories, like tangent spaces
+(Definition 2.8) and vector fields (Definition 2.10).
+2.1
+Basics of Tangent Categories
+The following definition of a tangent category is the one provided in [8, Definition 2.1], which when compared
+to the original definition provided in [5, Definion 2.3] is the same except for the universality of the vertical
+lift which is presented as a pullback instead of an equalizer. That said, these two axiomatizations are indeed
+equivalent [8, Lemma 2.10].
+Definition 2.1 [5, Definion 2.3] A tangent structure on a category X is a sextuple T := (T, p, +, 0, ℓ, c)
+consisting of:
+(i) An endofunctor T : X −→ X, called the tangent bundle functor;
+4
+
+(ii) A natural transformation pA : T(A) −→ A, called the projection, such that for each n ∈ N, the pullback
+of n copies of pA exists, which we denote as Tn(A) with n projections πj : Tn(A) −→ T(A), for all
+1 ≤ j ≤ n, so pA ◦ πj = pA ◦ πi for all 1 ≤ i, j ≤ n, and for all m ∈ N, Tm preserves these pullbacks;
+(iii) A natural transformation1 +A : T2(A) −→ T(A), called the sum;
+(iv) A natural transformation 0A : A −→ T(A), called the zero;
+(v) A natural transformation ℓA : T(A) −→ T2(A), called the vertical lift;
+(vi) A natural transformation cA : T2(A) −→ T2(A), called the canonical flip;
+and such that:
+[T.1] (pA, +A, 0A) is an additive bundle over A [5, Definition 2.1], that is, the following diagrams commute:
+T2(A)
+πj
+�
++A
+� T(A)
+pA
+�
+A
+0A
+�
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+T(A)
+pA
+�
+T(A)
+pA
+� A
+A
+T3(A)
+⟨+A◦⟨π1,π2⟩,π3⟩ �
+⟨π1,+A◦⟨π2,π3⟩⟩
+�
+T2(A)
++A
+�
+T(A)
+⟨0A◦pA,1T(A)⟩
+�
+⟨1T(A),0A◦pA⟩
+�
+❙
+❙
+❙
+❙
+❙
+❙
+❙
+❙
+❙
+❙
+❙
+❙
+❙
+❙
+❙
+❙
+❙
+❙
+❙
+❙
+❙
+❙
+❙
+❙
+❙
+❙
+❙
+❙
+❙
+❙
+❙
+❙
+❙
+❙
+T2(A)
++A
+�
+T2(A)
++A
+� T(A)
+T2(A)
++A
+� T(A)
+T2(A)
++A
+�◗
+◗
+◗
+◗
+◗
+◗
+◗
+◗
+◗
+◗
+◗
+◗
+◗
+◗
+⟨π2,π1⟩
+� T2(A)
++A
+�
+T(A)
+(1)
+[T.2] The vertical lift ℓA preserves the additive bundle structure, that is, the following diagrams commute:
+T(A)
+ℓA
+�
+pA
+�
+T2(A)
+T(pA)
+�
+A
+0A
+� T(A)
+T2(A)
+⟨ℓA◦π1,ℓA◦π2⟩
+�
++A
+�
+TT2(A)
+T(+A)
+�
+A
+0A
+�
+0A
+�
+T(A)
+ℓA
+�
+T(A)
+ℓA
+� T2(A)
+T(A)
+T(0A)
+� T2(A)
+(2)
+1Note that by the universal property of the pullback, it follows that we can define functors Tn : X −→ X.
+5
+
+[T.3] The canonical flip cA preserves the additive bundle structure, that is, the following diagrams commute:
+T2(A)
+cA
+�
+T(pA)
+�
+T2(A)
+pT(A)
+�
+T(A)
+T2(A)
+TT2(A)
+⟨cA◦T(π1),cA◦T(π2)⟩
+�
+T(+A)
+�
+T2T(A)
++T(A)
+�
+T(A)
+T(0A)
+�
+T(A)
+0T(A)
+�
+T2(A)
+cA
+� T2(A)
+T2(A)
+cA
+� T2(A)
+(3)
+[T.4] The following diagrams commute:
+T2(A)
+cA
+�
+◗
+◗
+◗
+◗
+◗
+◗
+◗
+◗
+◗
+◗
+◗
+◗
+◗
+◗
+◗
+◗
+◗
+◗
+◗
+◗
+◗
+◗
+◗
+◗
+◗
+◗
+◗
+◗
+T2(A)
+cA
+�
+T3(A)
+cT(A)
+�
+T(cA)
+� T3(A)
+cT(A)
+� T3(A)
+T(cA)
+�
+T2(A)
+T3(A)
+T(cA)
+� T3(A)
+cT(A)
+� T3(A)
+(4)
+[T.5] The following diagrams commute:
+T(A)
+ℓA
+�
+ℓA
+�
+T2(A)
+ℓT(A)
+�
+T(A)
+ℓA
+�
+ℓA
+�■
+■
+■
+■
+■
+■
+■
+■
+■
+T2(A)
+cA
+�
+T2(A)
+ℓT(A) �
+cA
+�
+T3(A)
+T(cA) � T3(A)
+cT(A)
+�
+T2(A)
+T(ℓA)
+� T3(A)
+T2(A)
+T2(A)
+T(ℓA)
+� T3(A)
+(5)
+[T.6] Universality of the vertical lift ℓA, that is, the following square is a pullback:
+T2(A)
+pA◦πj
+�
+νA
+� T2(A)
+T(pA)
+�
+A
+0A
+� T(A)
+(6)
+where νA : T2(A) −→ T2(A) is defined as follows:
+νA := T2(A)
+⟨ℓ◦π1,0T(A)◦π2⟩ � TT2(A)
+T(+A)
+� T(A)
+(7)
+and such that the above pullback square is preserved by all Tn.
+A tangent category is a pair (X, T) consisting of a category X equipped with a tangent structure T on X.
+Tangent categories formalize the properties of the tangent bundle on smooth manifolds from classical
+differential geometry, as we will review in Examples 2.5 and 2.6 below. An object A should be interpreted
+as a base space, and T(A) as its abstract tangent bundle. The projection pA is the analogue of the natural
+projection from the tangent bundle to its base space, making T(A) an abstract bundle over A. The sum +A
+and the zero 0A make T(A) into a generalized version of a smooth additive bundle, and so each fiber is a
+6
+
+commutative monoid. To make this more precise, this notion is captured by the concept of an additive bundle
+[5, Section 2.1], which can be defined in any arbitrary category. Briefly, additive bundles are commutative
+monoid objects in slice categories. So in the case of a tangent category, pA is a commutative monoid in the
+slice category over A with binary operation +A and unit 0A. The pullbacks of n copies of pA is required to
+sum multiple times, while preservation by Tm implies that Tm(pA) is also an additive bundle with Tm(+A)
+and Tm(0A). The top two diagrams in [T.1] simply say that +A and 0A are maps in the slice category,
+while the remaining three diagrams are the axioms of a commutative monoid: associativity of the sum, that
+zero is a unit, and commutativity of the sum.
+To explain the vertical lift, recall that in differential geometry, the double tangent bundle (that is, the
+tangent bundle of the tangent bundle) admits a canonical sub-bundle called the vertical bundle which is
+isomorphic to the tangent bundle. Thus, the vertical lift ℓA is an analogue of the embedding of the tangent
+bundle into the double tangent bundle via the vertical bundle. The canonical flip cA is an analogue of the
+natural canonical flip, which is a smooth involution on the double tangent bundle. The diagrams in [T.2]
+and [T.3] say respectively that ℓA and cA are additive bundle morphisms [5, Definition 2.2], that is, monoid
+morphisms in the slice category over A. The diagrams in [T.4] express that the canonical flip cA is a sort of
+symmetry map: the left diagram says that cA is a self-inverse isomorphism, while the right diagram is the
+Yang-Baxter associativity identity. The diagrams in [T.5] are compatibility relations between the vertical lift
+and canonical flip. The universality of the vertical lift in [T.6] is essential for generalizing desired important
+properties of the tangent bundle from differential geometry, see [5, Section 2.5] for more details on this
+axiom. Lastly, for maps, T(f) is interpreted as the differential of f, and so the functoriality of T represents
+the chain rule. The naturality of p says that T(f) is a bundle map between the tangent bundles, and the
+naturality of + and 0 implies that T(f) preserves the additive structure, while the naturality of ℓ represents
+that the differential is linear, and the naturality of c represents the symmetry of the partial differentials.
+We now add negatives to the story and obtain Rosick´y’s original definition of a tangent category [25,
+Section 2], which is essentially the same as the above definition but with an added natural transformation
+which makes each fiber of the tangent bundle into an Abelian group. In [5, 22], such a setting was simply
+called a tangent category with negatives. Here, we introduce new terminology and call such a setting a
+Rosick´y tangent category.
+Definition 2.2 [5, Section 3.3] A tangent structure with negatives on a category X is a septuple
+T := (T, p, +, 0, ℓ, c, −) consisting of:
+(i) A tangent structure (T, p, +, 0, ℓ, c) on X
+(ii) A natural transformation −A : T(A) −→ T(A), called the negative;
+such that:
+[T.N] (pA, +A, 0A, −A) is an Abelian group bundle over A [25, Section 1], that is, the following diagrams
+commute:
+T(A)
+−A
+�
+pA
+�◗
+◗
+◗
+◗
+◗
+◗
+◗
+◗
+◗
+◗
+◗
+◗
+◗
+◗
+◗
+T(A)
+pA
+�
+T(A)
+pA
+�P
+P
+P
+P
+P
+P
+P
+P
+P
+P
+P
+P
+P
+P
+⟨1T(A),−A⟩
+�
+⟨−A,1T(A)⟩
+�
+T2(A)
++A
+�
+A
+A
+0A
+�P
+P
+P
+P
+P
+P
+P
+P
+P
+P
+P
+P
+P
+P
+T2(A)
++A
+� T(A)
+(8)
+A Rosick´y tangent category is a pair (X, T) consisting of a category X and tangent structure with negatives
+T on X.
+7
+
+In a Rosick´y tangent category, the negative nA makes each fiber an Abelian group. The left diagram of
+[T.N] says that the negative −A is a map in the slice category over A, while the right diagram is the extra
+axiom about inverses required for Abelian groups. It is also worth mentioning that in a Rosick´y tangent
+category, the universality of the vertical lift can be replaced with the following which expresses the vertical
+lift as an equalizer [5, Lemma 3.13]:
+[T.6’] The following is an equalizer diagram:
+T(A)
+ℓA
+� T2(A)
+pT(A)
+�
+T(pA)
+�
+pT(A)
+� T(A)
+pA
+� A
+0A
+� T(A)
+(9)
+and such that the above equalizer is preserved by all Tn.
+Furthermore, in a Rosick´y tangent category, the vertical lift ℓA and the canonical flip cA also preserve
+the group structure, that is, they are Abelian group bundle morphisms.
+Indeed, recall that in classical
+group theory that morphisms which preserve the group’s addition also preserve inverses. The same is true
+for Abelian group bundles in the sense that additive bundle morphisms between Abelian group bundles
+automatically also preserve inverses. Explicitly:
+Lemma 2.3 In a Rosick´y tangent category (X, T), the following diagrams commute:
+T(A)
+ℓA
+�
+−A
+�
+T2(A)
+T(−A)
+�
+T2(A)
+cA
+�
+T(−A)
+�
+T2(A)
+−T(A)
+�
+T(A)
+ℓA
+� T2(A)
+T2(A)
+cA
+� T2(A)
+(10)
+We now discuss Cartesian tangent categories, which are tangent categories that also have finite products
+which are compatible with the tangent structure. The extra coherences for a Cartesian tangent category
+ensure that the tangent bundle of a product is naturally isomorphic to the product of the tangent bundles
+and that the tangent bundle of the terminal object is the terminal object.
+Definition 2.4 [5, Definition 2.8] A Cartesian (Rosick´y) tangent category is a (Rosick´y) tangent
+category (X, T) such that X has finite products, with binary product × and terminal object ∗, and that the
+canonical natural transformation ⟨T(π1), T(π2)⟩ : T(A × B) −→ T(A) × T(B) is a natural isomorphism, and
+the unique map T(∗) −→ ∗ is an isomorphism, so T(A × B) ∼= T(A) × T(B) and T(∗) ∼= ∗.
+The main example of a (Cartesian) tangent category is the category of smooth manifolds, where the
+tangent structure is induced by the tangent bundle of a smooth manifold. This example provides a direct
+link between tangent categories and differential geometry. Here we review in full the tangent structure on
+the subcategory of Euclidean spaces, as it is simpler to describe in detail. For lists of other examples of
+tangent categories see [8, Example 2.2] and [14, Example 2].
+Example 2.5 The category of Euclidean spaces and smooth functions is a Cartesian Rosick´y tangent cate-
+gory where the tangent structure is induced by the total derivative of smooth functions. Let SMOOTH be the
+category whose objects are Euclidean spaces Rn and whose maps are smooth functions. SMOOTH has finite
+products where the binary product is given by the standard Cartesian product, Rm×Rn = Rm+n, and where
+the terminal object is the singleton, R0 = {0}. To define the tangent structure, recall that for a smooth
+8
+
+function F : Rm −→ Rn, which is actually an n-tuple F = ⟨f1, . . . , fn⟩ of smooth functions fi : Rm −→ R, that
+the total derivative of F is the smooth function D[F] : Rm × Rm −→ Rn defined as the sum of the partial
+derivatives of the fi:
+D[F](⃗x, ⃗y) =
+� m
+�
+j=1
+∂f1
+∂uj
+(⃗x)yj, . . . ,
+m
+�
+j=1
+∂fn
+∂uj
+(⃗x)yj
+�
+The total derivative D[F] can also be expressed in terms of the Jacobian of F. We define a Rosick´y tangent
+structure T on SMOOTH as follows:
+(i) The endofunctor T : SMOOTH −→ SMOOTH is defined on a Euclidean space as T(Rn) = Rn × Rn and
+on a smooth function F : Rm −→ Rn as the smooth function T(F) : Rm × Rm −→ Rn × Rn defined as:
+T(F)(⃗x, ⃗y) =
+�
+F(⃗x), D[F](⃗x, ⃗y)
+�
+(ii) The projection pRn : Rn × Rn −→ Rn is defined as the projection of the first component:
+pRn(⃗x, ⃗y) = ⃗x
+(iii) The pullback of m copies of pRn is given by taking the product of m + 1 copies of Rn:
+Tm(Rn) = Rn × . . . × Rn
+�
+��
+�
+m+1 times
+and where the projection πj : Tm(Rn) −→ Rn × Rn projects out the first and j-th components:
+πj(⃗x, ⃗y1, . . . , ⃗
+ym) = (⃗x, ⃗yj)
+(iv) The sum +Rn : Rn × Rn × Rn −→ Rn × Rn adds the second and third components:
++Rn(⃗x, ⃗y,⃗z) = (⃗x, ⃗y + ⃗z)
+(v) The zero 0Rn : Rn −→ Rn × Rn inserts the zero vector into the second component:
+0Rn(⃗x) = (⃗x,⃗0)
+(vi) The vertical lift ℓRn : Rn × Rn −→ Rn × Rn × Rn × Rn inserts zero vectors into the middle components:
+ℓRn(⃗x, ⃗y) = (⃗x,⃗0,⃗0, ⃗y)
+(vii) The canonical flip cRn : Rn × Rn × Rn × Rn −→ Rn × Rn × Rn × Rn flips the middle two components:
+cRn(⃗x, ⃗y,⃗z, ⃗w) = (⃗x,⃗z, ⃗y, ⃗w)
+(viii) The negative −Rn : Rn × Rn −→ Rn × Rn makes the second component negative:
+−Rn(⃗x, ⃗y) = (⃗x, −⃗y)
+So T = (T, p, s, z, l, c, n) is a tangent structure with negatives on SMOOTH.
+Lastly, we also have that
+Rn × Rn × Rm × Rm ∼= Rn × Rm × Rn × Rm and R0 × R0 ∼= R0. So (SMOOTH, T) is a Cartesian Rosick´y
+tangent category. In fact, SMOOTH is a Cartesian differential category [3], and every Cartesian differential
+category is a Cartesian tangent category by generalizing the above construction [5, Proposition 4.7].
+9
+
+Example 2.6 The category of smooth manifolds is a Cartesian Rosick´y tangent category where the tangent
+structure is given by the classical tangent bundle (here we follow [27, Defn. 5.9] and allow our manifolds
+to have different dimensions in different connected components). Let SMAN be the category whose objects
+are (finite-dimensional real) smooth manifolds M and whose maps are smooth functions between them. For
+a smooth manifold M, for each point x ∈ M let Tx(M) be the tangent space at x. Then recall that the
+tangent bundle of M is the smooth manifold T(M) which is the (disjoint) union of each tangent space:
+T(M) :=
+�
+x∈M
+Tx(M)
+This induces a functor T : SMAN −→ SMAN which is part of a tangent structure with negatives T on SMAN,
+which in local coordinates is defined in the same way as in Example 2.6. So (SMAN, T) is a Cartesian Rosick´y
+tangent category, for which (SMOOTH, T) is a sub-Cartesian Rosick´y tangent category.
+There are many ways to make new tangent categories from existing ones, but one of the most fundamental
+(assuming the existence of certain well-behaved limits) is by slicing.
+We will use this construction, in
+particular, to construct tangent categories of algebras from tangent categories of rings.
+Proposition 2.7 [5, Proposition 2.5] Suppose that (X, T) is a tangent category, and A is an object of X.
+Then the slice category X/A can be given the structure of a tangent category, where the tangent bundle of an
+object f : X −→ A, TA(f), is given by the pullback
+TA(f)
+�
+�
+T X
+T (f)
+�
+A
+0A
+� T A
+(assuming such pullbacks exist and are preserved by each T n).
+We end this section by reviewing two simple concepts from differential geometry that can be generalized
+to any (Cartesian) tangent category: vector fields and tangent spaces. In the examples above, vector fields
+and tangent spaces correspond precisely to their namesakes from classical differential geometry. Below, we
+will also discuss these tangent spaces and vector fields for the tangent categories of commutative rings and
+(affine) schemes.
+Recall that in a category with finite products, a point of an object A is a map from the terminal object
+to A. In a Cartesian tangent category, the tangent space at a point is given by the pullback (if it exists) of
+said point and tangent structure projection.
+Definition 2.8 [5, Definition 4.13] In a Cartesian tangent category (X, T), if A is an object of X and
+a : ∗ −→ A is a point of A, then the tangent space of A at a is an object Ta(A) equipped with a map
+πa : Ta(A) −→ T(A) such that the following diagram is a pullback:
+Ta(A)
+πa
+�
+�
+T(A)
+pA
+�
+∗
+a
+� A
+and is preserved by all Tn for all n ∈ N.
+Example 2.9 In SMOOTH, a point of Rn in the categorical sense corresponds precisely to elements of
+⃗x ∈ Rn. So in (SMOOTH, T), the tangent space of Rn at ⃗x ∈ Rn is T⃗x(Rn) = Rn and π⃗x : Rn −→ Rn × Rn
+is defined as the injection π⃗x(⃗y) = (⃗x, ⃗y). Similarly, in SMAN, a point of a smooth manifold M in the
+categorical sense is precisely a point x ∈ X. So in (SMAN, T), the tangent space of M at x ∈ M is the
+classical tangent space Tx(M) = M.
+10
+
+Tangent spaces are commutative monoid objects, where monoid structure is induced by the tangent
+bundle [5, Theorem 4.15], and in a Cartesian Rosick´y tangent category, tangent spaces are also Abelian
+group objects. The category of tangent spaces is a Cartesian differential category [5, Corollary 4.16]. Also
+observe that, trivially, for the terminal object ∗ the only point is the identity 1∗ : ∗ −→ ∗ and that T1∗(∗) = ∗.
+We now turn our attention to vector fields. In a tangent category, a vector field is simply a section of the
+tangent bundle’s projection.
+Definition 2.10 [5, Definition 3.1] In a tangent category (X, T), a vector field on an object A of X is a
+map v : A −→ T(A) which is a section of pA, that is, the following diagram commutes:
+A
+v
+�
+P
+P
+P
+P
+P
+P
+P
+P
+P
+P
+P
+P
+P
+P
+P
+P
+P
+P
+P
+P
+P
+P
+P
+P
+P
+P
+P
+P
+P
+P
+T(A)
+pA
+�
+A
+Example 2.11 In (SMOOTH, T), a vector field on Rn is given by a smooth function v : Rn −→ Rn ×Rn such
+that v(⃗x) = (⃗x, f(⃗x)) for some smooth functions f : Rn −→ Rn. Therefore, vector fields in (SMOOTH, T)
+correspond precisely to endomorphisms in SMOOTH. In (SMAN, T), vector fields in the tangent category
+sense correspond precisely to vector fields in the usual sense.
+In any tangent category, the zero 0A : A −→ T(A) is a vector field, and the map νA : T2(A) −→ T2(A)
+from [T.6] induces a vector field for the tangent bundle LA : T(A) −→ T2(A) which generalizes the canonical
+vector field on the tangent bundle, also called the Liouville vector field [5, Section 3.1]. One can also define
+the sum of vector fields using the sum + [5, Proposition 3.2], as well as a new category whose objects are
+vector fields and whose maps commute with vector fields in the obvious way [9, Definition 2.8], and said
+category of vector fields is also a tangent category [9, Proposition 2.10]. In a Rosick´y tangent category, it
+is possible to define the Lie Bracket of vector fields [5, Definition 3.14], which in particular also satisfies the
+Jacobi identity [6]. Vector fields can also be used to describe differential equations, dynamical systems, and
+their solutions in a tangent category [9].
+There are numerous other interesting properties and concepts that one can discuss in a tangent category
+such as the fact the tangent bundle functor T admits a canonical monad structure [5, Proposition 3.4] or
+the notion of a representable tangent category [5, Section 5], which provides a link to synthetic differential
+geometry (SDG). Furthermore, there are many other concepts from differential geometry that one can
+generalize to a tangent category, such as connections [7], and de Rham cohomology [11].
+2.2
+Commutative rings as a Tangent Category
+In this section, we provide a full description of the tangent category of commutative rings, whose tangent
+bundle is given by the ring of dual numbers. This was one of the main examples in Rosick´y’s original paper
+[25, Example 2].
+By a commutative ring, we mean a commutative, unital, and associative ring.
+For a
+commutative ring R and a, b ∈ R, we denote the addition by a + b, the zero by 0 ∈ R, the negation by −a,
+the multiplication by ab, and the unit by 1 ∈ R. Let CRING be the category whose objects are commutative
+rings and whose maps are ring morphisms.
+For a commutative ring R, its ring of dual numbers is the commutative ring R[ε] defined as follows:
+R[ε] = {a + bε| ∀a, b ∈ R, ε2 = 0}
+where a and bε will be used respectively as shorthand for a + 0ε and 0 + bε. Then R[ε] is a commutative
+ring with multiplication induced by ε2 = 0, that is, the addition, multiplication, and negative are defined
+respectively as follows:
+(a + bε) + (c + dε) = (a + c) + (b + d)ε
+(a + bε)(c + dε) = ac + (ad + bc)ε
+−(a + bε) = −a − bε
+and where the zero is 0 and the unit is 1. Using the ring of dual numbers, we define a tangent structure with
+negatives
+T
+= (
+T
+, p, +, 0, ℓ, c, −) on CRING.
+11
+
+(i) The endofunctor
+T
+: CRING −→ CRING maps a commutative ring R to its ring of dual numbers
+T
+(R) = R[ε] and a ring morphism f : R −→ S is sent to the ring morphism
+T
+(f) : R[ε] −→ S[ε] defined
+as follows:
+T
+(f)(a + bε) = f(a) + f(b)ε
+(ii) The projection pR : R[ε] −→ R sends ε to zero, and so is defined as projecting out the first component:
+pR(a + bε) = a
+To describe the pullbacks of the projection, first recall that CRING is a complete category, and therefore
+all pullbacks exist in CRING. In particular, if R and R′ are commutative rings, then for any ring morphism
+f : R′ −→ R, the general construction of a pullback of n copies of f in CRING is given by:
+R′
+n = {(x1, . . . , xn)| xj ∈ E s.t. f(xi) = f(xj) for all 1 ≤ i, j ≤ n}
+and whose ring structure is given coordinate-wise. However for the projection of the ring of dual numbers,
+one can instead describe these pullbacks in terms of multivariable dual numbers. So for a commutative ring
+R, define R[ε1, . . . , εn] as follows:
+R[ε1, . . . , εn] = {a + b1ε1 + . . . + bnεn| ∀a, bi ∈ R and εiεj = 0}
+Then R[ε1, . . . , εn] is a commutative ring whose structure is defined in the obvious way, so in particular the
+multiplication is induced by εiεj = 0. We leave it as an exercise for the reader to check for themselves that
+R[ε1, . . . , εn] is indeed isomorphic to the pullback of n copies of pR. So we can continue to describe the
+tangent structure as follows:
+(iii) The pullback of n copies of pR is given by
+T
+n(R) = R[ε1, . . . , εn] and where πj : R[ε1, . . . , εn] −→ R[ε]
+sends εj to ε and the other nilpotents to zero, that is, πj projects out the first component and j-th
+nilpotent component:
+πj(a + b1ε1 + . . . + bnεn) = a + bjε
+(iv) The sum +R : R[ε1, ε2] −→ R[ε] maps both ε1 and ε2 to ε, which results in adding the nilpotent parts
+together:
++R(a + bε1 + cε2) = a + (b + c)ε
+(v) The zero 0R : R −→ R[ε] is the injection of R into its ring of dual numbers:
+0R(a) = a
+(vi) The negative −R : R[ε] −→ R[ε] maps ε to −ε, which results in making the nilpotent part negative:
+−R(a + bε) = a − bε
+It may be worth briefly discussing what additive bundles and Abelian group bundles are in CRING.
+In
+fact, Abelian group bundles in CRING were characterized by Beck in [2, Example 8], where it was explained
+that Abelian group bundles over a commutative ring are equivalent to modules over said commutative ring.
+Furthermore, it turns out that in CRING, additive bundles are always Abelian group bundles, so we also get
+an equivalence between additive bundles and modules.
+To describe the vertical lift and the canonical flip, let us first describe
+T
+2(R), the ring of dual numbers
+of the ring of dual numbers in terms of two nilpotent elements ε and ε′:
+T
+2(R) = R[ε][ε′] = {a + bε + cε′ + dεε′| ∀a, b, c, d ∈ R and ε2 = ε′2 = 0}
+where the multiplication is induced by ε2 = ε′2 = 0. So we define:
+12
+
+(vii) The vertical lift ℓR : R[ε] −→ R[ε][ε′] maps ε to ε′, and so maps the nilpotent component to the outer
+nilpotent component:
+ℓR(a + bε) = a + bεε′
+(viii) The canonical flip cR : R[ε][ε′] −→ R[ε][ε′] swaps ε and ε′, and so interchanges the middle nilpotent
+components:
+cR(a + bε + cε′ + dεε′) = a + cε + bε′ + dεε′
+So
+T
+= (
+T
+, p, +, 0, ℓ, c, −) is a tangent structure with negatives on CRING. Also, CRING has finite products
+where the binary product is given by the Cartesian product of rings R×S, where recall that the ring structure
+is given pointwise, and where the terminal object is the zero ring 0. We also have that (R×S)[ε] ∼= R[ε]×S[ε]
+and 0[ε] ∼= 0. So we have that:
+Lemma 2.12 (CRING,
+T
+) is a Cartesian Rosick´y tangent category.
+Remark 2.13 This tangent category construction nicely generalizes to other natural settings:
+• Instead of commutative rings, we could have considered commutative semirings (also called rigs, for
+rings without negatives), which are of particular interest throughout all of computer science. So the
+category of commutative semirings will be a Cartesian tangent category via dual numbers, but not a
+Rosick´y tangent category since we dropped negatives.
+• For any commutative (semi)ring R, the category of commutative R-algebras will also be a Cartesian
+tangent category; this follows from Proposition 2.7.
+• The Eilenberg-Moore category of a codifferential category (or dually the opposite category of the
+coEilenberg-Moore category of a differential category) is a Cartesian tangent category [10, Theorem
+22], whose tangent structure is indeed a generalization of the above dual numbers tangent structure. In
+fact, these tangent categories of commutative (semi)rings/algebras are precisely the Eilenberg-Moore
+categories of the appropriate polynomial models of codifferential categories.
+We conclude this section by discussing tangent spaces and vector fields.
+We first explain how in
+(CRING,
+T
+), there are no non-trivial tangent spaces. Indeed, since the zero ring 0 is the terminal object, a
+point of a commutative ring R would be a ring morphism of type f : 0 −→ R. However, since ring morphisms
+are required to preserve the unit and zero, and these are the same in the zero ring, we would have that
+1 = f(1) = f(0) = 0, which implies 1 = 0 in R. But the zero ring is the only ring for which the zero and
+unit are equal. Therefore, it follows that the only ring morphism with domain 0 is the identity 10 : 0 −→ 0,
+and the tangent space at this point is 0.
+Lemma 2.14 In (CRING,
+T
+), the only commutative ring with a tangent space at a point is the zero ring 0
+at the identity 10 : 0 −→ 0, and
+T
+10(0) = 0.
+Next we discuss vector fields in (CRING,
+T
+) and explain how they correspond precisely to derivations.
+Recall that for a commutative ring R, a derivation on R is a linear map D : R −→ R which satisfies the product
+rule: D(ab) = aD(b) + D(a)b. A commutative differential ring is a pair (R, D) consisting of a commutative
+ring R and derivation D on R. On the other hand, for a commutative ring R, a vector field on R is a ring
+morphism v : R −→ R[ε] such that pR ◦v = 1R, which implies that v(a) = a+Dv(a)ε for some Dv : R −→ R. It
+is a well-known result that ring morphisms v : R −→ R[ε] such that pR ◦ v = 1R, i.e. vector fields, correspond
+precisely to derivations on R. Indeed, if v is a vector field, then since it preserves the multiplication, it follows
+that Dv satisfies the product rule. Thus Dv is a derivation and (R, Dv) is a commutative differential ring.
+Conversely, given a derivation D : R −→ R on R, define the vector field vD : R −→ R[ε] as vD(a) = a + D(a)ε.
+Since these constructions are inverses of each other, we obtain the desired equivalence.
+Lemma 2.15 For a commutative ring R, vector fields on R in (CRING,
+T
+) are in bijective correspondence
+with derivations on R.
+13
+
+Therefore, it follows that the category of vector fields of (CRING,
+T
+) is equivalent to the category of
+commutative differential rings. Thus by [9, Proposition 2.10], the category of commutative differential rings
+is also a Cartesian Rosick´y tangent category, whose tangent structure is induced by dual numbers as above.
+Lastly, the tangent category Lie bracket corresponds precisely to the standard Lie bracket of derivations,
+[D1, D2] = D1 ◦ D2 − D2 ◦ D1.
+2.3
+Affine schemes as a Tangent Category
+In this section, we discuss the tangent categories of (affine) schemes, where the tangent structure is induced
+by K¨ahler differentials. In this paper, by the category of affine schemes we mean the opposite category of
+commutative rings CRINGop. As such, we will be working directly with CRINGop, so we will write in terms
+of commutative rings R instead of affine schemes Spec(R). So in this section, we provide a full description of
+the tangent structure on CRINGop. While CRINGop has been mentioned as an example of a tangent category
+in other papers [5, 14], a full explicit description of its tangent structure has not previously been given in
+the literature. We provide such a description here as it will both be useful for the story of this paper, and
+for future work on applications of tangent category theory in algebraic geometry.
+To give a tangent structure with negatives on CRINGop, we must give a “co-tangent structure with nega-
+tives” on CRING. Explicitly, this means giving a functor T : CRING −→ CRING and natural transformations,
+and so in particular ring morphisms, of type: pR : R −→ T(R), +R : T(R) −→ T2(R), 0R : T(R) −→ R,
+ℓR : T2(R) −→ T(R), cR : T2(R) −→ T2(R), and −R : T(R) −→ T(R).
+For a commutative ring R, its tangent bundle T(R) is the free symmetric R-algebra over its modules of
+K¨ahler differentials Ω(R):
+T(R) := SymR
+�
+Ω(R)
+�
+=
+∞
+�
+n=0
+Ω(R)⊗s
+R
+n = R ⊕ Ω(R) ⊕
+�
+Ω(R) ⊗s
+R Ω(R)
+�
+⊕ . . .
+where ⊗s
+R is the symmetrized tensor product over R. In [15, Definition 16.5.12.I], Grothendieck calls T(R)
+the “fibr´e tangente” (French for tangent bundle) of R, while in [17, Section 2.6], Jubin calls T(R) the tangent
+algebra of R. For the story of this paper, it will be useful to have a more explicit description of T(R). So
+equivalently, T(R) is the free R-algebra generated by the set {d(a)| a ∈ R} modulo the equations:
+d(1) = 0
+d(a + b) = d(a) + d(b)
+d(ab) = ad(b) + bd(a)
+which are the same equations that are modded out to construct the module of K¨ahler differentials of R. Thus,
+an arbitrary element of T(R) is a finite sum of monomials of the form ad(b1) . . . d(bn). So the ring structure of
+T(R) is essentially the same as polynomials. Furthermore, T(R) also has a universal property similar to that
+of the module of K¨ahler differentials, but instead for algebras. For a commutative R-algebra A, a derivation
+evaluated in A is a linear map D : R −→ A which satisfies the product rule D(ab) = a · D(b) + b · D(a), where
+· is the R-module action on A. Now T(R) is a commutative R-algebra A via the R-module action given by
+multiplication, a · w = aw for a ∈ R and w ∈ T(R). Then the map d : R −→ T(R), which maps a to d(a), is
+a derivation and is universal in the sense that for any commutative R-algebra A equipped with a derivation
+D : R −→ A, there exists a unique R-algebra morphism D♭ : T(R) −→ A such that D♭(d(a)) = D(a).
+Example 2.16 In may be useful to work out some basic examples of tangent bundles:
+(i) For the ring of integers Z, its tangent bundle is itself: T(Z) = Z
+(ii) For the polynomial ring in n-variables Z[x1, . . . , xn], its tangent bundle is the 2n-variable polynomial
+ring: T(Z[x1, . . . , xn]) = Z[x1, . . . , xn, d(x1), . . . , d(xn)], with no added assumptions on the variables
+d(xi);
+(iii) For coordinate rings of varieties, that is, the polynomial rings quotiented by some finitely generated ideal
+Z[x1, . . . , xn]/⟨p(⃗x), . . . , q(⃗x)⟩, its tangent bundle is the polynomial ring’s tangent bundle quotiented
+14
+
+by the ideal generated by the same polynomials and their total derivatives:
+T
+�
+Z[x1, . . . , xn]/⟨p(⃗x), . . . , q(⃗x)⟩
+�
+=Z[x1, . . . , xn, d(x1), . . . , d(xn)]/⟨p(⃗x), . . . , q(⃗x), d(p)(⃗x), . . . , d(q)(⃗x)⟩
+For example, for Z[x, y]/⟨x2 − xy2⟩, its the tangent bundle is:
+T
+�
+Z[x, y]/⟨x2 − xy2⟩
+�
+= Z[x, y, d(x), d(y)]/⟨x2 − xy2, 2xd(x) − y2d(x) − 2xyd(y)⟩
+To define the necessary ring morphisms for the tangent structure, note that T(R) is generated by a and
+d(a), for all a ∈ R. Therefore, to define ring morphisms with domain T(R), it suffices to define them on
+generators a and d(a). Using this to our advantage, we can define a tangent structure on CRINGop.
+(i) The endofunctor T : CRING −→ CRING maps a commutative ring R to its tangent bundle T(R) as
+defined above, and a ring morphism f : R −→ S is sent to the ring morphism T(f) : T(R) −→ T(S)
+defined as on generators as follows:
+T(f)(a) = f(a)
+T(f)(d(a)) = d(f(a))
+(ii) The projection pR : R −→ T(R) is defined as the injection of R into T(R):
+pR(a) = a
+We also need the pullback of n copies of pR in CRINGop, which means that we need the pushout of n
+copies of pR in CRING. Recall that CRING is cocomplete, and therefore admits all pushouts. To describe
+the desired pushout, note that for commutative rings R and R′, any ring morphism f : R −→ R′ induces an
+R-algebra structure on R′ via the R-module action a · x = f(a)x for all a ∈ R and x ∈ R′. Therefore, the
+pushout of n-copies of f : R −→ R′ is given by taking the tensor product over R of n copies of R′ viewed as
+an R-moudle: R′
+n := R′ ⊗R . . . ⊗R R′
+�
+��
+�
+n times
+, where ⊗R is the tensor product over R of R-modules. The induced
+R-algebra structure on T(R) via pR is precisely given by multiplication, as described above.
+(iii) The pushouts of n copies of pR is given by Tn(R) := T(R) ⊗R . . . ⊗R T(R)
+�
+��
+�
+n times
+and where the pushout
+injections πj : T(R) −→ Tn(R) injects T(R) into the j-th component:
+πj(w) = 1 ⊗R . . . ⊗R 1 ⊗R w ⊗R 1 ⊗R . . . ⊗R 1
+To describe the sum, zero, and negative, let us first explain what additive bundles and Abelian group
+bundles are in CRINGop. An additive bundle over R in CRINGop corresponds precisely to a commutative R-
+bialgebra over the tensor product ⊗R. The sum and zero of the additive bundle are the comultiplicaiton and
+counit respectively of the R-coalgebra structure. The fact that they are ring morphisms and they commute
+with the additive bundle’s projection will further imply that we obtain a commutative R-bialgebra. An
+Abelian group bundle over R in CRINGop corresponds precisely to a commutative R-Hopf algebra over the
+tensor product ⊗R. The negative of the Abelian group bundle gives the antipode for the R-Hopf algebra
+structure. So to give the sum, zero, and negative for our tangent structure, we must give a R-Hopf algebra
+structure on the tangent bundle T(R). Luckily, free symmetric R-algebras have a canonical commutative
+R-Hopf algebra.
+(iv) The sum +R : T(R) −→ T(R) ⊗R T(R) is given by the comultiplication of the canonical R-coalgebra
+structure of free symmetric R-algebras, that is, defined on generators as follows:
++R(a) = a ⊗R 1 = 1 ⊗R a
++R(d(a)) = d(a) ⊗R 1 + 1 ⊗R d(a)
+15
+
+(v) The zero 0R : T(R) −→ R is the counit of the canonical R-coalgebra structure of free symmetric
+R-algebras, that is, defined on generators as follows:
+0R(a) = a
+0R(d(a)) = 0
+(vi) The negative −R : T(R) −→ T(R) is the antipode of the canonical R-Hopf algebra structure of free
+symmetric R-algebras, that is, defined on generators as follows:
+−R(a) = a
+−R(d(a)) = −d(a)
+To describe the vertical lift and the canonical flip, let us first describe T2(R) as the free commutative
+R-algebra over the set {d(a)| a ∈ R} ∪ {d′(a)| a ∈ R} ∪ {d′d(a)| a ∈ R}, modulo the relations:
+d(1) = 0
+d(a + b) = d(a) + d(b)
+d(ab) = ad(b) + bd(a)
+d′(1) = 0
+d′(a + b) = d′(a) + d′(b)
+d′(ab) = ad′(b) + bd′(a)
+d′d(1) = 0
+d′d(a + b) = d′d(a) + d′d(b)
+d′d(ab) = d(b)d′(a) + ad′d(b) + d(a)d′(b) + bd′d(a)
+These relations say that d and d′ are derivations, and that d′d is the composite of derivations. Therefore, to
+define a ring morphism with domain T2(R), it suffices to define it on the four types of generators a, d(a),
+d′(a), and d′d(a) for a ∈ R.
+(vii) The vertical lift ℓR : T2(R) −→ T(R) is defined on generators as follows:
+ℓR(a) = a
+ℓR(d(a)) = 0
+ℓR(d′(a)) = 0
+ℓR(d′d(a)) = d(a)
+(viii) The canonical flip cR : T2(R) −→ T2(R) is defined on generators as follows:
+cR(a) = a
+cR(d(a)) = d′(a)
+cR(d′(a)) = d(a)
+cR(d′d(a)) = d′d(a)
+So T = (T, p, +, 0, ℓ, c, −) is a tangent structure with negatives on CRINGop. Also, CRING has finite coprod-
+ucts where the binary coproduct is given by the tensor product of rings R ⊗ S and where the initial object is
+the ring of integers Z. Thus CRINGop has finite products. Since one has that Ω(R⊗S) ∼= R⊗Ω(S)⊕S⊗Ω(R)
+and Ω(Z) ∼= 0, it follows that that T(R ⊗ S) ∼= T(R) ⊗ T(S) and T(Z) ∼= Z. So we have that:
+Lemma 2.17 (CRINGop, T) is a Cartesian Rosick´y tangent category.
+Remark 2.18 It is worth mentioning that the tangent structures for commutative rings and the tangent
+structure for affine schemes are related to one another via the adjoint tangent structure theorem. Per [5,
+Proposition 5.17], if the tangent bundle of a tangent category has a left adjoint, then this induces a tangent
+structure on the opposite category where the left adjoint is the tangent bundle. This is precisely what is
+happening between the tangent categories (CRING,
+T
+) and (CRINGop, T). Indeed, T : CRING −→ CRING is a
+left adjoint to
+T
+: CRING −→ CRING, so we have a natural bijective correspondence between ring morphisms
+of type R −→ R′[ε] and T(R) −→ R′.
+Explicitly, given a ring morphism f : R −→ R′[ε], which is of the
+form f(a) = f1(a) + f2(a)ε, define the ring morphism f ♯ : T(R) −→ R′ on generators as f ♯(a) = f1(a)
+and f ♯(d(a)) = f2(a), and conversely, given a ring morphism g : T(R) −→ R′, define the ring morphism
+g♭ : R −→ R′[ε] as: g♭(a) = g(a) + g(d(a))ε.
+Furthermore, (CRINGop, T) is not only a Cartesian Rosick´y
+tangent category but also a representable tangent category [5, Section 5.2]. Briefly, a representable tangent
+category is a Cartesian category whose tangent bundle functor T is a representable functor T ∼= (−)D for
+some object D, that is, T is a right adjoint for the functor ×D. The object D is called the infinitesimal object
+[5, Definition 5.6], and note that the opposite category of a representable category is a tangent category with
+tangent bundle functor
+× D (where × becomes a coproduct in the opposite category). (CRINGop, T) is a
+representable tangent category where the infinitesimal object is the ring dual of numbers for the integers,
+Z[ε]. So we have that T(R) ∼= RZ[ε] in CRINGop, and
+T
+(R) ∼= R ⊗ Z[ε] in CRING.
+16
+
+Using Proposition 2.7, we then get that for each commutative ring R, the slice category CRINGop/R is
+also a tangent category. But as is well-known, this slice category is equal to the (opposite of) the category
+of commutative R-algebras. Thus we have:
+Corollary 2.19 For any commutative ring R, the opposite of the category of algebras over R, (CALGR)op
+is a Cartesian Rosick´y tangent category, with tangent functor given as in Proposition 2.7.
+In particular, this tangent structure on objects is given by (the symmetric algebra of) the “relative” Kahler
+differentials: this is the same construction as seen earlier in this section, except with d(r) = 0 for all r ∈ R.
+Remark 2.20 There are also other ways to generalize the tangent category structure of CRINGop:
+• The opposite category of commutative semirings and the opposite category of commutative algebras
+over a commutative (semi)ring will be representable tangent categories via K¨ahler differentials in a
+similar fashion.
+• The coEilenberg-Moore category of a differential category (or dually the opposite category of the
+Eilenberg-Moore category of a codifferential category) is a (representable) tangent category [10, The-
+orem 26], and these tangent categories of opposite categories of commutative (semi)rings/algebras
+are precisely the coEilenberg-Moore categories of the appropriate polynomial models of differential
+categories.
+The category of schemes SCH is also a Cartesian Rosick´y tangent category in a similar fashion to the
+category of affine schemes. Indeed, recall that a scheme is by definition the gluing of affine schemes. So the
+tangent bundle of a scheme is defined as the gluing of the tangent bundles of each affine piece of the said
+scheme. Full details can be found in [14, Example 2.(iii)].
+Proposition 2.21 (SCH, T) is a Cartesian Rosick´y tangent category.
+As with affine schemes, we can apply Proposition 2.7 to tangent structure on each category of relative
+schemes:
+Corollary 2.22 For each scheme A, the slice category SCH/A has the structure of a Cartesian Rosick´y
+tangent category.
+We now discuss tangent spaces in (CRINGop, T). The terminal object in CRINGop is the initial object
+in CRING, which is the integers Z. So for a commutative ring R, a point of R in CRINGop corresponds to
+a ring morphism r : R −→ Z, which are better known as augmentations. Thus a tangent space of R at a
+point r in (CRINGop, T) corresponds to the pushout of r and pR in CRING. This essentially amounts to
+applying r on the R parts of the tangent bundle T(R). So let im(r) = {r(a)| ∀a ∈ R} be the image of r,
+which is a sub-ring of Z. Then the tangent space Tr(R) can explicitly be described as the free commutative
+im(r)-algebra generated by the set {d(a)| a ∈ R} modulo the equations:
+d(1) = 0
+d(a + b) = d(a) + d(b)
+d(ab) = r(a)d(b) + r(b)d(a)
+So an arbitrary element of Tr(R) is a finite sum of monomials of the form r(a)d(b1) . . . d(bn).
+Example 2.23 Here are some examples of tangent spaces:
+(i) The only point for Z is the identity, and T1Z(Z) = Z;
+(ii) For the polynomial ring in n-variables Z[x1, . . . , xn], points correspond precisely to evaluating polyno-
+mials at a point ⃗a ∈ Zn. However, for any point, the tangent space at that point is the polynomial ring
+in n-variables, T⃗a(Z[x1, . . . , xn]) = Z[d(x1), . . . , d(xn)];
+17
+
+(iii) For a polynomial ring quotiented by a finitely generated ideal Z[x1, . . . , xn]/⟨p(⃗x), . . . , q(⃗x)⟩, points
+correspond to points ⃗a ∈ Zn which are solutions to p(⃗a) = 0, ..., q(⃗a) = 0. The resulting tangent
+bundle is the polynomial ring in n-variables quotiented by the ideal generated by the evaluation of
+the polynomials d(p)(⃗x), . . . , d(q)(⃗x) in the xi variables at ⃗a. For example, for Z[x, y]/⟨xy⟩, its tangent
+bundle is
+Z[x, y, dx, dy]/⟨xdy + ydx⟩
+and thus its tangent space at the point (1, 1) is
+Z[dx, dy]/⟨dy + dx⟩
+which is isomorphic to the polynomial ring in one variable. However, at the point (0, 0), evaluating the
+relation xdy + ydx gives 0, and so in this case the tangent space is simply
+Z[dx, dy]
+the polynomial ring in two variables.
+This example is important as it shows that in this tangent
+category, the tangent spaces at different points can have different dimensions, even if the original space
+is connected. This is not true in the tangent category of smooth manifolds.
+Next, we discuss vector fields in (CRINGop, T) and explain how, like in the commutative ring case, they
+correspond precisely to derivations. This is expected since for a tangent category whose tangent bundle
+admits a left adjoint, vector fields for the left adjoint correspond precisely to vector fields for the right
+adjoint. So for a commutative ring R, a vector field on R in (CRINGop, T) is a ring morphism v : T(R) −→ R
+such that v ◦ pR = 1R, which implies that v(a) = a. Then define Dv : R −→ R as Dv(a) = v(d(a)). It
+follows that Dv is a derivation and (R, Dv) is a commutative differential ring. Conversely, given a derivation
+D : R −→ R on R, define the vector field vD : T(R) −→ R as the ring morphism defined on generators as
+vD(a) = a and vD(d(a)) = D(a). Since these constructions are inverses of each other, we obtain the desired
+equivalence.
+Lemma 2.24 For a commutative ring R, vector fields on R in (CRINGop, T) are in bijective correspondence
+with derivations on R.
+Therefore, it follows that the category of vector fields of (CRINGop, T) is equivalent to the opposite
+category of commutative differential rings. Thus by [9, Proposition 2.10], the opposite category of commu-
+tative differential rings is a Cartesian Rosick´y tangent category whose tangent structure is given by the free
+symmetric algebra over the module of K¨ahler differentials as above.
+3
+Differential Bundles
+In this section, we review differential bundles, as introduced by Cockett and Cruttwell in [8]. Differential
+bundles generalize the notion of smooth vector bundles to an arbitrary tangent category. We provide the full
+definition (Definition 3.1), review how smooth vector bundles do indeed correspond to differential bundles
+(Example 3.3, as shown by MacAdam in [22]), and also consider differential object (Definition 3.5), which
+are differential bundles over the terminal object. We then discuss morphisms between differential bundles
+and categories of differential bundles (Section 3.3). We will also review MacAdam’s notion of pre-differential
+bundles, as introduced in [22], which then allows for an equivalent alternative characterization of differential
+bundles that requires fewer structure data (Section 3.2). MacAdam’s characterization of differential bundles
+as pre-differential bundles is very important for the story of this paper, as we will use this approach to
+characterize differential bundles for commutative rings and (affine) schemes.
+18
+
+3.1
+Differential Bundles and Differential Objects
+One way of understanding the definition of a differential bundle over an object A in a tangent category is
+that it is a generalization of the structure involving the projection, sum, zero, and vertical lift on the tangent
+bundle T(A) in the definition of a tangent category (Definition 2.1).
+Definition 3.1 [8, Definion 2.3] In a tangent category (X, T), a differential bundle is a quadruple
+E = (q : E −→ A, σ : E2 −→ E, z : A −→ E, λ : E −→ T(E)) consisting of:
+(i) Objects A and E of X;
+(ii) A map q : E −→ A of X, called the projection, such that for each n ∈ N, the pullback of n copies of q
+exists, which we denote as En with n projection maps πj : En −→ E, for all 1 ≤ j ≤ n, so q ◦ πj = q ◦ πi
+for all 1 ≤ i, j ≤ n, and for all m ∈ N, Tm preserves these pullbacks;
+(iii) A map σ : E2 −→ E of X, called the sum;
+(iv) A map z : A −→ E of X, called the zero;
+(v) A map λ : E −→ T(E) of X, called the lift;
+and such that:
+[DB.1] (q, σ, z) is an additive bundle over A [5, Definition 2.1], that is, the following diagrams commute:
+E2
+πj
+�
+σ
+� E
+q
+�
+A
+z
+�
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+E
+q
+�
+E
+q
+� A
+A
+E3
+⟨σ◦⟨π1,π2⟩,π3⟩�
+⟨π1,σ◦⟨π2,π3⟩⟩
+�
+E2
+σ
+�
+E
+⟨z◦q,1E⟩
+�
+⟨1E,z◦q⟩
+�
+◆
+◆
+◆
+◆
+◆
+◆
+◆
+◆
+◆
+◆
+◆
+◆
+◆
+◆
+◆
+◆
+◆
+◆
+◆
+◆
+◆
+◆
+◆
+◆
+◆
+◆
+◆
+◆
+E2
+σ
+�
+E2
+σ
+�◆
+◆
+◆
+◆
+◆
+◆
+◆
+◆
+◆
+◆
+◆
+◆
+◆
+⟨π2,π1⟩
+� E2
+σ
+�
+E2
+σ
+� E
+E2
+σ
+� E
+E
+(11)
+[DB.2] The lift λ preserves the additive structure, that is, the following diagrams commute:
+E
+λ
+�
+q
+�
+T(E)
+T(q)
+�
+A
+0A
+� T(A)
+E2
+⟨λ◦π1,λ◦π2⟩
+�
+σ
+�
+T(E2)
+T(σ)
+�
+A
+0A
+�
+0A
+�
+T(A)
+T(z)
+�
+E
+λ
+� T(E)
+T(A)
+λ
+� T(E)
+(12)
+19
+
+[DB.3] The lift λ preserves the other possible additive structure, that is, the following diagrams commute:
+E
+λ
+�
+q
+�
+T(E)
+pE
+�
+A
+z
+� E
+E2
+⟨λ◦π1,λ◦π2⟩
+�
+σ
+�
+T2(E)
++E
+�
+A
+z
+�
+z
+�
+E
+0E
+�
+E
+λ
+� T(E)
+E
+λ
+� T(E)
+(13)
+[DB.4] The following diagram commutes:
+E
+λ
+�
+λ
+�
+T(E)
+T(λ)
+�
+T(E)
+ℓE
+� T2(E)
+(14)
+[DB.5] The following square is a pullback:
+E2
+q◦πj
+�
+µ
+� T(E)
+T(q)
+�
+A
+0A
+� T(A)
+(15)
+where µ : E2 −→ T(E) is defined as follows:
+µ := E2
+⟨λ◦π1,0E◦π2⟩ � T(E2)
+T(σ)
+� T(E)
+(16)
+and such that the above pullback square is preserved by all Tn.
+If E = (q : E −→ A, σ : E2 −→ E, z : A −→ E, λ : E −→ T(E)) is a differential bundle in (X, T), we also say
+that E is a differential bundle over A. When there is no confusion, differential bundles will be written as
+E = (q : E −→ A, σ, z, λ), and when the objects are specified simply as E = (q, σ, z, λ).
+Differential bundles generalize smooth vector bundles over smooth manifolds in the context of a tangent
+category, as we will review in Example 3.3 below. If E = (q : E −→ A, σ, z, λ) is a differential bundle, the
+object A is interpreted as a base space and the object E as the total space. The projection q is the analogue
+of the bundle projection from the total space to the base space, making E an “abstract bundle over A”.
+The sum σ and the zero z make each fiber into a commutative monoid, more precisely, make the projection
+q into additive bundle [5, Section 2.1], which recall is a commutative monoid in the slice category over A,
+which is what the diagrams of [DB.1] state.
+The lift and its universal property [DB.5] is related to local triviality for smooth vector bundles. Indeed,
+given a smooth vector bundle, each fibre Ea (for a ∈ A) is a vector space, and hence the tangent space at
+any point of said fibre is isomorphic to the fibre itself. As a result, it follows that the tangent bundle of
+the total space E, T E, admits a sub-bundle which is isomorphic to E itself. The lift λ (sometimes called
+the small vertical lift [24, Section 1]) is an analogue of the resulting embedding of the total space into its
+20
+
+tangent bundle. The fibres of the tangent bundle of the total space admit two monoid structures: one being
+the canonical one of a tangent bundle, and the other induced by the monoid structure of the fibres of the
+smooth vector bundle. Then [DB.2] and [DB.3] say the lift λ preserves both of these monoid structures, or
+more precisely, that λ is an additive bundle morphism [5, Definition 2.2], which recall is a monoid morphism
+in the slice category. Lastly, [DB.4] is the compatibility between the lift of a smooth vector bundle and the
+vertical lift of the tangent bundle.
+In any tangent category, for ever object A, its tangent bundle T(A) is a differential bundle over A, that
+is, (pA : T(A) −→ A, +A, 0A, ℓA) is a differential bundle [8, Example 2.4]. Also, if (q : E −→ A, σ, z, λ) is a
+differential bundle, then the tangent bundle of E is a differential bundle over the tangent bundle of A, that
+is,
+�
+T(q) : T(E) −→ T(A), T(σ), T(z), cE ◦ T(λ)
+�
+is a differential bundle [8, Lemma 2.5]. For more properties
+of differential bundles, see [8, Section 2.4].
+We now define differential bundles with negatives, which are differential bundles with an added structure
+map which makes each fiber into an Abelian group.
+Definition 3.2 [22, Lemma 5] In a tangent category (X, T), a differential bundle with negatives is a
+quintuple E = (q : E −→ A, σ : E2 −→ E, z : A −→ E, λ : E −→ T(E), ι : E −→ E) consisting of:
+(i) A differential bundle (q : E −→ A, σ, z, λ) in (X, T);
+(ii) A map ι : E −→ E of X, called the negative;
+such that:
+[D.N] (q, σ, z, ι) is an Abelian group bundle over A [25, Section 1], that is, the following diagrams commute:
+E
+ι
+�
+q
+�❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+E
+q
+�
+E
+q
+�❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+⟨1E,ι⟩
+�
+⟨ι,1E⟩
+�
+E2
+σ
+�
+A
+A
+z
+�❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+E2
+σ
+� E
+(17)
+If E = (q : E −→ A, σ : E2 −→ E, z : A −→ E, λ : E −→ T(E), ι : E −→ E) is a differential bundle with
+negatives in (X, T), we also say that E is a differential bundle over A.
+Note that a differential bundle can have negatives in any arbitrary tangent category and that the negative
+is necessarily unique. As was shown in [22], we will review below that in a Cartesian Rosick´y tangent category,
+every differential bundle comes equipped with a (necessarily unique) negative (Proposition 3.9). Therefore in
+a Cartesian Rosick´y tangent category, differential bundles are the same as differential bundles with negatives.
+We now review how smooth vector bundles correspond precisely to differential bundles (with negatives)
+in the tangent category of smooth manifolds, as was shown by MacAdam in [22, Theorem 1]. The result is
+somewhat surprising, as the definition of differential bundles contains no mention of local triviality.
+Example 3.3 For a smooth vector bundle q : E −→ M, as in the definition of manifolds, we allow the vector
+bundle to have different dimensions in different connected components. Given such a smooth vector bundle,
+in local co-ordinates we can represent an element of E as a pair (m, v) and an element of T E as a quadruple
+(m, v, w, a), and we can define a lift λ : E −→ T E by λ(m, v) = (m, 0, 0, v). Proposition 4.1.2 of [22] shows
+that this indeed gives a differential bundle in the category of smooth manifolds. To go the other direction,
+MacAdam proves a general result: in a Rosick´y tangent category, every differential bundle is a retract of a
+pullback of a tangent bundle [22, Corollary 3.1.4] Then every differential bundle is a smooth vector bundle,
+since the tangent bundle is a smooth vector bundle, and smooth vector bundles are closed under pullbacks
+and retracts.
+21
+
+The following result about differential bundles in slice tangent categories is easy to check:
+Proposition 3.4 If (X, T) is a tangent category with an object A which satisfies the requirements of Propo-
+sition 2.7, then in the slice tangent category X/A, a differential bundle over f : X −→ A is the same as a
+differential bundle over X in (X, T).
+We conclude this section by briefly discussing differential objects, which are the differential bundles over
+the terminal object. Differential objects were first defined in [5, Definition 4.8], before the introduction
+of differential bundles. Differential objects are quite important since they provide the link from tangent
+categories to Cartesian differential categories [3]. Indeed, the subcategory of differential objects (and all
+maps between them) is a Cartesian differential category [5, Theorem 4.11]. Conversely, every Cartesian
+differential category is a tangent category in which every object is a differential object [8, Lemma 3.13].
+From this, it follows that we obtain an adjunction between the category of Cartesian tangent categories and
+the category of Cartesian differential categories [5, Theorem 4.12]. Later, it was shown in [8, Proposition
+3.4] that differential objects were precisely the same thing as differential bundles over the terminal object.
+Since the focus of this paper is on differential bundles, we take this approach to defining differential objects.
+Definition 3.5 [8, Proposition 3.4] In a Cartesian tangent category (X, T), a differential object is a
+differential bundle over the terminal object ∗.
+Alternatively, a differential object can also be described as an object A equipped with maps ˆp : T(A) −→ A,
++ : A×A −→ A, and 0 : ∗ −→ A such that (A, +, 0) is a commutative monoid, T(A) ∼= A×A via pA and ˆp, and
+the diagrams from [5, Definition 4.8] commute. In a Cartesian Rosick´y tangent category, every differential
+object is automatically an Abelian group.
+Example 3.6 In (SMAN, T), the differential objects are precisely the Euclidean spaces since in particular
+T(Rn) = Rn × Rn. Therefore (SMOOTH, T) is equivalent to the resulting Cartesian differential category of
+differential objects of (SMAN, T).
+3.2
+Differential Bundles as Pre-Differential Bundles
+In this section, we review MacAdam’s pre-differential bundles as introduced in [21]. These allow for an
+alternative characterization of differential bundles, which in particular requires less data and axioms. Indeed,
+MacAdam cleverly observed that in the definition of a differential bundle, the sum (and negative), and any
+axioms involving it, can be replaced by a pullback square, called Rosick´y’s universality diagram. From this
+special pullback, the sum (and negative) for the differential bundle can be constructed from the sum (and
+negative) of the tangent bundle. MacAdam then introduced pre-differential bundles, which are defined using
+only the projection, zero, and lift, and showed that differential bundles are precisely pre-differential bundles
+such that the n-fold pullbacks of the projection exist and the Rosick´y’s universality diagram holds. This
+pre-differential bundle approach to differential bundles is quite useful since it requires less data and fewer
+axioms to check when one wants to construct a differential bundle. This will be particularly useful when we
+will characterize differential bundles for commutative rings and (affine) schemes.
+The definition of a pre-differential bundle is what remains from the definition of a differential bundle
+after removing the sum (and negative) and any required pullback.
+Definition 3.7 [21, Definition 10] In a tangent category (X, T), a pre-differential bundle is a triple
+(q : E −→ A, z : A −→ E, λ : E −→ T(E)) consisting of objects A and E of X, and maps q : E −→ A, z : A −→ E,
+and λ : E −→ T(E) of X such that the following diagrams commute:
+A
+z
+�
+❊
+❊
+❊
+❊
+❊
+❊
+❊
+❊
+❊
+❊
+❊
+❊
+❊
+❊
+❊
+❊
+❊
+❊
+❊
+❊
+E
+q
+�
+E
+λ
+�
+q
+�
+T(E)
+pE
+�
+A
+z
+�
+z
+�
+E
+0E
+�
+E
+λ
+�
+λ
+�
+T(E)
+T(λ)
+�
+A
+A
+z
+� E
+E
+λ
+� T(E)
+T(E)
+ℓE
+� T2(E)
+(18)
+22
+
+If (q : E −→ A, z : A −→ E, λ : E −→ T(E)) is a pre-differential bundle, we say that it is a pre-differential
+bundle over A. When there is no confusion, pre-differential bundles will be denoted as (q : E −→ A, z, λ),
+and when the objects are specified simply as (q, z, λ).
+By definition, the projection, zero, and lift of a differential bundle gives a pre-differential bundle, since
+the diagrams in Definition 3.7 all appear in Definition 3.1. On the other hand, a pre-differential bundle
+is a differential bundle precisely when the pullback of n copies of the projection exists and certain squares
+are pullbacks [22, Proposition 6]. Since the main tangent categories of interest in this paper are Cartesian
+Rosick´y tangent, we review when a pre-differential bundle is a differential bundle in this setting, where
+only one square is required to be a pullback [22, Corollary 3]. This pullback is called Rosick´y’s universality
+diagram, and using the pullback universal property, we can construct the sum and negative for the differential
+bundle [22, Lemma 5].
+Proposition 3.8 [22, Corollary 3] Let (X, T) be a Cartesian Rosick´y tangent and let (q : E −→ A, z, λ) be a
+pre-differential bundle in (X, T) such that:
+(i) For each n ∈ N, the pullback of n copies of q exists, which we denote as En with n projection maps
+πj : En −→ E, for all 1 ≤ j ≤ n, so q ◦ πj = q ◦ πi for all 1 ≤ i, j ≤ n, and for all m ∈ N, Tm preserves
+these pullbacks;
+(ii) The following commuting square is a pullback, called the Rosick´y’s universality diagram:
+E
+λ
+�
+q
+�
+T(E)
+⟨T(q),pE⟩
+�
+A
+⟨0A,z⟩
+� T(A) × E
+(19)
+and for all m ∈ N, Tm preserves this pullback.
+Then define the maps σ : E2 −→ E and ι : E −→ E respectively as follows using the universal property of the
+above pullback:
+E2
+σ
+�❑
+❑
+❑
+❑
+❑
+❑
+πj
+�
+⟨λ◦π1,λ◦π2⟩
+� T2(E)
++E
+�
+E
+ι
+�❏
+❏
+❏
+❏
+❏
+❏
+q
+�
+λ
+� T(E)
+−E
+�
+E
+λ
+�
+q
+�
+T(E)
+⟨T(q),pE⟩
+�
+E
+λ
+�
+q
+�
+T(E)
+⟨T(q),pE⟩
+�
+E
+q
+� A
+⟨0A,z⟩
+� T(A) × E
+A
+⟨0A,z⟩
+� T(A) × E
+(20)
+Then E = (q, σ, z, λ, ι) is a differential bundle with negatives over A.
+Conversely, if E = (q : E −→ A, σ, z, λ) is a differential bundle in a Cartesian Rosick´y tangent category,
+then (q, z, λ) is a pre-differential bundle which satisfies (i) and (ii) in Proposition 3.8. Furthermore, the
+induced sum as constructed in Proposition 3.8 is precisely the sum σ one started with, and so (q, σ, z, λ, ι) is
+a differential bundle with negatives. Similarly, if (q : E −→ A, σ, z, λ, ι) is a differential bundle with negatives,
+then the induced negative as constructed in Proposition 3.8 is precisely the negative ι one started with.
+Therefore, in a Cartesian Rosick´y tangent category, every differential bundle is in fact a differential bundle
+with negatives. In conclusion, we have the following equivalence:
+Proposition 3.9 [21, Proposition 6 & Corollary 3] In a Cartesian Rosick´y tangent category (X, T), the
+following are in bijective correspondence:
+23
+
+(i) Differential bundles;
+(ii) Differential bundles with negatives;
+(iii) Pre-differential bundles that satisfy (i) and (ii) in Proposition 3.8.
+3.3
+Morphisms and Categories of Differential Bundles
+In this section, we discuss morphisms between differential bundles.
+There are two possible kinds: one
+where the base objects can vary and one where the base object is fixed. The former is used as the maps
+in the category of all differential bundles of a tangent category, while the latter is used in the category of
+differential bundles over a specified object. In either case, a differential bundle morphism is asked to preserve
+the projections and the lifts of the differential bundles.
+Definition 3.10 [8, Definion 2.3] Let (X, T) be a (Rosick´y) tangent category.
+(i) Let E = (q : E −→ A, σ, z, λ) and E′ = (q′ : E′ −→ A′, σ′, z′, λ′) be differential bundles in (X, T). A
+differential bundle morphism (f, g) : E −→ E′ is a pair of maps f : E −→ E′ and g : A −→ A′ such
+that the following diagram commutes:
+E
+f
+�
+q
+�
+E′
+q′
+�
+E
+λ
+�
+f
+� E′
+λ′
+�
+A
+g
+� A′
+T(E)
+T(f)
+� T(E′)
+(21)
+Let DBun
+�
+(X, T)
+�
+be the category whose objects are differential bundles in (X, T), maps are differential
+bundle morphisms between them, identity maps are pairs of identity maps (1E, 1A) : E −→ E, and
+composition is defined point-wise, that is, (f, g) ◦ (h, k) = (f ◦ h, g ◦ k).
+(ii) Let A be an object in X and E = (q : E −→ A, σ, z, λ) and E′ = (q′ : E′ −→ A, σ′, z′, λ′) be differential
+bundles over A in (X, T). A differential bundle morphism f : E −→ E′ over A is a map f : E −→ E′
+such that (f, 1A) : E −→ E′ is a differential bundle morphism.
+Explicitly, the following diagrams
+commute:
+E
+f
+�
+q
+�❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+❖
+E′
+q′
+�
+E
+λ
+�
+f
+� E′
+λ′
+�
+A
+T(E)
+T(f)
+� T(E′)
+(22)
+Let DBunT[A] be the category whose objects are differential bundles over A in (X, T) and whose maps
+are differential bundle morphisms over A between them, and where identity maps and composition are
+the same as in X.
+Differential bundle morphisms automatically preserve the sum and zero, and negatives if they exist:
+Lemma 3.11 [8, Proposition 2.16] Let (X, T) be a tangent category, and let E = (q : E −→ A, σ, z, λ) and
+E′ = (q′ : E′ −→ A′, σ′, z′, λ′) be differential bundles in (X, T), and let (f, g) : E −→ E′ be a differential
+bundle morphism between them. Then (f, g) is an additive bundle morphism [5, Definition 2.2], that is, the
+following diagrams commute:
+E2
+σ
+�
+⟨f◦π1,f◦π2⟩
+� E′
+2
+σ′
+�
+A
+z
+�
+g
+� A′
+z′
+�
+E
+f
+� E′
+E
+f
+� E′
+(23)
+24
+
+Similarly, let (q : E −→ A, σ, z, λ, ι) and (q′ : E′ −→ A′, σ′, z′, λ′, ι′) be differential bundles with negatives in
+(X, T), and let (f, g) : (q, σ, z, λ) −→ (q′, σ′, z′, λ′) be a differential bundle morphism between the underlying
+differential bundles. Then f preserves the negative, that is, the following diagram commutes:
+E
+ι
+�
+f
+� E′
+ι′
+�
+E
+f
+� E′
+(24)
+Other properties of differential bundle morphisms can be found in [8, Section 2.5].
+Note that since differential bundle morphisms preserve negatives, the notion of a morphism between
+differential bundles with negatives is the same as a differential bundle morphism. Therefore for a Rosick´y
+tangent category, it follows from Proposition 3.9 that its category of differential bundles is the same as its
+category of differential bundles with negatives. As such, abusing notation slightly, for a Rosick´y tangent cat-
+egory (X, T), we will consider DBun
+�
+(X, T)
+�
+and DBunT[A] to be the categories whose objects are differential
+bundles with negatives and whose maps are differential bundle morphisms.
+For a Cartesian (Rosick´y) tangent category, its category of differential objects is the category of differential
+bundles over the terminal object. Note that this is not the same as the Cartesian differential category of
+differential objects [5, Theorem 4.11], since in that category the morphisms are not required to preserve the
+lift, sum, zero, or negative.
+Definition 3.12 Let (X, T) be a Cartesian (Rosick´y) tangent category. Define DIFF
+�
+(X, T)
+�
+to be the cate-
+gory of differential objects and differential bundle morphisms over ∗ between them, DIFF
+�
+(X, T)
+�
+= DBunT[∗].
+We conclude this section by discussing differential bundle isomorphisms. If (X, T) is a (Rosick´y) tangent
+category, then a differential bundle isomorphism is an isomorphism in the category DBun
+�
+(X, T)
+�
+. Explicitly,
+this is a differential bundle morphism (f, g) such that there exists a differential bundle morphism of opposite
+type (f −1, g−1) such that (f, g) ◦ (f −1, g−1) = (1, 1) and (f −1, g−1) ◦ (f, g) = (1, 1). By definition of the
+composition in DBun
+�
+(X, T)
+�
+, this is precisely the same as requiring that f and g are isomorphisms in X.
+Similarly, for an object A, a differential bundle isomorphism over A is an isomorphism in the category
+DBunT[A], which is a differential bundle morphism f which is an isomorphism in X whose inverse f −1 is also
+a differential bundle morphism. We will now prove the converse, that if the underlying maps of a differential
+bundle morphism are isomorphisms in the base category, then their inverses are also a differential bundle
+morphism. This will allow us to reduce the number of things to check when characterizing differential bundles
+in various tangent categories.
+Lemma 3.13 Let (X, T) be a tangent category.
+(i) Let E = (q : E −→ A, σ, z, λ) and E′ = (q′ : E′ −→ A′, σ′, z′, λ′) be differential bundles in (X, T), and let
+(f, g) : E −→ E′ be a differential bundle morphism between them. If f : E −→ E′ and g : A −→ A′ are
+isomorphisms in X, then (f −1, g−1) : E′ −→ E is a differential bundle morphism. Therefore, (f, g) is a
+differential bundle isomorphism with inverse (f −1, g−1).
+(ii) Let A an object in X, and let E = (q : E −→ A, σ, z, λ) and E′ = (q′ : E′ −→ A, σ′, z′, λ′) be differential
+bundles over A in (X, T), and let f : E −→ E′ be a differential bundle morphism over A between them.
+If f : E −→ E′ is an isomorphism in X, then f −1 : E′ −→ E is a differential bundle morphism over A.
+Therefore f is a differential bundle isomorphism with inverse f −1.
+Proof: For (i), we compute:
+g−1 ◦ q′ = g−1 ◦ q′ ◦ f ◦ f −1 = g−1 ◦ g ◦ q ◦ f −1 = q ◦ f −1
+25
+
+The fact that (f −1, g−1) is then an isomorphism in the category of differential bundles follows from [8,
+Lemma 2.18.ii]. For (ii), if f is a differential bundle morphism over A, then (f, 1A) is a differential bundle
+morphism. The identity is always an isomorphism, so if f is also an isomorphism, it follows from (i) that
+(f −1, 1A) is a differential bundle morphism, which implies that f −1 is a differential bundle morphism over
+A as desired.
+✷
+4
+Differential Bundles for Commutative Rings
+In this section, we characterize differential bundles (with negatives) in the tangent category of commutative
+rings and prove that they correspond precisely to modules (Proposition 4.5). To go from a module to a
+differential bundle, we use a semi-direct product to build a sort of ring of dual numbers from said module
+(Lemma 4.2). To go from a differential bundle to a module, we take the kernel of the projection (Lemma 4.1).
+We then obtain that the category of differential bundles is equivalent to the category of modules (Theorem
+4.7 and Theorem 4.8). We will also explain how the only differential object is the zero ring (Corollary 4.6).
+For a commutative ring R, for a (left) R-module M, unless otherwise specified, we denote the action by
+a · m, where a ∈ R and m ∈ M.
+4.1
+From Differential Bundles to Modules
+We begin by unpacking what a differential bundle with negatives would consist of in (CRING,
+T
+). First
+recall that (CRING,
+T
+) is a Cartesian Rosick´y tangent category, so by Proposition 3.9, differential bundles
+are the same thing as differential bundles with negatives. Also, as discussed in Section 2.2, CRING admits
+all pullbacks, so for any ring morphism q : E −→ R between commutative rings, the general construction of
+a pullback of n copies of q in CRING is given by:
+En = {(x1, . . . , xn)| xj ∈ E s.t. q(xi) = q(xj) for all 1 ≤ i, j ≤ n}
+and whose ring structure is given coordinate-wise. In particular, E2 = {(x, y)| x, y ∈ E s.t. q(x) = q(y)}. So
+for a commutative ring R, a differential with negatives over R in (CRING,
+T
+) would consist of a commutative
+ring E and five ring morphisms: q : E −→ R, σ : E2 −→ E, z : R −→ E, λ : E −→ E[ε], and ι : E −→ E. These
+also need to satisfy the equalities and properties of Definition 3.1, many of which we will expand further in
+the proof of Lemma 4.4 below. To obtain an R-module, we take the kernel of the projection q.
+Lemma 4.1 Let R be a commutative ring and E = (q : E −→ R, σ, z, λ, ι) be a differential bundle with
+negatives over R in (CRING,
+T
+). Then the kernel of the projection ker(q) = {x| q(x) = 0} is an R-module
+with action a · x = z(a)x.
+Proof: Since q : E −→ R is a ring morphism, this induces an R-module structure on E with action
+a · e = z(a)e. Then viewing R as an R-module with action given by multiplication a · b = ab, this makes the
+projection q : E −→ R an R-linear morphism. Therefore since the kernel of an R-linear morphism is always
+an R-module, we indeed have that ker(q), with the same action as E, is an R-module.
+✷
+4.2
+From Modules to Differential Bundles
+We now construct a differential bundle from a module. For a commutative ring R and an R-module M,
+define M[ε] as follows:
+M[ε] = {a + mε| a ∈ R, m ∈ M and ε2 = 0}
+where a and mε will be used respectively as shorthand for a + 0ε and 0 + mε. Then M[ε] is a commutative
+ring with multiplication induced by ε2 = 0, that is, the addition, multiplication, and negative are defined
+respectively as follows:
+(a + mε) + (b + nε) = (a + b) + (m + n)ε
+(a + mε)(b + nε) = ab + (a · m + b · n)ε
+−(a + mε)=−a − mε
+26
+
+and where the zero is 0 and the unit is 1. Note that when M = R and the action is given by multiplication
+a · b = ab, then this construction gives us the ring of dual numbers over R, or in other words, the tangent
+bundle
+T
+(R) = R[ε]. We now define a differential bundle over R structure on M[ε].
+(i) The projection qM : M[ε] −→ R is defined as projecting out the R component:
+qM(a + mε) = a
+As noted above, there is a general construction of pullbacks in CRING.
+However for the projection
+qM : M[ε] −→ R, we can instead describe these pullbacks in terms of multivariable dual numbers, like for the
+pullbacks of the tangent bundle. So define M[ε1, . . . , εn] as follows:
+M[ε1, . . . , εn] = {a + m1ε1 + . . . + mnεn| ∀a ∈ R, mj ∈ M and εiεj = 0}
+Then M[ε1, . . . , εn] is a commutative ring whose structure is defined in the obvious way, so in particular
+the multiplication is induced by εiεj = 0. We leave it as an exercise for the reader to check for themselves
+that M[ε1, . . . , εn] is the pullback of n copies of pR. We can then describe the rest of the differential bundle
+structure as follows:
+(ii) The pullback of n copies of pR is given by M[ε]n = M[ε1, . . . , εn] and where the pullback projection
+πj : M[ε1, . . . , εn] −→ M[ε] sends εj to ε and the other nilpotents to zero, that is, πj projects out the
+R component and j-th M component:
+πj(a + m1ε1 + . . . + mnεn) = a + mjε
+(iii) The sum σ : M[ε1, ε2] −→ M[ε] maps both ε1 and ε2 to ε, which results in adding the M components
+together:
+σ(a + mε1 + nε2) = a + (m + n)ε
+(iv) The zero z : R −→ M[ε] is the injection of R into the R component:
+0R(a) = a
+(v) The negative ι : M[ε] −→ M[ε] maps ε to −ε, which results in making the M component negative:
+ι(a + mε) = a − mε
+To describe the lift, let us describe
+T
+�
+M[ε]
+�
+, the ring of dual numbers of M[ε] in terms of two nilpotent
+elements ε and ε′:
+T
+�
+M[ε]
+�
+= M[ε][ε′] = {a + mε + bε′ + nεε′| ∀a, b ∈ R, m, n ∈ M and ε2 = ε′2 = 0}
+where the multiplication is induced by ε2 = ε′2 = 0. So we define:
+(vii) The lift λ : M[ε] −→ M[ε][ε′] maps ε to ε′, and so maps the R component of M[ε] to the first R
+component of M[ε][ε′], and the M component of M[ε] to the second M component of M[ε][ε′]:
+λ(a + mε) = a + mεε′
+We leave it as an exercise for the reader to check that these are all well-defined ring morphisms.
+Lemma 4.2 For every commutative ring R and R-moulde M,
+M
+R(M) := (qM, σM, zM, λM, ιM) is a differ-
+ential bundle with negatives over R in (CRING,
+T
+).
+27
+
+Proof: To show that we have a differential bundle, we will instead show that we have a pre-differential
+bundle which satisfies (i) and (ii) in Proposition 3.8. To show that (qM, zM, λM) is a pre-differential bundle,
+we must show that the four equalities from Definition 3.7 hold, but these all follow from straightforward
+computation, which we leave to the reader.
+Next, we must show that this pre-differential bundle also satisfies the extra assumptions required to make
+it a differential bundle. Firstly, it is straightforward to observe that M[ε1, . . . , εn] is indeed the pullback
+of n copies of the projection q. Also, since
+T
+is a right adjoint, it preserves all limits, and therefore all
+T
+n
+preserves these pullbacks. So (qM, zM, λM) satisfies assumption (i) of Proposition 3.8. Next, we must show
+that the following square is a pullback:
+M[ε]
+λM
+�
+qM
+�
+M[ε][ε′]
+⟨
+T
+(qM),pM[ε]⟩
+�
+R
+⟨0R,zM⟩
+� R[ε] × M[ε]
+(25)
+So suppose S is a commutative ring, and we have ring morphisms f : S −→ M[ε][ε′] and g : S −→ R such
+that ⟨
+T
+(qM), pM[ε]⟩ ◦ f = ⟨0R, zM⟩ ◦ g, that is, for every x ∈ S the following equality holds:
+�
+T
+(qM)(f(x)), pM[ε](f(x))
+�
+=
+�
+g(x), g(x)
+�
+Now f(x) ∈ M[ε][ε′] is of the form: f(x) = f1(x) + f2(x)ε + f3(x)ε′ + f4(x)εε′ for some f1(x), f3(x) ∈ R and
+f2(x), f4(x) ∈ M. Then the above equality tells us that:
+(g(x), g(x)) =
+�
+T
+(qM)(f(x)), pM[ε](f(x))
+�
+=
+�
+T
+(qM)
+�
+f1(x) + f2(x)ε + f3(x)ε′ + f4(x)εε′�
+, pM[ε]
+�
+f1(x) + f2(x)ε + f3(x)ε′ + f4(x)εε′��
+=
+�
+qM(f1(x) + f2(x)ε) + qM(f3(x) + f4(x)ε)ε, pM[ε]
+�
+f1(x) + f2(x)ε + f3(x)ε′ + f4(x)εε′��
+=
+�
+f1(x) + f3(x)ε, f1(x) + f2(x)ε
+�
+So this implies that g(x) = f1(x) + f2(x)ε and g(x) = f1(x) + f3(x)ε. However, in both equalities, the
+left-hand side has no nilpotent component. Therefore, we have that g(x) = f1(x), f2(x) = 0, and f3(x) = 0.
+So f(x) = g(x) + f4(x)εε′. Then define ⟨f, g⟩ : S −→ M[ε] to be f but without ε′, that is, as follows:
+⟨f, g⟩(x) = g(x) + f4(x)ε
+(26)
+That ⟨f, g⟩ is a ring morphism essentially follows from the fact that f is a ring morphism. Next we compute
+that ⟨f, g⟩ also satisfies the following:
+λM(⟨f, g⟩(x)) = λM(g(x) + f4(x)ε) = g(x) + f4(x)εε′ = f(x)
+qM(⟨f, g⟩(x)) = qM(g(x) + f4(x)ε) = g(x)
+So λM ◦ ⟨f, g⟩ = f and qM ◦ ⟨f, g⟩ = g as desired. Lastly, it remains to show that ⟨f, g⟩ is the unique such
+ring morphism. So suppose we have a ring morphism h : S −→ M[ε] such that λM ◦ h = f and qM ◦ h = g.
+Now h(x) ∈ M[ε] is of the form h(x) = h1(x) + h2(x)ε for some h1(x) ∈ R and h2(x) ∈ M. By assumption,
+we have that:
+g(x) + f4(x)εε′ = f(x) = λM(h(x)) = λM(h1(x) + h2(x)ε) = h1(x) + h2(x)εε′
+So g(x) + f4(x)εε′ = h1(x) + h2(x)εε′, which implies that h1(x) = g(x) and h2(x) = f4(x). Therefore,
+h(x) = g(x) + f4(x)ε = ⟨f, g⟩(x), and so ⟨f, g⟩ is unique. So we conclude that the above square is a pullback
+28
+
+diagram. Furthermore, since
+T
+is a right adjoint, we also have that
+T
+n preserves these pullbacks. Thus
+(qM, zM, λM) satisfies assumption (ii) of Proposition 3.8. Therefore, (qM, zM, λM) will induce a differential
+bundle with negatives.
+It remains to construct the sum and the negative as in Proposition 3.8, and show that these are the same
+as the proposed σ and ι above. The sum σ will be given by:
+σ =
+�
++M[ε] ◦ ⟨λM ◦ π1, λM ◦ π2⟩, qM ◦ πj
+�
+We leave it to the reader to check for themselves that the following equalities hold:
++M[ε]
+�
+⟨λM ◦ π1, λM ◦ π2⟩(a + mε1 + nε2)
+�
+= a + (m + n)εε′
+Therefore by construction, we have that σ(a + mε1 + nε2) = a + (m + n)ε as desired. The negative ι will be
+given by:
+ι =
+�
+−M[ε] ◦ λM, qM
+�
+We then compute that:
+−M[ε](λM(a + mε)) = a − mεε′
+So by construction, we have that ι(a + mε) = a − mε. So we conclude that
+M
+R(M) = (qM, σM, zM, λM, ιM)
+is a differential bundle with negatives over R.
+✷
+4.3
+Equivalence
+We will now show that the constructions of Lemma 4.1 and Lemma 4.2 are inverses of each other.
+Beginning from the module side of things, let R be a commutative ring and M be an R-module. Consider
+ker(qM), the kernel of the projection of the induced differential bundle
+M
+R(M). However, qM(a + mε) = 0
+implies that a = 0. So the kernel of the projection consists solely of the M component, that is, ker(qM) =
+{mε| ∀m ∈ M}, which is clearly isomorphic to M. Explicitly, αM : M −→ ker(qM) is defined as αM(m) = mε,
+and α−1
+M : ker(qM) −→ M is defined as α−1
+M (mε) = m.
+Lemma 4.3 For every commutative ring R and R-module M, αM : M −→ ker(qM) is an R-linear isomor-
+phism with inverse α−1
+M : ker(qM) −→ M.
+Proof: Clearly for every R-module M, αM and α−1
+M are inverses of each other, that is, α−1
+M (αM(m)) = m
+and αM(α−1
+M (mε)) = mε. However, we must explain why αM and α−1
+M are also R-linear morphisms. Clearly,
+they are both linear, so we must show that they preserve the action. We start by showing that αM does,
+where recall that the action on ker(qM) is defined as a · (mε) = zM(a)mε:
+αM(a · m) = (a · m)ε = (a + 0ε)mε = zM(a)mε = a · mε = a · αM(m)
+So αM is an R-module morphism. Since αM and α−1
+M are inverses as functions, it then follows that α−1
+M will
+also be an R-module morphism. So we conclude that αM and α−1
+M are inverse R-linear isomorphisms.
+✷
+Let’s now start from the differential bundle side of the story.
+Let E = (q : E −→ R, σ, z, λ, ι) be a
+differential bundle with negatives over a commutative ring R in (CRING,
+T
+). To define differential bundle
+isomorphisms between E and
+M
+R
+�
+ker(q)
+�
+, we will first need to define a ring isomorphism between E and
+ker(q)[ε].
+To do so, we must first take a closer look at the lift λ : E −→ E[ε].
+Since the lift is a ring
+morphism whose codomain is a ring of dual numbers, it is well-known that it must be of the following form:
+λ(x) = pE(λ(x)) + Dλ(x)ε, where Dλ : E −→ E is a derivation. Now by the first diagram of [DB.3], we have
+that pE ◦ λ = z ◦ q. This implies that the lift is in fact of the form:
+λ(x) = z(q(x)) + Dλ(x)ε
+29
+
+and the product rule for the derivation Dλ is given by Dλ(xy) = z(q(x))Dλ(y) + z(q(y))Dλ(x). Then define
+the function βE : E −→ ker(q)[ε] as follows:
+βE(x) = q(x) + Dλ(x)ε
+(27)
+To define its inverse β−1
+E
+: ker(q)[ε] −→ E, we will need to make use of Rosick´y’s universality diagram,
+that is, the pullback square from Proposition 3.8. First, define the ring morphism ζE : ker(q)[ε] −→ E[ε]
+as ζE(a + xε) = z(a) + xε. By universality of the pullback, define β−1
+E
+: ker(q)[ε] −→ E as the unique ring
+morphism which makes the following diagram commute:
+ker(q)[ε]
+qker(q)
+�
+ζE
+�
+β−1
+E
+�P
+P
+P
+P
+P
+P
+P
+E
+q
+�
+λ
+� E[ε]
+⟨
+T
+(q),pE⟩
+�
+R
+⟨0R,z⟩
+� R[ε] × E
+(28)
+so β−1
+E
+= ⟨qker(q), ζE⟩. We will show below that β−1
+E
+is a differential bundle morphism, from which it follows
+from the compatibility with the lift that β−1
+E (a + xε) = z(a) + x.
+Lemma 4.4 For commutative ring R and a differential bundle with negatives E = (q : E −→ R, σ, z, λ, ι)
+over R in (CRING,
+T
+), βE : E −→
+M
+R
+�
+ker(q)
+�
+is a differential bundle isomorphism over R with inverse
+β−1
+E
+:
+M
+R
+�
+ker(q)
+�
+−→ E.
+Proof: We first explain why βE and β−1
+E
+are well-defined ring morphisms. Starting with βE, we must
+first explain why Dλ(x) is in the kernel of the projection q. By the first diagram of [DB.2], we have that
+T
+(q)◦ λ = 0R ◦ q. Therefore, for all x ∈ E, we have that q(z(q(x)))+ q(Dλ(x))ε = q(x). Since the right-hand
+side has no nilpotent component, this implies that q(Dλ(x)) = 0. So for all x ∈ E, Dλ(x) ∈ ker(q), and so
+βE is well-defined. We leave it to the reader to check for themselves that βE is indeed a ring morphism.
+Next we explain why β−1
+E
+is a well-defined. To do so, we must show that the outer diagram of (28)
+commutes. First, note that by the second diagram of [DB.1], q ◦ z = 1R, so q(z(a)) = a for all a ∈ R. Then
+for all a ∈ R and x ∈ ker(q) we compute:
+⟨
+T
+(q), pE⟩
+�
+ζE(a + xε)
+�
+= ⟨
+T
+(q), pE⟩
+�
+z(a) + xε
+�
+=
+�
+T
+(q)(z(a) + xε), pE(z(a) + xε)
+�
+=
+�
+q(z(a)) + q(x)ε), pE(z(a) + xε)
+�
+=
+�
+a, z(a)
+�
+=
+�
+0R(a), z(a)
+�
+= ⟨0R, z⟩(a) = ⟨0R, z⟩
+�
+qker(q)(a + xε
+�
+So ⟨
+T
+(q), pE⟩ ◦ ζE = ⟨0R, z⟩ ◦ qker(q). Therefore, by the universal property of the pullback square, there exists
+a unique ring morphism β−1
+E
+: ker(q)[ε] −→ E such that λ ◦ β−1
+E
+= ζE and q ◦ β−1
+E
+= qker(q). In particular,
+these imply that for every a ∈ R and x ∈ ker(q) the following equalities hold:
+q
+�
+β−1
+E (a + xε)
+�
+= a
+Dλ(β−1
+E (a + xε)) = x
+Next we show that βE and β−1
+E
+are inverses of each other. To show that βE ◦ β−1
+E
+= 1ker(q)[ε], we use the
+above identities:
+βE(β−1
+E (a + xε)) = q(β−1
+E (a + xε)) + Dλ(β−1
+E (a + xε))ε = a + xε
+To show that β−1
+E
+◦ βE = 1E, we will first show that q ◦ β−1
+E
+◦ βE = q and λ ◦ β−1
+E
+◦ βE = λ:
+q(β−1
+E (βE(x))) = q(βE(x)) = q((q(x) + Dλ(x)ε)) = q(x)
+30
+
+λ(β−1
+E (βE(x))) = ζE(βE(x)) = ζE(q(x) + Dλ(x)ε) = z(q(x)) + Dλ(x)ε = λ(x)
+Therefore, by the universal property of the pullback, it follows that β−1
+E
+◦ βE = 1E. So βE and β−1
+E
+are
+inverse ring isomorphisms.
+Lastly, we must show that βE and β−1
+E
+are also differential bundle morphisms over R. To do so, we will
+need to know a bit more about Dλ. The third diagram of [DB.3] is 0E ◦ z = λ ◦ z, which implies that for
+all a ∈ R, z(a) = z(a) + Dλ(z(a))ε. Since the left-hand side has no nilpotent component, it follows that
+Dλ(z(a)) = 0 for all a ∈ R. On the other hand, the diagram of [DB.4] says that
+T
+(λ)◦λ = ℓE ◦λ. Then using
+that q(Dλ(x)) = 0, q(z(a)) = a, and Dλ(z(a)) = 0, [DB.4] explicitly states that q(z(x)) + Dλ(Dλ(x))εε′ =
+q(z(x)) + Dλ(x)εε′. This implies that Dλ(Dλ(x)) = Dλ(x) for all x ∈ E. With these identities, we can now
+show that βE is a differential bundle morphism over R. So we show that the diagrams of (22) hold:
+(i) qker(q) ◦ βE = q:
+qker(q)(βE(x)) = qker(q)(q(x) + Dλ(x)ε) = q(x)
+(ii)
+T
+(βE) ◦ λ = λker(q) ◦ βE:
+T
+(βE)(λ(x)) =
+T
+(βE)(z(q(x)) + Dλ(x)ε) = βE(z(q(x)) + βE(Dλ(x)ε)ε′
+= q(z(q(x)))+Dλ(z(q(x)))ε+z(q(Dλ(x)))ε′+Dλ(Dλ(x))εε′ = q(x)+0ε+0ε′+Dλ(x)εε′ = q(x)+Dλ(x)εε′
+= λker(q)(q(x) + Dλ(x)ε) = λker(q)(βE(x))
+So βE is a differential bundle morphism. Since βE is a ring isomorphism, by Lemma 3.13 it then follows that
+β−1
+E
+is also a differential bundle morphism. In particular, note that this implies that λ◦β−1
+E
+=
+T
+(β−1
+E )◦λker(q).
+But by definition, we have that λ◦β−1
+E
+= ζE, and so we also have that
+T
+(β−1
+E )◦λker(q) = ζE. This implies that
+β−1
+E (a) + β−1
+E (xε)ε = z(a) + xε, and so β−1
+E (a) = z(a) and β−1
+E (xε) = x. Therefore, β−1
+E (a + xε) = z(a) + x.
+So we conclude that βE and β−1
+E
+are differential bundle isomorphisms over R.
+✷
+Therefore, the construction from a module to a differential bundle is the inverse of the construction from
+a differential bundle to a module. So we conclude that:
+Proposition 4.5 For a commutative ring R, there is a bijective correspondence between R-modules and
+differential bundles (with negatives) over R in (CRING,
+T
+).
+In CRING, recall that the terminal object is the zero ring 0. So differential objects in (CRING,
+T
+) corre-
+spond precisely to 0-modules. However, the only 0-module is 0. Therefore, there are no non-trivial differential
+objects in (CRING,
+T
+).
+Corollary 4.6 The only differential object in (CRING,
+T
+) is the zero ring 0.
+We now extend Proposition 4.5 to an equivalence of categories. For a commutative ring R, let MODR be
+the category of R-modules and R-linear morphisms between them. We define an equivalence of categories
+between MODR from DBUN
+T
+[R] as follows:
+(i) Define the functor
+M
+R : MODR −→ DBUN
+T
+[R] which sends an R-module M to the differential bundle
+M
+R(M), and sends an R-linear morphism f : M −→ M ′ to the differential bundle morphism over R
+M
+R(f) :
+M
+R(M) −→
+M
+R(M ′) where
+M
+R(f) : M[ε] −→ M ′[ε] is defined as:
+M
+R(f)(a + mε) = a + f(m)ε
+(ii) Define the functor
+M
+◦
+R : DBUN
+T
+[R] −→ MODR which sends a differential bundle with negatives over R,
+E = (q : E −→ R, σ, z, λ, ι) to the R-module
+M
+◦
+R(E) = ker(q), and sends a differential bundle morphism
+f : E = (q : E −→ R, σ, z, λ, ι) −→ E′ = (q′ : E′ −→ R, σ′, z′, λ′, ι′) over R to the R-linear morphism
+M
+◦
+R(f) : ker(q) −→ ker(q′) defined as:
+M
+◦
+R(f)(x) = f(x)
+31
+
+(iii) Define the natural isomorphism α : 1MODR ⇒
+M
+◦
+R ◦
+M
+R with inverse α−1 :
+M
+◦
+R ◦
+M
+R ⇒ 1MODR as αM
+α−1
+M defined in Lemma 4.3.
+(iv) Define the natural isomorphism β : 1DBUN
+T
+[R] ⇒
+M
+R ◦
+M
+◦
+R with inverse β−1 :
+M
+◦
+R ◦
+M
+R ⇒ 1DBUN
+T
+[R]
+as βE β−1
+E
+defined in Lemma 4.4.
+Theorem 4.7 For a commutative ring R, we have an equivalence of categories: MODR ≃ DBUN
+T
+[R].
+Proof: We must first explain why
+M
+R and
+M
+◦
+R are well-defined on morphisms.
+So given an R-linear
+morphism f : M −→ M ′, we must show that
+M
+R(f) is a differential bundle morphism over R. We leave it to
+the reader to check for themselves that
+M
+R(f) is a ring morphism. So it remains to show that the diagrams
+of (22) also hold:
+(i) qM′ ◦
+M
+R(f) = qM:
+qM′ �
+M
+R(f)(a + mε)
+�
+= qM′(a + f(m)ε) = a = qM(a + mε)
+(ii)
+T
+�
+M
+R(f)
+�
+◦ λM = λM′ ◦
+M
+R(f):
+T
+�
+M
+R(f)
+� �
+λM(a + mε)
+�
+=
+T
+�
+M
+R(f)
+� �
+a + mεε′�
+=
+M
+R(f)(a) +
+M
+R(f)(mε)ε′
+= a + f(m)εε′ = λM′ �
+a + f(m)ε
+�
+= λM′ �
+M
+R(f)(a + mε)
+�
+So we conclude that
+M
+R(f) is a differential bundle morphism over R. On the other hand, given a differential
+bundle morphism f : E −→ E′ over R, we must first explain why if x ∈ ker(q) then
+M
+◦
+R(f)(x) ∈ ker(q′).
+Note that since f is a differential bundle morphism over R, by definition this means that for all x ∈ E,
+q′(f(x)) = q(x). So it follows that if x ∈ ker(q), we have that:
+q′ �
+M
+◦
+R(f)(x)
+�
+= q′(f(x)) = q(x) = 0
+and so
+M
+◦
+R(f)(x) ∈ ker(q′). Thus
+M
+◦
+R(f) : ker(q) −→ ker(q′) is well-defined. To show that
+M
+◦
+R(f) is R-linear,
+clearly since f is linear,
+M
+◦
+R(f) will be linear, therefore it remains to show
+M
+◦
+R(f) preserves the action. Since
+f is a differential bundle morphisms over R, by Lemma 3.11, we have that f preserves the zero, that is,
+f(z(a)) = z′(a) for all a ∈ R. So we compute:
+a ·
+M
+◦
+R(f)(x) = a · f(x) = z′(a)f(x) = f(z(a)x) = f(a · x) =
+M
+◦
+R(f)(a · x)
+So we conclude that
+M
+◦
+R(f) is an R-linear morphism. So
+M
+R and
+M
+◦
+R are well-defined, and it is straightforward
+to see that they also preserve composition and identities, so
+M
+R and
+M
+◦
+R are indeed functors.
+Next we explain why α, α−1, β, and β−1 are natural transformations. In fact, it suffices to explain why
+α and β−1 are natural, and it will then follow that α−1 and β are as well since we have already shown they
+are isomorphisms on each object. So for an R-linear morphism f : M −→ M ′, we compute:
+M
+◦
+R
+�
+M
+R(f)
+� �
+αM(m)
+�
+=
+M
+◦
+R
+�
+M
+R(f)
+�
+(mε) =
+M
+R(f)(mε) = f(m)ε = αM′(f(m))
+So α is indeed a natural transformation, and so α−1 will also be a natural transformation. Therefore, α and
+α−1 are inverse natural isomorphism. On the other hand, for a differential bundle morphism f : E −→ E′
+over R, we compute:
+β−1
+E′
+�
+M
+R
+�
+M
+◦
+R(f)
+�
+(a + xε)
+�
+= β−1
+E′
+�
+a +
+M
+◦
+R(f)(x)ε
+�
+= β−1
+E′
+�
+a + f(x)ε
+�
+= z′(a) + f(x)ε = f(z(a)) + f(x) = f(z(a) + x) = f
+�
+β−1
+E (a + xε)
+�
+32
+
+So β−1 is indeed a natural transformation, and so β will also be a natural transformation. Therefore, β
+and β−1 are inverse natural isomorphism. So we conclude that we have an equivalence of categories, and so
+MODR ≃ DBUN
+T
+[R].
+✷
+We also obtain an equivalence of categories between the category of all differential bundles and the
+category of modules. Let MOD be the category whose objects are pairs (R, M) consisting of a commutative
+ring R and an R-module M, and where a map (g, f) : (R, M) −→ (R′, M ′) is a pair consisting of a ring
+morphism g : R −→ R′ and an R-linear map f : M −→ M ′, where M ′ is an R-module via the action
+a•m = g(a)·m, so explicitly, f(a·m) = g(a)·f(m). Composition is defined as (g′, f ′)◦(g, f) = (g′ ◦g, f ′ ◦f)
+and identities are (1R, 1M). We define an equivalence of categories between MOD and DBUN
+�
+(CRING,
+T
+)
+�
+as follows:
+(i) Define the functor
+M
+: MOD −→ DBUN
+�
+(CRING,
+T
+)
+�
+which sends an object (R, M) to the differential
+bundle
+M
+(R, M) =
+M
+R(M), and sends a map (g, f) : (R, M) −→ (R′, M ′) to the differential bundle
+morphism
+M
+(g, f) :
+M
+R(M) −→
+M
+R′(M ′) defined as:
+M
+(g, f)(a + mε) = g(a) + f(m)ε
+(ii) Define the functor
+M
+◦ : DBUN
+�
+(CRING,
+T
+)
+�
+−→ MOD which sends a differential bundle with negatives
+E = (q : E −→ R, σ, z, λ, ι) to the pair
+M
+◦(E) = (R, ker(q)), and sends a differential bundle morphism
+(f, g) : E = (q : E −→ R, σ, z, λ, ι) −→ E′ = (q′ : E′ −→ R′, σ′, z′, λ′, ι′) to the pair
+M
+◦(f, g) = (g,
+M
+◦
+R(f)).
+(iii) Define the natural isomorphism α : 1MOD ⇒
+M
+◦ ◦
+M
+as α(R,M) = (1R, αM), with inverse natural
+isomorphism α−1 :
+M
+◦ ◦
+M
+⇒ 1MOD defined as α−1
+(R,M) = (1R, α−1
+M ).
+(iv) Define the natural isomorphism β : 1DBUN
+�
+(CRING,
+T
+)
+� ⇒
+M
+◦
+M
+◦ as βE = (1, βE), with inverse natural
+isomorphism β
+−1 :
+M
+◦
+R ◦
+M
+R ⇒ 1DBUN
+�
+(CRING,
+T
+)
+� as β
+−1
+E
+= (1, β−1
+E ).
+Theorem 4.8 We have an equivalence of categories: MOD ≃ DBUN
+�
+(CRING,
+T
+)
+�
+.
+Proof: That
+M
+and
+M
+◦ are well-defined on morphisms is similar to the proofs that
+M
+R and
+M
+◦
+R were well-
+defined on morphisms in the proof of Theorem 4.7. So
+M
+and
+M
+◦ are indeed functors. Next, since αM and
+α−1
+M are R-linear morphisms, it follows that α(R,M) = (1R, αM) and α−1
+(R,M) = (1R, α−1
+M ) are indeed maps in
+MOD, so α and α−1 are well-defined. On the other hand, since βE and β−1
+E
+are differential bundle morphisms
+over the base commutative ring, it follows by definition that βE = (1, βE) and β
+−1
+E
+= (1, β−1
+E ) are differential
+bundle morphisms, so β and β
+−1 are well-defined. Lastly, that α, α−1, β, and β
+−1 are natural isomorphisms
+follows directly from the fact that α, α−1, β, and β−1 are natural isomorphisms. So we conclude that we
+have an equivalence of categories: MOD ≃ DBUN
+�
+(CRING,
+T
+)
+�
+.
+✷
+Remark 4.9 The equivalence between modules and differential bundles is also true in more general settings.
+Indeed, both for the tangent category of commutative semirings and the tangent category of commutative
+algebras over a (semi)ring, differential bundles correspond precisely to modules via the above constructions.
+However, in a setting where one does not have negatives, we would have also needed to prove [DB.5], since
+this is also required to make a pre-differential bundle a differential bundle in a Cartesian tangent category
+without negatives [22, Proposition 6]. Even more generally, in a codifferential category, every module of
+an algebra of the monad will induce a differential bundle in the Eilenberg-Moore category via [4, Theorem
+5.1] and a generalization of Lemma 4.2.
+If a codifferential category has kernels, then every differential
+bundle induces a module by generalizing Lemma 4.1, and so in the presence of kernels, differential bundles
+in the Eilenberg-Moore category also correspond precisely to modules. However, since not all codifferential
+categories have all kernels, there may be differential bundles which are not induced by modules.
+33
+
+5
+Differential Bundles for (Affine) Schemes
+In this section, we characterize differential bundles (with negatives) in the tangent category of affine schemes
+and prove that they also correspond to modules (Proposition 5.5). However, the constructions are quite
+different in this case. To go from a module to a differential bundle, we take the free symmetric algebra over
+said module (Lemma 5.2). To go from a differential bundle to a module, we take the image of the derivation
+induced by the lift (Lemma 5.1). Moreover, in contrast to the previous section, in this case, we obtain
+that the category of differential bundles is equivalent to the opposite category of modules (Theorem 5.7 and
+Theorem 5.9). To the best of our understanding, there is no general reason why the fact that differential
+bundles in commutative rings are equivalent to the category of modules would also imply that differential
+bundles in commutative rings opposite are equivalent to the opposite category of modules. We conclude the
+section by generalizing these results to the category of schemes, where differential bundles are equivalent to
+the opposite category of quasicoherent sheaves of modules.
+5.1
+From Differential Bundles to Modules
+Let us begin by unravelling what a differential bundle with negatives would be in (CRINGop, T). First recall
+that (CRINGop, T) is a Cartesian Rosick´y tangent category, so by Proposition 3.9, differential bundles are
+the same thing as differential bundles with negatives. Also, as discussed in Section 2.3, CRINGop admits all
+pullbacks, since CRING admits all pushouts. For any ring morphism q : R −→ E between commutative rings,
+recall that E becomes a commutative R-algebra, so, in particular, an R-module, with action a · x = q(a)x.
+Then the pushout of n copies of q in CRING is given by taking the tensor product over R of n copies
+of E: En = E ⊗R . . . ⊗R E
+�
+��
+�
+n times
+.
+Then a differential bundle with negatives over a commutative ring R in
+(CRINGop, T) viewed in CRING would consist of a commutative ring E and five ring morphisms: q : R −→ E,
+σ : E −→ E ⊗R E, z : E −→ R, λ : T(E) −→ E, and ι : E −→ E. These must also satisfy the dual equalities
+and properties of Definition 3.1. In particular, note that [DB.1] and [DB.N] imply that E is a commutative
+R-Hopf algebra, where the sum σ is the comultiplication, the zero z is the counit, and the negative ι is the
+antipode.
+To obtain an R-module from a differential bundle, we take the image of the map Dλ : E −→ E defined as
+Dλ(x) = λ(d(x)), which is, in fact, a derivation whose product rule is Dλ(ab) = λ(a)Dλ(b) + λ(b)Dλ(a).
+Lemma 5.1 Let R be a commutative ring, and let E = (q : E −→ R, σ, z, λ, ι) be a differential bundle (with
+negatives) over R in (CRINGop, T). Then the image of the derivation im(Dλ) = {Dλ(x) = λ(d(x))| ∀x ∈ E}
+is an R-module with action a · Dλ(x) = Dλ(q(a)x).
+Proof: Recall that for any R-linear map f : M −→ N, the image im(f) = {f(m)| ∀m ∈ M} is an R-module
+with action a · f(m) = f(a · m). Therefore, to prove that im(Dλ) is an R-module, it suffices to show that
+Dλ is an R-linear map. Clearly Dλ is linear, so it remains to show that Dλ also preserves the action. First
+note that by the dual of the first diagram of [DB.2], that λ ◦ T(q) = q ◦ 0R. In particular this implies
+that λ(q(a)) = q(a) and λ(d(q(a))) = 0 for all a ∈ R. Note that the second equality can be rewritten as
+Dλ(q(a)) = 0 for all a ∈ R. So we compute:
+Dλ(a · x) = Dλ(q(a)x) = λ(q(a))Dλ(x) + λ(x)Dλ(q(a)) = q(a)Dλ(x) + 0 = a · Dλ(x)
+So Dλ is R-linear and we conclude that im(Dλ) is an R-module.
+✷
+5.2
+From Modules to Differential Bundles
+We now construct a differential bundle from a module. For a commutative ring R and an R-module M, let
+SymR(M) be the free symmetric R-algebra over M, that is:
+SymR (M) =
+∞
+�
+n=0
+M ⊗s
+R
+n = R ⊕ M ⊕ (M ⊗s
+A M) ⊕ . . .
+34
+
+where ⊗s
+R is the symmetrized tensor product over R. Note that as a commutative ring, SymR(M) is generated
+by all a ∈ R and m ∈ M. Therefore, to define ring morphisms with domain SymR(M), it suffices to define
+them on generators a and m. Using this to our advantage, we define a differential bundle with negatives over
+R structure on SymR(M) viewed in CRING (so the differential bundle structure maps will all be backwards)
+as follows:
+(i) The projection qM : R −→ SymR(M) is defined as the injection of R into SymR(M):
+qM(a) = a
+(ii) The pushouts (which recall are pullbacks in CRINGop) are given by taking the tensor product over
+R of n copies of SymR(M), so SymR(M)n := SymR(M) ⊗R . . . ⊗R SymR(M)
+�
+��
+�
+n times
+, where the jth injection
+πj : SymR(M) −→ SymR(M)n injects SymR(M) into the j-th component:
+πj(w) = 1 ⊗R . . . ⊗R 1 ⊗R w ⊗R 1 ⊗R . . . ⊗R 1
+(iii) The sum σM : SymR(M) −→ SymR(M) ⊗R SymR(M) is the canonical comultiplication of the free
+symmetric R-algebras, that is, defined on generators as follows:
+σM(a) = a ⊗R 1 = 1 ⊗R a
+σM(m) = m ⊗R 1 + 1 ⊗R m
+(iv) The zero 0R : SymR(M) −→ R is the canonical counit of the free symmetric R-algebras, that is, defined
+on generators as follows:
+zM(a) = a
+zM(m) = 0
+(v) The negative ιM : SymR(M) −→ SymR(M) is the canonical antipode of the free symmetric R-algebras,
+that is, defined on generators as follows:
+ιM(a) = a
+ιM(m) = −m
+To describe the lift, note that T(SymR(M)) as a commutative ring is generated by a, m, d(a), and d(m) for
+all a ∈ R and m ∈ M (and modulo the appropriate equations).
+(vii) The lift λM : T(SymR(M)) −→ SymR(M) is defined on generators as follows:
+λM(a) = a
+λM(m) = 0
+λM(d(a)) = 0
+λM(d(m)) = m
+Lemma 5.2 For every commutative ring R and R-module M, MR(M) := (qM, σM, zM, λM, ιM) is a differ-
+ential bundle with negatives over R in (CRINGop, T).
+Proof: To show that we have a differential bundle, we will instead show that we have a pre-differential
+bundle which satisfies (i) and (ii) in Proposition 3.8. So to show that (qM, zM, λM) is a pre-differential
+bundle in (CRINGop, T), we must show that the dual of the four equalities from Definition 3.7 hold in CRING.
+To do so, we show that these hold on the generators.
+(i) zM ◦ qM = 1R
+zM(qM(a)) = zM(a) = a
+(ii) λM ◦ pSymR(M) = qM ◦ zM
+λM(pSymR(M)(a)) = λM(a) = a = qM(a) = qM(zM(a))
+λM(pSymR(M)(m)) = λM(m) = 0 = qM(0) = qM(zM(m))
+35
+
+(iii) zM ◦ 0SymR(M) = zM ◦ λM
+zM
+�
+0SymR(M)(a)
+�
+= zM(a) = zM(λM(a))
+zM
+�
+0SymR(M)(m)
+�
+= zM(m) = 0 = zM(0) = zM(λM(0))
+(iv) λM ◦T(λM) = λM ◦ℓSymR(M): Note that T2(SymR(M)) has eight kinds of generators, a, m, d(a), d(m),
+d′(a), d′(m), d′d(a), and d′d(m) for all a ∈ R and m ∈ M.
+λM(T(λM)(a)) = λM(λM(a)) = λM(a) = λM(ℓSymR(M)(a))
+λM(T(λM)(m)) = λM(λM(m)) = λM(0) = 0 = λM(m) = λM(ℓSymR(M)(m))
+λM(T(λM)(d(a))) = λM(λM(d(a))) = λM(0) = λM(ℓSymR(M)(d(a)))
+λM(T(λM)(d(m))) = λM(λM(d(m))) = λM(0) = λM(ℓSymR(M)(d(m)))
+λM(T(λM)(d′(a))) = λM(d(λM(a))) = λM(d(a)) = 0 = λM(0) = λM(ℓSymR(M)(d′(a)))
+λM(T(λM)(d′(m))) = λM(d(λM(m))) = λM(d(0)) = λM(0) = λM(ℓSymR(M)(d′(m)))
+λM(T(λM)(d′d(a)))=λM(d(λM(d(a)))) = λM(d(0)) = λM(0) = 0 = λM(d(a))=λM(ℓSymR(M)(d′d(a)))
+λM(T(λM)(d′d(m))) = λM(d(λM(d(m)))) = λM(d(m)) = λM(ℓSymR(M)(d′d(m)))
+So the desired equalities hold and we conclude that (qM, zM, λM) is a pre-differential bundle in (CRINGop, T).
+Next, we must show that this pre-differential bundle also satisfies the extra assumptions required to make
+it a differential bundle, or rather that the dual of the assumptions hold in CRING. As explained above, the
+pushout of n copies of the projection qM exists, chosen here to be SymR(M)n, and since T is a left adjoint,
+it preserves all colimits, so Tn preserves these pushouts. Dualizing this, we conclude that (qM, zM, λM)
+satisfies assumption (i) of Proposition 3.8 in CRINGop.
+Next, we must show that the dual of (ii) of Proposition 3.8 also holds, that is, we must show that the
+following square is a pushout in CRING:
+T(R) ⊗ SymR(M)
+[T(qM),pSymR(M)]
+�
+[0R,zM]
+� R
+qM
+�
+T(SymR(M))
+λM
+� SymR(M)
+(29)
+where [−, −] is the copairing operation of the coproduct, which recall in CRING is given by the tensor
+product. Now suppose that S is a commutative ring, and we have ring morphisms f : T(SymR(M)) −→ S
+and g : R −→ S such that f ◦[T(qM), pSymR(M)] = g ◦[0R, zM]. In particular, this implies that for every a ∈ R
+and m ∈ M,the following equalities hold:
+f(a) = g(a)
+f(d(a)) = 0
+f(m) = 0
+Then define the map [f, g] : SymR(M) −→ S as the ring morphism defined on generators as follows:
+[f, g](a) = g(a)
+[f, g](m) = f(d(m))
+(30)
+Next, we compute the following on generators:
+[f, g](qM(a)) = [f, g](a) = g(a)
+[f, g](λM(a)) = [f, g](a) = g(a) = f(a)
+36
+
+[f, g](λM(m)) = [f, g](0) = 0 = f(m)
+[f, g](λM(d(a))) = [f, g](0) = 0 = f(d(a))
+[f, g](λM(d(m))) = [f, g](m) = f(d(m))
+Thus it follows that [f, g]◦ λM = f and [f, g]◦ qM = g as desired. Lastly, it remains to show that [f, g] is the
+unique such ring morphism. So suppose we have a ring morphism h : SymR(M) −→ S such that h ◦ λM = f
+and h ◦ qM = g. Then on generators, we compute that:
+h(a) = h(qM(a)) = g(a) = [f, g](a)
+h(m) = h(λM(d(m))) = f(d(m)) = [f, g](m)
+Since h and [f, g] are ring morphisms that are equal on generators, it follows that h = [f, g], thus [f, g] is
+unique. Thus we conclude the above diagram is a pushout in CRING. Furthermore, since T is a left adjoint in
+CRING, we also have that Tn preserves these pushouts. Dualizing this, it follows that (qM, zM, λM) satisfies
+assumption (ii) of Proposition 3.8 in CRINGop. Therefore by Proposition 3.8, the pre-differential bundle
+(qM, zM, λM) will induce a differential bundle with negatives in (CRINGop, T).
+It remains to construct the sum and the negative as in Proposition 3.8, and show that these are the same
+as the proposed σ and ι above. By dualizing the construction, the sum σ is:
+σM =
+�
+[π1 ◦ λM, π2 ◦ λM] ◦ +SymR(M), πj ◦ qM
+�
+On generators, we compute:
+σM(a) =
+�
+[π1 ◦ λM, π2 ◦ λM] ◦ +SymR(M), πj ◦ qM
+�
+(a) = πj(qM(a)) = πj(a) = a ⊗R 1 = 1 ⊗R a
+σM(m) =
+�
+[π1 ◦ λM, π2 ◦ λM] ◦ +SymR(M), πj ◦ qM
+�
+(m) = [π1 ◦ λM, π2 ◦ λM](+SymR(M)(d(m)))
+= [π1 ◦ λM, π2 ◦ λM](d(m) ⊗R 1) + [π1 ◦ λM, π2 ◦ λM](1 ⊗R d(m))
+= π1(λM(d(m))) + π2(λM(d(m))) = π1(m) + π2(m) = m ⊗R 1 + 1 ⊗R m
+Thus on generators, σM(a) = a ⊗R 1 = 1 ⊗R a and σ(m) = m ⊗R 1 + 1 ⊗R m, as defined above. On the
+other hand, the negative ι is:
+ιM =
+�
+λM ◦ −SymR(M), qM
+�
+On generators, we compute:
+ιM(a) =
+�
+λM ◦ −SymR(M), qM
+�
+(a) = qM(a) = a
+ιM(m) =
+�
+λM ◦ −SymR(M), qM
+�
+(m) = λM(−SymR(M)(d(m)) = λM(−d(m)) = −λM(d(m)) = −m
+So on generators ιM(a) = a, and ιM(m) = −m as desired. So we conclude that (qM, σM, zM, λM, ιM) is a
+differential bundle with negatives over R in (CRINGop, T).
+✷
+5.3
+Equivalence
+We will now show that the constructions of Lemma 5.1 and Lemma 5.2 are inverses of each other. Starting
+from the module side of things, let R be a commutative ring, M an R-module, and consider the induced
+derivation DλM : SymR(M) −→ SymR(M). We will show that the image of the derivation is precisely M.
+Lemma 5.3 For every commutative ring R and R-module M, im(DλM ) = M as R-modules.
+37
+
+Proof: Let us compute what this derivation does on pure symmetrized tensors. For degree 0, that is, for
+a ∈ R we have that:
+DλM (a) = λM(d(a)) = 0
+so DλM (a) = 0. For degree 1, that is, for m ∈ M we have that:
+DλM (m) = λM(d(m)) = m
+so DλM (m) = m. For degree 2, that is, for m, n ∈ M using the product rule, we have that:
+DλM (mn) = λM(m)DλM (n) + λM(n)DλM (m) = 0 + 0 = 0
+And similarly for degree n ≥ 2, again by using the product rule, we have that DλM (m1m2 . . . mn) = 0. So
+it follows that im(DλM ) = {m| ∀m ∈ M}, so im(DλM ) = M. Furthermore, note that the multiplication of a
+and m in SymR(M) is precisely the module action, am = a · m. Thus the induced action on im(DλM ) from
+Lemma 5.1 is given by:
+a · DλM (m) = DλM (q(a)m) = DλM (am) = DλM (a · m) = a · m
+So im(DλM ) = M as R-modules.
+✷
+Conversely, let us start from a differential bundle, so let E = (q : E −→ R, σ, z, λ, ι) be a differential bundle
+with negatives over a commutative ring R in (CRINGop, T). To define a differential bundle isomorphism
+between E and M(im(Dλ), we will first need to define ring isomorphisms between E and SymR
+�
+im(Dλ)
+�
+.
+Define the ring morphism ψE : SymR
+�
+im(Dλ)
+�
+−→ E on generators a ∈ R and x ∈ E as follows:
+ψE(a) = q(a)
+ψE
+�
+Dλ(x)
+�
+= Dλ(x)
+(31)
+Note that ψE can also be defined by the universal property of the free symmetric R-algebra, that is, it is
+the unique R-algebra morphism induced by the inclusion im(Dλ) −→ E. To define the inverse we will need
+to use the dual of the Rosick´y’s universality diagram, which in this case asks that the following diagram be
+a pushout:
+T(R) ⊗ E
+[T(q),pE]
+�
+[0R,z]
+�
+T(E)
+λ
+�
+R
+q
+� E
+(32)
+So define the ring morphism δE : T(E) −→ SymR
+�
+im(Dλ)
+�
+on generators x ∈ E as follows:
+δE(x) = z(x)
+δE(d(x)) = Dλ(x)
+(33)
+By universality of the pushout, define ψ−1
+E
+: ker(q)[ε] −→ E as the unique ring morphism which makes the
+following diagram commute:
+T(R) ⊗ E
+[T(q),pE]
+�
+[0R,z]
+�
+T(E)
+λ
+�
+δE
+�
+R
+q
+�
+qim(Dλ)
+�
+E
+ψ−1
+E
+�❚
+❚
+❚
+❚
+❚
+❚
+❚
+❚
+❚
+SymR
+�
+im(Dλ)
+�
+(34)
+so ψ−1
+E
+=
+�
+qim(Dλ), δE
+�
+.
+38
+
+Lemma 5.4 For a commutative ring R and a differential bundle with negatives E = (q : E −→ R, σ, z, λ, ι)
+over R in (CRINGop, T), ψE : E −→ M(im(Dλ)) is a differential bundle isomorphism over R in (CRINGop, T)
+with inverse ψ−1
+E
+: M(im(Dλ)) −→ E.
+Proof: We first explain why ψE and ψ−1
+E
+are well-defined ring morphisms. Clearly, ψE is well-defined by
+construction. On the other hand, to explain why ψ−1
+E
+is well-defined, we must show that the outer diagram
+of (34) commutes. First, note that by the dual of the second diagram of [DB.1], z(q(a)) = a for all a ∈ R,
+and recall that Dλ(q(a)) = 0 for all a ∈ R as well. Then on generators a ∈ R and x ∈ E we compute:
+δE
+�
+[T(q), pE](a ⊗ x)
+�
+= δE
+�
+(T(q)(a)pE(x))
+�
+= δE
+�
+q(a)x
+�
+= δE
+�
+q(a)
+�
+δE (x)= qim(Dλ)
+�
+z(q(a))
+�
+qim(Dλ)
+�
+z(x)
+�
+= qim(Dλ) (a) qim(Dλ)
+�
+z(x)
+�
+= qim(Dλ)(az(x)) = qim(Dλ)
+�
+0R(a)z(x)
+�
+= qim(Dλ)
+�
+[0R, z](a ⊗ x)
+�
+and
+δE
+�
+[T(q), pE](d(a) ⊗ x)
+�
+= δE
+�
+T(q)(d(a))pE(x)
+�
+= δE
+�
+d(q(a))x
+�
+= δE
+�
+d(q(a))
+�
+δE (x) = Dλ(q(a))x = 0
+= qim(Dλ)(0) = qim(Dλ)(0z(x)) = qim(Dλ)
+�
+0R(d(a))z(x)
+�
+= qim(Dλ)
+�
+[0R, z](d(a) ⊗ x)
+�
+So δE ◦ [T(q), pE] = qim(Dλ) ◦ [0R, z]. Therefore, by the universal property of the pushout square, there exists
+a unique ring morphism ψ−1
+E
+: E −→ SymR
+�
+im(Dλ)
+�
+such that ψ−1
+E
+◦ λ = δE and ψ−1
+E
+◦ q = qim(Dλ). In
+particular, these imply that for every a ∈ R and x ∈ E the following equalities hold:
+ψ−1
+E (q(a)) = a
+ψ−1
+E (Dλ(x)) = Dλ(x)
+Next we show that ψE and ψ−1
+E
+are inverses of each other. To show that ψ−1
+E
+◦ ψE = 1SymR(im(Dλ)), we use
+the above identities and compute the following on generators a ∈ R and x ∈ E:
+ψ−1
+E (ψE(a)) = ψ−1
+E (q(a)) = a
+ψ−1
+E
+�
+ψE
+�
+Dλ(x)
+��
+= ψ−1
+E (Dλ(x)) = Dλ(x)
+So ψ−1
+E
+◦ ψE = 1SymR(im(Dλ)). On the other hand, to show that ψE ◦ ψ−1
+E
+= 1E, we will first show that
+ψE ◦ ψ−1
+E
+◦ q = q and ψE ◦ ψ−1
+E
+◦ λ = λ. So on generators a ∈ R and x ∈ E, we compute:
+ψE(ψ−1
+E (q(a))) = ψE(a) = q(a)
+ψE(ψ−1
+E (λ(x))) = ψE(δE(x)) = ψE(z(x)) = q(z(x)) = x
+ψE(ψ−1
+E (λ(d(x)))) = ψE(δE(d(x))) = ψE(Dλ(x)) = Dλ(x) = λ(d(x))
+Therefore, by the universal property of the pushout, it follows that ψE ◦ ψ−1
+E
+= 1E. So ψE and ψ−1
+E
+are
+inverse ring isomorphisms.
+Lastly, we must show that ψE and ψ−1
+E
+are also differential bundle morphisms over R in (CRINGop, T),
+that is, we must show the dual of the axioms in Definition 3.10 hold.
+We will first show that ψE is a
+differential bundle morphism. To do so, first recall that λ(q(a)) = q(a) and Dλ(q(a)) = 0, and that the
+dual of [DB.4] states that λ ◦ T(λ) = λ ◦ ℓE. So we show that the desired equalities hold by computing the
+following on generators:
+(i) ψE ◦ qim(Dλ) = q:
+ψE(qim(Dλ)(a)) = ψE(a) = q(a)
+(ii) λ ◦ T(βE) = ψE ◦ λim(Dλ), on a:
+λ
+�
+T(βE)(a)
+�
+= λ
+�
+βE(a)
+�
+= λ(q(a)) = q(a) = ψE(a) = ψE(λim(Dλ)(a)
+39
+
+on Dλ(x):
+λ
+�
+T(βE)
+�
+Dλ(x)
+��
+= λ
+�
+βE
+�
+Dλ(x)
+��
+= λ
+�
+Dλ(x)
+�
+= λ
+�
+λ(d(x))
+�
+= λ
+�
+T(λ)(d(x))
+�
+= λ
+�
+ℓE(d(x))
+�
+= λ(0) = 0 = ψE(0) = ψE
+�
+λim(Dλ)
+�
+Dλ(x)
+��
+on d(a):
+λ
+�
+T(βE)
+�
+d(a)
+��
+= λ
+�
+d
+�
+βE(a)
+��
+= λ
+�
+d
+�
+q(a)
+��
+= Dλ(q(a)) = 0 = ψE(0) = ψE
+�
+λim(Dλ)
+�
+d(a)
+��
+and finally on d
+�
+Dλ(x)
+�
+:
+λ
+�
+T(βE)
+�
+d
+�
+Dλ(x)
+���
+= λ
+�
+d
+�
+βE
+�
+Dλ(x)
+���
+= λ
+�
+d
+�
+Dλ(x)
+��
+= λ
+�
+d
+�
+λ(d(x))
+��
+= λ
+�
+T(λ)(d′d(x))
+�
+= λ
+�
+ℓE(d′d(x))
+�
+= λ
+�
+d(x)
+�
+= Dλ(x) = βE
+�
+Dλ(x)
+�
+= ψE
+�
+λim(Dλ)
+�
+d
+�
+Dλ(x)
+���
+So it follows that ψE is a differential bundle morphism over R in (CRINGop, T). By Lemma 3.13 it then follows
+that ψ−1
+E
+is also a differential bundle morphism over R. So we conclude that ψE and ψ−1
+E
+are differential
+bundle isomorphisms over R in (CRINGop, T).
+✷
+Thus, the construction from a module to a differential bundle is the inverse of the construction from a
+differential bundle to a module. So we conclude that:
+Proposition 5.5 For a commutative ring R, there is a bijective correspondence between R-modules and
+differential bundles (with negatives) over R in (CRINGop, T).
+In CRING, recall that initial object is Z, which means that Z is the terminal object in CRINGop. So
+differential objects in (CRINGop, T) correspond precisely to Z-modules, which are precisely Abelian groups.
+Corollary 5.6 There is a bijective correspondence between Z-modules/Abelian groups and differential objects
+in (CRINGop, T).
+We now extend Proposition 5.5 to an equivalence of categories. For a commutative ring R, we define an
+equivalence of categories between MODop
+R and DBUNT [R] as follows:
+(i) Define the functor MR : MODop
+R −→ DBUNT [R] which sends an R-module M to the differential bundle
+MR(M), and sends an R-linear morphism f : M −→ M ′ to the differential bundle morphism over R
+MR(f) : MR(M ′) −→ MR(M) defined to be the ring morphism MR(f) : SymR(M) −→ SymR(M ′) defined
+on generators as follows:
+MR(f)(a) = a
+MR(f)(m) = f(m)
+(ii) Define the functor M◦
+R : DBUNT [R] −→ MODop
+R which sends a differential bundle with negatives over R,
+E = (q : E −→ R, σ, z, λ, ι) to the R-module M◦
+R(E) = im(Dλ), and sends a differential bundle morphism
+f : E = (q : E −→ R, σ, z, λ, ι) −→ E′ = (q′ : E′ −→ R, σ′, z′, λ′, ι′) over R to the R-linear morphism
+M◦
+R(f) : im(Dλ′) −→ im(Dλ) defined as:
+M◦
+R(f)(Dλ′(x)) = Dλ(f(x))
+(iii) Observe that M◦
+R ◦ MR = 1MODop
+R .
+40
+
+(iv) Define the natural isomorphism ψ : 1DBUNT[R] ⇒ MR ◦ M◦
+R with inverse ψ−1 : MR ◦ M◦
+R ⇒ 1DBUNT[R] as
+ψE and ψ−1
+E
+as defined in Lemma 5.4.
+Theorem 5.7 For a commutative ring R, we have an equivalence of categories: MODop
+R ≃ DBUNT [R].
+Proof: We must first explain why MR and M◦
+R are well-defined. Clearly, MR is well-defined on objects
+and maps and preserves composition and identities. So MR is indeed a functor. On the other hand, let
+f : E −→ E′ be a differential bundle morphism over R in (CRINGop, T). This implies that f : E′ −→ E is a
+ring morphism and also that f(q′(a)) = q(a) for all a ∈ R. Since MR(f) is clearly linear, we show that it
+also preserves the action:
+M◦
+R(f)
+�
+a · Dλ′(x)
+�
+= M◦
+R(f)
+�
+Dλ′(q(a)x)
+�
+= Dλ
+�
+f(q(a)x)
+�
+= Dλ
+�
+f(q′(a))f(x)
+�
+= Dλ
+�
+q(a)f(x)
+�
+= a · Dλ(f(x)) = a · M◦
+R(f)(Dλ′(x))
+So we have that MR(f) is an R-linear morphism, and so M◦
+R is well-defined. Clearly, M◦
+R also preserves
+composition and identities, so M◦
+R is also a functor. Furthermore, we also have that M◦
+R ◦ MR = 1MODop
+R .
+Next, ψ and ψ−1 are well-defined component-wise and are inverses at each component. Therefore, it suffices
+to show that ψ is natural and then it will follow that ψ−1 is also natural. If f : E −→ E′ is a differential
+bundle morphism over R in (CRINGop, T), then f ◦λ′ = λ◦T(f). In particular, this means that f(λ′(d(x))) =
+λ(d(f(x))). However, we can rewrite this as f
+�
+Dλ′(x)
+�
+= Dλ
+�
+f(x)
+�
+. Therefore, we compute on generators
+that:
+ψE
+�
+MR
+�
+M◦
+R(f)
+�
+(a)
+�
+= ψE(a) = q(a) = f(q′(a)) = f(ψE′(a))
+and
+ψE
+�
+MR
+�
+M◦
+R(f)
+� �
+Dλ′(x)
+��
+= ψE
+�
+M◦
+R(f)
+�
+Dλ′ (x)
+��
+= ψE
+�
+Dλ
+�
+f(x)
+��
+= Dλ
+�
+f(x)
+�
+=
+�
+Dλ′(x)
+�
+= f
+�
+ψE′ �
+Dλ′(x)
+��
+So ψE ◦ MR
+�
+M◦
+R(f)
+�
+= f ◦ ψE′ in CRING. Therefore ψ is a natural transformation, and it follows that so is
+ψ−1. Thus, ψ and ψ−1 are natural isomorphisms. So we conclude that we have an equivalence of categories:
+MODop
+R ≃ DBUNT [R].
+✷
+It then follows that we have an equivalence between the category of differential objects and the opposite
+category of Abelian groups. So let Ab be the category whose objects are Abelian groups and whose morphisms
+are group morphisms.
+Corollary 5.8 There is an equivalence of categories: DBUN
+�
+(CRINGop, T)
+�
+≃ MODZ ≃ Abop.
+We now define an equivalence of categories between MODop and DBUN
+�
+(CRINGop, T)
+�
+as follows:
+(i) Define the functor M : MODop −→ DBUNT [R] which sends an object (R, M) to the differential bundle
+M(R, M) = MR(M), and sends a map (g, f) : (R, M) −→ (R′, M ′) in MOD to the differential bundle
+morphism M(f) = (MR(f), g) : MR′(M ′) −→ MR(M).
+(ii) Define the functor M◦ : DBUN
+�
+(CRINGop, T)
+�
+−→ MODop which sends a differential bundle with
+negatives E = (q : E −→ R, σ, z, λ, ι) to the pair M◦(E) = (R, im(Dλ)), and sends a differential bun-
+dle morphism (f, g) : E = (q : E −→ R, σ, z, λ, ι) −→ E′ = (q′ : E′ −→ R′, σ′, z′, λ′, ι′) to the pair
+M◦(f, g) = (g, M◦
+R(f)).
+(iii) Observe that M◦ ◦ M = 1MODop.
+(iv) Define the natural isomorphism ψ : 1DBUN[(CRINGop,T)] ⇒ M ◦ M◦ as ψE = (1, ψE), with inverse natural
+isomrophism ψ
+−1 : M ◦ M◦ ⇒ 1DBUN[(CRINGop,T)] as ψ
+−1
+E
+= (1, ψ−1
+E ).
+41
+
+Theorem 5.9 We have an equivalence of categories: MODop ≃ DBUN
+�
+(CRINGop, T)
+�
+.
+Proof: The proof that M and M◦ are well-defined functors is similar to the proof that MR and M◦
+R in the
+proof of Theorem 5.9. Furthermore, it also follows that M◦ ◦ M = 1MODop. On the other hand, since ψE and
+ψ−1
+E
+are differential bundle morphisms over the base commutative ring, it follows by definition that ψE =
+(1, ψE) and ψ
+−1
+E
+= (1, ψ−1
+E ) are differential bundle morphisms, so ψ and ψ
+−1 are well-defined. Lastly, that ψ,
+and ψ
+−1 are natural isomorphisms follows directly from the fact that ψ, and ψ−1 are natural isomorphisms.
+So we conclude that we indeed have an equivalence of categories: MODop ≃ DBUN
+�
+(CRINGop, T)
+�
+.
+✷
+Remark 5.10 The equivalence between modules and differential bundles is also true in more general set-
+tings. Indeed, both for the opposite category of commutative semirings and the opposite category of com-
+mutative algebras over a (semi)ring, differential bundles correspond precisely to modules via the above
+constructions (where the latter follows from Corollary 2.19 and Proposition 3.4). As explained before, in
+a setting where one does not have negatives, we would also need to prove [DB.5]. On the other hand, it
+is unclear if this result always generalizes to the coEilenberg-Moore category of a differential category. If
+the differential category has enough limits and colimits, then it is possible to generalize the constructions of
+Lemma 5.1 and Lemma 5.2, and then we obtain a bijective correspondence between differential bundles and
+comodules of the colagebras of the comonad of said differential category. However, in general, a differential
+category need not have all limits or colimits. In future work, it would be interesting to characterize differ-
+ential bundles in arbitrary differential categories and understand what assumptions are needed so that they
+correspond to (co)modules.
+5.4
+Differential bundles in schemes
+In this section, we show how we can extend the characterization of differential bundles in affine schemes to
+differential bundles in the larger category of schemes. Since schemes are the gluing of affine schemes, this
+follows relatively straightforwardly from the results of the previous sections, so here we merely sketch the
+proofs. Our first goal is to show that for any differential bundle q : E −→ A in schemes, the projection q is
+an affine map. Let us first quickly recall the definition of affine morphisms and equivalent characterizations
+[26, Section 29.11].
+Definition 5.11 [26, Definition 29.11.1] A morphism of schemes f : X −→ Y is affine if for all affine
+opens U of Y , the inverse image f −1(U), that is, the following pullback:
+f −1(U)
+�
+�
+X
+�
+U
+� Y
+is itself affine.
+Proposition 5.12 [26, Lemma 29.11.3] For a scheme morphism f : X −→ Y , the following are equivalent:
+(i) f is affine;
+(ii) Y has a covering by affine opens {Ui}i∈I such that for all i ∈ I, f −1(Ui) is affine;
+(iii) X = Spec(A) for some quasicoherent sheaf of algebras A on the sheaf OY .
+The following is a general result about affine morphisms which will be useful below:
+Lemma 5.13 Affine morphisms are closed under retract, that is, if we have scheme morphisms
+42
+
+X1
+s
+�
+f1
+�❆
+❆
+❆
+❆
+❆
+❆
+❆
+❆
+X2
+r
+�
+f2
+�⑥⑥⑥⑥⑥⑥⑥⑥
+Y
+with (s, r) a section/retraction pair in the category of schemes over Y and f2 is affine, then so is f1.
+Proof: Let U be an affine open subset of Y . Then we can define a section/retraction pair (sU, rU) between
+f −1
+1 (U) and f −1
+2 (U) with both defined by pullback. For example, here is the defining diagram for sU:
+f −1
+1 (U)
+�
+sU
+�
+�
+X1
+s
+�❅
+❅
+❅
+❅
+❅
+❅
+❅
+❅
+f −1
+2 (U)
+�
+�
+X2
+f2
+�
+U
+� Y
+Thus f −1
+1 (U) is a retract of a representable element in the presheaf category [CRING, SET] (where SET is the
+category of sets and arbitrary functions between them). But so long as a category X has split idempotents,
+then representables in the functor category [Xop, SET] are closed under retract [13, Lemma 6.5.6]. So f −1
+1 (U)
+is itself representable, and so by definition f1 is affine, as required.
+✷
+We may now prove that for a differential bundle in the category of schemes, the projection is affine.
+Proposition 5.14 In the category of schemes, if q : E −→ A is a differential bundle, then q is affine.
+Proof: By [22, Corollary 3.1.4], q is a retract of a pullback of a tangent bundle projection pA : T(A) −→ A.
+By definition, T(A) is Spec of a quasicoherent sheaf of algebras on OA, so by Lemma 5.12, pA is affine. But
+affines are closed under pullback [26, Lemma 29.11.8] and retracts (Lemma 5.13), so q is affine.
+✷
+We may now prove that every differential bundle is a Spec of Sym of a quasicoherent sheaf of modules.
+Proposition 5.15 If q : E −→ A is a differential bundle in the category of schemes, then E is Spec of Sym
+of a quasicoherent sheaf of modules.
+Proof: Cover A by affines Ui, and since q is affine, each pullback q−1(Ui):
+q−1(U)
+�
+�
+E
+q
+�
+Ui
+� A
+is also affine. Moreover, by [8, Lemma 2.7], differential bundles are closed under pullback. Thus each map
+q−1(Ui) −→ Ui is a differential bundle in the category of affine schemes, and hence by Proposition 4.5, each
+q−1(Ui) is Sym of a module on Ui. Thus as E is the gluing of these, E is itself Spec of Sym of a quasicoherent
+sheaf of modules [28, pg. 379].
+✷
+Conversely, we now prove that every quasicoherent sheaf of modules induces a differential bundle.
+Proposition 5.16 If M is a quasicoherent sheaf of modules on a scheme A, then Spec of Sym of M is a
+differential bundle over A.
+43
+
+Proof: Suppose that A is covered by affines Ui. Then by [28, pg.379], if M is a quasicoherent sheaf of
+modules on A, then M is the gluing of modules Mi over the Ui, and Spec of Sym of M is the gluing of
+Spec of Sym of the Mi’s. Thus it suffices to show that such a gluing is a differential bundle over A. But
+by Lemma 5.2, Spec of Sym of each Mi is a differential bundle over Ai.
+It then follows that since the
+tangent functor on schemes preserves gluings (for an abstract proof of this, see [5, Prop. 6.15.ii]), the lifts
+of each such differential bundle λi glue together to give a lift λ for Spec of Sym of M, and it follows through
+straightforward calculations that this satisfies the required conditions to be a differential bundle.
+✷
+The results on morphisms follow similarly, and therefore we obtain:
+Theorem 5.17 For a scheme A, there is an equivalence of categories between differential bundles over A
+in the tangent category SCH and the opposite category of quasicoherent sheaves of modules over A.
+Remark 5.18 By Corollary 2.22 and Proposition 3.4, for any scheme A, there is a similar result for the
+tangent category of schemes over A.
+6
+Future work
+Understanding differential bundles in the tangent categories of commutative rings, affine schemes, and
+schemes is just the beginning of applying tangent category theory to algebra and algebraic geometry. There
+are many possible future avenues for exploration based on this work, such as:
+• The most immediate next step is to understand how connections in tangent categories apply to these
+examples. They seem closely related to connections on modules [23, Section 8.2], but more work needs
+to be done to understand the precise relationship between the two notions.
+• Tangent categories have a notion of differential forms and de Rham cohomology [11]. Initial inves-
+tigation with this idea suggests that for affine schemes over R, when the coefficient object is taken
+to be the polynomial ring R[x], then this tangent category cohomology recreates algebraic de Rham
+cohomology. However, again more investigation is required to prove this completely. Moreover, [11]
+also develops a second notion of cohomology: sector form cohomology. It is not clear what this should
+give in the algebraic geometry setting.
+• In [16], Dominic Joyce develops algebraic geometry in the setting of C∞-rings. It seems likely that
+the categories involved are tangent categories, and one expects many of the tangent categories theory
+ideas, applied to this example, recreate the corresponding notions Joyce has developed.
+• A key idea in algebraic geometry is that of a smooth morphism or object. It would be interesting to see
+if such a notion could be generalized to arbitrary tangent categories (in such a way, that, for example,
+all objects in the tangent category of smooth manifolds are smooth).
+• Finally, the Serre-Swan theorem provides a very different way to compare vector bundles to modules.
+It would be interesting to see a proof for the Serre-Swan theorem based on some of the results of this
+paper.
+Thus, while the results of this paper are interesting enough on their own, we hope they will also serve as
+inspiration for future work in this area.
+References
+[1] K. Bauer,
+M. Burke,
+and M. Ching.
+Tangent infinity-categories and Goodwillie calculus.
+arXiv.org:2101.07819, 2022.
+44
+
+[2] J. M. Beck. Triples, algebras and cohomology. Columbia University, 1967.
+[3] R. F. Blute, J. R. B. Cockett, and R. A. G. Seely.
+Cartesian differential categories.
+Theory and
+Applications of Categories, 22(23):622–672, 2009.
+[4] R. F. Blute, R. B. B. Lucyshyn-Wright, and K. O’Neill. Derivations in codifferential categories. Cahiers
+de Topologie et G´eom´etrie Diff´erentielle Cat´egoriques, 57:243–280, 2016.
+[5] J. R. B. Cockett and G. S. H. Cruttwell. Differential structure, tangent structure, and SDG. Applied
+Categorical Structures, 22(2):331–417, 2014.
+[6] J. R. B. Cockett and G. S. H. Cruttwell. The Jacobi identity for tangent categories. Cahiers de Topologie
+et G´eom´etrie Diff´erentielle Cat´egoriques, LVI(4):301–316, 2015.
+[7] J. R. B. Cockett and G. S. H. Cruttwell. Connections in tangent categories. Theory and applications of
+categories, 32(26):835–888, 2017.
+[8] J. R. B. Cockett and G. S. H. Cruttwell. Differential bundles and fibrations for tangent categories.
+Cahiers de Topologie et G´eom´etrie Diff´erentielle Cat´egoriques, LIX:10–92, 2018.
+[9] J. R. B. Cockett, G.S.H. Cruttwell, and J.-S.P. Lemay. Differential equations in a tangent category I:
+Complete vector fields, flows, and exponentials. Applied Categorical Structures, 29(5):773–825, 2021.
+[10] J. R. B. Cockett, J.-S. P. Lemay, and R. B. B. Lucyshyn-Wright. Tangent Categories from the Coal-
+gebras of Differential Categories.
+In M. Fern´andez and A. Muscholl, editors, 28th EACSL Annual
+Conference on Computer Science Logic (CSL 2020), volume 152 of Leibniz International Proceedings in
+Informatics (LIPIcs), pages 17:1–17:17, Dagstuhl, Germany, 2020. Schloss Dagstuhl–Leibniz-Zentrum
+fuer Informatik.
+[11] G. S. H. Cruttwell and R.B.B. Lucyshyn-Wright. A simplicial foundation for differential and sector
+forms in tangent categories. Journal of Homotopy and Related Structures volume, 13:867–925, 2018.
+[12] T. Ehrhard and L. Regnier. The differential lambda-calculus. Theoretical Computer Science, 309(1):1–
+41, 2003.
+[13] B. Francis. Handbook of Categorical Algebra, Volume I. Cambridge University Press, 1994.
+[14] R. Garner. An embedding theorem for tangent categories. Advances in Mathematics, 323:668–687, 2018.
+[15] A. Grothendieck. ´El´ements de g´eom´etrie alg´ebrique IV. Publications Math´ematiques de l’IH´ES, 28:5–
+255, 1966.
+[16] D. Joyce. An introduction to C-infinity schemes and C-infinity algebraic geometry. Surveys in Differ-
+ential Geometry, 79:299–325, 2012.
+[17] B. Jubin. The tangent functor monad and foliations. arXiv preprint arXiv:1401.0940, 2014.
+[18] A. Kock. Synthetic differential geometry. Cambridge University Press, 2006.
+[19] A. Kriegl and P. Michor. The convenient setting of global analysis. American Mathematical Society,
+1997.
+[20] B. Lawevere. Categorical Dynamics, pages 1–28. Aarhus University Press, 1979.
+[21] S. Mac Lane. Categories for the working mathematician, volume 5. Springer Science & Business Media,
+2013.
+[22] B. MacAdam. Vector bundles and differential bundles in the category of smooth manifolds. Applied
+categorical structures, 29(2):285–310, 2021.
+45
+
+[23] L. Mangiarotti and G. Sardanashvily. Connections In Classical And Quantum Field Theory. World
+Scientific Publishing Company, 2000.
+[24] P. Michor. The Jacobi flow. Rend. Sem. Mat. Univ. Pol. Torino, 54(4):365–372, 1996.
+[25] J. Rosick`y. Abstract tangent functors. Diagrammes, 12:JR1–JR11, 1984.
+[26] The Stacks Project Authors. Stacks Project. https://stacks.math.columbia.edu, 2018.
+[27] L. W. Tu. An introduction to manifolds. Springer, 2011.
+[28] R. Vakil. The rising sea: Foundations of algebraic geometry. Online textbook, 2017.
+46
+
diff --git a/DdE5T4oBgHgl3EQfUQ9g/content/tmp_files/load_file.txt b/DdE5T4oBgHgl3EQfUQ9g/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..cfa6a0126ee235f15312e7481df7850716524fb6
--- /dev/null
+++ b/DdE5T4oBgHgl3EQfUQ9g/content/tmp_files/load_file.txt
@@ -0,0 +1,2221 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf,len=2220
+page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='05542v1  [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='CT]  13 Jan 2023  Tangent categories as a bridge between  differential geometry and algebraic geometry  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Cruttwell∗ and Jean-Simon Pacaud Lemay†  January 16, 2023  Abstract  Discussions of tangent vectors, tangent spaces, and differentials are important in both differential  geometry and algebraic geometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' In this paper, we use the abstract notion of a tangent category to  make some of these commonalities precise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' In particular, we focus on the idea of a differential bundle in  a tangent category, which gives a new way to compare smooth vector bundles and modules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' The results  of this paper also give a new characterization of the opposite category of modules over a commutative  ring and the opposite category of quasicoherent sheaves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Contents  1  Introduction  2  2  Tangent Categories  4  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='1  Basics of Tangent Categories  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  4  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='2  Commutative rings as a Tangent Category .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  11  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='3  Affine schemes as a Tangent Category .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  14  3  Differential Bundles  18  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='1  Differential Bundles and Differential Objects  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  19  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='2  Differential Bundles as Pre-Differential Bundles .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  22  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='3  Morphisms and Categories of Differential Bundles .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  24  4  Differential Bundles for Commutative Rings  26  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='1  From Differential Bundles to Modules  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  26  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='2  From Modules to Differential Bundles  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  26  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='3  Equivalence .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  29  5  Differential Bundles for (Affine) Schemes  34  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='1  From Differential Bundles to Modules  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  34  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='2  From Modules to Differential Bundles  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  34  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='3  Equivalence .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  37  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='4  Differential bundles in schemes .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  42  6  Future work  44  ∗Partially supported by an NSERC Discovery grant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  †For this research, author was financially supported by NSERC Postdoctoral Fellowship - Award #: 456414649 and a JSPS  Postdoctoral Fellowship, Award #: P21746  1  1  Introduction  What exactly is the relationship between differential geometry and algebraic geometry?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' While there are  many differences between these two subjects, one common thread is the use of “differential” methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Indeed, discussions of tangent vectors, tangent spaces, and differentials are important in both subjects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' A  natural question to ask then is: can we precisely relate and contrast how differential geometry and algebraic  geometry use these ideas?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' This paper gives one way to approach this question, via the theory of tangent  categories, and in particular through investigating differential bundles in tangent categories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Tangent categories were first introduced by Rosick´y in [25], and later generalized and further developed by  Cockett and Cruttwell in [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' A tangent category (Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='1) is a category equipped with an endofunctor  T which for every object A associates an object T(A) that “behaves like a tangent bundle” for A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' More  precisely, this behaviour is captured through various natural transformations related to the endofunctor T  which encode basic properties such as linearity of the derivative and symmetry of mixed partial derivatives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  The canonical example of a tangent category is the category of smooth manifolds, where the endofunctor  is the tangent bundle functor (Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' But there are many other interesting examples of tangent  categories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' In fact, almost any category which has some form of “differentiation” for its morphisms can be  given the structure of a tangent category.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Examples of tangent categories include:  Most generalizations of smooth manifolds form tangent categories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  The category of “convenient”  manifolds [19], the category of C∞ rings [20], and any model of synthetic differential geometry (SDG)  [18], all give tangent categories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Any Cartesian differential category [3], which formalizes differential calculus over Euclidean spaces,  gives a tangent category.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' In particular, there are many examples of Cartesian differential categories  from computer science, such as models of the differential lambda-calculus [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  The category of commutative rings and the category of commutative algebras are tangent categories,  with a particularly simple tangent structure induced by dual numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' This example will be discussed  in more detail below (Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  “Tangent infinity” categories model ideas in Goodwillie functor calculus [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  The theory of tangent categories is now well-established with a rich literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' There are also many things  one can do in an arbitrary tangent category.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' In particular, one can discuss:  Vector fields (Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='10), and prove important ideas such as the Jacobi identity [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  The analogue of vector bundles, known as differential bundles [8], which is one of the main structures  of focus in this paper (Section 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Connections on differential bundles and corresponding results such as the Bianchi identities and the  existence of geodesics [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Solutions to differential equations and dynamical systems [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Differential forms and de Rham cohomology [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  It is worth noting that translating these ideas from the category of smooth manifolds to an arbitrary tangent  category is not a trivial process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' The definition of a tangent category involves various natural transformations  which appear in the category of smooth manifolds, but are not generally seen as central to differential  geometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' In a tangent category, these natural transformations are the core part of the structure, and so  to translate a desired notion to an arbitrary tangent category, one must translate the definition to make  appropriate use of those natural transformations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' The fact that one can do so with many of the central  notions of differential geometry provides evidence that the abstract notion of a tangent category is indeed  a good categorical generalization of differential geometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' A central question of tangent category theory  2  is to understand what these notions look like in the various examples of tangent categories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' In categories  which generalize the category of smooth manifolds (such as convenient manifolds, or synthetic differential  geometry), these generally reconstruct existing definitions in these subjects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' But in other areas, what these  notions give is less obvious.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  One particular focus of this paper is examples of tangent categories in algebra and algebraic geometry,  and investigating what tangent structure definitions look like in these particular examples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' In particular,  categories of (affine) schemes (potentially over some fixed ring or scheme).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' All such categories are also tangent  categories, with the endofunctor given by the Spec of the symmetric algebra of the Kahler differentials of a  scheme, which is precisely what Grothendieck himself called the “tangent bundle” of a scheme [15, Definition  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='I].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' While this example was mentioned in [5], as a corollary to a more general result, the tangent  structure was not explored explicitly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' One of the contributions of this paper is an explicit description of the  natural transformations for this tangent structure (Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' This is a necessary component to further  understand how the theory of tangent categories applies to algebraic geometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Given this, then, the next  important question is: what do the concepts which can be applied to any tangent category give you when  applied to the algebraic geometry examples?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Do they recreate existing notions?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Do they give us new  perspectives on existing ideas?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  The main focus of this paper is on differential bundles (Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='1) in the examples of tangent cate-  gories in algebra and algebraic geometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Differential bundles are a central structure in tangent categories,  as they generalize smooth vector bundles in the category of smooth manifolds (Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' However,  intriguingly, they are defined quite differently than vector bundles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' The definition of a differential bundle  contains no mention of either vector spaces, a base field, or local triviality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Instead, their central structure is  the existence of a vertical lift, which is a map from the total space to its tangent bundle, which satisfies a key  universal property.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' That such a structure, when looked at in the category of smooth manifolds, gives exactly  smooth vector bundles [22], is already interesting enough, as structures like the vector spaces in each fibre,  and the local triviality, all come “for free” from the universality of the vertical lift.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' But what are differential  bundles in the tangent categories of (affine) schemes?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' It is not immediately obvious what they should be.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  The main objective of this paper is to answer this question, and in doing also providing new and interesting  results which hopefully opens up the possibility for many future investigations in this area.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' In summary, the  main results of this paper are that:  Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='5 and Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='7: In the tangent category of commutative rings, differential bundles  over a commutative ring R correspond to modules over R, and the category of differential bundles over  R is equivalent to the category of modules over R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Proposition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='5 and Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='7: In the tangent category of affine schemes (or equivalently the opposite  category of commutative rings), differential bundles over a commutative ring R correspond to modules  over R, and the category of differential bundles over R is equivalent to the opposite category of modules  over R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='17: In the tangent category of schemes, differential bundles over a scheme A correspond to  quasicoherent sheaves of modules over A, and the category of differential bundles over A is equivalent  to the opposite of the category of quasicoherent sheaves of modules over A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  These results are fascinating for several reasons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' For one, they show how diverse differential bundles can  be.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' In the canonical tangent category example of smooth manifolds, differential bundles are exactly smooth  vector bundles, which includes the strict condition of local triviality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' However, for these algebra or algebraic  geometry examples of tangent categories, differential bundles still give categories of central importance  (modules) but in which the objects have no sort of local triviality condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Independently, these results  are also interesting as they give a new characterization of these categories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' In particular, differential bundles  provide a novel characterization of the opposite of the category of (quasicoherent sheaves of) modules over  a commutative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' To the best of the authors’ knowledge, there is no known previous characterization of the  opposite of the category of modules for an arbitrary commutative ring (though there are some results in  3  special cases, like characterizations of the opposite category of Abelian groups).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  These results are thus  interesting in and of themselves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Even more promising than the results themselves is what future results and ideas they can lead to.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' As  described above, in any tangent category one can define and prove results about connections on such bundles;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  again, when applied to the tangent category of smooth manifolds, this recreates the usual notion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' But now  via tangent categories, we get a notion of connection on modules - what do these look like?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' What examples  of them are there?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Do they recreate existing notions of connections in algebraic geometry?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' We hope to  explore these questions in future work (Section 6), and continue to use these ideas to bridge the gap between  differential geometry and algebraic geometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Outline:  In section 2, we review the definition of tangent categories and explore some of their basic  examples and theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' We also explicitly describe the tangent structure of the category of (affine) schemes,  which as noted above, has not previously been given.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  In section 3, we recall the theory of differential  bundles in tangent categories, and review MacAdam’s characterization of differential bundles in the tangent  category of smooth manifolds [22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  In Section 4, we give our first major result: a characterization of  differential bundles in the tangent category of commutative rings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Section 5 contains our most important  results: characterizations of differential bundles in the tangent categories of affine schemes and schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' As  mentioned above, as far as we know, these results provide new characterizations of the opposites of categories  of (quasicoherent sheaves of) modules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Lastly, in Section 6, we describe future work that we hope to pursue  that builds on the ideas presented in this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Conventions:  We assume the reader is familiar with the basic notions of category theory such as categories,  opposite categories, functors, natural transformations, and (co)limits like (co)products, pullbacks, pushouts,  terminal/initial objects, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' In an arbitrary category, we denote identity maps as 1A : A −→ A, and we use  the classical notation for composition, g ◦ f, as opposed to diagrammatic order which was used in other  papers on tangent categories (such as in [5, 8] for example).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' For pullbacks and products (which recall are  specific kinds of pullbacks), we use πj for the projections and ⟨−, −⟩ for the pairing operation which is  induced by the universal property.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  2  Tangent Categories  In this section, we review the basics of tangent categories and provide full detailed descriptions of the main  tangent categories of interest for this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Tangent categories were first defined by Rosick´y [25], then later  generalized by Cockett and Cruttwell [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' We begin by providing the full definition of a tangent category, both  the Cockett and Cruttwell version without negatives (Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='1), and the Rosick´y version with negatives  (Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Afterwards, we provide a detailed description of the tangent categories of commutative  rings (Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='2) and (affine) schemes (Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='3), the latter of which has not been previously done in  full.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' We also discuss some basic, but important, concepts in these tangent categories, like tangent spaces  (Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='8) and vector fields (Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='1  Basics of Tangent Categories  The following definition of a tangent category is the one provided in [8, Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='1], which when compared  to the original definition provided in [5, Definion 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='3] is the same except for the universality of the vertical  lift which is presented as a pullback instead of an equalizer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' That said, these two axiomatizations are indeed  equivalent [8, Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='1 [5, Definion 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='3] A tangent structure on a category X is a sextuple T := (T, p, +, 0, ℓ, c)  consisting of:  (i) An endofunctor T : X −→ X, called the tangent bundle functor;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  4  (ii) A natural transformation pA : T(A) −→ A, called the projection, such that for each n ∈ N, the pullback  of n copies of pA exists, which we denote as Tn(A) with n projections πj : Tn(A) −→ T(A), for all  1 ≤ j ≤ n, so pA ◦ πj = pA ◦ πi for all 1 ≤ i, j ≤ n, and for all m ∈ N, Tm preserves these pullbacks;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  (iii) A natural transformation1 +A : T2(A) −→ T(A), called the sum;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  (iv) A natural transformation 0A : A −→ T(A), called the zero;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  (v) A natural transformation ℓA : T(A) −→ T2(A), called the vertical lift;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  (vi) A natural transformation cA : T2(A) −→ T2(A), called the canonical flip;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  and such that:  [T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='1] (pA, +A, 0A) is an additive bundle over A [5, Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='1],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' that is,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' the following diagrams commute:  T2(A)  πj  �  +A  � T(A)  pA  �  A  0A  �  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  T(A)  pA  �  T(A)  pA  � A  A  T3(A)  ⟨+A◦⟨π1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='π2⟩,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='π3⟩ �  ⟨π1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='+A◦⟨π2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='π3⟩⟩  �  T2(A)  +A  �  T(A)  ⟨0A◦pA,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='1T(A)⟩  �  ⟨1T(A),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='0A◦pA⟩  �  ❙  ❙  ❙  ❙  ❙  ❙  ❙  ❙  ❙  ❙  ❙  ❙  ❙  ❙  ❙  ❙  ❙  ❙  ❙  ❙  ❙  ❙  ❙  ❙  ❙  ❙  ❙  ❙  ❙  ❙  ❙  ❙  ❙  ❙  T2(A)  +A  �  T2(A)  +A  � T(A)  T2(A)  +A  � T(A)  T2(A)  +A  �◗  ◗  ◗  ◗  ◗  ◗  ◗  ◗  ◗  ◗  ◗  ◗  ◗  ◗  ⟨π2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='π1⟩  � T2(A)  +A  �  T(A)  (1)  [T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='2] The vertical lift ℓA preserves the additive bundle structure, that is, the following diagrams commute:  T(A)  ℓA  �  pA  �  T2(A)  T(pA)  �  A  0A  � T(A)  T2(A)  ⟨ℓA◦π1,ℓA◦π2⟩  �  +A  �  TT2(A)  T(+A)  �  A  0A  �  0A  �  T(A)  ℓA  �  T(A)  ℓA  � T2(A)  T(A)  T(0A)  � T2(A)  (2)  1Note that by the universal property of the pullback, it follows that we can define functors Tn : X −→ X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  5  [T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='3] The canonical flip cA preserves the additive bundle structure, that is, the following diagrams commute:  T2(A)  cA  �  T(pA)  �  T2(A)  pT(A)  �  T(A)  T2(A)  TT2(A)  ⟨cA◦T(π1),cA◦T(π2)⟩  �  T(+A)  �  T2T(A)  +T(A)  �  T(A)  T(0A)  �  T(A)  0T(A)  �  T2(A)  cA  � T2(A)  T2(A)  cA  � T2(A)  (3)  [T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='4] The following diagrams commute:  T2(A)  cA  �  ◗  ◗  ◗  ◗  ◗  ◗  ◗  ◗  ◗  ◗  ◗  ◗  ◗  ◗  ◗  ◗  ◗  ◗  ◗  ◗  ◗  ◗  ◗  ◗  ◗  ◗  ◗  ◗  T2(A)  cA  �  T3(A)  cT(A)  �  T(cA)  � T3(A)  cT(A)  � T3(A)  T(cA)  �  T2(A)  T3(A)  T(cA)  � T3(A)  cT(A)  � T3(A)  (4)  [T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='5] The following diagrams commute:  T(A)  ℓA  �  ℓA  �  T2(A)  ℓT(A)  �  T(A)  ℓA  �  ℓA  �■  ■  ■  ■  ■  ■  ■  ■  ■  T2(A)  cA  �  T2(A)  ℓT(A) �  cA  �  T3(A)  T(cA) � T3(A)  cT(A)  �  T2(A)  T(ℓA)  � T3(A)  T2(A)  T2(A)  T(ℓA)  � T3(A)  (5)  [T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='6] Universality of the vertical lift ℓA, that is, the following square is a pullback:  T2(A)  pA◦πj  �  νA  � T2(A)  T(pA)  �  A  0A  � T(A)  (6)  where νA : T2(A) −→ T2(A) is defined as follows:  νA := T2(A)  ⟨ℓ◦π1,0T(A)◦π2⟩ � TT2(A)  T(+A)  � T(A)  (7)  and such that the above pullback square is preserved by all Tn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  A tangent category is a pair (X, T) consisting of a category X equipped with a tangent structure T on X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Tangent categories formalize the properties of the tangent bundle on smooth manifolds from classical  differential geometry, as we will review in Examples 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='5 and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='6 below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' An object A should be interpreted  as a base space, and T(A) as its abstract tangent bundle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' The projection pA is the analogue of the natural  projection from the tangent bundle to its base space, making T(A) an abstract bundle over A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' The sum +A  and the zero 0A make T(A) into a generalized version of a smooth additive bundle, and so each fiber is a  6  commutative monoid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' To make this more precise, this notion is captured by the concept of an additive bundle  [5, Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='1], which can be defined in any arbitrary category.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Briefly, additive bundles are commutative  monoid objects in slice categories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' So in the case of a tangent category, pA is a commutative monoid in the  slice category over A with binary operation +A and unit 0A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' The pullbacks of n copies of pA is required to  sum multiple times, while preservation by Tm implies that Tm(pA) is also an additive bundle with Tm(+A)  and Tm(0A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' The top two diagrams in [T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='1] simply say that +A and 0A are maps in the slice category,  while the remaining three diagrams are the axioms of a commutative monoid: associativity of the sum, that  zero is a unit, and commutativity of the sum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  To explain the vertical lift, recall that in differential geometry, the double tangent bundle (that is, the  tangent bundle of the tangent bundle) admits a canonical sub-bundle called the vertical bundle which is  isomorphic to the tangent bundle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Thus, the vertical lift ℓA is an analogue of the embedding of the tangent  bundle into the double tangent bundle via the vertical bundle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' The canonical flip cA is an analogue of the  natural canonical flip, which is a smooth involution on the double tangent bundle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' The diagrams in [T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='2]  and [T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='3] say respectively that ℓA and cA are additive bundle morphisms [5, Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='2], that is, monoid  morphisms in the slice category over A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' The diagrams in [T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='4] express that the canonical flip cA is a sort of  symmetry map: the left diagram says that cA is a self-inverse isomorphism, while the right diagram is the  Yang-Baxter associativity identity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' The diagrams in [T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='5] are compatibility relations between the vertical lift  and canonical flip.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' The universality of the vertical lift in [T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='6] is essential for generalizing desired important  properties of the tangent bundle from differential geometry, see [5, Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='5] for more details on this  axiom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Lastly, for maps, T(f) is interpreted as the differential of f, and so the functoriality of T represents  the chain rule.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' The naturality of p says that T(f) is a bundle map between the tangent bundles, and the  naturality of + and 0 implies that T(f) preserves the additive structure, while the naturality of ℓ represents  that the differential is linear, and the naturality of c represents the symmetry of the partial differentials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  We now add negatives to the story and obtain Rosick´y’s original definition of a tangent category [25,  Section 2], which is essentially the same as the above definition but with an added natural transformation  which makes each fiber of the tangent bundle into an Abelian group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' In [5, 22], such a setting was simply  called a tangent category with negatives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Here, we introduce new terminology and call such a setting a  Rosick´y tangent category.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='2 [5, Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='3] A tangent structure with negatives on a category X is a septuple  T := (T, p, +, 0, ℓ, c, −) consisting of:  (i) A tangent structure (T, p, +, 0, ℓ, c) on X  (ii) A natural transformation −A : T(A) −→ T(A), called the negative;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  such that:  [T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='N] (pA, +A, 0A, −A) is an Abelian group bundle over A [25, Section 1], that is, the following diagrams  commute:  T(A)  −A  �  pA  �◗  ◗  ◗  ◗  ◗  ◗  ◗  ◗  ◗  ◗  ◗  ◗  ◗  ◗  ◗  T(A)  pA  �  T(A)  pA  �P  P  P  P  P  P  P  P  P  P  P  P  P  P  ⟨1T(A),−A⟩  �  ⟨−A,1T(A)⟩  �  T2(A)  +A  �  A  A  0A  �P  P  P  P  P  P  P  P  P  P  P  P  P  P  T2(A)  +A  � T(A)  (8)  A Rosick´y tangent category is a pair (X, T) consisting of a category X and tangent structure with negatives  T on X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  7  In a Rosick´y tangent category, the negative nA makes each fiber an Abelian group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' The left diagram of  [T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='N] says that the negative −A is a map in the slice category over A, while the right diagram is the extra  axiom about inverses required for Abelian groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' It is also worth mentioning that in a Rosick´y tangent  category, the universality of the vertical lift can be replaced with the following which expresses the vertical  lift as an equalizer [5, Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='13]:  [T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='6’] The following is an equalizer diagram:  T(A)  ℓA  � T2(A)  pT(A)  �  T(pA)  �  pT(A)  � T(A)  pA  � A  0A  � T(A)  (9)  and such that the above equalizer is preserved by all Tn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Furthermore, in a Rosick´y tangent category, the vertical lift ℓA and the canonical flip cA also preserve  the group structure, that is, they are Abelian group bundle morphisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Indeed, recall that in classical  group theory that morphisms which preserve the group’s addition also preserve inverses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' The same is true  for Abelian group bundles in the sense that additive bundle morphisms between Abelian group bundles  automatically also preserve inverses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Explicitly:  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='3 In a Rosick´y tangent category (X, T), the following diagrams commute:  T(A)  ℓA  �  −A  �  T2(A)  T(−A)  �  T2(A)  cA  �  T(−A)  �  T2(A)  −T(A)  �  T(A)  ℓA  � T2(A)  T2(A)  cA  � T2(A)  (10)  We now discuss Cartesian tangent categories, which are tangent categories that also have finite products  which are compatible with the tangent structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' The extra coherences for a Cartesian tangent category  ensure that the tangent bundle of a product is naturally isomorphic to the product of the tangent bundles  and that the tangent bundle of the terminal object is the terminal object.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='4 [5, Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='8] A Cartesian (Rosick´y) tangent category is a (Rosick´y) tangent  category (X, T) such that X has finite products, with binary product × and terminal object ∗, and that the  canonical natural transformation ⟨T(π1), T(π2)⟩ : T(A × B) −→ T(A) × T(B) is a natural isomorphism, and  the unique map T(∗) −→ ∗ is an isomorphism, so T(A × B) ∼= T(A) × T(B) and T(∗) ∼= ∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  The main example of a (Cartesian) tangent category is the category of smooth manifolds, where the  tangent structure is induced by the tangent bundle of a smooth manifold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' This example provides a direct  link between tangent categories and differential geometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Here we review in full the tangent structure on  the subcategory of Euclidean spaces, as it is simpler to describe in detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' For lists of other examples of  tangent categories see [8, Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='2] and [14, Example 2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='5 The category of Euclidean spaces and smooth functions is a Cartesian Rosick´y tangent cate-  gory where the tangent structure is induced by the total derivative of smooth functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Let SMOOTH be the  category whose objects are Euclidean spaces Rn and whose maps are smooth functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' SMOOTH has finite  products where the binary product is given by the standard Cartesian product, Rm×Rn = Rm+n, and where  the terminal object is the singleton, R0 = {0}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' To define the tangent structure, recall that for a smooth  8  function F : Rm −→ Rn, which is actually an n-tuple F = ⟨f1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' , fn⟩ of smooth functions fi : Rm −→ R, that  the total derivative of F is the smooth function D[F] : Rm × Rm −→ Rn defined as the sum of the partial  derivatives of the fi:  D[F](⃗x, ⃗y) =  � m  �  j=1  ∂f1  ∂uj  (⃗x)yj, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' ,  m  �  j=1  ∂fn  ∂uj  (⃗x)yj  �  The total derivative D[F] can also be expressed in terms of the Jacobian of F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' We define a Rosick´y tangent  structure T on SMOOTH as follows:  (i) The endofunctor T : SMOOTH −→ SMOOTH is defined on a Euclidean space as T(Rn) = Rn × Rn and  on a smooth function F : Rm −→ Rn as the smooth function T(F) : Rm × Rm −→ Rn × Rn defined as:  T(F)(⃗x,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' ⃗y) =  �  F(⃗x),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' D[F](⃗x,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' ⃗y)  �  (ii) The projection pRn : Rn × Rn −→ Rn is defined as the projection of the first component:  pRn(⃗x,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' ⃗y) = ⃗x  (iii) The pullback of m copies of pRn is given by taking the product of m + 1 copies of Rn:  Tm(Rn) = Rn × .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' × Rn  �  ��  �  m+1 times  and where the projection πj : Tm(Rn) −→ Rn × Rn projects out the first and j-th components:  πj(⃗x, ⃗y1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' ⃗  ym) = (⃗x,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' ⃗yj)  (iv) The sum +Rn : Rn × Rn × Rn −→ Rn × Rn adds the second and third components:  +Rn(⃗x,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' ⃗y,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='⃗z) = (⃗x,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' ⃗y + ⃗z)  (v) The zero 0Rn : Rn −→ Rn × Rn inserts the zero vector into the second component:  0Rn(⃗x) = (⃗x,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='⃗0)  (vi) The vertical lift ℓRn : Rn × Rn −→ Rn × Rn × Rn × Rn inserts zero vectors into the middle components:  ℓRn(⃗x,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' ⃗y) = (⃗x,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='⃗0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='⃗0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' ⃗y)  (vii) The canonical flip cRn : Rn × Rn × Rn × Rn −→ Rn × Rn × Rn × Rn flips the middle two components:  cRn(⃗x,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' ⃗y,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='⃗z,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' ⃗w) = (⃗x,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='⃗z,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' ⃗y,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' ⃗w)  (viii) The negative −Rn : Rn × Rn −→ Rn × Rn makes the second component negative:  −Rn(⃗x,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' ⃗y) = (⃗x,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' −⃗y)  So T = (T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' s,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' z,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' l,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' c,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' n) is a tangent structure with negatives on SMOOTH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Lastly, we also have that  Rn × Rn × Rm × Rm ∼= Rn × Rm × Rn × Rm and R0 × R0 ∼= R0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' So (SMOOTH, T) is a Cartesian Rosick´y  tangent category.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' In fact, SMOOTH is a Cartesian differential category [3], and every Cartesian differential  category is a Cartesian tangent category by generalizing the above construction [5, Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  9  Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='6 The category of smooth manifolds is a Cartesian Rosick´y tangent category where the tangent  structure is given by the classical tangent bundle (here we follow [27, Defn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='9] and allow our manifolds  to have different dimensions in different connected components).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Let SMAN be the category whose objects  are (finite-dimensional real) smooth manifolds M and whose maps are smooth functions between them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' For  a smooth manifold M, for each point x ∈ M let Tx(M) be the tangent space at x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Then recall that the  tangent bundle of M is the smooth manifold T(M) which is the (disjoint) union of each tangent space:  T(M) :=  �  x∈M  Tx(M)  This induces a functor T : SMAN −→ SMAN which is part of a tangent structure with negatives T on SMAN,  which in local coordinates is defined in the same way as in Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' So (SMAN, T) is a Cartesian Rosick´y  tangent category, for which (SMOOTH, T) is a sub-Cartesian Rosick´y tangent category.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  There are many ways to make new tangent categories from existing ones, but one of the most fundamental  (assuming the existence of certain well-behaved limits) is by slicing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  We will use this construction, in  particular, to construct tangent categories of algebras from tangent categories of rings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='7 [5, Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='5] Suppose that (X, T) is a tangent category, and A is an object of X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Then the slice category X/A can be given the structure of a tangent category, where the tangent bundle of an  object f : X −→ A, TA(f), is given by the pullback  TA(f)  �  �  T X  T (f)  �  A  0A  � T A  (assuming such pullbacks exist and are preserved by each T n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  We end this section by reviewing two simple concepts from differential geometry that can be generalized  to any (Cartesian) tangent category: vector fields and tangent spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' In the examples above, vector fields  and tangent spaces correspond precisely to their namesakes from classical differential geometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Below, we  will also discuss these tangent spaces and vector fields for the tangent categories of commutative rings and  (affine) schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Recall that in a category with finite products, a point of an object A is a map from the terminal object  to A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' In a Cartesian tangent category, the tangent space at a point is given by the pullback (if it exists) of  said point and tangent structure projection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='8 [5, Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='13] In a Cartesian tangent category (X, T), if A is an object of X and  a : ∗ −→ A is a point of A, then the tangent space of A at a is an object Ta(A) equipped with a map  πa : Ta(A) −→ T(A) such that the following diagram is a pullback:  Ta(A)  πa  �  �  T(A)  pA  �  ∗  a  � A  and is preserved by all Tn for all n ∈ N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='9 In SMOOTH, a point of Rn in the categorical sense corresponds precisely to elements of  ⃗x ∈ Rn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' So in (SMOOTH, T), the tangent space of Rn at ⃗x ∈ Rn is T⃗x(Rn) = Rn and π⃗x : Rn −→ Rn × Rn  is defined as the injection π⃗x(⃗y) = (⃗x, ⃗y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Similarly, in SMAN, a point of a smooth manifold M in the  categorical sense is precisely a point x ∈ X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' So in (SMAN, T), the tangent space of M at x ∈ M is the  classical tangent space Tx(M) = M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  10  Tangent spaces are commutative monoid objects, where monoid structure is induced by the tangent  bundle [5, Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='15], and in a Cartesian Rosick´y tangent category, tangent spaces are also Abelian  group objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' The category of tangent spaces is a Cartesian differential category [5, Corollary 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Also  observe that, trivially, for the terminal object ∗ the only point is the identity 1∗ : ∗ −→ ∗ and that T1∗(∗) = ∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  We now turn our attention to vector fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' In a tangent category, a vector field is simply a section of the  tangent bundle’s projection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='10 [5, Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='1] In a tangent category (X, T), a vector field on an object A of X is a  map v : A −→ T(A) which is a section of pA, that is, the following diagram commutes:  A  v  �  P  P  P  P  P  P  P  P  P  P  P  P  P  P  P  P  P  P  P  P  P  P  P  P  P  P  P  P  P  P  T(A)  pA  �  A  Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='11 In (SMOOTH, T), a vector field on Rn is given by a smooth function v : Rn −→ Rn ×Rn such  that v(⃗x) = (⃗x, f(⃗x)) for some smooth functions f : Rn −→ Rn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Therefore, vector fields in (SMOOTH, T)  correspond precisely to endomorphisms in SMOOTH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' In (SMAN, T), vector fields in the tangent category  sense correspond precisely to vector fields in the usual sense.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  In any tangent category, the zero 0A : A −→ T(A) is a vector field, and the map νA : T2(A) −→ T2(A)  from [T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='6] induces a vector field for the tangent bundle LA : T(A) −→ T2(A) which generalizes the canonical  vector field on the tangent bundle, also called the Liouville vector field [5, Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' One can also define  the sum of vector fields using the sum + [5, Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='2], as well as a new category whose objects are  vector fields and whose maps commute with vector fields in the obvious way [9, Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='8], and said  category of vector fields is also a tangent category [9, Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' In a Rosick´y tangent category, it  is possible to define the Lie Bracket of vector fields [5, Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='14], which in particular also satisfies the  Jacobi identity [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Vector fields can also be used to describe differential equations, dynamical systems, and  their solutions in a tangent category [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  There are numerous other interesting properties and concepts that one can discuss in a tangent category  such as the fact the tangent bundle functor T admits a canonical monad structure [5, Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='4] or  the notion of a representable tangent category [5, Section 5], which provides a link to synthetic differential  geometry (SDG).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Furthermore, there are many other concepts from differential geometry that one can  generalize to a tangent category, such as connections [7], and de Rham cohomology [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='2  Commutative rings as a Tangent Category  In this section, we provide a full description of the tangent category of commutative rings, whose tangent  bundle is given by the ring of dual numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' This was one of the main examples in Rosick´y’s original paper  [25, Example 2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  By a commutative ring, we mean a commutative, unital, and associative ring.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  For a  commutative ring R and a, b ∈ R, we denote the addition by a + b, the zero by 0 ∈ R, the negation by −a,  the multiplication by ab, and the unit by 1 ∈ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Let CRING be the category whose objects are commutative  rings and whose maps are ring morphisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  For a commutative ring R, its ring of dual numbers is the commutative ring R[ε] defined as follows:  R[ε] = {a + bε| ∀a, b ∈ R, ε2 = 0}  where a and bε will be used respectively as shorthand for a + 0ε and 0 + bε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Then R[ε] is a commutative  ring with multiplication induced by ε2 = 0, that is, the addition, multiplication, and negative are defined  respectively as follows:  (a + bε) + (c + dε) = (a + c) + (b + d)ε  (a + bε)(c + dε) = ac + (ad + bc)ε  −(a + bε) = −a − bε  and where the zero is 0 and the unit is 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Using the ring of dual numbers, we define a tangent structure with  negatives  T  = (  T  , p, +, 0, ℓ, c, −) on CRING.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  11  (i) The endofunctor  T  : CRING −→ CRING maps a commutative ring R to its ring of dual numbers  T  (R) = R[ε] and a ring morphism f : R −→ S is sent to the ring morphism  T  (f) : R[ε] −→ S[ε] defined  as follows:  T  (f)(a + bε) = f(a) + f(b)ε  (ii) The projection pR : R[ε] −→ R sends ε to zero,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' and so is defined as projecting out the first component:  pR(a + bε) = a  To describe the pullbacks of the projection,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' first recall that CRING is a complete category,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' and therefore  all pullbacks exist in CRING.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' In particular, if R and R′ are commutative rings, then for any ring morphism  f : R′ −→ R, the general construction of a pullback of n copies of f in CRING is given by:  R′  n = {(x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' , xn)| xj ∈ E s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' f(xi) = f(xj) for all 1 ≤ i, j ≤ n}  and whose ring structure is given coordinate-wise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' However for the projection of the ring of dual numbers,  one can instead describe these pullbacks in terms of multivariable dual numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' So for a commutative ring  R, define R[ε1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' , εn] as follows:  R[ε1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' , εn] = {a + b1ε1 + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' + bnεn| ∀a, bi ∈ R and εiεj = 0}  Then R[ε1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' , εn] is a commutative ring whose structure is defined in the obvious way, so in particular the  multiplication is induced by εiεj = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' We leave it as an exercise for the reader to check for themselves that  R[ε1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' , εn] is indeed isomorphic to the pullback of n copies of pR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' So we can continue to describe the  tangent structure as follows:  (iii) The pullback of n copies of pR is given by  T  n(R) = R[ε1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' , εn] and where πj : R[ε1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' , εn] −→ R[ε]  sends εj to ε and the other nilpotents to zero, that is, πj projects out the first component and j-th  nilpotent component:  πj(a + b1ε1 + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' + bnεn) = a + bjε  (iv) The sum +R : R[ε1, ε2] −→ R[ε] maps both ε1 and ε2 to ε, which results in adding the nilpotent parts  together:  +R(a + bε1 + cε2) = a + (b + c)ε  (v) The zero 0R : R −→ R[ε] is the injection of R into its ring of dual numbers:  0R(a) = a  (vi) The negative −R : R[ε] −→ R[ε] maps ε to −ε, which results in making the nilpotent part negative:  −R(a + bε) = a − bε  It may be worth briefly discussing what additive bundles and Abelian group bundles are in CRING.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  In  fact, Abelian group bundles in CRING were characterized by Beck in [2, Example 8], where it was explained  that Abelian group bundles over a commutative ring are equivalent to modules over said commutative ring.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Furthermore, it turns out that in CRING, additive bundles are always Abelian group bundles, so we also get  an equivalence between additive bundles and modules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  To describe the vertical lift and the canonical flip, let us first describe  T  2(R), the ring of dual numbers  of the ring of dual numbers in terms of two nilpotent elements ε and ε′:  T  2(R) = R[ε][ε′] = {a + bε + cε′ + dεε′| ∀a, b, c, d ∈ R and ε2 = ε′2 = 0}  where the multiplication is induced by ε2 = ε′2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' So we define:  12  (vii) The vertical lift ℓR : R[ε] −→ R[ε][ε′] maps ε to ε′, and so maps the nilpotent component to the outer  nilpotent component:  ℓR(a + bε) = a + bεε′  (viii) The canonical flip cR : R[ε][ε′] −→ R[ε][ε′] swaps ε and ε′, and so interchanges the middle nilpotent  components:  cR(a + bε + cε′ + dεε′) = a + cε + bε′ + dεε′  So  T  = (  T  , p, +, 0, ℓ, c, −) is a tangent structure with negatives on CRING.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Also, CRING has finite products  where the binary product is given by the Cartesian product of rings R×S, where recall that the ring structure  is given pointwise, and where the terminal object is the zero ring 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' We also have that (R×S)[ε] ∼= R[ε]×S[ε]  and 0[ε] ∼= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' So we have that:  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='12 (CRING,  T  ) is a Cartesian Rosick´y tangent category.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='13 This tangent category construction nicely generalizes to other natural settings:  Instead of commutative rings, we could have considered commutative semirings (also called rigs, for  rings without negatives), which are of particular interest throughout all of computer science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' So the  category of commutative semirings will be a Cartesian tangent category via dual numbers, but not a  Rosick´y tangent category since we dropped negatives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  For any commutative (semi)ring R, the category of commutative R-algebras will also be a Cartesian  tangent category;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' this follows from Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  The Eilenberg-Moore category of a codifferential category (or dually the opposite category of the  coEilenberg-Moore category of a differential category) is a Cartesian tangent category [10, Theorem  22], whose tangent structure is indeed a generalization of the above dual numbers tangent structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' In  fact, these tangent categories of commutative (semi)rings/algebras are precisely the Eilenberg-Moore  categories of the appropriate polynomial models of codifferential categories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  We conclude this section by discussing tangent spaces and vector fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  We first explain how in  (CRING,  T  ), there are no non-trivial tangent spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Indeed, since the zero ring 0 is the terminal object, a  point of a commutative ring R would be a ring morphism of type f : 0 −→ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' However, since ring morphisms  are required to preserve the unit and zero, and these are the same in the zero ring, we would have that  1 = f(1) = f(0) = 0, which implies 1 = 0 in R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' But the zero ring is the only ring for which the zero and  unit are equal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Therefore, it follows that the only ring morphism with domain 0 is the identity 10 : 0 −→ 0,  and the tangent space at this point is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='14 In (CRING,  T  ), the only commutative ring with a tangent space at a point is the zero ring 0  at the identity 10 : 0 −→ 0, and  T  10(0) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Next we discuss vector fields in (CRING,  T  ) and explain how they correspond precisely to derivations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Recall that for a commutative ring R, a derivation on R is a linear map D : R −→ R which satisfies the product  rule: D(ab) = aD(b) + D(a)b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' A commutative differential ring is a pair (R, D) consisting of a commutative  ring R and derivation D on R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' On the other hand, for a commutative ring R, a vector field on R is a ring  morphism v : R −→ R[ε] such that pR ◦v = 1R, which implies that v(a) = a+Dv(a)ε for some Dv : R −→ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' It  is a well-known result that ring morphisms v : R −→ R[ε] such that pR ◦ v = 1R, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' vector fields, correspond  precisely to derivations on R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Indeed, if v is a vector field, then since it preserves the multiplication, it follows  that Dv satisfies the product rule.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Thus Dv is a derivation and (R, Dv) is a commutative differential ring.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Conversely, given a derivation D : R −→ R on R, define the vector field vD : R −→ R[ε] as vD(a) = a + D(a)ε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Since these constructions are inverses of each other, we obtain the desired equivalence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='15 For a commutative ring R, vector fields on R in (CRING,  T  ) are in bijective correspondence  with derivations on R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  13  Therefore, it follows that the category of vector fields of (CRING,  T  ) is equivalent to the category of  commutative differential rings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Thus by [9, Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='10], the category of commutative differential rings  is also a Cartesian Rosick´y tangent category, whose tangent structure is induced by dual numbers as above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Lastly, the tangent category Lie bracket corresponds precisely to the standard Lie bracket of derivations,  [D1, D2] = D1 ◦ D2 − D2 ◦ D1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='3  Affine schemes as a Tangent Category  In this section, we discuss the tangent categories of (affine) schemes, where the tangent structure is induced  by K¨ahler differentials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' In this paper, by the category of affine schemes we mean the opposite category of  commutative rings CRINGop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' As such, we will be working directly with CRINGop, so we will write in terms  of commutative rings R instead of affine schemes Spec(R).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' So in this section, we provide a full description of  the tangent structure on CRINGop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' While CRINGop has been mentioned as an example of a tangent category  in other papers [5, 14], a full explicit description of its tangent structure has not previously been given in  the literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' We provide such a description here as it will both be useful for the story of this paper, and  for future work on applications of tangent category theory in algebraic geometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  To give a tangent structure with negatives on CRINGop, we must give a “co-tangent structure with nega-  tives” on CRING.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Explicitly, this means giving a functor T : CRING −→ CRING and natural transformations,  and so in particular ring morphisms, of type: pR : R −→ T(R), +R : T(R) −→ T2(R), 0R : T(R) −→ R,  ℓR : T2(R) −→ T(R), cR : T2(R) −→ T2(R), and −R : T(R) −→ T(R).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  For a commutative ring R, its tangent bundle T(R) is the free symmetric R-algebra over its modules of  K¨ahler differentials Ω(R):  T(R) := SymR  �  Ω(R)  �  =  ∞  �  n=0  Ω(R)⊗s  R  n = R ⊕ Ω(R) ⊕  �  Ω(R) ⊗s  R Ω(R)  �  ⊕ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  where ⊗s  R is the symmetrized tensor product over R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' In [15, Definition 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='I], Grothendieck calls T(R)  the “fibr´e tangente” (French for tangent bundle) of R, while in [17, Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='6], Jubin calls T(R) the tangent  algebra of R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' For the story of this paper, it will be useful to have a more explicit description of T(R).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' So  equivalently, T(R) is the free R-algebra generated by the set {d(a)| a ∈ R} modulo the equations:  d(1) = 0  d(a + b) = d(a) + d(b)  d(ab) = ad(b) + bd(a)  which are the same equations that are modded out to construct the module of K¨ahler differentials of R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Thus,  an arbitrary element of T(R) is a finite sum of monomials of the form ad(b1) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' d(bn).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' So the ring structure of  T(R) is essentially the same as polynomials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Furthermore, T(R) also has a universal property similar to that  of the module of K¨ahler differentials, but instead for algebras.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' For a commutative R-algebra A, a derivation  evaluated in A is a linear map D : R −→ A which satisfies the product rule D(ab) = a · D(b) + b · D(a), where  is the R-module action on A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Now T(R) is a commutative R-algebra A via the R-module action given by  multiplication, a · w = aw for a ∈ R and w ∈ T(R).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Then the map d : R −→ T(R), which maps a to d(a), is  a derivation and is universal in the sense that for any commutative R-algebra A equipped with a derivation  D : R −→ A, there exists a unique R-algebra morphism D♭ : T(R) −→ A such that D♭(d(a)) = D(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='16 In may be useful to work out some basic examples of tangent bundles:  (i) For the ring of integers Z, its tangent bundle is itself: T(Z) = Z  (ii) For the polynomial ring in n-variables Z[x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' , xn], its tangent bundle is the 2n-variable polynomial  ring: T(Z[x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' , xn]) = Z[x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' , xn, d(x1), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' , d(xn)], with no added assumptions on the variables  d(xi);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  (iii) For coordinate rings of varieties, that is, the polynomial rings quotiented by some finitely generated ideal  Z[x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' , xn]/⟨p(⃗x), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' , q(⃗x)⟩, its tangent bundle is the polynomial ring’s tangent bundle quotiented  14  by the ideal generated by the same polynomials and their total derivatives:  T  �  Z[x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' , xn]/⟨p(⃗x), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' , q(⃗x)⟩  �  =Z[x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' , xn, d(x1), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' , d(xn)]/⟨p(⃗x), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' , q(⃗x), d(p)(⃗x), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' , d(q)(⃗x)⟩  For example, for Z[x, y]/⟨x2 − xy2⟩, its the tangent bundle is:  T  �  Z[x, y]/⟨x2 − xy2⟩  �  = Z[x, y, d(x), d(y)]/⟨x2 − xy2, 2xd(x) − y2d(x) − 2xyd(y)⟩  To define the necessary ring morphisms for the tangent structure, note that T(R) is generated by a and  d(a), for all a ∈ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Therefore, to define ring morphisms with domain T(R), it suffices to define them on  generators a and d(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Using this to our advantage, we can define a tangent structure on CRINGop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  (i) The endofunctor T : CRING −→ CRING maps a commutative ring R to its tangent bundle T(R) as  defined above, and a ring morphism f : R −→ S is sent to the ring morphism T(f) : T(R) −→ T(S)  defined as on generators as follows:  T(f)(a) = f(a)  T(f)(d(a)) = d(f(a))  (ii) The projection pR : R −→ T(R) is defined as the injection of R into T(R):  pR(a) = a  We also need the pullback of n copies of pR in CRINGop, which means that we need the pushout of n  copies of pR in CRING.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Recall that CRING is cocomplete, and therefore admits all pushouts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' To describe  the desired pushout, note that for commutative rings R and R′, any ring morphism f : R −→ R′ induces an  R-algebra structure on R′ via the R-module action a · x = f(a)x for all a ∈ R and x ∈ R′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Therefore, the  pushout of n-copies of f : R −→ R′ is given by taking the tensor product over R of n copies of R′ viewed as  an R-moudle: R′  n := R′ ⊗R .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' ⊗R R′  �  ��  �  n times  , where ⊗R is the tensor product over R of R-modules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' The induced  R-algebra structure on T(R) via pR is precisely given by multiplication, as described above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  (iii) The pushouts of n copies of pR is given by Tn(R) := T(R) ⊗R .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' ⊗R T(R)  �  ��  �  n times  and where the pushout  injections πj : T(R) −→ Tn(R) injects T(R) into the j-th component:  πj(w) = 1 ⊗R .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' ⊗R 1 ⊗R w ⊗R 1 ⊗R .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' ⊗R 1  To describe the sum, zero, and negative, let us first explain what additive bundles and Abelian group  bundles are in CRINGop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' An additive bundle over R in CRINGop corresponds precisely to a commutative R-  bialgebra over the tensor product ⊗R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' The sum and zero of the additive bundle are the comultiplicaiton and  counit respectively of the R-coalgebra structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' The fact that they are ring morphisms and they commute  with the additive bundle’s projection will further imply that we obtain a commutative R-bialgebra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' An  Abelian group bundle over R in CRINGop corresponds precisely to a commutative R-Hopf algebra over the  tensor product ⊗R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' The negative of the Abelian group bundle gives the antipode for the R-Hopf algebra  structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' So to give the sum, zero, and negative for our tangent structure, we must give a R-Hopf algebra  structure on the tangent bundle T(R).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Luckily, free symmetric R-algebras have a canonical commutative  R-Hopf algebra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  (iv) The sum +R : T(R) −→ T(R) ⊗R T(R) is given by the comultiplication of the canonical R-coalgebra  structure of free symmetric R-algebras,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' that is,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' defined on generators as follows:  +R(a) = a ⊗R 1 = 1 ⊗R a  +R(d(a)) = d(a) ⊗R 1 + 1 ⊗R d(a)  15  (v) The zero 0R : T(R) −→ R is the counit of the canonical R-coalgebra structure of free symmetric  R-algebras,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' that is,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' defined on generators as follows:  0R(a) = a  0R(d(a)) = 0  (vi) The negative −R : T(R) −→ T(R) is the antipode of the canonical R-Hopf algebra structure of free  symmetric R-algebras,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' that is,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' defined on generators as follows:  −R(a) = a  −R(d(a)) = −d(a)  To describe the vertical lift and the canonical flip,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' let us first describe T2(R) as the free commutative  R-algebra over the set {d(a)| a ∈ R} ∪ {d′(a)| a ∈ R} ∪ {d′d(a)| a ∈ R},' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' modulo the relations:  d(1) = 0  d(a + b) = d(a) + d(b)  d(ab) = ad(b) + bd(a)  d′(1) = 0  d′(a + b) = d′(a) + d′(b)  d′(ab) = ad′(b) + bd′(a)  d′d(1) = 0  d′d(a + b) = d′d(a) + d′d(b)  d′d(ab) = d(b)d′(a) + ad′d(b) + d(a)d′(b) + bd′d(a)  These relations say that d and d′ are derivations,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' and that d′d is the composite of derivations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Therefore, to  define a ring morphism with domain T2(R), it suffices to define it on the four types of generators a, d(a),  d′(a), and d′d(a) for a ∈ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  (vii) The vertical lift ℓR : T2(R) −→ T(R) is defined on generators as follows:  ℓR(a) = a  ℓR(d(a)) = 0  ℓR(d′(a)) = 0  ℓR(d′d(a)) = d(a)  (viii) The canonical flip cR : T2(R) −→ T2(R) is defined on generators as follows:  cR(a) = a  cR(d(a)) = d′(a)  cR(d′(a)) = d(a)  cR(d′d(a)) = d′d(a)  So T = (T, p, +, 0, ℓ, c, −) is a tangent structure with negatives on CRINGop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Also, CRING has finite coprod-  ucts where the binary coproduct is given by the tensor product of rings R ⊗ S and where the initial object is  the ring of integers Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Thus CRINGop has finite products.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Since one has that Ω(R⊗S) ∼= R⊗Ω(S)⊕S⊗Ω(R)  and Ω(Z) ∼= 0, it follows that that T(R ⊗ S) ∼= T(R) ⊗ T(S) and T(Z) ∼= Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' So we have that:  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='17 (CRINGop, T) is a Cartesian Rosick´y tangent category.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='18 It is worth mentioning that the tangent structures for commutative rings and the tangent  structure for affine schemes are related to one another via the adjoint tangent structure theorem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Per [5,  Proposition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='17], if the tangent bundle of a tangent category has a left adjoint, then this induces a tangent  structure on the opposite category where the left adjoint is the tangent bundle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' This is precisely what is  happening between the tangent categories (CRING,  T  ) and (CRINGop, T).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Indeed, T : CRING −→ CRING is a  left adjoint to  T  : CRING −→ CRING, so we have a natural bijective correspondence between ring morphisms  of type R −→ R′[ε] and T(R) −→ R′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Explicitly, given a ring morphism f : R −→ R′[ε], which is of the  form f(a) = f1(a) + f2(a)ε, define the ring morphism f ♯ : T(R) −→ R′ on generators as f ♯(a) = f1(a)  and f ♯(d(a)) = f2(a), and conversely, given a ring morphism g : T(R) −→ R′, define the ring morphism  g♭ : R −→ R′[ε] as: g♭(a) = g(a) + g(d(a))ε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Furthermore, (CRINGop, T) is not only a Cartesian Rosick´y  tangent category but also a representable tangent category [5, Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Briefly, a representable tangent  category is a Cartesian category whose tangent bundle functor T is a representable functor T ∼= (−)D for  some object D, that is, T is a right adjoint for the functor ×D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' The object D is called the infinitesimal object  [5, Definition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='6], and note that the opposite category of a representable category is a tangent category with  tangent bundle functor  × D (where × becomes a coproduct in the opposite category).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' (CRINGop, T) is a  representable tangent category where the infinitesimal object is the ring dual of numbers for the integers,  Z[ε].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' So we have that T(R) ∼= RZ[ε] in CRINGop, and  T  (R) ∼= R ⊗ Z[ε] in CRING.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  16  Using Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='7, we then get that for each commutative ring R, the slice category CRINGop/R is  also a tangent category.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' But as is well-known, this slice category is equal to the (opposite of) the category  of commutative R-algebras.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Thus we have:  Corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='19 For any commutative ring R, the opposite of the category of algebras over R, (CALGR)op  is a Cartesian Rosick´y tangent category, with tangent functor given as in Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  In particular, this tangent structure on objects is given by (the symmetric algebra of) the “relative” Kahler  differentials: this is the same construction as seen earlier in this section, except with d(r) = 0 for all r ∈ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='20 There are also other ways to generalize the tangent category structure of CRINGop:  The opposite category of commutative semirings and the opposite category of commutative algebras  over a commutative (semi)ring will be representable tangent categories via K¨ahler differentials in a  similar fashion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  The coEilenberg-Moore category of a differential category (or dually the opposite category of the  Eilenberg-Moore category of a codifferential category) is a (representable) tangent category [10, The-  orem 26], and these tangent categories of opposite categories of commutative (semi)rings/algebras  are precisely the coEilenberg-Moore categories of the appropriate polynomial models of differential  categories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  The category of schemes SCH is also a Cartesian Rosick´y tangent category in a similar fashion to the  category of affine schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Indeed, recall that a scheme is by definition the gluing of affine schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' So the  tangent bundle of a scheme is defined as the gluing of the tangent bundles of each affine piece of the said  scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Full details can be found in [14, Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' (iii)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='21 (SCH, T) is a Cartesian Rosick´y tangent category.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  As with affine schemes, we can apply Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='7 to tangent structure on each category of relative  schemes:  Corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='22 For each scheme A, the slice category SCH/A has the structure of a Cartesian Rosick´y  tangent category.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  We now discuss tangent spaces in (CRINGop, T).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' The terminal object in CRINGop is the initial object  in CRING, which is the integers Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' So for a commutative ring R, a point of R in CRINGop corresponds to  a ring morphism r : R −→ Z, which are better known as augmentations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Thus a tangent space of R at a  point r in (CRINGop, T) corresponds to the pushout of r and pR in CRING.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' This essentially amounts to  applying r on the R parts of the tangent bundle T(R).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' So let im(r) = {r(a)| ∀a ∈ R} be the image of r,  which is a sub-ring of Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Then the tangent space Tr(R) can explicitly be described as the free commutative  im(r)-algebra generated by the set {d(a)| a ∈ R} modulo the equations:  d(1) = 0  d(a + b) = d(a) + d(b)  d(ab) = r(a)d(b) + r(b)d(a)  So an arbitrary element of Tr(R) is a finite sum of monomials of the form r(a)d(b1) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' d(bn).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='23 Here are some examples of tangent spaces:  (i) The only point for Z is the identity, and T1Z(Z) = Z;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  (ii) For the polynomial ring in n-variables Z[x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' , xn], points correspond precisely to evaluating polyno-  mials at a point ⃗a ∈ Zn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' However, for any point, the tangent space at that point is the polynomial ring  in n-variables, T⃗a(Z[x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' , xn]) = Z[d(x1), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' , d(xn)];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  17  (iii) For a polynomial ring quotiented by a finitely generated ideal Z[x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' , xn]/⟨p(⃗x), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' , q(⃗x)⟩, points  correspond to points ⃗a ∈ Zn which are solutions to p(⃗a) = 0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=', q(⃗a) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' The resulting tangent  bundle is the polynomial ring in n-variables quotiented by the ideal generated by the evaluation of  the polynomials d(p)(⃗x), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' , d(q)(⃗x) in the xi variables at ⃗a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' For example, for Z[x, y]/⟨xy⟩, its tangent  bundle is  Z[x, y, dx, dy]/⟨xdy + ydx⟩  and thus its tangent space at the point (1, 1) is  Z[dx, dy]/⟨dy + dx⟩  which is isomorphic to the polynomial ring in one variable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' However, at the point (0, 0), evaluating the  relation xdy + ydx gives 0, and so in this case the tangent space is simply  Z[dx, dy]  the polynomial ring in two variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  This example is important as it shows that in this tangent  category, the tangent spaces at different points can have different dimensions, even if the original space  is connected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' This is not true in the tangent category of smooth manifolds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Next, we discuss vector fields in (CRINGop, T) and explain how, like in the commutative ring case, they  correspond precisely to derivations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' This is expected since for a tangent category whose tangent bundle  admits a left adjoint, vector fields for the left adjoint correspond precisely to vector fields for the right  adjoint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' So for a commutative ring R, a vector field on R in (CRINGop, T) is a ring morphism v : T(R) −→ R  such that v ◦ pR = 1R, which implies that v(a) = a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Then define Dv : R −→ R as Dv(a) = v(d(a)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' It  follows that Dv is a derivation and (R, Dv) is a commutative differential ring.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Conversely, given a derivation  D : R −→ R on R, define the vector field vD : T(R) −→ R as the ring morphism defined on generators as  vD(a) = a and vD(d(a)) = D(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Since these constructions are inverses of each other, we obtain the desired  equivalence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='24 For a commutative ring R, vector fields on R in (CRINGop, T) are in bijective correspondence  with derivations on R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Therefore, it follows that the category of vector fields of (CRINGop, T) is equivalent to the opposite  category of commutative differential rings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Thus by [9, Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='10], the opposite category of commu-  tative differential rings is a Cartesian Rosick´y tangent category whose tangent structure is given by the free  symmetric algebra over the module of K¨ahler differentials as above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  3  Differential Bundles  In this section, we review differential bundles, as introduced by Cockett and Cruttwell in [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Differential  bundles generalize the notion of smooth vector bundles to an arbitrary tangent category.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' We provide the full  definition (Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='1), review how smooth vector bundles do indeed correspond to differential bundles  (Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='3, as shown by MacAdam in [22]), and also consider differential object (Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='5), which  are differential bundles over the terminal object.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' We then discuss morphisms between differential bundles  and categories of differential bundles (Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' We will also review MacAdam’s notion of pre-differential  bundles, as introduced in [22], which then allows for an equivalent alternative characterization of differential  bundles that requires fewer structure data (Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' MacAdam’s characterization of differential bundles  as pre-differential bundles is very important for the story of this paper, as we will use this approach to  characterize differential bundles for commutative rings and (affine) schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  18  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='1  Differential Bundles and Differential Objects  One way of understanding the definition of a differential bundle over an object A in a tangent category is  that it is a generalization of the structure involving the projection, sum, zero, and vertical lift on the tangent  bundle T(A) in the definition of a tangent category (Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='1 [8, Definion 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='3] In a tangent category (X, T), a differential bundle is a quadruple  E = (q : E −→ A, σ : E2 −→ E, z : A −→ E, λ : E −→ T(E)) consisting of:  (i) Objects A and E of X;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  (ii) A map q : E −→ A of X, called the projection, such that for each n ∈ N, the pullback of n copies of q  exists, which we denote as En with n projection maps πj : En −→ E, for all 1 ≤ j ≤ n, so q ◦ πj = q ◦ πi  for all 1 ≤ i, j ≤ n, and for all m ∈ N, Tm preserves these pullbacks;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  (iii) A map σ : E2 −→ E of X, called the sum;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  (iv) A map z : A −→ E of X, called the zero;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  (v) A map λ : E −→ T(E) of X, called the lift;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  and such that:  [DB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='1] (q, σ, z) is an additive bundle over A [5, Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='1], that is, the following diagrams commute:  E2  πj  �  σ  � E  q  �  A  z  �  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  E  q  �  E  q  � A  A  E3  ⟨σ◦⟨π1,π2⟩,π3⟩�  ⟨π1,σ◦⟨π2,π3⟩⟩  �  E2  σ  �  E  ⟨z◦q,1E⟩  �  ⟨1E,z◦q⟩  �  ◆  ◆  ◆  ◆  ◆  ◆  ◆  ◆  ◆  ◆  ◆  ◆  ◆  ◆  ◆  ◆  ◆  ◆  ◆  ◆  ◆  ◆  ◆  ◆  ◆  ◆  ◆  ◆  E2  σ  �  E2  σ  �◆  ◆  ◆  ◆  ◆  ◆  ◆  ◆  ◆  ◆  ◆  ◆  ◆  ⟨π2,π1⟩  � E2  σ  �  E2  σ  � E  E2  σ  � E  E  (11)  [DB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='2] The lift λ preserves the additive structure, that is, the following diagrams commute:  E  λ  �  q  �  T(E)  T(q)  �  A  0A  � T(A)  E2  ⟨λ◦π1,λ◦π2⟩  �  σ  �  T(E2)  T(σ)  �  A  0A  �  0A  �  T(A)  T(z)  �  E  λ  � T(E)  T(A)  λ  � T(E)  (12)  19  [DB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='3] The lift λ preserves the other possible additive structure, that is, the following diagrams commute:  E  λ  �  q  �  T(E)  pE  �  A  z  � E  E2  ⟨λ◦π1,λ◦π2⟩  �  σ  �  T2(E)  +E  �  A  z  �  z  �  E  0E  �  E  λ  � T(E)  E  λ  � T(E)  (13)  [DB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='4] The following diagram commutes:  E  λ  �  λ  �  T(E)  T(λ)  �  T(E)  ℓE  � T2(E)  (14)  [DB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='5] The following square is a pullback:  E2  q◦πj  �  µ  � T(E)  T(q)  �  A  0A  � T(A)  (15)  where µ : E2 −→ T(E) is defined as follows:  µ := E2  ⟨λ◦π1,0E◦π2⟩ � T(E2)  T(σ)  � T(E)  (16)  and such that the above pullback square is preserved by all Tn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  If E = (q : E −→ A, σ : E2 −→ E, z : A −→ E, λ : E −→ T(E)) is a differential bundle in (X, T), we also say  that E is a differential bundle over A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' When there is no confusion, differential bundles will be written as  E = (q : E −→ A, σ, z, λ), and when the objects are specified simply as E = (q, σ, z, λ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Differential bundles generalize smooth vector bundles over smooth manifolds in the context of a tangent  category, as we will review in Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='3 below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' If E = (q : E −→ A, σ, z, λ) is a differential bundle, the  object A is interpreted as a base space and the object E as the total space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' The projection q is the analogue  of the bundle projection from the total space to the base space, making E an “abstract bundle over A”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  The sum σ and the zero z make each fiber into a commutative monoid, more precisely, make the projection  q into additive bundle [5, Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='1], which recall is a commutative monoid in the slice category over A,  which is what the diagrams of [DB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='1] state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  The lift and its universal property [DB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='5] is related to local triviality for smooth vector bundles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Indeed,  given a smooth vector bundle, each fibre Ea (for a ∈ A) is a vector space, and hence the tangent space at  any point of said fibre is isomorphic to the fibre itself.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' As a result, it follows that the tangent bundle of  the total space E, T E, admits a sub-bundle which is isomorphic to E itself.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' The lift λ (sometimes called  the small vertical lift [24, Section 1]) is an analogue of the resulting embedding of the total space into its  20  tangent bundle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' The fibres of the tangent bundle of the total space admit two monoid structures: one being  the canonical one of a tangent bundle, and the other induced by the monoid structure of the fibres of the  smooth vector bundle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Then [DB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='2] and [DB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='3] say the lift λ preserves both of these monoid structures, or  more precisely, that λ is an additive bundle morphism [5, Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='2], which recall is a monoid morphism  in the slice category.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Lastly, [DB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='4] is the compatibility between the lift of a smooth vector bundle and the  vertical lift of the tangent bundle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  In any tangent category, for ever object A, its tangent bundle T(A) is a differential bundle over A, that  is, (pA : T(A) −→ A, +A, 0A, ℓA) is a differential bundle [8, Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Also, if (q : E −→ A, σ, z, λ) is a  differential bundle, then the tangent bundle of E is a differential bundle over the tangent bundle of A, that  is,  �  T(q) : T(E) −→ T(A), T(σ), T(z), cE ◦ T(λ)  �  is a differential bundle [8, Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' For more properties  of differential bundles, see [8, Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  We now define differential bundles with negatives, which are differential bundles with an added structure  map which makes each fiber into an Abelian group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='2 [22, Lemma 5] In a tangent category (X, T), a differential bundle with negatives is a  quintuple E = (q : E −→ A, σ : E2 −→ E, z : A −→ E, λ : E −→ T(E), ι : E −→ E) consisting of:  (i) A differential bundle (q : E −→ A, σ, z, λ) in (X, T);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  (ii) A map ι : E −→ E of X, called the negative;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  such that:  [D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='N] (q, σ, z, ι) is an Abelian group bundle over A [25, Section 1], that is, the following diagrams commute:  E  ι  �  q  �❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  E  q  �  E  q  �❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ⟨1E,ι⟩  �  ⟨ι,1E⟩  �  E2  σ  �  A  A  z  �❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  E2  σ  � E  (17)  If E = (q : E −→ A, σ : E2 −→ E, z : A −→ E, λ : E −→ T(E), ι : E −→ E) is a differential bundle with  negatives in (X, T), we also say that E is a differential bundle over A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Note that a differential bundle can have negatives in any arbitrary tangent category and that the negative  is necessarily unique.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' As was shown in [22], we will review below that in a Cartesian Rosick´y tangent category,  every differential bundle comes equipped with a (necessarily unique) negative (Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Therefore in  a Cartesian Rosick´y tangent category, differential bundles are the same as differential bundles with negatives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  We now review how smooth vector bundles correspond precisely to differential bundles (with negatives)  in the tangent category of smooth manifolds, as was shown by MacAdam in [22, Theorem 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' The result is  somewhat surprising, as the definition of differential bundles contains no mention of local triviality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='3 For a smooth vector bundle q : E −→ M, as in the definition of manifolds, we allow the vector  bundle to have different dimensions in different connected components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Given such a smooth vector bundle,  in local co-ordinates we can represent an element of E as a pair (m, v) and an element of T E as a quadruple  (m, v, w, a), and we can define a lift λ : E −→ T E by λ(m, v) = (m, 0, 0, v).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='2 of [22] shows  that this indeed gives a differential bundle in the category of smooth manifolds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' To go the other direction,  MacAdam proves a general result: in a Rosick´y tangent category, every differential bundle is a retract of a  pullback of a tangent bundle [22, Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='4] Then every differential bundle is a smooth vector bundle,  since the tangent bundle is a smooth vector bundle, and smooth vector bundles are closed under pullbacks  and retracts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  21  The following result about differential bundles in slice tangent categories is easy to check:  Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='4 If (X, T) is a tangent category with an object A which satisfies the requirements of Propo-  sition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='7, then in the slice tangent category X/A, a differential bundle over f : X −→ A is the same as a  differential bundle over X in (X, T).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  We conclude this section by briefly discussing differential objects, which are the differential bundles over  the terminal object.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Differential objects were first defined in [5, Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='8], before the introduction  of differential bundles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Differential objects are quite important since they provide the link from tangent  categories to Cartesian differential categories [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Indeed, the subcategory of differential objects (and all  maps between them) is a Cartesian differential category [5, Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Conversely, every Cartesian  differential category is a tangent category in which every object is a differential object [8, Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  From this, it follows that we obtain an adjunction between the category of Cartesian tangent categories and  the category of Cartesian differential categories [5, Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Later, it was shown in [8, Proposition  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='4] that differential objects were precisely the same thing as differential bundles over the terminal object.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Since the focus of this paper is on differential bundles, we take this approach to defining differential objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='5 [8, Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='4] In a Cartesian tangent category (X, T), a differential object is a  differential bundle over the terminal object ∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Alternatively, a differential object can also be described as an object A equipped with maps ˆp : T(A) −→ A,  + : A×A −→ A, and 0 : ∗ −→ A such that (A, +, 0) is a commutative monoid, T(A) ∼= A×A via pA and ˆp, and  the diagrams from [5, Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='8] commute.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' In a Cartesian Rosick´y tangent category, every differential  object is automatically an Abelian group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='6 In (SMAN, T), the differential objects are precisely the Euclidean spaces since in particular  T(Rn) = Rn × Rn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Therefore (SMOOTH, T) is equivalent to the resulting Cartesian differential category of  differential objects of (SMAN, T).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='2  Differential Bundles as Pre-Differential Bundles  In this section, we review MacAdam’s pre-differential bundles as introduced in [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' These allow for an  alternative characterization of differential bundles, which in particular requires less data and axioms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Indeed,  MacAdam cleverly observed that in the definition of a differential bundle, the sum (and negative), and any  axioms involving it, can be replaced by a pullback square, called Rosick´y’s universality diagram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' From this  special pullback, the sum (and negative) for the differential bundle can be constructed from the sum (and  negative) of the tangent bundle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' MacAdam then introduced pre-differential bundles, which are defined using  only the projection, zero, and lift, and showed that differential bundles are precisely pre-differential bundles  such that the n-fold pullbacks of the projection exist and the Rosick´y’s universality diagram holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' This  pre-differential bundle approach to differential bundles is quite useful since it requires less data and fewer  axioms to check when one wants to construct a differential bundle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' This will be particularly useful when we  will characterize differential bundles for commutative rings and (affine) schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  The definition of a pre-differential bundle is what remains from the definition of a differential bundle  after removing the sum (and negative) and any required pullback.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='7 [21,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Definition 10] In a tangent category (X,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' T),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' a pre-differential bundle is a triple  (q : E −→ A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' z : A −→ E,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' λ : E −→ T(E)) consisting of objects A and E of X,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' and maps q : E −→ A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' z : A −→ E,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  and λ : E −→ T(E) of X such that the following diagrams commute:  A  z  �  ❊  ❊  ❊  ❊  ❊  ❊  ❊  ❊  ❊  ❊  ❊  ❊  ❊  ❊  ❊  ❊  ❊  ❊  ❊  ❊  E  q  �  E  λ  �  q  �  T(E)  pE  �  A  z  �  z  �  E  0E  �  E  λ  �  λ  �  T(E)  T(λ)  �  A  A  z  � E  E  λ  � T(E)  T(E)  ℓE  � T2(E)  (18)  22  If (q : E −→ A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' z : A −→ E,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' λ : E −→ T(E)) is a pre-differential bundle,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' we say that it is a pre-differential  bundle over A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' When there is no confusion, pre-differential bundles will be denoted as (q : E −→ A, z, λ),  and when the objects are specified simply as (q, z, λ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  By definition, the projection, zero, and lift of a differential bundle gives a pre-differential bundle, since  the diagrams in Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='7 all appear in Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' On the other hand, a pre-differential bundle  is a differential bundle precisely when the pullback of n copies of the projection exists and certain squares  are pullbacks [22, Proposition 6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Since the main tangent categories of interest in this paper are Cartesian  Rosick´y tangent, we review when a pre-differential bundle is a differential bundle in this setting, where  only one square is required to be a pullback [22, Corollary 3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' This pullback is called Rosick´y’s universality  diagram, and using the pullback universal property, we can construct the sum and negative for the differential  bundle [22, Lemma 5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='8 [22, Corollary 3] Let (X, T) be a Cartesian Rosick´y tangent and let (q : E −→ A, z, λ) be a  pre-differential bundle in (X, T) such that:  (i) For each n ∈ N, the pullback of n copies of q exists, which we denote as En with n projection maps  πj : En −→ E, for all 1 ≤ j ≤ n, so q ◦ πj = q ◦ πi for all 1 ≤ i, j ≤ n, and for all m ∈ N, Tm preserves  these pullbacks;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  (ii) The following commuting square is a pullback, called the Rosick´y’s universality diagram:  E  λ  �  q  �  T(E)  ⟨T(q),pE⟩  �  A  ⟨0A,z⟩  � T(A) × E  (19)  and for all m ∈ N, Tm preserves this pullback.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Then define the maps σ : E2 −→ E and ι : E −→ E respectively as follows using the universal property of the  above pullback:  E2  σ  �❑  ❑  ❑  ❑  ❑  ❑  πj  �  ⟨λ◦π1,λ◦π2⟩  � T2(E)  +E  �  E  ι  �❏  ❏  ❏  ❏  ❏  ❏  q  �  λ  � T(E)  −E  �  E  λ  �  q  �  T(E)  ⟨T(q),pE⟩  �  E  λ  �  q  �  T(E)  ⟨T(q),pE⟩  �  E  q  � A  ⟨0A,z⟩  � T(A) × E  A  ⟨0A,z⟩  � T(A) × E  (20)  Then E = (q, σ, z, λ, ι) is a differential bundle with negatives over A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Conversely, if E = (q : E −→ A, σ, z, λ) is a differential bundle in a Cartesian Rosick´y tangent category,  then (q, z, λ) is a pre-differential bundle which satisfies (i) and (ii) in Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Furthermore, the  induced sum as constructed in Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='8 is precisely the sum σ one started with, and so (q, σ, z, λ, ι) is  a differential bundle with negatives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Similarly, if (q : E −→ A, σ, z, λ, ι) is a differential bundle with negatives,  then the induced negative as constructed in Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='8 is precisely the negative ι one started with.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Therefore, in a Cartesian Rosick´y tangent category, every differential bundle is in fact a differential bundle  with negatives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' In conclusion, we have the following equivalence:  Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='9 [21, Proposition 6 & Corollary 3] In a Cartesian Rosick´y tangent category (X, T), the  following are in bijective correspondence:  23  (i) Differential bundles;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  (ii) Differential bundles with negatives;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  (iii) Pre-differential bundles that satisfy (i) and (ii) in Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='3  Morphisms and Categories of Differential Bundles  In this section, we discuss morphisms between differential bundles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  There are two possible kinds: one  where the base objects can vary and one where the base object is fixed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' The former is used as the maps  in the category of all differential bundles of a tangent category, while the latter is used in the category of  differential bundles over a specified object.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' In either case, a differential bundle morphism is asked to preserve  the projections and the lifts of the differential bundles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='10 [8, Definion 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='3] Let (X, T) be a (Rosick´y) tangent category.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  (i) Let E = (q : E −→ A, σ, z, λ) and E′ = (q′ : E′ −→ A′, σ′, z′, λ′) be differential bundles in (X, T).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' A  differential bundle morphism (f,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' g) : E −→ E′ is a pair of maps f : E −→ E′ and g : A −→ A′ such  that the following diagram commutes:  E  f  �  q  �  E′  q′  �  E  λ  �  f  � E′  λ′  �  A  g  � A′  T(E)  T(f)  � T(E′)  (21)  Let DBun  �  (X,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' T)  �  be the category whose objects are differential bundles in (X,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' T),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' maps are differential  bundle morphisms between them,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' identity maps are pairs of identity maps (1E,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' 1A) : E −→ E,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' and  composition is defined point-wise,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' that is,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' (f,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' g) ◦ (h,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' k) = (f ◦ h,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' g ◦ k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  (ii) Let A be an object in X and E = (q : E −→ A, σ, z, λ) and E′ = (q′ : E′ −→ A, σ′, z′, λ′) be differential  bundles over A in (X, T).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' A differential bundle morphism f : E −→ E′ over A is a map f : E −→ E′  such that (f, 1A) : E −→ E′ is a differential bundle morphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Explicitly, the following diagrams  commute:  E  f  �  q  �❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  ❖  E′  q′  �  E  λ  �  f  � E′  λ′  �  A  T(E)  T(f)  � T(E′)  (22)  Let DBunT[A] be the category whose objects are differential bundles over A in (X, T) and whose maps  are differential bundle morphisms over A between them, and where identity maps and composition are  the same as in X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Differential bundle morphisms automatically preserve the sum and zero, and negatives if they exist:  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='11 [8, Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='16] Let (X, T) be a tangent category, and let E = (q : E −→ A, σ, z, λ) and  E′ = (q′ : E′ −→ A′, σ′, z′, λ′) be differential bundles in (X, T), and let (f, g) : E −→ E′ be a differential  bundle morphism between them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Then (f, g) is an additive bundle morphism [5, Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='2], that is, the  following diagrams commute:  E2  σ  �  ⟨f◦π1,f◦π2⟩  � E′  2  σ′  �  A  z  �  g  � A′  z′  �  E  f  � E′  E  f  � E′  (23)  24  Similarly, let (q : E −→ A, σ, z, λ, ι) and (q′ : E′ −→ A′, σ′, z′, λ′, ι′) be differential bundles with negatives in  (X, T), and let (f, g) : (q, σ, z, λ) −→ (q′, σ′, z′, λ′) be a differential bundle morphism between the underlying  differential bundles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Then f preserves the negative, that is, the following diagram commutes:  E  ι  �  f  � E′  ι′  �  E  f  � E′  (24)  Other properties of differential bundle morphisms can be found in [8, Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Note that since differential bundle morphisms preserve negatives, the notion of a morphism between  differential bundles with negatives is the same as a differential bundle morphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Therefore for a Rosick´y  tangent category, it follows from Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='9 that its category of differential bundles is the same as its  category of differential bundles with negatives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' As such, abusing notation slightly, for a Rosick´y tangent cat-  egory (X, T), we will consider DBun  �  (X, T)  �  and DBunT[A] to be the categories whose objects are differential  bundles with negatives and whose maps are differential bundle morphisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  For a Cartesian (Rosick´y) tangent category, its category of differential objects is the category of differential  bundles over the terminal object.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Note that this is not the same as the Cartesian differential category of  differential objects [5, Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='11], since in that category the morphisms are not required to preserve the  lift, sum, zero, or negative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='12 Let (X, T) be a Cartesian (Rosick´y) tangent category.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Define DIFF  �  (X, T)  �  to be the cate-  gory of differential objects and differential bundle morphisms over ∗ between them, DIFF  �  (X, T)  �  = DBunT[∗].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  We conclude this section by discussing differential bundle isomorphisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' If (X, T) is a (Rosick´y) tangent  category, then a differential bundle isomorphism is an isomorphism in the category DBun  �  (X, T)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Explicitly,  this is a differential bundle morphism (f, g) such that there exists a differential bundle morphism of opposite  type (f −1, g−1) such that (f, g) ◦ (f −1, g−1) = (1, 1) and (f −1, g−1) ◦ (f, g) = (1, 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' By definition of the  composition in DBun  �  (X, T)  �  , this is precisely the same as requiring that f and g are isomorphisms in X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Similarly, for an object A, a differential bundle isomorphism over A is an isomorphism in the category  DBunT[A], which is a differential bundle morphism f which is an isomorphism in X whose inverse f −1 is also  a differential bundle morphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' We will now prove the converse, that if the underlying maps of a differential  bundle morphism are isomorphisms in the base category, then their inverses are also a differential bundle  morphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' This will allow us to reduce the number of things to check when characterizing differential bundles  in various tangent categories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='13 Let (X, T) be a tangent category.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  (i) Let E = (q : E −→ A, σ, z, λ) and E′ = (q′ : E′ −→ A′, σ′, z′, λ′) be differential bundles in (X, T), and let  (f, g) : E −→ E′ be a differential bundle morphism between them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' If f : E −→ E′ and g : A −→ A′ are  isomorphisms in X, then (f −1, g−1) : E′ −→ E is a differential bundle morphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Therefore, (f, g) is a  differential bundle isomorphism with inverse (f −1, g−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  (ii) Let A an object in X, and let E = (q : E −→ A, σ, z, λ) and E′ = (q′ : E′ −→ A, σ′, z′, λ′) be differential  bundles over A in (X, T), and let f : E −→ E′ be a differential bundle morphism over A between them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  If f : E −→ E′ is an isomorphism in X, then f −1 : E′ −→ E is a differential bundle morphism over A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Therefore f is a differential bundle isomorphism with inverse f −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Proof: For (i), we compute:  g−1 ◦ q′ = g−1 ◦ q′ ◦ f ◦ f −1 = g−1 ◦ g ◦ q ◦ f −1 = q ◦ f −1  25  The fact that (f −1, g−1) is then an isomorphism in the category of differential bundles follows from [8,  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='ii].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' For (ii), if f is a differential bundle morphism over A, then (f, 1A) is a differential bundle  morphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' The identity is always an isomorphism, so if f is also an isomorphism, it follows from (i) that  (f −1, 1A) is a differential bundle morphism, which implies that f −1 is a differential bundle morphism over  A as desired.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  ✷  4  Differential Bundles for Commutative Rings  In this section, we characterize differential bundles (with negatives) in the tangent category of commutative  rings and prove that they correspond precisely to modules (Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' To go from a module to a  differential bundle, we use a semi-direct product to build a sort of ring of dual numbers from said module  (Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' To go from a differential bundle to a module, we take the kernel of the projection (Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  We then obtain that the category of differential bundles is equivalent to the category of modules (Theorem  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='7 and Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' We will also explain how the only differential object is the zero ring (Corollary 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  For a commutative ring R, for a (left) R-module M, unless otherwise specified, we denote the action by  a · m, where a ∈ R and m ∈ M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='1  From Differential Bundles to Modules  We begin by unpacking what a differential bundle with negatives would consist of in (CRING,  T  ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' First  recall that (CRING,  T  ) is a Cartesian Rosick´y tangent category, so by Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='9, differential bundles  are the same thing as differential bundles with negatives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Also, as discussed in Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='2, CRING admits  all pullbacks, so for any ring morphism q : E −→ R between commutative rings, the general construction of  a pullback of n copies of q in CRING is given by:  En = {(x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' , xn)| xj ∈ E s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' q(xi) = q(xj) for all 1 ≤ i, j ≤ n}  and whose ring structure is given coordinate-wise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' In particular, E2 = {(x, y)| x, y ∈ E s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' q(x) = q(y)}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' So  for a commutative ring R, a differential with negatives over R in (CRING,  T  ) would consist of a commutative  ring E and five ring morphisms: q : E −→ R, σ : E2 −→ E, z : R −→ E, λ : E −→ E[ε], and ι : E −→ E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' These  also need to satisfy the equalities and properties of Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='1, many of which we will expand further in  the proof of Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='4 below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' To obtain an R-module, we take the kernel of the projection q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='1 Let R be a commutative ring and E = (q : E −→ R, σ, z, λ, ι) be a differential bundle with  negatives over R in (CRING,  T  ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Then the kernel of the projection ker(q) = {x| q(x) = 0} is an R-module  with action a · x = z(a)x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Proof: Since q : E −→ R is a ring morphism, this induces an R-module structure on E with action  a · e = z(a)e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Then viewing R as an R-module with action given by multiplication a · b = ab, this makes the  projection q : E −→ R an R-linear morphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Therefore since the kernel of an R-linear morphism is always  an R-module, we indeed have that ker(q), with the same action as E, is an R-module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  ✷  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='2  From Modules to Differential Bundles  We now construct a differential bundle from a module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' For a commutative ring R and an R-module M,  define M[ε] as follows:  M[ε] = {a + mε| a ∈ R, m ∈ M and ε2 = 0}  where a and mε will be used respectively as shorthand for a + 0ε and 0 + mε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Then M[ε] is a commutative  ring with multiplication induced by ε2 = 0, that is, the addition, multiplication, and negative are defined  respectively as follows:  (a + mε) + (b + nε) = (a + b) + (m + n)ε  (a + mε)(b + nε) = ab + (a · m + b · n)ε  −(a + mε)=−a − mε  26  and where the zero is 0 and the unit is 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Note that when M = R and the action is given by multiplication  a · b = ab, then this construction gives us the ring of dual numbers over R, or in other words, the tangent  bundle  T  (R) = R[ε].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' We now define a differential bundle over R structure on M[ε].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  (i) The projection qM : M[ε] −→ R is defined as projecting out the R component:  qM(a + mε) = a  As noted above, there is a general construction of pullbacks in CRING.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  However for the projection  qM : M[ε] −→ R, we can instead describe these pullbacks in terms of multivariable dual numbers, like for the  pullbacks of the tangent bundle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' So define M[ε1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' , εn] as follows:  M[ε1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' , εn] = {a + m1ε1 + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' + mnεn| ∀a ∈ R, mj ∈ M and εiεj = 0}  Then M[ε1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' , εn] is a commutative ring whose structure is defined in the obvious way, so in particular  the multiplication is induced by εiεj = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' We leave it as an exercise for the reader to check for themselves  that M[ε1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' , εn] is the pullback of n copies of pR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' We can then describe the rest of the differential bundle  structure as follows:  (ii) The pullback of n copies of pR is given by M[ε]n = M[ε1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' , εn] and where the pullback projection  πj : M[ε1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' , εn] −→ M[ε] sends εj to ε and the other nilpotents to zero, that is, πj projects out the  R component and j-th M component:  πj(a + m1ε1 + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' + mnεn) = a + mjε  (iii) The sum σ : M[ε1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' ε2] −→ M[ε] maps both ε1 and ε2 to ε,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' which results in adding the M components  together:  σ(a + mε1 + nε2) = a + (m + n)ε  (iv) The zero z : R −→ M[ε] is the injection of R into the R component:  0R(a) = a  (v) The negative ι : M[ε] −→ M[ε] maps ε to −ε,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' which results in making the M component negative:  ι(a + mε) = a − mε  To describe the lift,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' let us describe  T  �  M[ε]  �  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' the ring of dual numbers of M[ε] in terms of two nilpotent  elements ε and ε′:  T  �  M[ε]  �  = M[ε][ε′] = {a + mε + bε′ + nεε′| ∀a,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' b ∈ R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' m,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' n ∈ M and ε2 = ε′2 = 0}  where the multiplication is induced by ε2 = ε′2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' So we define:  (vii) The lift λ : M[ε] −→ M[ε][ε′] maps ε to ε′, and so maps the R component of M[ε] to the first R  component of M[ε][ε′], and the M component of M[ε] to the second M component of M[ε][ε′]:  λ(a + mε) = a + mεε′  We leave it as an exercise for the reader to check that these are all well-defined ring morphisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='2 For every commutative ring R and R-moulde M,  M  R(M) := (qM, σM, zM, λM, ιM) is a differ-  ential bundle with negatives over R in (CRING,  T  ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  27  Proof: To show that we have a differential bundle, we will instead show that we have a pre-differential  bundle which satisfies (i) and (ii) in Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' To show that (qM, zM, λM) is a pre-differential bundle,  we must show that the four equalities from Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='7 hold, but these all follow from straightforward  computation, which we leave to the reader.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Next, we must show that this pre-differential bundle also satisfies the extra assumptions required to make  it a differential bundle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Firstly, it is straightforward to observe that M[ε1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' , εn] is indeed the pullback  of n copies of the projection q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Also, since  T  is a right adjoint, it preserves all limits, and therefore all  T  n  preserves these pullbacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' So (qM, zM, λM) satisfies assumption (i) of Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Next,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' we must show  that the following square is a pullback:  M[ε]  λM  �  qM  �  M[ε][ε′]  ⟨  T  (qM),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='pM[ε]⟩  �  R  ⟨0R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='zM⟩  � R[ε] × M[ε]  (25)  So suppose S is a commutative ring,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' and we have ring morphisms f : S −→ M[ε][ε′] and g : S −→ R such  that ⟨  T  (qM),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' pM[ε]⟩ ◦ f = ⟨0R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' zM⟩ ◦ g,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' that is,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' for every x ∈ S the following equality holds:  �  T  (qM)(f(x)),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' pM[ε](f(x))  �  =  �  g(x),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' g(x)  �  Now f(x) ∈ M[ε][ε′] is of the form: f(x) = f1(x) + f2(x)ε + f3(x)ε′ + f4(x)εε′ for some f1(x),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' f3(x) ∈ R and  f2(x),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' f4(x) ∈ M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Then the above equality tells us that:  (g(x), g(x)) =  �  T  (qM)(f(x)), pM[ε](f(x))  �  =  �  T  (qM)  �  f1(x) + f2(x)ε + f3(x)ε′ + f4(x)εε′�  , pM[ε]  �  f1(x) + f2(x)ε + f3(x)ε′ + f4(x)εε′��  =  �  qM(f1(x) + f2(x)ε) + qM(f3(x) + f4(x)ε)ε, pM[ε]  �  f1(x) + f2(x)ε + f3(x)ε′ + f4(x)εε′��  =  �  f1(x) + f3(x)ε, f1(x) + f2(x)ε  �  So this implies that g(x) = f1(x) + f2(x)ε and g(x) = f1(x) + f3(x)ε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' However, in both equalities, the  left-hand side has no nilpotent component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Therefore, we have that g(x) = f1(x), f2(x) = 0, and f3(x) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  So f(x) = g(x) + f4(x)εε′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Then define ⟨f, g⟩ : S −→ M[ε] to be f but without ε′, that is, as follows:  ⟨f, g⟩(x) = g(x) + f4(x)ε  (26)  That ⟨f, g⟩ is a ring morphism essentially follows from the fact that f is a ring morphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Next we compute  that ⟨f, g⟩ also satisfies the following:  λM(⟨f, g⟩(x)) = λM(g(x) + f4(x)ε) = g(x) + f4(x)εε′ = f(x)  qM(⟨f, g⟩(x)) = qM(g(x) + f4(x)ε) = g(x)  So λM ◦ ⟨f, g⟩ = f and qM ◦ ⟨f, g⟩ = g as desired.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Lastly, it remains to show that ⟨f, g⟩ is the unique such  ring morphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' So suppose we have a ring morphism h : S −→ M[ε] such that λM ◦ h = f and qM ◦ h = g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Now h(x) ∈ M[ε] is of the form h(x) = h1(x) + h2(x)ε for some h1(x) ∈ R and h2(x) ∈ M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' By assumption,  we have that:  g(x) + f4(x)εε′ = f(x) = λM(h(x)) = λM(h1(x) + h2(x)ε) = h1(x) + h2(x)εε′  So g(x) + f4(x)εε′ = h1(x) + h2(x)εε′, which implies that h1(x) = g(x) and h2(x) = f4(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Therefore,  h(x) = g(x) + f4(x)ε = ⟨f, g⟩(x), and so ⟨f, g⟩ is unique.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' So we conclude that the above square is a pullback  28  diagram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Furthermore, since  T  is a right adjoint, we also have that  T  n preserves these pullbacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Thus  (qM, zM, λM) satisfies assumption (ii) of Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Therefore, (qM, zM, λM) will induce a differential  bundle with negatives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  It remains to construct the sum and the negative as in Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='8, and show that these are the same  as the proposed σ and ι above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' The sum σ will be given by:  σ =  �  +M[ε] ◦ ⟨λM ◦ π1, λM ◦ π2⟩, qM ◦ πj  �  We leave it to the reader to check for themselves that the following equalities hold:  +M[ε]  �  ⟨λM ◦ π1, λM ◦ π2⟩(a + mε1 + nε2)  �  = a + (m + n)εε′  Therefore by construction, we have that σ(a + mε1 + nε2) = a + (m + n)ε as desired.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' The negative ι will be  given by:  ι =  �  −M[ε] ◦ λM, qM  �  We then compute that:  −M[ε](λM(a + mε)) = a − mεε′  So by construction, we have that ι(a + mε) = a − mε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' So we conclude that  M  R(M) = (qM, σM, zM, λM, ιM)  is a differential bundle with negatives over R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  ✷  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='3  Equivalence  We will now show that the constructions of Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='1 and Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='2 are inverses of each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Beginning from the module side of things, let R be a commutative ring and M be an R-module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Consider  ker(qM), the kernel of the projection of the induced differential bundle  M  R(M).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' However, qM(a + mε) = 0  implies that a = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' So the kernel of the projection consists solely of the M component, that is, ker(qM) =  {mε| ∀m ∈ M}, which is clearly isomorphic to M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Explicitly, αM : M −→ ker(qM) is defined as αM(m) = mε,  and α−1  M : ker(qM) −→ M is defined as α−1  M (mε) = m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='3 For every commutative ring R and R-module M, αM : M −→ ker(qM) is an R-linear isomor-  phism with inverse α−1  M : ker(qM) −→ M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Proof: Clearly for every R-module M, αM and α−1  M are inverses of each other, that is, α−1  M (αM(m)) = m  and αM(α−1  M (mε)) = mε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' However, we must explain why αM and α−1  M are also R-linear morphisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Clearly,  they are both linear, so we must show that they preserve the action.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' We start by showing that αM does,  where recall that the action on ker(qM) is defined as a · (mε) = zM(a)mε:  αM(a · m) = (a · m)ε = (a + 0ε)mε = zM(a)mε = a · mε = a · αM(m)  So αM is an R-module morphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Since αM and α−1  M are inverses as functions, it then follows that α−1  M will  also be an R-module morphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' So we conclude that αM and α−1  M are inverse R-linear isomorphisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  ✷  Let’s now start from the differential bundle side of the story.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Let E = (q : E −→ R, σ, z, λ, ι) be a  differential bundle with negatives over a commutative ring R in (CRING,  T  ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' To define differential bundle  isomorphisms between E and  M  R  �  ker(q)  �  , we will first need to define a ring isomorphism between E and  ker(q)[ε].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  To do so, we must first take a closer look at the lift λ : E −→ E[ε].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Since the lift is a ring  morphism whose codomain is a ring of dual numbers, it is well-known that it must be of the following form:  λ(x) = pE(λ(x)) + Dλ(x)ε, where Dλ : E −→ E is a derivation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Now by the first diagram of [DB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='3], we have  that pE ◦ λ = z ◦ q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' This implies that the lift is in fact of the form:  λ(x) = z(q(x)) + Dλ(x)ε  29  and the product rule for the derivation Dλ is given by Dλ(xy) = z(q(x))Dλ(y) + z(q(y))Dλ(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Then define  the function βE : E −→ ker(q)[ε] as follows:  βE(x) = q(x) + Dλ(x)ε  (27)  To define its inverse β−1  E  : ker(q)[ε] −→ E, we will need to make use of Rosick´y’s universality diagram,  that is, the pullback square from Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' First, define the ring morphism ζE : ker(q)[ε] −→ E[ε]  as ζE(a + xε) = z(a) + xε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' By universality of the pullback, define β−1  E  : ker(q)[ε] −→ E as the unique ring  morphism which makes the following diagram commute:  ker(q)[ε]  qker(q)  �  ζE  �  β−1  E  �P  P  P  P  P  P  P  E  q  �  λ  � E[ε]  ⟨  T  (q),pE⟩  �  R  ⟨0R,z⟩  � R[ε] × E  (28)  so β−1  E  = ⟨qker(q), ζE⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' We will show below that β−1  E  is a differential bundle morphism, from which it follows  from the compatibility with the lift that β−1  E (a + xε) = z(a) + x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='4 For commutative ring R and a differential bundle with negatives E = (q : E −→ R, σ, z, λ, ι)  over R in (CRING,  T  ), βE : E −→  M  R  �  ker(q)  �  is a differential bundle isomorphism over R with inverse  β−1  E  :  M  R  �  ker(q)  �  −→ E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Proof: We first explain why βE and β−1  E  are well-defined ring morphisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Starting with βE, we must  first explain why Dλ(x) is in the kernel of the projection q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' By the first diagram of [DB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='2], we have that  T  (q)◦ λ = 0R ◦ q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Therefore, for all x ∈ E, we have that q(z(q(x)))+ q(Dλ(x))ε = q(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Since the right-hand  side has no nilpotent component, this implies that q(Dλ(x)) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' So for all x ∈ E, Dλ(x) ∈ ker(q), and so  βE is well-defined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' We leave it to the reader to check for themselves that βE is indeed a ring morphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Next we explain why β−1  E  is a well-defined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' To do so, we must show that the outer diagram of (28)  commutes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' First, note that by the second diagram of [DB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='1], q ◦ z = 1R, so q(z(a)) = a for all a ∈ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Then  for all a ∈ R and x ∈ ker(q) we compute:  ⟨  T  (q), pE⟩  �  ζE(a + xε)  �  = ⟨  T  (q), pE⟩  �  z(a) + xε  �  =  �  T  (q)(z(a) + xε), pE(z(a) + xε)  �  =  �  q(z(a)) + q(x)ε), pE(z(a) + xε)  �  =  �  a, z(a)  �  =  �  0R(a), z(a)  �  = ⟨0R, z⟩(a) = ⟨0R, z⟩  �  qker(q)(a + xε  �  So ⟨  T  (q), pE⟩ ◦ ζE = ⟨0R, z⟩ ◦ qker(q).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Therefore, by the universal property of the pullback square, there exists  a unique ring morphism β−1  E  : ker(q)[ε] −→ E such that λ ◦ β−1  E  = ζE and q ◦ β−1  E  = qker(q).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' In particular,  these imply that for every a ∈ R and x ∈ ker(q) the following equalities hold:  q  �  β−1  E (a + xε)  �  = a  Dλ(β−1  E (a + xε)) = x  Next we show that βE and β−1  E  are inverses of each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' To show that βE ◦ β−1  E  = 1ker(q)[ε], we use the  above identities:  βE(β−1  E (a + xε)) = q(β−1  E (a + xε)) + Dλ(β−1  E (a + xε))ε = a + xε  To show that β−1  E  βE = 1E, we will first show that q ◦ β−1  E  βE = q and λ ◦ β−1  E  βE = λ:  q(β−1  E (βE(x))) = q(βE(x)) = q((q(x) + Dλ(x)ε)) = q(x)  30  λ(β−1  E (βE(x))) = ζE(βE(x)) = ζE(q(x) + Dλ(x)ε) = z(q(x)) + Dλ(x)ε = λ(x)  Therefore, by the universal property of the pullback, it follows that β−1  E  βE = 1E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' So βE and β−1  E  are  inverse ring isomorphisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Lastly, we must show that βE and β−1  E  are also differential bundle morphisms over R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' To do so, we will  need to know a bit more about Dλ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' The third diagram of [DB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='3] is 0E ◦ z = λ ◦ z, which implies that for  all a ∈ R, z(a) = z(a) + Dλ(z(a))ε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Since the left-hand side has no nilpotent component, it follows that  Dλ(z(a)) = 0 for all a ∈ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' On the other hand, the diagram of [DB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='4] says that  T  (λ)◦λ = ℓE ◦λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Then using  that q(Dλ(x)) = 0, q(z(a)) = a, and Dλ(z(a)) = 0, [DB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='4] explicitly states that q(z(x)) + Dλ(Dλ(x))εε′ =  q(z(x)) + Dλ(x)εε′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' This implies that Dλ(Dλ(x)) = Dλ(x) for all x ∈ E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' With these identities, we can now  show that βE is a differential bundle morphism over R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' So we show that the diagrams of (22) hold:  (i) qker(q) ◦ βE = q:  qker(q)(βE(x)) = qker(q)(q(x) + Dλ(x)ε) = q(x)  (ii)  T  (βE) ◦ λ = λker(q) ◦ βE:  T  (βE)(λ(x)) =  T  (βE)(z(q(x)) + Dλ(x)ε) = βE(z(q(x)) + βE(Dλ(x)ε)ε′  = q(z(q(x)))+Dλ(z(q(x)))ε+z(q(Dλ(x)))ε′+Dλ(Dλ(x))εε′ = q(x)+0ε+0ε′+Dλ(x)εε′ = q(x)+Dλ(x)εε′  = λker(q)(q(x) + Dλ(x)ε) = λker(q)(βE(x))  So βE is a differential bundle morphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Since βE is a ring isomorphism, by Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='13 it then follows that  β−1  E  is also a differential bundle morphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' In particular, note that this implies that λ◦β−1  E  =  T  (β−1  E )◦λker(q).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  But by definition, we have that λ◦β−1  E  = ζE, and so we also have that  T  (β−1  E )◦λker(q) = ζE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' This implies that  β−1  E (a) + β−1  E (xε)ε = z(a) + xε, and so β−1  E (a) = z(a) and β−1  E (xε) = x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Therefore, β−1  E (a + xε) = z(a) + x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  So we conclude that βE and β−1  E  are differential bundle isomorphisms over R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  ✷  Therefore, the construction from a module to a differential bundle is the inverse of the construction from  a differential bundle to a module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' So we conclude that:  Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='5 For a commutative ring R, there is a bijective correspondence between R-modules and  differential bundles (with negatives) over R in (CRING,  T  ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  In CRING, recall that the terminal object is the zero ring 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' So differential objects in (CRING,  T  ) corre-  spond precisely to 0-modules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' However, the only 0-module is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Therefore, there are no non-trivial differential  objects in (CRING,  T  ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Corollary 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='6 The only differential object in (CRING,  T  ) is the zero ring 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  We now extend Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='5 to an equivalence of categories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' For a commutative ring R, let MODR be  the category of R-modules and R-linear morphisms between them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' We define an equivalence of categories  between MODR from DBUN  T  [R] as follows:  (i) Define the functor  M  R : MODR −→ DBUN  T  [R] which sends an R-module M to the differential bundle  M  R(M),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' and sends an R-linear morphism f : M −→ M ′ to the differential bundle morphism over R  M  R(f) :  M  R(M) −→  M  R(M ′) where  M  R(f) : M[ε] −→ M ′[ε] is defined as:  M  R(f)(a + mε) = a + f(m)ε  (ii) Define the functor  M R : DBUN  T  [R] −→ MODR which sends a differential bundle with negatives over R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  E = (q : E −→ R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' σ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' z,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' λ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' ι) to the R-module  M R(E) = ker(q),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' and sends a differential bundle morphism  f : E = (q : E −→ R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' σ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' z,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' λ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' ι) −→ E′ = (q′ : E′ −→ R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' σ′,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' z′,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' λ′,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' ι′) over R to the R-linear morphism  M R(f) : ker(q) −→ ker(q′) defined as:  M R(f)(x) = f(x)  31  (iii) Define the natural isomorphism α : 1MODR ⇒  M R ◦  M  R with inverse α−1 :  M R ◦  M  R ⇒ 1MODR as αM  α−1  M defined in Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  (iv) Define the natural isomorphism β : 1DBUN  T  [R] ⇒  M  R ◦  M R with inverse β−1 :  M R ◦  M  R ⇒ 1DBUN  T  [R]  as βE β−1  E  defined in Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='7 For a commutative ring R, we have an equivalence of categories: MODR ≃ DBUN  T  [R].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Proof: We must first explain why  M  R and  M R are well-defined on morphisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  So given an R-linear  morphism f : M −→ M ′, we must show that  M  R(f) is a differential bundle morphism over R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' We leave it to  the reader to check for themselves that  M  R(f) is a ring morphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' So it remains to show that the diagrams  of (22) also hold:  (i) qM′ ◦  M  R(f) = qM:  qM′ �  M  R(f)(a + mε)  �  = qM′(a + f(m)ε) = a = qM(a + mε)  (ii)  T  �  M  R(f)  �  λM = λM′ ◦  M  R(f):  T  �  M  R(f)  � �  λM(a + mε)  �  =  T  �  M  R(f)  � �  a + mεε′�  =  M  R(f)(a) +  M  R(f)(mε)ε′  = a + f(m)εε′ = λM′ �  a + f(m)ε  �  = λM′ �  M  R(f)(a + mε)  �  So we conclude that  M  R(f) is a differential bundle morphism over R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' On the other hand, given a differential  bundle morphism f : E −→ E′ over R, we must first explain why if x ∈ ker(q) then  M R(f)(x) ∈ ker(q′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Note that since f is a differential bundle morphism over R, by definition this means that for all x ∈ E,  q′(f(x)) = q(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' So it follows that if x ∈ ker(q), we have that:  q′ �  M R(f)(x)  �  = q′(f(x)) = q(x) = 0  and so  M R(f)(x) ∈ ker(q′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Thus  M R(f) : ker(q) −→ ker(q′) is well-defined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' To show that  M R(f) is R-linear,  clearly since f is linear,  M R(f) will be linear, therefore it remains to show  M R(f) preserves the action.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Since  f is a differential bundle morphisms over R, by Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='11, we have that f preserves the zero, that is,  f(z(a)) = z′(a) for all a ∈ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' So we compute:  a ·  M R(f)(x) = a · f(x) = z′(a)f(x) = f(z(a)x) = f(a · x) =  M R(f)(a · x)  So we conclude that  M R(f) is an R-linear morphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' So  M  R and  M R are well-defined, and it is straightforward  to see that they also preserve composition and identities, so  M  R and  M R are indeed functors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Next we explain why α, α−1, β, and β−1 are natural transformations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' In fact, it suffices to explain why  α and β−1 are natural, and it will then follow that α−1 and β are as well since we have already shown they  are isomorphisms on each object.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' So for an R-linear morphism f : M −→ M ′, we compute:  M R  �  M  R(f)  � �  αM(m)  �  =  M R  �  M  R(f)  �  (mε) =  M  R(f)(mε) = f(m)ε = αM′(f(m))  So α is indeed a natural transformation, and so α−1 will also be a natural transformation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Therefore, α and  α−1 are inverse natural isomorphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' On the other hand, for a differential bundle morphism f : E −→ E′  over R, we compute:  β−1  E′  �  M  R  �  M R(f)  �  (a + xε)  �  = β−1  E′  �  a +  M R(f)(x)ε  �  = β−1  E′  �  a + f(x)ε  �  = z′(a) + f(x)ε = f(z(a)) + f(x) = f(z(a) + x) = f  �  β−1  E (a + xε)  �  32  So β−1 is indeed a natural transformation, and so β will also be a natural transformation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Therefore, β  and β−1 are inverse natural isomorphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' So we conclude that we have an equivalence of categories, and so  MODR ≃ DBUN  T  [R].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  ✷  We also obtain an equivalence of categories between the category of all differential bundles and the  category of modules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Let MOD be the category whose objects are pairs (R, M) consisting of a commutative  ring R and an R-module M, and where a map (g, f) : (R, M) −→ (R′, M ′) is a pair consisting of a ring  morphism g : R −→ R′ and an R-linear map f : M −→ M ′, where M ′ is an R-module via the action  a•m = g(a)·m, so explicitly, f(a·m) = g(a)·f(m).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Composition is defined as (g′, f ′)◦(g, f) = (g′ ◦g, f ′ ◦f)  and identities are (1R, 1M).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' We define an equivalence of categories between MOD and DBUN  �  (CRING,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  T  )  �  as follows:  (i) Define the functor  M  : MOD −→ DBUN  �  (CRING,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  T  )  �  which sends an object (R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' M) to the differential  bundle  M  (R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' M) =  M  R(M),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' and sends a map (g,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' f) : (R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' M) −→ (R′,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' M ′) to the differential bundle  morphism  M  (g,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' f) :  M  R(M) −→  M  R′(M ′) defined as:  M  (g,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' f)(a + mε) = g(a) + f(m)ε  (ii) Define the functor  M  : DBUN  �  (CRING,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  T  )  �  −→ MOD which sends a differential bundle with negatives  E = (q : E −→ R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' σ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' z,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' λ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' ι) to the pair  M  (E) = (R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' ker(q)),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' and sends a differential bundle morphism  (f,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' g) : E = (q : E −→ R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' σ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' z,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' λ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' ι) −→ E′ = (q′ : E′ −→ R′,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' σ′,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' z′,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' λ′,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' ι′) to the pair  M  (f,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' g) = (g,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  M R(f)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  (iii) Define the natural isomorphism α : 1MOD ⇒  M  ◦  M  as α(R,M) = (1R, αM), with inverse natural  isomorphism α−1 :  M  ◦  M  ⇒ 1MOD defined as α−1  (R,M) = (1R, α−1  M ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  (iv) Define the natural isomorphism β : 1DBUN  �  (CRING,  T  )  � ⇒  M M  as βE = (1, βE), with inverse natural  isomorphism β  −1 :  M R ◦  M  R ⇒ 1DBUN  �  (CRING,  T  )  � as β  −1  E  = (1, β−1  E ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='8 We have an equivalence of categories: MOD ≃ DBUN  �  (CRING,  T  )  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Proof: That  M  and  M  are well-defined on morphisms is similar to the proofs that  M  R and  M R were well-  defined on morphisms in the proof of Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' So  M  and  M  are indeed functors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Next, since αM and  α−1  M are R-linear morphisms, it follows that α(R,M) = (1R, αM) and α−1  (R,M) = (1R, α−1  M ) are indeed maps in  MOD, so α and α−1 are well-defined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' On the other hand, since βE and β−1  E  are differential bundle morphisms  over the base commutative ring, it follows by definition that βE = (1, βE) and β  −1  E  = (1, β−1  E ) are differential  bundle morphisms, so β and β  −1 are well-defined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Lastly, that α, α−1, β, and β  −1 are natural isomorphisms  follows directly from the fact that α, α−1, β, and β−1 are natural isomorphisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' So we conclude that we  have an equivalence of categories: MOD ≃ DBUN  �  (CRING,  T  )  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  ✷  Remark 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='9 The equivalence between modules and differential bundles is also true in more general settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Indeed, both for the tangent category of commutative semirings and the tangent category of commutative  algebras over a (semi)ring, differential bundles correspond precisely to modules via the above constructions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  However, in a setting where one does not have negatives, we would have also needed to prove [DB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='5], since  this is also required to make a pre-differential bundle a differential bundle in a Cartesian tangent category  without negatives [22, Proposition 6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Even more generally, in a codifferential category, every module of  an algebra of the monad will induce a differential bundle in the Eilenberg-Moore category via [4, Theorem  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='1] and a generalization of Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  If a codifferential category has kernels, then every differential  bundle induces a module by generalizing Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='1, and so in the presence of kernels, differential bundles  in the Eilenberg-Moore category also correspond precisely to modules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' However, since not all codifferential  categories have all kernels, there may be differential bundles which are not induced by modules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  33  5  Differential Bundles for (Affine) Schemes  In this section, we characterize differential bundles (with negatives) in the tangent category of affine schemes  and prove that they also correspond to modules (Proposition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' However, the constructions are quite  different in this case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' To go from a module to a differential bundle, we take the free symmetric algebra over  said module (Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' To go from a differential bundle to a module, we take the image of the derivation  induced by the lift (Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Moreover, in contrast to the previous section, in this case, we obtain  that the category of differential bundles is equivalent to the opposite category of modules (Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='7 and  Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' To the best of our understanding, there is no general reason why the fact that differential  bundles in commutative rings are equivalent to the category of modules would also imply that differential  bundles in commutative rings opposite are equivalent to the opposite category of modules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' We conclude the  section by generalizing these results to the category of schemes, where differential bundles are equivalent to  the opposite category of quasicoherent sheaves of modules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='1  From Differential Bundles to Modules  Let us begin by unravelling what a differential bundle with negatives would be in (CRINGop, T).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' First recall  that (CRINGop, T) is a Cartesian Rosick´y tangent category, so by Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='9, differential bundles are  the same thing as differential bundles with negatives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Also, as discussed in Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='3, CRINGop admits all  pullbacks, since CRING admits all pushouts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' For any ring morphism q : R −→ E between commutative rings,  recall that E becomes a commutative R-algebra, so, in particular, an R-module, with action a · x = q(a)x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Then the pushout of n copies of q in CRING is given by taking the tensor product over R of n copies  of E: En = E ⊗R .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' ⊗R E  �  ��  �  n times  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Then a differential bundle with negatives over a commutative ring R in  (CRINGop, T) viewed in CRING would consist of a commutative ring E and five ring morphisms: q : R −→ E,  σ : E −→ E ⊗R E, z : E −→ R, λ : T(E) −→ E, and ι : E −→ E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' These must also satisfy the dual equalities  and properties of Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' In particular, note that [DB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='1] and [DB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='N] imply that E is a commutative  R-Hopf algebra, where the sum σ is the comultiplication, the zero z is the counit, and the negative ι is the  antipode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  To obtain an R-module from a differential bundle, we take the image of the map Dλ : E −→ E defined as  Dλ(x) = λ(d(x)), which is, in fact, a derivation whose product rule is Dλ(ab) = λ(a)Dλ(b) + λ(b)Dλ(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='1 Let R be a commutative ring, and let E = (q : E −→ R, σ, z, λ, ι) be a differential bundle (with  negatives) over R in (CRINGop, T).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Then the image of the derivation im(Dλ) = {Dλ(x) = λ(d(x))| ∀x ∈ E}  is an R-module with action a · Dλ(x) = Dλ(q(a)x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Proof: Recall that for any R-linear map f : M −→ N, the image im(f) = {f(m)| ∀m ∈ M} is an R-module  with action a · f(m) = f(a · m).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Therefore, to prove that im(Dλ) is an R-module, it suffices to show that  Dλ is an R-linear map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Clearly Dλ is linear, so it remains to show that Dλ also preserves the action.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' First  note that by the dual of the first diagram of [DB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='2], that λ ◦ T(q) = q ◦ 0R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' In particular this implies  that λ(q(a)) = q(a) and λ(d(q(a))) = 0 for all a ∈ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Note that the second equality can be rewritten as  Dλ(q(a)) = 0 for all a ∈ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' So we compute:  Dλ(a · x) = Dλ(q(a)x) = λ(q(a))Dλ(x) + λ(x)Dλ(q(a)) = q(a)Dλ(x) + 0 = a · Dλ(x)  So Dλ is R-linear and we conclude that im(Dλ) is an R-module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  ✷  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='2  From Modules to Differential Bundles  We now construct a differential bundle from a module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' For a commutative ring R and an R-module M, let  SymR(M) be the free symmetric R-algebra over M, that is:  SymR (M) =  ∞  �  n=0  M ⊗s  R  n = R ⊕ M ⊕ (M ⊗s  A M) ⊕ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  34  where ⊗s  R is the symmetrized tensor product over R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Note that as a commutative ring, SymR(M) is generated  by all a ∈ R and m ∈ M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Therefore, to define ring morphisms with domain SymR(M), it suffices to define  them on generators a and m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Using this to our advantage, we define a differential bundle with negatives over  R structure on SymR(M) viewed in CRING (so the differential bundle structure maps will all be backwards)  as follows:  (i) The projection qM : R −→ SymR(M) is defined as the injection of R into SymR(M):  qM(a) = a  (ii) The pushouts (which recall are pullbacks in CRINGop) are given by taking the tensor product over  R of n copies of SymR(M), so SymR(M)n := SymR(M) ⊗R .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' ⊗R SymR(M)  �  ��  �  n times  , where the jth injection  πj : SymR(M) −→ SymR(M)n injects SymR(M) into the j-th component:  πj(w) = 1 ⊗R .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' ⊗R 1 ⊗R w ⊗R 1 ⊗R .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' ⊗R 1  (iii) The sum σM : SymR(M) −→ SymR(M) ⊗R SymR(M) is the canonical comultiplication of the free  symmetric R-algebras,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' that is,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' defined on generators as follows:  σM(a) = a ⊗R 1 = 1 ⊗R a  σM(m) = m ⊗R 1 + 1 ⊗R m  (iv) The zero 0R : SymR(M) −→ R is the canonical counit of the free symmetric R-algebras,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' that is,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' defined  on generators as follows:  zM(a) = a  zM(m) = 0  (v) The negative ιM : SymR(M) −→ SymR(M) is the canonical antipode of the free symmetric R-algebras,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  that is,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' defined on generators as follows:  ιM(a) = a  ιM(m) = −m  To describe the lift,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' note that T(SymR(M)) as a commutative ring is generated by a,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' m,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' d(a),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' and d(m) for  all a ∈ R and m ∈ M (and modulo the appropriate equations).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  (vii) The lift λM : T(SymR(M)) −→ SymR(M) is defined on generators as follows:  λM(a) = a  λM(m) = 0  λM(d(a)) = 0  λM(d(m)) = m  Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='2 For every commutative ring R and R-module M, MR(M) := (qM, σM, zM, λM, ιM) is a differ-  ential bundle with negatives over R in (CRINGop, T).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Proof: To show that we have a differential bundle, we will instead show that we have a pre-differential  bundle which satisfies (i) and (ii) in Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' So to show that (qM, zM, λM) is a pre-differential  bundle in (CRINGop, T), we must show that the dual of the four equalities from Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='7 hold in CRING.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  To do so, we show that these hold on the generators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  (i) zM ◦ qM = 1R  zM(qM(a)) = zM(a) = a  (ii) λM ◦ pSymR(M) = qM ◦ zM  λM(pSymR(M)(a)) = λM(a) = a = qM(a) = qM(zM(a))  λM(pSymR(M)(m)) = λM(m) = 0 = qM(0) = qM(zM(m))  35  (iii) zM ◦ 0SymR(M) = zM ◦ λM  zM  �  0SymR(M)(a)  �  = zM(a) = zM(λM(a))  zM  �  0SymR(M)(m)  �  = zM(m) = 0 = zM(0) = zM(λM(0))  (iv) λM ◦T(λM) = λM ◦ℓSymR(M): Note that T2(SymR(M)) has eight kinds of generators, a, m, d(a), d(m),  d′(a), d′(m), d′d(a), and d′d(m) for all a ∈ R and m ∈ M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='λM(T(λM)(a)) = λM(λM(a)) = λM(a) = λM(ℓSymR(M)(a))  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='λM(T(λM)(m)) = λM(λM(m)) = λM(0) = 0 = λM(m) = λM(ℓSymR(M)(m))  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='λM(T(λM)(d(a))) = λM(λM(d(a))) = λM(0) = λM(ℓSymR(M)(d(a)))  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='λM(T(λM)(d(m))) = λM(λM(d(m))) = λM(0) = λM(ℓSymR(M)(d(m)))  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='λM(T(λM)(d′(a))) = λM(d(λM(a))) = λM(d(a)) = 0 = λM(0) = λM(ℓSymR(M)(d′(a)))  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='λM(T(λM)(d′(m))) = λM(d(λM(m))) = λM(d(0)) = λM(0) = λM(ℓSymR(M)(d′(m)))  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='λM(T(λM)(d′d(a)))=λM(d(λM(d(a)))) = λM(d(0)) = λM(0) = 0 = λM(d(a))=λM(ℓSymR(M)(d′d(a)))  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='λM(T(λM)(d′d(m))) = λM(d(λM(d(m)))) = λM(d(m)) = λM(ℓSymR(M)(d′d(m)))  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='So the desired equalities hold and we conclude that (qM,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' zM,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' λM) is a pre-differential bundle in (CRINGop,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' T).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Next, we must show that this pre-differential bundle also satisfies the extra assumptions required to make  it a differential bundle, or rather that the dual of the assumptions hold in CRING.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' As explained above, the  pushout of n copies of the projection qM exists, chosen here to be SymR(M)n, and since T is a left adjoint,  it preserves all colimits, so Tn preserves these pushouts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Dualizing this, we conclude that (qM, zM, λM)  satisfies assumption (i) of Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='8 in CRINGop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Next, we must show that the dual of (ii) of Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='8 also holds, that is, we must show that the  following square is a pushout in CRING:  T(R) ⊗ SymR(M)  [T(qM),pSymR(M)]  �  [0R,zM]  � R  qM  �  T(SymR(M))  λM  � SymR(M)  (29)  where [−, −] is the copairing operation of the coproduct, which recall in CRING is given by the tensor  product.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Now suppose that S is a commutative ring, and we have ring morphisms f : T(SymR(M)) −→ S  and g : R −→ S such that f ◦[T(qM), pSymR(M)] = g ◦[0R, zM].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' In particular,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' this implies that for every a ∈ R  and m ∈ M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='the following equalities hold:  f(a) = g(a)  f(d(a)) = 0  f(m) = 0  Then define the map [f,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' g] : SymR(M) −→ S as the ring morphism defined on generators as follows:  [f,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' g](a) = g(a)  [f,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' g](m) = f(d(m))  (30)  Next,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' we compute the following on generators:  [f,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' g](qM(a)) = [f,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' g](a) = g(a)  [f,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' g](λM(a)) = [f,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' g](a) = g(a) = f(a)  36  [f,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' g](λM(m)) = [f,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' g](0) = 0 = f(m)  [f,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' g](λM(d(a))) = [f,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' g](0) = 0 = f(d(a))  [f,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' g](λM(d(m))) = [f,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' g](m) = f(d(m))  Thus it follows that [f,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' g]◦ λM = f and [f,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' g]◦ qM = g as desired.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Lastly, it remains to show that [f, g] is the  unique such ring morphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' So suppose we have a ring morphism h : SymR(M) −→ S such that h ◦ λM = f  and h ◦ qM = g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Then on generators, we compute that:  h(a) = h(qM(a)) = g(a) = [f, g](a)  h(m) = h(λM(d(m))) = f(d(m)) = [f, g](m)  Since h and [f, g] are ring morphisms that are equal on generators, it follows that h = [f, g], thus [f, g] is  unique.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Thus we conclude the above diagram is a pushout in CRING.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Furthermore, since T is a left adjoint in  CRING, we also have that Tn preserves these pushouts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Dualizing this, it follows that (qM, zM, λM) satisfies  assumption (ii) of Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='8 in CRINGop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Therefore by Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='8, the pre-differential bundle  (qM, zM, λM) will induce a differential bundle with negatives in (CRINGop, T).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  It remains to construct the sum and the negative as in Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='8, and show that these are the same  as the proposed σ and ι above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' By dualizing the construction,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' the sum σ is:  σM =  �  [π1 ◦ λM,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' π2 ◦ λM] ◦ +SymR(M),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' πj ◦ qM  �  On generators,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' we compute:  σM(a) =  �  [π1 ◦ λM,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' π2 ◦ λM] ◦ +SymR(M),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' πj ◦ qM  �  (a) = πj(qM(a)) = πj(a) = a ⊗R 1 = 1 ⊗R a  σM(m) =  �  [π1 ◦ λM,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' π2 ◦ λM] ◦ +SymR(M),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' πj ◦ qM  �  (m) = [π1 ◦ λM,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' π2 ◦ λM](+SymR(M)(d(m)))  = [π1 ◦ λM,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' π2 ◦ λM](d(m) ⊗R 1) + [π1 ◦ λM,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' π2 ◦ λM](1 ⊗R d(m))  = π1(λM(d(m))) + π2(λM(d(m))) = π1(m) + π2(m) = m ⊗R 1 + 1 ⊗R m  Thus on generators,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' σM(a) = a ⊗R 1 = 1 ⊗R a and σ(m) = m ⊗R 1 + 1 ⊗R m,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' as defined above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' On the  other hand, the negative ι is:  ιM =  �  λM ◦ −SymR(M), qM  �  On generators, we compute:  ιM(a) =  �  λM ◦ −SymR(M), qM  �  (a) = qM(a) = a  ιM(m) =  �  λM ◦ −SymR(M), qM  �  (m) = λM(−SymR(M)(d(m)) = λM(−d(m)) = −λM(d(m)) = −m  So on generators ιM(a) = a, and ιM(m) = −m as desired.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' So we conclude that (qM, σM, zM, λM, ιM) is a  differential bundle with negatives over R in (CRINGop, T).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  ✷  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='3  Equivalence  We will now show that the constructions of Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='1 and Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='2 are inverses of each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Starting  from the module side of things, let R be a commutative ring, M an R-module, and consider the induced  derivation DλM : SymR(M) −→ SymR(M).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' We will show that the image of the derivation is precisely M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='3 For every commutative ring R and R-module M, im(DλM ) = M as R-modules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  37  Proof: Let us compute what this derivation does on pure symmetrized tensors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' For degree 0, that is, for  a ∈ R we have that:  DλM (a) = λM(d(a)) = 0  so DλM (a) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' For degree 1, that is, for m ∈ M we have that:  DλM (m) = λM(d(m)) = m  so DλM (m) = m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' For degree 2, that is, for m, n ∈ M using the product rule, we have that:  DλM (mn) = λM(m)DλM (n) + λM(n)DλM (m) = 0 + 0 = 0  And similarly for degree n ≥ 2, again by using the product rule, we have that DλM (m1m2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' mn) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' So  it follows that im(DλM ) = {m| ∀m ∈ M}, so im(DλM ) = M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Furthermore, note that the multiplication of a  and m in SymR(M) is precisely the module action, am = a · m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Thus the induced action on im(DλM ) from  Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='1 is given by:  a · DλM (m) = DλM (q(a)m) = DλM (am) = DλM (a · m) = a · m  So im(DλM ) = M as R-modules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  ✷  Conversely, let us start from a differential bundle, so let E = (q : E −→ R, σ, z, λ, ι) be a differential bundle  with negatives over a commutative ring R in (CRINGop, T).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' To define a differential bundle isomorphism  between E and M(im(Dλ), we will first need to define ring isomorphisms between E and SymR  �  im(Dλ)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Define the ring morphism ψE : SymR  �  im(Dλ)  �  −→ E on generators a ∈ R and x ∈ E as follows:  ψE(a) = q(a)  ψE  �  Dλ(x)  �  = Dλ(x)  (31)  Note that ψE can also be defined by the universal property of the free symmetric R-algebra, that is, it is  the unique R-algebra morphism induced by the inclusion im(Dλ) −→ E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' To define the inverse we will need  to use the dual of the Rosick´y’s universality diagram,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' which in this case asks that the following diagram be  a pushout:  T(R) ⊗ E  [T(q),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='pE]  �  [0R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='z]  �  T(E)  λ  �  R  q  � E  (32)  So define the ring morphism δE : T(E) −→ SymR  �  im(Dλ)  �  on generators x ∈ E as follows:  δE(x) = z(x)  δE(d(x)) = Dλ(x)  (33)  By universality of the pushout,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' define ψ−1  E  : ker(q)[ε] −→ E as the unique ring morphism which makes the  following diagram commute:  T(R) ⊗ E  [T(q),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='pE]  �  [0R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='z]  �  T(E)  λ  �  δE  �  R  q  �  qim(Dλ)  �  E  ψ−1  E  �❚  ❚  ❚  ❚  ❚  ❚  ❚  ❚  ❚  SymR  �  im(Dλ)  �  (34)  so ψ−1  E  =  �  qim(Dλ),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' δE  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  38  Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='4 For a commutative ring R and a differential bundle with negatives E = (q : E −→ R, σ, z, λ, ι)  over R in (CRINGop, T), ψE : E −→ M(im(Dλ)) is a differential bundle isomorphism over R in (CRINGop, T)  with inverse ψ−1  E  : M(im(Dλ)) −→ E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Proof: We first explain why ψE and ψ−1  E  are well-defined ring morphisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Clearly, ψE is well-defined by  construction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' On the other hand, to explain why ψ−1  E  is well-defined, we must show that the outer diagram  of (34) commutes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' First, note that by the dual of the second diagram of [DB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='1], z(q(a)) = a for all a ∈ R,  and recall that Dλ(q(a)) = 0 for all a ∈ R as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Then on generators a ∈ R and x ∈ E we compute:  δE  �  [T(q),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' pE](a ⊗ x)  �  = δE  �  (T(q)(a)pE(x))  �  = δE  �  q(a)x  �  = δE  �  q(a)  �  δE (x)= qim(Dλ)  �  z(q(a))  �  qim(Dλ)  �  z(x)  �  = qim(Dλ) (a) qim(Dλ)  �  z(x)  �  = qim(Dλ)(az(x)) = qim(Dλ)  �  0R(a)z(x)  �  = qim(Dλ)  �  [0R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' z](a ⊗ x)  �  and  δE  �  [T(q),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' pE](d(a) ⊗ x)  �  = δE  �  T(q)(d(a))pE(x)  �  = δE  �  d(q(a))x  �  = δE  �  d(q(a))  �  δE (x) = Dλ(q(a))x = 0  = qim(Dλ)(0) = qim(Dλ)(0z(x)) = qim(Dλ)  �  0R(d(a))z(x)  �  = qim(Dλ)  �  [0R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' z](d(a) ⊗ x)  �  So δE ◦ [T(q),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' pE] = qim(Dλ) ◦ [0R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' z].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Therefore, by the universal property of the pushout square, there exists  a unique ring morphism ψ−1  E  : E −→ SymR  �  im(Dλ)  �  such that ψ−1  E  λ = δE and ψ−1  E  q = qim(Dλ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' In  particular, these imply that for every a ∈ R and x ∈ E the following equalities hold:  ψ−1  E (q(a)) = a  ψ−1  E (Dλ(x)) = Dλ(x)  Next we show that ψE and ψ−1  E  are inverses of each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' To show that ψ−1  E  ψE = 1SymR(im(Dλ)), we use  the above identities and compute the following on generators a ∈ R and x ∈ E:  ψ−1  E (ψE(a)) = ψ−1  E (q(a)) = a  ψ−1  E  �  ψE  �  Dλ(x)  ��  = ψ−1  E (Dλ(x)) = Dλ(x)  So ψ−1  E  ψE = 1SymR(im(Dλ)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' On the other hand, to show that ψE ◦ ψ−1  E  = 1E, we will first show that  ψE ◦ ψ−1  E  q = q and ψE ◦ ψ−1  E  λ = λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' So on generators a ∈ R and x ∈ E, we compute:  ψE(ψ−1  E (q(a))) = ψE(a) = q(a)  ψE(ψ−1  E (λ(x))) = ψE(δE(x)) = ψE(z(x)) = q(z(x)) = x  ψE(ψ−1  E (λ(d(x)))) = ψE(δE(d(x))) = ψE(Dλ(x)) = Dλ(x) = λ(d(x))  Therefore, by the universal property of the pushout, it follows that ψE ◦ ψ−1  E  = 1E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' So ψE and ψ−1  E  are  inverse ring isomorphisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Lastly, we must show that ψE and ψ−1  E  are also differential bundle morphisms over R in (CRINGop, T),  that is, we must show the dual of the axioms in Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='10 hold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  We will first show that ψE is a  differential bundle morphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' To do so, first recall that λ(q(a)) = q(a) and Dλ(q(a)) = 0, and that the  dual of [DB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='4] states that λ ◦ T(λ) = λ ◦ ℓE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' So we show that the desired equalities hold by computing the  following on generators:  (i) ψE ◦ qim(Dλ) = q:  ψE(qim(Dλ)(a)) = ψE(a) = q(a)  (ii) λ ◦ T(βE) = ψE ◦ λim(Dλ),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' on a:  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='λ  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='T(βE)(a)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='= λ  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='βE(a)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='= λ(q(a)) = q(a) = ψE(a) = ψE(λim(Dλ)(a)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='39  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='on Dλ(x):  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='λ  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='T(βE)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='Dλ(x)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='��  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='= λ  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='βE  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='Dλ(x)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='��  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='= λ  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='Dλ(x)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='= λ  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='λ(d(x))  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='= λ  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='T(λ)(d(x))  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='= λ  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='ℓE(d(x))  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='= λ(0) = 0 = ψE(0) = ψE  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='λim(Dλ)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='Dλ(x)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='��  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='on d(a):  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='λ  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='T(βE)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='d(a)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='��  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='= λ  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='d  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='βE(a)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='��  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='= λ  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='d  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='q(a)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='��  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='= Dλ(q(a)) = 0 = ψE(0) = ψE  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='λim(Dλ)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='d(a)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='��  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='and finally on d  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='Dλ(x)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=':  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='λ  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='T(βE)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='d  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='Dλ(x)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='���  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='= λ  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='d  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='βE  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='Dλ(x)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='���  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='= λ  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='d  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='Dλ(x)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='��  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='= λ  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='d  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='λ(d(x))  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='��  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='= λ  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='T(λ)(d′d(x))  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='= λ  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='ℓE(d′d(x))  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='= λ  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='d(x)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='= Dλ(x) = βE  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='Dλ(x)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='= ψE  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='λim(Dλ)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='d  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='Dλ(x)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='���  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='So it follows that ψE is a differential bundle morphism over R in (CRINGop,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' T).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' By Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='13 it then follows  that ψ−1  E  is also a differential bundle morphism over R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' So we conclude that ψE and ψ−1  E  are differential  bundle isomorphisms over R in (CRINGop, T).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  ✷  Thus, the construction from a module to a differential bundle is the inverse of the construction from a  differential bundle to a module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' So we conclude that:  Proposition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='5 For a commutative ring R, there is a bijective correspondence between R-modules and  differential bundles (with negatives) over R in (CRINGop, T).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  In CRING, recall that initial object is Z, which means that Z is the terminal object in CRINGop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' So  differential objects in (CRINGop, T) correspond precisely to Z-modules, which are precisely Abelian groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Corollary 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='6 There is a bijective correspondence between Z-modules/Abelian groups and differential objects  in (CRINGop, T).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  We now extend Proposition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='5 to an equivalence of categories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' For a commutative ring R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' we define an  equivalence of categories between MODop  R and DBUNT [R] as follows:  (i) Define the functor MR : MODop  R −→ DBUNT [R] which sends an R-module M to the differential bundle  MR(M),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' and sends an R-linear morphism f : M −→ M ′ to the differential bundle morphism over R  MR(f) : MR(M ′) −→ MR(M) defined to be the ring morphism MR(f) : SymR(M) −→ SymR(M ′) defined  on generators as follows:  MR(f)(a) = a  MR(f)(m) = f(m)  (ii) Define the functor M◦  R : DBUNT [R] −→ MODop  R which sends a differential bundle with negatives over R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  E = (q : E −→ R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' σ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' z,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' λ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' ι) to the R-module M◦  R(E) = im(Dλ),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' and sends a differential bundle morphism  f : E = (q : E −→ R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' σ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' z,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' λ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' ι) −→ E′ = (q′ : E′ −→ R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' σ′,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' z′,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' λ′,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' ι′) over R to the R-linear morphism  M◦  R(f) : im(Dλ′) −→ im(Dλ) defined as:  M◦  R(f)(Dλ′(x)) = Dλ(f(x))  (iii) Observe that M◦  R ◦ MR = 1MODop  R .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  40  (iv) Define the natural isomorphism ψ : 1DBUNT[R] ⇒ MR ◦ M◦  R with inverse ψ−1 : MR ◦ M◦  R ⇒ 1DBUNT[R] as  ψE and ψ−1  E  as defined in Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='7 For a commutative ring R, we have an equivalence of categories: MODop  R ≃ DBUNT [R].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Proof: We must first explain why MR and M◦  R are well-defined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Clearly, MR is well-defined on objects  and maps and preserves composition and identities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' So MR is indeed a functor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' On the other hand, let  f : E −→ E′ be a differential bundle morphism over R in (CRINGop, T).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' This implies that f : E′ −→ E is a  ring morphism and also that f(q′(a)) = q(a) for all a ∈ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Since MR(f) is clearly linear, we show that it  also preserves the action:  M◦  R(f)  �  a · Dλ′(x)  �  = M◦  R(f)  �  Dλ′(q(a)x)  �  = Dλ  �  f(q(a)x)  �  = Dλ  �  f(q′(a))f(x)  �  = Dλ  �  q(a)f(x)  �  = a · Dλ(f(x)) = a · M◦  R(f)(Dλ′(x))  So we have that MR(f) is an R-linear morphism, and so M◦  R is well-defined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Clearly, M◦  R also preserves  composition and identities, so M◦  R is also a functor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Furthermore, we also have that M◦  R ◦ MR = 1MODop  R .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Next, ψ and ψ−1 are well-defined component-wise and are inverses at each component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Therefore, it suffices  to show that ψ is natural and then it will follow that ψ−1 is also natural.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' If f : E −→ E′ is a differential  bundle morphism over R in (CRINGop, T), then f ◦λ′ = λ◦T(f).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' In particular, this means that f(λ′(d(x))) =  λ(d(f(x))).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' However, we can rewrite this as f  �  Dλ′(x)  �  = Dλ  �  f(x)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Therefore, we compute on generators  that:  ψE  �  MR  �  M◦  R(f)  �  (a)  �  = ψE(a) = q(a) = f(q′(a)) = f(ψE′(a))  and  ψE  �  MR  �  M◦  R(f)  � �  Dλ′(x)  ��  = ψE  �  M◦  R(f)  �  Dλ′ (x)  ��  = ψE  �  Dλ  �  f(x)  ��  = Dλ  �  f(x)  �  =  �  Dλ′(x)  �  = f  �  ψE′ �  Dλ′(x)  ��  So ψE ◦ MR  �  M◦  R(f)  �  = f ◦ ψE′ in CRING.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Therefore ψ is a natural transformation, and it follows that so is  ψ−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Thus, ψ and ψ−1 are natural isomorphisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' So we conclude that we have an equivalence of categories:  MODop  R ≃ DBUNT [R].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  ✷  It then follows that we have an equivalence between the category of differential objects and the opposite  category of Abelian groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' So let Ab be the category whose objects are Abelian groups and whose morphisms  are group morphisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Corollary 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='8 There is an equivalence of categories: DBUN  �  (CRINGop, T)  �  ≃ MODZ ≃ Abop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  We now define an equivalence of categories between MODop and DBUN  �  (CRINGop, T)  �  as follows:  (i) Define the functor M : MODop −→ DBUNT [R] which sends an object (R, M) to the differential bundle  M(R, M) = MR(M), and sends a map (g, f) : (R, M) −→ (R′, M ′) in MOD to the differential bundle  morphism M(f) = (MR(f), g) : MR′(M ′) −→ MR(M).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  (ii) Define the functor M◦ : DBUN  �  (CRINGop, T)  �  −→ MODop which sends a differential bundle with  negatives E = (q : E −→ R, σ, z, λ, ι) to the pair M◦(E) = (R, im(Dλ)), and sends a differential bun-  dle morphism (f, g) : E = (q : E −→ R, σ, z, λ, ι) −→ E′ = (q′ : E′ −→ R′, σ′, z′, λ′, ι′) to the pair  M◦(f, g) = (g, M◦  R(f)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  (iii) Observe that M◦ ◦ M = 1MODop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  (iv) Define the natural isomorphism ψ : 1DBUN[(CRINGop,T)] ⇒ M ◦ M◦ as ψE = (1, ψE), with inverse natural  isomrophism ψ  −1 : M ◦ M◦ ⇒ 1DBUN[(CRINGop,T)] as ψ  −1  E  = (1, ψ−1  E ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  41  Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='9 We have an equivalence of categories: MODop ≃ DBUN  �  (CRINGop, T)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Proof: The proof that M and M◦ are well-defined functors is similar to the proof that MR and M◦  R in the  proof of Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Furthermore, it also follows that M◦ ◦ M = 1MODop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' On the other hand, since ψE and  ψ−1  E  are differential bundle morphisms over the base commutative ring, it follows by definition that ψE =  (1, ψE) and ψ  −1  E  = (1, ψ−1  E ) are differential bundle morphisms, so ψ and ψ  −1 are well-defined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Lastly, that ψ,  and ψ  −1 are natural isomorphisms follows directly from the fact that ψ, and ψ−1 are natural isomorphisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  So we conclude that we indeed have an equivalence of categories: MODop ≃ DBUN  �  (CRINGop, T)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  ✷  Remark 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='10 The equivalence between modules and differential bundles is also true in more general set-  tings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Indeed, both for the opposite category of commutative semirings and the opposite category of com-  mutative algebras over a (semi)ring, differential bundles correspond precisely to modules via the above  constructions (where the latter follows from Corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='19 and Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' As explained before, in  a setting where one does not have negatives, we would also need to prove [DB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' On the other hand, it  is unclear if this result always generalizes to the coEilenberg-Moore category of a differential category.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' If  the differential category has enough limits and colimits, then it is possible to generalize the constructions of  Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='1 and Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='2, and then we obtain a bijective correspondence between differential bundles and  comodules of the colagebras of the comonad of said differential category.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' However, in general, a differential  category need not have all limits or colimits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' In future work, it would be interesting to characterize differ-  ential bundles in arbitrary differential categories and understand what assumptions are needed so that they  correspond to (co)modules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='4  Differential bundles in schemes  In this section, we show how we can extend the characterization of differential bundles in affine schemes to  differential bundles in the larger category of schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Since schemes are the gluing of affine schemes, this  follows relatively straightforwardly from the results of the previous sections, so here we merely sketch the  proofs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Our first goal is to show that for any differential bundle q : E −→ A in schemes, the projection q is  an affine map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Let us first quickly recall the definition of affine morphisms and equivalent characterizations  [26, Section 29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Definition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='11 [26, Definition 29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='1] A morphism of schemes f : X −→ Y is affine if for all affine  opens U of Y , the inverse image f −1(U), that is, the following pullback:  f −1(U)  �  �  X  �  U  � Y  is itself affine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Proposition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='12 [26, Lemma 29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='3] For a scheme morphism f : X −→ Y , the following are equivalent:  (i) f is affine;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  (ii) Y has a covering by affine opens {Ui}i∈I such that for all i ∈ I, f −1(Ui) is affine;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  (iii) X = Spec(A) for some quasicoherent sheaf of algebras A on the sheaf OY .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  The following is a general result about affine morphisms which will be useful below:  Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='13 Affine morphisms are closed under retract, that is, if we have scheme morphisms  42  X1  s  �  f1  �❆  ❆  ❆  ❆  ❆  ❆  ❆  ❆  X2  r  �  f2  �⑥⑥⑥⑥⑥⑥⑥⑥  Y  with (s, r) a section/retraction pair in the category of schemes over Y and f2 is affine, then so is f1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Proof: Let U be an affine open subset of Y .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Then we can define a section/retraction pair (sU, rU) between  f −1  1 (U) and f −1  2 (U) with both defined by pullback.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' For example, here is the defining diagram for sU:  f −1  1 (U)  �  sU  �  �  X1  s  �❅  ❅  ❅  ❅  ❅  ❅  ❅  ❅  f −1  2 (U)  �  �  X2  f2  �  U  � Y  Thus f −1  1 (U) is a retract of a representable element in the presheaf category [CRING, SET] (where SET is the  category of sets and arbitrary functions between them).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' But so long as a category X has split idempotents,  then representables in the functor category [Xop, SET] are closed under retract [13, Lemma 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' So f −1  1 (U)  is itself representable, and so by definition f1 is affine, as required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  ✷  We may now prove that for a differential bundle in the category of schemes, the projection is affine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Proposition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='14 In the category of schemes, if q : E −→ A is a differential bundle, then q is affine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Proof: By [22, Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='4], q is a retract of a pullback of a tangent bundle projection pA : T(A) −→ A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  By definition, T(A) is Spec of a quasicoherent sheaf of algebras on OA, so by Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='12, pA is affine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' But  affines are closed under pullback [26, Lemma 29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='8] and retracts (Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='13), so q is affine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  ✷  We may now prove that every differential bundle is a Spec of Sym of a quasicoherent sheaf of modules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Proposition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='15 If q : E −→ A is a differential bundle in the category of schemes, then E is Spec of Sym  of a quasicoherent sheaf of modules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Proof: Cover A by affines Ui, and since q is affine, each pullback q−1(Ui):  q−1(U)  �  �  E  q  �  Ui  � A  is also affine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Moreover, by [8, Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='7], differential bundles are closed under pullback.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Thus each map  q−1(Ui) −→ Ui is a differential bundle in the category of affine schemes, and hence by Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='5, each  q−1(Ui) is Sym of a module on Ui.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Thus as E is the gluing of these, E is itself Spec of Sym of a quasicoherent  sheaf of modules [28, pg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' 379].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  ✷  Conversely, we now prove that every quasicoherent sheaf of modules induces a differential bundle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Proposition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='16 If M is a quasicoherent sheaf of modules on a scheme A, then Spec of Sym of M is a  differential bundle over A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  43  Proof: Suppose that A is covered by affines Ui.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Then by [28, pg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='379], if M is a quasicoherent sheaf of  modules on A, then M is the gluing of modules Mi over the Ui, and Spec of Sym of M is the gluing of  Spec of Sym of the Mi’s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Thus it suffices to show that such a gluing is a differential bundle over A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' But  by Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='2, Spec of Sym of each Mi is a differential bundle over Ai.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  It then follows that since the  tangent functor on schemes preserves gluings (for an abstract proof of this, see [5, Prop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='ii]), the lifts  of each such differential bundle λi glue together to give a lift λ for Spec of Sym of M, and it follows through  straightforward calculations that this satisfies the required conditions to be a differential bundle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  ✷  The results on morphisms follow similarly, and therefore we obtain:  Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='17 For a scheme A, there is an equivalence of categories between differential bundles over A  in the tangent category SCH and the opposite category of quasicoherent sheaves of modules over A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Remark 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='18 By Corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='22 and Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='4, for any scheme A, there is a similar result for the  tangent category of schemes over A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  6  Future work  Understanding differential bundles in the tangent categories of commutative rings, affine schemes, and  schemes is just the beginning of applying tangent category theory to algebra and algebraic geometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' There  are many possible future avenues for exploration based on this work, such as:  The most immediate next step is to understand how connections in tangent categories apply to these  examples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' They seem closely related to connections on modules [23, Section 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='2], but more work needs  to be done to understand the precise relationship between the two notions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Tangent categories have a notion of differential forms and de Rham cohomology [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Initial inves-  tigation with this idea suggests that for affine schemes over R, when the coefficient object is taken  to be the polynomial ring R[x], then this tangent category cohomology recreates algebraic de Rham  cohomology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' However, again more investigation is required to prove this completely.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Moreover, [11]  also develops a second notion of cohomology: sector form cohomology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' It is not clear what this should  give in the algebraic geometry setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  In [16], Dominic Joyce develops algebraic geometry in the setting of C∞-rings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' It seems likely that  the categories involved are tangent categories, and one expects many of the tangent categories theory  ideas, applied to this example, recreate the corresponding notions Joyce has developed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  A key idea in algebraic geometry is that of a smooth morphism or object.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' It would be interesting to see  if such a notion could be generalized to arbitrary tangent categories (in such a way, that, for example,  all objects in the tangent category of smooth manifolds are smooth).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Finally, the Serre-Swan theorem provides a very different way to compare vector bundles to modules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  It would be interesting to see a proof for the Serre-Swan theorem based on some of the results of this  paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Thus, while the results of this paper are interesting enough on their own, we hope they will also serve as  inspiration for future work in this area.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  References  [1] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Bauer,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Burke,  and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Ching.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Tangent infinity-categories and Goodwillie calculus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  arXiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='org:2101.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='07819, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  44  [2] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Beck.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Triples, algebras and cohomology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Columbia University, 1967.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  [3] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Blute, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Cockett, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Seely.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Cartesian differential categories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Theory and  Applications of Categories, 22(23):622–672, 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  [4] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Blute, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Lucyshyn-Wright, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' O’Neill.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Derivations in codifferential categories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Cahiers  de Topologie et G´eom´etrie Diff´erentielle Cat´egoriques, 57:243–280, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  [5] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Cockett and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Cruttwell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Differential structure, tangent structure, and SDG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Applied  Categorical Structures, 22(2):331–417, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  [6] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Cockett and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Cruttwell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' The Jacobi identity for tangent categories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Cahiers de Topologie  et G´eom´etrie Diff´erentielle Cat´egoriques, LVI(4):301–316, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  [7] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Cockett and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Cruttwell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Connections in tangent categories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Theory and applications of  categories, 32(26):835–888, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  [8] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Cockett and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Cruttwell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Differential bundles and fibrations for tangent categories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  Cahiers de Topologie et G´eom´etrie Diff´erentielle Cat´egoriques, LIX:10–92, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  [9] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Cockett, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Cruttwell, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Lemay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Differential equations in a tangent category I:  Complete vector fields, flows, and exponentials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Applied Categorical Structures, 29(5):773–825, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  [10] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Cockett, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Lemay, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Lucyshyn-Wright.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Tangent Categories from the Coal-  gebras of Differential Categories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  In M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Fern´andez and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Muscholl, editors, 28th EACSL Annual  Conference on Computer Science Logic (CSL 2020), volume 152 of Leibniz International Proceedings in  Informatics (LIPIcs), pages 17:1–17:17, Dagstuhl, Germany, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Schloss Dagstuhl–Leibniz-Zentrum  fuer Informatik.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  [11] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Cruttwell and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Lucyshyn-Wright.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' A simplicial foundation for differential and sector  forms in tangent categories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Journal of Homotopy and Related Structures volume, 13:867–925, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  [12] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Ehrhard and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Regnier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' The differential lambda-calculus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Theoretical Computer Science, 309(1):1–  41, 2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  [13] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Francis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Handbook of Categorical Algebra, Volume I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Cambridge University Press, 1994.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  [14] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Garner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' An embedding theorem for tangent categories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Advances in Mathematics, 323:668–687, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  [15] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Grothendieck.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' ´El´ements de g´eom´etrie alg´ebrique IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Publications Math´ematiques de l’IH´ES, 28:5–  255, 1966.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  [16] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Joyce.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' An introduction to C-infinity schemes and C-infinity algebraic geometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Surveys in Differ-  ential Geometry, 79:299–325, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  [17] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Jubin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' The tangent functor monad and foliations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' arXiv preprint arXiv:1401.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='0940, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  [18] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Kock.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Synthetic differential geometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Cambridge University Press, 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  [19] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Kriegl and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Michor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' The convenient setting of global analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' American Mathematical Society,  1997.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  [20] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Lawevere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Categorical Dynamics, pages 1–28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Aarhus University Press, 1979.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  [21] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Mac Lane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Categories for the working mathematician, volume 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Springer Science & Business Media,  2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  [22] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' MacAdam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Vector bundles and differential bundles in the category of smooth manifolds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Applied  categorical structures, 29(2):285–310, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  45  [23] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Mangiarotti and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Sardanashvily.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Connections In Classical And Quantum Field Theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' World  Scientific Publishing Company, 2000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  [24] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Michor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' The Jacobi flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Rend.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Sem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Mat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Univ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Pol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Torino, 54(4):365–372, 1996.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  [25] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Rosick`y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Abstract tangent functors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Diagrammes, 12:JR1–JR11, 1984.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  [26] The Stacks Project Authors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Stacks Project.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' https://stacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='columbia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='edu, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  [27] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Tu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' An introduction to manifolds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Springer, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  [28] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Vakil.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' The rising sea: Foundations of algebraic geometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content=' Online textbook, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
+page_content='  46' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE5T4oBgHgl3EQfUQ9g/content/2301.05542v1.pdf'}
diff --git a/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf b/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..f58ac1c7fa0664968e7d24dd09c919a6c42b56f9
--- /dev/null
+++ b/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:d25df5f2a017ce78ef7118056a1f5d77188bd45ff6b498708456553465282715
+size 1111783
diff --git a/F9E4T4oBgHgl3EQfHQxB/vector_store/index.pkl b/F9E4T4oBgHgl3EQfHQxB/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..a6965d6466f54c484e614426b66fef663e586ded
--- /dev/null
+++ b/F9E4T4oBgHgl3EQfHQxB/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:e509fa701b1390ac8592bbe2aa7b84964cedacf34dacaf4fe2652d79cdfdef32
+size 185772
diff --git a/FtE1T4oBgHgl3EQf-waO/content/tmp_files/2301.03573v1.pdf.txt b/FtE1T4oBgHgl3EQf-waO/content/tmp_files/2301.03573v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..26e9de3ce239f34681627fda5c90c540037f2a65
--- /dev/null
+++ b/FtE1T4oBgHgl3EQf-waO/content/tmp_files/2301.03573v1.pdf.txt
@@ -0,0 +1,3400 @@
+Balance is Essence: Accelerating Sparse Training via Adap-
+tive Gradient Correction
+Bowen Lei
+bowenlei@stat.tamu.edu
+Texas A&M University
+Dongkuan Xu
+dxu27@ncsu.edu
+North Carolina State University
+Ruqi Zhang
+ruqiz@purdue.edu
+Purdue University
+Shuren He
+dri.tea@tamu.edu
+Texas A&M University
+Bani K. Mallick
+bmallick@stat.tamu.edu
+Texas A&M University
+Abstract
+Despite impressive performance on a wide variety of tasks, deep neural networks re-
+quire significant memory and computation costs, prohibiting their application in resource-
+constrained scenarios. Sparse training is one of the most common techniques to reduce these
+costs, however, the sparsity constraints add difficulty to the optimization, resulting in an
+increase in training time and instability. In this work, we aim to overcome this problem and
+achieve space-time co-efficiency. To accelerate and stabilize the convergence of sparse train-
+ing, we analyze the gradient changes and develop an adaptive gradient correction method.
+Specifically, we approximate the correlation between the current and previous gradients,
+which is used to balance the two gradients to obtain a corrected gradient. Our method can
+be used with most popular sparse training pipelines under both standard and adversarial se-
+tups. Theoretically, we prove that our method can accelerate the convergence rate of sparse
+training. Extensive experiments on multiple datasets, model architectures, and sparsities
+demonstrate that our method outperforms leading sparse training methods by up to 5.0%
+in accuracy given the same number of training epochs, and reduces the number of training
+epochs by up to 52.1% to achieve the same accuracy.
+1
+Introduction
+With the development of deep neural networks (DNNs), there is a trend towards larger and more intensive
+computational models to enhance task performance. Despite of the good performance, such large models are
+not applicable when memory or computational resources are limited (Bellec et al., 2017; Evci et al., 2020;
+Liu et al., 2022). In addition, these large models consume a considerable amount of energy and produce a
+large amount of carbon footprint (Thompson et al., 2021; Patterson et al., 2021; Matus & Veale, 2022). As a
+result, it attracts more efforts in research to find resource-efficient ways (e.g., less memory & less compute)
+to train DNNs while maintaining results comparable to the state of the art (Yu & Li, 2021; Rock et al., 2021;
+Leite & Xiao, 2021).
+Sparse training (Mocanu et al., 2018; Evci et al., 2020; Liu et al., 2022) is one of the most popular classes of
+methods to improve efficiency in terms of space (e.g. memory storage) and is receiving increasing attention.
+During sparse training, a certain percentage of connections are removed to save memory (Bellec et al.,
+2017; Evci et al., 2020). Sparse patterns, which describe where connections are retained or removed, are
+1
+arXiv:2301.03573v1  [cs.LG]  9 Jan 2023
+
+iteratively updated with various criteria (Dettmers & Zettlemoyer, 2019; Evci et al., 2020; Liu et al., 2021;
+Özdenizci & Legenstein, 2021). The goal is to find a resource-efficient sparse neural network (i.e., removing
+some connections) with comparable or even higher performance compared to the original dense model (i.e.,
+keeping all connections).
+However, sparse training can bring some side effects to the training process, especially in the case of high
+sparsity (e.g., 99% weights are zero). First, sparsity can increase the variance of stochastic gradients, leading
+the model to move in a sub-optimal direction and hence slow convergence (Hoefler et al., 2021; Graesser
+et al., 2022). As shown in Figure 1 (a), we empirically see that the gradient variance grows with increasing
+sparsity (more details in Section C.1). Second, it can result in training instability (i.e., a noisy trajectory of
+test accuracy w.r.t. iterations) (Sehwag et al., 2020; Bartoldson et al., 2020), which requires additional time
+to compensate for the accuracy drop, resulting in slow convergence (Xiao et al., 2019). Additionally, the
+need to consider the robustness of the model during sparse training is highlighted in order to apply sparse
+training to a wide range of real-world scenarios where there are often challenges with dataset shifts (Ye et al.,
+2019; Hoefler et al., 2021; Kundu et al., 2021; Özdenizci & Legenstein, 2021). To address these issues, we
+raise the following questions:
+Question 1. How to simultaneously improve convergence speed and training stability of sparse training?
+Prior gradient correction methods, such as variance reduction (Zou et al., 2018; Chen et al., 2019; Gorbunov
+et al., 2020), are used to accelerate and stabilize dense training, while we find that it fails in sparse training.
+They usually assume that current and previous gradients are highly correlated, and therefore they add a
+large constant amount of previous gradients to correct the gradient (Dubey et al., 2016; Chatterji et al.,
+2018; Chen et al., 2019). However, this assumption does not hold in sparse training. Figure 1 (b) shows the
+gradient correlation at different sparsities, implying that the gradient correlation decreases with increasing
+sparsity (more details in Section C.1), which breaks the balance between current and previous gradients.
+Therefore, we propose to adaptively change the weights of previous and current gradients based on their
+correlation to add an appropriate amount of previous gradients.
+Question 2. How to design an accelerated and stabilized sparse training method that is effective in real-world
+scenarios with dataset shifts?
+Moreover, real-world applications are under-studied in sparse training. Prior methods use adversarial training
+to improve model robustness and address the challenge of data shifts, which usually introduces additional bias
+beyond the variance in the gradient estimation (Li et al., 2020), increasing the difficulty of gradient correction
+(more details in Section 4.2). Thus, to more accurately approximate the full gradient, especially during the
+adversarial setup, we design a scaling strategy to control the weights of the two gradients, determining the
+amount of previous gradient information to be added to the current gradient, which helps the balance and
+further accelerates the convergence.
+In this work, we propose an adaptive gradient correction (AGENT) method to accelerate and stabilize sparse
+training for both standard and adversarial setups. Theoretically, we prove that our method can accelerate the
+convergence rate of sparse training. Empirically, we perform extensive experiments on multiple benchmark
+datasets, model architectures, and sparsities. In both standard and adversarial setups, our method improves
+the accuracy by up to 5.0% given the same number of epochs and reduces the number of epochs up to
+52.1% to achieve the same performance compared to the leading sparse training methods. In contrast to
+previous efforts of sparse training acceleration which mainly focus on structured sparse patterns, our method
+is compatible with both unstructured ans structured sparse training pipelines (Hubara et al., 2021; Chen
+et al., 2021).
+2
+Related Work
+2.1
+Sparse Training
+Interest in sparse DNNs has been on the rise recently, especially when dealing with resource constraints.
+The goal is to achieve comparable performance with sparse weights to satisfy the constraints. Different
+sparse training methods have emerged, where sparse weights are maintained in the training process. Various
+2
+
+0%
+50%
+80%
+90%
+95%
+Sparsity
+2.5
+5.0
+7.5
+10.0
+12.5
+15.0
+17.5
+20.0
+Gradient Variance (e-8)
+RigL
+SET
+(a) Gradient Variance
+0%
+50%
+80%
+90%
+95%
+Sparsity
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+Gradient Correlation
+RigL
+SET
+(b) Gradient Correlation
+Figure 1: Gradient variance (a) and gradient correlation (b) of models obtained by RigL and SET at different
+sparsities including 0% (dense), 50%, 80%, 90%, 95%. Gradient variance grows with increasing sparsity.
+Gradient correlation drops with increasing sparsity. The sparse models have larger gradient variance and
+smaller gradient correlation compared to dense models.
+pruning and growth criteria are proposed, such as weight/gradient magnitude, random selection, and weight
+sign (Mocanu et al., 2018; Bellec et al., 2018; Frankle & Carbin, 2019; Mostafa & Wang, 2019; Dettmers &
+Zettlemoyer, 2019; Evci et al., 2020; Jayakumar et al., 2020; Liu et al., 2021; Özdenizci & Legenstein, 2021;
+Zhou et al., 2021b; Schwarz et al., 2021; Huang et al., 2022; Liu et al., 2022).
+However, the aforementioned studies focus on improving the performance of sparse training, while neglect-
+ing the side effect of sparse training. Sparsity not only increases gradient variance, thus delaying conver-
+gence (Hoefler et al., 2021; Graesser et al., 2022), but also leads to training instability (Bartoldson et al.,
+2020). It is a challenge to achieve both space and time efficiency. Additionally, sparse training can also
+exacerbate models’ vulnerability to adversarial samples, which is one of the weaknesses of DNNs (Özdenizci
+& Legenstein, 2021). When the model encounters intentionally manipulated data, its performances may
+deteriorate rapidly, leading to increasing security concerns Rakin et al. (2019); Akhtar & Mian (2018). In
+this paper, we focus on sparse training. In general, our method can be applied to any SGD-based sparse
+training pipelines.
+2.2
+Accelerating Training
+Studies have been conducted in recent years on how to achieve time efficiency in DNNs, and one popular
+direction is to obtain a more accurate gradient estimate to update the model (Gorbunov et al., 2020), such
+as variance reduction. SGD is the most common training method, where one uses small batches of data
+to approach the full gradient. In standard training, the batch estimator is unbiased, but can have a large
+variance and misguide the model, leading to studies on variance reduction (Johnson & Zhang, 2013; Xiao
+& Zhang, 2014; Shang et al., 2018; Zou et al., 2018; Chen et al., 2019; Gorbunov et al., 2020).
+While
+adversarial training brings bias in the gradient estimation (Li et al., 2020), and we need to face the bias-
+variance tradeoff when doing gradient correction. A shared idea is to balance the gradient noise with a
+less-noisy old gradient (Nguyen et al., 2017; Fang et al., 2018; Chen et al., 2019). Some other momentum-
+based methods have a similar strategy of using old information (Cutkosky & Orabona, 2019; Chayti &
+Karimireddy, 2022) However, all the above work considers only the acceleration in non-sparse case.
+Acceleration is more challenging in sparse training, and previous research on it has focused on structured
+sparse training (Hubara et al., 2021; Chen et al., 2021; Zhou et al., 2021a). First, sparse training will induce
+larger variance (Hoefler et al., 2021). In addition, some key assumptions associated with gradient correction
+methods do not hold under sparsity constraint. In the non-sparse case, the old and new gradients are assumed
+to be highly correlated, so we can collect a large amount of knowledge from the old gradients (Chen et al.,
+3
+
+2019; Chatterji et al., 2018; Dubey et al., 2016). However, sparsity tends to lead to lower correlations, and
+this irrelevant information can be harmful, making previous methods no longer applicable to sparse training
+and requiring a finer balance between new and old gradients. Furthermore, the structured sparsity pattern
+is not flexible enough, which can lead to lower model accuracy. In contrast, our method accelerates sparse
+training from an optimization perspective and is compatible with both unstructured and structured sparse
+training pipelines.
+3
+Preliminaries: Stochastic Variance Reduced Gradient
+Stochastic variance reduced gradient (SVRG) (Johnson & Zhang, 2013; Allen-Zhu & Hazan, 2016; Dubey
+et al., 2016) is a widely-used gradient correction method designed to obtain more accurate gradient estimates,
+which has been followed by many studies (Zou et al., 2018; Baker et al., 2019; Chen et al., 2019). Specifically,
+after each epoch of training, we evaluate the full gradients �g based on �θ at that time and store them for
+later use. In the next epoch, the batch gradient estimate on Bt is updated using the stored old gradients
+via Eq. (1).
+ˆg(θt) = 1
+n
+�
+i∈Bt
+�
+gi(θt) − gi(�θ)
+�
++ �g
+(1)
+where gi(θt) = ∇G(xi|θt), G(θt) = (�N
+i=1 G(xi|θt))/N is the loss function, �g = ∇G(�θ), θt is the current
+parameters, n is the number of samples in each mini-batch data, and N is the total number of samples.
+SVRG successfully accelerates many training tasks in the non-sparse case, but does not work well in sparse
+training, which is similar to many other gradient correction methods.
+4
+Method
+We propose an adaptive gradient correction (AGENT) method and integrate it with recent sparse training
+pipelines to achieve accelerations and improve training stability. Specifically, to accomplish the goal, our
+AGENT filters out less relevant information and obtains a well-controlled and time-varying amount of knowl-
+edge from the old gradients. Our method overcomes the limitations of previous acceleration methods such
+as SVRG (Allen-Zhu & Hazan, 2016; Dubey et al., 2016; Elibol et al., 2020), and successfully accelerates and
+stabilizes sparse training. We will illustrate each part of our method in the following sections. Our AGENT
+method is outlined in Algorithm 1.
+4.1
+Adaptive Control over Old Gradients
+In AGENT, we designed an adaptive addition of old gradients to new gradients to filter less relevant informa-
+tion and achieve a balance between new and old gradients. Specifically, we add an adaptive weight ct ∈ [0, 1]
+to the old gradient as shown in Eq. (2), where we use gnew = 1
+n
+�
+i∈Bt gi(θt) and gold = 1
+n
+�
+i∈Bt gi(�θ) to de-
+note the gradient on current parameters θt and previous parameters �θ for a random subset Bt, respectively.
+When the old and new gradients are highly correlated, we need a large c to get more useful information from
+the old gradient. Conversely, when the relevance is low, we need a smaller c so that we do not let irrelevant
+information corrupt the new gradient.
+ˆg(θt) = 1
+n
+�
+i∈Bt
+�
+gi(θt) − ct · gi(�θ)
+�
++ ct · �g = gnew − ct · gold + ct · �g.
+(2)
+A suitable ct should effectively reduce the variance of ˆg(θt). To understand how ct influence the variance
+of updated gradient, we decompose the variance of ˆg(θt) in Eq. (3) with some abuse of notation, where the
+variance of updated gradient is a quadratic function of ct. For simplicity, considering the case where ˆg(θt)
+is a scalar, the optimal c∗
+t will be in the form of Eq. (3). As we can see, c∗
+t is not closed to 1 when the new
+gradient is not highly correlated with the old gradient. Since low correlation between gnew and gold is more
+common in sparse training, directly setting ct = 1 in previous methods is not appropriate and we need to
+estimate adaptive weights c∗
+t . In support of this claim, we include a discussion and empirical analysis in
+4
+
+the Appendix B.6 to demonstrate that as sparsity increases, the gradient changes faster, leading to lower
+correlations between gnew and gold.
+Var(ˆg(θt)) = Var(gnew) + c2
+t · Var(gold) − 2ct · Cov(gnew, gold),
+c∗
+t = Cov(gnew, gold)
+Var(gold)
+.
+(3)
+We find it impractical to compute the exact c∗
+t and thus propose an approximation algorithm for it to obtain
+a balance between the new and old gradient. There are two challenges to calculate the exact c∗
+t . On the
+one hand, to approach the exact value, we need to calculate the gradients on every batch data, which is too
+expensive to do it in each iteration. On the other hand, the gradients are often high-dimensional and the
+exact optimal c∗
+t will be different for different gradients. Thus, inspired by Deng et al. (2020), we design
+an approximation algorithm that makes good use of the loss information and leads to only a small increase
+in computational effort. More specifically, we estimate c∗
+t according to the changes of loss as shown in Eq.
+(4) and update �c∗
+t adaptively before each epoch using momentum. Loss is a scalar, which makes it possible
+to estimate the shared correlation for all current and previous gradients. In addition, the loss is intuitively
+related to gradients and the correlation between losses can give us some insights into that of the gradients
+(some empirical analyses are included in the Appendix B.7).
+�c∗
+t = Cov(G(B|θt), G(B|�θ))
+Var(G(B|�θ))
+,
+(4)
+where B denotes a subset of samples used to estimate the gradients.
+Algorithm 1 Adaptive Gradient Correction
+Input: �θ = θ0, epoch length m, step size ηt, c0 = 0, scaling
+parameter γ, smoothing factor α
+for t = 0 to T − 1 do
+if t mod m = 0 then
+�θ = θt
+�g = (�N
+i=1 ∇G(xi|�θ))/N
+if t > 0 then
+Calculate ˆc∗
+t via Eq. (4)
+ct = (1 − α)ct−1 + α ˆc∗
+t
+end if
+else
+ct = ct−1
+end if
+Sample a mini-batch data Bt with size n
+θt+1 = θt − ηt ·
+�
+1
+n
+�
+i∈Bt
+�
+gi(θt) − γct · gi(�θ)�
++ γct · �g
+�
+end for
+We empirically justify the loss-based approxi-
+mation in Eq. (4). Experimental details are
+included in Section B.7).
+We compare the
+approximation �c∗
+t and the correlation between
+the gradient of current weights and the gradi-
+ent of previous epoch weights.
+We find that
+�c∗
+t and the correlation have similar up-and-
+down patterns, indicating that our approxima-
+tion captures the dynamic patterns of the cor-
+relation. For differences in magnitude, they can
+be matched by the scaling strategy we will de-
+scribe in the next Section 4.2.
+4.2
+Additional
+Scaling Parameter is Important
+To guarantee successful acceleration in sparse
+and adversarial training, we further propose a
+scaling strategy that multiplies the estimated
+c∗
+t by a small scaling parameter γ. There are two main benefits of using a scaling parameter. First, the
+scaling parameter γ can reduce the bias of the gradient estimates in adversarial training (Li et al., 2020). In
+standard training, the batch gradient estimator is an unbiased estimator of the full gradient. However, in
+adversarial training, we perturb the mini-batch of samples Bt into ¯Bt. The old gradients gold are calculated
+on batch data ¯Bt, but the stored old gradients �g are obtained from the original data including Bt, which
+makes E[gold−�g] unequal to zero. Consequently, as shown in Eq. (5), the corrected estimator for full gradients
+will no longer be unbiased. It may have a small variance but a large bias, resulting in poor performance.
+Therefore, we propose a scaling parameter γ between 0 and 1 to reduce the bias from ct(gold − �g) to
+γct(gold − �g).
+E[ˆg(θt)] = E[gnew − ct(gold − �g)] ̸= E[gold] = 1
+N
+N
+�
+i=1
+gi(θt).
+(5)
+Second, the scaling parameter γ guarantees that the variance can still be reduced in the face of worst-case
+estimates of c∗
+t to accelerate the training.
+The key idea is illustrated in Figure 2, where x and y axis
+5
+
+correspond to the weight ct and the gradient variance, respectively. The blue curve is a quadratic function
+that represents the relationship between ct and the variance. Suppose the true optimal is c∗, and we make
+an approximation to it. In the worst case, this approximation may be as bad as ˆc1, making the variance
+even larger than a3 (variance in SGD) and slowing down the training. Then, if we replace ˆc1 with γˆc1, we
+can reduce the variance and accelerate the training.
+4.3
+Connection to Momentum-based Method
+To some extent, our AGENT is designed with a similar idea to the momentum-based method (Qian, 1999;
+Ruder, 2016), where old gradients are used to improve the current batch gradient. However, the momentum-
+based method still suffers from optimization difficulties due to sparsity constraints. The reason is that it does
+not take into account sparse and adversarial training characteristics such as the reduced correlation between
+current and previous gradients and potential bias of gradient estimator, and fails to provide an adaptive
+balance between old and new information. When the correlation is low, the momentum-based method can
+still incorporate too much of the old information and increase the gradient variance or bias. In contrast, our
+AGENT is designed for sparse and adversarial training and can establish finer adaptive control over how
+much information we should take from the old to help the new.
+4.4
+Connection to Adaptive Gradient Method
+c∗
+a3
+ˆc1
+γˆc1
+y = a1c2 − 2a2c + a3
+Figure 2: Illustration of how the scaling parameter
+γ = 0.1 ensures the acceleration in the face of worst-
+case estimate of c∗
+t . The blue curve is a quadratic
+function, representing the relationship between ct
+and the variance. c∗ is the optimal value. ˆc1 is a
+poor estimate making the variance larger than a3
+(variance in SGD). γˆc1 can reduce the variance.
+Our AGENT can be viewed as a new type of adaptive
+gradient method that adaptively adjusts the amount
+of gradient information used to update parameters,
+such as Adam (Kingma & Ba, 2014). However, pre-
+vious adaptive gradient methods are not designed for
+sparse training. Although they also provide adaptive
+gradients, their adaptivity is different and does not
+take the reduced correlation into account.
+On the
+contrary, our AGENT is designed for sparse training
+and is tailored to the characteristics of sparse training.
+When old information is used to correct the gradients,
+the main problem is the reduced correlation between
+the old and new gradients. Therefore, our AGENT
+approximates the correlation and adds an adaptive
+weight to the old gradient to establish a balance be-
+tween the old and new gradients.
+5
+Theoretical Justification
+Theoretically, we provide a convergence analysis for our AGENT and compare it to SVRG (Reddi et al.,
+2016).
+We use G(.) to denote the loss function and g to denote the gradient.
+Our proof is based on
+Assumptions 1-2, and detailed derivation is included in Appendix A.
+Assumption 1. (L-smooth): The differentiable loss function G : Rn → R is L-smooth, i.e., for all x, y ∈ Rn
+is satisfies ||∇G(x) − ∇G(y)|| ≤ L||x − y||. And an equivalent definition is for. all x, y ∈ Rn:
+−L
+2 ||x − y||2 ≤ G(x) − G(y) − ⟨∇G(x), x − y⟩ ≤ L
+2 ||x − y||2
+Assumption 2. (σ-bounded): The loss function G has a σ-bounded gradient, i.e., ||∇Gi(x)|| ≤ σ for all
+i ∈ [N] and x ∈ Rn.
+Our convergence analysis framework outlines four steps:
+• We first show that an appropriate choice of ct will result in smaller variance in our gradient estimates
+compared to SVRG.
+6
+
+• Next, we show the convergence rate of one arbitrary training epoch.
+• We then extend the one-epoch results and analyze the convergence rate for the whole epoch.
+• After obtaining the convergence rate, we bring it to the real case of sparse learning and find that our
+method indeed yields a tighter bound.
+Given Assumptions 1-2, we follow the analysis framework above and establish Theorem 1 to show the
+convergence rate of our AGENT:
+Theorem 1. Under Assumptions 1-2, with proper choice of step size ηt and ct, the gradient E[||g(θπ)||2]
+using AGENT after T training epochs can be bounded by:
+E[||g(θπ)||2] ≤ (G(θ0) − G(θ∗))LN α
+Tnν
++ 2κµ2σ2
+N αmν
+where θπ is sampled uniformly from {{θs
+t }m−1
+t=0 }T −1
+s=0 , N denotes the data size, n denotes the mini-batch size,
+m denotes the epoch length, θ0 is the initial point and θ∗ is the optimal solution, ν, µ, κ, α > 0 are constants
+depending on ηt and ct, N and n.
+In regard to Theorem 1, we make the following remarks to justify the acceleration from our AGENT:
+Remark 1. (Faster Gradient Change Speed) An influential difference between sparse and dense training is
+the gradient change speed, which is reflected in Assumption 1 (L-smooth). Typically, L in sparse training
+will be larger than L in dense training.
+Remark 2. (First Term Analysis) In Theorem 1, the first term in the bound of our AGENT measures the
+error introduced by deviations from the optimal parameters, which goes to zero when the number of epochs
+T reaches infinity. However, in real sparse training applications, T is finite and this term is expanded due
+to the increase of L in sparse training, which implies that the optimization under sparse constraints is more
+challenging.
+Remark 3. (Second Term Analysis) In Theorem 1, the second term measures the error introduced by the
+noisy gradient and the finite data during the optimization. Since σ2 is relatively small and N is usually large
+in our DNNs training, the second term is negligible or much smaller compared to the first term when T is
+assumed to be finite.
+From the above analysis, we can compare the bounds of AGENT and SVRG and find that in the case of
+sparse training, an appropriate choice of ct can make the bound for our AGENT tighter than the bound for
+SVRG by well-corrected gradients.
+Remark 4. (Comparison with SVRG) Under Assumptions 1-2, the gradient E[||g(θπ)||2] using SVRG after
+T training epochs can be bounded by (Reddi et al., 2016):
+E[||g(θπ)||2] ≤ (G(θ0) − G(θ∗))LN α
+Tnν∗
+.
+This bound is of a similar form to the first term in Theorem 1. Since the second term of Theorem 1 is
+negligible or much smaller than the first one, we only need to compare the first term. With a proper choice
+of ct, the variance of ˆg(θt) will decrease, which leads to a smaller ν for AGENT than ν∗ for SVRG (detailed
+proof is included in Appendix A Remark 6). Thus, AGENT can bring a smaller first term compared to
+SVRG, which indicates that AGENT effectively reduces the error due to the deviations and has a tighter
+bound compared to SVRG.
+6
+Experiments
+We add our AGENT to three recent sparse training pipelines, namely SET (Mocanu et al., 2018), RigL (Evci
+et al., 2020), BSR-Net (Özdenizci & Legenstein, 2021) and ITOP (Liu et al., 2021). SET is a broadly-used
+sparse training method that prunes and regrows connections by examining the magnitude of the weights.
+7
+
+Table 1: Testing accuracy (%) of BSR-Net-based models.
+Sparse VGG-16 are learned in standard and
+adversarial setups. Results are presented as clean/robust accuracy (%). For the same number of training
+epochs, our method has higher accuracy compared to BSR-Net in almost all cases.
+90% Sparsity
+99% Sparsity
+BSR-Net
+Ours
+BSR-Net
+Ours
+AT
+20-th
+55.0 (1.59)/38.2
+63.6 (1.31)/37.3
+49.8 (1.46)/31.0
+56.4 (1.39)/31.4
+40-th
+62.2 (1.88)/39.2
+64.9 (0.81)/37.9
+54.1 (1.72)/33.9
+57.7 (0.39)/34.5
+70-th
+73.1 (0.39)/37.8
+75.1 (0.27)/45.2
+64.7 (0.30)/34.9
+66.0 (0.23)/39.4
+90-th
+73.2 (0.29)/33.6
+74.1 (0.25)/44.8
+63.7 (0.25)/35.8
+65.8 (0.24)/39.8
+140-th
+76.7 (0.27)/46.5
+77.4 (0.26)/43.8
+68.4 (0.20)/40.8
+69.8 (0.14)/41.2
+200-th
+76.6 (0.25)/43.3
+78.1 (0.24)/44.6
+69.0 (0.15)/42.2
+70.7 (0.06)/42.0
+TRADES
+20-th
+62.0 (0.82)/33.3
+65.0 (0.61)/37.6
+55.7 (0.76)/25.5
+57.6 (0.45)/31.6
+40-th
+65.4 (0.97)/35.3
+66.0 (0.34)/37.2
+60.6 (0.69)/28.9
+58.4 (0.34)/33.4
+70-th
+73.4 (0.52)/34.8
+73.5 (0.33)/45.4
+66.3 (0.35)/33.5
+67.3 (0.30)/39.0
+90-th
+73.0 (0.36)/36.8
+73.6 (0.28)/44.8
+66.2 (0.33)/31.7
+67.5 (0.24)/39.1
+140-th
+76.4 (0.25)/45.1
+76.8 (0.25)/46.3
+70.0 (0.29)/38.2
+69.9 (0.21)/41.5
+200-th
+75.6 (0.23)/47.2
+77.0 (0.24)/46.2
+70.8 (0.19)/39.3
+70.9 (0.25)/41.2
+Standard
+20-th
+70.4 (2.50)/0.0
+81.8 (0.62)/0.0
+60.6 (1.26)/0.0
+69.8 (1.45)/0.0
+40-th
+77.6 (1.39)/0.0
+82.4 (0.47)/0.0
+62.6 (2.47)/0.0
+73.7 (0.36)/0.0
+70-th
+86.8 (0.78)/0.0
+89.7 (0.38)/0.0
+79.7 (0.72)/0.0
+83.7 (0.24)/0.0
+90-th
+87.6 (0.63)/0.0
+89.3 (0.22)/0.0
+80.5 (0.55)/0.0
+83.9 (0.42)/0.0
+140-th
+91.7 (0.44)/0.0
+92.5 (0.06)/0.0
+85.7 (0.42)/0.0
+86.9 (0.07)/0.0
+200-th
+91.8 (0.23)/0.0
+92.6 (0.12)/0.0
+85.8 (0.12)/0.0
+87.1 (0.25)/0.0
+RigL is another popular dynamic sparse training method which uses weight and gradient magnitudes to
+learn the connections. BSR-Net is a recent sparse training method that updates connections by Bayesian
+sampling and also includes adversarial setups for model robustness. ITOP is another recent pipeline for
+dynamic sparse training, which uses sufficient and reliable parameter exploration to achieve in-time over-
+parameterization and find well-performing sparse models. Detailed information about the dataset, model
+architectures, and other training and evaluation setups is provided below.
+Datasets & Model Architectures: The datasets we use include CIFAR-10, CIFAR-100 (Krizhevsky
+et al., 2009), SVHN (Netzer et al., 2011), and ImageNet-2012 (see Appendix) (Russakovsky et al., 2015).
+For model architectures, we use VGG-16 (Simonyan & Zisserman, 2015), ResNet-18, ResNet-50 (He et al.,
+2016), and Wide-ResNet-28-4 (Zagoruyko & Komodakis, 2016).
+Training Settings: For sparse training, we choose two sparsity levels, namely 90% and 99%. For BSR-Net,
+we consider both standard and adversarial setups. In RigL and ITOP, we focus on standard training. In
+standard training, we only use the original data to update the parameters instead of using perturbed samples.
+For adversarial part, we use the perturbed data with two popular objective (AT and TRADES) (Madry et al.,
+2018; Zhang et al., 2019). Following Özdenizci & Legenstein (2021), we evaluate robust accuracy against
+PGD attacks with random starts using 50 iterations (PGD50) (Madry et al., 2018; Brendel et al., 2019).
+Implementations:
+Aligned with the choice of Evci et al. (2020); Sundar & Dwaraknath (2021); Özdenizci
+& Legenstein (2021), the parameters of the model are optimized by SGD with momentum.
+Thus, the
+comparison between the popular sparse training pipelines can be viewed as a comparison between AGENT
+and momentum-based SGD.
+6.1
+Convergence Speed & Stability Comparisons
+We compare the convergence speed by two criteria, including (a) the test accuracy at the same number of
+pass data (epoch) and (b) the number of pass data (epoch) required to achieve the same test accuracy,
+8
+
+0
+50
+100
+150
+200
+250
+Number of epochs
+0.55
+0.60
+0.65
+0.70
+0.75
+0.80
+0.85
+0.90
+Testing accuracy
+A-RigL-ITOP
+RigL-ITOP
+(a) VGG-C(RigL)
+0
+50
+100
+150
+200
+250
+Number of epochs
+0.60
+0.65
+0.70
+0.75
+0.80
+0.85
+0.90
+0.95
+Testing accuracy
+A-RigL-ITOP
+RigL-ITOP
+(b) ResNet-34(RigL)
+0
+50
+100
+150
+200
+250
+Number of epochs
+0.60
+0.65
+0.70
+0.75
+0.80
+0.85
+0.90
+Testing accuracy
+A-SET-ITOP
+SET-ITOP
+(c) VGG-C(SET)
+0
+50
+100
+150
+200
+250
+Number of epochs
+0.65
+0.70
+0.75
+0.80
+0.85
+0.90
+0.95
+Testing accuracy
+A-SET-ITOP
+SET-ITOP
+(d) ResNet-34(SET)
+Figure 3: Testing accuracy for ITOP-based models at 99% sparsity on CIFAR-10. A-RigL-ITOP and A-
+SET-ITOP (blue curves) converge faster than RigL-ITOP and SET-ITOP (pink curves).
+0.60
+0.65
+0.70
+0.75
+0.80
+0.85
+Testing accuracy
+0
+20
+40
+60
+80
+100
+120
+140
+Number of epochs
+A-BSR-Net
+BSR-Net
+(a) VGG-16, Standard
+0.60
+0.65
+0.70
+0.75
+0.80
+0.85
+Testing accuracy
+0
+20
+40
+60
+80
+100
+Number of epochs
+A-BSR-Net
+BSR-Net
+(b) WRN-28-4, Standard
+0.500 0.525 0.550 0.575 0.600 0.625 0.650 0.675
+Testing accuracy
+20
+40
+60
+80
+100
+120
+140
+160
+Number of epochs
+A-BSR-Net
+BSR-Net
+(c) VGG-16, AT
+0.500 0.525 0.550 0.575 0.600 0.625 0.650 0.675 0.700
+Testing accuracy
+20
+40
+60
+80
+100
+120
+Number of epochs
+A-BSR-Net
+BSR-Net
+(d) WRN-28-4, AT
+Figure 4: Number of training epochs required to achieve the accuracy at 99% sparsity. Our A-BSR-Net
+(blue curves) need less time to achieve the accuracy compared to BSR-Net (pink curves).
+which is widely used to compare the speed of optimization algorithms (Allen-Zhu & Hazan, 2016; Chatterji
+et al., 2018; Zou et al., 2018; Cutkosky & Orabona, 2019).
+For BSR-Net-based results using criterion (a), Table 1 lists the accuracies on both clean and adver-
+sarial samples after 20, 40, 70, 90, 140, and 200 epochs of training, where the higher accuracies are bolded.
+Sparse VGG-16 are learned on CIFAR-10 in both standard and adversarial sutups. For the standard setup,
+we only present the clean accuracy. As we can see, our method maintains higher clean and robust accuracies
+for almost all training epochs and setups which demonstrates the successful acceleration from our method.
+In particular, for limited time periods like 20 epochs, our A-BSR-Net usually shows dramatic improvements
+with clean accuracy as high as 11.4%, indicating a significant reduction in early search time. In addition,
+considering the average accuracy improvement over the 6 time budgets, our method outperforms BSR-Net
+in accuracy by upto 5.0%.
+Table 2: Final accuracy (%) of RigL-based models at 0% (dense),
+90% and 99% sparsity. AGENT + RigL (A-RigL) maintains or
+even improves the accuracy compared to that of RigL.
+Dense
+90%
+99%
+CIFAR-10
+A-RigL 95.2 (0.24) 95.0 (0.21) 93.1 (0.25)
+RigL
+95.0 (0.26)
+94.2 (0.22)
+92.5 (0.33)
+CIFAR-100 A-RigL 72.9 (0.19) 72.1 (0.20) 66.4 (0.14)
+RigL
+73.1 (0.17) 71.6 (0.26)
+66.0 (0.19)
+For ITOP-based results using cri-
+terion (a), as shown in Figure 3, the
+blue curves (A-RigL-ITOP and A-SET-
+ITOP) are always higher than the pink
+curves (RigL-ITOP and SET-ITOP), in-
+dicating faster training when using our
+AGENT. In addition, we can see that
+the pink curves experience severe up and
+down fluctuations, especially in the early
+stages of training. In contrast, the blue
+curves are more stable all the settings, which indicates AGENT is effective in stabilizing the sparse training.
+For BSR-Net-based results using criterion (b), Figure 4 depicts the number of training epochs required
+to achieve certain accuracy. We can see that the blue curves (A-BSR-Net) are always lower than the pink
+curves (BSR-Net), and on average our method reduces the number of training epochs by up to 52.1%,
+indicating faster training when using our proposed A-BSR-Net.
+9
+
+0
+50
+100
+150
+200
+250
+Number of epoch
+0.4
+0.5
+0.6
+0.7
+0.8
+0.9
+Testing accuracy
+A-RigL-ITOP
+RigL-ITOP + SVRG
+RigL-ITOP
+(a) VGG-C
+0
+50
+100
+150
+200
+250
+Number of epoch
+0.50
+0.55
+0.60
+0.65
+0.70
+0.75
+0.80
+0.85
+0.90
+0.95
+Testing accuracy
+A-RigL-ITOP
+RigL-ITOP + SVRG
+RigL-ITOP
+(b) ResNet-34
+0
+50
+100
+150
+200
+250
+Number of epoch
+0.4
+0.5
+0.6
+0.7
+0.8
+0.9
+Testing accuracy
+A-SET-ITOP
+SET-ITOP + SVRG
+SET-ITOP
+(c) VGG-C
+0
+50
+100
+150
+200
+250
+Number of epoch
+0.55
+0.60
+0.65
+0.70
+0.75
+0.80
+0.85
+0.90
+0.95
+Testing accuracy
+A-SET-ITOP
+SET-ITOP + SVRG
+SET-ITOP
+(d) ResNet-34
+Figure 5: Testing accuracy for ITOP-based models at 99% sparsity on CIFAR-10. SVRG (green curves)
+slows down the training compared to SGD (pink curves). Our AGENT (blue curves) accelerates the training.
+6.2
+Final Accuracy Comparisons
+In addition, we compare the final accuracy after sufficient training. RigL-based results on CIFAR-10/100 are
+shown in Table 2. Our method A-RigL tends to be the best in almost all the scenarios. For BSR-Net-based
+results in Table 3, we compare our A-BSR-Net with BSR-Net on SVHN using VGG-16 and WideResNet-28-4
+(WRN-28-4), and our method is often the best again. This shows that our AGENT can accelerate sparse
+training while maintaining or even improving the accuracy.
+6.3
+Comparison with Other Gradient Correction Methods
+Table 3: Final accuracy (%) of BSR-Net-based mod-
+els at 90% and 99% sparsity on SVHN with adversarial
+training objectives (TRADES). Our AGENT maintains
+or even improves the accuracy.
+BSR-Net
+Ours
+90%
+VGG-16
+89.4 (0.29) 94.4 (0.25)
+WRN-28-4 92.8 (0.24) 95.5 (0.23)
+99%
+VGG-16
+86.4 (0.25) 90.9 (0.26)
+WRN-28-4 89.5 (0.22) 92.2 (0.19)
+We also compare our AGENT with SVRG (Baker
+et
+al.,
+2019),
+a
+popular
+gradient
+correction
+method in the non-sparse case.
+The presented
+ITOP-based results are based on sparse (99%)
+VGG-C and ResNet-34 on CIFAR-10.
+Fig-
+ure 5 (a)-(b) show the testing accuracy of A-
+RigL-ITOP (blue), RigL-ITOP (pink), and RigL-
+ITOP+SVRG (green) at different epochs. We can
+see that the green curve for RigL-ITOP+SVRG is
+often lower than the other two curves for A-RigL-
+ITOP and RigL-ITOP, indicating that model con-
+vergence is slowed down by SVRG. As for the blue
+curve for our A-RigL-ITOP, it is always on the top
+of the pink curve for RigL-ITOP and also smoother than the green curve for RigL-ITOP+SVRG, indicating
+a successful acceleration and stabilization. The SET-ITOP-based results depicted in Figure 5 (c)-(d) show a
+similar pattern. The green curve (SET-ITOP+SVRG) is often lower than the blue (A-SET-ITOP) and pink
+(SET-ITOP) curves. This demonstrates that SVRG does not work for sparse training, while our AGENT
+overcomes its limitations, leading to accelerated and stabilized sparse training.
+6.4
+Comparison with Other Adaptive Gradient Methods
+We also compare our AGENT with other adaptive gradient methods, where we take Adam (Kingma & Ba,
+2014) as an example. As shown in Figure 6, AGENT-RigL-ITOP and AGENT-SET-ITOP (blue curves) are
+usually above Adam-RigL-ITOP and Adam-SET-ITOP (pink curves), indicating that our AGENT converges
+faster compared to Adam. This demonstrates the importance of using correlation in sparse training to balance
+old and new information.
+6.5
+Combination with Other Gradient Correction Methods
+In addition to working with SVRG, our AGENT can be combined with other gradient correction meth-
+ods to achieve sparse training acceleration, such as the momentum-based variance reduction method
+10
+
+0
+50
+100
+150
+200
+250
+Number of epochs
+0.45
+0.50
+0.55
+0.60
+0.65
+0.70
+0.75
+0.80
+0.85
+0.90
+Testing accuracy
+AGENT-RigL-ITOP
+Adam-RigL-ITOP
+(a) VGG-C(RigL)
+0
+50
+100
+150
+200
+250
+Number of epochs
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+0.8
+0.9
+Testing accuracy
+AGENT-RigL-ITOP
+Adam-RigL-ITOP
+(b) ResNet-34(RigL)
+0
+50
+100
+150
+200
+250
+Number of epochs
+0.50
+0.55
+0.60
+0.65
+0.70
+0.75
+0.80
+0.85
+0.90
+Testing accuracy
+AGENT-SET-ITOP
+Adam-SET-ITOP
+(c) VGG-C(SET)
+0
+50
+100
+150
+200
+250
+Number of epochs
+0.3
+0.4
+0.5
+0.6
+0.7
+0.8
+0.9
+Testing accuracy
+AGENT-SET-ITOP
+Adam-SET-ITOP
+(d) ResNet-34(SET)
+Figure 6: Testing accuracy for ITOP-based models at 99% sparsity on CIFAR-10. AGENT-based training
+(blue curves) converge faster than Adam-based training (pink curves).
+(MVR) (Cutkosky & Orabona, 2019).
+We train 99% SET-ITOP-based sparse VGG-C using MVR and
+MVR+AGENT, respectively. As shown in Table 4, MVR+AGENT usually achieves higher test accuracy
+than MVR for different number of training epochs (20, 40, 70, 90, 140, and 200), which demonstrates the
+acceleration effect of AGENT and the generality of our AGENT.
+6.6
+Ablation Studies
+Table 4: Testing accuracy (%) comparisons between MVR and
+AGENT+MVR. AGENT can accelerate MVR in sparse training.
+20-th 40-th 70-th 90-th 140-th 200-th
+MVR
+62.6
+66.8
+69.8
+71.2
+73.5
+74.4
+AGENT+MVR
+71.6
+75.7
+77.9
+79.1
+82.3
+82.3
+We demonstrate the importance of each
+component in our method AGENT by
+removing them one by one and compar-
+ing the results. Specifically, we consider
+examining the contribution of the time-
+varying weight ct of the old gradients and
+the scaling parameter γ. The term "Fixed
+ct" corresponds to fixing weight ct = 0.1 during training, and "No γ" represents a direct use of ˆc∗
+t in Eq. (4)
+and the momentum scheme without adding the scaling parameter γ.
+Table 5 shows the clean and robust accuracies of standard and adversarial (AT or TRADES) training at
+90% and 99% sparsity on CIFAR-10 using VGG-16 under different number of training epoch budgets. In the
+adversarial training (AT and TRADES), we can see that "No γ" is poorly learned and has the worst results.
+While our method outperforms "Fix ct" and "No γ" in almost all cases, especially in highly sparse tasks (i.e.,
+99% sparsity). For standard training, "No γ" can learn some information, but still performs worse than the
+other two methods. For "Fix ct", it provides similar convergence speed as our method, while ours tends to
+have a better final score.
+From the above discussion, both the adaptive update of ct and the multiplication of the scaling parameter γ
+are important for the acceleration. On the one hand, the traditional way of setting ct = 1 is not desirable in
+sparse training and can cause model divergence under sparsity constraints. Fixing it as a smaller value, such
+as 0.1, sometimes can work in standard training. But updating ct adaptively with loss-dependent information
+usually provides some benefits, such as a better final score. These benefits become more significant in sparse
+and adversarial training which are more challenging and of great value. On the other hand, we recommend
+adding a scaling parameter γ (e.g., γ = 0.1) to ct to avoid increasing the variance and reduce the potential
+bias in adversarial training, which helps the balance and further accelerates the convergence.
+6.7
+Scaling Parameter Setting
+The scaling parameter γ is to avoid introducing large variance due to error in approximating c∗
+t and bias
+due to the adversarial training. The choice of γ is important and can be seen as a hyper-parameter tuning
+process. Our results are based on γ = 0.1 and the best value for γ depends on many factors such as the
+dataset, architecture, and sparsity. Therefore, if we tune the value of γ according to the gradient correlation
+of different settings, it is possible to obtain a faster convergence rate than the reported results.
+11
+
+Table 5: Ablation Studies: testing accuracy (%) comparisons with Fixed c and No γ on sparse VGG-16.
+Results are presented as clean/robust accuracy (%). For the same number of training epochs, our method
+has higher accuracy compared to Fixed c and No γ in almost all cases.
+90% Sparsity
+99% Sparsity
+Fixed ct
+No γ
+Ours
+Fixed ct
+No γ
+Ours
+AT
+20-th
+54.1/36.2
+28.6/20.1
+63.6/37.3
+10.0/10.0
+10.0/10.0
+56.4/31.4
+40-th
+58.9/37.1
+20.4/13.0
+64.9/37.9
+10.0/10.0
+10.0/10.0
+57.7/34.5
+70-th
+66.8/41.6
+19.9/14.7
+75.1/45.2
+10.0/10.0
+10.0/10.0
+66.0/39.4
+90-th
+67.7/43.3
+21.8/15.6
+74.1/44.8
+10.0/10.0
+10.0/10.0
+65.8/39.8
+140-th
+71.4/43.4
+20.0/12.1
+77.4/43.8
+10.0/10.0
+10.0/10.0
+69.8/41.2
+200-th
+71.7/43.0
+20.5/9.5
+78.1/44.6
+10.0/10.0
+10.0/10.0
+70.7/42.0
+TRADES
+20-th
+62.6/35.2
+38.5/21.8
+65.0/37.6
+54.5/31.2
+35.2/21.6
+57.6/31.6
+40-th
+65.0/38.0
+34.7/20.2
+66.0/37.2
+56.0/30.5
+21.5/10.0
+58.4/33.4
+70-th
+73.9/44.5
+28.8/18.4
+73.5/45.4
+62.5/36.8
+18.8/16.2
+67.3/39.0
+90-th
+75.1/44.4
+25.8/15.9
+73.6/44.8
+63.9/37.4
+16.9/15.9
+67.5/39.1
+140-th
+76.7/46.5
+28.6/14.1
+76.8/46.3
+65.5/39.0
+19.7/14.4
+69.9/41.5
+200-th
+76.8/46.1
+30.7/12.7
+77.0/46.2
+70.3/38.5
+20.1/13.2
+70.9/41.2
+Standard
+20-th
+80.9/0.0
+70.6/0.0
+81.8/0.0
+73.7/0.0
+51.8/0.0
+69.8/0.0
+40-th
+83.3/0.0
+68.0/0.0
+82.4/0.0
+74.9/0.0
+55.2/0.0
+73.7/0.0
+70-th
+90.2/0.0
+77.3/0.0
+89.7/0.0
+84.1/0.0
+65.9/0.0
+83.7/0.0
+90-th
+89.8/0.0
+77.8/0.0
+89.3/0.0
+80.5/0.0
+67.8/0.0
+83.9/0.0
+140-th
+92.4/0.0
+80.7/0.0
+92.5/0.0
+87.2/0.0
+71.9/0.0
+86.9/0.0
+200-th
+92.1/0.0
+78.6/0.0
+92.6/0.0
+86.4/0.0
+70.0/0.0
+87.1/0.0
+We check different values from 0 to 1 and find that it is generally better not to set γ to close to 1 or 0.
+If setting γ close to 1, we will not be able to completely avoid the increase in variance, which leads to
+performance drop, similar to "No γ" in Table 5. If γ is set too small, such as 0.01, the weight of the old
+gradients will be too small and the old gradients will have limited influence on the model update, which
+will return to SGD’s slowdown and training instability. More detailed experimental results using different
+scaling parameters γ are included in the Appendix B.3.
+7
+Discussion and Conclusion
+We develop an adaptive gradient correction (AGENT) method for sparse training to achieve the time ef-
+ficiency and reduce training instability from an optimization perspective, which can be incorporated into
+any SGD-based sparse training pipeline and work in both standard and adversarial setups. To achieve a
+fine-grained control over the balance of current and previous gradients, we use loss information to analyze
+gradient changes, and add an adaptive weight to the old gradients. In addition, we design a scaling parameter
+to reduce the bias of the gradient estimator introduced by the adversarial samples and improve the worst case
+of the adaptive weight estimate. In theory, we show that our AGENT can accelerate the convergence rate
+of sparse training. Experiment results on multiple datasets, model architectures, and sparsities demonstrate
+that our method outperforms state-of-the-art sparse training methods in terms of accuracy by up to 5.0%
+and reduces the number of training epochs by up to 52.1% for the same accuracy achieved.
+A number of methods can be employed to reduce the FLOPs in our AGENT. Similar to SVRG, our AGENT
+increases the training FLOPs in each iteration due to the extra forward and backward used to compute the
+old gradients. To reduce the FLOPs, the first method is to use sparse gradients (Elibol et al., 2020), which
+effectively reduces the cost of backward in sparse training and can be easily applied to our method. The
+second method is parallel computing Allen-Zhu & Hazan (2016). Since the additional forward and backward
+over the old model parameters are fully parallelizable, we can view it as doubling the mini-batch size. Third,
+we can follow the idea of SAGA (Defazio et al., 2014) by storing gradients for each single sample. By this
+way, we do not need extra forward and backward steps, saving the computation. However, it requires extra
+memory to store the gradients.
+12
+
+References
+Naveed Akhtar and Ajmal Mian. Threat of adversarial attacks on deep learning in computer vision: A
+survey. Ieee Access, 6:14410–14430, 2018.
+Zeyuan Allen-Zhu and Elad Hazan. Variance reduction for faster non-convex optimization. In International
+conference on machine learning, pp. 699–707. PMLR, 2016.
+Jack Baker, Paul Fearnhead, Emily B Fox, and Christopher Nemeth. Control variates for stochastic gradient
+mcmc. Statistics and Computing, 29(3):599–615, 2019.
+Brian Bartoldson, Ari Morcos, Adrian Barbu, and Gordon Erlebacher. The generalization-stability tradeoff
+in neural network pruning. Advances in Neural Information Processing Systems, 33:20852–20864, 2020.
+Guillaume Bellec, David Kappel, Wolfgang Maass, and Robert Legenstein. Deep rewiring: Training very
+sparse deep networks. arXiv preprint arXiv:1711.05136, 2017.
+Guillaume Bellec, David Kappel, Wolfgang Maass, and Robert Legenstein. Deep rewiring: Training very
+sparse deep networks. International Conference on Learning Representations (ICLR), 2018.
+Wieland Brendel, Jonas Rauber, Matthias Kümmerer, Ivan Ustyuzhaninov, and Matthias Bethge. Accurate,
+reliable and fast robustness evaluation. arXiv preprint arXiv:1907.01003, 2019.
+Niladri Chatterji, Nicolas Flammarion, Yian Ma, Peter Bartlett, and Michael Jordan. On the theory of
+variance reduction for stochastic gradient monte carlo. In International Conference on Machine Learning,
+pp. 764–773. PMLR, 2018.
+El Mahdi Chayti and Sai Praneeth Karimireddy. Optimization with access to auxiliary information. arXiv
+preprint arXiv:2206.00395, 2022.
+Beidi Chen, Tri Dao, Kaizhao Liang, Jiaming Yang, Zhao Song, Atri Rudra, and Christopher Re. Pixelated
+butterfly: Simple and efficient sparse training for neural network models. arXiv preprint arXiv:2112.00029,
+2021.
+Changyou Chen, Wenlin Wang, Yizhe Zhang, Qinliang Su, and Lawrence Carin. A convergence analysis for
+a class of practical variance-reduction stochastic gradient mcmc. Science China Information Sciences, 62
+(1):1–13, 2019.
+Ashok Cutkosky and Francesco Orabona. Momentum-based variance reduction in non-convex sgd. Advances
+in neural information processing systems, 32, 2019.
+Aaron Defazio, Francis Bach, and Simon Lacoste-Julien. Saga: A fast incremental gradient method with
+support for non-strongly convex composite objectives. Advances in neural information processing systems,
+27, 2014.
+Wei Deng, Qi Feng, Georgios Karagiannis, Guang Lin, and Faming Liang.
+Accelerating convergence of
+replica exchange stochastic gradient mcmc via variance reduction. arXiv preprint arXiv:2010.01084, 2020.
+Tim Dettmers and Luke Zettlemoyer. Sparse networks from scratch: Faster training without losing perfor-
+mance. arXiv preprint arXiv:1907.04840, 2019.
+Kumar Avinava Dubey, Sashank J Reddi, Sinead A Williamson, Barnabas Poczos, Alexander J Smola, and
+Eric P Xing. Variance reduction in stochastic gradient langevin dynamics. Advances in neural information
+processing systems, 29:1154–1162, 2016.
+Melih Elibol, Lihua Lei, and Michael I Jordan. Variance reduction with sparse gradients. arXiv preprint
+arXiv:2001.09623, 2020.
+Utku Evci, Trevor Gale, Jacob Menick, Pablo Samuel Castro, and Erich Elsen. Rigging the lottery: Making
+all tickets winners. In International Conference on Machine Learning, pp. 2943–2952. PMLR, 2020.
+13
+
+Cong Fang, Chris Junchi Li, Zhouchen Lin, and Tong Zhang. Spider: Near-optimal non-convex optimization
+via stochastic path-integrated differential estimator. Advances in Neural Information Processing Systems,
+31, 2018.
+Jonathan Frankle and Michael Carbin.
+The lottery ticket hypothesis: Finding sparse, trainable neural
+networks. International Conference on Learning Representations (ICLR), 2019.
+Eduard Gorbunov, Filip Hanzely, and Peter Richtárik. A unified theory of sgd: Variance reduction, sampling,
+quantization and coordinate descent. In International Conference on Artificial Intelligence and Statistics,
+pp. 680–690. PMLR, 2020.
+Laura Graesser, Utku Evci, Erich Elsen, and Pablo Samuel Castro. The state of sparse training in deep
+reinforcement learning. In International Conference on Machine Learning, pp. 7766–7792. PMLR, 2022.
+Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Delving deep into rectifiers: Surpassing human-
+level performance on imagenet classification.
+In Proceedings of the IEEE international conference on
+computer vision, pp. 1026–1034, 2015.
+Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. In
+Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 770–778, 2016.
+Torsten Hoefler, Dan Alistarh, Tal Ben-Nun, Nikoli Dryden, and Alexandra Peste.
+Sparsity in deep
+learning: Pruning and growth for efficient inference and training in neural networks.
+arXiv preprint
+arXiv:2102.00554, 2021.
+Shaoyi Huang, Bowen Lei, Dongkuan Xu, Hongwu Peng, Yue Sun, Mimi Xie, and Caiwen Ding. Dynamic
+sparse training via balancing the exploration-exploitation trade-off.
+arXiv preprint arXiv:2211.16667,
+2022.
+Itay Hubara, Brian Chmiel, Moshe Island, Ron Banner, Joseph Naor, and Daniel Soudry. Accelerated sparse
+neural training: A provable and efficient method to find n: m transposable masks. Advances in Neural
+Information Processing Systems, 34, 2021.
+Siddhant Jayakumar, Razvan Pascanu, Jack Rae, Simon Osindero, and Erich Elsen. Top-kast: Top-k always
+sparse training. Advances in Neural Information Processing Systems, 33:20744–20754, 2020.
+Rie Johnson and Tong Zhang. Accelerating stochastic gradient descent using predictive variance reduction.
+Advances in neural information processing systems, 26:315–323, 2013.
+Diederik P Kingma and Jimmy Ba.
+Adam:
+A method for stochastic optimization.
+arXiv preprint
+arXiv:1412.6980, 2014.
+Alex Krizhevsky, Geoffrey Hinton, et al. Learning multiple layers of features from tiny images. Technical
+report, University of Toronto, 2009.
+Souvik Kundu, Mahdi Nazemi, Peter A Beerel, and Massoud Pedram.
+Dnr: A tunable robust pruning
+framework through dynamic network rewiring of dnns. In Proceedings of the 26th Asia and South Pacific
+Design Automation Conference, pp. 344–350, 2021.
+Clayton Frederick Souza Leite and Yu Xiao. Optimal sensor channel selection for resource-efficient deep
+activity recognition. In Proceedings of the 20th International Conference on Information Processing in
+Sensor Networks (co-located with CPS-IoT Week 2021), pp. 371–383, 2021.
+Yan Li, Ethan Fang, Huan Xu, and Tuo Zhao. Implicit bias of gradient descent based adversarial training
+on separable data. In International Conference on Learning Representations, 2020.
+Chuang Liu, Xueqi Ma, Yinbing Zhan, Liang Ding, Dapeng Tao, Bo Du, Wenbin Hu, and Danilo Mandic.
+Comprehensive graph gradual pruning for sparse training in graph neural networks.
+arXiv preprint
+arXiv:2207.08629, 2022.
+14
+
+Shiwei Liu, Lu Yin, Decebal Constantin Mocanu, and Mykola Pechenizkiy.
+Do we actually need dense
+over-parameterization? in-time over-parameterization in sparse training. In International Conference on
+Machine Learning, pp. 6989–7000. PMLR, 2021.
+Ilya Loshchilov and Frank Hutter. Decoupled weight decay regularization. In International Conference on
+Learning Representations (ICLR), 2019.
+Aleksander Madry, Aleksandar Makelov, Ludwig Schmidt, Dimitris Tsipras, and Adrian Vladu. Towards deep
+learning models resistant to adversarial attacks. In International Conference on Learn- ing Representations
+(ICLR), 2018.
+Kira JM Matus and Michael Veale. Certification systems for machine learning: Lessons from sustainability.
+Regulation & Governance, 16(1):177–196, 2022.
+Decebal Constantin Mocanu, Elena Mocanu, Peter Stone, Phuong H Nguyen, Madeleine Gibescu, and An-
+tonio Liotta. Scalable training of artificial neural networks with adaptive sparse connectivity inspired by
+network science. Nature communications, 9(1):1–12, 2018.
+Hesham Mostafa and Xin Wang.
+Parameter efficient training of deep convolutional neural networks by
+dynamic sparse reparameterization. In International Conference on Machine Learning, pp. 4646–4655.
+PMLR, 2019.
+Yuval Netzer, Tao Wang, Adam Coates, Alessandro Bissacco, Bo Wu, and Andrew Y Ng. Reading digits in
+natural images with unsupervised feature learning. 2011.
+Lam M Nguyen, Jie Liu, Katya Scheinberg, and Martin Takáč. Sarah: A novel method for machine learning
+problems using stochastic recursive gradient. In International Conference on Machine Learning, pp. 2613–
+2621. PMLR, 2017.
+Ozan Özdenizci and Robert Legenstein. Training adversarially robust sparse networks via bayesian connec-
+tivity sampling. In International Conference on Machine Learning, pp. 8314–8324. PMLR, 2021.
+David Patterson, Joseph Gonzalez, Quoc Le, Chen Liang, Lluis-Miquel Munguia, Daniel Rothchild, David
+So, Maud Texier, and Jeff Dean. Carbon emissions and large neural network training. arXiv preprint
+arXiv:2104.10350, 2021.
+Ning Qian. On the momentum term in gradient descent learning algorithms. Neural networks, 12(1):145–151,
+1999.
+Adnan Siraj Rakin, Zhezhi He, Li Yang, Yanzhi Wang, Liqiang Wang, and Deliang Fan. Robust sparse
+regularization: Simultaneously optimizing neural network robustness and compactness. arXiv preprint
+arXiv:1905.13074, 2019.
+Sashank J Reddi, Ahmed Hefny, Suvrit Sra, Barnabás Póczos, and Alex Smola. Stochastic variance reduction
+for nonconvex optimization. In International conference on machine learning, pp. 314–323. PMLR, 2016.
+Johanna Rock, Wolfgang Roth, Mate Toth, Paul Meissner, and Franz Pernkopf. Resource-efficient deep
+neural networks for automotive radar interference mitigation. IEEE Journal of Selected Topics in Signal
+Processing, 15(4):927–940, 2021.
+Sebastian Ruder. An overview of gradient descent optimization algorithms. arXiv preprint arXiv:1609.04747,
+2016.
+Olga Russakovsky, Jia Deng, Hao Su, Jonathan Krause, Sanjeev Satheesh, Sean Ma, Zhiheng Huang, Andrej
+Karpathy, Aditya Khosla, Michael Bernstein, et al. Imagenet large scale visual recognition challenge.
+International journal of computer vision, 115(3):211–252, 2015.
+Jonathan Schwarz, Siddhant Jayakumar, Razvan Pascanu, Peter E Latham, and Yee Teh. Powerpropagation:
+A sparsity inducing weight reparameterisation. Advances in Neural Information Processing Systems, 34:
+28889–28903, 2021.
+15
+
+Vikash Sehwag, Shiqi Wang, Prateek Mittal, and Suman Jana. Hydra: Pruning adversarially robust neural
+networks. Advances in Neural Information Processing Systems, 33:19655–19666, 2020.
+Fanhua Shang, Kaiwen Zhou, Hongying Liu, James Cheng, Ivor W Tsang, Lijun Zhang, Dacheng Tao,
+and Licheng Jiao. Vr-sgd: A simple stochastic variance reduction method for machine learning. IEEE
+Transactions on Knowledge and Data Engineering, 32(1):188–202, 2018.
+Karen Simonyan and Andrew Zisserman. Very deep convolutional networks for large-scale image recognition.
+Interna- tional Conference on Learning Representations (ICLR), 2015.
+Varun Sundar and Rajat Vadiraj Dwaraknath. [reproducibility report] rigging the lottery: Making all tickets
+winners. arXiv preprint arXiv:2103.15767, 2021.
+Neil C Thompson, Kristjan Greenewald, Keeheon Lee, and Gabriel F Manso. Deep learning’s diminishing
+returns: the cost of improvement is becoming unsustainable. IEEE Spectrum, 58(10):50–55, 2021.
+Lin Xiao and Tong Zhang. A proximal stochastic gradient method with progressive variance reduction.
+SIAM Journal on Optimization, 24(4):2057–2075, 2014.
+Xia Xiao, Zigeng Wang, and Sanguthevar Rajasekaran. Autoprune: Automatic network pruning by regular-
+izing auxiliary parameters. Advances in neural information processing systems, 32, 2019.
+Shaokai Ye, Kaidi Xu, Sijia Liu, Hao Cheng, Jan-Henrik Lambrechts, Huan Zhang, Aojun Zhou, Kaisheng
+Ma, Yanzhi Wang, and Xue Lin. Adversarial robustness vs. model compression, or both? In Proceedings
+of the IEEE/CVF International Conference on Computer Vision, pp. 111–120, 2019.
+Rong Yu and Peichun Li. Toward resource-efficient federated learning in mobile edge computing. IEEE
+Network, 35(1):148–155, 2021.
+Sergey Zagoruyko and Nikos Komodakis. Wide residual networks. British Machine Vision Conference, 2016.
+Hongyang Zhang, Yaodong Yu, Jiantao Jiao, Eric Xing, Laurent El Ghaoui, and Michael Jordan. Theo-
+retically principled trade-off between robustness and accuracy. In International Conference on Machine
+Learning, pp. 7472–7482. PMLR, 2019.
+Xiao Zhou, Weizhong Zhang, Zonghao Chen, Shizhe Diao, and Tong Zhang. Efficient neural network training
+via forward and backward propagation sparsification. Advances in Neural Information Processing Systems,
+34:15216–15229, 2021a.
+Xiao Zhou, Weizhong Zhang, Hang Xu, and Tong Zhang. Effective sparsification of neural networks with
+global sparsity constraint. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern
+Recognition, pp. 3599–3608, 2021b.
+Difan Zou, Pan Xu, and Quanquan Gu. Subsampled stochastic variance-reduced gradient langevin dynamics.
+In International Conference on Uncertainty in Artificial Intelligence, 2018.
+References
+Naveed Akhtar and Ajmal Mian. Threat of adversarial attacks on deep learning in computer vision: A
+survey. Ieee Access, 6:14410–14430, 2018.
+Zeyuan Allen-Zhu and Elad Hazan. Variance reduction for faster non-convex optimization. In International
+conference on machine learning, pp. 699–707. PMLR, 2016.
+Jack Baker, Paul Fearnhead, Emily B Fox, and Christopher Nemeth. Control variates for stochastic gradient
+mcmc. Statistics and Computing, 29(3):599–615, 2019.
+Brian Bartoldson, Ari Morcos, Adrian Barbu, and Gordon Erlebacher. The generalization-stability tradeoff
+in neural network pruning. Advances in Neural Information Processing Systems, 33:20852–20864, 2020.
+16
+
+Guillaume Bellec, David Kappel, Wolfgang Maass, and Robert Legenstein. Deep rewiring: Training very
+sparse deep networks. arXiv preprint arXiv:1711.05136, 2017.
+Guillaume Bellec, David Kappel, Wolfgang Maass, and Robert Legenstein. Deep rewiring: Training very
+sparse deep networks. International Conference on Learning Representations (ICLR), 2018.
+Wieland Brendel, Jonas Rauber, Matthias Kümmerer, Ivan Ustyuzhaninov, and Matthias Bethge. Accurate,
+reliable and fast robustness evaluation. arXiv preprint arXiv:1907.01003, 2019.
+Niladri Chatterji, Nicolas Flammarion, Yian Ma, Peter Bartlett, and Michael Jordan. On the theory of
+variance reduction for stochastic gradient monte carlo. In International Conference on Machine Learning,
+pp. 764–773. PMLR, 2018.
+El Mahdi Chayti and Sai Praneeth Karimireddy. Optimization with access to auxiliary information. arXiv
+preprint arXiv:2206.00395, 2022.
+Beidi Chen, Tri Dao, Kaizhao Liang, Jiaming Yang, Zhao Song, Atri Rudra, and Christopher Re. Pixelated
+butterfly: Simple and efficient sparse training for neural network models. arXiv preprint arXiv:2112.00029,
+2021.
+Changyou Chen, Wenlin Wang, Yizhe Zhang, Qinliang Su, and Lawrence Carin. A convergence analysis for
+a class of practical variance-reduction stochastic gradient mcmc. Science China Information Sciences, 62
+(1):1–13, 2019.
+Ashok Cutkosky and Francesco Orabona. Momentum-based variance reduction in non-convex sgd. Advances
+in neural information processing systems, 32, 2019.
+Aaron Defazio, Francis Bach, and Simon Lacoste-Julien. Saga: A fast incremental gradient method with
+support for non-strongly convex composite objectives. Advances in neural information processing systems,
+27, 2014.
+Wei Deng, Qi Feng, Georgios Karagiannis, Guang Lin, and Faming Liang.
+Accelerating convergence of
+replica exchange stochastic gradient mcmc via variance reduction. arXiv preprint arXiv:2010.01084, 2020.
+Tim Dettmers and Luke Zettlemoyer. Sparse networks from scratch: Faster training without losing perfor-
+mance. arXiv preprint arXiv:1907.04840, 2019.
+Kumar Avinava Dubey, Sashank J Reddi, Sinead A Williamson, Barnabas Poczos, Alexander J Smola, and
+Eric P Xing. Variance reduction in stochastic gradient langevin dynamics. Advances in neural information
+processing systems, 29:1154–1162, 2016.
+Melih Elibol, Lihua Lei, and Michael I Jordan. Variance reduction with sparse gradients. arXiv preprint
+arXiv:2001.09623, 2020.
+Utku Evci, Trevor Gale, Jacob Menick, Pablo Samuel Castro, and Erich Elsen. Rigging the lottery: Making
+all tickets winners. In International Conference on Machine Learning, pp. 2943–2952. PMLR, 2020.
+Cong Fang, Chris Junchi Li, Zhouchen Lin, and Tong Zhang. Spider: Near-optimal non-convex optimization
+via stochastic path-integrated differential estimator. Advances in Neural Information Processing Systems,
+31, 2018.
+Jonathan Frankle and Michael Carbin.
+The lottery ticket hypothesis: Finding sparse, trainable neural
+networks. International Conference on Learning Representations (ICLR), 2019.
+Eduard Gorbunov, Filip Hanzely, and Peter Richtárik. A unified theory of sgd: Variance reduction, sampling,
+quantization and coordinate descent. In International Conference on Artificial Intelligence and Statistics,
+pp. 680–690. PMLR, 2020.
+Laura Graesser, Utku Evci, Erich Elsen, and Pablo Samuel Castro. The state of sparse training in deep
+reinforcement learning. In International Conference on Machine Learning, pp. 7766–7792. PMLR, 2022.
+17
+
+Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Delving deep into rectifiers: Surpassing human-
+level performance on imagenet classification.
+In Proceedings of the IEEE international conference on
+computer vision, pp. 1026–1034, 2015.
+Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. In
+Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 770–778, 2016.
+Torsten Hoefler, Dan Alistarh, Tal Ben-Nun, Nikoli Dryden, and Alexandra Peste.
+Sparsity in deep
+learning: Pruning and growth for efficient inference and training in neural networks.
+arXiv preprint
+arXiv:2102.00554, 2021.
+Shaoyi Huang, Bowen Lei, Dongkuan Xu, Hongwu Peng, Yue Sun, Mimi Xie, and Caiwen Ding. Dynamic
+sparse training via balancing the exploration-exploitation trade-off.
+arXiv preprint arXiv:2211.16667,
+2022.
+Itay Hubara, Brian Chmiel, Moshe Island, Ron Banner, Joseph Naor, and Daniel Soudry. Accelerated sparse
+neural training: A provable and efficient method to find n: m transposable masks. Advances in Neural
+Information Processing Systems, 34, 2021.
+Siddhant Jayakumar, Razvan Pascanu, Jack Rae, Simon Osindero, and Erich Elsen. Top-kast: Top-k always
+sparse training. Advances in Neural Information Processing Systems, 33:20744–20754, 2020.
+Rie Johnson and Tong Zhang. Accelerating stochastic gradient descent using predictive variance reduction.
+Advances in neural information processing systems, 26:315–323, 2013.
+Diederik P Kingma and Jimmy Ba.
+Adam:
+A method for stochastic optimization.
+arXiv preprint
+arXiv:1412.6980, 2014.
+Alex Krizhevsky, Geoffrey Hinton, et al. Learning multiple layers of features from tiny images. Technical
+report, University of Toronto, 2009.
+Souvik Kundu, Mahdi Nazemi, Peter A Beerel, and Massoud Pedram.
+Dnr: A tunable robust pruning
+framework through dynamic network rewiring of dnns. In Proceedings of the 26th Asia and South Pacific
+Design Automation Conference, pp. 344–350, 2021.
+Clayton Frederick Souza Leite and Yu Xiao. Optimal sensor channel selection for resource-efficient deep
+activity recognition. In Proceedings of the 20th International Conference on Information Processing in
+Sensor Networks (co-located with CPS-IoT Week 2021), pp. 371–383, 2021.
+Yan Li, Ethan Fang, Huan Xu, and Tuo Zhao. Implicit bias of gradient descent based adversarial training
+on separable data. In International Conference on Learning Representations, 2020.
+Chuang Liu, Xueqi Ma, Yinbing Zhan, Liang Ding, Dapeng Tao, Bo Du, Wenbin Hu, and Danilo Mandic.
+Comprehensive graph gradual pruning for sparse training in graph neural networks.
+arXiv preprint
+arXiv:2207.08629, 2022.
+Shiwei Liu, Lu Yin, Decebal Constantin Mocanu, and Mykola Pechenizkiy.
+Do we actually need dense
+over-parameterization? in-time over-parameterization in sparse training. In International Conference on
+Machine Learning, pp. 6989–7000. PMLR, 2021.
+Ilya Loshchilov and Frank Hutter. Decoupled weight decay regularization. In International Conference on
+Learning Representations (ICLR), 2019.
+Aleksander Madry, Aleksandar Makelov, Ludwig Schmidt, Dimitris Tsipras, and Adrian Vladu. Towards deep
+learning models resistant to adversarial attacks. In International Conference on Learn- ing Representations
+(ICLR), 2018.
+Kira JM Matus and Michael Veale. Certification systems for machine learning: Lessons from sustainability.
+Regulation & Governance, 16(1):177–196, 2022.
+18
+
+Decebal Constantin Mocanu, Elena Mocanu, Peter Stone, Phuong H Nguyen, Madeleine Gibescu, and An-
+tonio Liotta. Scalable training of artificial neural networks with adaptive sparse connectivity inspired by
+network science. Nature communications, 9(1):1–12, 2018.
+Hesham Mostafa and Xin Wang.
+Parameter efficient training of deep convolutional neural networks by
+dynamic sparse reparameterization. In International Conference on Machine Learning, pp. 4646–4655.
+PMLR, 2019.
+Yuval Netzer, Tao Wang, Adam Coates, Alessandro Bissacco, Bo Wu, and Andrew Y Ng. Reading digits in
+natural images with unsupervised feature learning. 2011.
+Lam M Nguyen, Jie Liu, Katya Scheinberg, and Martin Takáč. Sarah: A novel method for machine learning
+problems using stochastic recursive gradient. In International Conference on Machine Learning, pp. 2613–
+2621. PMLR, 2017.
+Ozan Özdenizci and Robert Legenstein. Training adversarially robust sparse networks via bayesian connec-
+tivity sampling. In International Conference on Machine Learning, pp. 8314–8324. PMLR, 2021.
+David Patterson, Joseph Gonzalez, Quoc Le, Chen Liang, Lluis-Miquel Munguia, Daniel Rothchild, David
+So, Maud Texier, and Jeff Dean. Carbon emissions and large neural network training. arXiv preprint
+arXiv:2104.10350, 2021.
+Ning Qian. On the momentum term in gradient descent learning algorithms. Neural networks, 12(1):145–151,
+1999.
+Adnan Siraj Rakin, Zhezhi He, Li Yang, Yanzhi Wang, Liqiang Wang, and Deliang Fan. Robust sparse
+regularization: Simultaneously optimizing neural network robustness and compactness. arXiv preprint
+arXiv:1905.13074, 2019.
+Sashank J Reddi, Ahmed Hefny, Suvrit Sra, Barnabás Póczos, and Alex Smola. Stochastic variance reduction
+for nonconvex optimization. In International conference on machine learning, pp. 314–323. PMLR, 2016.
+Johanna Rock, Wolfgang Roth, Mate Toth, Paul Meissner, and Franz Pernkopf. Resource-efficient deep
+neural networks for automotive radar interference mitigation. IEEE Journal of Selected Topics in Signal
+Processing, 15(4):927–940, 2021.
+Sebastian Ruder. An overview of gradient descent optimization algorithms. arXiv preprint arXiv:1609.04747,
+2016.
+Olga Russakovsky, Jia Deng, Hao Su, Jonathan Krause, Sanjeev Satheesh, Sean Ma, Zhiheng Huang, Andrej
+Karpathy, Aditya Khosla, Michael Bernstein, et al. Imagenet large scale visual recognition challenge.
+International journal of computer vision, 115(3):211–252, 2015.
+Jonathan Schwarz, Siddhant Jayakumar, Razvan Pascanu, Peter E Latham, and Yee Teh. Powerpropagation:
+A sparsity inducing weight reparameterisation. Advances in Neural Information Processing Systems, 34:
+28889–28903, 2021.
+Vikash Sehwag, Shiqi Wang, Prateek Mittal, and Suman Jana. Hydra: Pruning adversarially robust neural
+networks. Advances in Neural Information Processing Systems, 33:19655–19666, 2020.
+Fanhua Shang, Kaiwen Zhou, Hongying Liu, James Cheng, Ivor W Tsang, Lijun Zhang, Dacheng Tao,
+and Licheng Jiao. Vr-sgd: A simple stochastic variance reduction method for machine learning. IEEE
+Transactions on Knowledge and Data Engineering, 32(1):188–202, 2018.
+Karen Simonyan and Andrew Zisserman. Very deep convolutional networks for large-scale image recognition.
+Interna- tional Conference on Learning Representations (ICLR), 2015.
+Varun Sundar and Rajat Vadiraj Dwaraknath. [reproducibility report] rigging the lottery: Making all tickets
+winners. arXiv preprint arXiv:2103.15767, 2021.
+19
+
+Neil C Thompson, Kristjan Greenewald, Keeheon Lee, and Gabriel F Manso. Deep learning’s diminishing
+returns: the cost of improvement is becoming unsustainable. IEEE Spectrum, 58(10):50–55, 2021.
+Lin Xiao and Tong Zhang. A proximal stochastic gradient method with progressive variance reduction.
+SIAM Journal on Optimization, 24(4):2057–2075, 2014.
+Xia Xiao, Zigeng Wang, and Sanguthevar Rajasekaran. Autoprune: Automatic network pruning by regular-
+izing auxiliary parameters. Advances in neural information processing systems, 32, 2019.
+Shaokai Ye, Kaidi Xu, Sijia Liu, Hao Cheng, Jan-Henrik Lambrechts, Huan Zhang, Aojun Zhou, Kaisheng
+Ma, Yanzhi Wang, and Xue Lin. Adversarial robustness vs. model compression, or both? In Proceedings
+of the IEEE/CVF International Conference on Computer Vision, pp. 111–120, 2019.
+Rong Yu and Peichun Li. Toward resource-efficient federated learning in mobile edge computing. IEEE
+Network, 35(1):148–155, 2021.
+Sergey Zagoruyko and Nikos Komodakis. Wide residual networks. British Machine Vision Conference, 2016.
+Hongyang Zhang, Yaodong Yu, Jiantao Jiao, Eric Xing, Laurent El Ghaoui, and Michael Jordan. Theo-
+retically principled trade-off between robustness and accuracy. In International Conference on Machine
+Learning, pp. 7472–7482. PMLR, 2019.
+Xiao Zhou, Weizhong Zhang, Zonghao Chen, Shizhe Diao, and Tong Zhang. Efficient neural network training
+via forward and backward propagation sparsification. Advances in Neural Information Processing Systems,
+34:15216–15229, 2021a.
+Xiao Zhou, Weizhong Zhang, Hang Xu, and Tong Zhang. Effective sparsification of neural networks with
+global sparsity constraint. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern
+Recognition, pp. 3599–3608, 2021b.
+Difan Zou, Pan Xu, and Quanquan Gu. Subsampled stochastic variance-reduced gradient langevin dynamics.
+In International Conference on Uncertainty in Artificial Intelligence, 2018.
+20
+
+A
+Appendix: Theoretical Proof of Convergence Rate
+In this section, we provide a detailed proof for the convergence rate of our AGENT method. We start with
+some assumptions on which we will give some useful lemmas. Then, we will establish the convergence rate
+of our AGENT method based on these lemmas.
+A.1
+Algorithm Reformulation
+We reformulate our Adaptive Gradient Correction (AGENT) into a math-friendly version that is shown in
+Algorithm 2.
+Algorithm 2 Adaptive Gradient Correction
+Input: Initialize θ0
+0 and c−1 = 0, set the number of epochs S, epoch length m, step sizes ht, scaling parameter γ,
+and smoothing factor α
+for s = 0 to S − 1 do
+�θ = θs
+0
+�g = (�N
+i=1 ∇G(xi; �θ))/N
+Calculate �c∗
+s via Eq. (4)
+�cs = (1 − α)�cs−1 + α�c∗
+s
+cs = γ�cs
+for t = 0 to m − 1 do
+Sample a mini-batch data Bt with size n
+θs
+t+1 = θs
+t − ηt
+�
+1
+n
+�
+i∈Bt
+�
+gi(θs
+t ) − cs · gi(�θ)�
++ cs · �g
+�
+end for
+θs+1
+0
+= θs
+m
+end for
+Output: Iterates θπ chosen uniformly random from {{θs
+t }m−1
+t=0 }S−1
+s=0
+A.2
+Assumptions
+L-smooth: A differentiable function G : Rn → R is said to be L-smooth if for all x, y ∈ Rn is satisfies
+||∇G(x) − ∇G(y)|| ≤ L||x − y||. And an equivalent definition is for. all x, y ∈ Rn:
+−L
+2 ||x − y||2 ≤ G(x) − G(y) − ⟨∇G(x), x − y⟩ ≤ L
+2 ||x − y||2
+σ-bounded: We say function G has a σ-bounded gradient if ||∇Gi(x)|| ≤ σ for all i ∈ [N] and x ∈ Rn
+A.3
+Analysis framework
+Under the above assumptions, we are ready to analyze the convergence rate of AGENT in Algorithm 2.
+To introduce the convergence analysis more clearly, we provide a brief analytical framework for our proof.
+• First, we need to show that the variance of our gradient estimator is smaller than that of minibatch
+SVRG under proper choice of cs.
+Since the gradient estimator of both AGENT and minibatch
+SVRG are unbiased estimators in standard training, we only need to show that our bound E[||ut||2]
+is smaller than minibatch SVRG. (See in Lemma 1)
+• Based on above fact, we next apply the Lyapunov function to prove the convergence rate of AGENT
+in one arbitrary epoch. (See in Lemma 3)
+21
+
+• Then, we extend our previous results to the entire epoch (from 0 to S-th epoch) and derive the
+convergence rate of the output θπ of Algorithm 2. (See in Lemma 4)
+• Finally, we compare the convergence rate of our AGENT with that of minibatch SVRG. Setting the
+parameters in Lemma 4 according to the actual situation of sparse learning, we obtain a bound that
+is more stringent than minibatch SVRG.
+A.4
+lemma
+We first denote step length ηt = N · ht. Since we mainly focus on a single epoch, we drop the superscript s
+and denote ut = 1
+n
+�
+i∈Bt
+�
+gi(θt) − c · gi(�θ)
+�
++ c · �g which is the gradient estimator in our algorithm and
+τt = 1
+n
+�
+i∈Bt
+�
+gi(θt) − c · gi(�θ)
+�
+, then lines the update procedure in Algorithm 2 can be replaced with
+θt+1 = θt − ηt · ut
+A.4.1
+lemma 1
+For the ut defined above and function G is a L-smooth, λ - strongly convex function with σ-bounded gradient,
+then we have the following results:
+E
+�
+||ut||2�
+≤ 2E
+�
+||g(θt)||2�
++ 4c2L2
+n
+E
+�
+||θt − ˜θ||2�
++ 4(1 − c)2
+n
+σ2
+(6)
+Proof :
+E
+�
+||ut||2�
+= E
+�
+||τt + c · �g||2�
+= E
+�
+||τt + c · �g − g(θt) + g(θt)||2�
+≤ 2E
+�
+||g(θt)||2�
++ 2E
+�
+||τt − E(τt)||2�
+≤ 2E
+�
+||g(θt)||2�
++ 2
+nE
+�
+τ 2
+t
+�
+= 2E
+�
+||g(θ)||2�
++ 2
+nE
+�
+||c(gi(θt) − gi(˜θ)) + (1 − c)gi(θt)||2�
+≤ 2E
+�
+||g(θ)||2�
++ 4
+nE
+�
+||c(gi(θt) − gi(˜θ))||2�
++ 4(1 − c)2
+n
+E
+�
+||gi(θt)||2�
+≤ 2E
+�
+||g(θ)||2�
++ 4c2L2
+n
+E
+�
+||θt − ˜θ||2�
++ 4(1 − c)2
+n
+σ2
+The first and third inequality are because ||a + b||2 ≤ 2||a||2 + 2||b||2 , the second inequality follows the
+E
+�
+||τ − E [τ] ||2�
+≤ E
+�
+||τ||2�
+and the last inequality follows the L-smoothness and σ-bounded of function
+Gi.
+Remark 5. Compared with the gradient estimator of minibatch SVRG, the bound of E[||ut||2] is smaller
+when L is large, σ is relative small and c is properly chosen.
+A.4.2
+Lemma 2
+E [G(θt+1)] ≤ E
+�
+G(θt) + ηt||g(θt)||2 + Lη2
+2 ||ut||2
+�
+(7)
+Proof :
+By the L-smoothness of function G, we have
+22
+
+E [G(θt+1)] ≤ E
+�
+G(θt) + ⟨g(θt), θt+1 − θt⟩ + L
+2 ||θt+1 − θt||2
+�
+By the update procedure in algorithm 2 and unbiasedness, the right hand side can further upper bounded
+by
+E
+�
+G(θt) + ηt||g(θt)||2 + Lη2
+t
+2 ||ut||2
+�
+A.4.3
+Lemma 3
+For bt, bt+1, ζt > 0 and bt and bt+1 have the following relationship
+bt = bt+1(1 + ηtζt + 4c2η2
+t L2
+n
+) + 2c2η2
+t L3
+n
+and define
+Φt := ηt − bt+1ηt
+ζt
+− η2
+t L − 2bt+1η2
+t
+Ψt := E
+�
+G(θt) + bt||θt − ˜θ||2�
+(8)
+ηt, ζt and bt+1 can be chosen such that Φt > 0.Then the xt in Algorithm 1 have the bound:
+E[||g(θt)||2] ≤ Ψt − Ψt+1 + 2(Lη2
+t +2bt+1η2
+t )(1−c)2
+n
+σ2
+Φt
+Proof :
+We apply Lyapunov function
+Ψt = E
+�
+G(θt) + bt||θt − ˜θ||2�
+Then we need to bound ||θt − ˜θ||
+E
+�
+||θt+1 − ˜θ||2�
+= E
+�
+||θt+1 − θt + θt − ˜θ||2�
+= E
+�
+||θt+1 − θt||2 + ||θt − ˜θ||2 + 2⟨θt+1 − θt, θt − ˜θ⟩
+�
+= E
+�
+η2
+t||ut||2 + ||θt − ˜θ||2�
+− 2ηtE
+�
+⟨g(θt), θt − ˜θ⟩
+�
+≤ E[η2
+t ||us+1
+t
+||2 + ||θt − ˜θ||2] + 2ηtE
+� 1
+2ζt
+||g(θt)|| + ζt
+2 ||θt − ˜θ||2
+�
+(9)
+The third equality due to the unbiasedness of the update and the last inequality follows Cauchy-Schwarz
+and Young’s inequality. Plugging Equation (6), Equation (7) and Equation (9) into Equation (8), we can
+get the following bound:
+Ψt+1 ≤ E [G(θt)] +
+�
+bt+1(1 + ηtζt + 4c2η2
+t L2
+n
+) + 2c2η2
+t L3
+n
+�
+E[||θt − ˜θ||2]
+− (ηt − bt+1ηt
+ζt
+− Lη2
+t − 2bt+1η2
+t )E
+�
+||g(θt)||2�
++ 4(Lη2
+t
+2
++ bt+1η2
+t )(1 − c)2
+n
+σ2
+= Ψt − (ηt − bt+1ηt
+ζt
+− Lη2
+t − 2bt+1η2
+t )E
+�
+||g(θt)||2�
++ 4(Lη2
+t
+2
++ bt+1η2
+t )(1 − c)2
+n
+σ2
+23
+
+A.4.4
+Lemma 4
+Now we consider the effect of epoch and use s to denote the epoch number. Let bs
+m = 0, ηs
+t = η, ζs
+t = ζ and
+bs
+t = bs
+t+1(1 + ηζ + 4c2
+sηL2
+n
+) + 2 c2
+sη2L2
+n
+, Φs
+t = η −
+bs
+t+1η
+ζt
+− η2L − 2bs
+t+1η2 Define φ := mint,s Φs
+t. Then we can
+conclude that:
+E[||g(θπ)||2] ≤ G(θ0) − G(θ∗)
+Tφ
++
+S−1
+�
+s=0
+m−1
+�
+t=0
+2(L + 2bs
+t+1)(1 − cs)2η2σ2
+Tnφ
+Proof :
+Under the condition of ηs
+t = η, we apply telescoping sum on Lemma 3, then we will get:
+m−1
+�
+t=1
+E[||g(θs
+t )||2] ≤ Ψs
+0 − Ψs
+m
+φ
++
+m−1
+�
+t=0
+2(L + 2bs
+t+1)(1 − cs)2η2σ2
+nφ
+From previous definition, we know Ψs
+0 = G(˜θs), Ψs
+m = G(˜θs+1) and plugging into previous equation, we
+obtain:
+m−1
+�
+t=1
+E[||g(θs
+t )||2] ≤ G(˜θs) − G(˜θs+1)
+φ
++
+m−1
+�
+t=0
+2(L + 2bs
+t+1)(1 − cs)2η2σ2
+nφ
+Take summation over all the epochs and using the fact that ˜θ0 = θ0, G(˜θS) ≤ G(θ∗) we immediately obtain:
+1
+T
+S−1
+�
+s=0
+m−1
+�
+t=1
+E[||g(θs
+t )||2] ≤ G(θ0) − G(θ∗)
+φ
++
+S−1
+�
+s=0
+m−1
+�
+t=0
+2(L + 2bs
+t+1)(1 − cs)2η2σ2
+Tnφ
+(10)
+A.5
+Theorem
+A.5.1
+Theorem 1
+Define ξs = �m−1
+t=0 (L + 2bs
+t+1) and ξ := mins ξs. Let η =
+µn
+LNα
+(0 < µ < 1)
+and
+(0 < α ≤ 1), ζ =
+L
+N α/2
+and m = N
+3α
+2
+µn . Then there exists constant ν, µ, α, κ > 0 such that φ ≥
+nν
+LNα and ξ ≤ κL. Then E[||g(θπ)||2]
+can be future bounded by:
+E[||g(θπ)||2] ≤ (G(θ0) − G(θ∗))LN α
+Tnν
++ 2κµ2σ2
+N ανm
+Proof :
+By applying summation formula of geometric progression on the relation bs
+t = bs
+t+1(1 + ηtζt + 4c2
+sη2
+t L2
+n
+) +
+2 c2
+sη2
+t L3
+n
+, we have bs
+t = 2c2
+sη2L3
+n
+(1+ωs)m−t−1
+ωs
+where:
+ωs = ηζ + 4c2
+sη2L
+n
+= µn
+N
+3α
+2 + 4c2
+sµ2n
+N 2α
+≤ (4c2
+s + 1)µn
+N
+3α
+2
+24
+
+This bound holds because µ ≤ 1 and N ≥ 1 and thus 4c2
+sµ2n
+N2α
+= 4c2
+sµn
+N
+3α
+2
+×
+µ
+N
+α
+2 ≤ 4c2
+sµn
+N
+3α
+2 . And using this bound,
+we obtain:
+bs
+0 = 2η2c2
+sL3
+n
+(1 + ωs)m − 1
+ωs
+= 2µ2nc2
+sL
+N 2α
+(1 + ωs)m − 1
+ωs
+≤ 2µnc2
+sL((1 + ωs)m − 1)
+N
+α
+2 (4cs + 1)
+≤
+2µnc2
+sL((1 + (4c2
+s+1)µn
+N
+3α
+2
+)
+N
+3α
+2
+µn − 1)
+N
+α
+2 (4c2s + 1)
+≤ 2µnc2
+sL(e
+1
+4c2s+1 − 1)
+N
+α
+2 (4c2s + 1)
+The last inequality holds because (1 + 1
+x)x is a monotone increasing function of x when x > 0.
+Thus
+(1 + (4c2
+s+1)µn
+N
+3α
+2
+)
+N
+3α
+2
+µn
+≤ e
+1
+4c2s+1 in the third inequality. And we can obtain the lower bound for φ
+φ = min
+t,s Φs
+t ≥ min
+s (η − bs
+0η
+ζ
+− η2L − 2bs
+0η2) ≥
+nν
+LN α
+The first inequality holds since bt
+s is a decrease function of t. Meanwhile, the second inequality holds because
+there exist uniform constant ν such that ν ≥ µ(1 − bs
+0η
+ζ − Lη − bs
+0η).
+Remark 6. In practice, bs
+0 ≈ 0 because both γ and cs is both smaller than 0.1 which leads to µ(1 − bs
+0
+ζ −
+Lη − bs
+0η) ≈ µ(1 − Lη) and this value is usually much bigger than the ν∗ in the bound of minibatch SVRG.
+We need to find the upper bound for ξ
+ξs =
+m−1
+�
+t=0
+(L + 2bs
+t+1) = mL + 2
+m−1
+�
+t=0
+bs
+t+1
+= mL + 2
+m−1
+�
+t=0
+2c2
+sη2L3
+n
+(1 + ωs)m−t − 1
+ωs
+= mL + 2c2
+sη2L3
+nωs
+[(1 + ωs)m+1 − (1 + ωs)
+ωs
+− m]
+≤ mL + 2c2
+sη2L3
+n
+[1 + ωs
+ω2s
+(e
+1
+4c2s+1 − 1) − m]
+≤ mL + 2c2
+sLN α
+n
+(1 +
+µn
+N 3α/2 )(e
+1
+4c2s+1 − 1) − 2c2
+sµ2nmL
+N 2α
+= L[(1 − 2c2
+sµ2nL
+N 2α
+)m + 2c2
+sN α
+n
+(1 +
+µn
+N 3α/2 )(e
+1
+4c2s+1 − 1)]
+The reason why the first inequality holds is explained before and the second inequality holds because 1+x
+x2
+is a monotone decreasing function of x when x > 0, ωs =
+µn
+N
+3α
+2
++ 4c2
+sµ2n
+N2α
+≤
+µn
+N
+3α
+2
+and η =
+µn
+LNα . Then
+ξ = maxs ξs ≤ κL where κ ≥ maxs((1 − 2c2
+sµ2nL
+N2α
+)m + 2c2
+sNα
+n
+(1 +
+µn
+N 3α/2 )(e
+1
+4c2s+1 − 1)).
+When cs ≈ 0,
+(1 − 2c2
+sµ2nL
+N2α
+)m + 2c2
+sNα
+n
+(1 +
+µn
+N3α/2 )(e
+1
+4c2s+1 − 1) ≈ m.
+Now we obtain the lower bound for φ and upper bound for ξ, plugging them into equation (10), we will have:
+25
+
+E[||g(θπ)||2] ≤ G(θ0) − G(θ∗)
+φ
++
+S−1
+�
+s=0
+m−1
+�
+t=0
+2(L + 2bs
+t+1)(1 − cs)2η2σ2
+Tnφ
+≤ (G(θ0) − G(θ∗))LN α
+Tnν
++
+S−1
+�
+s=0
+m−1
+�
+t=0
+2(L + 2bs
+t+1)η2σ2
+Tnφ
+≤ (G(θ0) − G(θ∗))LN α
+Tnν
++
+S−1
+�
+s=0
+(2η2σ2
+Tnφ )
+m−1
+�
+t=0
+(L + 2bs
+t+1)
+≤ (G(θ0) − G(θ∗))LN α
+Tnν
++ 2κµ2σ2
+N ανm
+Remark 7. In our theoretical analysis above, we consider c as a constant in each epoch, which is still
+consistent with our practical algorithm for the following reasons.
+(i) In our Algorithm 1, �c∗
+t is actually a fixed constant within each epoch, which can be different in different
+epochs. Since it is too expensive to compute the exact �c∗
+t in each iteration, we compute it at the beginning
+of each epoch and use it as an approximation in the following epoch.
+(ii) As for our proof, we first show the convergence rate of one arbitrary training epoch. In this step, treating
+c as a constant is aligned with our practical algorithm.
+(iii) Then, when we extend the results of one epoch to the whole epoch, we establish an upper bound for
+different c in each epoch. Thus, the bound can be applied when c differs across epochs, which enables our
+theoretical analysis consistent with our practical algorithm.
+A.6
+Real Case Analysis for Sparse Training
+A.6.1
+CIFAR-10/100 dataset
+In our experiments, we apply both SVRG and AGENT on CIFAR-10 and CIFAR-100 dataset with η = 0.1,
+γ = 0.1, batch size m = 128 and in total 50000 training sample. Under this parameter setting, ν and ν∗in
+Theorem 1 and Remark 4 are about 0.1 and 0.06, respectively. While 2κµ2σ2
+Nανm is around 10−5 which is
+negligible so we know AGENT should have a tighter bound than SVRG in this situation which matches with
+the experimental results show in Figure 6.
+A.6.2
+svhn dataset
+Meanwhile, in SVHN dataset, we train our model with parameters: η = 0.1, γ = 0.1, batch size m = 573
+and sample size N = 73257. ν, ν∗ equal 0.4 and 0.06 respectively and 2κµ2σ2
+N ανm is around 10−4. Although the
+second term in Theorem 1 is bigger. Since ν here is a lot bigger than ν∗ which lead to the first term in
+Theorem 1 much smaller than that of Remark 4. So we still obtain a more stringent bound compared
+with SVRG which also meets with the outcome presented in Figure 9.
+26
+
+B
+Additional Experimental Results
+We summarize additional experimental results for the BSR-Net-based Özdenizci & Legenstein (2021), RigL-
+based Evci et al. (2020), and ITOP-based Liu et al. (2021) models.
+B.1
+Accuracy Comparisons in Different Epochs
+Aligned with the main manuscript, we compare the accuracy for a given number of epochs to compare both
+the speed of convergence and training stability. We first show BSR-Net-based results in this section. Since
+our approach has faster convergence and does not require a long warm-up period, the dividing points for the
+decay scheduler are set to the 50th and 100th epochs. In the manuscript, we also use this schedule for BSR-
+Net for an accurate comparison. In the Appendix, we include the results using its original schedule. BSR-Net
+and BSR-Net (ori) represent the results learned using our learning rate schedule and original schedule in
+Özdenizci & Legenstein (2021), respectively. As shown in Figures 7, 8, 9, 10, 11, 12, 13, the blue curves
+(A-BSR-Net) are always higher than the yellow curves and also much smoother than yellow curves (BSR-Net
+and BSR-Net (ori)), indicating faster and more stable training when using our proposed A-BSR-Net.
+(a) 90% Sparsity
+(b) 90% Sparsity
+(c) 99% Sparsity
+(d) 99% Sparsity
+Figure 7: Comparisons (accuracy given the number of epochs) with BSR-Net Özdenizci & Legenstein (2021).
+We evaluate sparse networks (99% or 90%) learned with natural training on CIFAR-10 using VGG-16.
+(a) 90% Sparsity
+(b) 90% Sparsity
+(c) 99% Sparsity
+(d) 99% Sparsity
+Figure 8: Comparisons (accuracy given the number of epochs) with BSR-Net Özdenizci & Legenstein (2021).
+We evaluate sparse networks (99% or 90%) learned with adversarial training (objective: AT) on CIFAR-10
+using VGG-16.
+27
+
+Koangoe Jugra.
+0.B
+0.6
+0.4 
+A-BSR-Net
+BSR-Net
+0
+50
+lio
+150
+2i0
+Number of epochs0.B
+0.6
+0.4 
+A-BSR-Net
+BSR-Net (ori)
+0
+50
+140
+150
+240
+Number of epochs0.B 
+accurecy
+0.6 
+Bugga
+0.4
+0.2
+A-BSR-Net
+BSR-Net
+0
+50
+lio
+150
+2i0
+Number of epochs0.B
+accurecy
+0.6 
+Buggal
+0.4
+0.2 
+A-BSR-Net
+BSR-Net (ori)
+0
+50
+140
+150
+240
+Number of epochs0.B
+0.7
+0.5
+fiugs
+0.4
+EO
+0.2 
+A-BSR-Net
+0.1 
+BSR-Net
+0
+50
+140
+150
+240
+Number of epochs0.B
+1
+0.5
+0.4
+EO
+0.2 
+A-BSR-Net
+0.1 
+BSR-Net (ori)
+0
+50
+lio
+150
+2i0
+Number of epochs0.7 
+Koangoe Jugra.
+0.6
+0.5
+0.4 
+0.3 
+0.2 
+A-BSR-Net
+0.1 
+BSR-Net
+0
+50
+lio
+150
+2i0
+Number of epochs0.7
+0.6 
+0.5
+0.4
+0.3 
+0.2
+A-BSR-Net
+0.1
+BSR-Net (ori)
+0
+50
+lio
+150
+2i0
+Number of epochs(a) 90% Sparsity
+(b) 90% Sparsity
+(c) 99% Sparsity
+(d) 99% Sparsity
+Figure 9: Comparisons (accuracy given the number of epochs) with BSR-Net Özdenizci & Legenstein (2021).
+We evaluate sparse networks (99% or 90%) learned with natural training on CIFAR-10 using Wide-ResNet-
+28-4.
+(a) 90% Sparsity
+(b) 90% Sparsity
+(c) 99% Sparsity
+(d) 99% Sparsity
+Figure 10: Comparisons (accuracy given the number of epochs) with BSR-Net Özdenizci & Legenstein
+(2021). We evaluate sparse networks (99% or 90%) learned with adversarial training (objective: AT) on
+CIFAR-10 using Wide-ResNet-28-4.
+(a) 90% Sparsity
+(b) 90% Sparsity
+(c) 99% Sparsity
+(d) 99% Sparsity
+Figure 11: Comparisons (accuracy given the number of epochs) with BSR-Net Özdenizci & Legenstein
+(2021). We evaluate sparse networks (99% or 90%) learned with natural training on SVHN using VGG-16.
+28
+
+0.B
+Kaunoe fugsa.
+0.6
+0.4 
+0.2
+A-BSR-Net
+BSR-Net
+0
+50
+lio
+150
+2i0
+Number of epochs0.B
+0.6
+0.4
+0.2
+A-BSR-Net
+BSR-Net (ori)
+0
+50
+140
+150
+240
+Number of epochs0.B
+accurecy
+0.6
+fugra.
+0.4
+0.2
+A-BSR-Net
+BSR-Net
+0
+50
+140
+150
+240
+Number of epochs0.B
+accurecy
+0.6
+Eesting
+0.4
+0.2
+A-BSR-Net
+BSR-Net (ori)
+0
+50
+140
+150
+240
+Number of epochs0.B
+10
+0.6 
+0.5
+0.4
+0.3
+0.2 
+A-BSR-Net
+0.1 
+BSR-Net
+0
+50
+lio
+150
+2i0
+Number of epochs0.B 
+0.7
+0.6
+0.5 
+0.4
+0.3
+0.2
+A-BSR-Net
+0.1
+BSR-Net (ori)
+0
+50
+lio
+150
+240
+Number of epochs0.7
+Koangoe Jugra.
+0.6 
+0.5
+0.4
+EO
+0.2
+A-BSR-Net
+0.1
+BSR-Net
+0
+50
+lio
+150
+240
+Number of epochs0.7
+0.6
+0.5
+0.4
+0.3 
+0.2
+A-BSR-Net
+BSR-Net (ori)
+0.1
+0
+50
+140
+150
+240
+Number of epochsLD
+0.B
+0.6
+ 0.4 -
+A-BSR-Net
+0.2 -
+BSR-Net
+0
+50
+1+0
+150
+20
+Number of epochaLD
+0.B
+0.6
+A-BSR-Net
+BSR-Net (ori)
+0.2
+0
+50
+140
+150
+20
+Number of epochsaccurecy
+0.B
+0.6
+Bugs
+0.4
+A-BSR-Net
+0.2 -
+BSR-Net
+0
+50
+150
+240
+Number of epochs0.B
+0.6
+A-BSR-Net
+0.2
+BSR-Net (ori)
+0
+50
+140
+150
+240
+Number of epochs(a) 90% Sparsity
+(b) 90% Sparsity
+(c) 99% Sparsity
+(d) 99% Sparsity
+Figure 12: Comparisons (accuracy given the number of epochs) with BSR-Net Özdenizci & Legenstein
+(2021). We evaluate sparse networks (99% or 90%) learned with adversarial training (objective: TRADES)
+on SVHN using VGG-16.
+(a) CIFAR-100,VGG-16
+(b) SVHN,VGG-16
+(c) CIFAR-100,WRN-28-4
+(d) SVHN,WRN-28-4
+Figure 13: Training curve (accuracy given number of epochs) of BSR-Net-based models (Özdenizci & Leg-
+enstein, 2021). Sparse networks (99%) are learned in standard setups on (a) CIFAR-100 using VGG-16, (b)
+SVHN using VGG-16, (c) CIFAR-100 using WRN-28-4, (d) SVHN using WRN-28-4.
+(a) Standard
+(b) Adversarial (AT)
+Figure 14: Training curve (required epochs to reach given accuracy) of BSR-Net-based models (Özdenizci
+& Legenstein, 2021). Dense networks are learned in standard and adversarial setups on CIFAR-10 using
+VGG-16.
+29
+
+0.B
+accurecy
+0.6
+Bugs
+-0.4
+A-BSR-Net
+0.2 -
+BSR-Net
+0
+50
+lio
+150
+240
+Number of epochs0.B
+0.6
+fugri
+-0.4
+A-BSR-Net
+0.2 
+BSR-Net (ori)
+0
+50
+150
+240
+Number of epochs0.9
+0.B 
+accurecy
+0.7
+0.6
+fiugri
+0.5
+0.4 
+0.3 
+A-BSR-Net
+0.2 
+BSR-Net
+0
+50
+lio
+150
+2i0
+Number of epochs0.9
+0.B
+0.7
+0.6
+0.5
+0.4
+0.3 .
+A-BSR-Net
+0.2
+BSR-Net (ori)
+0
+50
+140
+150
+240
+Number of epochs0.6
+0.5
+0.3
+0.1
+A-BSR-Net
+BSR-Net
+0.D
+50
+10
+150
+240
+Number of epochaaccurecy
+0.B
+0.6
+Bugs
+0.4
+A-BSR-Net
+0.2 -
+BSR-Net
+0
+50
+150
+240
+Number of epochs0.6 
+0.5
+0.4
+0.3
+0.2
+0.1
+A-BSR-Net
+BSR-Net
+0.D
+0
+50
+lio
+150
+2i0
+Number of epochsLD
+0.B
+0.4
+0.2 
+A-BSR-Net
+BSR-Net
+0
+50
+140
+150
+240
+Number of epocha0.B
+0.6
+0.4
+0.2
+A-BSR-Net
+BSR-Net
+0
+25
+50
+1i0
+125
+150
+175
+240
+Number of epochs0.B -
+0.7
+ecy
+0.6
+0.3
+0.2 -
+A-BSR-Net
+0.1 
+BSR-Net
+0
+25
+50
+75
+140
+125
+150
+175
+240
+ Number of epochs0
+20
+40
+60
+80
+100
+Number of epochs
+10
+20
+30
+40
+50
+60
+70
+Testing accuracy
+RigL-ITOP
+A-RigL-ITOP
+(a) 80% Sparsity
+0
+20
+40
+60
+80
+100
+Number of epochs
+10
+20
+30
+40
+50
+60
+70
+Testing accuracy
+RigL-ITOP
+A-RigL-ITOP
+(b) 90% Sparsity
+Figure 15: Training curve (required epochs to reach given accuracy) of ITOP-based models (Liu et al., 2021).
+Sparse networks are learned in standard setup on ImageNet-2012 using ResNet-50.
+In Figure 14, we also compare the convergence speed without sparsity. We show a BSR-Net-based result,
+where dense network is learned by adversarial training (AT) and standard training on CIFAR-10 using VGG-
+16. The blue curve of our A-BSR-Net tends to be above the yellow curve of BSR-Net, indicating successful
+acceleration. This demonstrates the broad applicability of our method.
+Then, we also show ITOP-based results on ImageNet-2012. As shown in Figure 15, the red and blue curve
+represent AGENT + RigL-ITOP and RigL-ITOP on 80% and 90% sparse ResNet-50, respectively. For 80%
+sparsity, we can see that the red curve is above the blue curve, demonstrating the acceleration effect of our
+AGENT, especially in the early stages. For 90% sparity, we can see that the red curve is more stable than
+the blue curve, which shows the stable effect of our AGENT on large data sets and is a slightly different
+manifestation of the strengths of our AGENT. If we use SVRG in this case, we will not only fail to train
+stably, but also slow down the training speed. In contrast, our AGENT can solve the limitation of SVRG.
+For other sparsity levels, we can expect advantages of our AGENT, in terms of acceleration or stability.
+Moreover, we can expect more significant speedups at different sparsity levels with more hyperparameter
+tuning, as the speedups are guaranteed by theoretical proofs.
+B.2
+Number of Training Epoch Comparisons
+We also compare the number of training epochs required to reach the same accuracy in BSR-Net-based
+results. In Figures 16, 17, 18, 19, 20, 21, 22, the blue curves (A-BSR-Net) are always lower than yellow
+curves (BSR-Net and BSR-Net (ori)), indicating faster convergence of A-BSR-Net.
+30
+
+(a) Wide-ResNet-28-4
+(b) ResNet-18
+Figure 16: Comparisons (required hours to reach given accuracy. We evaluate sparse networks (99%) learned
+with natural training on CIFAR-100 using (a) Wide-ResNet-28-4, and (b) ResNet-18.
+(a) 90% Sparsity
+(b) 90% Sparsity
+(c) 99% Sparsity
+(d) 99% Sparsity
+Figure 17: Comparisons (required hours to reach given accuracy. We evaluate sparse networks (99% or 90%)
+learned with natural training on CIFAR-10 using VGG-16.
+(a) 90% Sparsity
+(b) 90% Sparsity
+(c) 99% Sparsity
+(d) 99% Sparsity
+Figure 18: Comparisons (required hours to reach given accuracy). We evaluate sparse networks (99% or
+90%) learned with adversarial training (objective: AT) on CIFAR-10 using VGG-16.
+31
+
+A-BSR-Net
+BSR-NetA-BSR-Net
+BSR-NetA-BSR-Net
+BSR-NetA-BSR-Net
+BSR-Net (ori)A-BSR-Net
+BSR-NetA-BSR-Net
+BSR-Net (ori)A-BSR-Net
+BSR-NetA-BSR-Net
+BSR-Net (ori)(a) 90% Sparsity
+(b) 90% Sparsity
+(c) 99% Sparsity
+(d) 99% Sparsity
+Figure 19: Comparisons (required hours to reach given accuracy). We evaluate sparse networks (99% or
+90%) learned with natural training on CIFAR-10 using Wide-ResNet-28-4.
+(a) 90% Sparsity
+(b) 90% Sparsity
+(c) 99% Sparsity
+(d) 99% Sparsity
+Figure 20: Comparisons (required hours to reach given accuracy). We evaluate sparse networks (99% or
+90%) learned with adversarial training (objective: AT) on CIFAR-10 using Wide-ResNet-28-4.
+(a) 90% Sparsity
+(b) 90% Sparsity
+(c) 99% Sparsity
+(d) 99% Sparsity
+Figure 21: Comparisons (required hours to reach given accuracy). We evaluate sparse networks (99% or
+90%) learned with natural training on SVHN using VGG-16.
+(a) 90% Sparsity
+(b) 90% Sparsity
+(c) 99% Sparsity
+(d) 99% Sparsity
+Figure 22: Comparisons (required hours to reach given accuracy). We evaluate sparse networks (99% or
+90%) learned with adversarial training (objective: TRADES) on SVHN using VGG-16.
+32
+
+A-BSR-Net
+BSR-NetA-BSR-Net
+BSR-Net (ori)A-BSR-Net
+BSR-NetA-BSR-Net
+BSR-Net (ori)A-BSR-Net
+BSR-NetA-BSR-Net
+BSR-Net (ori)A-BSR-Net
+BSR-NetA-BSR-Net
+BSR-Net (ori)A-BSR-Net
+BSR-NetA-BSR-Net
+BSR-Net (ori)A-BSR-Net
+BSR-NetA-BSR-Net
+BSR-Net (ori)A-BSR-Net
+BSR-NetA-BSR-Net
+BSR-Net (ori)A-BSR-Net
+BSR-NetA-BSR-Net
+BSR-Net (ori)B.3
+Scaling Parameter Setting
+The choice of the scaling parameter γ is important to the acceleration and can be seen as a hyper-parameter
+tuning process. We experiment with different values of γ and find that setting γ = 0.1 is a good choice for
+effective acceleration of training. The presented results are based on sparse networks (99%) learned with
+adversarial training (objective: AT) on CIFAR-10 using VGG-16.
+As shown in Figure 23 (a), we compare the training curves (testing accuracy at different epochs) A-BSR-Net
+(γ = 0.1), A-BSR-Net (γ = 0.5), and BSR-Net. The yellow curve for A-BSR-Net (γ = 0.5) collapses after
+around 40 epochs training, indicating a model divergence. The reason is that if setting γ close to 1, e.g., like
+0.5, we will not be able to completely avoid the increase in variance. The increase in variance will lead to a
+decrease in performance, which is similar to "No γ" in section 5.4 of the manuscript.
+As shown in Figure 23 (b), we compare the training curves (testing accuracy at different epochs) A-BSR-Net
+(γ = 0.1), A-BSR-Net (γ = 0.01), and BSR-Net. The yellow curve for A-BSR-Net (γ = 0.01) is below the
+blue curve for A-BSR-Net (γ = 0.1), indicating a slower convergence speed. The reason is that if γ is set
+small, such as 0.01, the weight of the old gradients will be small. Thus, the old gradients will have limited
+influence on the updated direction of the model, which tends to slow down the convergence and sometimes
+can lead to more training instability.
+0
+25
+50
+75
+100
+125
+150
+175
+200
+Number of epochs
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+Testing accuracy
+A-BSR-Net, 0.1
+A-BSR-Net, 0.5
+BSR-Net
+(a) Scaling parameter = 0.1 or 0.5
+0
+25
+50
+75
+100
+125
+150
+175
+200
+Number of epochs
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+Testing accuracy
+A-BSR-Net, 0.1
+A-BSR-Net, 0.01
+BSR-Net
+(b) Scaling parameter = 0.1 or 0.01
+Figure 23: Comparisons (testing accuracy given the number of epochs) with different scaling parameters in
+BSR-Net-based models Özdenizci & Legenstein (2021). We evaluate sparse networks (99%) learned with
+adversarial training (objective: AT) on CIFAR-10 using VGG-16. (a) scaling parameter = 0.1 or 0.5, (b)
+scaling parameter = 0.1 or 0.01.
+B.4
+Other Variance Reduction Method Comparisons
+We also include more results about comparison between our ADSVRG and stochastic variance reduced
+gradient (SVRG) Baker et al. (2019); Chen et al. (2019); Zou et al. (2018), a popular variance reduction
+method in non-sparse case, to show the limitations of previous methods.
+B.4.1
+BSR-Net-based Results
+The presented results are based on sparse networks (99%) learned with adversarial training (objective: AT)
+on CIFAR-10 using VGG-16. As presented in Figure 24, we show the training curves (testing accuracy
+at different epochs)of A-BSR-Net, BSR-Net, and BSR-Net using SVRG. The yellow curve for BSR-Net
+using SVRG rises to around 0.4 and then rapidly decreases to a small value around 0.1, indicating a model
+divergence. This demonstrates that SVRG does not work for sparse training. As for the blue curve for our
+A-BSR-Net, it is always above the green curve for BSR-Net, indicating a successful acceleration.
+33
+
+0
+25
+50
+75
+100
+125
+150
+175
+200
+Number of epochs
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+Testing accuracy
+A-BSR-Net
+BSR-Net, SVRG
+BSR-Net
+Figure 24: Comparisons (testing accuracy given the number of epochs) with different variance reduction
+methods in BSR-Net-based models Özdenizci & Legenstein (2021).
+We evaluate sparse networks (99%)
+learned with adversarial training (objective: AT) on CIFAR-10 using VGG-16.
+B.4.2
+RigL-based Results
+The presented results are based on sparse networks (90%) learned with standard training on CIFAR-100
+using ResNet-50.
+As presented in Figure 25, we show the training curves (testing accuracy at different
+epochs) of A-RigL, RigL, and RigL using SVRG. The yellow curve for RigL using SVRG is always below
+the other two curves, indicating a slower model convergence. This demonstrate that SVRG does not work
+for sparse training. As for the blue curve for our A-RigL, it is always on the top of the green curve for RigL,
+indicating that the speedup is successful.
+0
+50
+100
+150
+200
+250
+Number of epoch
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+Accuracy
+A-RigL
+RigL, SVRG
+RigL
+Figure 25: Comparisons (testing accuracy given the number of epochs) with different variance reduction
+methods in RigL-based models Evci et al. (2020). We evaluate sparse networks (90%) learned with standard
+training on CIFAR-100 using ResNet-50.
+34
+
+Table 6: Comparisons the BSR-Net Özdenizci & Legenstein (2021) and HYDRA Sehwag et al. (2020).
+Evaluations of sparse networks learned with robust training objectives (TRADES) on SVHN using VGG-
+16 and WideResNet-28-4. Evaluations are after full training (200 epochs) and presented as clean/robust
+accuracy (%). Robust accuracy is evaluated via PGD50 with 10 restarts ϵ = 8/255.
+BSR-Net
+HYDRA
+Ours
+90% Sparsity
+VGG-16
+89.4/53.7 89.2/52.8 94.4/51.9
+WRN-28-4 92.8/55.6 94.4/43.9 95.5/46.2
+99% Sparsity
+VGG-16
+86.4/48.7 84.4/47.8 90.9/47.9
+WRN-28-4 89.5/52.7 88.9/39.1 92.2/51.1
+B.5
+Final Accuracy Comparisons
+We also provide additional BSR-Net-based results for the final accuracy comparison. In addition to the
+BSR-Net and A-BSR-Net in the manuscript, we also include HYDRA in the appendix, which is also a SOTA
+sparse and adversarial training pipeline. The results are trained on SVHN using VGG-16 and WideResNet-
+28-4 (WRN-28-4). The final results for BSR-Net and HYDRA are obtained from Özdenizci & Legenstein
+(2021) using their original learning rate schedules. As shown in Table 6, it is encouraging to note that our
+method tends to be the best in all cases when given clean test samples. In terms of the robustness, our
+A-BSR-Net beats HYDRA in most cases, while experience a performance degradation compared to BSR-Net.
+B.6
+Gradient Change Speed & Sparsity Level
+In sparse training, when there is a small change in the weights, the gradient changes faster than in dense
+training, and this phenomenon can be expressed as a low correlation between the current and previous
+gradients, making the existing variance reduction methods ineffective.
+We first demonstrate this lower correlation from an intuitive point of view. Considering the weights on which
+the current and previous gradients were calculated, there are three cases to be discussed in sparse training
+when the masks of current and previous gradients are different. First, if current weights are pruned, we
+do not need to consider their correlation because we do not need to update the current weights using the
+corresponding previous weights. Second, if current weights are not pruned but previous weights are pruned,
+the previous weights are zero and the difference between two weights is relatively large, leading to a lower
+relevance. Third, if neither the current nor the previous weights are pruned, which weights are pruned can
+still change significantly, leading to large changes in the current and previous models. Thus, the correlation
+between the current and previous gradients of the weights will be relatively small. Thus, it is not a good idea
+to set c = 1 directly in sparse training which can even increase the variance and slow down the convergence.
+When the masks of the current and previous gradients are the same, the correlation still tends to be weaker.
+As we know, c∗
+t = Cov(gnew,gold)
+Var(gold)
+. Even if Cov(gnew, gold) does not decrease, the variance Var(gold) increases
+in sparse training, leading to a decrease in c∗
+t .
+Apart from the analysis above, we also do some experiments to demonstrate that the gradient changes
+faster as the sparsity increases. To measure the rate of change, our experiments are described below. We
+begin with fully-trained checkpoints from ResNet-50 on CIFAR-100 with RigL and SET at 0%, 50%, 80%,
+90%, and 95% sparsity. We calculate and store the gradient of each weight on all training data. Then, we
+add Gaussian perturbations (std = 0.015) to all the weights and calculate the gradients again. Lastly, we
+calculate the correlation between the gradient of the new perturbed weights and the old original weights.
+As we know, there is always a difference between the old and new weights. If the gradients become very
+different after adding some small noise to the weights, the new and old gradients will tend to have smaller
+correlations. If the gradients do not change a lot after adding some small noise, the old and new gradients
+will have a higher correlation. Thus, we add Gaussian noise to the weights to simulate the difference between
+35
+
+the new and old gradients. As shown in Table 7, the correlation decreases with increasing sparsity, which
+indicates a weaker correlation in sparse training and supports our claim.
+Table 7: Correlation between the gradient of the new perturbed weights and the old original weights from
+ResNet-50 on CIFAR-100 produced by RigL and SET at different sparsity including 0%, 50%, 80%, 90%,
+95%, 99%.
+Sparsity
+0%
+50%
+80%
+90%
+95%
+ResNet-50, CIFAR-100 (RigL)
+0.6005
+0.4564
+0.3217
+0.1886
+0.1590
+ResNet-50, CIFAR-100 (SET)
+0.6005
+0.4535
+0.2528
+0.1763
+0.1195
+B.7
+Comparison between True Correlation & Our Approximation
+In this section, to test how well our approximation estimates the true optimum c, we empirically compare
+the approximation c∗ in Eq. (4) (in the main manuscript) and the correlation between gradient of current
+weights and gradient of previous epoch weights. As shown in Figure 26, the yellow and blue curves represent
+the approximation c∗ and the correlation, respectively. The two curves tend to have similar up-and-down
+patterns, and the yellow curves usually have a larger magnitude. This suggests that our c approximation
+captures the dynamic patterns of the correlation. For the larger magnitude, it can be matched by our scaling
+parameter.
+5
+10
+15
+20
+25
+30
+Number of epoch
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+0.8
+Value
+True Correlation
+c Approximation
+(a) 90%
+5
+10
+15
+20
+25
+30
+Number of epoch
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+0.8
+Value
+True Correlation
+c Approximation
+(b) 99%
+Figure 26: Comparisons between the approximation c∗ and correlation between gradient of current weights
+and gradient of previous epoch weights. We evaluate sparse networks learned with RigL-based standard
+training on CIFAR-10 using ResNet-50 with (a) 90% sparsity and (b) 99% sparsity.
+B.8
+Variants of RigL
+RigL is one of the most popular dynamic sparse training pipeline which uses weight magnitude for pruning
+and gradient magnitude for growing. Our method adaptively updates the new batch gradient using the old
+storage gradient which usually has less noise. As a result, the variance of the new batch gradient is reduced,
+leading to fast convergence. Currently, we only use gradients with corrected variance in weight updates. A
+natural question is how does it perform if we also use this variance-corrected gradient for weight growth in
+RigL.
+We do some experiments in RigL-based models trained on CIFAR-10. As shown in Figure 27, the blue
+curves (RigL-ITOP-G) and yellow curves (RigL-ITOP) correspond to the weight growth with and without
+the variance-corrected gradient, respectively. We can see that in the initial stage, the blue curves are higher
+than the yellow curves. But after the first learning rate decay, they tend to be lower than the yellow curves.
+This suggests that weight growth using a variance-corrected gradient at the beginning of training can help
+36
+
+the model improve accuracy faster. However, this may lead to a slight decrease in accuracy in the later
+training stages. This may be due to the fact that some variance in the gradient can help the model explore
+local regions better and find better masks as the model approaches its optimal point.
+0
+50
+100
+150
+200
+250
+Number of epoch
+0.5
+0.6
+0.7
+0.8
+0.9
+Accuracy
+RigL-ITOP-G
+RigL-ITOP
+(a) VGG-C
+0
+50
+100
+150
+200
+250
+Number of epoch
+0.5
+0.6
+0.7
+0.8
+0.9
+Accuracy
+RigL-ITOP-G
+RigL-ITOP
+(b) ResNet-34
+Figure 27: Comparisons (testing accuracy given the number of epochs) between weight growth with (RigL-
+ITOP-G) and without (RigL-ITOP) variance-corrected gradient Liu et al. (2021). We evaluate sparse net-
+works (99%) learned with standard training on CIFAR-10 using (a) VGG-C and (b) ResNet-34.
+B.9
+Comparison with Reducing Learning Rate
+To demonstrate the design of the scaling parameter γ, we compare our AGENT with "Reduce LR", where
+we remove the scaling parameter γ from AGENT and set the learning rate to 0.1 times the original one. As
+shown in Table 8, reducing the learning rate can lead to a comparable convergence rate in the early stage.
+However, it slows down the later stages of training and leads to sub-optimal final accuracy. The reason is
+that it reduces both signal and noise, and therefore does not improve the signal-to-noise ratio or speed up
+the sparse training.
+The motivation of γ is to avoid introducing large variance due to error in approximating ct and bias due to
+the adversarial training. The true correlation depends on many factors such as the dataset, architecture, and
+sparsity. In some cases, it can be greater or smaller than 10%. For the value of γ, it is a hyperparameter and
+we can choose different values for different settings. In our case, for simplicity, we choose γ = 0.1 for all the
+settings, and find that it works well and accelerates the convergence. If we tune the value of γ for different
+settings according to their corresponding correlations, it is possible to obtain faster convergence rates.
+Table 8: Testing accuracy (%) of SET-ITOP-based models for AGENT (ours) and "Reduce LR". Sparse
+VGG-C and ResNet-34 are learned in standard setups.
+Epoch
+20
+80
+130
+180
+240
+Reduce LR (VGG-C, SET-ITOP)
+76.5
+81.3
+84.6
+85.5
+85.5
+AGENT (VGG-C, SET-ITOP)
+76.1
+81.5
+87.6
+87.1
+88.6
+Reduce LR (ResNet-34, SET-ITOP)
+81.4
+85.9
+89.3
+89.5
+89.8
+AGENT (ResNet-34, SET-ITOP)
+83.0
+85.6
+92.0
+92.3
+92.5
+B.10
+Comparison with Momentum-based Methods
+The momentum-based approach works well in general, but it still suffers from optimization difficulties due to
+sparsity constraints. For example, in our baseline SGD, following the original code base, we have also added
+momentum to the optimizer. However, as shown in the pink curves in Figure 2, it still has training instability
+and convergence problems. The reason is that they do not take into account the sparse and adversarial
+training characteristics and cannot provide an adaptive balance between old and new information.
+37
+
+Our method AGENT is designed for sparse and adversarial training and can establish a finer control over
+how much information we should get from the old to help the new. To demonstrate the importance of this
+fine-grained adaptive balance, we do ablation studies in Section 6.4. In "Fixed ct", we set ct = 0.1 and test
+the convergence rate without the adaptive control. We find that the adaptive balance (ours) outperforms
+"Fixed ct" in almost all cases, especially in adversarial training. For standard training, "Fix ct" provides
+similar convergence rates to our method, while ours tends to have better final scores.
+C
+Additional Details about Experiment Settings
+C.1
+Gradient Variance and Correlation Calculation
+We calculate the gradient variance and correlation of the ResNet-50 on CIFAR-100 from RigL (Evci et al.,
+2020) and SET (Mocanu et al., 2018) at different sparsities including 0%, 50%, 80%, 90%, and 95%. The
+calculation is based on the checkpoints from Sundar & Dwaraknath (2021).
+Gradient variance: We first load fully trained checkpoints for the 0%, 50%, 80%, 90%, and 95% sparse
+models. Then, to see the gradient variance around the converged optimum, we add small perturbations to
+the weights and compute the mean of the gradient variance. For each checkpoint, we do three replicates.
+Gradient correlation: We begin with fully-trained checkpoints at 0%, 50%, 80%, 90%, and 95% sparsity.
+We calculate and store the gradient of each weight on all training data. Then, we add Gaussian perturbations
+to all the weights and calculate the gradients again. Lastly, we calculate the correlation between the gradient
+of the new perturbed weights and the old original weights. For each checkpoint, we do three replicates.
+C.2
+Implementations
+In BSR-Net-based results, aligned with the choice of Özdenizci & Legenstein (2021), the gradients for
+all models are calculated by SGD with momentum and decoupled weight decay (Loshchilov & Hutter, 2019).
+All models are trained for 200 epochs with a batch size of 128.
+In RigL-based results, we follow the settings in Evci et al. (2020); Sundar & Dwaraknath (2021). We
+train all the models for 250 epochs with a batch size of 128, and parameters are optimized by SGD with
+momentum.
+In ITOP-based results, we follow the settings in Liu et al. (2021). For CIFAR-10 and CIFAR-100, we
+train all the models for 250 epochs with a batch size of 128. For ImageNet-2012, we train all the models for
+100 epochs with a batch size of 64. Parameters are optimized by SGD with momentum.
+C.3
+Learning Rate
+Aligned with popular sparse training methods (Evci et al., 2020; Özdenizci & Legenstein, 2021; Liu et al.,
+2021), we choose piecewise constant decay schedulers for learning rate and weight decay. In our A-BSR-Net,
+we use the 50th and 100th epochs as the dividing points of our learning rate decay scheduler. The reason
+is that our approach has faster convergence and doesn’t require a long warm-up period. In the evaluation
+shown in the manuscript, we also use this scheduler for BSR-Net for a more accurate and fair comparison.
+C.4
+Initialization (BSR-Net-based results)
+Consistent with Özdenizci & Legenstein (2021), we also choose Kaiming initialization to initialize the network
+weights He et al. (2015)
+C.5
+Benchmark Datasets (BSR-Net-based results)
+For a fair comparison, we choose the same benchmark datasets as Özdenizci & Legenstein (2021). Specifically,
+we use CIFAR-10 and CIFAR-100 Krizhevsky et al. (2009) and SVHN Netzer et al. (2011) in our experiments.
+38
+
+Both CIFAR-10 and CIFAR-100 datasets include 50, 000 training and 10, 000 test images. SVHN dataset
+includes 73, 257 training and 26, 032 test samples.
+C.6
+Data Augmentation
+We follow a popular data augmentation method used in Özdenizci & Legenstein (2021); He et al. (2016). In
+particular, we randomly shift the images to the left or right, crop them back to their original size, and flip
+them in the horizontal direction. In addition, all the pixel values are normalized in the range of [0, 1].
+D
+Sparse Training Method Description
+D.1
+Bayesian Sparse Robust Training
+Bayesian Sparse Robust Training (BSR-Net) Özdenizci & Legenstein (2021) is a Bayesian Sparse and Robust
+training pipeline. Based on a Bayesian posterior sampling principle, a network rewiring process simultane-
+ously learns the sparse connectivity structure and the robustness-accuracy trade-off based on the adversarial
+learning objective. More specifically, regarding its mask update, it prunes all negative weights and grows
+new weights randomly.
+E
+Limitations of Our Adaptive Gradient Correction Method
+E.1
+Extra FLOPs
+Similar to SVRG, our ADSVRG increases the training FLOPs in each iteration due to the extra forward
+and backward used to compute the old gradients.
+However, the true computation difference can be smaller and the GPU-based runining time of SVRG will not
+be affected that much. For example, in the adversarial setting, we need additional computations to generate
+the adversarial samples, which is time-consuming and only needs to be done once in each iteration of our
+AVR and SGD. For BSR-Net, we empirically find that the ratio of time required for each iteration of our
+AVR and SGD is about 1.2.
+There are also several methods to reduce the extra computation caused by SVRG. The first approach is
+to use the sparse gradients proposed by M Elibol (2020) Elibol et al. (2020). It can effectively reduce the
+computational cost of SVRG and can be easily applied to our method. The second approach is suggested
+by Allen-Zhu and Hazan (2016) Allen-Zhu & Hazan (2016). The extra cost on computing batch gradient on
+old model parameters is totally parallelizable. Thus, we can view SVRG as doubling the mini-batch size.
+Third, we can follow the idea of SAGA Defazio et al. (2014) and store gradients for individual samples. By
+this way, we do not need the extra forward and backward step and save the computation. But it requires
+extra memory to store the gradients.
+In the main manuscript, we choose to compare the convergence speed of our ADSVRG and SGD for the
+same number of pass data (epoch), which is widely used as a criterion to compare SVRG-based optimization
+and SGD (Allen-Zhu & Hazan, 2016; Chatterji et al., 2018; Zou et al., 2018; Cutkosky & Orabona, 2019). A
+comparison in this way in this way can demonstrate the accelerating effect of the optimization method and
+provide inspiration for future work.
+E.2
+Scaling parameter tuning
+In our adaptive variance reduction method (AVR), we add an additional scaling parameter γ which need to
+be adjusted. We find that setting γ = 0.1 is a good choice for BSR-Net, RigL, and ITOP. However, it can
+be different for other different sparse training pipelines.
+39
+
+E.3
+Robust Accuracy Degradation
+For the final accuracy results of BSR-Net-based models, there is a small decrease in the robustness accuracy
+after using our AVR. It is still an open question how to further improve the robust accuracy when using
+adaptive variance reduction in sparse and adversarial training.
+40
+
diff --git a/FtE1T4oBgHgl3EQf-waO/content/tmp_files/load_file.txt b/FtE1T4oBgHgl3EQf-waO/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..db08e55695fe857c6cd320b8eca4f04226124676
--- /dev/null
+++ b/FtE1T4oBgHgl3EQf-waO/content/tmp_files/load_file.txt
@@ -0,0 +1,2397 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf,len=2396
+page_content='Balance is Essence: Accelerating Sparse Training via Adap-  tive Gradient Correction  Bowen Lei  bowenlei@stat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='tamu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='edu  Texas A&M University  Dongkuan Xu  dxu27@ncsu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='edu  North Carolina State University  Ruqi Zhang  ruqiz@purdue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='edu  Purdue University  Shuren He  dri.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='tea@tamu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='edu  Texas A&M University  Bani K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Mallick  bmallick@stat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='tamu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='edu  Texas A&M University  Abstract  Despite impressive performance on a wide variety of tasks, deep neural networks re-  quire significant memory and computation costs, prohibiting their application in resource-  constrained scenarios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Sparse training is one of the most common techniques to reduce these  costs, however, the sparsity constraints add difficulty to the optimization, resulting in an  increase in training time and instability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In this work, we aim to overcome this problem and  achieve space-time co-efficiency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' To accelerate and stabilize the convergence of sparse train-  ing, we analyze the gradient changes and develop an adaptive gradient correction method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Specifically, we approximate the correlation between the current and previous gradients,  which is used to balance the two gradients to obtain a corrected gradient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Our method can  be used with most popular sparse training pipelines under both standard and adversarial se-  tups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Theoretically, we prove that our method can accelerate the convergence rate of sparse  training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Extensive experiments on multiple datasets, model architectures, and sparsities  demonstrate that our method outperforms leading sparse training methods by up to 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0%  in accuracy given the same number of training epochs, and reduces the number of training  epochs by up to 52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1% to achieve the same accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  1  Introduction  With the development of deep neural networks (DNNs), there is a trend towards larger and more intensive  computational models to enhance task performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Despite of the good performance, such large models are  not applicable when memory or computational resources are limited (Bellec et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Evci et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In addition, these large models consume a considerable amount of energy and produce a  large amount of carbon footprint (Thompson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Patterson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Matus & Veale, 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' As a  result, it attracts more efforts in research to find resource-efficient ways (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', less memory & less compute)  to train DNNs while maintaining results comparable to the state of the art (Yu & Li, 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Rock et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Leite & Xiao, 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Sparse training (Mocanu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Evci et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2022) is one of the most popular classes of  methods to improve efficiency in terms of space (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' memory storage) and is receiving increasing attention.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  During sparse training, a certain percentage of connections are removed to save memory (Bellec et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=',  2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Evci et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Sparse patterns, which describe where connections are retained or removed, are  1  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='03573v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='LG]  9 Jan 2023  iteratively updated with various criteria (Dettmers & Zettlemoyer, 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Evci et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Özdenizci & Legenstein, 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' The goal is to find a resource-efficient sparse neural network (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', removing  some connections) with comparable or even higher performance compared to the original dense model (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=',  keeping all connections).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  However, sparse training can bring some side effects to the training process, especially in the case of high  sparsity (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 99% weights are zero).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' First, sparsity can increase the variance of stochastic gradients, leading  the model to move in a sub-optimal direction and hence slow convergence (Hoefler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Graesser  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' As shown in Figure 1 (a), we empirically see that the gradient variance grows with increasing  sparsity (more details in Section C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Second, it can result in training instability (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', a noisy trajectory of  test accuracy w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' iterations) (Sehwag et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Bartoldson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2020), which requires additional time  to compensate for the accuracy drop, resulting in slow convergence (Xiao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Additionally, the  need to consider the robustness of the model during sparse training is highlighted in order to apply sparse  training to a wide range of real-world scenarios where there are often challenges with dataset shifts (Ye et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=',  2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Hoefler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Kundu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Özdenizci & Legenstein, 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' To address these issues, we  raise the following questions:  Question 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' How to simultaneously improve convergence speed and training stability of sparse training?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Prior gradient correction methods, such as variance reduction (Zou et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Gorbunov  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2020), are used to accelerate and stabilize dense training, while we find that it fails in sparse training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  They usually assume that current and previous gradients are highly correlated, and therefore they add a  large constant amount of previous gradients to correct the gradient (Dubey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Chatterji et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=',  2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' However, this assumption does not hold in sparse training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Figure 1 (b) shows the  gradient correlation at different sparsities, implying that the gradient correlation decreases with increasing  sparsity (more details in Section C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1), which breaks the balance between current and previous gradients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Therefore, we propose to adaptively change the weights of previous and current gradients based on their  correlation to add an appropriate amount of previous gradients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Question 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' How to design an accelerated and stabilized sparse training method that is effective in real-world  scenarios with dataset shifts?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Moreover, real-world applications are under-studied in sparse training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Prior methods use adversarial training  to improve model robustness and address the challenge of data shifts, which usually introduces additional bias  beyond the variance in the gradient estimation (Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2020), increasing the difficulty of gradient correction  (more details in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Thus, to more accurately approximate the full gradient, especially during the  adversarial setup, we design a scaling strategy to control the weights of the two gradients, determining the  amount of previous gradient information to be added to the current gradient, which helps the balance and  further accelerates the convergence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  In this work, we propose an adaptive gradient correction (AGENT) method to accelerate and stabilize sparse  training for both standard and adversarial setups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Theoretically, we prove that our method can accelerate the  convergence rate of sparse training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Empirically, we perform extensive experiments on multiple benchmark  datasets, model architectures, and sparsities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In both standard and adversarial setups, our method improves  the accuracy by up to 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0% given the same number of epochs and reduces the number of epochs up to  52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1% to achieve the same performance compared to the leading sparse training methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In contrast to  previous efforts of sparse training acceleration which mainly focus on structured sparse patterns, our method  is compatible with both unstructured ans structured sparse training pipelines (Hubara et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Chen  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  2  Related Work  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1  Sparse Training  Interest in sparse DNNs has been on the rise recently, especially when dealing with resource constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  The goal is to achieve comparable performance with sparse weights to satisfy the constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Different  sparse training methods have emerged, where sparse weights are maintained in the training process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Various  2  0%  50%  80%  90%  95%  Sparsity  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  Gradient Variance (e-8)  RigL  SET  (a) Gradient Variance  0%  50%  80%  90%  95%  Sparsity  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6  Gradient Correlation  RigL  SET  (b) Gradient Correlation  Figure 1: Gradient variance (a) and gradient correlation (b) of models obtained by RigL and SET at different  sparsities including 0% (dense), 50%, 80%, 90%, 95%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Gradient variance grows with increasing sparsity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Gradient correlation drops with increasing sparsity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' The sparse models have larger gradient variance and  smaller gradient correlation compared to dense models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  pruning and growth criteria are proposed, such as weight/gradient magnitude, random selection, and weight  sign (Mocanu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Bellec et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Frankle & Carbin, 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Mostafa & Wang, 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Dettmers &  Zettlemoyer, 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Evci et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Jayakumar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Özdenizci & Legenstein, 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Zhou et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2021b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Schwarz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Huang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  However, the aforementioned studies focus on improving the performance of sparse training, while neglect-  ing the side effect of sparse training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Sparsity not only increases gradient variance, thus delaying conver-  gence (Hoefler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Graesser et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2022), but also leads to training instability (Bartoldson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=',  2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' It is a challenge to achieve both space and time efficiency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Additionally, sparse training can also  exacerbate models’ vulnerability to adversarial samples, which is one of the weaknesses of DNNs (Özdenizci  & Legenstein, 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' When the model encounters intentionally manipulated data, its performances may  deteriorate rapidly, leading to increasing security concerns Rakin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' (2019);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Akhtar & Mian (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In  this paper, we focus on sparse training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In general, our method can be applied to any SGD-based sparse  training pipelines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2  Accelerating Training  Studies have been conducted in recent years on how to achieve time efficiency in DNNs, and one popular  direction is to obtain a more accurate gradient estimate to update the model (Gorbunov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2020), such  as variance reduction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' SGD is the most common training method, where one uses small batches of data  to approach the full gradient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In standard training, the batch estimator is unbiased, but can have a large  variance and misguide the model, leading to studies on variance reduction (Johnson & Zhang, 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Xiao  & Zhang, 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Shang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Zou et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Gorbunov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  While  adversarial training brings bias in the gradient estimation (Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2020), and we need to face the bias-  variance tradeoff when doing gradient correction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' A shared idea is to balance the gradient noise with a  less-noisy old gradient (Nguyen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Fang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Some other momentum-  based methods have a similar strategy of using old information (Cutkosky & Orabona, 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Chayti &  Karimireddy, 2022) However, all the above work considers only the acceleration in non-sparse case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Acceleration is more challenging in sparse training, and previous research on it has focused on structured  sparse training (Hubara et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Zhou et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2021a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' First, sparse training will induce  larger variance (Hoefler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In addition, some key assumptions associated with gradient correction  methods do not hold under sparsity constraint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In the non-sparse case, the old and new gradients are assumed  to be highly correlated, so we can collect a large amount of knowledge from the old gradients (Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=',  3  2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Chatterji et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Dubey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' However, sparsity tends to lead to lower correlations, and  this irrelevant information can be harmful, making previous methods no longer applicable to sparse training  and requiring a finer balance between new and old gradients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Furthermore, the structured sparsity pattern  is not flexible enough, which can lead to lower model accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In contrast, our method accelerates sparse  training from an optimization perspective and is compatible with both unstructured and structured sparse  training pipelines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  3  Preliminaries: Stochastic Variance Reduced Gradient  Stochastic variance reduced gradient (SVRG) (Johnson & Zhang, 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Allen-Zhu & Hazan, 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Dubey  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2016) is a widely-used gradient correction method designed to obtain more accurate gradient estimates,  which has been followed by many studies (Zou et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Baker et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Specifically,  after each epoch of training, we evaluate the full gradients �g based on �θ at that time and store them for  later use.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In the next epoch, the batch gradient estimate on Bt is updated using the stored old gradients  via Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' (1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  ˆg(θt) = 1  n  �  i∈Bt  �  gi(θt) − gi(�θ)  �  + �g  (1)  where gi(θt) = ∇G(xi|θt), G(θt) = (�N  i=1 G(xi|θt))/N is the loss function, �g = ∇G(�θ), θt is the current  parameters, n is the number of samples in each mini-batch data, and N is the total number of samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  SVRG successfully accelerates many training tasks in the non-sparse case, but does not work well in sparse  training, which is similar to many other gradient correction methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  4  Method  We propose an adaptive gradient correction (AGENT) method and integrate it with recent sparse training  pipelines to achieve accelerations and improve training stability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Specifically, to accomplish the goal, our  AGENT filters out less relevant information and obtains a well-controlled and time-varying amount of knowl-  edge from the old gradients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Our method overcomes the limitations of previous acceleration methods such  as SVRG (Allen-Zhu & Hazan, 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Dubey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Elibol et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2020), and successfully accelerates and  stabilizes sparse training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' We will illustrate each part of our method in the following sections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Our AGENT  method is outlined in Algorithm 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1  Adaptive Control over Old Gradients  In AGENT, we designed an adaptive addition of old gradients to new gradients to filter less relevant informa-  tion and achieve a balance between new and old gradients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Specifically, we add an adaptive weight ct ∈ [0, 1]  to the old gradient as shown in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' (2), where we use gnew = 1  n  �  i∈Bt gi(θt) and gold = 1  n  �  i∈Bt gi(�θ) to de-  note the gradient on current parameters θt and previous parameters �θ for a random subset Bt, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  When the old and new gradients are highly correlated, we need a large c to get more useful information from  the old gradient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Conversely, when the relevance is low, we need a smaller c so that we do not let irrelevant  information corrupt the new gradient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  ˆg(θt) = 1  n  �  i∈Bt  �  gi(θt) − ct · gi(�θ)  �  + ct · �g = gnew − ct · gold + ct · �g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  (2)  A suitable ct should effectively reduce the variance of ˆg(θt).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' To understand how ct influence the variance  of updated gradient, we decompose the variance of ˆg(θt) in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' (3) with some abuse of notation, where the  variance of updated gradient is a quadratic function of ct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' For simplicity, considering the case where ˆg(θt)  is a scalar, the optimal c∗  t will be in the form of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' (3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' As we can see, c∗  t is not closed to 1 when the new  gradient is not highly correlated with the old gradient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Since low correlation between gnew and gold is more  common in sparse training, directly setting ct = 1 in previous methods is not appropriate and we need to  estimate adaptive weights c∗  t .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In support of this claim, we include a discussion and empirical analysis in  4  the Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6 to demonstrate that as sparsity increases, the gradient changes faster, leading to lower  correlations between gnew and gold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Var(ˆg(θt)) = Var(gnew) + c2  t · Var(gold) − 2ct · Cov(gnew, gold),  c∗  t = Cov(gnew, gold)  Var(gold)  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  (3)  We find it impractical to compute the exact c∗  t and thus propose an approximation algorithm for it to obtain  a balance between the new and old gradient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' There are two challenges to calculate the exact c∗  t .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' On the  one hand, to approach the exact value, we need to calculate the gradients on every batch data, which is too  expensive to do it in each iteration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' On the other hand, the gradients are often high-dimensional and the  exact optimal c∗  t will be different for different gradients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Thus, inspired by Deng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' (2020), we design  an approximation algorithm that makes good use of the loss information and leads to only a small increase  in computational effort.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' More specifically, we estimate c∗  t according to the changes of loss as shown in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  (4) and update �c∗  t adaptively before each epoch using momentum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Loss is a scalar, which makes it possible  to estimate the shared correlation for all current and previous gradients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In addition, the loss is intuitively  related to gradients and the correlation between losses can give us some insights into that of the gradients  (some empirical analyses are included in the Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  �c∗  t = Cov(G(B|θt), G(B|�θ))  Var(G(B|�θ))  ,  (4)  where B denotes a subset of samples used to estimate the gradients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Algorithm 1 Adaptive Gradient Correction  Input: �θ = θ0, epoch length m, step size ηt, c0 = 0, scaling  parameter γ, smoothing factor α  for t = 0 to T − 1 do  if t mod m = 0 then  �θ = θt  �g = (�N  i=1 ∇G(xi|�θ))/N  if t > 0 then  Calculate ˆc∗  t via Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' (4)  ct = (1 − α)ct−1 + α ˆc∗  t  end if  else  ct = ct−1  end if  Sample a mini-batch data Bt with size n  θt+1 = θt − ηt ·  �  1  n  �  i∈Bt  �  gi(θt) − γct · gi(�θ)�  + γct · �g  �  end for  We empirically justify the loss-based approxi-  mation in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' (4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Experimental details are  included in Section B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  We compare the  approximation �c∗  t and the correlation between  the gradient of current weights and the gradi-  ent of previous epoch weights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  We find that  �c∗  t and the correlation have similar up-and-  down patterns, indicating that our approxima-  tion captures the dynamic patterns of the cor-  relation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' For differences in magnitude, they can  be matched by the scaling strategy we will de-  scribe in the next Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2  Additional  Scaling Parameter is Important  To guarantee successful acceleration in sparse  and adversarial training, we further propose a  scaling strategy that multiplies the estimated  c∗  t by a small scaling parameter γ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' There are two main benefits of using a scaling parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' First, the  scaling parameter γ can reduce the bias of the gradient estimates in adversarial training (Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In  standard training, the batch gradient estimator is an unbiased estimator of the full gradient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' However, in  adversarial training, we perturb the mini-batch of samples Bt into ¯Bt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' The old gradients gold are calculated  on batch data ¯Bt, but the stored old gradients �g are obtained from the original data including Bt, which  makes E[gold−�g] unequal to zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Consequently, as shown in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' (5), the corrected estimator for full gradients  will no longer be unbiased.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' It may have a small variance but a large bias, resulting in poor performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Therefore, we propose a scaling parameter γ between 0 and 1 to reduce the bias from ct(gold − �g) to  γct(gold − �g).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  E[ˆg(θt)] = E[gnew − ct(gold − �g)] ̸= E[gold] = 1  N  N  �  i=1  gi(θt).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  (5)  Second, the scaling parameter γ guarantees that the variance can still be reduced in the face of worst-case  estimates of c∗  t to accelerate the training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  The key idea is illustrated in Figure 2, where x and y axis  5  correspond to the weight ct and the gradient variance, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' The blue curve is a quadratic function  that represents the relationship between ct and the variance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Suppose the true optimal is c∗, and we make  an approximation to it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In the worst case, this approximation may be as bad as ˆc1, making the variance  even larger than a3 (variance in SGD) and slowing down the training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Then, if we replace ˆc1 with γˆc1, we  can reduce the variance and accelerate the training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='3  Connection to Momentum-based Method  To some extent, our AGENT is designed with a similar idea to the momentum-based method (Qian, 1999;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Ruder, 2016), where old gradients are used to improve the current batch gradient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' However, the momentum-  based method still suffers from optimization difficulties due to sparsity constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' The reason is that it does  not take into account sparse and adversarial training characteristics such as the reduced correlation between  current and previous gradients and potential bias of gradient estimator, and fails to provide an adaptive  balance between old and new information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' When the correlation is low, the momentum-based method can  still incorporate too much of the old information and increase the gradient variance or bias.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In contrast, our  AGENT is designed for sparse and adversarial training and can establish finer adaptive control over how  much information we should take from the old to help the new.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4  Connection to Adaptive Gradient Method  c∗  a3  ˆc1  γˆc1  y = a1c2 − 2a2c + a3  Figure 2: Illustration of how the scaling parameter  γ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1 ensures the acceleration in the face of worst-  case estimate of c∗  t .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' The blue curve is a quadratic  function, representing the relationship between ct  and the variance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' c∗ is the optimal value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' ˆc1 is a  poor estimate making the variance larger than a3  (variance in SGD).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' γˆc1 can reduce the variance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Our AGENT can be viewed as a new type of adaptive  gradient method that adaptively adjusts the amount  of gradient information used to update parameters,  such as Adam (Kingma & Ba, 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' However, pre-  vious adaptive gradient methods are not designed for  sparse training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Although they also provide adaptive  gradients, their adaptivity is different and does not  take the reduced correlation into account.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  On the  contrary, our AGENT is designed for sparse training  and is tailored to the characteristics of sparse training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  When old information is used to correct the gradients,  the main problem is the reduced correlation between  the old and new gradients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Therefore, our AGENT  approximates the correlation and adds an adaptive  weight to the old gradient to establish a balance be-  tween the old and new gradients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  5  Theoretical Justification  Theoretically, we provide a convergence analysis for our AGENT and compare it to SVRG (Reddi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=',  2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  We use G(.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=') to denote the loss function and g to denote the gradient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Our proof is based on  Assumptions 1-2, and detailed derivation is included in Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Assumption 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' (L-smooth): The differentiable loss function G : Rn → R is L-smooth, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', for all x, y ∈ Rn  is satisfies ||∇G(x) − ∇G(y)|| ≤ L||x − y||.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' And an equivalent definition is for.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' all x, y ∈ Rn:  −L  2 ||x − y||2 ≤ G(x) − G(y) − ⟨∇G(x), x − y⟩ ≤ L  2 ||x − y||2  Assumption 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' (σ-bounded): The loss function G has a σ-bounded gradient, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', ||∇Gi(x)|| ≤ σ for all  i ∈ [N] and x ∈ Rn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Our convergence analysis framework outlines four steps:  We first show that an appropriate choice of ct will result in smaller variance in our gradient estimates  compared to SVRG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  6  Next, we show the convergence rate of one arbitrary training epoch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  We then extend the one-epoch results and analyze the convergence rate for the whole epoch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  After obtaining the convergence rate, we bring it to the real case of sparse learning and find that our  method indeed yields a tighter bound.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Given Assumptions 1-2, we follow the analysis framework above and establish Theorem 1 to show the  convergence rate of our AGENT:  Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Under Assumptions 1-2, with proper choice of step size ηt and ct, the gradient E[||g(θπ)||2]  using AGENT after T training epochs can be bounded by:  E[||g(θπ)||2] ≤ (G(θ0) − G(θ∗))LN α  Tnν  + 2κµ2σ2  N αmν  where θπ is sampled uniformly from {{θs  t }m−1  t=0 }T −1  s=0 , N denotes the data size, n denotes the mini-batch size,  m denotes the epoch length, θ0 is the initial point and θ∗ is the optimal solution, ν, µ, κ, α > 0 are constants  depending on ηt and ct, N and n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  In regard to Theorem 1, we make the following remarks to justify the acceleration from our AGENT:  Remark 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' (Faster Gradient Change Speed) An influential difference between sparse and dense training is  the gradient change speed, which is reflected in Assumption 1 (L-smooth).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Typically, L in sparse training  will be larger than L in dense training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' (First Term Analysis) In Theorem 1, the first term in the bound of our AGENT measures the  error introduced by deviations from the optimal parameters, which goes to zero when the number of epochs  T reaches infinity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' However, in real sparse training applications, T is finite and this term is expanded due  to the increase of L in sparse training, which implies that the optimization under sparse constraints is more  challenging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' (Second Term Analysis) In Theorem 1, the second term measures the error introduced by the  noisy gradient and the finite data during the optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Since σ2 is relatively small and N is usually large  in our DNNs training, the second term is negligible or much smaller compared to the first term when T is  assumed to be finite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  From the above analysis, we can compare the bounds of AGENT and SVRG and find that in the case of  sparse training, an appropriate choice of ct can make the bound for our AGENT tighter than the bound for  SVRG by well-corrected gradients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Remark 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' (Comparison with SVRG) Under Assumptions 1-2, the gradient E[||g(θπ)||2] using SVRG after  T training epochs can be bounded by (Reddi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2016):  E[||g(θπ)||2] ≤ (G(θ0) − G(θ∗))LN α  Tnν∗  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  This bound is of a similar form to the first term in Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Since the second term of Theorem 1 is  negligible or much smaller than the first one, we only need to compare the first term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' With a proper choice  of ct, the variance of ˆg(θt) will decrease, which leads to a smaller ν for AGENT than ν∗ for SVRG (detailed  proof is included in Appendix A Remark 6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Thus, AGENT can bring a smaller first term compared to  SVRG, which indicates that AGENT effectively reduces the error due to the deviations and has a tighter  bound compared to SVRG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  6  Experiments  We add our AGENT to three recent sparse training pipelines, namely SET (Mocanu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2018), RigL (Evci  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2020), BSR-Net (Özdenizci & Legenstein, 2021) and ITOP (Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' SET is a broadly-used  sparse training method that prunes and regrows connections by examining the magnitude of the weights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  7  Table 1: Testing accuracy (%) of BSR-Net-based models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Sparse VGG-16 are learned in standard and  adversarial setups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Results are presented as clean/robust accuracy (%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' For the same number of training  epochs, our method has higher accuracy compared to BSR-Net in almost all cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  90% Sparsity  99% Sparsity  BSR-Net  Ours  BSR-Net  Ours  AT  20-th  55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='59)/38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='31)/37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='3  49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='8 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='46)/31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='39)/31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4  40-th  62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='88)/39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2  64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='9 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='81)/37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='9  54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='72)/33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='9  57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='7 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='39)/34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5  70-th  73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='39)/37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='8  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='27)/45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2  64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='7 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='30)/34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='9  66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='23)/39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4  90-th  73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='29)/33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6  74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='25)/44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='8  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='7 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='25)/35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='8  65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='8 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='24)/39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='8  140-th  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='7 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='27)/46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5  77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='26)/43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='8  68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='20)/40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='8  69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='8 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='14)/41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2  200-th  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='25)/43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='3  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='24)/44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6  69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='15)/42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='7 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='06)/42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  TRADES  20-th  62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='82)/33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='3  65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='61)/37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6  55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='7 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='76)/25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5  57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='45)/31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6  40-th  65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='97)/35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='3  66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='34)/37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='69)/28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='9  58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='34)/33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4  70-th  73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='52)/34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='8  73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='33)/45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4  66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='3 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='35)/33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5  67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='3 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='30)/39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  90-th  73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='36)/36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='8  73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='28)/44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='8  66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='33)/31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='7  67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='24)/39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1  140-th  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='25)/45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='8 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='25)/46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='3  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='29)/38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2  69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='9 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='21)/41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5  200-th  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='23)/47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2  77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='24)/46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='8 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='19)/39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='3  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='9 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='25)/41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2  Standard  20-th  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4 (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='50)/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='8 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='62)/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='26)/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='8 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='45)/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  40-th  77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='39)/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='47)/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6 (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='47)/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='7 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='36)/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  70-th  86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='8 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='78)/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='7 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='38)/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='7 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='72)/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='7 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='24)/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  90-th  87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='63)/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='3 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='22)/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='55)/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='9 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='42)/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  140-th  91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='7 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='44)/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='06)/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='7 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='42)/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='9 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='07)/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  200-th  91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='8 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='23)/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='12)/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='8 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='12)/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='25)/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  RigL is another popular dynamic sparse training method which uses weight and gradient magnitudes to  learn the connections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' BSR-Net is a recent sparse training method that updates connections by Bayesian  sampling and also includes adversarial setups for model robustness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' ITOP is another recent pipeline for  dynamic sparse training, which uses sufficient and reliable parameter exploration to achieve in-time over-  parameterization and find well-performing sparse models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Detailed information about the dataset, model  architectures, and other training and evaluation setups is provided below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Datasets & Model Architectures: The datasets we use include CIFAR-10, CIFAR-100 (Krizhevsky  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2009), SVHN (Netzer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2011), and ImageNet-2012 (see Appendix) (Russakovsky et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  For model architectures, we use VGG-16 (Simonyan & Zisserman, 2015), ResNet-18, ResNet-50 (He et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=',  2016), and Wide-ResNet-28-4 (Zagoruyko & Komodakis, 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Training Settings: For sparse training, we choose two sparsity levels, namely 90% and 99%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' For BSR-Net,  we consider both standard and adversarial setups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In RigL and ITOP, we focus on standard training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In  standard training, we only use the original data to update the parameters instead of using perturbed samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  For adversarial part, we use the perturbed data with two popular objective (AT and TRADES) (Madry et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=',  2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Following Özdenizci & Legenstein (2021), we evaluate robust accuracy against  PGD attacks with random starts using 50 iterations (PGD50) (Madry et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Brendel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Implementations:  Aligned with the choice of Evci et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' (2020);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Sundar & Dwaraknath (2021);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Özdenizci  & Legenstein (2021), the parameters of the model are optimized by SGD with momentum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Thus, the  comparison between the popular sparse training pipelines can be viewed as a comparison between AGENT  and momentum-based SGD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1  Convergence Speed & Stability Comparisons  We compare the convergence speed by two criteria, including (a) the test accuracy at the same number of  pass data (epoch) and (b) the number of pass data (epoch) required to achieve the same test accuracy,  8  0  50  100  150  200  250  Number of epochs  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='55  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='60  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='65  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='70  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='75  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='80  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='85  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='90  Testing accuracy  A-RigL-ITOP  RigL-ITOP  (a) VGG-C(RigL)  0  50  100  150  200  250  Number of epochs  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='60  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='65  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='70  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='75  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='80  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='85  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='90  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='95  Testing accuracy  A-RigL-ITOP  RigL-ITOP  (b) ResNet-34(RigL)  0  50  100  150  200  250  Number of epochs  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='60  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='65  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='70  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='75  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='80  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='85  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='90  Testing accuracy  A-SET-ITOP  SET-ITOP  (c) VGG-C(SET)  0  50  100  150  200  250  Number of epochs  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='65  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='70  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='75  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='80  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='85  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='90  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='95  Testing accuracy  A-SET-ITOP  SET-ITOP  (d) ResNet-34(SET)  Figure 3: Testing accuracy for ITOP-based models at 99% sparsity on CIFAR-10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' A-RigL-ITOP and A-  SET-ITOP (blue curves) converge faster than RigL-ITOP and SET-ITOP (pink curves).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='60  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='65  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='70  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='75  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='80  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='85  Testing accuracy  0  20  40  60  80  100  120  140  Number of epochs  A-BSR-Net  BSR-Net  (a) VGG-16, Standard  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='60  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='65  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='70  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='75  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='80  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='85  Testing accuracy  0  20  40  60  80  100  Number of epochs  A-BSR-Net  BSR-Net  (b) WRN-28-4, Standard  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='500 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='525 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='550 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='575 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='600 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='625 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='650 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='675  Testing accuracy  20  40  60  80  100  120  140  160  Number of epochs  A-BSR-Net  BSR-Net  (c) VGG-16, AT  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='500 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='525 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='550 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='575 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='600 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='625 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='650 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='675 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='700  Testing accuracy  20  40  60  80  100  120  Number of epochs  A-BSR-Net  BSR-Net  (d) WRN-28-4, AT  Figure 4: Number of training epochs required to achieve the accuracy at 99% sparsity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Our A-BSR-Net  (blue curves) need less time to achieve the accuracy compared to BSR-Net (pink curves).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  which is widely used to compare the speed of optimization algorithms (Allen-Zhu & Hazan, 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Chatterji  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Zou et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Cutkosky & Orabona, 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  For BSR-Net-based results using criterion (a), Table 1 lists the accuracies on both clean and adver-  sarial samples after 20, 40, 70, 90, 140, and 200 epochs of training, where the higher accuracies are bolded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Sparse VGG-16 are learned on CIFAR-10 in both standard and adversarial sutups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' For the standard setup,  we only present the clean accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' As we can see, our method maintains higher clean and robust accuracies  for almost all training epochs and setups which demonstrates the successful acceleration from our method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  In particular, for limited time periods like 20 epochs, our A-BSR-Net usually shows dramatic improvements  with clean accuracy as high as 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4%, indicating a significant reduction in early search time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In addition,  considering the average accuracy improvement over the 6 time budgets, our method outperforms BSR-Net  in accuracy by upto 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Table 2: Final accuracy (%) of RigL-based models at 0% (dense),  90% and 99% sparsity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' AGENT + RigL (A-RigL) maintains or  even improves the accuracy compared to that of RigL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Dense  90%  99%  CIFAR-10  A-RigL 95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='24) 95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='21) 93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='25)  RigL  95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='26)  94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='22)  92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='33)  CIFAR-100 A-RigL 72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='9 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='19) 72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='20) 66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='14)  RigL  73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='17) 71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='26)  66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='19)  For ITOP-based results using cri-  terion (a), as shown in Figure 3, the  blue curves (A-RigL-ITOP and A-SET-  ITOP) are always higher than the pink  curves (RigL-ITOP and SET-ITOP), in-  dicating faster training when using our  AGENT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In addition, we can see that  the pink curves experience severe up and  down fluctuations, especially in the early  stages of training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In contrast, the blue  curves are more stable all the settings, which indicates AGENT is effective in stabilizing the sparse training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  For BSR-Net-based results using criterion (b), Figure 4 depicts the number of training epochs required  to achieve certain accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' We can see that the blue curves (A-BSR-Net) are always lower than the pink  curves (BSR-Net), and on average our method reduces the number of training epochs by up to 52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1%,  indicating faster training when using our proposed A-BSR-Net.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  9  0  50  100  150  200  250  Number of epoch  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='9  Testing accuracy  A-RigL-ITOP  RigL-ITOP + SVRG  RigL-ITOP  (a) VGG-C  0  50  100  150  200  250  Number of epoch  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='50  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='55  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='60  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='65  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='70  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='75  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='80  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='85  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='90  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='95  Testing accuracy  A-RigL-ITOP  RigL-ITOP + SVRG  RigL-ITOP  (b) ResNet-34  0  50  100  150  200  250  Number of epoch  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='9  Testing accuracy  A-SET-ITOP  SET-ITOP + SVRG  SET-ITOP  (c) VGG-C  0  50  100  150  200  250  Number of epoch  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='55  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='60  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='65  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='70  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='75  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='80  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='85  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='90  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='95  Testing accuracy  A-SET-ITOP  SET-ITOP + SVRG  SET-ITOP  (d) ResNet-34  Figure 5: Testing accuracy for ITOP-based models at 99% sparsity on CIFAR-10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' SVRG (green curves)  slows down the training compared to SGD (pink curves).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Our AGENT (blue curves) accelerates the training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2  Final Accuracy Comparisons  In addition, we compare the final accuracy after sufficient training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' RigL-based results on CIFAR-10/100 are  shown in Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Our method A-RigL tends to be the best in almost all the scenarios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' For BSR-Net-based  results in Table 3, we compare our A-BSR-Net with BSR-Net on SVHN using VGG-16 and WideResNet-28-4  (WRN-28-4), and our method is often the best again.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' This shows that our AGENT can accelerate sparse  training while maintaining or even improving the accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='3  Comparison with Other Gradient Correction Methods  Table 3: Final accuracy (%) of BSR-Net-based mod-  els at 90% and 99% sparsity on SVHN with adversarial  training objectives (TRADES).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Our AGENT maintains  or even improves the accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  BSR-Net  Ours  90%  VGG-16  89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='29) 94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='25)  WRN-28-4 92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='8 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='24) 95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='23)  99%  VGG-16  86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='25) 90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='9 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='26)  WRN-28-4 89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='22) 92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='19)  We also compare our AGENT with SVRG (Baker  et  al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=',  2019),  a  popular  gradient  correction  method in the non-sparse case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  The presented  ITOP-based results are based on sparse (99%)  VGG-C and ResNet-34 on CIFAR-10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Fig-  ure 5 (a)-(b) show the testing accuracy of A-  RigL-ITOP (blue), RigL-ITOP (pink), and RigL-  ITOP+SVRG (green) at different epochs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' We can  see that the green curve for RigL-ITOP+SVRG is  often lower than the other two curves for A-RigL-  ITOP and RigL-ITOP, indicating that model con-  vergence is slowed down by SVRG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' As for the blue  curve for our A-RigL-ITOP, it is always on the top  of the pink curve for RigL-ITOP and also smoother than the green curve for RigL-ITOP+SVRG, indicating  a successful acceleration and stabilization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' The SET-ITOP-based results depicted in Figure 5 (c)-(d) show a  similar pattern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' The green curve (SET-ITOP+SVRG) is often lower than the blue (A-SET-ITOP) and pink  (SET-ITOP) curves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' This demonstrates that SVRG does not work for sparse training, while our AGENT  overcomes its limitations, leading to accelerated and stabilized sparse training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4  Comparison with Other Adaptive Gradient Methods  We also compare our AGENT with other adaptive gradient methods, where we take Adam (Kingma & Ba,  2014) as an example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' As shown in Figure 6, AGENT-RigL-ITOP and AGENT-SET-ITOP (blue curves) are  usually above Adam-RigL-ITOP and Adam-SET-ITOP (pink curves), indicating that our AGENT converges  faster compared to Adam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' This demonstrates the importance of using correlation in sparse training to balance  old and new information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5  Combination with Other Gradient Correction Methods  In addition to working with SVRG, our AGENT can be combined with other gradient correction meth-  ods to achieve sparse training acceleration, such as the momentum-based variance reduction method  10  0  50  100  150  200  250  Number of epochs  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='45  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='50  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='55  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='60  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='65  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='70  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='75  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='80  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='85  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='90  Testing accuracy  AGENT-RigL-ITOP  Adam-RigL-ITOP  (a) VGG-C(RigL)  0  50  100  150  200  250  Number of epochs  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='9  Testing accuracy  AGENT-RigL-ITOP  Adam-RigL-ITOP  (b) ResNet-34(RigL)  0  50  100  150  200  250  Number of epochs  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='50  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='55  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='60  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='65  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='70  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='75  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='80  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='85  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='90  Testing accuracy  AGENT-SET-ITOP  Adam-SET-ITOP  (c) VGG-C(SET)  0  50  100  150  200  250  Number of epochs  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='9  Testing accuracy  AGENT-SET-ITOP  Adam-SET-ITOP  (d) ResNet-34(SET)  Figure 6: Testing accuracy for ITOP-based models at 99% sparsity on CIFAR-10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' AGENT-based training  (blue curves) converge faster than Adam-based training (pink curves).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  (MVR) (Cutkosky & Orabona, 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  We train 99% SET-ITOP-based sparse VGG-C using MVR and  MVR+AGENT, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' As shown in Table 4, MVR+AGENT usually achieves higher test accuracy  than MVR for different number of training epochs (20, 40, 70, 90, 140, and 200), which demonstrates the  acceleration effect of AGENT and the generality of our AGENT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6  Ablation Studies  Table 4: Testing accuracy (%) comparisons between MVR and  AGENT+MVR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' AGENT can accelerate MVR in sparse training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  20-th 40-th 70-th 90-th 140-th 200-th  MVR  62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6  66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='8  69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='8  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2  73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5  74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4  AGENT+MVR  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='7  77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='9  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1  82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='3  82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='3  We demonstrate the importance of each  component in our method AGENT by  removing them one by one and compar-  ing the results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Specifically, we consider  examining the contribution of the time-  varying weight ct of the old gradients and  the scaling parameter γ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' The term "Fixed  ct" corresponds to fixing weight ct = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1 during training, and "No γ" represents a direct use of ˆc∗  t in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' (4)  and the momentum scheme without adding the scaling parameter γ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Table 5 shows the clean and robust accuracies of standard and adversarial (AT or TRADES) training at  90% and 99% sparsity on CIFAR-10 using VGG-16 under different number of training epoch budgets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In the  adversarial training (AT and TRADES), we can see that "No γ" is poorly learned and has the worst results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  While our method outperforms "Fix ct" and "No γ" in almost all cases, especially in highly sparse tasks (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=',  99% sparsity).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' For standard training, "No γ" can learn some information, but still performs worse than the  other two methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' For "Fix ct", it provides similar convergence speed as our method, while ours tends to  have a better final score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  From the above discussion, both the adaptive update of ct and the multiplication of the scaling parameter γ  are important for the acceleration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' On the one hand, the traditional way of setting ct = 1 is not desirable in  sparse training and can cause model divergence under sparsity constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Fixing it as a smaller value, such  as 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1, sometimes can work in standard training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' But updating ct adaptively with loss-dependent information  usually provides some benefits, such as a better final score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' These benefits become more significant in sparse  and adversarial training which are more challenging and of great value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' On the other hand, we recommend  adding a scaling parameter γ (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', γ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1) to ct to avoid increasing the variance and reduce the potential  bias in adversarial training, which helps the balance and further accelerates the convergence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='7  Scaling Parameter Setting  The scaling parameter γ is to avoid introducing large variance due to error in approximating c∗  t and bias  due to the adversarial training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' The choice of γ is important and can be seen as a hyper-parameter tuning  process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Our results are based on γ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1 and the best value for γ depends on many factors such as the  dataset, architecture, and sparsity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Therefore, if we tune the value of γ according to the gradient correlation  of different settings, it is possible to obtain a faster convergence rate than the reported results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  11  Table 5: Ablation Studies: testing accuracy (%) comparisons with Fixed c and No γ on sparse VGG-16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Results are presented as clean/robust accuracy (%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' For the same number of training epochs, our method  has higher accuracy compared to Fixed c and No γ in almost all cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  90% Sparsity  99% Sparsity  Fixed ct  No γ  Ours  Fixed ct  No γ  Ours  AT  20-th  54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1/36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6/20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6/37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='3  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4/31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4  40-th  58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='9/37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4/13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='9/37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='9  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='7/34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5  70-th  66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='8/41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='9/14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='7  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1/45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0/39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4  90-th  67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='7/43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='3  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='8/15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6  74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1/44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='8  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='8/39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='8  140-th  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4/43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0/12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1  77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4/43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='8  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='8/41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2  200-th  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='7/43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5/9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1/44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='7/42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  TRADES  20-th  62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6/35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5/21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='8  65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0/37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6  54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5/31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2  35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2/21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6  57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6/31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6  40-th  65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0/38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='7/20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2  66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0/37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0/30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4/33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4  70-th  73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='9/44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='8/18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4  73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5/45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4  62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5/36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='8  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='8/16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2  67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='3/39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  90-th  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1/44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4  25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='8/15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='9  73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6/44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='8  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='9/37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='9/15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='9  67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5/39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1  140-th  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='7/46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6/14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='8/46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='3  65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5/39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='7/14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4  69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='9/41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5  200-th  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='8/46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1  30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='7/12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='7  77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0/46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='3/38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1/13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='9/41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2  Standard  20-th  80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='9/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='8/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='7/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='8/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='8/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  40-th  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='3/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='9/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='7/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  70-th  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='3/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='7/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='9/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='7/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  90-th  89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='8/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='8/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='3/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='8/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='9/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  140-th  92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='7/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='9/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='9/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  200-th  92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  We check different values from 0 to 1 and find that it is generally better not to set γ to close to 1 or 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  If setting γ close to 1, we will not be able to completely avoid the increase in variance, which leads to  performance drop, similar to "No γ" in Table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' If γ is set too small, such as 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='01, the weight of the old  gradients will be too small and the old gradients will have limited influence on the model update, which  will return to SGD’s slowdown and training instability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' More detailed experimental results using different  scaling parameters γ are included in the Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  7  Discussion and Conclusion  We develop an adaptive gradient correction (AGENT) method for sparse training to achieve the time ef-  ficiency and reduce training instability from an optimization perspective, which can be incorporated into  any SGD-based sparse training pipeline and work in both standard and adversarial setups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' To achieve a  fine-grained control over the balance of current and previous gradients, we use loss information to analyze  gradient changes, and add an adaptive weight to the old gradients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In addition, we design a scaling parameter  to reduce the bias of the gradient estimator introduced by the adversarial samples and improve the worst case  of the adaptive weight estimate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In theory, we show that our AGENT can accelerate the convergence rate  of sparse training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Experiment results on multiple datasets, model architectures, and sparsities demonstrate  that our method outperforms state-of-the-art sparse training methods in terms of accuracy by up to 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0%  and reduces the number of training epochs by up to 52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1% for the same accuracy achieved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  A number of methods can be employed to reduce the FLOPs in our AGENT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Similar to SVRG, our AGENT  increases the training FLOPs in each iteration due to the extra forward and backward used to compute the  old gradients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' To reduce the FLOPs, the first method is to use sparse gradients (Elibol et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2020), which  effectively reduces the cost of backward in sparse training and can be easily applied to our method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' The  second method is parallel computing Allen-Zhu & Hazan (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Since the additional forward and backward  over the old model parameters are fully parallelizable, we can view it as doubling the mini-batch size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Third,  we can follow the idea of SAGA (Defazio et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2014) by storing gradients for each single sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' By this  way, we do not need extra forward and backward steps, saving the computation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' However, it requires extra  memory to store the gradients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  12  References  Naveed Akhtar and Ajmal Mian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Threat of adversarial attacks on deep learning in computer vision: A  survey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Ieee Access, 6:14410–14430, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Zeyuan Allen-Zhu and Elad Hazan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Variance reduction for faster non-convex optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In International  conference on machine learning, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' 699–707.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' PMLR, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Jack Baker, Paul Fearnhead, Emily B Fox, and Christopher Nemeth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Control variates for stochastic gradient  mcmc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Statistics and Computing, 29(3):599–615, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Brian Bartoldson, Ari Morcos, Adrian Barbu, and Gordon Erlebacher.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' The generalization-stability tradeoff  in neural network pruning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Advances in Neural Information Processing Systems, 33:20852–20864, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Guillaume Bellec, David Kappel, Wolfgang Maass, and Robert Legenstein.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Deep rewiring: Training very  sparse deep networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' arXiv preprint arXiv:1711.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='05136, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Guillaume Bellec, David Kappel, Wolfgang Maass, and Robert Legenstein.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Deep rewiring: Training very  sparse deep networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' International Conference on Learning Representations (ICLR), 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Wieland Brendel, Jonas Rauber, Matthias Kümmerer, Ivan Ustyuzhaninov, and Matthias Bethge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Accurate,  reliable and fast robustness evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' arXiv preprint arXiv:1907.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='01003, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Niladri Chatterji, Nicolas Flammarion, Yian Ma, Peter Bartlett, and Michael Jordan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' On the theory of  variance reduction for stochastic gradient monte carlo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In International Conference on Machine Learning,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' 764–773.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' PMLR, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  El Mahdi Chayti and Sai Praneeth Karimireddy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Optimization with access to auxiliary information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' arXiv  preprint arXiv:2206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='00395, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Beidi Chen, Tri Dao, Kaizhao Liang, Jiaming Yang, Zhao Song, Atri Rudra, and Christopher Re.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Pixelated  butterfly: Simple and efficient sparse training for neural network models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' arXiv preprint arXiv:2112.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='00029,  2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Changyou Chen, Wenlin Wang, Yizhe Zhang, Qinliang Su, and Lawrence Carin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' A convergence analysis for  a class of practical variance-reduction stochastic gradient mcmc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Science China Information Sciences, 62  (1):1–13, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Ashok Cutkosky and Francesco Orabona.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Momentum-based variance reduction in non-convex sgd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Advances  in neural information processing systems, 32, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Aaron Defazio, Francis Bach, and Simon Lacoste-Julien.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Saga: A fast incremental gradient method with  support for non-strongly convex composite objectives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Advances in neural information processing systems,  27, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Wei Deng, Qi Feng, Georgios Karagiannis, Guang Lin, and Faming Liang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Accelerating convergence of  replica exchange stochastic gradient mcmc via variance reduction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' arXiv preprint arXiv:2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='01084, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Tim Dettmers and Luke Zettlemoyer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Sparse networks from scratch: Faster training without losing perfor-  mance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' arXiv preprint arXiv:1907.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='04840, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Kumar Avinava Dubey, Sashank J Reddi, Sinead A Williamson, Barnabas Poczos, Alexander J Smola, and  Eric P Xing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Variance reduction in stochastic gradient langevin dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Advances in neural information  processing systems, 29:1154–1162, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Melih Elibol, Lihua Lei, and Michael I Jordan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Variance reduction with sparse gradients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' arXiv preprint  arXiv:2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='09623, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Utku Evci, Trevor Gale, Jacob Menick, Pablo Samuel Castro, and Erich Elsen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Rigging the lottery: Making  all tickets winners.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In International Conference on Machine Learning, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' 2943–2952.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' PMLR, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  13  Cong Fang, Chris Junchi Li, Zhouchen Lin, and Tong Zhang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Spider: Near-optimal non-convex optimization  via stochastic path-integrated differential estimator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Advances in Neural Information Processing Systems,  31, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Jonathan Frankle and Michael Carbin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  The lottery ticket hypothesis: Finding sparse, trainable neural  networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' International Conference on Learning Representations (ICLR), 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Eduard Gorbunov, Filip Hanzely, and Peter Richtárik.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' A unified theory of sgd: Variance reduction, sampling,  quantization and coordinate descent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In International Conference on Artificial Intelligence and Statistics,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' 680–690.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' PMLR, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Laura Graesser, Utku Evci, Erich Elsen, and Pablo Samuel Castro.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' The state of sparse training in deep  reinforcement learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In International Conference on Machine Learning, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' 7766–7792.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' PMLR, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Delving deep into rectifiers: Surpassing human-  level performance on imagenet classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  In Proceedings of the IEEE international conference on  computer vision, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' 1026–1034, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Deep residual learning for image recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In  Proceedings of the IEEE conference on computer vision and pattern recognition, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' 770–778, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Torsten Hoefler, Dan Alistarh, Tal Ben-Nun, Nikoli Dryden, and Alexandra Peste.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Sparsity in deep  learning: Pruning and growth for efficient inference and training in neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  arXiv preprint  arXiv:2102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='00554, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Shaoyi Huang, Bowen Lei, Dongkuan Xu, Hongwu Peng, Yue Sun, Mimi Xie, and Caiwen Ding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Dynamic  sparse training via balancing the exploration-exploitation trade-off.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  arXiv preprint arXiv:2211.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='16667,  2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Itay Hubara, Brian Chmiel, Moshe Island, Ron Banner, Joseph Naor, and Daniel Soudry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Accelerated sparse  neural training: A provable and efficient method to find n: m transposable masks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Advances in Neural  Information Processing Systems, 34, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Siddhant Jayakumar, Razvan Pascanu, Jack Rae, Simon Osindero, and Erich Elsen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Top-kast: Top-k always  sparse training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Advances in Neural Information Processing Systems, 33:20744–20754, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Rie Johnson and Tong Zhang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Accelerating stochastic gradient descent using predictive variance reduction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Advances in neural information processing systems, 26:315–323, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Diederik P Kingma and Jimmy Ba.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Adam:  A method for stochastic optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  arXiv preprint  arXiv:1412.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6980, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Alex Krizhevsky, Geoffrey Hinton, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Learning multiple layers of features from tiny images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Technical  report, University of Toronto, 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Souvik Kundu, Mahdi Nazemi, Peter A Beerel, and Massoud Pedram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Dnr: A tunable robust pruning  framework through dynamic network rewiring of dnns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In Proceedings of the 26th Asia and South Pacific  Design Automation Conference, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' 344–350, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Clayton Frederick Souza Leite and Yu Xiao.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Optimal sensor channel selection for resource-efficient deep  activity recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In Proceedings of the 20th International Conference on Information Processing in  Sensor Networks (co-located with CPS-IoT Week 2021), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' 371–383, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Yan Li, Ethan Fang, Huan Xu, and Tuo Zhao.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Implicit bias of gradient descent based adversarial training  on separable data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In International Conference on Learning Representations, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Chuang Liu, Xueqi Ma, Yinbing Zhan, Liang Ding, Dapeng Tao, Bo Du, Wenbin Hu, and Danilo Mandic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Comprehensive graph gradual pruning for sparse training in graph neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  arXiv preprint  arXiv:2207.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='08629, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  14  Shiwei Liu, Lu Yin, Decebal Constantin Mocanu, and Mykola Pechenizkiy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Do we actually need dense  over-parameterization?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' in-time over-parameterization in sparse training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In International Conference on  Machine Learning, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' 6989–7000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' PMLR, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Ilya Loshchilov and Frank Hutter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Decoupled weight decay regularization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In International Conference on  Learning Representations (ICLR), 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Aleksander Madry, Aleksandar Makelov, Ludwig Schmidt, Dimitris Tsipras, and Adrian Vladu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Towards deep  learning models resistant to adversarial attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In International Conference on Learn- ing Representations  (ICLR), 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Kira JM Matus and Michael Veale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Certification systems for machine learning: Lessons from sustainability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Regulation & Governance, 16(1):177–196, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Decebal Constantin Mocanu, Elena Mocanu, Peter Stone, Phuong H Nguyen, Madeleine Gibescu, and An-  tonio Liotta.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Scalable training of artificial neural networks with adaptive sparse connectivity inspired by  network science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Nature communications, 9(1):1–12, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Hesham Mostafa and Xin Wang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Parameter efficient training of deep convolutional neural networks by  dynamic sparse reparameterization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In International Conference on Machine Learning, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' 4646–4655.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  PMLR, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Yuval Netzer, Tao Wang, Adam Coates, Alessandro Bissacco, Bo Wu, and Andrew Y Ng.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Reading digits in  natural images with unsupervised feature learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Lam M Nguyen, Jie Liu, Katya Scheinberg, and Martin Takáč.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Sarah: A novel method for machine learning  problems using stochastic recursive gradient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In International Conference on Machine Learning, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' 2613–  2621.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' PMLR, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Ozan Özdenizci and Robert Legenstein.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Training adversarially robust sparse networks via bayesian connec-  tivity sampling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In International Conference on Machine Learning, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' 8314–8324.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' PMLR, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  David Patterson, Joseph Gonzalez, Quoc Le, Chen Liang, Lluis-Miquel Munguia, Daniel Rothchild, David  So, Maud Texier, and Jeff Dean.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Carbon emissions and large neural network training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' arXiv preprint  arXiv:2104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='10350, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Ning Qian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' On the momentum term in gradient descent learning algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Neural networks, 12(1):145–151,  1999.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Adnan Siraj Rakin, Zhezhi He, Li Yang, Yanzhi Wang, Liqiang Wang, and Deliang Fan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Robust sparse  regularization: Simultaneously optimizing neural network robustness and compactness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' arXiv preprint  arXiv:1905.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='13074, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Sashank J Reddi, Ahmed Hefny, Suvrit Sra, Barnabás Póczos, and Alex Smola.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Stochastic variance reduction  for nonconvex optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In International conference on machine learning, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' 314–323.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' PMLR, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Johanna Rock, Wolfgang Roth, Mate Toth, Paul Meissner, and Franz Pernkopf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Resource-efficient deep  neural networks for automotive radar interference mitigation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' IEEE Journal of Selected Topics in Signal  Processing, 15(4):927–940, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Sebastian Ruder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' An overview of gradient descent optimization algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' arXiv preprint arXiv:1609.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='04747,  2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Olga Russakovsky, Jia Deng, Hao Su, Jonathan Krause, Sanjeev Satheesh, Sean Ma, Zhiheng Huang, Andrej  Karpathy, Aditya Khosla, Michael Bernstein, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Imagenet large scale visual recognition challenge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  International journal of computer vision, 115(3):211–252, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Jonathan Schwarz, Siddhant Jayakumar, Razvan Pascanu, Peter E Latham, and Yee Teh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Powerpropagation:  A sparsity inducing weight reparameterisation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Advances in Neural Information Processing Systems, 34:  28889–28903, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  15  Vikash Sehwag, Shiqi Wang, Prateek Mittal, and Suman Jana.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Hydra: Pruning adversarially robust neural  networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Advances in Neural Information Processing Systems, 33:19655–19666, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Fanhua Shang, Kaiwen Zhou, Hongying Liu, James Cheng, Ivor W Tsang, Lijun Zhang, Dacheng Tao,  and Licheng Jiao.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Vr-sgd: A simple stochastic variance reduction method for machine learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' IEEE  Transactions on Knowledge and Data Engineering, 32(1):188–202, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Karen Simonyan and Andrew Zisserman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Very deep convolutional networks for large-scale image recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Interna- tional Conference on Learning Representations (ICLR), 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Varun Sundar and Rajat Vadiraj Dwaraknath.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' [reproducibility report] rigging the lottery: Making all tickets  winners.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' arXiv preprint arXiv:2103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='15767, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Neil C Thompson, Kristjan Greenewald, Keeheon Lee, and Gabriel F Manso.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Deep learning’s diminishing  returns: the cost of improvement is becoming unsustainable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' IEEE Spectrum, 58(10):50–55, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Lin Xiao and Tong Zhang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' A proximal stochastic gradient method with progressive variance reduction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  SIAM Journal on Optimization, 24(4):2057–2075, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Xia Xiao, Zigeng Wang, and Sanguthevar Rajasekaran.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Autoprune: Automatic network pruning by regular-  izing auxiliary parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Advances in neural information processing systems, 32, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Shaokai Ye, Kaidi Xu, Sijia Liu, Hao Cheng, Jan-Henrik Lambrechts, Huan Zhang, Aojun Zhou, Kaisheng  Ma, Yanzhi Wang, and Xue Lin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Adversarial robustness vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' model compression, or both?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In Proceedings  of the IEEE/CVF International Conference on Computer Vision, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' 111–120, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Rong Yu and Peichun Li.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Toward resource-efficient federated learning in mobile edge computing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' IEEE  Network, 35(1):148–155, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Sergey Zagoruyko and Nikos Komodakis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Wide residual networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' British Machine Vision Conference, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Hongyang Zhang, Yaodong Yu, Jiantao Jiao, Eric Xing, Laurent El Ghaoui, and Michael Jordan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Theo-  retically principled trade-off between robustness and accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In International Conference on Machine  Learning, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' 7472–7482.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' PMLR, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Xiao Zhou, Weizhong Zhang, Zonghao Chen, Shizhe Diao, and Tong Zhang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Efficient neural network training  via forward and backward propagation sparsification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Advances in Neural Information Processing Systems,  34:15216–15229, 2021a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Xiao Zhou, Weizhong Zhang, Hang Xu, and Tong Zhang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Effective sparsification of neural networks with  global sparsity constraint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern  Recognition, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' 3599–3608, 2021b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Difan Zou, Pan Xu, and Quanquan Gu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Subsampled stochastic variance-reduced gradient langevin dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  In International Conference on Uncertainty in Artificial Intelligence, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  References  Naveed Akhtar and Ajmal Mian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Threat of adversarial attacks on deep learning in computer vision: A  survey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Ieee Access, 6:14410–14430, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Zeyuan Allen-Zhu and Elad Hazan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Variance reduction for faster non-convex optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In International  conference on machine learning, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' 699–707.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' PMLR, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Jack Baker, Paul Fearnhead, Emily B Fox, and Christopher Nemeth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Control variates for stochastic gradient  mcmc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Statistics and Computing, 29(3):599–615, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Brian Bartoldson, Ari Morcos, Adrian Barbu, and Gordon Erlebacher.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' The generalization-stability tradeoff  in neural network pruning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Advances in Neural Information Processing Systems, 33:20852–20864, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  16  Guillaume Bellec, David Kappel, Wolfgang Maass, and Robert Legenstein.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Deep rewiring: Training very  sparse deep networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' arXiv preprint arXiv:1711.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='05136, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Guillaume Bellec, David Kappel, Wolfgang Maass, and Robert Legenstein.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Deep rewiring: Training very  sparse deep networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' International Conference on Learning Representations (ICLR), 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Wieland Brendel, Jonas Rauber, Matthias Kümmerer, Ivan Ustyuzhaninov, and Matthias Bethge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Accurate,  reliable and fast robustness evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' arXiv preprint arXiv:1907.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='01003, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Niladri Chatterji, Nicolas Flammarion, Yian Ma, Peter Bartlett, and Michael Jordan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' On the theory of  variance reduction for stochastic gradient monte carlo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In International Conference on Machine Learning,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' 764–773.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' PMLR, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  El Mahdi Chayti and Sai Praneeth Karimireddy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Optimization with access to auxiliary information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' arXiv  preprint arXiv:2206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='00395, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Beidi Chen, Tri Dao, Kaizhao Liang, Jiaming Yang, Zhao Song, Atri Rudra, and Christopher Re.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Pixelated  butterfly: Simple and efficient sparse training for neural network models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' arXiv preprint arXiv:2112.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='00029,  2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Changyou Chen, Wenlin Wang, Yizhe Zhang, Qinliang Su, and Lawrence Carin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' A convergence analysis for  a class of practical variance-reduction stochastic gradient mcmc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Science China Information Sciences, 62  (1):1–13, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Ashok Cutkosky and Francesco Orabona.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Momentum-based variance reduction in non-convex sgd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Advances  in neural information processing systems, 32, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Aaron Defazio, Francis Bach, and Simon Lacoste-Julien.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Saga: A fast incremental gradient method with  support for non-strongly convex composite objectives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Advances in neural information processing systems,  27, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Wei Deng, Qi Feng, Georgios Karagiannis, Guang Lin, and Faming Liang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Accelerating convergence of  replica exchange stochastic gradient mcmc via variance reduction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' arXiv preprint arXiv:2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='01084, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Tim Dettmers and Luke Zettlemoyer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Sparse networks from scratch: Faster training without losing perfor-  mance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' arXiv preprint arXiv:1907.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='04840, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Kumar Avinava Dubey, Sashank J Reddi, Sinead A Williamson, Barnabas Poczos, Alexander J Smola, and  Eric P Xing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Variance reduction in stochastic gradient langevin dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Advances in neural information  processing systems, 29:1154–1162, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Melih Elibol, Lihua Lei, and Michael I Jordan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Variance reduction with sparse gradients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' arXiv preprint  arXiv:2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='09623, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Utku Evci, Trevor Gale, Jacob Menick, Pablo Samuel Castro, and Erich Elsen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Rigging the lottery: Making  all tickets winners.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In International Conference on Machine Learning, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' 2943–2952.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' PMLR, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Cong Fang, Chris Junchi Li, Zhouchen Lin, and Tong Zhang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Spider: Near-optimal non-convex optimization  via stochastic path-integrated differential estimator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Advances in Neural Information Processing Systems,  31, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Jonathan Frankle and Michael Carbin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  The lottery ticket hypothesis: Finding sparse, trainable neural  networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' International Conference on Learning Representations (ICLR), 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Eduard Gorbunov, Filip Hanzely, and Peter Richtárik.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' A unified theory of sgd: Variance reduction, sampling,  quantization and coordinate descent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In International Conference on Artificial Intelligence and Statistics,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' 680–690.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' PMLR, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Laura Graesser, Utku Evci, Erich Elsen, and Pablo Samuel Castro.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' The state of sparse training in deep  reinforcement learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In International Conference on Machine Learning, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' 7766–7792.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' PMLR, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  17  Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Delving deep into rectifiers: Surpassing human-  level performance on imagenet classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  In Proceedings of the IEEE international conference on  computer vision, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' 1026–1034, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Deep residual learning for image recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In  Proceedings of the IEEE conference on computer vision and pattern recognition, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' 770–778, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Torsten Hoefler, Dan Alistarh, Tal Ben-Nun, Nikoli Dryden, and Alexandra Peste.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Sparsity in deep  learning: Pruning and growth for efficient inference and training in neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  arXiv preprint  arXiv:2102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='00554, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Shaoyi Huang, Bowen Lei, Dongkuan Xu, Hongwu Peng, Yue Sun, Mimi Xie, and Caiwen Ding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Dynamic  sparse training via balancing the exploration-exploitation trade-off.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  arXiv preprint arXiv:2211.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='16667,  2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Itay Hubara, Brian Chmiel, Moshe Island, Ron Banner, Joseph Naor, and Daniel Soudry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Accelerated sparse  neural training: A provable and efficient method to find n: m transposable masks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Advances in Neural  Information Processing Systems, 34, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Siddhant Jayakumar, Razvan Pascanu, Jack Rae, Simon Osindero, and Erich Elsen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Top-kast: Top-k always  sparse training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Advances in Neural Information Processing Systems, 33:20744–20754, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Rie Johnson and Tong Zhang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Accelerating stochastic gradient descent using predictive variance reduction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Advances in neural information processing systems, 26:315–323, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Diederik P Kingma and Jimmy Ba.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Adam:  A method for stochastic optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  arXiv preprint  arXiv:1412.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6980, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Alex Krizhevsky, Geoffrey Hinton, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Learning multiple layers of features from tiny images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Technical  report, University of Toronto, 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Souvik Kundu, Mahdi Nazemi, Peter A Beerel, and Massoud Pedram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Dnr: A tunable robust pruning  framework through dynamic network rewiring of dnns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In Proceedings of the 26th Asia and South Pacific  Design Automation Conference, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' 344–350, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Clayton Frederick Souza Leite and Yu Xiao.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Optimal sensor channel selection for resource-efficient deep  activity recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In Proceedings of the 20th International Conference on Information Processing in  Sensor Networks (co-located with CPS-IoT Week 2021), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' 371–383, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Yan Li, Ethan Fang, Huan Xu, and Tuo Zhao.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Implicit bias of gradient descent based adversarial training  on separable data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In International Conference on Learning Representations, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Chuang Liu, Xueqi Ma, Yinbing Zhan, Liang Ding, Dapeng Tao, Bo Du, Wenbin Hu, and Danilo Mandic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Comprehensive graph gradual pruning for sparse training in graph neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  arXiv preprint  arXiv:2207.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='08629, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Shiwei Liu, Lu Yin, Decebal Constantin Mocanu, and Mykola Pechenizkiy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Do we actually need dense  over-parameterization?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' in-time over-parameterization in sparse training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In International Conference on  Machine Learning, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' 6989–7000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' PMLR, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Ilya Loshchilov and Frank Hutter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Decoupled weight decay regularization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In International Conference on  Learning Representations (ICLR), 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Aleksander Madry, Aleksandar Makelov, Ludwig Schmidt, Dimitris Tsipras, and Adrian Vladu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Towards deep  learning models resistant to adversarial attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In International Conference on Learn- ing Representations  (ICLR), 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Kira JM Matus and Michael Veale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Certification systems for machine learning: Lessons from sustainability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Regulation & Governance, 16(1):177–196, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  18  Decebal Constantin Mocanu, Elena Mocanu, Peter Stone, Phuong H Nguyen, Madeleine Gibescu, and An-  tonio Liotta.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Scalable training of artificial neural networks with adaptive sparse connectivity inspired by  network science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Nature communications, 9(1):1–12, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Hesham Mostafa and Xin Wang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Parameter efficient training of deep convolutional neural networks by  dynamic sparse reparameterization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In International Conference on Machine Learning, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' 4646–4655.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  PMLR, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Yuval Netzer, Tao Wang, Adam Coates, Alessandro Bissacco, Bo Wu, and Andrew Y Ng.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Reading digits in  natural images with unsupervised feature learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Lam M Nguyen, Jie Liu, Katya Scheinberg, and Martin Takáč.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Sarah: A novel method for machine learning  problems using stochastic recursive gradient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In International Conference on Machine Learning, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' 2613–  2621.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' PMLR, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Ozan Özdenizci and Robert Legenstein.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Training adversarially robust sparse networks via bayesian connec-  tivity sampling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In International Conference on Machine Learning, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' 8314–8324.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' PMLR, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  David Patterson, Joseph Gonzalez, Quoc Le, Chen Liang, Lluis-Miquel Munguia, Daniel Rothchild, David  So, Maud Texier, and Jeff Dean.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Carbon emissions and large neural network training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' arXiv preprint  arXiv:2104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='10350, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Ning Qian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' On the momentum term in gradient descent learning algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Neural networks, 12(1):145–151,  1999.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Adnan Siraj Rakin, Zhezhi He, Li Yang, Yanzhi Wang, Liqiang Wang, and Deliang Fan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Robust sparse  regularization: Simultaneously optimizing neural network robustness and compactness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' arXiv preprint  arXiv:1905.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='13074, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Sashank J Reddi, Ahmed Hefny, Suvrit Sra, Barnabás Póczos, and Alex Smola.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Stochastic variance reduction  for nonconvex optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In International conference on machine learning, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' 314–323.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' PMLR, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Johanna Rock, Wolfgang Roth, Mate Toth, Paul Meissner, and Franz Pernkopf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Resource-efficient deep  neural networks for automotive radar interference mitigation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' IEEE Journal of Selected Topics in Signal  Processing, 15(4):927–940, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Sebastian Ruder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' An overview of gradient descent optimization algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' arXiv preprint arXiv:1609.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='04747,  2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Olga Russakovsky, Jia Deng, Hao Su, Jonathan Krause, Sanjeev Satheesh, Sean Ma, Zhiheng Huang, Andrej  Karpathy, Aditya Khosla, Michael Bernstein, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Imagenet large scale visual recognition challenge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  International journal of computer vision, 115(3):211–252, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Jonathan Schwarz, Siddhant Jayakumar, Razvan Pascanu, Peter E Latham, and Yee Teh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Powerpropagation:  A sparsity inducing weight reparameterisation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Advances in Neural Information Processing Systems, 34:  28889–28903, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Vikash Sehwag, Shiqi Wang, Prateek Mittal, and Suman Jana.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Hydra: Pruning adversarially robust neural  networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Advances in Neural Information Processing Systems, 33:19655–19666, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Fanhua Shang, Kaiwen Zhou, Hongying Liu, James Cheng, Ivor W Tsang, Lijun Zhang, Dacheng Tao,  and Licheng Jiao.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Vr-sgd: A simple stochastic variance reduction method for machine learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' IEEE  Transactions on Knowledge and Data Engineering, 32(1):188–202, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Karen Simonyan and Andrew Zisserman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Very deep convolutional networks for large-scale image recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Interna- tional Conference on Learning Representations (ICLR), 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Varun Sundar and Rajat Vadiraj Dwaraknath.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' [reproducibility report] rigging the lottery: Making all tickets  winners.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' arXiv preprint arXiv:2103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='15767, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  19  Neil C Thompson, Kristjan Greenewald, Keeheon Lee, and Gabriel F Manso.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Deep learning’s diminishing  returns: the cost of improvement is becoming unsustainable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' IEEE Spectrum, 58(10):50–55, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Lin Xiao and Tong Zhang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' A proximal stochastic gradient method with progressive variance reduction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  SIAM Journal on Optimization, 24(4):2057–2075, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Xia Xiao, Zigeng Wang, and Sanguthevar Rajasekaran.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Autoprune: Automatic network pruning by regular-  izing auxiliary parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Advances in neural information processing systems, 32, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Shaokai Ye, Kaidi Xu, Sijia Liu, Hao Cheng, Jan-Henrik Lambrechts, Huan Zhang, Aojun Zhou, Kaisheng  Ma, Yanzhi Wang, and Xue Lin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Adversarial robustness vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' model compression, or both?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In Proceedings  of the IEEE/CVF International Conference on Computer Vision, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' 111–120, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Rong Yu and Peichun Li.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Toward resource-efficient federated learning in mobile edge computing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' IEEE  Network, 35(1):148–155, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Sergey Zagoruyko and Nikos Komodakis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Wide residual networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' British Machine Vision Conference, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Hongyang Zhang, Yaodong Yu, Jiantao Jiao, Eric Xing, Laurent El Ghaoui, and Michael Jordan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Theo-  retically principled trade-off between robustness and accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In International Conference on Machine  Learning, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' 7472–7482.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' PMLR, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Xiao Zhou, Weizhong Zhang, Zonghao Chen, Shizhe Diao, and Tong Zhang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Efficient neural network training  via forward and backward propagation sparsification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Advances in Neural Information Processing Systems,  34:15216–15229, 2021a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Xiao Zhou, Weizhong Zhang, Hang Xu, and Tong Zhang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Effective sparsification of neural networks with  global sparsity constraint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern  Recognition, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' 3599–3608, 2021b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Difan Zou, Pan Xu, and Quanquan Gu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Subsampled stochastic variance-reduced gradient langevin dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  In International Conference on Uncertainty in Artificial Intelligence, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  20  A  Appendix: Theoretical Proof of Convergence Rate  In this section, we provide a detailed proof for the convergence rate of our AGENT method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' We start with  some assumptions on which we will give some useful lemmas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Then, we will establish the convergence rate  of our AGENT method based on these lemmas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1  Algorithm Reformulation  We reformulate our Adaptive Gradient Correction (AGENT) into a math-friendly version that is shown in  Algorithm 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Algorithm 2 Adaptive Gradient Correction  Input: Initialize θ0  0 and c−1 = 0, set the number of epochs S, epoch length m, step sizes ht, scaling parameter γ,  and smoothing factor α  for s = 0 to S − 1 do  �θ = θs  0  �g = (�N  i=1 ∇G(xi;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' �θ))/N  Calculate �c∗  s via Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' (4)  �cs = (1 − α)�cs−1 + α�c∗  s  cs = γ�cs  for t = 0 to m − 1 do  Sample a mini-batch data Bt with size n  θs  t+1 = θs  t − ηt  �  1  n  �  i∈Bt  �  gi(θs  t ) − cs · gi(�θ)�  + cs · �g  �  end for  θs+1  0  = θs  m  end for  Output: Iterates θπ chosen uniformly random from {{θs  t }m−1  t=0 }S−1  s=0  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2  Assumptions  L-smooth: A differentiable function G : Rn → R is said to be L-smooth if for all x, y ∈ Rn is satisfies  ||∇G(x) − ∇G(y)|| ≤ L||x − y||.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' And an equivalent definition is for.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' all x, y ∈ Rn:  −L  2 ||x − y||2 ≤ G(x) − G(y) − ⟨∇G(x), x − y⟩ ≤ L  2 ||x − y||2  σ-bounded: We say function G has a σ-bounded gradient if ||∇Gi(x)|| ≤ σ for all i ∈ [N] and x ∈ Rn  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='3  Analysis framework  Under the above assumptions, we are ready to analyze the convergence rate of AGENT in Algorithm 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  To introduce the convergence analysis more clearly, we provide a brief analytical framework for our proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  First, we need to show that the variance of our gradient estimator is smaller than that of minibatch  SVRG under proper choice of cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Since the gradient estimator of both AGENT and minibatch  SVRG are unbiased estimators in standard training, we only need to show that our bound E[||ut||2]  is smaller than minibatch SVRG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' (See in Lemma 1)  Based on above fact, we next apply the Lyapunov function to prove the convergence rate of AGENT  in one arbitrary epoch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' (See in Lemma 3)  21  Then, we extend our previous results to the entire epoch (from 0 to S-th epoch) and derive the  convergence rate of the output θπ of Algorithm 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' (See in Lemma 4)  Finally, we compare the convergence rate of our AGENT with that of minibatch SVRG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Setting the  parameters in Lemma 4 according to the actual situation of sparse learning, we obtain a bound that  is more stringent than minibatch SVRG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4  lemma  We first denote step length ηt = N · ht.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Since we mainly focus on a single epoch, we drop the superscript s  and denote ut = 1  n  �  i∈Bt  �  gi(θt) − c · gi(�θ)  �  + c · �g which is the gradient estimator in our algorithm and  τt = 1  n  �  i∈Bt  �  gi(θt) − c · gi(�θ)  �  , then lines the update procedure in Algorithm 2 can be replaced with  θt+1 = θt − ηt · ut  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1  lemma 1  For the ut defined above and function G is a L-smooth,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' λ - strongly convex function with σ-bounded gradient,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='then we have the following results:  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='E  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='||ut||2�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='≤ 2E  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='||g(θt)||2�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='+ 4c2L2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='n  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='E  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='||θt − ˜θ||2�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='+ 4(1 − c)2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='n  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='σ2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='(6)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='Proof :  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='E  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='||ut||2�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='= E  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='||τt + c · �g||2�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='= E  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='||τt + c · �g − g(θt) + g(θt)||2�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='≤ 2E  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='||g(θt)||2�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='+ 2E  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='||τt − E(τt)||2�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='≤ 2E  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='||g(θt)||2�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='+ 2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='nE  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='τ 2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='t  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='= 2E  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='||g(θ)||2�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='+ 2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='nE  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='||c(gi(θt) − gi(˜θ)) + (1 − c)gi(θt)||2�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='≤ 2E  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='||g(θ)||2�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='+ 4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='nE  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='||c(gi(θt) − gi(˜θ))||2�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='+ 4(1 − c)2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='n  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='E  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='||gi(θt)||2�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='≤ 2E  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='||g(θ)||2�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='+ 4c2L2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='n  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='E  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='||θt − ˜θ||2�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='+ 4(1 − c)2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='n  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='σ2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='The first and third inequality are because ||a + b||2 ≤ 2||a||2 + 2||b||2 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' the second inequality follows the  E  �  ||τ − E [τ] ||2�  ≤ E  �  ||τ||2�  and the last inequality follows the L-smoothness and σ-bounded of function  Gi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Remark 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Compared with the gradient estimator of minibatch SVRG, the bound of E[||ut||2] is smaller  when L is large, σ is relative small and c is properly chosen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2  Lemma 2  E [G(θt+1)] ≤ E  �  G(θt) + ηt||g(θt)||2 + Lη2  2 ||ut||2  �  (7)  Proof :  By the L-smoothness of function G, we have  22  E [G(θt+1)] ≤ E  �  G(θt) + ⟨g(θt), θt+1 − θt⟩ + L  2 ||θt+1 − θt||2  �  By the update procedure in algorithm 2 and unbiasedness, the right hand side can further upper bounded  by  E  �  G(θt) + ηt||g(θt)||2 + Lη2  t  2 ||ut||2  �  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='3  Lemma 3  For bt, bt+1, ζt > 0 and bt and bt+1 have the following relationship  bt = bt+1(1 + ηtζt + 4c2η2  t L2  n  ) + 2c2η2  t L3  n  and define  Φt := ηt − bt+1ηt  ζt  − η2  t L − 2bt+1η2  t  Ψt := E  �  G(θt) + bt||θt − ˜θ||2�  (8)  ηt, ζt and bt+1 can be chosen such that Φt > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='Then the xt in Algorithm 1 have the bound:  E[||g(θt)||2] ≤ Ψt − Ψt+1 + 2(Lη2  t +2bt+1η2  t )(1−c)2  n  σ2  Φt  Proof :  We apply Lyapunov function  Ψt = E  �  G(θt) + bt||θt − ˜θ||2�  Then we need to bound ||θt − ˜θ||  E  �  ||θt+1 − ˜θ||2�  = E  �  ||θt+1 − θt + θt − ˜θ||2�  = E  �  ||θt+1 − θt||2 + ||θt − ˜θ||2 + 2⟨θt+1 − θt,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' θt − ˜θ⟩  �  = E  �  η2  t||ut||2 + ||θt − ˜θ||2�  − 2ηtE  �  ⟨g(θt),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' θt − ˜θ⟩  �  ≤ E[η2  t ||us+1  t  ||2 + ||θt − ˜θ||2] + 2ηtE  � 1  2ζt  ||g(θt)|| + ζt  2 ||θt − ˜θ||2  �  (9)  The third equality due to the unbiasedness of the update and the last inequality follows Cauchy-Schwarz  and Young’s inequality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Plugging Equation (6), Equation (7) and Equation (9) into Equation (8), we can  get the following bound:  Ψt+1 ≤ E [G(θt)] +  �  bt+1(1 + ηtζt + 4c2η2  t L2  n  ) + 2c2η2  t L3  n  �  E[||θt − ˜θ||2]  − (ηt − bt+1ηt  ζt  − Lη2  t − 2bt+1η2  t )E  �  ||g(θt)||2�  + 4(Lη2  t  2  + bt+1η2  t )(1 − c)2  n  σ2  = Ψt − (ηt − bt+1ηt  ζt  − Lη2  t − 2bt+1η2  t )E  �  ||g(θt)||2�  + 4(Lη2  t  2  + bt+1η2  t )(1 − c)2  n  σ2  23  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4  Lemma 4  Now we consider the effect of epoch and use s to denote the epoch number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Let bs  m = 0, ηs  t = η, ζs  t = ζ and  bs  t = bs  t+1(1 + ηζ + 4c2  sηL2  n  ) + 2 c2  sη2L2  n  , Φs  t = η −  bs  t+1η  ζt  − η2L − 2bs  t+1η2 Define φ := mint,s Φs  t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Then we can  conclude that:  E[||g(θπ)||2] ≤ G(θ0) − G(θ∗)  Tφ  +  S−1  �  s=0  m−1  �  t=0  2(L + 2bs  t+1)(1 − cs)2η2σ2  Tnφ  Proof :  Under the condition of ηs  t = η,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' we apply telescoping sum on Lemma 3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' then we will get:  m−1  �  t=1  E[||g(θs  t )||2] ≤ Ψs  0 − Ψs  m  φ  +  m−1  �  t=0  2(L + 2bs  t+1)(1 − cs)2η2σ2  nφ  From previous definition,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' we know Ψs  0 = G(˜θs),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Ψs  m = G(˜θs+1) and plugging into previous equation,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' we  obtain:  m−1  �  t=1  E[||g(θs  t )||2] ≤ G(˜θs) − G(˜θs+1)  φ  +  m−1  �  t=0  2(L + 2bs  t+1)(1 − cs)2η2σ2  nφ  Take summation over all the epochs and using the fact that ˜θ0 = θ0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' G(˜θS) ≤ G(θ∗) we immediately obtain:  1  T  S−1  �  s=0  m−1  �  t=1  E[||g(θs  t )||2] ≤ G(θ0) − G(θ∗)  φ  +  S−1  �  s=0  m−1  �  t=0  2(L + 2bs  t+1)(1 − cs)2η2σ2  Tnφ  (10)  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5  Theorem  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1  Theorem 1  Define ξs = �m−1  t=0 (L + 2bs  t+1) and ξ := mins ξs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Let η =  µn  LNα  (0 < µ < 1)  and  (0 < α ≤ 1), ζ =  L  N α/2  and m = N  3α  2  µn .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Then there exists constant ν, µ, α, κ > 0 such that φ ≥  nν  LNα and ξ ≤ κL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Then E[||g(θπ)||2]  can be future bounded by:  E[||g(θπ)||2] ≤ (G(θ0) − G(θ∗))LN α  Tnν  + 2κµ2σ2  N ανm  Proof :  By applying summation formula of geometric progression on the relation bs  t = bs  t+1(1 + ηtζt + 4c2  sη2  t L2  n  ) +  2 c2  sη2  t L3  n  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' we have bs  t = 2c2  sη2L3  n  (1+ωs)m−t−1  ωs  where:  ωs = ηζ + 4c2  sη2L  n  = µn  N  3α  2 + 4c2  sµ2n  N 2α  ≤ (4c2  s + 1)µn  N  3α  2  24  This bound holds because µ ≤ 1 and N ≥ 1 and thus 4c2  sµ2n  N2α  = 4c2  sµn  N  3α  2  ×  µ  N  α  2 ≤ 4c2  sµn  N  3α  2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' And using this bound,  we obtain:  bs  0 = 2η2c2  sL3  n  (1 + ωs)m − 1  ωs  = 2µ2nc2  sL  N 2α  (1 + ωs)m − 1  ωs  ≤ 2µnc2  sL((1 + ωs)m − 1)  N  α  2 (4cs + 1)  ≤  2µnc2  sL((1 + (4c2  s+1)µn  N  3α  2  )  N  3α  2  µn − 1)  N  α  2 (4c2s + 1)  ≤ 2µnc2  sL(e  1  4c2s+1 − 1)  N  α  2 (4c2s + 1)  The last inequality holds because (1 + 1  x)x is a monotone increasing function of x when x > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Thus  (1 + (4c2  s+1)µn  N  3α  2  )  N  3α  2  µn  ≤ e  1  4c2s+1 in the third inequality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' And we can obtain the lower bound for φ  φ = min  t,s Φs  t ≥ min  s (η − bs  0η  ζ  − η2L − 2bs  0η2) ≥  nν  LN α  The first inequality holds since bt  s is a decrease function of t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Meanwhile, the second inequality holds because  there exist uniform constant ν such that ν ≥ µ(1 − bs  0η  ζ − Lη − bs  0η).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Remark 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In practice, bs  0 ≈ 0 because both γ and cs is both smaller than 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1 which leads to µ(1 − bs  0  ζ −  Lη − bs  0η) ≈ µ(1 − Lη) and this value is usually much bigger than the ν∗ in the bound of minibatch SVRG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='We need to find the upper bound for ξ  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='ξs =  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='m−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='t=0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='(L + 2bs  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='t+1) = mL + 2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='m−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='t=0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='bs  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='t+1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='= mL + 2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='m−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='t=0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2c2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='sη2L3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='n  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='(1 + ωs)m−t − 1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='ωs  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='= mL + 2c2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='sη2L3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='nωs  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='[(1 + ωs)m+1 − (1 + ωs)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='ωs  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='− m]  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='≤ mL + 2c2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='sη2L3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='n  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='[1 + ωs  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='ω2s  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='(e  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4c2s+1 − 1) − m]  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='≤ mL + 2c2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='sLN α  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='n  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='(1 +  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='µn  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='N 3α/2 )(e  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4c2s+1 − 1) − 2c2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='sµ2nmL  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='N 2α  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='= L[(1 − 2c2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='sµ2nL  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='N 2α  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=')m + 2c2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='sN α  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='n  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='(1 +  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='µn  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='N 3α/2 )(e  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4c2s+1 − 1)]  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='The reason why the first inequality holds is explained before and the second inequality holds because 1+x  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='is a monotone decreasing function of x when x > 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' ωs =  µn  N  3α  2  + 4c2  sµ2n  N2α  ≤  µn  N  3α  2  and η =  µn  LNα .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Then  ξ = maxs ξs ≤ κL where κ ≥ maxs((1 − 2c2  sµ2nL  N2α  )m + 2c2  sNα  n  (1 +  µn  N 3α/2 )(e  1  4c2s+1 − 1)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  When cs ≈ 0,  (1 − 2c2  sµ2nL  N2α  )m + 2c2  sNα  n  (1 +  µn  N3α/2 )(e  1  4c2s+1 − 1) ≈ m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Now we obtain the lower bound for φ and upper bound for ξ, plugging them into equation (10), we will have:  25  E[||g(θπ)||2] ≤ G(θ0) − G(θ∗)  φ  +  S−1  �  s=0  m−1  �  t=0  2(L + 2bs  t+1)(1 − cs)2η2σ2  Tnφ  ≤ (G(θ0) − G(θ∗))LN α  Tnν  +  S−1  �  s=0  m−1  �  t=0  2(L + 2bs  t+1)η2σ2  Tnφ  ≤ (G(θ0) − G(θ∗))LN α  Tnν  +  S−1  �  s=0  (2η2σ2  Tnφ )  m−1  �  t=0  (L + 2bs  t+1)  ≤ (G(θ0) − G(θ∗))LN α  Tnν  + 2κµ2σ2  N ανm  Remark 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In our theoretical analysis above, we consider c as a constant in each epoch, which is still  consistent with our practical algorithm for the following reasons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  (i) In our Algorithm 1, �c∗  t is actually a fixed constant within each epoch, which can be different in different  epochs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Since it is too expensive to compute the exact �c∗  t in each iteration, we compute it at the beginning  of each epoch and use it as an approximation in the following epoch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  (ii) As for our proof, we first show the convergence rate of one arbitrary training epoch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In this step, treating  c as a constant is aligned with our practical algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  (iii) Then, when we extend the results of one epoch to the whole epoch, we establish an upper bound for  different c in each epoch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Thus, the bound can be applied when c differs across epochs, which enables our  theoretical analysis consistent with our practical algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6  Real Case Analysis for Sparse Training  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1  CIFAR-10/100 dataset  In our experiments, we apply both SVRG and AGENT on CIFAR-10 and CIFAR-100 dataset with η = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1,  γ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1, batch size m = 128 and in total 50000 training sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Under this parameter setting, ν and ν∗in  Theorem 1 and Remark 4 are about 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='06, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' While 2κµ2σ2  Nανm is around 10−5 which is  negligible so we know AGENT should have a tighter bound than SVRG in this situation which matches with  the experimental results show in Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2  svhn dataset  Meanwhile, in SVHN dataset, we train our model with parameters: η = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1, γ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1, batch size m = 573  and sample size N = 73257.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' ν, ν∗ equal 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='06 respectively and 2κµ2σ2  N ανm is around 10−4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Although the  second term in Theorem 1 is bigger.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Since ν here is a lot bigger than ν∗ which lead to the first term in  Theorem 1 much smaller than that of Remark 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' So we still obtain a more stringent bound compared  with SVRG which also meets with the outcome presented in Figure 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  26  B  Additional Experimental Results  We summarize additional experimental results for the BSR-Net-based Özdenizci & Legenstein (2021), RigL-  based Evci et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' (2020), and ITOP-based Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' (2021) models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1  Accuracy Comparisons in Different Epochs  Aligned with the main manuscript, we compare the accuracy for a given number of epochs to compare both  the speed of convergence and training stability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' We first show BSR-Net-based results in this section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Since  our approach has faster convergence and does not require a long warm-up period, the dividing points for the  decay scheduler are set to the 50th and 100th epochs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In the manuscript, we also use this schedule for BSR-  Net for an accurate comparison.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In the Appendix, we include the results using its original schedule.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' BSR-Net  and BSR-Net (ori) represent the results learned using our learning rate schedule and original schedule in  Özdenizci & Legenstein (2021), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' As shown in Figures 7, 8, 9, 10, 11, 12, 13, the blue curves  (A-BSR-Net) are always higher than the yellow curves and also much smoother than yellow curves (BSR-Net  and BSR-Net (ori)), indicating faster and more stable training when using our proposed A-BSR-Net.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  (a) 90% Sparsity  (b) 90% Sparsity  (c) 99% Sparsity  (d) 99% Sparsity  Figure 7: Comparisons (accuracy given the number of epochs) with BSR-Net Özdenizci & Legenstein (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  We evaluate sparse networks (99% or 90%) learned with natural training on CIFAR-10 using VGG-16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  (a) 90% Sparsity  (b) 90% Sparsity  (c) 99% Sparsity  (d) 99% Sparsity  Figure 8: Comparisons (accuracy given the number of epochs) with BSR-Net Özdenizci & Legenstein (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  We evaluate sparse networks (99% or 90%) learned with adversarial training (objective: AT) on CIFAR-10  using VGG-16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  27  Koangoe Jugra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='B  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4  A-BSR-Net  BSR-Net  0  50  lio  150  2i0  Number of epochs0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='B  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4  A-BSR-Net  BSR-Net (ori)  0  50  140  150  240  Number of epochs0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='B  accurecy  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6  Bugga  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2  A-BSR-Net  BSR-Net  0  50  lio  150  2i0  Number of epochs0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='B  accurecy  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6  Buggal  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2  A-BSR-Net  BSR-Net (ori)  0  50  140  150  240  Number of epochs0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='B  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5  fiugs  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4  EO  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2  A-BSR-Net  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1  BSR-Net  0  50  140  150  240  Number of epochs0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='B  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4  EO  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2  A-BSR-Net  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1  BSR-Net (ori)  0  50  lio  150  2i0  Number of epochs0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='7  Koangoe Jugra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2  A-BSR-Net  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1  BSR-Net  0  50  lio  150  2i0  Number of epochs0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2  A-BSR-Net  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1  BSR-Net (ori)  0  50  lio  150  2i0  Number of epochs(a) 90% Sparsity  (b) 90% Sparsity  (c) 99% Sparsity  (d) 99% Sparsity  Figure 9: Comparisons (accuracy given the number of epochs) with BSR-Net Özdenizci & Legenstein (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  We evaluate sparse networks (99% or 90%) learned with natural training on CIFAR-10 using Wide-ResNet-  28-4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  (a) 90% Sparsity  (b) 90% Sparsity  (c) 99% Sparsity  (d) 99% Sparsity  Figure 10: Comparisons (accuracy given the number of epochs) with BSR-Net Özdenizci & Legenstein  (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' We evaluate sparse networks (99% or 90%) learned with adversarial training (objective: AT) on  CIFAR-10 using Wide-ResNet-28-4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  (a) 90% Sparsity  (b) 90% Sparsity  (c) 99% Sparsity  (d) 99% Sparsity  Figure 11: Comparisons (accuracy given the number of epochs) with BSR-Net Özdenizci & Legenstein  (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' We evaluate sparse networks (99% or 90%) learned with natural training on SVHN using VGG-16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  28  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='B  Kaunoe fugsa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2  A-BSR-Net  BSR-Net  0  50  lio  150  2i0  Number of epochs0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='B  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2  A-BSR-Net  BSR-Net (ori)  0  50  140  150  240  Number of epochs0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='B  accurecy  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6  fugra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2  A-BSR-Net  BSR-Net  0  50  140  150  240  Number of epochs0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='B  accurecy  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6  Eesting  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2  A-BSR-Net  BSR-Net (ori)  0  50  140  150  240  Number of epochs0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='B  10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2  A-BSR-Net  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1  BSR-Net  0  50  lio  150  2i0  Number of epochs0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='B  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2  A-BSR-Net  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1  BSR-Net (ori)  0  50  lio  150  240  Number of epochs0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='7  Koangoe Jugra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4  EO  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2  A-BSR-Net  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1  BSR-Net  0  50  lio  150  240  Number of epochs0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2  A-BSR-Net  BSR-Net (ori)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1  0  50  140  150  240  Number of epochsLD  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='B  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4 -  A-BSR-Net  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2 -  BSR-Net  0  50  1+0  150  20  Number of epochaLD  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='B  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6  A-BSR-Net  BSR-Net (ori)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2  0  50  140  150  20  Number of epochsaccurecy  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='B  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6  Bugs  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4  A-BSR-Net  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2 -  BSR-Net  0  50  150  240  Number of epochs0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='B  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6  A-BSR-Net  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2  BSR-Net (ori)  0  50  140  150  240  Number of epochs(a) 90% Sparsity  (b) 90% Sparsity  (c) 99% Sparsity  (d) 99% Sparsity  Figure 12: Comparisons (accuracy given the number of epochs) with BSR-Net Özdenizci & Legenstein  (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' We evaluate sparse networks (99% or 90%) learned with adversarial training (objective: TRADES)  on SVHN using VGG-16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  (a) CIFAR-100,VGG-16  (b) SVHN,VGG-16  (c) CIFAR-100,WRN-28-4  (d) SVHN,WRN-28-4  Figure 13: Training curve (accuracy given number of epochs) of BSR-Net-based models (Özdenizci & Leg-  enstein, 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Sparse networks (99%) are learned in standard setups on (a) CIFAR-100 using VGG-16, (b)  SVHN using VGG-16, (c) CIFAR-100 using WRN-28-4, (d) SVHN using WRN-28-4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  (a) Standard  (b) Adversarial (AT)  Figure 14: Training curve (required epochs to reach given accuracy) of BSR-Net-based models (Özdenizci  & Legenstein, 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Dense networks are learned in standard and adversarial setups on CIFAR-10 using  VGG-16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  29  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='B  accurecy  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6  Bugs  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4  A-BSR-Net  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2 -  BSR-Net  0  50  lio  150  240  Number of epochs0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='B  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6  fugri  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4  A-BSR-Net  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2  BSR-Net (ori)  0  50  150  240  Number of epochs0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='9  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='B  accurecy  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6  fiugri  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='3  A-BSR-Net  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2  BSR-Net  0  50  lio  150  2i0  Number of epochs0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='9  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='B  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='3 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  A-BSR-Net  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2  BSR-Net (ori)  0  50  140  150  240  Number of epochs0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1  A-BSR-Net  BSR-Net  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='D  50  10  150  240  Number of epochaaccurecy  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='B  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6  Bugs  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4  A-BSR-Net  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2 -  BSR-Net  0  50  150  240  Number of epochs0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1  A-BSR-Net  BSR-Net  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='D  0  50  lio  150  2i0  Number of epochsLD  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='B  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2  A-BSR-Net  BSR-Net  0  50  140  150  240  Number of epocha0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='B  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2  A-BSR-Net  BSR-Net  0  25  50  1i0  125  150  175  240  Number of epochs0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='B -  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='7  ecy  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2 -  A-BSR-Net  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1  BSR-Net  0  25  50  75  140  125  150  175  240  Number of epochs0  20  40  60  80  100  Number of epochs  10  20  30  40  50  60  70  Testing accuracy  RigL-ITOP  A-RigL-ITOP  (a) 80% Sparsity  0  20  40  60  80  100  Number of epochs  10  20  30  40  50  60  70  Testing accuracy  RigL-ITOP  A-RigL-ITOP  (b) 90% Sparsity  Figure 15: Training curve (required epochs to reach given accuracy) of ITOP-based models (Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Sparse networks are learned in standard setup on ImageNet-2012 using ResNet-50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  In Figure 14, we also compare the convergence speed without sparsity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' We show a BSR-Net-based result,  where dense network is learned by adversarial training (AT) and standard training on CIFAR-10 using VGG-  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' The blue curve of our A-BSR-Net tends to be above the yellow curve of BSR-Net, indicating successful  acceleration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' This demonstrates the broad applicability of our method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Then, we also show ITOP-based results on ImageNet-2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' As shown in Figure 15, the red and blue curve  represent AGENT + RigL-ITOP and RigL-ITOP on 80% and 90% sparse ResNet-50, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' For 80%  sparsity, we can see that the red curve is above the blue curve, demonstrating the acceleration effect of our  AGENT, especially in the early stages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' For 90% sparity, we can see that the red curve is more stable than  the blue curve, which shows the stable effect of our AGENT on large data sets and is a slightly different  manifestation of the strengths of our AGENT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' If we use SVRG in this case, we will not only fail to train  stably, but also slow down the training speed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In contrast, our AGENT can solve the limitation of SVRG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  For other sparsity levels, we can expect advantages of our AGENT, in terms of acceleration or stability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Moreover, we can expect more significant speedups at different sparsity levels with more hyperparameter  tuning, as the speedups are guaranteed by theoretical proofs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2  Number of Training Epoch Comparisons  We also compare the number of training epochs required to reach the same accuracy in BSR-Net-based  results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In Figures 16, 17, 18, 19, 20, 21, 22, the blue curves (A-BSR-Net) are always lower than yellow  curves (BSR-Net and BSR-Net (ori)), indicating faster convergence of A-BSR-Net.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  30  (a) Wide-ResNet-28-4  (b) ResNet-18  Figure 16: Comparisons (required hours to reach given accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' We evaluate sparse networks (99%) learned  with natural training on CIFAR-100 using (a) Wide-ResNet-28-4, and (b) ResNet-18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  (a) 90% Sparsity  (b) 90% Sparsity  (c) 99% Sparsity  (d) 99% Sparsity  Figure 17: Comparisons (required hours to reach given accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' We evaluate sparse networks (99% or 90%)  learned with natural training on CIFAR-10 using VGG-16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  (a) 90% Sparsity  (b) 90% Sparsity  (c) 99% Sparsity  (d) 99% Sparsity  Figure 18: Comparisons (required hours to reach given accuracy).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' We evaluate sparse networks (99% or  90%) learned with adversarial training (objective: AT) on CIFAR-10 using VGG-16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  31  A-BSR-Net  BSR-NetA-BSR-Net  BSR-NetA-BSR-Net  BSR-NetA-BSR-Net  BSR-Net (ori)A-BSR-Net  BSR-NetA-BSR-Net  BSR-Net (ori)A-BSR-Net  BSR-NetA-BSR-Net  BSR-Net (ori)(a) 90% Sparsity  (b) 90% Sparsity  (c) 99% Sparsity  (d) 99% Sparsity  Figure 19: Comparisons (required hours to reach given accuracy).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' We evaluate sparse networks (99% or  90%) learned with natural training on CIFAR-10 using Wide-ResNet-28-4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  (a) 90% Sparsity  (b) 90% Sparsity  (c) 99% Sparsity  (d) 99% Sparsity  Figure 20: Comparisons (required hours to reach given accuracy).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' We evaluate sparse networks (99% or  90%) learned with adversarial training (objective: AT) on CIFAR-10 using Wide-ResNet-28-4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  (a) 90% Sparsity  (b) 90% Sparsity  (c) 99% Sparsity  (d) 99% Sparsity  Figure 21: Comparisons (required hours to reach given accuracy).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' We evaluate sparse networks (99% or  90%) learned with natural training on SVHN using VGG-16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  (a) 90% Sparsity  (b) 90% Sparsity  (c) 99% Sparsity  (d) 99% Sparsity  Figure 22: Comparisons (required hours to reach given accuracy).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' We evaluate sparse networks (99% or  90%) learned with adversarial training (objective: TRADES) on SVHN using VGG-16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  32  A-BSR-Net  BSR-NetA-BSR-Net  BSR-Net (ori)A-BSR-Net  BSR-NetA-BSR-Net  BSR-Net (ori)A-BSR-Net  BSR-NetA-BSR-Net  BSR-Net (ori)A-BSR-Net  BSR-NetA-BSR-Net  BSR-Net (ori)A-BSR-Net  BSR-NetA-BSR-Net  BSR-Net (ori)A-BSR-Net  BSR-NetA-BSR-Net  BSR-Net (ori)A-BSR-Net  BSR-NetA-BSR-Net  BSR-Net (ori)A-BSR-Net  BSR-NetA-BSR-Net  BSR-Net (ori)B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='3  Scaling Parameter Setting  The choice of the scaling parameter γ is important to the acceleration and can be seen as a hyper-parameter  tuning process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' We experiment with different values of γ and find that setting γ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1 is a good choice for  effective acceleration of training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' The presented results are based on sparse networks (99%) learned with  adversarial training (objective: AT) on CIFAR-10 using VGG-16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  As shown in Figure 23 (a), we compare the training curves (testing accuracy at different epochs) A-BSR-Net  (γ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1), A-BSR-Net (γ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5), and BSR-Net.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' The yellow curve for A-BSR-Net (γ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5) collapses after  around 40 epochs training, indicating a model divergence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' The reason is that if setting γ close to 1, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', like  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5, we will not be able to completely avoid the increase in variance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' The increase in variance will lead to a  decrease in performance, which is similar to "No γ" in section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4 of the manuscript.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  As shown in Figure 23 (b), we compare the training curves (testing accuracy at different epochs) A-BSR-Net  (γ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1), A-BSR-Net (γ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='01), and BSR-Net.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' The yellow curve for A-BSR-Net (γ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='01) is below the  blue curve for A-BSR-Net (γ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1), indicating a slower convergence speed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' The reason is that if γ is set  small, such as 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='01, the weight of the old gradients will be small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Thus, the old gradients will have limited  influence on the updated direction of the model, which tends to slow down the convergence and sometimes  can lead to more training instability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  0  25  50  75  100  125  150  175  200  Number of epochs  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='7  Testing accuracy  A-BSR-Net, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1  A-BSR-Net, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5  BSR-Net  (a) Scaling parameter = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1 or 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5  0  25  50  75  100  125  150  175  200  Number of epochs  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='7  Testing accuracy  A-BSR-Net, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1  A-BSR-Net, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='01  BSR-Net  (b) Scaling parameter = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1 or 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='01  Figure 23: Comparisons (testing accuracy given the number of epochs) with different scaling parameters in  BSR-Net-based models Özdenizci & Legenstein (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' We evaluate sparse networks (99%) learned with  adversarial training (objective: AT) on CIFAR-10 using VGG-16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' (a) scaling parameter = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1 or 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5, (b)  scaling parameter = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1 or 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='01.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4  Other Variance Reduction Method Comparisons  We also include more results about comparison between our ADSVRG and stochastic variance reduced  gradient (SVRG) Baker et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' (2019);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' (2019);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Zou et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' (2018), a popular variance reduction  method in non-sparse case, to show the limitations of previous methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1  BSR-Net-based Results  The presented results are based on sparse networks (99%) learned with adversarial training (objective: AT)  on CIFAR-10 using VGG-16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' As presented in Figure 24, we show the training curves (testing accuracy  at different epochs)of A-BSR-Net, BSR-Net, and BSR-Net using SVRG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' The yellow curve for BSR-Net  using SVRG rises to around 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4 and then rapidly decreases to a small value around 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1, indicating a model  divergence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' This demonstrates that SVRG does not work for sparse training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' As for the blue curve for our  A-BSR-Net, it is always above the green curve for BSR-Net, indicating a successful acceleration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  33  0  25  50  75  100  125  150  175  200  Number of epochs  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='7  Testing accuracy  A-BSR-Net  BSR-Net, SVRG  BSR-Net  Figure 24: Comparisons (testing accuracy given the number of epochs) with different variance reduction  methods in BSR-Net-based models Özdenizci & Legenstein (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  We evaluate sparse networks (99%)  learned with adversarial training (objective: AT) on CIFAR-10 using VGG-16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2  RigL-based Results  The presented results are based on sparse networks (90%) learned with standard training on CIFAR-100  using ResNet-50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  As presented in Figure 25, we show the training curves (testing accuracy at different  epochs) of A-RigL, RigL, and RigL using SVRG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' The yellow curve for RigL using SVRG is always below  the other two curves, indicating a slower model convergence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' This demonstrate that SVRG does not work  for sparse training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' As for the blue curve for our A-RigL, it is always on the top of the green curve for RigL,  indicating that the speedup is successful.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  0  50  100  150  200  250  Number of epoch  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='7  Accuracy  A-RigL  RigL, SVRG  RigL  Figure 25: Comparisons (testing accuracy given the number of epochs) with different variance reduction  methods in RigL-based models Evci et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' We evaluate sparse networks (90%) learned with standard  training on CIFAR-100 using ResNet-50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  34  Table 6: Comparisons the BSR-Net Özdenizci & Legenstein (2021) and HYDRA Sehwag et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Evaluations of sparse networks learned with robust training objectives (TRADES) on SVHN using VGG-  16 and WideResNet-28-4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Evaluations are after full training (200 epochs) and presented as clean/robust  accuracy (%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Robust accuracy is evaluated via PGD50 with 10 restarts ϵ = 8/255.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  BSR-Net  HYDRA  Ours  90% Sparsity  VGG-16  89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4/53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='7 89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2/52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='8 94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4/51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='9  WRN-28-4 92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='8/55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6 94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4/43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='9 95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5/46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2  99% Sparsity  VGG-16  86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4/48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='7 84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4/47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='8 90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='9/47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='9  WRN-28-4 89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5/52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='7 88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='9/39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1 92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2/51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5  Final Accuracy Comparisons  We also provide additional BSR-Net-based results for the final accuracy comparison.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In addition to the  BSR-Net and A-BSR-Net in the manuscript, we also include HYDRA in the appendix, which is also a SOTA  sparse and adversarial training pipeline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' The results are trained on SVHN using VGG-16 and WideResNet-  28-4 (WRN-28-4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' The final results for BSR-Net and HYDRA are obtained from Özdenizci & Legenstein  (2021) using their original learning rate schedules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' As shown in Table 6, it is encouraging to note that our  method tends to be the best in all cases when given clean test samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In terms of the robustness, our  A-BSR-Net beats HYDRA in most cases, while experience a performance degradation compared to BSR-Net.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6  Gradient Change Speed & Sparsity Level  In sparse training, when there is a small change in the weights, the gradient changes faster than in dense  training, and this phenomenon can be expressed as a low correlation between the current and previous  gradients, making the existing variance reduction methods ineffective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  We first demonstrate this lower correlation from an intuitive point of view.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Considering the weights on which  the current and previous gradients were calculated, there are three cases to be discussed in sparse training  when the masks of current and previous gradients are different.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' First, if current weights are pruned, we  do not need to consider their correlation because we do not need to update the current weights using the  corresponding previous weights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Second, if current weights are not pruned but previous weights are pruned,  the previous weights are zero and the difference between two weights is relatively large, leading to a lower  relevance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Third, if neither the current nor the previous weights are pruned, which weights are pruned can  still change significantly, leading to large changes in the current and previous models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Thus, the correlation  between the current and previous gradients of the weights will be relatively small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Thus, it is not a good idea  to set c = 1 directly in sparse training which can even increase the variance and slow down the convergence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  When the masks of the current and previous gradients are the same, the correlation still tends to be weaker.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  As we know, c∗  t = Cov(gnew,gold)  Var(gold)  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Even if Cov(gnew, gold) does not decrease, the variance Var(gold) increases  in sparse training, leading to a decrease in c∗  t .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Apart from the analysis above, we also do some experiments to demonstrate that the gradient changes  faster as the sparsity increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' To measure the rate of change, our experiments are described below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' We  begin with fully-trained checkpoints from ResNet-50 on CIFAR-100 with RigL and SET at 0%, 50%, 80%,  90%, and 95% sparsity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' We calculate and store the gradient of each weight on all training data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Then, we  add Gaussian perturbations (std = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='015) to all the weights and calculate the gradients again.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Lastly, we  calculate the correlation between the gradient of the new perturbed weights and the old original weights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  As we know, there is always a difference between the old and new weights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' If the gradients become very  different after adding some small noise to the weights, the new and old gradients will tend to have smaller  correlations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' If the gradients do not change a lot after adding some small noise, the old and new gradients  will have a higher correlation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Thus, we add Gaussian noise to the weights to simulate the difference between  35  the new and old gradients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' As shown in Table 7, the correlation decreases with increasing sparsity, which  indicates a weaker correlation in sparse training and supports our claim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Table 7: Correlation between the gradient of the new perturbed weights and the old original weights from  ResNet-50 on CIFAR-100 produced by RigL and SET at different sparsity including 0%, 50%, 80%, 90%,  95%, 99%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Sparsity  0%  50%  80%  90%  95%  ResNet-50, CIFAR-100 (RigL)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6005  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4564  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='3217  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1886  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1590  ResNet-50, CIFAR-100 (SET)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6005  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4535  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2528  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1763  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1195  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='7  Comparison between True Correlation & Our Approximation  In this section, to test how well our approximation estimates the true optimum c, we empirically compare  the approximation c∗ in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' (4) (in the main manuscript) and the correlation between gradient of current  weights and gradient of previous epoch weights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' As shown in Figure 26, the yellow and blue curves represent  the approximation c∗ and the correlation, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' The two curves tend to have similar up-and-down  patterns, and the yellow curves usually have a larger magnitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' This suggests that our c approximation  captures the dynamic patterns of the correlation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' For the larger magnitude, it can be matched by our scaling  parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  5  10  15  20  25  30  Number of epoch  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='8  Value  True Correlation  c Approximation  (a) 90%  5  10  15  20  25  30  Number of epoch  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='8  Value  True Correlation  c Approximation  (b) 99%  Figure 26: Comparisons between the approximation c∗ and correlation between gradient of current weights  and gradient of previous epoch weights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' We evaluate sparse networks learned with RigL-based standard  training on CIFAR-10 using ResNet-50 with (a) 90% sparsity and (b) 99% sparsity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='8  Variants of RigL  RigL is one of the most popular dynamic sparse training pipeline which uses weight magnitude for pruning  and gradient magnitude for growing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Our method adaptively updates the new batch gradient using the old  storage gradient which usually has less noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' As a result, the variance of the new batch gradient is reduced,  leading to fast convergence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Currently, we only use gradients with corrected variance in weight updates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' A  natural question is how does it perform if we also use this variance-corrected gradient for weight growth in  RigL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  We do some experiments in RigL-based models trained on CIFAR-10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' As shown in Figure 27, the blue  curves (RigL-ITOP-G) and yellow curves (RigL-ITOP) correspond to the weight growth with and without  the variance-corrected gradient, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' We can see that in the initial stage, the blue curves are higher  than the yellow curves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' But after the first learning rate decay, they tend to be lower than the yellow curves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  This suggests that weight growth using a variance-corrected gradient at the beginning of training can help  36  the model improve accuracy faster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' However, this may lead to a slight decrease in accuracy in the later  training stages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' This may be due to the fact that some variance in the gradient can help the model explore  local regions better and find better masks as the model approaches its optimal point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  0  50  100  150  200  250  Number of epoch  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='9  Accuracy  RigL-ITOP-G  RigL-ITOP  (a) VGG-C  0  50  100  150  200  250  Number of epoch  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='9  Accuracy  RigL-ITOP-G  RigL-ITOP  (b) ResNet-34  Figure 27: Comparisons (testing accuracy given the number of epochs) between weight growth with (RigL-  ITOP-G) and without (RigL-ITOP) variance-corrected gradient Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' We evaluate sparse net-  works (99%) learned with standard training on CIFAR-10 using (a) VGG-C and (b) ResNet-34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='9  Comparison with Reducing Learning Rate  To demonstrate the design of the scaling parameter γ, we compare our AGENT with "Reduce LR", where  we remove the scaling parameter γ from AGENT and set the learning rate to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1 times the original one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' As  shown in Table 8, reducing the learning rate can lead to a comparable convergence rate in the early stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  However, it slows down the later stages of training and leads to sub-optimal final accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' The reason is  that it reduces both signal and noise, and therefore does not improve the signal-to-noise ratio or speed up  the sparse training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  The motivation of γ is to avoid introducing large variance due to error in approximating ct and bias due to  the adversarial training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' The true correlation depends on many factors such as the dataset, architecture, and  sparsity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In some cases, it can be greater or smaller than 10%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' For the value of γ, it is a hyperparameter and  we can choose different values for different settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In our case, for simplicity, we choose γ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1 for all the  settings, and find that it works well and accelerates the convergence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' If we tune the value of γ for different  settings according to their corresponding correlations, it is possible to obtain faster convergence rates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Table 8: Testing accuracy (%) of SET-ITOP-based models for AGENT (ours) and "Reduce LR".' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Sparse  VGG-C and ResNet-34 are learned in standard setups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Epoch  20  80  130  180  240  Reduce LR (VGG-C, SET-ITOP)  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='3  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5  AGENT (VGG-C, SET-ITOP)  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5  87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6  87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1  88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6  Reduce LR (ResNet-34, SET-ITOP)  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='9  89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='3  89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5  89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='8  AGENT (ResNet-34, SET-ITOP)  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6  92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='0  92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='3  92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='10  Comparison with Momentum-based Methods  The momentum-based approach works well in general, but it still suffers from optimization difficulties due to  sparsity constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' For example, in our baseline SGD, following the original code base, we have also added  momentum to the optimizer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' However, as shown in the pink curves in Figure 2, it still has training instability  and convergence problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' The reason is that they do not take into account the sparse and adversarial  training characteristics and cannot provide an adaptive balance between old and new information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  37  Our method AGENT is designed for sparse and adversarial training and can establish a finer control over  how much information we should get from the old to help the new.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' To demonstrate the importance of this  fine-grained adaptive balance, we do ablation studies in Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In "Fixed ct", we set ct = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1 and test  the convergence rate without the adaptive control.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' We find that the adaptive balance (ours) outperforms  "Fixed ct" in almost all cases, especially in adversarial training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' For standard training, "Fix ct" provides  similar convergence rates to our method, while ours tends to have better final scores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  C  Additional Details about Experiment Settings  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1  Gradient Variance and Correlation Calculation  We calculate the gradient variance and correlation of the ResNet-50 on CIFAR-100 from RigL (Evci et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=',  2020) and SET (Mocanu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2018) at different sparsities including 0%, 50%, 80%, 90%, and 95%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' The  calculation is based on the checkpoints from Sundar & Dwaraknath (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Gradient variance: We first load fully trained checkpoints for the 0%, 50%, 80%, 90%, and 95% sparse  models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Then, to see the gradient variance around the converged optimum, we add small perturbations to  the weights and compute the mean of the gradient variance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' For each checkpoint, we do three replicates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Gradient correlation: We begin with fully-trained checkpoints at 0%, 50%, 80%, 90%, and 95% sparsity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  We calculate and store the gradient of each weight on all training data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Then, we add Gaussian perturbations  to all the weights and calculate the gradients again.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Lastly, we calculate the correlation between the gradient  of the new perturbed weights and the old original weights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' For each checkpoint, we do three replicates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2  Implementations  In BSR-Net-based results, aligned with the choice of Özdenizci & Legenstein (2021), the gradients for  all models are calculated by SGD with momentum and decoupled weight decay (Loshchilov & Hutter, 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  All models are trained for 200 epochs with a batch size of 128.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  In RigL-based results, we follow the settings in Evci et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' (2020);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Sundar & Dwaraknath (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' We  train all the models for 250 epochs with a batch size of 128, and parameters are optimized by SGD with  momentum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  In ITOP-based results, we follow the settings in Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' For CIFAR-10 and CIFAR-100, we  train all the models for 250 epochs with a batch size of 128.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' For ImageNet-2012, we train all the models for  100 epochs with a batch size of 64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Parameters are optimized by SGD with momentum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='3  Learning Rate  Aligned with popular sparse training methods (Evci et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Özdenizci & Legenstein, 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=',  2021), we choose piecewise constant decay schedulers for learning rate and weight decay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In our A-BSR-Net,  we use the 50th and 100th epochs as the dividing points of our learning rate decay scheduler.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' The reason  is that our approach has faster convergence and doesn’t require a long warm-up period.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In the evaluation  shown in the manuscript, we also use this scheduler for BSR-Net for a more accurate and fair comparison.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='4  Initialization (BSR-Net-based results)  Consistent with Özdenizci & Legenstein (2021), we also choose Kaiming initialization to initialize the network  weights He et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' (2015)  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='5  Benchmark Datasets (BSR-Net-based results)  For a fair comparison, we choose the same benchmark datasets as Özdenizci & Legenstein (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Specifically,  we use CIFAR-10 and CIFAR-100 Krizhevsky et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' (2009) and SVHN Netzer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' (2011) in our experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  38  Both CIFAR-10 and CIFAR-100 datasets include 50, 000 training and 10, 000 test images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' SVHN dataset  includes 73, 257 training and 26, 032 test samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='6  Data Augmentation  We follow a popular data augmentation method used in Özdenizci & Legenstein (2021);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' He et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In  particular, we randomly shift the images to the left or right, crop them back to their original size, and flip  them in the horizontal direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' In addition, all the pixel values are normalized in the range of [0, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  D  Sparse Training Method Description  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1  Bayesian Sparse Robust Training  Bayesian Sparse Robust Training (BSR-Net) Özdenizci & Legenstein (2021) is a Bayesian Sparse and Robust  training pipeline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Based on a Bayesian posterior sampling principle, a network rewiring process simultane-  ously learns the sparse connectivity structure and the robustness-accuracy trade-off based on the adversarial  learning objective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' More specifically, regarding its mask update, it prunes all negative weights and grows  new weights randomly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  E  Limitations of Our Adaptive Gradient Correction Method  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1  Extra FLOPs  Similar to SVRG, our ADSVRG increases the training FLOPs in each iteration due to the extra forward  and backward used to compute the old gradients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  However, the true computation difference can be smaller and the GPU-based runining time of SVRG will not  be affected that much.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' For example, in the adversarial setting, we need additional computations to generate  the adversarial samples, which is time-consuming and only needs to be done once in each iteration of our  AVR and SGD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' For BSR-Net, we empirically find that the ratio of time required for each iteration of our  AVR and SGD is about 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  There are also several methods to reduce the extra computation caused by SVRG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' The first approach is  to use the sparse gradients proposed by M Elibol (2020) Elibol et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' It can effectively reduce the  computational cost of SVRG and can be easily applied to our method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' The second approach is suggested  by Allen-Zhu and Hazan (2016) Allen-Zhu & Hazan (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' The extra cost on computing batch gradient on  old model parameters is totally parallelizable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Thus, we can view SVRG as doubling the mini-batch size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  Third, we can follow the idea of SAGA Defazio et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' (2014) and store gradients for individual samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' By  this way, we do not need the extra forward and backward step and save the computation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' But it requires  extra memory to store the gradients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  In the main manuscript, we choose to compare the convergence speed of our ADSVRG and SGD for the  same number of pass data (epoch), which is widely used as a criterion to compare SVRG-based optimization  and SGD (Allen-Zhu & Hazan, 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Chatterji et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Zou et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=', 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' Cutkosky & Orabona, 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' A  comparison in this way in this way can demonstrate the accelerating effect of the optimization method and  provide inspiration for future work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='2  Scaling parameter tuning  In our adaptive variance reduction method (AVR), we add an additional scaling parameter γ which need to  be adjusted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' We find that setting γ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='1 is a good choice for BSR-Net, RigL, and ITOP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' However, it can  be different for other different sparse training pipelines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  39  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='3  Robust Accuracy Degradation  For the final accuracy results of BSR-Net-based models, there is a small decrease in the robustness accuracy  after using our AVR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content=' It is still an open question how to further improve the robust accuracy when using  adaptive variance reduction in sparse and adversarial training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
+page_content='  40' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FtE1T4oBgHgl3EQf-waO/content/2301.03573v1.pdf'}
diff --git a/GNAzT4oBgHgl3EQfi_3N/vector_store/index.faiss b/GNAzT4oBgHgl3EQfi_3N/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..4274f75af40cda0f86e58ea4cf64744b489ce056
--- /dev/null
+++ b/GNAzT4oBgHgl3EQfi_3N/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:589220eedb7a6d99990fe7a7cd08d203545b818d8a9d124332c506bb2f9e801c
+size 3932205
diff --git a/GdAyT4oBgHgl3EQffPg-/content/tmp_files/2301.00335v1.pdf.txt b/GdAyT4oBgHgl3EQffPg-/content/tmp_files/2301.00335v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..214c27e1a64899d906a09c36cf07386e0cf14130
--- /dev/null
+++ b/GdAyT4oBgHgl3EQffPg-/content/tmp_files/2301.00335v1.pdf.txt
@@ -0,0 +1,4917 @@
+Theoretical Characterization of How Neural Network
+Pruning Affects its Generalization
+Hongru Yang ∗
+Yingbin Liang †
+Xiaojie Guo‡
+Lingfei Wu§
+Zhangyang Wang ¶
+Abstract
+It has been observed in practice that applying pruning-at-initialization methods to neural
+networks and training the sparsified networks can not only retain the testing performance of the
+original dense models, but also sometimes even slightly boost the generalization performance.
+Theoretical understanding for such experimental observations are yet to be developed. This
+work makes the first attempt to study how different pruning fractions affect the model’s gradient
+descent dynamics and generalization. Specifically, this work considers a classification task for
+overparameterized two-layer neural networks, where the network is randomly pruned according
+to different rates at the initialization. It is shown that as long as the pruning fraction is below
+a certain threshold, gradient descent can drive the training loss toward zero and the network
+exhibits good generalization performance.
+More surprisingly, the generalization bound gets
+better as the pruning fraction gets larger. To complement this positive result, this work further
+shows a negative result: there exists a large pruning fraction such that while gradient descent
+is still able to drive the training loss toward zero (by memorizing noise), the generalization
+performance is no better than random guessing. This further suggests that pruning can change
+the feature learning process, which leads to the performance drop of the pruned neural network.
+Up to our knowledge, this is the first generalization result for pruned neural networks, suggesting
+that pruning can improve the neural network’s generalization.
+1
+Introduction
+Neural network pruning can be dated back to the early stage of the development of neural networks
+(LeCun et al., 1989). Since then, many research works have been focusing on using neural network
+pruning as a model compression technique, e.g. (Molchanov et al., 2019; Luo and Wu, 2017; Ye
+et al., 2020; Yang et al., 2021). However, all these work focused on pruning neural networks after
+training to reduce inference time, and, thus, the efficiency gain from pruning cannot be directly
+transferred to the training phase. It is not until the recent days that Frankle and Carbin (2018)
+showed a surprising phenomenon: a neural network pruned at the initialization can be trained to
+achieve competitive performance to the dense model. They called this phenomenon the lottery
+ticket hypothesis. The lottery ticket hypothesis states that there exists a sparse subnetwork inside
+∗Department of Computer Science, The University of Texas at Austin; e-mail: hy6385@utexas.edu
+†Department of Electrical and Computer Engineering, The Ohio State University; e-mail: liang.889@osu.edu
+‡IBM Thomas.J. Watson Research Center; e-mail: xguo7@gmu.edu
+§Pinterest; e-mail: lwu@email.wm.edu
+¶Department
+of
+Electrical
+and
+Computer
+Engineering,
+The
+University
+of
+Texas
+at
+Austin;
+e-mail:
+atlaswang@utexas.edu
+1
+arXiv:2301.00335v1  [cs.LG]  1 Jan 2023
+
+a dense network at the random initialization stage such that when trained in isolation, it can
+match the test accuracy of the original dense network after training for at most the same number
+of iterations. On the other hand, the algorithm Frankle and Carbin (2018) proposed to find the
+lottery ticket requires many rounds of pruning and retraining which is computationally expensive.
+Many subsequent works focused on developing new methods to reduce the cost of finding such a
+network at the initialization (Lee et al., 2018; Wang et al., 2019; Tanaka et al., 2020; Liu and Zenke,
+2020; Chen et al., 2021a). A further investigation by Frankle et al. (2020) showed that some of
+these methods merely discover the layer-wise pruning ratio instead of sparsity pattern.
+The discovery of the lottery ticket hypothesis sparkled further interest in understanding this
+phenomenon. Another line of research focused on finding a subnetwork inside a dense network
+at the random initialization such that the subnetwork can achieve good performance (Zhou et al.,
+2019; Ramanujan et al., 2020). Shortly after that, Malach et al. (2020) formalized this phenomenon
+which they called the strong lottery ticket hypothesis: under certain assumption on the weight ini-
+tialization distribution, a sufficiently overparameterized neural network at the initialization contains
+a subnetwork with roughly the same accuracy as the target network. Later, Pensia et al. (2020)
+improved the overparameterization parameters and Sreenivasan et al. (2021) showed that such a
+type of result holds even if the weight is binary. Unsurprisingly, as it was pointed out by Malach
+et al. (2020), finding such a subnetwork is computationally hard. Nonetheless, all of the analysis is
+from a function approximation perspective and none of the aforementioned works have considered
+the effect of pruning on gradient descent dynamics, let alone the neural networks’ generalization.
+Interestingly, via empirical experiments, people have found that sparsity can further improve
+generalization in certain scenarios (Chen et al., 2021b; Ding et al., 2021; He et al., 2022). There
+have also been empirical works showing that random pruning can be effective (Frankle et al., 2020;
+Su et al., 2020; Liu et al., 2021b). However, theoretical understanding of such benefit of pruning
+of neural networks is still limited. In this work, we take the first step to answer the following
+important open question from a theoretical perspective:
+How does pruning fraction affect the training dynamics and the model’s generalization,
+if the model is pruned at the initialization and trained by gradient descent?
+We study this question using random pruning. We consider a classification task where the input
+data consists of class-dependent sparse signal and random noise. We analyze the training dynamics
+of a two-layer convolutional neural network pruned at the initialization. Specifically, this work
+makes the following contributions:
+• Mild pruning. We prove that there indeed exists a range of pruning fraction where the
+pruning fraction is small and the generalization error bound gets better as pruning fraction
+gets larger. In this case, the signal in the feature is well-preserved and due to the effect of
+pruning purifying the feature, the effect from noise is reduced. We provide detailed explana-
+tion in Section 3. Up to our knowledge, this is the first theoretical result on generalization for
+pruned neural networks, which suggests that pruning can improve generalization under some
+setting. Further, we conduct experiments to verify our results.
+• Over pruning. To complement the above positive result, we also show a negative result: if
+the pruning fraction is larger than a certain threshold, then the generalization performance
+is no better than a simple random guessing, although gradient descent is still able to drive
+the training loss toward zero. This further suggests that the performance drop of the pruned
+2
+
+Probability Density
+Signal Strength
+μ
+Mild Pruning
+Full model
+Over Pruning
+Figure 1: A pictorial demonstration of our results. The bell-shaped curves model the distribution of
+the signal in the features, where the mean represents the signal strength and the width of the curve
+indicates the variance of noise. Our results show that mild pruning preserves the signal strength
+and reduces the noise variance (and hence yields better generalization), whereas over pruning lowers
+signal strength albeit reducing noise variance.
+neural network is not solely caused by the pruned network’s own lack of trainability or ex-
+pressiveness, but also by the change of gradient descent dynamics due to pruning.
+• Technically, we develop novel analysis to bound pruning effect to weight-noise and weight-
+signal correlation.
+Further, in contrast to many previous works that considered only the
+binary case, our analysis handles multi-class classification with general cross-entropy loss.
+Here, a key technical development is a gradient upper bound for multi-class cross-entropy
+loss, which might be of independent interest.
+Pictorially, our result is summarized in Figure 1. We point out that the neural network training we
+consider is in the feature learning regime, where the weight parameters can go far away from their
+initialization. This is fundamentally different from the popular neural tangent kernel regime,
+where the neural networks essentially behave similar to its linearization.
+1.1
+Related Works
+The Lottery Ticket Hypothesis and Sparse Training. The discovery of the lottery ticket
+hypothesis (Frankle and Carbin, 2018) has inspired further investigation and applications. One line
+of research has focused on developing computationally efficient methods to enable sparse training:
+the static sparse training methods are aiming at identifying a sparse mask at the initialization stage
+based on different criterion such as SNIP (loss-based) (Lee et al., 2018), GraSP (gradient-based)
+(Wang et al., 2019), SynFlow (synaptic strength-based) (Tanaka et al., 2020), neural tangent kernel
+based method (Liu and Zenke, 2020) and one-shot pruning (Chen et al., 2021a). Random pruning
+has also been considered in static sparse training such as uniform pruning (Mariet and Sra, 2015;
+He et al., 2017; Gale et al., 2019; Suau et al., 2018), non-uniform pruning (Mocanu et al., 2016),
+expander-graph-related techniques (Prabhu et al., 2018; Kepner and Robinett, 2019) Erd¨os-R´enyi
+(Mocanu et al., 2018) and Erd¨os-R´enyi-Kernel (Evci et al., 2020). On the other hand, dynamic
+sparse training allows the sparse mask to be updated (Mocanu et al., 2018; Mostafa and Wang,
+2019; Evci et al., 2020; Jayakumar et al., 2020; Liu et al., 2021c,d,a; Peste et al., 2021). The sparsity
+pattern can also be learned by using sparsity-inducing regularizer (Yang et al., 2020). Recently, He
+et al. (2022) discovered that pruning can exhibit a double descent phenomenon when the data-set
+labels are corrupted.
+Another line of research has focused on studying pruning the neural networks at its random
+initialization to achieve good performance (Zhou et al., 2019; Ramanujan et al., 2020). In particular,
+3
+
+Ramanujan et al. (2020) showed that it is possible to prune a randomly initialized wide ResNet-50
+to match the performance of a ResNet-34 trained on ImageNet. This phenomenon is named the
+strong lottery ticket hypothesis. Later, Malach et al. (2020) proved that under certain assumption
+on the initialization distribution, a target network of width d and depth l can be approximated by
+pruning a randomly initialized network that is of a polynomial factor (in d, l) wider and twice deeper
+even without any further training. However finding such a network is computationally hard, which
+can be shown by reducing the pruning problem to optimizing a neural network. Later, Pensia et al.
+(2020) improved the widening factor to being logarithmic and Sreenivasan et al. (2021) proved that
+with a polylogarithmic widening factor, such a result holds even if the network weight is binary. A
+follow-up work shows that it is possible to find a subnetwork achieving good performance at the
+initialization and then fine-tune (Sreenivasan et al., 2022). Our work, on the other hand, analyzes
+the gradient descent dynamics of a pruned neural network and its generalization after training.
+Analyses of Training Neural Networks by Gradient Descent. A series of work (Allen-
+Zhu et al., 2019; Du et al., 2019; Lee et al., 2019; Zou et al., 2020; Zou and Gu, 2019; Ji and
+Telgarsky, 2019; Chen et al., 2020b; Song and Yang, 2019; Oymak and Soltanolkotabi, 2020) has
+proved that if a deep neural network is wide enough, then (stochastic) gradient descent provably can
+drive the training loss toward zero in a fast rate based on neural tangent kernel (NTK) (Jacot et al.,
+2018). Further, under certain assumption on the data, the learned network is able to generalize
+(Cao and Gu, 2019; Arora et al., 2019). However, as it is pointed out by Chizat et al. (2019), in the
+NTK regime, the gradient descent dynamics of the neural network essentially behaves similarly to
+its linearization and the learned weight is not far away from the initialization, which prohibits the
+network from performing any useful feature learning. In order to go beyond NTK regime, one line
+of research has focused on the mean field limit (Song et al., 2018; Chizat and Bach, 2018; Rotskoff
+and Vanden-Eijnden, 2018; Wei et al., 2019; Chen et al., 2020a; Sirignano and Spiliopoulos, 2020;
+Fang et al., 2021). Recently, people have started to study the neural network training dynamics in
+the feature learning regime where data from different class is defined by a set of class-related signals
+which are low rank (Allen-Zhu and Li, 2020, 2022; Cao et al., 2022; Shi et al., 2021; Telgarsky,
+2022). However, all previous works did not consider the effect of pruning. Our work also focuses
+on the aforementioned feature learning regime, but for the first time characterizes the impact of
+pruning on the generalization performance of neural networks.
+2
+Preliminaries and Problem Formulation
+In this section, we introduce our notation, data generation process, neural network architecture
+and the optimization algorithm.
+Notations. We use lower case letters to denote scalars and boldface letters and symbols (e.g.
+x) to denote vectors and matrices. We use ⊙ to denote element-wise product. For an integer n, we
+use [n] to denote the set of integers {1, 2, . . . , n}. We use x = O(y), x = Ω(y), x = Θ(y) to denote
+that there exists a constant C such that x ≤ Cy, x ≥ Cy, x = Cy respectively. We use �O, �Ω and
+�Θ to hide polylogarithmic factor in these notations.
+Finally, we use x = poly(y) if x = O(yC) for
+some positive constant C, and x = poly log y if x = poly(log y).
+2.1
+Settings
+Definition 2.1 (Data distribution of K classes). Consider we are given the set of signal vectors
+{µei}K
+i=1, where µ > 0 denotes the strength of the signal, and ei denotes the i-th standard basis
+4
+
+vector with its i-th entry being 1 and all other coordinates being 0. Each data point (x, y) with
+x = [x⊤
+1 , x⊤
+2 ]⊤ ∈ R2d and y ∈ [K] is generated from the following distribution D:
+1. The label y is generated from a uniform distribution over [K].
+2. A noise vector ξ is generated from the Gaussian distribution N(0, σ2
+nI).
+3. With probability 1/2, assign x1 = µy, x2 = ξ; with probability 1/2, assign x2 = µy, x1 = ξ
+where µy = µey.
+The sparse signal model is motivated by the empirical observation that during the process of
+training neural networks, the output of each layer of ReLU is usually sparse instead of dense. This
+is partially due to the fact that in practice the bias term in the linear layer is used (Song et al.,
+2021). For samples from different classes, usually a different set of neurons fire. Our study can be
+seen as a formal analysis on pruning the second last layer of a deep neural network in the layer-
+peeled model as in Zhu et al. (2021); Zhou et al. (2022). We also point out that our assumption on
+the sparsity of the signal is necessary for our analysis. If we don’t have this sparsity assumption
+and only make assumption on the ℓ2 norm of the signal, then in the extreme case, the signal is
+uniformly distributed across all coordinate and the effect of pruning to the signal and the noise will
+be essentially the same: their ℓ2 norm will both be reduced by a factor of √p.
+Network architecture and random pruning. We consider a two-layer convolutional neural
+network model with polynomial ReLU activation σ(z) = (max{0, z})q, where we focus on the case
+when q = 3 1 The network is pruned at the initialization by mask M where each entry in the mask
+M is generated i.i.d. from Bernoulli(p). Let mj,r denotes the r-th row of Mj. Given the data (x, y),
+the output of the neural network can be written as F(W ⊙ M, x) = (F1(W1 ⊙ M1, x), F2(W2 ⊙
+M2, x), . . . , Fk(Wk ⊙ Mk, x)) where the j-th output is given by
+Fj(Wj ⊙ Mj, x) =
+m
+�
+r=1
+[σ(⟨wj,r ⊙ mj,r, x1⟩) + σ(⟨wj,r ⊙ mj,r, x2⟩)]
+=
+m
+�
+r=1
+[σ(⟨wj,r ⊙ mj,r, µ⟩) + σ(⟨wj,r ⊙ mj,r, ξ⟩)].
+The mask M is only sampled once at the initialization and remains fixed through the entire training
+process. From now on, we use tilde over a symbol to denote its masked version, e.g.,
+�
+W = W ⊙ M and �wj,r = wj,r ⊙ mj,r.
+Since µj ⊙ mj,r = 0 with probability 1 − p, some neurons will not receive the corresponding
+signal at all and will only learn noise. Therefore, for each class j ∈ [k], we split the neurons into
+two sets based on whether it receives its corresponding signal or not:
+Sj
+signal = {r ∈ [m] : µj ⊙ mj,r ̸= 0},
+Sj
+noise = {r ∈ [m] : µj ⊙ mj,r = 0}.
+Gradient descent algorithm. We consider the network is trained by cross-entropy loss with
+softmax. We denote by logiti(F, x) :=
+eFi(x)
+�
+j∈[k] eFj(x) and the cross-entropy loss can be written as
+1We point out that as many previous works (Allen-Zhu and Li, 2020; Zou et al., 2021; Cao et al., 2022), polynomial
+ReLU activation can help us simplify the analysis of gradient descent, because polynomial ReLU activation can give
+a much larger separation of signal and noise (thus, cleaner analysis) than ReLU. Our analysis can be generalized to
+ReLU activation by using the arguments in (Allen-Zhu and Li, 2022).
+5
+
+ℓ(F(x, y)) = − log logity(F, x). The convolutional neural network is trained by minimizing the
+empirical cross-entropy loss given by
+LS(W) = 1
+n
+n
+�
+i=1
+ℓ[F(W ⊙ M; xi, yi)] = E
+S ℓ[F(W ⊙ M; xi, yi)],
+where S = {(xi, yi)}n
+i=1 is the training data set. Similarly, we define the generalization loss as
+LD := E
+(x,y)[ℓ(F(W ⊙ M; x, y))].
+The model weights are initialized from a i.i.d. Gaussian N(0, σ2
+0). The gradient of the cross-entropy
+loss is given by ℓ′
+j,i := ℓ′
+j(xi, yi) = logitj(F, xi) − I(j = yi). Since
+∇wj,rLS(W ⊙ M) = ∇wj,r⊙mj,rLS(W ⊙ M) ⊙ mj,r = ∇ �wj,rLS(�
+W) ⊙ mj,r,
+we can write the full-batch gradient descent update of the weights as
+�w(t+1)
+j,r
+= �w(t)
+j,r − η∇ �wj,rLS(�
+W) ⊙ mj,r
+= �w(t)
+j,r − η
+n
+n
+�
+i=1
+ℓ′(t)
+j,i · σ′ ��
+�w(t)
+j,r, ξi
+��
+· �ξj,r,i − η
+n
+n
+�
+i=1
+ℓ′(t)
+j,i σ′ ��
+�w(t)
+j,r, µyi
+��
+µyi ⊙ mj,r,
+for j ∈ [K] and r ∈ [m], where �ξj,r,i = ξi ⊙ mj,r.
+Condition 2.2. We consider the parameter regime described as follows: (1) Number of classes
+K = O(log d). (2) Total number of training samples n = poly log d. (3) Dimension d ≥ Cd for
+some sufficiently large constant Cd. (4) Relationship between signal strength and noise strength:
+µ = Θ(σn
+√
+d log d) = Θ(1). (5) The number of neurons in the network m = Ω(poly log d). (6)
+Initialization variance: σ0 = �Θ(m−4n−1µ−1). (7) Learning rate: Ω(1/ poly(d)) ≤ η ≤ �O(1/µ2).
+(8) Target training loss: ϵ = Θ(1/ poly(d)).
+Conditions (1) and (2) ensure that there are enough samples in each class with high probability.
+Condition (3) ensures that our setting is in high-dimensional regime. Condition (4) ensures that
+the full model can be trained to exhibit good generalization. Condition (5), (6) and (7) ensures that
+the neural network is sufficiently overparameterized and can be optimized efficiently by gradient
+descent. Condition (7) and (8) further ensures that training time is polynomial in d. We further
+discuss the practical consideration of η and ϵ to justify their condition in Remark D.9.
+3
+Mild Pruning
+3.1
+Main result
+The first main result shows that there exists a threshold on the pruning fraction p such that pruning
+helps the neural network’s generalization.
+Theorem 3.1 (Main Theorem for Mild Pruning, Informal). Under Condition 2.2, if p ∈ [C1
+log d
+m , 1]
+for some constant C1, then with probability at least 1 − O(d−1) over the randomness in the data,
+network initialization and pruning, there exists T = �O(Kη−1σ2−q
+0
+µ−q +K2m4µ−2η−1ϵ−1) such that
+6
+
+1. The training loss is below ϵ: LS(�
+W(T)) ≤ ϵ.
+2. The generalization loss can be bounded by LD(�
+W(T)) ≤ O(Kϵ) + exp(−n2/p).
+Theorem 3.1 indicates that there exists a threshold in the order of Θ(log d
+m ) such that if p is
+above this threshold (i.e., the fraction of the pruned weights is small), gradient descent is able to
+drive the training loss towards zero (as item 1 claims) and the overparameterized network achieves
+good testing performance (as item 2 claims). In the next subsection, we explain why pruning can
+help generalization via an outline of our proof, and we defer all the detailed proofs in Appendix D.
+3.2
+Proof Outline
+Our proof contains the establishment of the following two properties:
+• First we show that after mild pruning the network is still able to learn the signal, and the
+magnitude of the signal in the feature is preserved.
+• Then we show that given a new sample, pruning reduces the noise effect in the feature which
+leads to the improvement of generalization.
+We first show the above properties for three stages of gradient descent: initialization, feature
+growing phase, and converging phase, and then establish the generalization property.
+Initialization. First of all, readers might wonder why pruning can even preserve signal at all.
+Intuitively, a network will achieve good performance if its weights are highly correlated with the
+signal (i.e., their inner product is large). Two intuitive but misleading heuristics are given by the
+following:
+• Consider a fixed neuron weight.
+At the random initialization, in expectation, the signal
+correlation with the weights is given by Ew,m[| ⟨w ⊙ m, µ⟩ |] ≤ pσ0µ and the noise correlation
+with the weights is given by Ew,m,ξ[| ⟨w ⊙ m, ξ⟩ |] ≤
+�
+Ew,m,ξ[⟨w ⊙ m, ξ⟩2] = σ0σn
+√pd by
+Jensen’s inequality. Based on this argument, taking a sum over all the neurons, pruning will
+hurt weight-signal correlation more than weight-noise correlation.
+• Since we are pruning with Bernoulli(p), a given neuron will not receive signal at all with
+probability 1 − p. Thus, there is roughly p fraction of the neurons receiving the signal and
+the rest 1 − p fraction will be purely learning from noise. Even though for every neuron,
+roughly √p portion of ℓ2 mass from the noise is reduced, at the same time, pruning also
+creates 1 − p fraction of neurons which do not receive signals at all and will purely output
+noise after training. Summing up the contributions from every neuron, the signal strength
+is reduced by a factor of p while the noise strength is reduced by a factor of √p. We again
+reach the conclusion of pruning under any rate will hurt the signal more than noise.
+The above analysis shows that under any pruning rate, it seems pruning can only hurt the signal
+more than noise at the initialization. Such analysis would be indicative if the network training is
+under the neural tangent kernel regime, where the weight of each neuron does not travel far from its
+initialization so that the above analysis can still hold approximately after training. However, when
+the neural network training is in the feature learning regime, this average type analysis becomes
+misleading. Namely, in such a regime, the weights with large correlation with the signal at the
+initialization will quickly evolve into singleton neurons and those weights with small correlation
+7
+
+will remain small. In our proof, we focus on the featuring learning regime, and analyze how the
+network weights change and what are the effect of pruning during various stages of gradient descent.
+We now analyze the effect of pruning on weight-signal correlation and weight-noise correlation at
+the initialization. Our first lemma leverages the sparsity of our signal and shows that if the pruning
+is mild, then it will not hurt the maximum weight-signal correlation much at the initialization. On
+the other hand, the maximum weight-noise correlation is reduced by a factor of √p.
+Lemma 3.2 (Initialization). With probability at least 1 − 2/d, for all i ∈ [n],
+σ0σn
+�
+pd ≤ max
+r
+�
+�w(0)
+j,r , ξi
+�
+≤
+�
+2 log(Kmd)σ0σn
+�
+pd.
+Further, suppose pm ≥ Ω(log(Kd)), with probability 1 − 2/d, for all j ∈ [K],
+σ0 ∥µj∥2 ≤
+max
+r∈Sj
+signal
+�
+�w(0)
+j,r , µj
+�
+≤
+�
+2 log(8pmKd)σ0 ∥µj∥2 .
+Given this lemma, we now prove that there exists at least one neuron that is heavily aligned
+with the signal after training. Similarly to previous works (Allen-Zhu and Li, 2020; Zou et al., 2021;
+Cao et al., 2022), the analysis is divided into two phases: feature growing phase and converging
+phase.
+Feature Growing Phase. In this phase, the gradient of the cross-entropy is large and the
+weight-signal correlation grows much more quickly than weight-noise correlation thanks to the
+polynomial ReLU. We show that the signal strength is relatively unaffected by pruning while the
+noise level is reduced by a factor of √p.
+Lemma 3.3 (Feature Growing Phase, Informal). Under Condition 2.2, there exists time T1 such
+that
+1. The max weight-signal correlation is large: maxr
+�
+�w(T1)
+j,r , µj
+�
+≥ m−1/q for j ∈ [K].
+2. The weight-noise and cross-class weight-signal correlations are small: if j ̸= yi, then maxj,r,i
+���
+�
+�w(T1)
+j,r , ξi
+���� ≤
+O(σ0σn
+√pd) and maxj,r,k
+���
+�
+�w(T1)
+j,r , µk
+���� ≤ �O(σ0µ).
+Converging Phase. We show that gradient descent can drive the training loss toward zero
+while the signal in the feature is still large. An important intermediate step in our argument is
+the development of the following gradient upper bound for multi-class cross-entropy loss which
+introduces an extra factor of K in the gradient upper bound.
+Lemma 3.4 (Gradient Upper Bound, Informal). Under Condition 2.2, we have
+���∇LS(�
+W(t)) ⊙ M
+���
+2
+F ≤ O(Km2/qµ2)LS(�
+W(t)).
+Proof Sketch. To prove this upper bound, note that for a given input (xi, yi), ℓ′(t)
+yi,i∇Fyi(xi) should
+make major contribution to
+���∇ℓ(�
+W; xi, yi)
+���
+F .
+Further note that |ℓ′(t)
+yi,i| = 1 − logityi(F; xi) =
+�
+j̸=yi eFj(xi)
+�
+j eFj(xi)
+≤
+�
+j̸=yi eFj(xi)
+eFyi (xi)
+. Now, apply the property that Fj(xi) is small for j ̸= yi (which we
+prove in the appendix), the numerator will contribute a factor of K. To bound the rest, we utilize
+8
+
+the special property of multi-class cross-entropy loss: |ℓ′(t)
+j,i | ≤ |ℓ′(t)
+yi,i| ≤ ℓ(t)
+i .
+However, a naive
+application of this inequality will result in a factor of K3 instead K in our bound. The trick is to
+further use the fact that �
+j̸=yi |ℓ′(t)
+j,i | = |ℓ′(t)
+yi,i|.
+Using the above gradient upper bound, we can show that the objective can be minimized.
+Lemma 3.5 (Converging Phase, Informal). Under Condition 2.2, there exists T2 such that for
+some time t ∈ [T1, T2] we have
+1. The results from the feature growing phase (Lemma 3.3) hold up to constant factors.
+2. The training loss is small LS(�
+W(t)) ≤ ϵ.
+Notice that the weight-noise correlation still remains reduced by a factor of √p after training.
+Lemma 3.5 proves the statement of the training loss in Theorem 3.1.
+Generalization Analysis. Finally, we show that pruning can purify the feature by reducing
+the variance of the noise by a factor of p when a new sample is given. The lemma below shows that
+the variance of weight-noise correlation for the trained weights is reduced by a factor of p.
+Lemma 3.6. The neural network weight �
+W⋆ after training satisfies that
+P
+ξ
+�
+max
+j,r
+����w⋆
+j,r, ξ
+��� ≥ (2m)−2/q
+�
+≤ 2Km exp
+�
+− (2m)−4/q
+O(σ2
+0σ2npd)
+�
+.
+Using this lemma, we can show that pruning yields better generalization bound (i.e., the bound
+on the generalization loss) claimed in Theorem 3.1.
+4
+Over Pruning
+Our second result shows that there exists a relatively large pruning fraction (i.e., small p) such that
+the learned model yields poor generalization, although gradient descent is still able to drive the
+training error toward zero. The full proof is defered to Appendix E.
+Theorem 4.1 (Main Theorem for Over Pruning, Informal). Under Condition 2.2 if p = Θ(
+1
+Km log d),
+then with probability at least 1−1/ poly log d over the randomness in the data, network initialization
+and pruning, there exists T = O(η−1nσq−2
+0
+σ−q
+n (pd)−q/2 + η−1ϵ−1m4nσ−2
+n (pd)−1) such that
+1. The training loss is below ϵ: LS(�
+W(T)) ≤ ϵ.
+2. The generalization loss is large: LD(�
+W(T)) ≥ Ω(log K).
+Remark 4.2. The above theorem indicates that in the over-pruning case, the training loss can still
+go to zero. However, the generalization loss of our neural network behaves no much better than
+random guessing, because given any sample, random guessing will assign each class with probability
+1/K, which yields a generalization loss of log K. The readers might wonder why the condition for
+this to happen is p = Θ(
+1
+Km log d) instead of O(
+1
+Km log d). Indeed, the generalization will still be bad
+if p is too small. However, now the neural network is not only unable to learn the signal but also
+cannot efficiently memorize the noise via gradient descent.
+Proof Outline. Now we analyze the over-pruning case. We first show that there is a good chance
+that the model will not receive any signal after pruning due to the sparse signal assumption and
+mild overparameterization of the neural network. Then, leveraging such a property, we bound the
+9
+
+weight-signal and weight-noise properties for the feature growing and converging phases of gradient
+descent, as stated in the following two lemmas, respectively. Our result indicates that the training
+loss can still be driven toward zero by letting the neural network memorize the noise, the proof of
+which further exploits the fact that high dimensional Gaussian noise are nearly orthogonal.
+Lemma 4.3 (Feature Growing Phase, Informal). Under Condition 2.2, there exists T1 such that
+• Some weights has large correlation with noise: maxr
+�
+�w(T1)
+yi,r , ξi
+�
+≥ m−1/q for all i ∈ [n].
+• The cross-class weight-noise and weight-signal correlations are small: if j ̸= yi, then maxj,r,i
+���
+�
+�w(T1)
+j,r , ξi
+���� =
+�O(σ0σn
+√pd) and maxj,r,k
+���
+�
+�w(T1)
+j,r , µk
+���� ≤ �O(σ0µ).
+Lemma 4.4 (Converging Phase, Informal). Under Condition 2.2, there exists a time T2 such that
+∃t ∈ [T1, T2], the results from phase 1 still holds (up to constant factors) and LS(�
+W(t)) ≤ ϵ.
+Finally, since the above lemmas show that the network is purely memorizing the noise, we
+further show that such a network yields poor generalization performance as stated in Theorem
+4.1.
+5
+Experiments
+5.1
+Simulations to Verify Our Results
+In this section, we conduct simulations to verify our results. We conduct our experiment using
+binary classification task and show that our result holds for ReLU networks.
+Our experiment
+settings are the follows: we choose input to be x = [x1, x2] = [ye1, ξ] ∈ R800 and x1, x2 ∈ R400,
+where ξi is sampled from a Gaussian distribution. The class labels y are {±1}. We use 100 training
+examples and 100 testing examples. The network has width 150 and is initialized with random
+Gaussian distribution with variance 0.01. Then, p fraction of the weights are randomly pruned.
+We use the learning rate of 0.001 and train the network over 1000 iterations by gradient descent.
+The observations are summarized as follows. In Figure 2a, when the noise level is σn = 0.5,
+the pruned network usually can perform at the similar level with the full model when p ≤ 0.5
+and noticably better when p = 0.3. When p > 0.5, the test error increases dramatically while
+the training accuracy still remains perfect. On the other hand, when the noise level becomes large
+σn = 1 (Figure 2b), the full model can no longer achieve good testing performance but mild pruning
+can improve the model’s generalization. Note that the training accuracy in this case is still perfect
+(omitted in the figure). We observe that in both settings when the model test error is large, the
+variance is also large. However, in Figure 2b, despite the large variance, the mean curve is already
+smooth. In particular, Figure 2c plots the testing error over the training iterations under p = 0.5
+pruning rate. This suggests that pruning can be beneficial even when the input noise is large.
+5.2
+On the Real World Dataset
+To further demonstrate the mild/over pruning phenomenon, we conduct experiments on MNIST
+(Deng, 2012) and CIFAR-10 (Krizhevsky et al., 2009) datasets. We consider neural network ar-
+chitectures including MLP with 2 hidden layers of width 1024, VGG, ResNets (He et al., 2016)
+and wide ResNet (Zagoruyko and Komodakis, 2016). In addition to random pruning, we also add
+10
+
+0.0
+0.2
+0.4
+0.6
+0.8
+Pruning rates
+0.00
+0.05
+0.10
+0.15
+0.20
+Error
+Training/Testing Error over Pruning Rates
+Testing error
+Training error
+(a)
+0.0
+0.2
+0.4
+0.6
+0.8
+Pruning rates
+0.20
+0.22
+0.24
+0.26
+0.28
+0.30
+0.32
+0.34
+Error
+Training/Testing Error over Pruning Rates
+Testing error
+(b)
+0
+200
+400
+600
+800
+1000
+Iterations
+0.20
+0.25
+0.30
+0.35
+0.40
+0.45
+0.50
+Error
+Testing error
+full
+pruned
+(c)
+Figure 2: Figure (a) shows the relationship between pruning rates p and training/testing error
+under noise variance σn = 0.5. Figure (b) shows the relationship between pruning rates p and
+testing error under noise variance σn = 1. The training error is omitted since it stays effectively
+at zero across all pruning rates. Figure (c) shows a particular training curve under pruning rate
+p = 50% and noise variance σn = 1. Each data point is created by taking an average over 10
+independent runs.
+0.0 20.0 36.0 48.8 59.0 67.2 73.8 79.0 83.2 86.6 89.3 91.4 93.1 94.5 95.6 96.5 97.2
+Sparsity
+96.5
+97.0
+97.5
+98.0
+98.5
+99.0
+99.5
+100.0
+Accuracy
+MLP MNIST Accuracy vs Sparsity
+Random (Train)
+Random (Test)
+IMP (Train)
+IMP (Test)
+(a)
+0.0 20.0 36.0 48.8 59.0 67.2 73.8 79.0 83.2 86.6 89.3 91.4 93.1 94.5 95.6 96.5 97.2
+Sparsity
+88
+90
+92
+94
+96
+98
+100
+Accuracy
+VGG-16 CIFAR-10 Accuracy vs Sparsity
+Random (Train)
+Random (Test)
+IMP (Train)
+IMP (Test)
+(b)
+Figure 3: Figure (a) shows the result between pruning rates p and accuracy on MLP-1024-1024
+on MNIST. Figure (b) shows the result on VGG-16 on CIFAR-10. Each data point is created by
+taking an average over 3 independent runs.
+iterative-magnitude-based pruning Frankle and Carbin (2018) into our experiments. Both pruning
+methods are prune-at-initialization methods. Our implementation is based on Chen et al. (2021c).
+Under the real world setting, we do not expect our theorem to hold exactly. Instead, our
+theorem implies that (1) there exists a threshold such that the testing performance is no much
+worse than (or sometimes may slightly better than) its dense counter part; and (2) the training
+error decreases later than the testing error decreases. Our experiments on MLP (Figure 3a) and
+VGG-16 (Figure 3b) show that this is the case: for MLP the test accuracy is steady competitive to
+its dense counterpart when the sparsity is less than 79% and 36% for VGG-16. We further provide
+experiments on ResNet in the appendix for validation of our theoretical results.
+6
+Discussion and Future Direction
+In this work, we provide theory on the generalization performance of pruned neural networks trained
+by gradient descent under different pruning rates. Our results characterize the effect of pruning
+under different pruning rates: in the mild pruning case, the signal in the feature is well-preserved
+11
+
+and the noise level is reduced which leads to improvement in the trained network’s generalization;
+on the other hand, over pruning significantly destroys signal strength despite of reducing noise
+variance. One open problem on this topic still appears challenging. In this paper, we characterize
+two cases of pruning: in mild pruning the signal is preserved and in over pruning the signal is
+completely destroyed.
+However, the transition between these two cases is not well-understood.
+Further, it would be interesting to consider more general data distribution, and understand how
+pruning affects training multi-layer neural networks. We leave these interesting directions as future
+works.
+References
+Allen-Zhu, Z. and Li, Y. (2020). Towards understanding ensemble, knowledge distillation and
+self-distillation in deep learning. arXiv preprint arXiv:2012.09816 .
+Allen-Zhu, Z. and Li, Y. (2022). Feature purification: How adversarial training performs robust
+deep learning. In 2021 IEEE 62nd Annual Symposium on Foundations of Computer Science
+(FOCS). IEEE.
+Allen-Zhu, Z., Li, Y. and Song, Z. (2019). A convergence theory for deep learning via over-
+parameterization. In International Conference on Machine Learning. PMLR.
+Arora, S., Du, S., Hu, W., Li, Z. and Wang, R. (2019). Fine-grained analysis of optimization
+and generalization for overparameterized two-layer neural networks. In International Conference
+on Machine Learning. PMLR.
+Cao, Y., Chen, Z., Belkin, M. and Gu, Q. (2022). Benign overfitting in two-layer convolutional
+neural networks. arXiv preprint arXiv:2202.06526 .
+Cao, Y. and Gu, Q. (2019). Generalization bounds of stochastic gradient descent for wide and
+deep neural networks. Advances in neural information processing systems 32.
+Chen, T., Ji, B., Ding, T., Fang, B., Wang, G., Zhu, Z., Liang, L., Shi, Y., Yi, S. and
+Tu, X. (2021a). Only train once: A one-shot neural network training and pruning framework.
+Advances in Neural Information Processing Systems 34.
+Chen, T., Zhang, Z., Balachandra, S., Ma, H., Wang, Z., Wang, Z. et al. (2021b).
+Sparsity winning twice: Better robust generalization from more efficient training. In International
+Conference on Learning Representations.
+Chen, X., Cheng, Y., Wang, S., Gan, Z., Liu, J. and Wang, Z. (2021c). The elastic lottery
+ticket hypothesis. Github Repository, MIT License .
+Chen, Z., Cao, Y., Gu, Q. and Zhang, T. (2020a). A generalized neural tangent kernel analysis
+for two-layer neural networks. Advances in Neural Information Processing Systems 33 13363–
+13373.
+Chen, Z., Cao, Y., Zou, D. and Gu, Q. (2020b). How much over-parameterization is sufficient
+to learn deep relu networks? In International Conference on Learning Representations.
+12
+
+Chizat, L. and Bach, F. (2018).
+On the global convergence of gradient descent for over-
+parameterized models using optimal transport. Advances in neural information processing sys-
+tems 31.
+Chizat, L., Oyallon, E. and Bach, F. (2019). On lazy training in differentiable programming.
+Advances in Neural Information Processing Systems 32.
+Deng, L. (2012). The mnist database of handwritten digit images for machine learning research
+[best of the web]. IEEE signal processing magazine 29 141–142.
+Ding, S., Chen, T. and Wang, Z. (2021).
+Audio lottery: Speech recognition made ultra-
+lightweight, noise-robust, and transferable. In International Conference on Learning Represen-
+tations.
+Du, S., Lee, J., Li, H., Wang, L. and Zhai, X. (2019). Gradient descent finds global minima of
+deep neural networks. In International conference on machine learning. PMLR.
+Evci, U., Gale, T., Menick, J., Castro, P. S. and Elsen, E. (2020). Rigging the lottery:
+Making all tickets winners. In International Conference on Machine Learning. PMLR.
+Fang, C., Lee, J., Yang, P. and Zhang, T. (2021). Modeling from features: a mean-field frame-
+work for over-parameterized deep neural networks. In Conference on learning theory. PMLR.
+Frankle, J. and Carbin, M. (2018). The lottery ticket hypothesis: Finding sparse, trainable
+neural networks. In International Conference on Learning Representations.
+Frankle, J., Dziugaite, G. K., Roy, D. and Carbin, M. (2020). Pruning neural networks
+at initialization: Why are we missing the mark?
+In International Conference on Learning
+Representations.
+Gale, T., Elsen, E. and Hooker, S. (2019). The state of sparsity in deep neural networks.
+arXiv preprint arXiv:1902.09574 .
+He, K., Zhang, X., Ren, S. and Sun, J. (2016). Deep residual learning for image recognition.
+In Proceedings of the IEEE conference on computer vision and pattern recognition.
+He, Y., Zhang, X. and Sun, J. (2017).
+Channel pruning for accelerating very deep neural
+networks. In Proceedings of the IEEE international conference on computer vision.
+He, Z., Xie, Z., Zhu, Q. and Qin, Z. (2022). Sparse double descent: Where network pruning
+aggravates overfitting. In International Conference on Machine Learning. PMLR.
+Jacot, A., Gabriel, F. and Hongler, C. (2018). Neural tangent kernel: Convergence and
+generalization in neural networks. Advances in neural information processing systems 31.
+Jayakumar, S., Pascanu, R., Rae, J., Osindero, S. and Elsen, E. (2020). Top-kast: Top-k
+always sparse training. Advances in Neural Information Processing Systems 33 20744–20754.
+Ji, Z. and Telgarsky, M. (2019). Polylogarithmic width suffices for gradient descent to achieve
+arbitrarily small test error with shallow relu networks. In International Conference on Learning
+Representations.
+13
+
+Kepner, J. and Robinett, R. (2019). Radix-net: Structured sparse matrices for deep neural
+networks. In 2019 IEEE International Parallel and Distributed Processing Symposium Workshops
+(IPDPSW). IEEE.
+Krizhevsky, A., Hinton, G. et al. (2009). Learning multiple layers of features from tiny images
+.
+LeCun, Y., Denker, J. and Solla, S. (1989).
+Optimal brain damage.
+Advances in neural
+information processing systems 2.
+Lee, J., Xiao, L., Schoenholz, S., Bahri, Y., Novak, R., Sohl-Dickstein, J. and Pen-
+nington, J. (2019). Wide neural networks of any depth evolve as linear models under gradient
+descent. Advances in neural information processing systems 32.
+Lee, N., Ajanthan, T. and Torr, P. (2018).
+Snip: Single-shot network pruning based on
+connection sensitivity. In International Conference on Learning Representations.
+Liu, S., Chen, T., Chen, X., Atashgahi, Z., Yin, L., Kou, H., Shen, L., Pechenizkiy, M.,
+Wang, Z. and Mocanu, D. C. (2021a). Sparse training via boosting pruning plasticity with
+neuroregeneration. Advances in Neural Information Processing Systems 34.
+Liu, S., Chen, T., Chen, X., Shen, L., Mocanu, D. C., Wang, Z. and Pechenizkiy, M.
+(2021b). The unreasonable effectiveness of random pruning: Return of the most naive baseline
+for sparse training. In International Conference on Learning Representations.
+Liu, S., Mocanu, D. C., Matavalam, A. R. R., Pei, Y. and Pechenizkiy, M. (2021c). Sparse
+evolutionary deep learning with over one million artificial neurons on commodity hardware.
+Neural Computing and Applications 33 2589–2604.
+Liu, S., Yin, L., Mocanu, D. C. and Pechenizkiy, M. (2021d). Do we actually need dense over-
+parameterization? in-time over-parameterization in sparse training. In International Conference
+on Machine Learning. PMLR.
+Liu, T. and Zenke, F. (2020). Finding trainable sparse networks through neural tangent transfer.
+In International Conference on Machine Learning. PMLR.
+Luo, J.-H. and Wu, J. (2017). An entropy-based pruning method for cnn compression. arXiv
+preprint arXiv:1706.05791 .
+Malach, E., Yehudai, G., Shalev-Schwartz, S. and Shamir, O. (2020). Proving the lottery
+ticket hypothesis: Pruning is all you need. In International Conference on Machine Learning.
+PMLR.
+Mariet, Z. and Sra, S. (2015). Diversity networks: Neural network compression using determi-
+nantal point processes. arXiv preprint arXiv:1511.05077 .
+Mocanu, D. C., Mocanu, E., Nguyen, P. H., Gibescu, M. and Liotta, A. (2016).
+A
+topological insight into restricted boltzmann machines. Machine Learning 104 243–270.
+Mocanu, D. C., Mocanu, E., Stone, P., Nguyen, P. H., Gibescu, M. and Liotta, A.
+(2018). Scalable training of artificial neural networks with adaptive sparse connectivity inspired
+by network science. Nature communications 9 1–12.
+14
+
+Molchanov, P., Tyree, S., Karras, T., Aila, T. and Kautz, J. (2019). Pruning convolutional
+neural networks for resource efficient inference. In 5th International Conference on Learning
+Representations, ICLR 2017-Conference Track Proceedings.
+Mostafa, H. and Wang, X. (2019). Parameter efficient training of deep convolutional neural net-
+works by dynamic sparse reparameterization. In International Conference on Machine Learning.
+PMLR.
+Oymak, S. and Soltanolkotabi, M. (2020). Toward moderate overparameterization: Global
+convergence guarantees for training shallow neural networks. IEEE Journal on Selected Areas in
+Information Theory 1 84–105.
+Pensia, A., Rajput, S., Nagle, A., Vishwakarma, H. and Papailiopoulos, D. (2020).
+Optimal lottery tickets via subset sum: Logarithmic over-parameterization is sufficient. Advances
+in Neural Information Processing Systems 33 2599–2610.
+Peste, A., Iofinova, E., Vladu, A. and Alistarh, D. (2021).
+Ac/dc: Alternating com-
+pressed/decompressed training of deep neural networks. Advances in Neural Information Pro-
+cessing Systems 34.
+Prabhu, A., Varma, G. and Namboodiri, A. (2018). Deep expander networks: Efficient deep
+networks from graph theory. In Proceedings of the European Conference on Computer Vision
+(ECCV).
+Ramanujan, V., Wortsman, M., Kembhavi, A., Farhadi, A. and Rastegari, M. (2020).
+What’s hidden in a randomly weighted neural network?
+In Proceedings of the IEEE CVF
+Conference on Computer Vision and Pattern Recognition.
+Rotskoff, G. M. and Vanden-Eijnden, E. (2018).
+Neural networks as interacting particle
+systems: Asymptotic convexity of the loss landscape and universal scaling of the approximation
+error. stat 1050 22.
+Shi, Z., Wei, J. and Liang, Y. (2021).
+A theoretical analysis on feature learning in neural
+networks: Emergence from inputs and advantage over fixed features. In International Conference
+on Learning Representations.
+Sirignano, J. and Spiliopoulos, K. (2020). Mean field analysis of neural networks: A law of
+large numbers. SIAM Journal on Applied Mathematics 80 725–752.
+Song, M., Montanari, A. and Nguyen, P. (2018).
+A mean field view of the landscape of
+two-layers neural networks. Proceedings of the National Academy of Sciences 115 E7665–E7671.
+Song, Z., Yang, S. and Zhang, R. (2021). Does preprocessing help training over-parameterized
+neural networks? Advances in Neural Information Processing Systems 34.
+Song, Z. and Yang, X. (2019). Quadratic suffices for over-parametrization via matrix chernoff
+bound. arXiv preprint arXiv:1906.03593 .
+Sreenivasan, K., Rajput, S., Sohn, J.-y. and Papailiopoulos, D. (2021). Finding everything
+within random binary networks. arXiv preprint arXiv:2110.08996 .
+15
+
+Sreenivasan, K., Sohn, J.-y., Yang, L., Grinde, M., Nagle, A., Wang, H., Lee, K. and
+Papailiopoulos, D. (2022). Rare gems: Finding lottery tickets at initialization. arXiv preprint
+arXiv:2202.12002 .
+Su, J., Chen, Y., Cai, T., Wu, T., Gao, R., Wang, L. and Lee, J. D. (2020).
+Sanity-
+checking pruning methods: Random tickets can win the jackpot. Advances in Neural Information
+Processing Systems 33 20390–20401.
+Suau, X., Zappella, L. and Apostoloff, N. (2018). Network compression using correlation
+analysis of layer responses .
+Tanaka, H., Kunin, D., Yamins, D. L. and Ganguli, S. (2020). Pruning neural networks with-
+out any data by iteratively conserving synaptic flow. Advances in Neural Information Processing
+Systems 33 6377–6389.
+Telgarsky, M. (2022). Feature selection with gradient descent on two-layer networks in low-
+rotation regimes. arXiv preprint arXiv:2208.02789 .
+Wang, C., Zhang, G. and Grosse, R. (2019). Picking winning tickets before training by pre-
+serving gradient flow. In International Conference on Learning Representations.
+Wei, C., Lee, J. D., Liu, Q. and Ma, T. (2019). Regularization matters: Generalization and
+optimization of neural nets vs their induced kernel. Advances in Neural Information Processing
+Systems 32.
+Yang, H., Wen, W. and Li, H. (2020).
+Deephoyer: Learning sparser neural network with
+differentiable scale-invariant sparsity measures. In International Conference on Learning Repre-
+sentations.
+Yang, Q., Mao, J., Wang, Z. and Hai, H. L. (2021). Dynamic regularization on activation
+sparsity for neural network efficiency improvement. ACM Journal on Emerging Technologies in
+Computing Systems (JETC) 17 1–16.
+Ye, M., Gong, C., Nie, L., Zhou, D., Klivans, A. and Liu, Q. (2020). Good subnetworks
+provably exist: Pruning via greedy forward selection. In International Conference on Machine
+Learning. PMLR.
+Zagoruyko, S. and Komodakis, N. (2016). Wide residual networks. In British Machine Vision
+Conference 2016. British Machine Vision Association.
+Zhou, H., Lan, J., Liu, R. and Yosinski, J. (2019). Deconstructing lottery tickets: Zeros, signs,
+and the supermask. Advances in neural information processing systems 32.
+Zhou, J., Li, X., Ding, T., You, C., Qu, Q. and Zhu, Z. (2022). On the optimization landscape
+of neural collapse under mse loss: Global optimality with unconstrained features. arXiv preprint
+arXiv:2203.01238 .
+Zhu, Z., Ding, T., Zhou, J., Li, X., You, C., Sulam, J. and Qu, Q. (2021). A geometric anal-
+ysis of neural collapse with unconstrained features. Advances in Neural Information Processing
+Systems 34.
+16
+
+Zou, D., Cao, Y., Li, Y. and Gu, Q. (2021).
+Understanding the generalization of adam in
+learning neural networks with proper regularization. arXiv preprint arXiv:2108.11371 .
+Zou, D., Cao, Y., Zhou, D. and Gu, Q. (2020). Gradient descent optimizes over-parameterized
+deep relu networks. Machine Learning 109 467–492.
+Zou, D. and Gu, Q. (2019). An improved analysis of training over-parameterized deep neural
+networks. Advances in neural information processing systems 32.
+17
+
+A
+Experiment Details
+The experiments of MLP, VGG and ResNet-32 are run on NVIDIA A5000 and ResNet-50 and
+ResNet-20-128 is run on 4 NIVIDIA V100s. We list the hyperparameters we used in training. All
+of our models are trained with SGD and the detailed settings are summarized below.
+Table 1: Summary of architectures, dataset and training hyperparameters
+Model
+Data
+Epoch
+Batch Size
+LR
+Momentum
+LR Decay, Epoch
+Weight Decay
+LeNet
+MNIST
+120
+128
+0.1
+0
+0
+0
+VGG
+CIFAR-10
+160
+128
+0.1
+0.9
+0.1 × [80, 120]
+0.0001
+ResNets
+CIFAR-10
+160
+128
+0.1
+0.9
+0.1 × [80, 120]
+0.0001
+B
+Further Experiment Results
+We plot the experiment result of ResNet-20-128 in Figure 4. This figure further verifies our results
+that there exists pruning rate threshold such that the testing performance of the pruned network
+is on par with the testing performance of the dense model while the training accuracy remains
+perfect.
+0.0
+20.0
+36.0
+48.8
+59.0
+67.2
+73.8
+79.0
+83.2
+86.6
+Sparsity
+95
+96
+97
+98
+99
+100
+Accuracy
+ResNet-20-128 CIFAR-10 Accuracy vs Sparsity
+Random (Train)
+Random (Test)
+IMP (Train)
+IMP (Test)
+Figure 4: The figure shows the experiment results of ResNet-20-128 under various sparsity by
+random pruning and IMP. Each data point is averaged over 2 runs.
+C
+Preliminary for Analysis
+In this section, we introduce the following signal-noise decomposition of each neuron weight from
+Cao et al. (2022), and some useful properties for the terms in such a decomposition, which are
+useful in our analysis.
+Definition C.1 (signal-noise decomposition). For each neuron weight j ∈ [K], r ∈ [m], there exist
+18
+
+coefficients γ(t)
+j,r,k, ζ(t)
+j,r,i, ω(t)
+j,r,i such that
+�w(t)
+j,r = �w(0)
+j,r +
+K
+�
+k=1
+γ(t)
+j,r,k · ∥µk∥−2
+2
+· µk ⊙ mj,r +
+n
+�
+i=1
+ζ(t)
+j,r,i ·
+����ξj,r,i
+���
+−2
+2
+· �ξj,r,i +
+n
+�
+i=1
+ω(t)
+j,r,i
+����ξj,r,i
+���
+−2
+2
+· �ξj,r,i,
+where γ(t)
+j,r,j ≥ 0, γ(t)
+j,r,k ≤ 0, ζ(t)
+j,r,i ≥ 0, ω(t)
+j,r,i ≤ 0.
+It is straightforward to see the following:
+γ(0)
+j,r,k, ζ(0)
+j,r,i, ω(0)
+j,r,i = 0,
+γ(t+1)
+j,r,j
+= γ(t)
+j,r,j − I(r ∈ Sj
+signal)η
+n
+n
+�
+i=1
+ℓ′(t)
+j,i · σ′ ��
+�w(t)
+j,r, µyi
+��
+∥µyi∥2
+2 I(yi = j),
+γ(t+1)
+j,r,k = γ(t)
+j,r,k − I((mj,r)k = 1)η
+n
+n
+�
+i=1
+ℓ′(t)
+j,i · σ′ ��
+�w(t)
+j,r, µyi
+��
+∥µyi∥2
+2 I(yi = k), ∀j ̸= k,
+ζ(t+1)
+j,r,i
+= ζ(t)
+j,r,i − η
+n · ℓ′(t)
+j,i · σ′ ��
+�w(t)
+j,r, ξi
+�� ����ξj,r,i
+���
+2
+2 I(j = yi),
+ω(t+1)
+j,r,i
+= ω(t)
+j,r,i − η
+n · ℓ′(t)
+j,i · σ′ ��
+�w(t)
+j,r, ξi
+�� ����ξj,r,i
+���
+2
+2 I(j ̸= yi),
+where {γ(t)
+j,r,j}T
+t=1, {ζ(t)
+j,r,i}T
+t=1 are increasing sequences and {γ(t)
+j,r,k}T
+t=1, {ω(t)
+j,r,i}T
+t=1 are decreasing se-
+quences, because −ℓ′(t)
+j,i ≥ 0 when j = yi, and −ℓ′(t)
+j,i ≤ 0 when j ̸= yi. By Lemma D.4, we have
+pd > n+K, and hence the set of vectors {µk}K
+k=1
+�{�ξi}n
+i=1 is linearly independent with probability
+measure 1 over the Gaussian distribution for each j ∈ [K], r ∈ [m]. Therefore the decomposition is
+unique.
+D
+Proof of Theorem 3.1
+We first formally restate Theorem 3.1.
+Theorem D.1 (Formal Restatement of Theorem 3.1). Under Condition 2.2, choose initialization
+variance σ0 = �Θ(m−4n−1µ−1) and learning rate η ≤ �O(1/µ2). For ϵ > 0, if p ≥ C1
+log d
+m
+for some
+sufficiently large constant C1, then with probability at least 1 − O(d−1) over the randomness in the
+data, network initialization and pruning, there exists T = �O(Kη−1σ2−q
+0
+µ−q + K2m4µ−2η−1ϵ−1)
+such that the following holds:
+1. The training loss is below ϵ: LS(�
+W(T)) ≤ ϵ.
+2. The weights of the CNN highly correlate with its corresponding class signal: maxr γ(T)
+j,r,j ≥
+Ω(m−1/q) for all j ∈ [K].
+3. The weights of the CNN doesn’t have high correlation with the signal from different classes:
+maxj̸=k,r∈[m] |γ(T)
+j,r,k| ≤ �O(σ0µ).
+4. None of the weights is highly correlated with the noise: maxj,r,i ζ(T)
+j,r,i = �O(σ0σn
+√pd), maxj,r,i |ω(T)
+j,r,i| =
+�O(σ0σn
+√pd).
+19
+
+Moreover, the testing loss is upper-bounded by
+LD(�
+W(T)) ≤ O(Kϵ) + exp(−n2/p).
+The proof of Theorem 3.1 consists of the analysis of the pruning on the signal and noise for
+three stages of gradient descent: initialization, feature growing phase, and converging phase, and the
+establishment of the generalization property. We present these analysis in detail in the following
+subsections.
+A special note is that the constant C showing up in the following proof of each
+subsequent Lemmas is defined locally instead of globally, which means the constant C within each
+Lemma is the same but may be different across different Lemma.
+D.1
+Initialization
+We analyze the effect of pruning on weight-signal correlation and weight-noise correlation at the
+initialization. We first present a few supporting lemmas, and finally provide our main result of
+Lemma D.7, which shows that if the pruning is mild, then it will not hurt the max weight-signal
+correlation much at the initialization.
+On the other hand, the max weight-noise correlation is
+reduced by a factor of √p.
+Lemma D.2. Assume n = Ω(K2 log Kd). Then, with probability at least 1 − 1/d,
+|{i ∈ [n] : yi = j}| = Θ(n/K)
+∀j ∈ [K].
+Proof. By Hoeffding’s inequality, with probability at least 1 − δ/2K, for a fixed j ∈ [K], we have
+�����
+1
+n
+n
+�
+i=1
+I(yi = j) − 1
+K
+����� ≤
+�
+log(4K/δ)
+2n
+.
+Therefore, as long as n ≥ 2K2 log(4K/δ), we have
+�����
+1
+n
+n
+�
+i=1
+I(yi = j) − 1
+K
+����� ≤
+1
+2K .
+Taking a union bound over j ∈ [K] and making δ = 1/d yield the result.
+Lemma D.3. Assume pm = Ω(log d) and m = poly log d. Then, with probability 1 − 1/d, for all
+j ∈ [K], k ∈ [K], we have �m
+r=1(mj,r)k = Θ(pm), which implies that |Sj
+signal| = Θ(pm) for all
+j ∈ [K].
+Proof. When pm = Ω(log d), by multiplicative Chernoff’s bound, for a given k ∈ [K], we have
+P
+������
+m
+�
+r=1
+(mj,r)k − pm
+����� ≥ 0.5pm
+�
+≤ 2 exp {−Ω (pm)} .
+Take a union bound over j ∈ [K], k ∈ [K], we have
+P
+������
+m
+�
+r=1
+(mj,r)k − pm
+����� ≥ 0.5pm, ∀j ∈ [K], k ∈ [K]
+�
+≤ 2K2 exp {−Ω (pm)} ≤ 1/d.
+20
+
+Lemma D.4. Assume p = 1/ poly log d. Then with probability at least 1 − 1/d, for all j ∈ [K],
+r ∈ [m], �d
+i=1(mj,r)i = Θ(pd).
+Proof. By multiplicative Chernoff’s bound, we have for a given j, r
+P
+������
+d
+�
+i=1
+(mj,r)i − pd
+����� ≥ 0.5pd
+�
+≤ 2 exp{−Ω(pd)}.
+Take a union bound over j, r, we have
+P
+������
+d
+�
+i=1
+(mj,r)i − pd
+����� ≥ 0.5pd, ∀j ∈ [K], r ∈ [m]
+�
+≤ 2Km exp{−Ω(pd)} ≤ 1/d,
+where the last inequality follows from our choices of p, K, m, d.
+Lemma D.5. Suppose p = Ω(1/ poly log d), and m, n = poly log d. With probability at least 1−1/d,
+we have
+����ξj,r,i
+���
+2
+2 = Θ(σ2
+npd),
+���
+�
+�ξj,r,i, ξi′
+���� ≤ O(σ2
+n
+�
+pd log d),
+���
+�
+µk, �ξj,r,i
+���� ≤ | ⟨µ, ξi⟩ | ≤ O(σnµ
+�
+log d),
+for all j ∈ {−1, 1}, r ∈ [m], i, i′ ∈ [n] and i ̸= i′.
+Proof. From Lemma D.4, we have with probability at least 1 − 1/d,
+d
+�
+k=1
+(mj,r)k = Θ(pd),
+∀j ∈ [K], r ∈ [m].
+For a set of Gaussian random variable g1, . . . , gN ∼ N(0, σ2), by Bernstein’s inequality, with prob-
+ability at least 1 − δ, we have
+�����
+N
+�
+i=1
+g2
+i − σ2N
+����� ≲ σ2
+�
+N log 1
+δ .
+Thus, by a union bound over j, r, i, with probability at least 1 − 1/d, we have
+����ξj,r,i
+���
+2
+2 = Θ(σ2
+npd).
+For i ̸= i′, again by Bernstein’s bound, we have with probability at least 1 − δ,
+���
+�
+�ξj,r,i, ξi′
+���� ≤ O
+�
+σ2
+n
+�
+pd log Kmn
+δ
+�
+,
+for all j, r, i. Plugging in δ = 1/d gives the result. The proof for | ⟨µ, ξi⟩ | is similar.
+21
+
+Lemma D.6. Suppose we have m independent Gaussian random variables g1, g2, . . . , gm ∼ N(0, σ2).
+Then with probability 1 − δ,
+max
+i
+gi ≥ σ
+�
+log
+m
+log 1/δ.
+Proof. By the standard tail bound of Gaussian random variable, we have for every x > 0,
+�σ
+x − σ3
+x3
+� e−x2/2σ2
+√
+2π
+≤ P [g > x] ≤ σ
+x
+e−x2/2σ2
+√
+2π
+.
+We want to pick a x⋆ such that
+P
+�
+max
+i
+gi ≤ x⋆
+�
+= (P [gi ≤ x⋆])m = (1 − P [gi ≥ x⋆])m ≤ e−m P[gi≥x⋆] ≤ δ
+⇒ P[gi ≥ x⋆] = Θ
+�log(1/δ)
+m
+�
+⇒ x⋆ = Θ(σ
+�
+log(m/(log(1/δ) log m))).
+Lemma D.7 (Formal Restatement of Lemma 3.2). With probability at least 1−2/d, for all i ∈ [n],
+σ0σn
+�
+pd ≤ max
+r
+�
+�w(0)
+j,r , ξi
+�
+≤
+�
+2 log(Kmd)σ0σn
+�
+pd.
+Further, suppose pm ≥ Ω(log(Kd)). Then with probability 1 − 2/d, for all j ∈ [K],
+σ0 ∥µj∥2 ≤
+max
+r∈Sj
+signal
+�
+�w(0)
+j,r , µj
+�
+≤
+�
+2 log(8pmKd)σ0 ∥µj∥2 .
+Proof. We first give a proof for the second inequality. From Lemma D.3, we know that |Sj
+signal| =
+Θ(pm). The upper bound can be obtained by taking a union bound over r ∈ Sj
+signal, j ∈ [K]. To
+prove the lower bound, applying Lemma D.6, with probability at least 1−δ/K, we have for a given
+j ∈ [K]
+max
+r∈Sj
+signal
+�
+�w(0)
+j,r , µj
+�
+≥ σ0 ∥µj∥2
+�
+log
+pm
+log K/δ.
+Now, notice that we can control the constant in pm (by controlling the constant in the lower bound
+of p) such that pm/ log(Kd) ≥ e. Thus, taking a union bound over j ∈ [K] and setting δ = 1/d
+yield the result.
+The proof of the first inequality is similar.
+D.2
+Supporting Properties for Entire Training Process
+This subsection establishes a few properties (summarized in Proposition D.10) that will be used in
+the analysis of feature growing phase and converging phase of gradient descent presented in the next
+two subsections. Define T ⋆ = η−1 poly(1/ϵ, µ, d−1, σ−2
+n , σ−1
+0 n, m, d). Denote α = Θ(log1/q(T ⋆)), β =
+22
+
+2 maxi,j,r,k
+����
+�
+�w(0)
+j,r , µk
+���� ,
+���
+�
+�w(0)
+j,r , ξi
+����
+�
+. We need the following bound holds for our subsequent
+analysis.
+4m1/q max
+j,r,i
+��
+�w(0)
+j,r , µyi
+�
+, Cnαµ√log d
+σnpd ,
+�
+�w(0)
+j,r , ξi
+�
+, 3Cnα
+�
+log d
+pd
+�
+≤ 1
+(D.1)
+Remark D.8. To see why Equation (D.1) can hold under Condition 2.2, we convert everything in
+terms of d. First recall from Condition 2.2 that m, n = poly(log d) and µ = Θ(σn
+√
+d log d) = Θ(1).
+In both mild pruning and over pruning we require p ≥ Ω(1/poly log d). Since α = Θ(log1/q(T ⋆)), if
+we assume T ⋆ ≤ O(poly(d)) for a moment (which we are going to justify in the next paragraph),
+then α = O(log1/q(d)). Then if we set d to be large enough, we have 4m1/qCnα µ√log d
+σnpd
+≤ poly log d
+√
+d
+≤
+1. Finally for the quantity 4m1/q maxj,r,i{⟨�w(0)
+j,r , µyi⟩, ⟨�w(0)
+j,r , ξi⟩}, by Lemma 3.2, our assumption
+of K = O(log d) in Condition 2.2 and our choice of σ0 = �Θ(m−4n−1µ−1) in Theorem 3.1 (or
+Theorem D.1), we can easily see that this quantity can also be made smaller than 1.
+Now, to justify that T ⋆ ≤ O(poly(d)), we only need to justify that all the quantities T ⋆ depend on
+is polynomial in d. First of all, based on Condition 2.2, n, m = poly log(d) and µ = Θ(σn
+√
+d log d) =
+Θ(1) further implies σ−2
+n
+= Θ(d log2 d). Since Theorem 3.1 only requires σ0 = �Θ(m−4n−1µ−1), this
+implies σ−1
+0
+≤ O(poly log d). Hence σ−1
+0 n = O(poly log d). Together with our assumption that
+ϵ, η ≥ Ω(1/ poly(d)) (which implies 1/ϵ, 1/η ≤ O(poly(d))), we have justified that all terms involved
+in T ⋆ are at most of order poly(d). Hence T ⋆ = poly(d).
+Remark D.9. Here we make remark on our assumption on ϵ and η in Condition 2.2.
+For our assumption on ϵ, since the cross-entropy loss is (1) not strongly-convex and (2) achieves
+its infimum at infinity. In practice, the cross-entropy loss is minimized to a constant level, say
+0.001. We make this assumption to avoid the pathological case where ϵ is exponentially small in
+d (say ϵ = 2−d) which is unrealistic. Thus, for realistic setting, we assume ϵ ≥ Ω(1/ poly(d)) or
+1/ϵ ≤ O(poly(d)).
+To deal with η, the only restriction we have is η = O(1/µ2) in Theorem 3.1 and Theorem 4.1.
+However, in practice, we don’t use a learning rate that is exponentially small, say η = 2−d. Thus,
+like dealing with ϵ, we assume η ≥ Ω(1/ poly(d)) or 1/η ≤ O(poly d).
+We make the above assumption to simplify analysis when analyzing the magnitude of Fj(X)
+for j ̸= y given sample (X, y).
+Proposition D.10. Under Condition 2.2, during the training time t < T ⋆, we have
+1. γ(t)
+j,r,j, ζ(t)
+j,r,i ≤ α,
+2. ω(t)
+j,r,i ≥ −β − 6Cnα
+�
+log d
+pd .
+3. γ(t)
+j,r,k ≥ −β − 2Cnα µ√log d
+σnpd .
+Notice that the lower bound has absolute value smaller than the upper bound.
+Proof of Proposition D.10. We use induction to prove Proposition D.10.
+23
+
+Induction Hypothesis:
+Suppose Proposition D.10 holds for all t < T ≤ T ⋆.
+We next show that this also holds for t = T via the following a few lemmas.
+Lemma D.11. Under Condition 2.2, for t < T, there exists a constant C such that
+�
+�w(t)
+j,r − �w(0)
+j,r , µk
+�
+=
+�
+γ(t)
+j,r,k ± Cnαµ√log d
+σnpd
+�
+I((mj,r)k = 1),
+�
+�w(t)
+j,r − �w(0)
+j,r , ξi
+�
+= ζ(t)
+j,r,i ± 3Cnα
+�
+log d
+pd ,
+�
+�w(t)
+j,r − �w(0)
+j,r , ξi
+�
+= ω(t)
+j,r,i ± 3Cnα
+�
+log d
+pd .
+Proof. From Lemma D.5, there exists a constant C such that with probability at least 1 − 1/d,
+���
+�
+�ξj,r,i, ξi′
+����
+����ξj,r,i
+���
+2
+2
+≤ C
+�
+log d
+pd ,
+���
+�
+�ξj,r,i, µk
+����
+����ξj,r,i
+���
+2
+2
+≤ C µ√log d
+σnpd ,
+| ⟨µk, ξi⟩ |
+∥µk∥2
+2
+≤ C σn
+√log d
+µ
+.
+Using the signal-noise decomposition and assuming (mj,r)k = 1, we have
+���
+�
+�w(t)
+j,r − �w(0)
+j,r , µk
+�
+− γ(t)
+j,r,k
+��� =
+�����
+n
+�
+i=1
+ζ(t)
+j,r,i ·
+����ξj,r,i
+���
+−2
+2
+·
+�
+�ξj,r,i, µk
+�
++
+n
+�
+i=1
+ω(t)
+j,r,i
+����ξj,r,i
+���
+−2
+2
+·
+�
+�ξj,r,i, µk
+������
+≤ C µ√log d
+σnpd
+n
+�
+i=1
+���ζ(t)
+j,r,i
+��� + C µ√log d
+σnpd
+n
+�
+i=1
+���ω(t)
+j,r,i
+���
+≤ 2C µ√log d
+σnpd nα.
+where the second last inequality is by Lemma D.5 and the last inequality is by induction hypothesis.
+To prove the second equality, for j = yi,
+���
+�
+�w(t)
+j,r − �w(0)
+j,r , ξi
+�
+− ζ(t)
+j,r,i
+��� =
+�������
+K
+�
+k=1
+γ(t)
+j,r,k · ⟨µk, ξi⟩
+∥µk∥2
+2
++
+�
+i′̸=i
+ζ(t)
+j,r,i′ ·
+�
+�ξj,r,i′, ξi
+�
+����ξj,r,i′
+���
+2
+2
++
+n
+�
+i′=1
+ω(t)
+j,r,i′
+�
+�ξj,r,i′, ξi
+�
+����ξj,r,i′
+���
+2
+2
+�������
+≤ C σn
+√log d
+µ
+K
+�
+k=1
+|γ(t)
+j,r,k| + C
+�
+log d
+pd
+�
+i′̸=i
+|ζ(t)
+j,r,i′| + C
+�
+log d
+pd
+n
+�
+i′=1
+|ω(t)
+j,r,i′|
+= C σn
+√log d
+µ
+Kα + 2Cnα
+�
+log d
+pd
+24
+
+≤ 3Cnα
+�
+log d
+pd .
+where the last inequality is by n ≫ K and µ = Θ(σn
+√
+d log d). The proof for the case of j ̸= yi is
+similar.
+Lemma D.12 (Off-diagonal Correlation Upper Bound). Under Condition 2.2, for t < T, j ̸= yi,
+we have that
+�
+�w(t)
+j,r, µyi
+�
+≤
+�
+�w(0)
+j,r , µyi
+�
++ Cnαµ√log d
+σnpd ,
+�
+�w(t)
+j,r, ξi
+�
+≤
+�
+�w(0)
+j,r , ξi
+�
++ 3Cnα
+�
+log d
+pd ,
+Fj(�
+W(t)
+j , xi) ≤ 1.
+Proof. If j ̸= yi, then γ(t)
+j,r,k ≤ 0 and we have that
+�
+�w(t)
+j,r, µyi
+�
+≤
+�
+�w(0)
+j,r , µyi
+�
++
+�
+γ(t)
+j,r,yi + Cnαµ√log d
+σnpd
+�
+I((mj,r)yi = 1)
+≤
+�
+�w(0)
+j,r , µyi
+�
++ Cnαµ√log d
+σnpd .
+Further, we can obtain
+�
+�w(t)
+j,r, ξi
+�
+≤
+�
+�w(0)
+j,r , ξi
+�
++ ω(t)
+j,r,i + 3Cnα
+�
+log d
+pd
+≤
+�
+�w(0)
+j,r , ξi
+�
++ 3Cnα
+�
+log d
+pd .
+Then, we have the following bound:
+Fj(�
+W(t)
+j , xi) =
+m
+�
+r=1
+[σ(⟨�wj,r, µyi⟩) + σ(⟨�wj,r, ξi⟩)]
+≤ m2q+1 max
+j,r,i
+��
+�w(0)
+j,r , µyi
+�
+, Cnαµ√log d
+σnpd ,
+�
+�w(0)
+j,r , ξi
+�
+, 3Cnα
+�
+log d
+pd
+�q
+≤ 1.
+where the first inequality is by Equation (D.1).
+Lemma D.13 (Diagonal Correlation Upper Bound). Under Condition 2.2, for t < T, j = yi, we
+have
+�
+�w(t)
+j,r, µj
+�
+≤
+�
+�w(0)
+j,r , µj
+�
++ γ(t)
+j,r,j + Cnαµ√log d
+σnpd ,
+25
+
+�
+�w(t)
+j,r, ξi
+�
+≤
+�
+�w(0)
+j,r , ξi
+�
++ ζ(t)
+j,r,i + 3Cnα
+�
+log d
+pd .
+If max{γ(t)
+j,r,j, ζ(t)
+j,r,i} ≤ m−1/q, we further have that Fj(�
+W(t)
+j , xi) ≤ O(1).
+Proof. The two inequalities are immediate consequences of Lemma D.11. If max{γ(t)
+j,r,j, ζ(t)
+j,r,i} ≤
+m−1/q, we have
+Fj(�
+W(t)
+j , xi) =
+m
+�
+r=1
+[σ(⟨�wj,r, µj⟩) + σ(⟨�wj,r, ξi⟩)]
+≤ 2 · 3qm max
+j,r,i
+�
+γ(t)
+j,r, ζ(t)
+j,r,i,
+���
+�
+�w(0)
+j,r , µj
+���� ,
+���
+�
+�w(0)
+j,r , ξi
+���� , Cnαµ√log d
+σnpd , 3Cnα
+�
+log d
+pd
+�q
+≤ O(1).
+Lemma D.14. Under Condition 2.2, for t ≤ T, we have that
+1. ω(t)
+j,r,i ≥ −β − 6Cnα
+�
+log d
+pd ;
+2. γ(t)
+j,r,k ≥ −β − 2Cnα µ√log d
+σnpd .
+Proof. When j = yi, we have ω(t)
+j,r,i = 0. We only need to consider the case of j ̸= yi. When
+ω(T−1)
+j,r,i
+≤ −0.5β − 3Cnα
+�
+log d
+pd , by Lemma D.11 we have
+�
+�w(T−1)
+j,r
+, ξi
+�
+≤
+�
+�w(0)
+j,r , ξi
+�
++ ω(T−1)
+j,r,i
++ 3Cnα
+�
+log d
+pd
+≤ 0.
+Thus,
+ω(T)
+j,r,i = ω(T−1)
+j,r,i
+− η
+n · ℓ′(T−1)
+j,i
+· σ′ ��
+�w(T−1)
+j,r
+, ξi
+�� ����ξj,r,i
+���
+2
+2 I(j ̸= yi)
+= ω(T−1)
+j,r,i
+≥ −β − 6Cnα
+�
+log d
+pd .
+When ω(T−1)
+j,r,i
+≥ −0.5β − 3Cnα
+�
+log d
+pd , we have
+ω(T)
+j,r,i = ω(T−1)
+j,r,i
+− η
+n · ℓ′(T−1)
+j,i
+· σ′ ��
+�w(T−1)
+j,r
+, ξi
+�� ����ξj,r,i
+���
+2
+2 I(j ̸= yi)
+≥ −0.5β − 3Cnα
+�
+log d
+pd
+− η
+nσ′
+�
+0.5β + 3Cnα
+�
+log d
+pd
+� ����ξj,r,i
+���
+2
+2
+≥ −β − 6Cnα
+�
+log d
+pd ,
+26
+
+where the last inequality is by setting η ≤ nq−1 �
+0.5β + 3Cnα
+�
+log d
+pd
+�2−q
+(C2σ2
+nd)−1 and C2 is the
+constant such that
+����ξj,r,i
+���
+2
+2 ≤ C2σ2
+npd for all j, r, i in Lemma D.5.
+For γ(t)
+j,r,k, the proof is similar. Consider I((mj,r)k) = 1. When γ(t)
+j,r,k ≤ −0.5β − Cnα µ√log d
+σnpd , by
+Lemma D.11, we have
+�
+�w(t)
+j,r, µk
+�
+≤
+�
+�w(0)
+j,r , µk
+�
++ γ(t)
+j,r,k + Cnαµ√log d
+σnpd
+≤ 0.
+Hence,
+γ(T)
+j,r,k = γ(T−1)
+j,r,k
+− η
+n
+n
+�
+i=1
+ℓ′(T−1)
+j,i
+σ′ ��
+�w(T−1)
+j,r
+, µk
+��
+µ2I(yi = k)
+= γ(T−1)
+j,r,k
+≥ −β − 2Cnαµ√log d
+σnpd .
+When γ(t)
+j,r,k ≥ −0.5β − Cnα µ√log d
+σnpd , we have
+γ(T)
+j,r,k = γ(T−1)
+j,r,k
+− η
+n
+n
+�
+i=1
+ℓ′(T−1)
+j,i
+σ′ ��
+�w(T−1)
+j,r
+, µk
+��
+µ2I(yi = k)
+≥ −0.5β − Cnαµ√log d
+σnpd
+− C2
+η
+K σ′
+�
+0.5β + Cnαµ√log d
+σnpd
+�
+µ2
+≥ −β − 2Cnαµ√log d
+σnpd ,
+where the first inequality follows from the fact that there are Θ( n
+K ) samples such that I(yi = k),
+and the last inequality follows from picking η ≤ K(0.5β + Cnα µ√log d
+σnpd )2−qµ−2q−1C−1
+2 .
+Lemma D.15. Under Condition 2.2, for t ≤ T, we have γ(t)
+j,r,j, ζ(t)
+j,r,i ≤ α.
+Proof. For yi ̸= j or r /∈ Sj
+signal, γ(t)
+j,r,j, ζ(t)
+j,r,i = 0 ≤ α.
+If yi = j, then by Lemma D.12 we have
+���ℓ′(t)
+j,i
+��� = 1 − logitj(F; X) =
+�
+i̸=j eFi(X)
+�K
+i=1 eFi(X) ≤
+Ke
+eFj(X) .
+(D.2)
+Recall that
+γ(t+1)
+j,r,j
+= γ(t)
+j,r,j − I(r ∈ Sj
+signal)η
+n
+n
+�
+i=1
+ℓ′(t)
+j,i · σ′ ��
+�w(t)
+j,r, µyi
+��
+∥µyi∥2
+2 I(yi = j),
+ζ(t+1)
+j,r,i
+= ζ(t)
+j,r,i − η
+n · ℓ′(t)
+j,i · σ′ ��
+�w(t)
+j,r, ξi
+�� ����ξj,r,i
+���
+2
+2 I(j = yi).
+27
+
+We first bound ζ(T)
+j,r,i. Let Tj,r,i be the last time t < T that ζ(t)
+j,r,i ≤ 0.5α. Then we have
+ζ(T)
+j,r,i = ζ(Tj,r,i)
+j,r,i
+− η
+nℓ′(Tj,r,i)
+i
+· σ′ ��
+�w(Tj,r,i)
+j,r
+, ξi
+��
+I(yi = j)
+����ξj,r,i
+���
+2
+2
+�
+��
+�
+I1
+−
+�
+Tj,r,i<t<T
+η
+nℓ′(Tj,r,i)
+j,i
+σ′ ��
+�w(t)
+j,r, ξi
+��
+I(yi = j)
+����ξj,r,i
+���
+2
+2
+�
+��
+�
+I2
+.
+We bound I1, I2 separately. We first bound I1 as follows.
+|I1| ≤ q η
+n
+�
+ζ(Tj,r,i)
+j,r,i
++ 0.5β + 3Cnα
+�
+log d
+pd
+�q−1
+C2σ2
+npd ≤ q2qn−1ηαq−1C2σ2
+npd ≤ 0.25α,
+where the first inequality follows from Lemma D.13, the second inequality follows because β ≤ 0.1α
+and 3Cnα
+�
+log d
+pd ≤ 0.1α, and the last inequality follows because η ≤ n/(q2q+2αq−2σ2
+nd).
+For Tj,r,i < t < T, by Lemma D.11, we have that
+�
+�w(t)
+j,r, ξi
+�
+≥ 0.5α−0.5β−3Cnα
+�
+log d
+pd ≥ 0.25α
+and
+�
+�w(t)
+j,r, ξi
+�
+≤ α + 0.5β + 3Cnα
+�
+log d
+pd ≤ 2α.
+Now we bound I2 as follows
+|I2| ≤
+�
+Tj,r,i<t<T
+η
+nKe exp {−Fj(X)} σ′ ��
+�w(t)
+j,r, ξi
+��
+I(yi = j)
+����ξj,r,i
+���
+2
+2
+≤
+�
+Tj,r,i<t<T
+η
+nKe exp
+�
+−σ
+��
+�w(t)
+j,r, ξi
+���
+σ′ ��
+�w(t)
+j,r, ξi
+��
+I(yi = j)
+����ξj,r,i
+���
+2
+2
+≤ qKeη2q−1T ⋆
+n
+exp(−αq/4q)αq−1σ2
+npd
+≤ 0.25T ⋆ exp(−αq/4q)αq−2α
+≤ 0.25α,
+where the first inequality follows from Equation (D.2), the second inequality follows because
+Fj(X) ≥ σ
+��
+�w(t)
+j,r, ξi
+��
+, the fourth inequality follows by choosing η ≤ n/(qKe2q+1σ2
+nd), and the
+last inequality follows by choosing α = Θ(log1/q(T ⋆)).
+Plugging the bounds on I1, I2 finishes the proof for ζ(T)
+j,r,i.
+To prove γ(t)
+j,r,j ≤ α, we pick η ≤ 1/(qe2q+2µ2) and the rest of the proof is similar.
+Lemma D.14 and Lemma D.15 imply Proposition D.10 holds for all t ≤ T.
+Induction Ends
+D.3
+Feature Growing Phase
+In this subsection, we first present a supporting lemma, and then provide our main result of
+Lemma D.17, which shows that the signal strength is relatively unaffected by pruning while the
+28
+
+noise level is reduced by a factor of √p.
+During the feature growing phase of training, the output of Fj(X) = O(1) for all j ∈ [K].
+Therefore, logiti(F, X) = O( 1
+K ) and 1 − logiti(F, X) = Θ(1) until
+�
+�w(t)
+j,r, µj
+�
+reaches m−1/q.
+Lemma D.16. Under the same assumption as Theorem D.1, for T =
+nη−1C4σ2−q
+0
+(σn
+√pd)−q
+C3(2C1)q−1[log d](q−1)/2 , the
+following results hold:
+• |ζ(t)
+j,r,i| = O(σ0σn
+√pd) for all j ∈ [K], r ∈ [m], i ∈ [n] and t ≤ T.
+• |ω(t)
+j,r,i| = O(σ0σn
+√pd) for all j ∈ [K], r ∈ [m], i ∈ [n] and t ≤ T.
+Proof. Define Ψ(t) = maxj,r,i{ζ(t)
+j,r,i, |ω(t)
+j,r,i|}. Then we have
+Ψ(t+1)
+≤ Ψ(t) + max
+j,r,i
+�
+�
+�
+�
+�
+η
+n|ℓ′(t)
+j,i | · σ′
+�
+�
+�
+�
+�w(0)
+j,r , ξi
+�
++
+K
+�
+k=1
+γ(t)
+j,r,k
+⟨µk, ξi⟩
+∥µk∥2
+2
++
+n
+�
+i′=1
+Ψ(t)
+�
+�ξj,r,i′, ξi
+�
+����ξj,r,i′
+���
+2
+2
+�
+�
+�
+����ξj,r,i
+���
+2
+2
+�
+�
+�
+�
+�
+≤ Ψ(t) + η
+nq
+�
+O(
+�
+log dσ0σn
+�
+pd) + K log1/q T ⋆ µσn
+√log d
+µ2
++ O(σ2
+npd) + nO(σ2
+n
+√pd log d)
+Θ(σ2npd)
+Ψ(t)
+�q−1
+O(σ2
+npd)
+≤ Ψ(t) + η
+n
+�
+O(
+�
+log dσ0σn
+�
+pd) + O(Ψ(t))
+�q−1
+O(σ2
+npd),
+where the second inequality follows by |ℓ′(t)
+j,i | and applying the bounds from Lemma D.5, and the last
+inequality follows by choosing 2K log T ⋆
+σnd√p
+= �O(1/
+√
+d) ≪ σ0. Let C1, C2, C3 be the constants for the up-
+per bound to hold in the big O notation. For any T = nη−1C4σ2−q
+0
+(σn
+√pd)−q
+C3(2C1)q−1[log d](q−1)/2 = Θ( nη−1σ2−q
+0
+(σn
+√pd)−q
+[log d](q−1)/2
+),
+we use induction to show that
+Ψ(t) ≤ C4σ0σn
+�
+pd, ∀t ∈ [T].
+(D.3)
+Suppose that Equation (D.3) holds for t ∈ [T ′] for T ′ ≤ T − 1. Then
+Ψ(T ′+1) ≤ Ψ(T ′) + η
+n
+�
+C1
+�
+log dσ0σn
+�
+pd + C2C4σ0σn
+�
+pd
+�q−1
+C3σ2
+npd
+≤ Ψ(T ′) + η
+n
+�
+2C1
+�
+log dσ0σn
+�
+pd
+�q−1
+C3σ2
+npd
+≤ (T ′ + 1)η
+n
+�
+2C1
+�
+log dσ0σn
+�
+pd
+�q−1
+C3σ2
+npd
+≤ T η
+n
+�
+2C1
+�
+log dσ0σn
+�
+pd
+�q−1
+C3σ2
+npd
+≤ C4σ0σn
+�
+pd,
+where the last inequality follows by picking T =
+nη−1C4σ2−q
+0
+(σn
+√pd)−q
+C3(2C1)q−1[log d](q−1)/2 = Θ( nη−1σ2−q
+0
+(σn
+√pd)−q
+[log d](q−1)/2
+).
+Therefore, by induction, we have Ψ(t) ≤ C4σ0σn
+√pd for all t ∈ [T].
+Lemma D.17 (Formal Restatement of Lemma 3.3). Under the same assumption as Theorem D.1,
+there exists time T1 =
+log 2m−1/q
+log(1+Θ( η
+K )µqσq−2
+0
+) = O(Kη−1σ2−q
+0
+µ−q log 2m−1/q) such that
+29
+
+1. maxr γ(T1)
+j,r,j ≥ m−1/q for j ∈ [K].
+2. |ζ(t)
+j,r,i|, |ω(t)
+j,r,i| ≤ O(σ0σn
+√pd) for all j ∈ [K], r ∈ [m], i ∈ [n] and t ≤ T1.
+3. |γ(t)
+j,r,k| ≤ O(σ0µ poly log d) for all j, k ∈ [K], j ̸= k, r ∈ [m] and t ≤ T1.
+Proof. Consider a fixed class j ∈ [K]. Denote T1 to be the last time for t ∈
+�
+0, nη−1C4σ2−q
+0
+(σn
+√pd)−q
+C3(2C1)q−1[log d](q−1)/2
+�
+satisfying maxr γ(t)
+j,r ≤ m−1/q. Then for t ≤ T1, maxj,r,i ζ(t)
+j,r,i, |ω(t)
+j,r,i| ≤ O(σ0σp
+√pd) ≤ O(m−1/q)
+and maxj,r γ(t)
+j,r,j. Thus, by Lemma D.13, we obtain that Fj(�
+W(t), xi) ≤ O(1), ∀yi = j. Thus,
+ℓ′(t)
+j,i = Θ(1). For j ∈ Sj
+signal, we have
+γ(t+1)
+j,r,j
+= γ(t)
+j,r,j − η
+n
+n
+�
+i=1
+ℓ′(t)
+j,i · σ′
+�
+�
+�
+�
+�w(0)
+j,r , µj
+�
++ γ(t)
+j,r,j +
+n
+�
+i′=1
+ζ(t)
+j,r,i
+�
+�ξj,r,i, µj
+�
+����ξj,r,i
+���
+2
+2
++
+n
+�
+i′=1
+ω(t)
+j,r,i
+�
+�ξj,r,i, µj
+�
+����ξj,r,i
+���
+2
+2
+�
+�
+� ∥µj∥2
+2 I(yi = j)
+≥ γ(t)
+j,r,j − η
+n
+n
+�
+i=1
+ℓ′(t)
+j,i σ′
+��
+�w(0)
+j,r , µj
+�
++ γ(t)
+j,r,j − O(nσ0σnpdσnµ√log d
+σ2npd
+)
+�
+I(yi = j).
+Let �γ(t)
+j,r,j = γ(t)
+j,r,j +
+�
+�w(0)
+j,r , µj
+�
+− O(nσ0σn
+√pd σnµ√log d
+σ2npd
+) and A(t) = maxr �γ(t)
+j,r,j.
+Note that by
+our choice of µ, we have
+nµ√log d
+σnpd
+= o(1).
+Since maxr
+�
+�w(0)
+j,r , µj
+�
+≥ Ω(σ0µ) by Lemma D.7,
+maxr
+�
+�w(0)
+j,r , µj
+�
+≥ Ω(σ0µ) − O(nσ0σnpd σnµ√log d
+σ2npd
+) = Ω(σ0µ). Then we have
+A(t+1) ≥ A(t) − η
+n
+n
+�
+i=1
+ℓ′(t)
+j,i σ′(A(t))µ2I(yi = j)
+≥ A(t) + Θ( η
+K )µ2[A(t)]q−1
+≥ (1 + Θ( η
+K µ2[A(t)]q−2))A(t)
+≥ (1 + Θ( η
+K µqσq−2
+0
+))A(t).
+Therefore, the sequence A(t) will exponentially grow and will reach 2m−1/q within
+log 2m−1/q
+log(1+Θ( η
+K )µqσq−2
+0
+) =
+O(Kη−1σ2−q
+0
+µ−q log 2m−1/q) ≤ Θ( nη−1σ2−q
+0
+(σn
+√pd)−q
+[log d](q−1)/2
+). Thus, maxr γ(t)
+j,r ≥ A(t)−maxj,r |
+�
+�w(0)
+j,r , µj
+�
+| ≥
+2m−1/q − O(σ0µ) ≥ 2 − m−1/q = m−1/q.
+Now we prove that under the same assumption as Theorem D.1, for T = O(Kη−1σ2−q
+0
+µ−q), we
+have |γ(t)
+j,r,k| ≤ O(σ0µ poly log d) for all r ∈ [m], j, k ∈ [K], j ̸= k and t ≤ T.
+We show that there exists a time T ′ ≥ T such that for all t ≤ T ′, maxj,r,k |γ(t)
+j,r,k| ≤ O(σ0µ poly log d).
+Let T ′ = O(K2η−1σ2−q
+0
+µ−q log d).
+Define Φ(t) = maxr∈[m], j,k∈[K], j̸=k{|γ(t)
+j,r,k|}. Since we assume T ≤ Θ( nη−1σ2−q
+0
+(σn
+√pd)−q
+[log d](q−1)/2
+), by
+30
+
+Lemma D.16, we have ζ(t)
+j,r,i, |ω(t)
+j,r,i| ≤ O(σ0σn
+√pd).
+Φ(t+1)
+≤ Φ(t) + max
+j,r,k,i
+�
+�
+�
+�
+�
+η
+n
+n
+�
+i=1
+I(yi = k)|ℓ′(t)
+j,i |σ′
+�
+�
+�
+�
+�w(0)
+j,r , µk
+�
++
+n
+�
+i′=1
+ζ(t)
+j,r,i′
+�
+�ξj,r,i′, µk
+�
+����ξj,r,i′
+���
+2
+2
++
+n
+�
+i′=1
+ω(t)
+j,r,i′
+�
+�ξj,r,i′, µk
+�
+����ξj,r,i′
+���
+2
+2
+�
+�
+� µ2
+�
+�
+�
+�
+�
+≤ Φ(t) + η
+K
+1
+K q
+�
+O(σ0µ
+�
+log d) + nO(σ0σn
+�
+pd)σnµ√log d
+σ2npd
+)
+�q−1
+µ2
+≤ Φ(t) + qη
+K2
+�
+O(σ0µ
+�
+log d)
+�q−1
+µ2,
+where the first inequality follows because γ(t)
+j,r,k < 0, the second inequality follows because there are
+Θ(n/K) samples from a given class k and |ℓ′(t)
+j,i | = Θ( 1
+K ), and the last inequality follows because
+µ = σn
+√
+d log d. Now, let C be the constant such that the above holds with big O. Then, we use
+induction to show that Φ(t) ≤ C2σ0µ for all t ≤ T. We proceed as follows.
+Φ(t+1) ≤ Φ(t) + qη
+K2
+�
+Cσ0µ
+�
+log d
+�q−1
+µ2
+≤ T qη
+K2
+�
+Cσ0µ
+�
+log d
+�q−1
+µ2
+≤ C2σ0µpoly log d,
+where the last inequality follows by picking T = C2K2η−1σ2−q
+0
+µ−q√log d
+Cq−1
+= O(K2η−1σ2−q
+0
+µ−q log d).
+D.4
+Converging Phase
+In this subsection, we show that gradient descent can drive the training loss toward zero while
+the signal in the feature is still large.
+An important intermediate step in our argument is the
+development of the following gradient upper bound for multi-class cross-entropy loss.
+In this phase, we are going to show that
+• maxr γ(t)
+j,r,j ≥ m1/q for all j ∈ [K].
+• maxj̸=k,r∈[m] |γ(t)
+j,r,k| ≤ β1 where β1 = �O(σ0µ).
+• maxj,r,i{ζ(t)
+j,r,i, |ω(t)
+j,r,i|} ≤ β2 where β2 = O(σ0σn
+√pd)
+Define W⋆ as follows:
+w⋆
+j,r = w(0)
+j,r + Θ(m log(1/ϵ))µj
+µ2 .
+Lemma D.18. Based on the result from the feature growing phase,
+����
+W(T1) − �
+W⋆���
+2
+F ≤ O(Km3 log2(1/ϵ)µ−2).
+Proof. We first compute
+����
+W(T1) − �
+W(0)���
+2
+F
+31
+
+=
+K
+�
+j=1
+m
+�
+r=1
+�������
+γ(T1)
+j,r,j
+µj ⊙ mj,r
+µ2
++
+�
+k̸=j
+γ(T1)
+j,r,k
+µk ⊙ mj,r
+µ2
++
+�
+i
+ζ(T1)
+j,r,i
+�ξj,r,i
+����ξj,r,i
+���
+2
+2
++
+�
+i
+ω(T1)
+j,r,i
+�ξj,r,i
+����ξj,r,i
+���
+2
+2
+�������
+2
+2
+≤
+�
+j
+�
+r
+�
+�γ(T1)
+j,r,j
+1
+µ +
+�
+k̸=j
+γ(T1)
+j,r,k
+1
+µ +
+�
+i
+ζ(T1)
+j,r,i
+1
+����ξj,r,i
+���
+2
++
+�
+i
+ω(T1)
+j,r,i
+1
+����ξj,r,i
+���
+2
+�
+�
+2
+≤
+�
+j
+�
+r
+�
+�O( 1
+µ) + K �O(σ0) + n �O(σ0)
+�2
+≤
+�
+j
+�
+r
+�O( 1
+µ2 )
+= �O(Km 1
+µ2 ),
+where the first inequality follows from triangle inequality, the second inequality follows from Lemma
+D.17, and the last inequality follows from our choice of σ0. On the other hand,
+����
+W(0) − �
+W⋆���
+2
+F =
+�
+j,r
+m2 log2(1ϵ) 1
+µ2 = O(Km3 log2(1/ϵ) 1
+µ2 ).
+Thus, we obtain
+����
+W(T1) − �
+W⋆���
+2
+F ≤ 4
+����
+W(T1) − �
+W(0)���
+2
+F + 4
+����
+W(0) − �
+W⋆���
+2
+F ≤ O(Km3 log2(1/ϵ) 1
+µ2 ).
+Lemma D.19 (Gradient Upper Bound). Under Condition 2.2, for t ≤ T ⋆, there exists constant
+C = O(Km2/q max{µ2, σ2
+npd}) such that
+���∇LS(�
+W(t)) ⊙ M
+���
+2
+F ≤ CLS(�
+W(t)).
+Proof. We need to prove that |ℓ′(t)
+yi,i|
+���∇F(�
+W(t), xi) ⊙ M
+���
+2
+F ≤ C. Assume yi ̸= j. Then we obtain
+���∇Fj(�
+Wj, xi) ⊙ M
+���
+F ≤
+�
+r
+���σ′ ��
+�w(t)
+j,r, µyi
+��
+µyi + σ′ ��
+�w(t)
+j,r, ξi
+��
+�ξi
+���
+2
+≤
+�
+r
+σ′ ��
+�w(t)
+j,r, µyi
+��
+∥µyi∥2 + σ′ ��
+�w(t)
+j,r, ξi
+�� ����ξi
+���
+2
+≤ m1/q �
+Fj(�
+Wj, xi)
+�(q−1)/q
+max{µ, Cσn
+�
+pd}
+≤ m1/q max{µ, Cσn
+�
+pd},
+where the first and second inequality follow from triangle inequality, the third inequality follows
+from H¨older’s inequality, and the last inequality follows from Lemma D.12. Similarly, on the other
+32
+
+hand, if yi = j, then
+���∇Fyi(�
+W) ⊙ M
+���
+F ≤ m1/q �
+Fyi(�
+Wyi, xi)
+�(q−1)/q
+max{µ, Cσn
+�
+pd}.
+Therefore,
+�
+j̸=yi
+|ℓ′(t)
+j,i |
+���∇Fj(�
+Wj, xi) ⊙ Mj
+���
+2
+F ≤
+�
+j̸=yi
+|ℓ′(t)
+j,i |m2/qO(max{µ2, σ2
+npd})
+= |ℓ′(t)
+yi,i|m2/qO(max{µ2, σ2
+npd})
+≤ Ke exp{−Fyi(xi)}m2/qO(max{µ2, σ2
+npd}),
+and
+|ℓ′(t)
+yi,i|
+���∇Fyi(�
+Wyi, xi) ⊙ Myi
+���
+2
+F
+≤ Ke exp{−Fyi(xi)}m2/q �
+Fyi(�
+Wyi, xi)
+�2(q−1)/q
+O(max{µ2, σ2
+npd},
+where the inequality follows from Equation (D.2). Thus,
+K
+�
+j=1
+|ℓ′(t)
+j,i |2 ���∇Fj(�
+Wj, xi) ⊙ Mj
+���
+2
+F
+≤ |ℓ′(t)
+yi,i|
+K
+�
+j=1
+|ℓ′(t)
+j,i |
+���∇Fj(�
+Wj, xi) ⊙ Mj
+���
+2
+F
+≤ |ℓ′(t)
+yi,i|Ke exp{−Fyi(xi)}m2/qO(max{µ2, σ2
+npd}
+��
+Fyi(�
+Wyi, xi)
+�(q−1)/q
++ 1
+�
+≤ |ℓ′(t)
+yi,i|O(Km2/q max{µ2, σ2
+npd}),
+(D.4)
+where the first inequality follows because |ℓ′(t)
+j,i | ≤ |ℓ′(t)
+yi,i|, and the last inequality uses the fact that
+exp{−x}(1 + x(q−1)/q) = O(1) for all x ≥ 0.
+The gradient norm can be bounded by
+���∇LS(�
+W(t))
+���
+2
+F ≤
+�
+1
+n
+n
+�
+i=1
+���∇L(�
+W(t), xi)
+���
+F
+�2
+=
+�
+� 1
+n
+n
+�
+i=1
+�
+�
+�
+�
+K
+�
+j=1
+|ℓ′(t)
+j,i |2
+���∇Fj(�
+W(t)
+j , xi)
+���
+2
+F
+�
+�
+2
+≤
+�
+1
+n
+n
+�
+i=1
+|ℓ′(t)
+yi,i|
+���∇F(�
+W(t)
+j , xi)
+���
+F
+�2
+≤
+�
+1
+n
+n
+�
+i=1
+�
+|ℓ′(t)
+yi,i|O(Km2/q max{µ2, σ2nd})
+�2
+33
+
+≤ O(Km2/q max{µ2, σ2
+nd}) 1
+n
+n
+�
+i=1
+|ℓ′(t)
+yi,i|
+≤ O(Km2/q max{µ2, σ2
+nd})LS(�
+W(t)),
+where the first inequality uses triangle inequality, the second inequality follows because |ℓ′(t)
+j,i | ≤
+|ℓ′(t)
+yi,i|, the third inequality uses the bound (D.4), the fourth inequality uses Jensen’s inequality and
+the last inequality follows because |ℓ′(t)
+yi,i| ≤ ℓ(t)
+i .
+Lemma D.20. For T1 ≤ t ≤ T ⋆, we have for all j ̸= yi,
+�
+∇Fyi(�
+W(t)
+yi , xi), �
+W⋆
+yi
+�
+−
+�
+∇Fj(�
+W(t)
+j , xi), �
+W⋆
+j
+�
+≥ q log 2qK
+ϵ
+.
+Proof of Lemma D.20. The proof of this lemma depends on the next two lemmas.
+Lemma D.21. For T1 ≤ t ≤ T ⋆ and j = yi, we have
+�
+∇Fj(�
+W(t)
+j , xi), �
+W⋆
+j
+�
+≥ Θ(m1/q log(1/ϵ)).
+Proof. By Lemma D.17, we have
+max
+r
+��
+�w(t)
+j,r, µj
+��
+= max
+r
+�
+�
+�
+�
+�
+�
+�w(0)
+j,r , µj
+�
++ γ(t)
+j,r,j +
+n
+�
+i=1
+ζ(t)
+j,r,i
+�
+�ξj,r,i, µj
+�
+����ξj,r,i
+���
+2
+2
++
+n
+�
+i=1
+ω(t)
+j,r,i
+�
+�ξj,r,i, µj
+�
+����ξj,r,i
+���
+2
+2
+�
+�
+�
+�
+�
+≥ m−1/q − O(σ0µ
+�
+log d) − O(nσ0σn
+√
+dµ√log d
+σnpd )
+≥ Θ(m−1/q),
+where the last inequality follows by picking σ0 ≤ O(m−1n−1µ−1(log d)−1/2). On the other hand,
+���
+�
+�w(t)
+j,r, ξi
+���� ≤
+���
+�
+�w(0)
+j,r , ξi
+���� + |ω(t)
+j,r,i| + |ζ(t)
+j,r,i| + O(n
+�
+log d
+pd α) + O(nµ√log d
+σnpd α) ≤ O(1),
+(D.5)
+where the first inequality follows from Lemma D.11 and the second inequality follows from Equa-
+tion (D.1) and Proposition D.10. Therefore,
+�
+∇Fj(�
+W(t)
+j , xi), �
+W⋆
+j
+�
+=
+�
+r
+σ′ ��
+�w(t)
+j,r, µj
+�� �
+µj, �w⋆
+j,r
+�
++
+�
+r
+σ′ ��
+�w(t)
+j,r, ξi
+�� �
+ξi, �w⋆
+j,r
+�
+≥
+�
+r
+σ′ ��
+�w(t)
+j,r, µj
+��
+Θ(m log(1/ϵ)) −
+�
+r
+O(σ0σn
+�
+pd log d + σn
+√log d
+µ
+m log(1/ϵ))
+≥ Θ(m1/q log(1/ϵ)) − O(mσ0σn
+�
+pd log d + σn
+√log d
+µ
+m2 log(1/ϵ))
+≥ Θ(m1/q log(1/ϵ)),
+where the last inequality follows because mσ0σn
+√pd log d = o(1) and σn
+√log d
+µ
+m2 = o(1) by our
+choices of µ, σ0.
+34
+
+Lemma D.22. For T1 ≤ t ≤ T and j ̸= yi, we have
+�
+∇Fj(�
+W(t)
+j , xi), �
+W⋆
+j
+�
+≤ O(1).
+Proof. First we have
+�
+�w(t)
+j,r, µyi
+�
+=
+�
+�w(0)
+j,r , µyi
+�
++ γ(t)
+j,r,yi +
+n
+�
+i=1
+ζ(t)
+j,r,i
+�
+�ξj,r,i, µj
+�
+����ξj,r,i
+���
+2
+2
++
+n
+�
+i=1
+ω(t)
+j,r,i
+�
+�ξj,r,i, µj
+�
+����ξj,r,i
+���
+2
+2
+≤ O(σ0µ
+�
+log d + σ0µ poly log d + nσ0σn
+�
+pdσnµ√log d
+σ2npd
+)
+≤ O(1),
+(D.6)
+where the first inequality follows from Lemma D.7, Lemma D.5 and Lemma D.17, and the last
+inequality follows from our choices of σ0, µ. Then, we have
+�
+∇Fj(�
+W(t)
+j , xi), �
+W⋆
+j
+�
+=
+�
+r
+σ′ ��
+�w(t)
+j,r, µyi
+�� �
+µyi, �w⋆
+j,r
+�
++
+�
+r
+σ′ ��
+�w(t)
+j,r, ξi
+�� �
+ξi, �w⋆
+j,r
+�
+≤ mO(σ0µ
+�
+log d) + mO(σ0σn
+�
+d log d + m log(1/ϵ)σn
+√log d
+µ
+)
+≤ O(1),
+where the second inequality follows from Equation (D.6) and Equation (D.5), and the last inequality
+follows from our choices of µ, σ0.
+Applying the lower bound and upper bound from Lemma D.21 and Lemma D.22, we have
+�
+∇Fyi(�
+W(t)
+yi , xi), �
+W⋆
+yi
+�
+−
+�
+∇Fj(�
+W(t)
+j , xi), �
+W⋆
+j
+�
+≥ Θ(m1/q log(1/ϵ)) − O(1)
+≥ q log 2qK
+ϵ
+.
+Lemma D.23. Under the same assumption as Theorem D.1, we have
+����
+W(t) − �
+W⋆���
+2
+F −
+����
+W(t+1) − �
+W⋆���
+2
+F ≥ 5ηLS(�
+W(t)) − ηϵ.
+Proof. To simplify our notation, we define �F (t)
+j (xi) =
+�
+∇Fj(�
+W(t)
+j , xi), �
+W⋆
+j
+�
+.
+We use the fact that the network is q-homogeneous.
+����
+W(t) − �
+W⋆���
+2
+F −
+����
+W(t+1) − �
+W⋆���
+2
+F
+= 2η
+�
+∇LS(�
+W(t)) ⊙ M, �
+W(t) − �
+W⋆�
+− η2 ���∇LS(�
+W(t)) ⊙ M
+���
+2
+F
+= 2η
+n
+n
+�
+i=1
+K
+�
+j=1
+ℓ′(t)
+j,i
+�
+qFj(�
+W(t)
+j ; xi, yi) −
+�
+∇Fj(�
+W(t)
+j , xi), �
+W⋆
+j
+��
+− η2 ���∇LS(�
+W(t)) ⊙ M
+���
+2
+F
+35
+
+≥ 2qη
+n
+n
+�
+i=1
+�
+�log(1 +
+K
+�
+j=1
+eFj−Fyi) − log(1 +
+K
+�
+j=1
+e( �Fj− �Fyi)/q)
+�
+� − η2 ���∇LS(�
+W(t)) ⊙ M
+���
+2
+F
+≥ 2qη
+n
+n
+�
+i=1
+�
+ℓ(�
+W(t); xi, yi) − log(1 + Ke− log(2qK/ϵ))
+�
+− η2 ���∇LS(�
+W(t)) ⊙ M
+���
+2
+F
+≥ 2qη
+n
+n
+�
+i=1
+�
+ℓ(�
+W(t); xi, yi) − ϵ
+2q
+�
+− η2 ���∇LS(�
+W(t)) ⊙ M
+���
+2
+F
+≥ CηLS(�
+W(t)) − ηϵ,
+where the first inequality follows from the convexity of the cross-entropy loss with softmax, the
+second inequality follows from Lemma D.20, the third inequality follows because log(1 + x) ≤ x,
+and the last inequality follows from Lemma D.19 for some constant C.
+Lemma D.24 (Formal Restatement of Lemma 3.5). Under the same assumption as Theorem D.1,
+choose T2 = T1+ ∥�
+W(T1)−�
+W⋆∥
+2
+F
+2ηϵ
+= T1+ �O(Km3 log2(1/ϵ)µ−2). Then for any time t during this stage,
+we have maxr γ(t)
+j,r,j ≥ m1/q for all j ∈ [K], maxj,r,i{|ζ(t)
+j,r,i|, |ω(t)
+j,r,i|} ≤ 2β1, maxj̸=k,r∈[m]{|γ(t)
+j,r,k|} ≤
+2β2, and
+1
+t − T1
+t
+�
+s=T1
+LS(�
+W(s)) ≤
+����
+W(T1) − �
+W⋆���
+2
+F
+Cη(t − T1)
++ ϵ
+C .
+Proof. From Lemma D.17, we have maxrγ(T1)
+j,r,j ≥ m1/q and since γ(t) is an increasing sequence over
+t, we have maxrγ(t)
+j,r,j ≥ m1/q for all t ∈ [T1, T2]. We have
+����
+W(s) − �
+W⋆���
+2
+F −
+����
+W(s+1) − �
+W⋆���
+2
+F ≥ CηLS(�
+W(s)) − ηϵ.
+Taking a telescopic sum from T1 to t yields
+t
+�
+s=T1
+LS(�
+W(s)) ≤
+����
+W(T1) − �
+W⋆���
+2
+F + ηϵ(t − T1)
+Cη
+.
+Combining Lemma D.18, we have
+t
+�
+s=T1
+LS(�
+W(s)) ≤ O(η−1 ����
+W(T1) − �
+W⋆���
+2
+F ) = O(η−1Km3 log2(1/ϵ)µ−2).
+(D.7)
+Define Ψ(t) = maxj,r,i{ζ(t)
+j,r,i, |ω(t)
+j,r,i|} and Φ(t) = maxj̸=k,r∈[m] |γ(t)
+j,r,k| and β2 = �O(σ0µ). Now we use
+induction to prove Ψ(t) ≤ 2β1 and Φ(t) ≤ 2β2. Suppose the result holds for time t ≤ t′. Then
+Ψ(t+1) ≤ Ψ(t) + max
+j,r,i
+�
+�
+�
+�
+�
+η
+n|ℓ′(t)
+j,i | · σ′
+�
+�
+�
+�
+�w(0)
+j,r , ξi
+�
++
+K
+�
+k=1
+γ(t)
+j,r,k
+⟨µk, ξi⟩
+∥µk∥2
+2
++
+n
+�
+i′=1
+Ψ(t)
+�
+�ξj,r,i′, ξi
+�
+����ξj,r,i′
+���
+2
+2
+�
+�
+�
+����ξj,r,i
+���
+2
+2
+�
+�
+�
+�
+�
+36
+
+≤ Ψ(t) + η
+nq max
+i
+|ℓ′(t)
+yi,i|
+�
+O(
+�
+log dσ0σn
+�
+pd) + K log1/q T ⋆ µσn
+√log d
+µ2
++ O(σ2
+npd) + nO(σ2
+n
+√pd log d)
+Θ(σ2npd)
+Ψ(t)
+�q−1
+O(σ2
+npd)
+≤ Ψ(t) + η
+n
+n
+�
+i=1
+|ℓ′(t)
+yi,i|
+�
+O(
+�
+log dσ0σn
+�
+pd) + O(Ψ(t))
+�q−1
+O(σ2
+npd),
+where the second inequality follows by |ℓ′(t)
+j,i | ≤ |ℓ′(t)
+yi,i| and applying the bounds from Lemma D.5,
+and the last inequality follows by choosing K log1/q T ⋆
+√
+d
+= �O( 1
+√
+d) ≪ σ0σn
+√pd. Unrolling the recursion
+by taking a sum from T1 to t′ we have
+Ψ(t′+1) (i)
+≤ Ψ(T1) + η
+n
+t′
+�
+s=T1
+n
+�
+i=1
+|ℓ′(s)
+yi,i|O(σ2
+npd poly log d)βq−1
+1
+(ii)
+≤ Ψ(T1) + η
+nO(σ2
+npd poly log d)βq−1
+1
+t′
+�
+s=T1
+n
+�
+i=1
+ℓ(s)
+i
+= Ψ(T1) + η
+nO(σ2
+npd poly log d)βq−1
+1
+t′
+�
+s=T1
+LS(�
+W(s))
+(iii)
+≤ Ψ(T1) + 1
+nO(Km3µ−2σ2
+npd poly log d)βq−1
+1
+(iv)
+≤ β1 + �O(Km3)βq−1
+1
+(v)
+≤ 2β1,
+where (i) follows from induction hypothesis Ψ(t) ≤ 2β1, (ii) follows from the property of cross-
+entropy loss with softmax |ℓ′
+j,i| ≤ |ℓ′
+yi,i| ≤ ℓi, (iii) follows from Equation (D.7), (iv) follows from
+our choice of µ, n, K, and (v) follows because �O(Km3)β1q−2 ≤ �O(Km3σ0σn
+√pd) ≤ 1. Therefore,
+by induction Ψ(t) ≤ 2β1 holds for time t ≤ t′ + 1.
+On the other hand,
+Φ(t′+1)
+(i)
+≤ Φ(t) + max
+j,r,k,i
+�
+�
+�
+�
+�
+η
+n
+n
+�
+i=1
+I(yi = k)|ℓ′(t)
+j,i |σ′
+�
+�
+�
+�
+�w(0)
+j,r , µk
+�
++
+n
+�
+i′=1
+ζ(t)
+j,r,i′
+�
+�ξj,r,i′, µk
+�
+����ξj,r,i′
+���
+2
+2
++
+n
+�
+i′=1
+ω(t)
+j,r,i′
+�
+�ξj,r,i′, µk
+�
+����ξj,r,i′
+���
+2
+2
+�
+�
+� µ2
+�
+�
+�
+�
+�
+(ii)
+≤ Φ(t) + Θ( η
+K ) max
+j,i |ℓ′(t)
+j,i |
+�
+O(σ0µ
+�
+log d) + nO(σ0σn
+�
+pd)σnµ√log d
+σ2npd
+)
+�q−1
+µ2
+(iii)
+≤ Φ(T1) + Θ( η
+K )µ2
+t
+�
+s=T1
+n
+�
+i=1
+ℓ(s)
+i
+�
+O(σ0µ
+�
+log d)
+�q−1
+(iv)
+≤ β2 + O(m3)βq−1
+2
+37
+
+(v)
+≤ 2β2,
+where (i) follows because γ(t)
+j,r,k ≤ 0, (ii) follows from Lemma D.7 and Lemma D.5, (iii) follows
+because maxj,i |ℓ′(t)
+j,i | ≤ maxi |ℓ′(t)
+yi,i| ≤ maxi ℓ(t)
+i
+≤ �
+i ℓ(t)
+i , (iv) follows from Equation (D.7), and (v)
+follows because O(m3)βq−2
+2
+≤ �O(m3σ0µ) ≤ 1.
+D.5
+Generalization Analysis
+In this subsection, we show that pruning can purify the feature by reducing the variance of the
+noise by a factor of p when a new sample is given.
+Now the network has parameter
+�w⋆
+j,r = �w(0)
+j,r +
+K
+�
+k=1
+γ⋆
+j,r,k
+µk ⊙ mj,r
+µ2
++
+n
+�
+i=1
+ζ⋆
+j,r,i
+�ξj,r,i
+����ξj,r,i
+���
+2
+2
++
+n
+�
+i=1
+ω⋆
+j,r,i
+�ξj,r,i
+����ξj,r,i
+���
+2
+2
+.
+We have
+����w⋆
+j,r
+���
+2 = O(σ0
+√pd + µ−1 log1/q(T ⋆) + Kσ0 poly log d + nσ0σn
+√pd
+1
+σn
+√pd) = O(σ0
+√pd).
+Lemma D.25 (Formal Restatement of Lemma 3.6). With probability at least 1−2Km exp
+�
+− (2m)−4/q
+O(σ2
+0σ2npd)
+�
+,
+max
+j,r
+����w⋆
+j,r, ξ
+��� ≤ (2m)−2/q.
+Proof. Since
+�
+�w⋆
+j,r, ξ
+�
+follows a Gaussian distribution with variance O(σ2
+0σ2
+npd), we have
+P
+�����w⋆
+j,r, ξ
+��� ≥ (2m)−2/q�
+≤ 2 exp
+�
+− (2m)−4/q
+O(σ2
+0σ2npd)
+�
+.
+Applying a union bound over j ∈ [K], r ∈ [m] gives the result.
+Theorem D.26 (Formal Restatement of Generalization Part of Theorem 3.1). Under the same
+assumptions as Theorem D.1, within �O(Kη−1σ2−q
+0
+µ−q + K2m4µ−2η−1ϵ−1) iterations, we can find
+�
+W⋆ such that
+• LS(�
+W⋆) ≤ ϵ.
+• LD ≤ O(Kϵ) + exp(−n2/p).
+Proof. Let E be the event that Lemma D.25 holds. Then, we can divide LD(�
+W⋆) into two parts:
+E[ℓ(F(�
+W⋆, x))] = E[I(E)ℓ(F(�
+W⋆, x))]
+�
+��
+�
+I1
++ E[I(Ec)ℓ(F(�
+W⋆, x))]
+�
+��
+�
+I2
+.
+Since LS(�
+W⋆) ≤ ϵ, for each class j ∈ [K] there must exist one training sample (xi, yi) ∈ S with yi =
+j such that ℓ(F(�
+W⋆, xi)) ≤ Kϵ ≤ 1 by pigeonhole principle. This implies that �
+j′̸=j exp(Fj′(xi) −
+Fj(xi)) ≤ 2Kϵ. Conditioning on the event E, by Lemma D.25, we have
+|Fj(�
+W⋆, x) − Fj(�
+W⋆, xi)| ≤
+�
+r
+σ(
+��w⋆
+j,r, ξi
+�
+) +
+�
+r
+σ(
+��w⋆
+j,r, ξ
+�
+)
+38
+
+≤
+�
+r
+(2m)−1 +
+�
+r
+(2m)−1
+≤ 1.
+Thus, we have exp(Fj′(x) − Fj(x)) ≤ 2Kϵe2 = O(Kϵ). Next we bound the term I2.
+ℓ(F(�
+W⋆, x)) = log
+�
+�1 +
+�
+j′̸=y
+exp(Fj′(x) − Fy(x))
+�
+�
+≤ log
+�
+�1 +
+�
+j′̸=y
+exp(Fj′(x))
+�
+�
+≤
+�
+j′̸=y
+log(1 + exp(Fj′(x)))
+≤ K +
+�
+j′̸=y
+Fj′(x)
+= K +
+�
+j′̸=y
+σ(
+��w⋆
+j′,r, µy
+�
+) + σ(
+��w⋆
+j′,r, ξ
+�
+)
+≤ K + Km(O(σ0µ
+�
+log d))q + �O(m(σ0σn
+√
+d)q) ∥ξ/σn∥q
+2
+≤ 2K + ∥ξ/σn∥q
+2 ,
+(D.8)
+where the first inequality follows because Fy(x) ≥ 0, the second and third inequalities follow from
+the property of log function, and the last inequality follows from our choice of σ0 ≤ �O(m−4n−1σ−1
+n d−1/2).
+We further have
+I2 ≤
+�
+E[I(E)]
+�
+E[ℓ(F(�
+W⋆, x))2]
+≤
+�
+P(Ec)
+�
+4K2 + E ∥ξ/σn∥2q
+2
+≤ exp(−Cm−2/qσ−2
+0 σ−2
+n p−1d−1 + log(d))
+≤ exp(−n2/p),
+where the first inequality follows from Cauchy-Schwarz inequality, the second inequality follows
+from Equation (D.8), the third inequality follows from Lemma D.25, and the last inequality follows
+because σ0 ≤ �O(m−4n−1σ−1
+n d−1/2).
+E
+Proof of Theorem 4.1
+In this section, we show that there exists a relatively large pruning fraction (i.e., small p) such that
+while gradient descent is still able to drive the training error toward zero, the learned model yields
+poor generalization. We first provide a formal restatement of Theorem 4.1.
+Theorem E.1 (Formal Restatement of Theorem 4.1). Under Condition 2.2, choose initialization
+variance σ0 = �Θ(m−4n−1µ−1) and learning rate η ≤ �O(1/µ2). For ϵ > 0, if p = Θ(
+1
+Km log d), then
+with probability at least 1−1/ log(d), there exists T = O(η−1nσq−2
+0
+σ−q
+n (pd)−q/2+η−1ϵ−1m4nσ−2
+n (pd)−1)
+39
+
+such that the following holds:
+1. The training loss is below ϵ: LS(�
+W(T)) ≤ ϵ.
+2. The model weight doesn’t learn any of its corresponding signal at all: γ(t)
+j,r,j = 0 for all j ∈
+[K], r ∈ [m].
+3. The model weights is highly correlated with the noise: maxr∈[m] ζ(T)
+j,r,i ≥ Ω(m−1/q) if yi = j.
+Moreover, the testing loss is large:
+LD(�
+W(T)) ≥ Ω(log K).
+The proof of Theorem 4.1 consists of the analysis of the over-pruning for three stages of gradient
+descent: initialization, feature growing phase, and converging phase, and the establishment of the
+generalization property. We present these analysis in detail in the following subsections.
+E.1
+Initialization
+Lemma E.2. When m = poly log d and p = Θ(
+1
+Km log d), with probability 1 − O(1/ log d), for all
+class j ∈ [K] we have |Sj
+signal| = 0.
+Proof. First, the probability that a given class j receives no signal is (1−p)m. We use the inequality
+that
+1 + t ≥ exp {O(t)}
+∀t ∈ (−1/4, 1/4).
+Then the probability that |Sj
+signal| = 0, ∀j ∈ [K] is given by
+(1 − p)Km ≥ exp {−O (pKm)} ≥ 1 − O
+�
+1
+log d
+�
+.
+E.2
+Feature Growing Phase
+Lemma E.3 (Formal Restatement of Lemma 4.3). Under the same assumption as Theorem E.1,
+there exists T1 < T ⋆ such that T1 = O(η−1nσq−2
+0
+σ−q
+n (pd)−q/2) and we have
+• maxr ζyi,r,i ≥ m−1/q for all i ∈ [n].
+• maxj,r,i |ω(t)
+j,r,i| = �O(σ0σn
+√pd).
+• maxj,r,k |γ(t)
+j,r,k| ≤ �O(σ0µ).
+Proof. First of all, recall that from Definition C.1 we have for j = yi
+�
+�w(t)
+j,r, ξi
+�
+=
+�
+�w(0)
+j,r , ξi
+�
++ ζ(t)
+j,r,i +
+�
+k̸=j
+γ(t)
+j,r,k
+�
+µk, �ξj,r,i
+�
+µ2
++
+�
+i′̸=i
+ζ(t)
+j,r,i
+�
+�ξj,r,i′, ξi
+�
+����ξj,r,i′
+���
+2
+2
++
+n
+�
+i′=1
+ω(t)
+j,r,i
+�
+�ξj,r,i′, ξi
+�
+����ξj,r,i′
+���
+2
+2
+.
+40
+
+Let
+B(t)
+i
+= max
+j=yi,r
+�
+ζ(t)
+j,r,i +
+�
+�w(0)
+j,r , ξi
+�
+− O(n log1/q T ⋆
+�
+log d
+pd ) − O(nσ0σn
+�
+pd
+�
+log d
+pd )
+�
+.
+Since maxj=yi,r
+�
+�w(0)
+j,r , ξi
+�
+≥ Ω(σ0σn
+√pd), we have
+B(0)
+i
+≥ Ω(σ0σn
+�
+pd) − O(n log1/q T ⋆
+�
+log d
+pd ) − O(nσ0σn
+�
+pd
+�
+log d
+pd ) ≥ Ω(σ0σn
+�
+pd).
+Let Ti to be the last time that ζ(t)
+j,r,i ≤ m−1/q. We can compute the growth of B(t)
+i
+as
+B(t+1)
+i
+≥ B(t)
+i
++ Θ(ησ2
+npd
+n
+)[B(t)
+i ]q−1
+≥ B(t)
+i
++ Θ(ησ2
+npd
+n
+)[B(0)
+i
+]q−2B(t)
+i
+≥
+�
+1 + Θ
+�
+ησq−2
+0
+σq
+npq/2dq/2
+n
+��
+B(t)
+i .
+Therefore, B(t)
+i
+will reach 2m−1/q within �O(η−1nσq−2
+0
+σ−q
+n (pd)−q/2) iterations.
+On the other hand, by Proposition D.10, we have |ω(t)
+j,r,i| ≤ β+6Cnα
+�
+log d
+pd = O(σ0σn
+√pd log d).
+E.3
+Converging Phase
+From the first stage we know that
+�w(T1)
+j,r
+= �w(0)
+j,r + +
+�
+k̸=j
+γ(t)
+j,r,k
+µk ⊙ mj,r
+µ2
++
+n
+�
+i=1
+ζ(T1)
+j,r,i
+�ξj,r,i
+����ξj,r,i
+���
+2
+2
++
+n
+�
+i=1
+ω(T1)
+j,r,i
+�ξj,r,i
+����ξj,r,i
+���
+2
+2
+.
+Now we define �
+W⋆ as follows:
+�w⋆
+j,r = �w(0)
+j,r + Θ(m log(1/ϵ))
+�
+��
+n
+�
+i=1
+I(j = yi)
+�ξj,r,i
+����ξj,r,i
+���
+2
+2
+�
+�� .
+Lemma E.4. Based on the result from feature growing phase,
+����
+W(T1) − �
+W⋆���
+F ≤ O(m2n1/2 log(1/ϵ)σ−1
+n (pd)−1/2).
+Proof. We derive the following bound:
+����
+W(T1) − �
+W⋆���
+F
+≤
+����
+W(T1) − �
+W(0)���
+F +
+����
+W(0) − �
+W⋆���
+F
+41
+
+≤
+�
+j,r
+�
+�
+�
+������
+�
+k̸=j
+γ(t)
+j,r,k
+µk
+µ2
+������
+2
++
+�������
+n
+�
+i=1
+ζ(T1)
+j,r,i
+�ξj,r,i
+����ξj,r,i
+���
+2
+2
+�������
+2
++
+�������
+n
+�
+i=1
+ω(T1)
+j,r,i
+�ξj,r,i
+����ξj,r,i
+���
+2
+2
+�������
+2
+�
+�
+� + Θ(m2n1/2 log(1/ϵ)σ−1
+n (pd)−1/2)
+≤ Km(O(
+√
+Kσ0) + O(n1/2σ−1
+n (pd)−1/2 log1/q T ⋆)) + �O(m2n1/2 log(1/ϵ)σ−1
+n (pd)−1/2)
+≤ �O(m2n1/2 log(1/ϵ)σ−1
+n (pd)−1/2),
+where the first inequality follows from triangle inequality, the second inequality follows from the
+expression of W(T1), W⋆, and the third inequality follows from Lemma D.5 and the fact that
+ζ(t)
+j,r,i > 0 if and only if j = yi.
+Lemma E.5. For T1 ≤ t ≤ T ⋆, we have
+�
+∇Fyi(�
+Wyi, xi), �
+W⋆
+yi
+�
+−
+�
+∇Fj(�
+Wj, xi), �
+W⋆
+j
+�
+≥ q log 2qK
+ϵ
+.
+Lemma E.6. For T1 ≤ t ≤ T ⋆ and j = yi, we have
+�
+∇Fj(�
+W(t)
+j , xi), �
+W⋆
+j
+�
+≥ Θ(m1/q log(1/ϵ)).
+Proof. By Lemma D.5, we have
+�
+�ξj,r,i, �w⋆
+j,r
+�
+= Θ(m log(1/ϵ)) and by Lemma E.3 for j = yi,
+maxr
+�
+�w(t)
+j,r, ξi
+�
+≥ maxr ζj,r,i − maxr
+�
+�w(0)
+j,r , ξi
+�
+− O(n
+�
+log d
+d α) ≥ Θ(m−1/q). Then we have
+�
+∇Fj(�
+W(t)
+j , xi), �
+W⋆
+j
+�
+=
+m
+�
+r=1
+σ′ ��
+�w(t)
+j,r, ξi
+�� �
+�ξj,r,i, �w⋆
+j,r
+�
+≥ Θ(m1/q log(1/ϵ)).
+Lemma E.7. For T1 ≤ t ≤ T ⋆ and j ̸= yi, we have
+�
+∇Fj(�
+W(t)
+j , xi), �
+W⋆
+j
+�
+≤ O(1).
+Proof. We first compute
+�
+�w⋆
+j,r, ξi
+�
+=
+�
+�w(0)
+j,r , ξi
+�
++Θ(m log(1/ϵ)) �n
+i=1 I(j = yi)⟨�ξj,r,i,ξi⟩
+∥�ξj,r,i∥
+2
+2
+= O(σ0σn
+√pd log d).
+Further,
+�
+�w(t)
+j,r, ξi
+�
+=
+�
+�w(0)
+j,r , ξi
+�
++
+�
+k̸=j
+γ(t)
+j,r,k
+�
+µk, �ξj,r,i
+�
+µ2
++
+n
+�
+i=1
+ζ(t)
+j,r,i
+�
+�ξj,r,i, ξi
+�
+����ξj,r,i
+���
+2
+2
++
+n
+�
+i=1
+ω(t)
+j,r,i
+�
+�ξj,r,i, ξi
+�
+����ξj,r,i
+���
+2
+2
+≤ O(σ0σn
+�
+pd log d),
+42
+
+where the inequality follows from Lemma D.5 and Lemma D.15. Thus, we have
+�
+∇Fj(�
+W(t)
+j , xi), �
+W⋆
+j
+�
+=
+m
+�
+r=1
+σ′ ��
+�w(t)
+j,r, ξi
+�� �
+�ξj,r,i, �w⋆
+j,r
+�
+≤ mO
+�
+σ0σn
+�
+pd log d
+�q
+≤ O(1),
+where the last inequality follows from our choice of σ0 ≤ �O(m−1/qµ−1).
+Lemma E.8. Under the same assumption as Theorem E.1, we have
+���W(t) − W⋆���
+2
+F −
+���W(t+1) − W⋆���
+2
+F ≥ CηLS(�
+W(t)) − ηϵ.
+Proof. To simplify our notation, we define �F (t)
+j (xi) =
+�
+∇Fj(�
+W(t)
+j , xi), �
+W⋆
+j
+�
+. The proof is exactly
+the same as the proof of Lemma D.23.
+����
+W(t) − �
+W⋆���
+2
+F −
+����
+W(t+1) − �
+W⋆���
+2
+F
+= 2η
+�
+∇LS(�
+W(t)) ⊙ M, �
+W(t) − �
+W⋆�
+− η2 ���∇LS(�
+W(t)) ⊙ M
+���
+2
+F
+= 2η
+n
+n
+�
+i=1
+K
+�
+j=1
+ℓ′(t)
+j,i
+�
+qFj(�
+W(t)
+j ; xi, yi) −
+�
+∇Fj(�
+W(t)
+j , xi), �
+W⋆
+j
+��
+− η2 ���∇LS(�
+W(t)) ⊙ M
+���
+2
+F
+≥ 2qη
+n
+n
+�
+i=1
+�
+�log(1 +
+K
+�
+j=1
+eFj−Fyi) − log(1 +
+K
+�
+j=1
+e( �Fj− �Fyi)/q)
+�
+� − η2 ���∇LS(�
+W(t)) ⊙ M
+���
+2
+F
+≥ 2qη
+n
+n
+�
+i=1
+�
+ℓ(�
+W(t); xi, yi) − log(1 + Ke− log(2qK/ϵ))
+�
+− η2 ���∇LS(�
+W(t)) ⊙ M
+���
+2
+F
+≥ 2qη
+n
+n
+�
+i=1
+�
+ℓ(�
+W(t); xi, yi) − ϵ
+2q
+�
+− η2 ���∇LS(�
+W(t)) ⊙ M
+���
+2
+F
+≥ CηLS(�
+W(t)) − ηϵ,
+where the first inequality follows from the convexity of the cross-entropy loss with softmax, the
+second inequality follows from Lemma D.20, the third inequality follows because log(1 + x) ≤ x,
+and the last inequality follows from Lemma D.19 for some constant C > 0.
+Lemma E.9 (Formal Restatement of Lemma 4.4). Under the same assumption as Theorem E.1,
+choose T2 = T1 +
+�
+∥�
+W(T1)−�
+W⋆∥
+2
+F
+2ηϵ
+�
+= T1 + �O(η−1ϵ−1m4nσ−2
+n (pd)−1). Then for any time t during
+this stage we have maxj,r |ω(t)
+j,r,i| = O(σ0
+√pd) and
+1
+t − T1
+t
+�
+s=T1
+LS(�
+W(s)) ≤
+����
+W(T1) − �
+W⋆���
+2
+F
+Cη(t − T1)
++ ϵ
+C .
+43
+
+Proof. We have
+����
+W(s) − �
+W⋆���
+2
+F −
+����
+W(s+1) − �
+W⋆���
+2
+F ≥ CηLS(�
+W(s)) − ηϵ.
+Taking a telescopic sum from T1 to t yields
+t
+�
+s=T1
+LS(�
+W(s)) ≤
+����
+W(T1) − �
+W⋆���
+2
+F + ηϵ(t − T1)
+Cη
+.
+Combining Lemma E.4, we have
+t
+�
+s=T1
+LS(�
+W(s)) ≤ O(η−1 ����
+W(T1) − �
+W⋆���
+2
+F ) = �O(η−1m4nσ−2
+n (pd)−1).
+E.4
+Generalization Analysis
+Theorem E.10 (Formal Restatement of the Generalization Part of Theorem 4.1). Under the same
+assumption as Theorem E.1, within O(η−1nσq−2
+0
+σ−q
+n (pd)−q/2+η−1ϵ−1m4nσ−2
+n (pd)−1) iterations, we
+can find �
+W(T) such that LS(�
+W(T)) ≤ ϵ, and LD(�
+W(t)) ≥ Ω(log K).
+Proof. First of all, from Lemma E.9 we know there exists t ∈ [T1, T2] such that LS(�
+W(T)) ≤ ϵ.
+Then, we can bound
+����w(t)
+j,r
+���
+2 =
+�������
+�w(0)
+j,r +
+�
+k̸=j
+γ(t)
+j,r,k
+µk
+µ2 +
+n
+�
+i=1
+ζ(t)
+j,r,i
+�ξj,r,i
+����ξj,r,i
+���
+2
+2
++
+n
+�
+i=1
+ω(t)
+j,r,i
+�ξj,r,i
+����ξj,r,i
+���
+2
+2
+�������
+2
+≤
+����w(0)
+j,r
+���
+2 +
+�
+k̸=j
+|γ(t)
+j,r,k| 1
+µ +
+n
+�
+i=1
+ζ(t)
+j,r,i
+1
+����ξj,r,i
+���
+2
++
+n
+�
+i=1
+|ω(t)
+j,r,i|
+1
+����ξj,r,i
+���
+2
+≤ O(σ0
+√
+d) + �O(nσ−1
+n (pd)−1/2).
+Consider a new example (x, y). Taking a union bound over r, with probability at least 1 − d−1, we
+have
+���
+�
+w(t)
+y,r, ξ
+���� = �O(σ0σn
+√
+d + n(pd)−1/2),
+for all r ∈ [m]. Then,
+Fy(x) =
+m
+�
+r=1
+σ
+��
+�w(t)
+j,r, µy
+��
++ σ
+��
+�w(t)
+j,r, ξ
+��
+≤ m max
+r
+���
+�
+w(t)
+y,r, ξ
+����
+q
+≤ m �O(σq
+0σq
+ndq/2 + nq(pd)−q/2)
+≤ 1,
+44
+
+where the last inequality follows because σ0 ≤ �O(m−1/qµ−1) and d ≥ �Ω(m2/qn2).
+Thus, with
+probability at least 1 − 1/d,
+ℓ(F(�
+W(t); x)) ≥ log(1 + (K − 1)e−1).
+45
+
diff --git a/GdAyT4oBgHgl3EQffPg-/content/tmp_files/load_file.txt b/GdAyT4oBgHgl3EQffPg-/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4cb5519e875260fbb699e38773a495f1d7cd50eb
--- /dev/null
+++ b/GdAyT4oBgHgl3EQffPg-/content/tmp_files/load_file.txt
@@ -0,0 +1,1939 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf,len=1938
+page_content='Theoretical Characterization of How Neural Network  Pruning Affects its Generalization  Hongru Yang ∗  Yingbin Liang †  Xiaojie Guo‡  Lingfei Wu§  Zhangyang Wang ¶  Abstract  It has been observed in practice that applying pruning-at-initialization methods to neural  networks and training the sparsified networks can not only retain the testing performance of the  original dense models, but also sometimes even slightly boost the generalization performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Theoretical understanding for such experimental observations are yet to be developed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' This  work makes the first attempt to study how different pruning fractions affect the model’s gradient  descent dynamics and generalization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Specifically, this work considers a classification task for  overparameterized two-layer neural networks, where the network is randomly pruned according  to different rates at the initialization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' It is shown that as long as the pruning fraction is below  a certain threshold, gradient descent can drive the training loss toward zero and the network  exhibits good generalization performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  More surprisingly, the generalization bound gets  better as the pruning fraction gets larger.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' To complement this positive result, this work further  shows a negative result: there exists a large pruning fraction such that while gradient descent  is still able to drive the training loss toward zero (by memorizing noise), the generalization  performance is no better than random guessing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' This further suggests that pruning can change  the feature learning process, which leads to the performance drop of the pruned neural network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Up to our knowledge, this is the first generalization result for pruned neural networks, suggesting  that pruning can improve the neural network’s generalization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  1  Introduction  Neural network pruning can be dated back to the early stage of the development of neural networks  (LeCun et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', 1989).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Since then, many research works have been focusing on using neural network  pruning as a model compression technique, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (Molchanov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Luo and Wu, 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Ye  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Yang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' However, all these work focused on pruning neural networks after  training to reduce inference time, and, thus, the efficiency gain from pruning cannot be directly  transferred to the training phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' It is not until the recent days that Frankle and Carbin (2018)  showed a surprising phenomenon: a neural network pruned at the initialization can be trained to  achieve competitive performance to the dense model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' They called this phenomenon the lottery  ticket hypothesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' The lottery ticket hypothesis states that there exists a sparse subnetwork inside  ∗Department of Computer Science, The University of Texas at Austin;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' e-mail: hy6385@utexas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='edu  †Department of Electrical and Computer Engineering, The Ohio State University;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' e-mail: liang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='889@osu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='edu  ‡IBM Thomas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Watson Research Center;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' e-mail: xguo7@gmu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='edu  §Pinterest;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' e-mail: lwu@email.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='wm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='edu  ¶Department  of  Electrical  and  Computer  Engineering,  The  University  of  Texas  at  Austin;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  e-mail:  atlaswang@utexas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='edu  1  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='00335v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='LG]  1 Jan 2023  a dense network at the random initialization stage such that when trained in isolation, it can  match the test accuracy of the original dense network after training for at most the same number  of iterations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' On the other hand, the algorithm Frankle and Carbin (2018) proposed to find the  lottery ticket requires many rounds of pruning and retraining which is computationally expensive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Many subsequent works focused on developing new methods to reduce the cost of finding such a  network at the initialization (Lee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Tanaka et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Liu and Zenke,  2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', 2021a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' A further investigation by Frankle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2020) showed that some of  these methods merely discover the layer-wise pruning ratio instead of sparsity pattern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  The discovery of the lottery ticket hypothesis sparkled further interest in understanding this  phenomenon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Another line of research focused on finding a subnetwork inside a dense network  at the random initialization such that the subnetwork can achieve good performance (Zhou et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=',  2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Ramanujan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Shortly after that, Malach et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2020) formalized this phenomenon  which they called the strong lottery ticket hypothesis: under certain assumption on the weight ini-  tialization distribution, a sufficiently overparameterized neural network at the initialization contains  a subnetwork with roughly the same accuracy as the target network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Later, Pensia et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2020)  improved the overparameterization parameters and Sreenivasan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2021) showed that such a  type of result holds even if the weight is binary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Unsurprisingly, as it was pointed out by Malach  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2020), finding such a subnetwork is computationally hard.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Nonetheless, all of the analysis is  from a function approximation perspective and none of the aforementioned works have considered  the effect of pruning on gradient descent dynamics, let alone the neural networks’ generalization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Interestingly, via empirical experiments, people have found that sparsity can further improve  generalization in certain scenarios (Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', 2021b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Ding et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' He et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' There  have also been empirical works showing that random pruning can be effective (Frankle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Su et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', 2021b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' However, theoretical understanding of such benefit of pruning  of neural networks is still limited.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' In this work, we take the first step to answer the following  important open question from a theoretical perspective:  How does pruning fraction affect the training dynamics and the model’s generalization,  if the model is pruned at the initialization and trained by gradient descent?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  We study this question using random pruning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' We consider a classification task where the input  data consists of class-dependent sparse signal and random noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' We analyze the training dynamics  of a two-layer convolutional neural network pruned at the initialization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Specifically, this work  makes the following contributions:  Mild pruning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' We prove that there indeed exists a range of pruning fraction where the  pruning fraction is small and the generalization error bound gets better as pruning fraction  gets larger.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' In this case, the signal in the feature is well-preserved and due to the effect of  pruning purifying the feature, the effect from noise is reduced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' We provide detailed explana-  tion in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Up to our knowledge, this is the first theoretical result on generalization for  pruned neural networks, which suggests that pruning can improve generalization under some  setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Further, we conduct experiments to verify our results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Over pruning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' To complement the above positive result, we also show a negative result: if  the pruning fraction is larger than a certain threshold, then the generalization performance  is no better than a simple random guessing, although gradient descent is still able to drive  the training loss toward zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' This further suggests that the performance drop of the pruned  2  Probability Density  Signal Strength  μ  Mild Pruning  Full model  Over Pruning  Figure 1: A pictorial demonstration of our results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' The bell-shaped curves model the distribution of  the signal in the features, where the mean represents the signal strength and the width of the curve  indicates the variance of noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Our results show that mild pruning preserves the signal strength  and reduces the noise variance (and hence yields better generalization), whereas over pruning lowers  signal strength albeit reducing noise variance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  neural network is not solely caused by the pruned network’s own lack of trainability or ex-  pressiveness, but also by the change of gradient descent dynamics due to pruning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Technically, we develop novel analysis to bound pruning effect to weight-noise and weight-  signal correlation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Further, in contrast to many previous works that considered only the  binary case, our analysis handles multi-class classification with general cross-entropy loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Here, a key technical development is a gradient upper bound for multi-class cross-entropy  loss, which might be of independent interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Pictorially, our result is summarized in Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' We point out that the neural network training we  consider is in the feature learning regime, where the weight parameters can go far away from their  initialization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' This is fundamentally different from the popular neural tangent kernel regime,  where the neural networks essentially behave similar to its linearization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='1  Related Works  The Lottery Ticket Hypothesis and Sparse Training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' The discovery of the lottery ticket  hypothesis (Frankle and Carbin, 2018) has inspired further investigation and applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' One line  of research has focused on developing computationally efficient methods to enable sparse training:  the static sparse training methods are aiming at identifying a sparse mask at the initialization stage  based on different criterion such as SNIP (loss-based) (Lee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', 2018), GraSP (gradient-based)  (Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', 2019), SynFlow (synaptic strength-based) (Tanaka et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', 2020), neural tangent kernel  based method (Liu and Zenke, 2020) and one-shot pruning (Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', 2021a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Random pruning  has also been considered in static sparse training such as uniform pruning (Mariet and Sra, 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  He et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Gale et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Suau et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', 2018), non-uniform pruning (Mocanu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', 2016),  expander-graph-related techniques (Prabhu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Kepner and Robinett, 2019) Erd¨os-R´enyi  (Mocanu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', 2018) and Erd¨os-R´enyi-Kernel (Evci et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' On the other hand, dynamic  sparse training allows the sparse mask to be updated (Mocanu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Mostafa and Wang,  2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Evci et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Jayakumar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', 2021c,d,a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Peste et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' The sparsity  pattern can also be learned by using sparsity-inducing regularizer (Yang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Recently, He  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2022) discovered that pruning can exhibit a double descent phenomenon when the data-set  labels are corrupted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Another line of research has focused on studying pruning the neural networks at its random  initialization to achieve good performance (Zhou et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Ramanujan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' In particular,  3  Ramanujan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2020) showed that it is possible to prune a randomly initialized wide ResNet-50  to match the performance of a ResNet-34 trained on ImageNet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' This phenomenon is named the  strong lottery ticket hypothesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Later, Malach et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2020) proved that under certain assumption  on the initialization distribution, a target network of width d and depth l can be approximated by  pruning a randomly initialized network that is of a polynomial factor (in d, l) wider and twice deeper  even without any further training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' However finding such a network is computationally hard, which  can be shown by reducing the pruning problem to optimizing a neural network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Later, Pensia et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  (2020) improved the widening factor to being logarithmic and Sreenivasan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2021) proved that  with a polylogarithmic widening factor, such a result holds even if the network weight is binary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' A  follow-up work shows that it is possible to find a subnetwork achieving good performance at the  initialization and then fine-tune (Sreenivasan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Our work, on the other hand, analyzes  the gradient descent dynamics of a pruned neural network and its generalization after training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Analyses of Training Neural Networks by Gradient Descent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' A series of work (Allen-  Zhu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Du et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Lee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Zou et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Zou and Gu, 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Ji and  Telgarsky, 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', 2020b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Song and Yang, 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Oymak and Soltanolkotabi, 2020) has  proved that if a deep neural network is wide enough, then (stochastic) gradient descent provably can  drive the training loss toward zero in a fast rate based on neural tangent kernel (NTK) (Jacot et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=',  2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Further, under certain assumption on the data, the learned network is able to generalize  (Cao and Gu, 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Arora et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' However, as it is pointed out by Chizat et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2019), in the  NTK regime, the gradient descent dynamics of the neural network essentially behaves similarly to  its linearization and the learned weight is not far away from the initialization, which prohibits the  network from performing any useful feature learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' In order to go beyond NTK regime, one line  of research has focused on the mean field limit (Song et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Chizat and Bach, 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Rotskoff  and Vanden-Eijnden, 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Wei et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', 2020a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Sirignano and Spiliopoulos, 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Fang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Recently, people have started to study the neural network training dynamics in  the feature learning regime where data from different class is defined by a set of class-related signals  which are low rank (Allen-Zhu and Li, 2020, 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Cao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Shi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Telgarsky,  2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' However, all previous works did not consider the effect of pruning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Our work also focuses  on the aforementioned feature learning regime, but for the first time characterizes the impact of  pruning on the generalization performance of neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  2  Preliminaries and Problem Formulation  In this section, we introduce our notation, data generation process, neural network architecture  and the optimization algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Notations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' We use lower case letters to denote scalars and boldface letters and symbols (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  x) to denote vectors and matrices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' We use ⊙ to denote element-wise product.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' For an integer n, we  use [n] to denote the set of integers {1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' , n}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' We use x = O(y), x = Ω(y), x = Θ(y) to denote  that there exists a constant C such that x ≤ Cy, x ≥ Cy, x = Cy respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' We use �O, �Ω and  �Θ to hide polylogarithmic factor in these notations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Finally, we use x = poly(y) if x = O(yC) for  some positive constant C, and x = poly log y if x = poly(log y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='1  Settings  Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='1 (Data distribution of K classes).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Consider we are given the set of signal vectors  {µei}K  i=1, where µ > 0 denotes the strength of the signal, and ei denotes the i-th standard basis  4  vector with its i-th entry being 1 and all other coordinates being 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Each data point (x, y) with  x = [x⊤  1 , x⊤  2 ]⊤ ∈ R2d and y ∈ [K] is generated from the following distribution D:  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' The label y is generated from a uniform distribution over [K].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' A noise vector ξ is generated from the Gaussian distribution N(0, σ2  nI).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' With probability 1/2, assign x1 = µy, x2 = ξ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' with probability 1/2, assign x2 = µy, x1 = ξ  where µy = µey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  The sparse signal model is motivated by the empirical observation that during the process of  training neural networks, the output of each layer of ReLU is usually sparse instead of dense.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' This  is partially due to the fact that in practice the bias term in the linear layer is used (Song et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=',  2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' For samples from different classes, usually a different set of neurons fire.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Our study can be  seen as a formal analysis on pruning the second last layer of a deep neural network in the layer-  peeled model as in Zhu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2021);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Zhou et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' We also point out that our assumption on  the sparsity of the signal is necessary for our analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' If we don’t have this sparsity assumption  and only make assumption on the ℓ2 norm of the signal, then in the extreme case, the signal is  uniformly distributed across all coordinate and the effect of pruning to the signal and the noise will  be essentially the same: their ℓ2 norm will both be reduced by a factor of √p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Network architecture and random pruning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' We consider a two-layer convolutional neural  network model with polynomial ReLU activation σ(z) = (max{0, z})q, where we focus on the case  when q = 3 1 The network is pruned at the initialization by mask M where each entry in the mask  M is generated i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' from Bernoulli(p).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Let mj,r denotes the r-th row of Mj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Given the data (x, y),  the output of the neural network can be written as F(W ⊙ M, x) = (F1(W1 ⊙ M1, x), F2(W2 ⊙  M2, x), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' , Fk(Wk ⊙ Mk, x)) where the j-th output is given by  Fj(Wj ⊙ Mj, x) =  m  �  r=1  [σ(⟨wj,r ⊙ mj,r, x1⟩) + σ(⟨wj,r ⊙ mj,r, x2⟩)]  =  m  �  r=1  [σ(⟨wj,r ⊙ mj,r, µ⟩) + σ(⟨wj,r ⊙ mj,r, ξ⟩)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  The mask M is only sampled once at the initialization and remains fixed through the entire training  process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' From now on, we use tilde over a symbol to denote its masked version, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=',  �  W = W ⊙ M and �wj,r = wj,r ⊙ mj,r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Since µj ⊙ mj,r = 0 with probability 1 − p, some neurons will not receive the corresponding  signal at all and will only learn noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Therefore, for each class j ∈ [k], we split the neurons into  two sets based on whether it receives its corresponding signal or not:  Sj  signal = {r ∈ [m] : µj ⊙ mj,r ̸= 0},  Sj  noise = {r ∈ [m] : µj ⊙ mj,r = 0}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Gradient descent algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' We consider the network is trained by cross-entropy loss with  softmax.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' We denote by logiti(F, x) :=  eFi(x)  �  j∈[k] eFj(x) and the cross-entropy loss can be written as  1We point out that as many previous works (Allen-Zhu and Li, 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Zou et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Cao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', 2022), polynomial  ReLU activation can help us simplify the analysis of gradient descent, because polynomial ReLU activation can give  a much larger separation of signal and noise (thus, cleaner analysis) than ReLU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Our analysis can be generalized to  ReLU activation by using the arguments in (Allen-Zhu and Li, 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  5  ℓ(F(x, y)) = − log logity(F, x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' The convolutional neural network is trained by minimizing the  empirical cross-entropy loss given by  LS(W) = 1  n  n  �  i=1  ℓ[F(W ⊙ M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' xi, yi)] = E  S ℓ[F(W ⊙ M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' xi, yi)],  where S = {(xi, yi)}n  i=1 is the training data set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Similarly, we define the generalization loss as  LD := E  (x,y)[ℓ(F(W ⊙ M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' x, y))].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  The model weights are initialized from a i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Gaussian N(0, σ2  0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' The gradient of the cross-entropy  loss is given by ℓ′  j,i := ℓ′  j(xi, yi) = logitj(F, xi) − I(j = yi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Since  ∇wj,rLS(W ⊙ M) = ∇wj,r⊙mj,rLS(W ⊙ M) ⊙ mj,r = ∇ �wj,rLS(�  W) ⊙ mj,r,  we can write the full-batch gradient descent update of the weights as  �w(t+1)  j,r  = �w(t)  j,r − η∇ �wj,rLS(�  W) ⊙ mj,r  = �w(t)  j,r − η  n  n  �  i=1  ℓ′(t)  j,i · σ′ ��  �w(t)  j,r, ξi  ��  �ξj,r,i − η  n  n  �  i=1  ℓ′(t)  j,i σ′ ��  �w(t)  j,r, µyi  ��  µyi ⊙ mj,r,  for j ∈ [K] and r ∈ [m], where �ξj,r,i = ξi ⊙ mj,r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Condition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' We consider the parameter regime described as follows: (1) Number of classes  K = O(log d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2) Total number of training samples n = poly log d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (3) Dimension d ≥ Cd for  some sufficiently large constant Cd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (4) Relationship between signal strength and noise strength:  µ = Θ(σn  √  d log d) = Θ(1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (5) The number of neurons in the network m = Ω(poly log d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (6)  Initialization variance: σ0 = �Θ(m−4n−1µ−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (7) Learning rate: Ω(1/ poly(d)) ≤ η ≤ �O(1/µ2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  (8) Target training loss: ϵ = Θ(1/ poly(d)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Conditions (1) and (2) ensure that there are enough samples in each class with high probability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Condition (3) ensures that our setting is in high-dimensional regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Condition (4) ensures that  the full model can be trained to exhibit good generalization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Condition (5), (6) and (7) ensures that  the neural network is sufficiently overparameterized and can be optimized efficiently by gradient  descent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Condition (7) and (8) further ensures that training time is polynomial in d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' We further  discuss the practical consideration of η and ϵ to justify their condition in Remark D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  3  Mild Pruning  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='1  Main result  The first main result shows that there exists a threshold on the pruning fraction p such that pruning  helps the neural network’s generalization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='1 (Main Theorem for Mild Pruning, Informal).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Under Condition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='2, if p ∈ [C1  log d  m , 1]  for some constant C1, then with probability at least 1 − O(d−1) over the randomness in the data,  network initialization and pruning, there exists T = �O(Kη−1σ2−q  0  µ−q +K2m4µ−2η−1ϵ−1) such that  6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' The training loss is below ϵ: LS(�  W(T)) ≤ ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' The generalization loss can be bounded by LD(�  W(T)) ≤ O(Kϵ) + exp(−n2/p).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='1 indicates that there exists a threshold in the order of Θ(log d  m ) such that if p is  above this threshold (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', the fraction of the pruned weights is small), gradient descent is able to  drive the training loss towards zero (as item 1 claims) and the overparameterized network achieves  good testing performance (as item 2 claims).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' In the next subsection, we explain why pruning can  help generalization via an outline of our proof, and we defer all the detailed proofs in Appendix D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='2  Proof Outline  Our proof contains the establishment of the following two properties:  First we show that after mild pruning the network is still able to learn the signal, and the  magnitude of the signal in the feature is preserved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Then we show that given a new sample, pruning reduces the noise effect in the feature which  leads to the improvement of generalization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  We first show the above properties for three stages of gradient descent: initialization, feature  growing phase, and converging phase, and then establish the generalization property.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Initialization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' First of all, readers might wonder why pruning can even preserve signal at all.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Intuitively, a network will achieve good performance if its weights are highly correlated with the  signal (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', their inner product is large).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Two intuitive but misleading heuristics are given by the  following:  Consider a fixed neuron weight.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  At the random initialization, in expectation, the signal  correlation with the weights is given by Ew,m[| ⟨w ⊙ m, µ⟩ |] ≤ pσ0µ and the noise correlation  with the weights is given by Ew,m,ξ[| ⟨w ⊙ m, ξ⟩ |] ≤  �  Ew,m,ξ[⟨w ⊙ m, ξ⟩2] = σ0σn  √pd by  Jensen’s inequality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Based on this argument, taking a sum over all the neurons, pruning will  hurt weight-signal correlation more than weight-noise correlation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Since we are pruning with Bernoulli(p), a given neuron will not receive signal at all with  probability 1 − p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Thus, there is roughly p fraction of the neurons receiving the signal and  the rest 1 − p fraction will be purely learning from noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Even though for every neuron,  roughly √p portion of ℓ2 mass from the noise is reduced, at the same time, pruning also  creates 1 − p fraction of neurons which do not receive signals at all and will purely output  noise after training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Summing up the contributions from every neuron, the signal strength  is reduced by a factor of p while the noise strength is reduced by a factor of √p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' We again  reach the conclusion of pruning under any rate will hurt the signal more than noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  The above analysis shows that under any pruning rate, it seems pruning can only hurt the signal  more than noise at the initialization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Such analysis would be indicative if the network training is  under the neural tangent kernel regime, where the weight of each neuron does not travel far from its  initialization so that the above analysis can still hold approximately after training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' However, when  the neural network training is in the feature learning regime, this average type analysis becomes  misleading.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Namely, in such a regime, the weights with large correlation with the signal at the  initialization will quickly evolve into singleton neurons and those weights with small correlation  7  will remain small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' In our proof, we focus on the featuring learning regime, and analyze how the  network weights change and what are the effect of pruning during various stages of gradient descent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  We now analyze the effect of pruning on weight-signal correlation and weight-noise correlation at  the initialization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Our first lemma leverages the sparsity of our signal and shows that if the pruning  is mild, then it will not hurt the maximum weight-signal correlation much at the initialization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' On  the other hand, the maximum weight-noise correlation is reduced by a factor of √p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='2 (Initialization).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' With probability at least 1 − 2/d, for all i ∈ [n],  σ0σn  �  pd ≤ max  r  �  �w(0)  j,r , ξi  �  ≤  �  2 log(Kmd)σ0σn  �  pd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Further, suppose pm ≥ Ω(log(Kd)), with probability 1 − 2/d, for all j ∈ [K],  σ0 ∥µj∥2 ≤  max  r∈Sj  signal  �  �w(0)  j,r , µj  �  ≤  �  2 log(8pmKd)σ0 ∥µj∥2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Given this lemma, we now prove that there exists at least one neuron that is heavily aligned  with the signal after training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Similarly to previous works (Allen-Zhu and Li, 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Zou et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Cao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', 2022), the analysis is divided into two phases: feature growing phase and converging  phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Feature Growing Phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' In this phase, the gradient of the cross-entropy is large and the  weight-signal correlation grows much more quickly than weight-noise correlation thanks to the  polynomial ReLU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' We show that the signal strength is relatively unaffected by pruning while the  noise level is reduced by a factor of √p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='3 (Feature Growing Phase, Informal).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Under Condition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='2, there exists time T1 such  that  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' The max weight-signal correlation is large: maxr  �  �w(T1)  j,r , µj  �  ≥ m−1/q for j ∈ [K].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' The weight-noise and cross-class weight-signal correlations are small: if j ̸= yi, then maxj,r,i  ���  �  �w(T1)  j,r , ξi  ���� ≤  O(σ0σn  √pd) and maxj,r,k  ���  �  �w(T1)  j,r , µk  ���� ≤ �O(σ0µ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Converging Phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' We show that gradient descent can drive the training loss toward zero  while the signal in the feature is still large.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' An important intermediate step in our argument is  the development of the following gradient upper bound for multi-class cross-entropy loss which  introduces an extra factor of K in the gradient upper bound.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='4 (Gradient Upper Bound, Informal).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Under Condition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='2, we have  ���∇LS(�  W(t)) ⊙ M  ���  2  F ≤ O(Km2/qµ2)LS(�  W(t)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Proof Sketch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' To prove this upper bound, note that for a given input (xi, yi), ℓ′(t)  yi,i∇Fyi(xi) should  make major contribution to  ���∇ℓ(�  W;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' xi, yi)  ���  F .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Further note that |ℓ′(t)  yi,i| = 1 − logityi(F;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' xi) =  �  j̸=yi eFj(xi)  �  j eFj(xi)  ≤  �  j̸=yi eFj(xi)  eFyi (xi)  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Now, apply the property that Fj(xi) is small for j ̸= yi (which we  prove in the appendix), the numerator will contribute a factor of K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' To bound the rest, we utilize  8  the special property of multi-class cross-entropy loss: |ℓ′(t)  j,i | ≤ |ℓ′(t)  yi,i| ≤ ℓ(t)  i .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  However, a naive  application of this inequality will result in a factor of K3 instead K in our bound.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' The trick is to  further use the fact that �  j̸=yi |ℓ′(t)  j,i | = |ℓ′(t)  yi,i|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Using the above gradient upper bound, we can show that the objective can be minimized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='5 (Converging Phase, Informal).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Under Condition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='2, there exists T2 such that for  some time t ∈ [T1, T2] we have  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' The results from the feature growing phase (Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='3) hold up to constant factors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' The training loss is small LS(�  W(t)) ≤ ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Notice that the weight-noise correlation still remains reduced by a factor of √p after training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='5 proves the statement of the training loss in Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Generalization Analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Finally, we show that pruning can purify the feature by reducing  the variance of the noise by a factor of p when a new sample is given.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' The lemma below shows that  the variance of weight-noise correlation for the trained weights is reduced by a factor of p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' The neural network weight �  W⋆ after training satisfies that  P  ξ  �  max  j,r  ����w⋆  j,r, ξ  ��� ≥ (2m)−2/q  �  ≤ 2Km exp  �  − (2m)−4/q  O(σ2  0σ2npd)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Using this lemma, we can show that pruning yields better generalization bound (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', the bound  on the generalization loss) claimed in Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  4  Over Pruning  Our second result shows that there exists a relatively large pruning fraction (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', small p) such that  the learned model yields poor generalization, although gradient descent is still able to drive the  training error toward zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' The full proof is defered to Appendix E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='1 (Main Theorem for Over Pruning, Informal).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Under Condition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='2 if p = Θ(  1  Km log d),  then with probability at least 1−1/ poly log d over the randomness in the data, network initialization  and pruning, there exists T = O(η−1nσq−2  0  σ−q  n (pd)−q/2 + η−1ϵ−1m4nσ−2  n (pd)−1) such that  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' The training loss is below ϵ: LS(�  W(T)) ≤ ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' The generalization loss is large: LD(�  W(T)) ≥ Ω(log K).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Remark 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' The above theorem indicates that in the over-pruning case, the training loss can still  go to zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' However, the generalization loss of our neural network behaves no much better than  random guessing, because given any sample, random guessing will assign each class with probability  1/K, which yields a generalization loss of log K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' The readers might wonder why the condition for  this to happen is p = Θ(  1  Km log d) instead of O(  1  Km log d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Indeed, the generalization will still be bad  if p is too small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' However, now the neural network is not only unable to learn the signal but also  cannot efficiently memorize the noise via gradient descent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Proof Outline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Now we analyze the over-pruning case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' We first show that there is a good chance  that the model will not receive any signal after pruning due to the sparse signal assumption and  mild overparameterization of the neural network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Then, leveraging such a property, we bound the  9  weight-signal and weight-noise properties for the feature growing and converging phases of gradient  descent, as stated in the following two lemmas, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Our result indicates that the training  loss can still be driven toward zero by letting the neural network memorize the noise, the proof of  which further exploits the fact that high dimensional Gaussian noise are nearly orthogonal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='3 (Feature Growing Phase, Informal).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Under Condition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='2, there exists T1 such that  Some weights has large correlation with noise: maxr  �  �w(T1)  yi,r , ξi  �  ≥ m−1/q for all i ∈ [n].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  The cross-class weight-noise and weight-signal correlations are small: if j ̸= yi, then maxj,r,i  ���  �  �w(T1)  j,r , ξi  ���� =  �O(σ0σn  √pd) and maxj,r,k  ���  �  �w(T1)  j,r , µk  ���� ≤ �O(σ0µ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='4 (Converging Phase, Informal).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Under Condition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='2, there exists a time T2 such that  ∃t ∈ [T1, T2], the results from phase 1 still holds (up to constant factors) and LS(�  W(t)) ≤ ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Finally, since the above lemmas show that the network is purely memorizing the noise, we  further show that such a network yields poor generalization performance as stated in Theorem  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  5  Experiments  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='1  Simulations to Verify Our Results  In this section, we conduct simulations to verify our results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' We conduct our experiment using  binary classification task and show that our result holds for ReLU networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Our experiment  settings are the follows: we choose input to be x = [x1, x2] = [ye1, ξ] ∈ R800 and x1, x2 ∈ R400,  where ξi is sampled from a Gaussian distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' The class labels y are {±1}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' We use 100 training  examples and 100 testing examples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' The network has width 150 and is initialized with random  Gaussian distribution with variance 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='01.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Then, p fraction of the weights are randomly pruned.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  We use the learning rate of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='001 and train the network over 1000 iterations by gradient descent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  The observations are summarized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' In Figure 2a, when the noise level is σn = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='5,  the pruned network usually can perform at the similar level with the full model when p ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='5  and noticably better when p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' When p > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='5, the test error increases dramatically while  the training accuracy still remains perfect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' On the other hand, when the noise level becomes large  σn = 1 (Figure 2b), the full model can no longer achieve good testing performance but mild pruning  can improve the model’s generalization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Note that the training accuracy in this case is still perfect  (omitted in the figure).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' We observe that in both settings when the model test error is large, the  variance is also large.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' However, in Figure 2b, despite the large variance, the mean curve is already  smooth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' In particular, Figure 2c plots the testing error over the training iterations under p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='5  pruning rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' This suggests that pruning can be beneficial even when the input noise is large.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='2  On the Real World Dataset  To further demonstrate the mild/over pruning phenomenon, we conduct experiments on MNIST  (Deng, 2012) and CIFAR-10 (Krizhevsky et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', 2009) datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' We consider neural network ar-  chitectures including MLP with 2 hidden layers of width 1024, VGG, ResNets (He et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', 2016)  and wide ResNet (Zagoruyko and Komodakis, 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' In addition to random pruning, we also add  10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='8  Pruning rates  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='20  Error  Training/Testing Error over Pruning Rates  Testing error  Training error  (a)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='8  Pruning rates  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='22  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='24  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='26  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='28  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='30  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='32  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='34  Error  Training/Testing Error over Pruning Rates  Testing error  (b)  0  200  400  600  800  1000  Iterations  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='30  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='35  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='40  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='45  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='50  Error  Testing error  full  pruned  (c)  Figure 2: Figure (a) shows the relationship between pruning rates p and training/testing error  under noise variance σn = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Figure (b) shows the relationship between pruning rates p and  testing error under noise variance σn = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' The training error is omitted since it stays effectively  at zero across all pruning rates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Figure (c) shows a particular training curve under pruning rate  p = 50% and noise variance σn = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Each data point is created by taking an average over 10  independent runs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='0 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='0 36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='0 48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='8 59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='0 67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='2 73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='8 79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='0 83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='2 86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='6 89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='3 91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='4 93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='1 94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='5 95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='6 96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='5 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='2  Sparsity  96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='5  97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='0  97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='5  98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='0  98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='5  99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='0  99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='5  100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='0  Accuracy  MLP MNIST Accuracy vs Sparsity  Random (Train)  Random (Test)  IMP (Train)  IMP (Test)  (a)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='0 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='0 36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='0 48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='8 59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='0 67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='2 73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='8 79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='0 83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='2 86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='6 89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='3 91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='4 93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='1 94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='5 95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='6 96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='5 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='2  Sparsity  88  90  92  94  96  98  100  Accuracy  VGG-16 CIFAR-10 Accuracy vs Sparsity  Random (Train)  Random (Test)  IMP (Train)  IMP (Test)  (b)  Figure 3: Figure (a) shows the result between pruning rates p and accuracy on MLP-1024-1024  on MNIST.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Figure (b) shows the result on VGG-16 on CIFAR-10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Each data point is created by  taking an average over 3 independent runs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  iterative-magnitude-based pruning Frankle and Carbin (2018) into our experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Both pruning  methods are prune-at-initialization methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Our implementation is based on Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2021c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Under the real world setting, we do not expect our theorem to hold exactly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Instead, our  theorem implies that (1) there exists a threshold such that the testing performance is no much  worse than (or sometimes may slightly better than) its dense counter part;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and (2) the training  error decreases later than the testing error decreases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Our experiments on MLP (Figure 3a) and  VGG-16 (Figure 3b) show that this is the case: for MLP the test accuracy is steady competitive to  its dense counterpart when the sparsity is less than 79% and 36% for VGG-16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' We further provide  experiments on ResNet in the appendix for validation of our theoretical results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  6  Discussion and Future Direction  In this work, we provide theory on the generalization performance of pruned neural networks trained  by gradient descent under different pruning rates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Our results characterize the effect of pruning  under different pruning rates: in the mild pruning case, the signal in the feature is well-preserved  11  and the noise level is reduced which leads to improvement in the trained network’s generalization;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  on the other hand, over pruning significantly destroys signal strength despite of reducing noise  variance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' One open problem on this topic still appears challenging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' In this paper, we characterize  two cases of pruning: in mild pruning the signal is preserved and in over pruning the signal is  completely destroyed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  However, the transition between these two cases is not well-understood.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Further, it would be interesting to consider more general data distribution, and understand how  pruning affects training multi-layer neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' We leave these interesting directions as future  works.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  References  Allen-Zhu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Li, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Towards understanding ensemble, knowledge distillation and  self-distillation in deep learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' arXiv preprint arXiv:2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='09816 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Allen-Zhu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Li, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Feature purification: How adversarial training performs robust  deep learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' In 2021 IEEE 62nd Annual Symposium on Foundations of Computer Science  (FOCS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' IEEE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Allen-Zhu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Li, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Song, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' A convergence theory for deep learning via over-  parameterization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' In International Conference on Machine Learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' PMLR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Arora, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Du, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Hu, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Li, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Wang, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Fine-grained analysis of optimization  and generalization for overparameterized two-layer neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' In International Conference  on Machine Learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' PMLR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Cao, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Chen, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Belkin, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Gu, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Benign overfitting in two-layer convolutional  neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' arXiv preprint arXiv:2202.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='06526 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Cao, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Gu, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Generalization bounds of stochastic gradient descent for wide and  deep neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Advances in neural information processing systems 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Chen, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Ji, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Ding, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Fang, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Wang, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Zhu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Liang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Shi, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Yi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and  Tu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2021a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Only train once: A one-shot neural network training and pruning framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Advances in Neural Information Processing Systems 34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Chen, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Zhang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Balachandra, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Ma, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Wang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Wang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2021b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Sparsity winning twice: Better robust generalization from more efficient training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' In International  Conference on Learning Representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Chen, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Cheng, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Wang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Gan, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Liu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Wang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2021c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' The elastic lottery  ticket hypothesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Github Repository, MIT License .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Chen, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Cao, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Gu, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Zhang, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2020a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' A generalized neural tangent kernel analysis  for two-layer neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Advances in Neural Information Processing Systems 33 13363–  13373.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Chen, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Cao, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Zou, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Gu, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2020b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' How much over-parameterization is sufficient  to learn deep relu networks?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' In International Conference on Learning Representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  12  Chizat, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Bach, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  On the global convergence of gradient descent for over-  parameterized models using optimal transport.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Advances in neural information processing sys-  tems 31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Chizat, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Oyallon, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Bach, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' On lazy training in differentiable programming.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Advances in Neural Information Processing Systems 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Deng, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' The mnist database of handwritten digit images for machine learning research  [best of the web].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' IEEE signal processing magazine 29 141–142.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Ding, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Chen, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Wang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Audio lottery: Speech recognition made ultra-  lightweight, noise-robust, and transferable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' In International Conference on Learning Represen-  tations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Du, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Lee, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Li, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Wang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Zhai, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Gradient descent finds global minima of  deep neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' In International conference on machine learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' PMLR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Evci, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Gale, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Menick, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Castro, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Elsen, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Rigging the lottery:  Making all tickets winners.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' In International Conference on Machine Learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' PMLR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Fang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Lee, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Yang, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Zhang, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Modeling from features: a mean-field frame-  work for over-parameterized deep neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' In Conference on learning theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' PMLR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Frankle, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Carbin, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' The lottery ticket hypothesis: Finding sparse, trainable  neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' In International Conference on Learning Representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Frankle, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Dziugaite, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Roy, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Carbin, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Pruning neural networks  at initialization: Why are we missing the mark?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  In International Conference on Learning  Representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Gale, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Elsen, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Hooker, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' The state of sparsity in deep neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  arXiv preprint arXiv:1902.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='09574 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  He, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Zhang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Ren, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Sun, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Deep residual learning for image recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  In Proceedings of the IEEE conference on computer vision and pattern recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  He, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Zhang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Sun, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Channel pruning for accelerating very deep neural  networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' In Proceedings of the IEEE international conference on computer vision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  He, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Xie, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Zhu, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Qin, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Sparse double descent: Where network pruning  aggravates overfitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' In International Conference on Machine Learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' PMLR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Jacot, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Gabriel, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Hongler, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Neural tangent kernel: Convergence and  generalization in neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Advances in neural information processing systems 31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Jayakumar, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Pascanu, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Rae, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Osindero, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Elsen, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Top-kast: Top-k  always sparse training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Advances in Neural Information Processing Systems 33 20744–20754.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Ji, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Telgarsky, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Polylogarithmic width suffices for gradient descent to achieve  arbitrarily small test error with shallow relu networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' In International Conference on Learning  Representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  13  Kepner, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Robinett, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Radix-net: Structured sparse matrices for deep neural  networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' In 2019 IEEE International Parallel and Distributed Processing Symposium Workshops  (IPDPSW).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' IEEE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Krizhevsky, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Hinton, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Learning multiple layers of features from tiny images  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  LeCun, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Denker, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Solla, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (1989).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Optimal brain damage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Advances in neural  information processing systems 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Lee, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Xiao, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Schoenholz, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Bahri, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Novak, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Sohl-Dickstein, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Pen-  nington, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Wide neural networks of any depth evolve as linear models under gradient  descent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Advances in neural information processing systems 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Lee, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Ajanthan, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Torr, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Snip: Single-shot network pruning based on  connection sensitivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' In International Conference on Learning Representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Liu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Chen, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Chen, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Atashgahi, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Yin, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Kou, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Shen, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Pechenizkiy, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=',  Wang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Mocanu, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2021a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Sparse training via boosting pruning plasticity with  neuroregeneration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Advances in Neural Information Processing Systems 34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Liu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Chen, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Chen, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Shen, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Mocanu, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Wang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Pechenizkiy, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  (2021b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' The unreasonable effectiveness of random pruning: Return of the most naive baseline  for sparse training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' In International Conference on Learning Representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Liu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Mocanu, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Matavalam, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Pei, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Pechenizkiy, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2021c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Sparse  evolutionary deep learning with over one million artificial neurons on commodity hardware.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Neural Computing and Applications 33 2589–2604.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Liu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Yin, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Mocanu, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Pechenizkiy, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2021d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Do we actually need dense over-  parameterization?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' in-time over-parameterization in sparse training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' In International Conference  on Machine Learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' PMLR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Liu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Zenke, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Finding trainable sparse networks through neural tangent transfer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  In International Conference on Machine Learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' PMLR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Luo, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Wu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' An entropy-based pruning method for cnn compression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' arXiv  preprint arXiv:1706.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='05791 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Malach, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Yehudai, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Shalev-Schwartz, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Shamir, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Proving the lottery  ticket hypothesis: Pruning is all you need.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' In International Conference on Machine Learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  PMLR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Mariet, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Sra, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Diversity networks: Neural network compression using determi-  nantal point processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' arXiv preprint arXiv:1511.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='05077 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Mocanu, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Mocanu, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Nguyen, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Gibescu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Liotta, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  A  topological insight into restricted boltzmann machines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Machine Learning 104 243–270.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Mocanu, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Mocanu, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Stone, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Nguyen, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Gibescu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Liotta, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Scalable training of artificial neural networks with adaptive sparse connectivity inspired  by network science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Nature communications 9 1–12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  14  Molchanov, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Tyree, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Karras, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Aila, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Kautz, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Pruning convolutional  neural networks for resource efficient inference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' In 5th International Conference on Learning  Representations, ICLR 2017-Conference Track Proceedings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Mostafa, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Wang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Parameter efficient training of deep convolutional neural net-  works by dynamic sparse reparameterization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' In International Conference on Machine Learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  PMLR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Oymak, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Soltanolkotabi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Toward moderate overparameterization: Global  convergence guarantees for training shallow neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' IEEE Journal on Selected Areas in  Information Theory 1 84–105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Pensia, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Rajput, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Nagle, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Vishwakarma, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Papailiopoulos, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Optimal lottery tickets via subset sum: Logarithmic over-parameterization is sufficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Advances  in Neural Information Processing Systems 33 2599–2610.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Peste, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Iofinova, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Vladu, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Alistarh, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Ac/dc: Alternating com-  pressed/decompressed training of deep neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Advances in Neural Information Pro-  cessing Systems 34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Prabhu, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Varma, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Namboodiri, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Deep expander networks: Efficient deep  networks from graph theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' In Proceedings of the European Conference on Computer Vision  (ECCV).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Ramanujan, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Wortsman, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Kembhavi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Farhadi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Rastegari, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  What’s hidden in a randomly weighted neural network?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  In Proceedings of the IEEE CVF  Conference on Computer Vision and Pattern Recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Rotskoff, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Vanden-Eijnden, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Neural networks as interacting particle  systems: Asymptotic convexity of the loss landscape and universal scaling of the approximation  error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' stat 1050 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Shi, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Wei, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Liang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  A theoretical analysis on feature learning in neural  networks: Emergence from inputs and advantage over fixed features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' In International Conference  on Learning Representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Sirignano, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Spiliopoulos, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Mean field analysis of neural networks: A law of  large numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' SIAM Journal on Applied Mathematics 80 725–752.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Song, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Montanari, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Nguyen, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  A mean field view of the landscape of  two-layers neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Proceedings of the National Academy of Sciences 115 E7665–E7671.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Song, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Yang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Zhang, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Does preprocessing help training over-parameterized  neural networks?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Advances in Neural Information Processing Systems 34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Song, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Yang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Quadratic suffices for over-parametrization via matrix chernoff  bound.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' arXiv preprint arXiv:1906.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='03593 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Sreenivasan, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Rajput, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Sohn, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='-y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Papailiopoulos, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Finding everything  within random binary networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' arXiv preprint arXiv:2110.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='08996 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  15  Sreenivasan, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Sohn, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='-y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Yang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Grinde, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Nagle, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Wang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Lee, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and  Papailiopoulos, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Rare gems: Finding lottery tickets at initialization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' arXiv preprint  arXiv:2202.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='12002 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Su, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Chen, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Cai, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Wu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Gao, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Wang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Lee, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Sanity-  checking pruning methods: Random tickets can win the jackpot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Advances in Neural Information  Processing Systems 33 20390–20401.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Suau, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Zappella, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Apostoloff, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Network compression using correlation  analysis of layer responses .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Tanaka, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Kunin, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Yamins, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Ganguli, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Pruning neural networks with-  out any data by iteratively conserving synaptic flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Advances in Neural Information Processing  Systems 33 6377–6389.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Telgarsky, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Feature selection with gradient descent on two-layer networks in low-  rotation regimes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' arXiv preprint arXiv:2208.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='02789 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Wang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Zhang, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Grosse, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Picking winning tickets before training by pre-  serving gradient flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' In International Conference on Learning Representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Wei, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Lee, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Liu, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Ma, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Regularization matters: Generalization and  optimization of neural nets vs their induced kernel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Advances in Neural Information Processing  Systems 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Yang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Wen, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Li, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Deephoyer: Learning sparser neural network with  differentiable scale-invariant sparsity measures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' In International Conference on Learning Repre-  sentations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Yang, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Mao, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Wang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Hai, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Dynamic regularization on activation  sparsity for neural network efficiency improvement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' ACM Journal on Emerging Technologies in  Computing Systems (JETC) 17 1–16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Ye, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Gong, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Nie, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Zhou, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Klivans, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Liu, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Good subnetworks  provably exist: Pruning via greedy forward selection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' In International Conference on Machine  Learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' PMLR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Zagoruyko, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Komodakis, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Wide residual networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' In British Machine Vision  Conference 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' British Machine Vision Association.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Zhou, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Lan, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Liu, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Yosinski, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Deconstructing lottery tickets: Zeros, signs,  and the supermask.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Advances in neural information processing systems 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Zhou, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Li, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Ding, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', You, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Qu, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Zhu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' On the optimization landscape  of neural collapse under mse loss: Global optimality with unconstrained features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' arXiv preprint  arXiv:2203.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='01238 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Zhu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Ding, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Zhou, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Li, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', You, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Sulam, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Qu, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' A geometric anal-  ysis of neural collapse with unconstrained features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Advances in Neural Information Processing  Systems 34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  16  Zou, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Cao, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Li, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Gu, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Understanding the generalization of adam in  learning neural networks with proper regularization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' arXiv preprint arXiv:2108.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='11371 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Zou, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Cao, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', Zhou, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Gu, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Gradient descent optimizes over-parameterized  deep relu networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Machine Learning 109 467–492.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Zou, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and Gu, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' An improved analysis of training over-parameterized deep neural  networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Advances in neural information processing systems 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  17  A  Experiment Details  The experiments of MLP, VGG and ResNet-32 are run on NVIDIA A5000 and ResNet-50 and  ResNet-20-128 is run on 4 NIVIDIA V100s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' We list the hyperparameters we used in training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' All  of our models are trained with SGD and the detailed settings are summarized below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Table 1: Summary of architectures, dataset and training hyperparameters  Model  Data  Epoch  Batch Size  LR  Momentum  LR Decay, Epoch  Weight Decay  LeNet  MNIST  120  128  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='1  0  0  0  VGG  CIFAR-10  160  128  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='9  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='1 × [80, 120]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='0001  ResNets  CIFAR-10  160  128  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='9  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='1 × [80, 120]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='0001  B  Further Experiment Results  We plot the experiment result of ResNet-20-128 in Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' This figure further verifies our results  that there exists pruning rate threshold such that the testing performance of the pruned network  is on par with the testing performance of the dense model while the training accuracy remains  perfect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='0  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='0  36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='0  48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='8  59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='0  67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='2  73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='8  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='0  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='2  86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='6  Sparsity  95  96  97  98  99  100  Accuracy  ResNet-20-128 CIFAR-10 Accuracy vs Sparsity  Random (Train)  Random (Test)  IMP (Train)  IMP (Test)  Figure 4: The figure shows the experiment results of ResNet-20-128 under various sparsity by  random pruning and IMP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Each data point is averaged over 2 runs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  C  Preliminary for Analysis  In this section, we introduce the following signal-noise decomposition of each neuron weight from  Cao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (2022), and some useful properties for the terms in such a decomposition, which are  useful in our analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Definition C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='1 (signal-noise decomposition).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' For each neuron weight j ∈ [K], r ∈ [m], there exist  18  coefficients γ(t)  j,r,k, ζ(t)  j,r,i, ω(t)  j,r,i such that  �w(t)  j,r = �w(0)  j,r +  K  �  k=1  γ(t)  j,r,k · ∥µk∥−2  2  µk ⊙ mj,r +  n  �  i=1  ζ(t)  j,r,i ·  ����ξj,r,i  ���  −2  2  �ξj,r,i +  n  �  i=1  ω(t)  j,r,i  ����ξj,r,i  ���  −2  2  �ξj,r,i,  where γ(t)  j,r,j ≥ 0, γ(t)  j,r,k ≤ 0, ζ(t)  j,r,i ≥ 0, ω(t)  j,r,i ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  It is straightforward to see the following:  γ(0)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='k,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' ζ(0)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' ω(0)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i = 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  γ(t+1)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='j  = γ(t)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='j − I(r ∈ Sj  signal)η  n  n  �  i=1  ℓ′(t)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i · σ′ ��  �w(t)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' µyi  ��  ∥µyi∥2  2 I(yi = j),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  γ(t+1)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='k = γ(t)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='k − I((mj,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r)k = 1)η  n  n  �  i=1  ℓ′(t)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i · σ′ ��  �w(t)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' µyi  ��  ∥µyi∥2  2 I(yi = k),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' ∀j ̸= k,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  ζ(t+1)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i  = ζ(t)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i − η  n · ℓ′(t)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i · σ′ ��  �w(t)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' ξi  �� ����ξj,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i  ���  2  2 I(j = yi),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  ω(t+1)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i  = ω(t)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i − η  n · ℓ′(t)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i · σ′ ��  �w(t)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' ξi  �� ����ξj,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i  ���  2  2 I(j ̸= yi),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  where {γ(t)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='j}T  t=1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' {ζ(t)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i}T  t=1 are increasing sequences and {γ(t)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='k}T  t=1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' {ω(t)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i}T  t=1 are decreasing se-  quences,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' because −ℓ′(t)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i ≥ 0 when j = yi,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and −ℓ′(t)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i ≤ 0 when j ̸= yi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' By Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='4, we have  pd > n+K, and hence the set of vectors {µk}K  k=1  �{�ξi}n  i=1 is linearly independent with probability  measure 1 over the Gaussian distribution for each j ∈ [K], r ∈ [m].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Therefore the decomposition is  unique.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  D  Proof of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='1  We first formally restate Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Theorem D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='1 (Formal Restatement of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Under Condition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='2, choose initialization  variance σ0 = �Θ(m−4n−1µ−1) and learning rate η ≤ �O(1/µ2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' For ϵ > 0, if p ≥ C1  log d  m  for some  sufficiently large constant C1, then with probability at least 1 − O(d−1) over the randomness in the  data, network initialization and pruning, there exists T = �O(Kη−1σ2−q  0  µ−q + K2m4µ−2η−1ϵ−1)  such that the following holds:  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' The training loss is below ϵ: LS(�  W(T)) ≤ ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' The weights of the CNN highly correlate with its corresponding class signal: maxr γ(T)  j,r,j ≥  Ω(m−1/q) for all j ∈ [K].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' The weights of the CNN doesn’t have high correlation with the signal from different classes:  maxj̸=k,r∈[m] |γ(T)  j,r,k| ≤ �O(σ0µ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' None of the weights is highly correlated with the noise: maxj,r,i ζ(T)  j,r,i = �O(σ0σn  √pd), maxj,r,i |ω(T)  j,r,i| =  �O(σ0σn  √pd).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  19  Moreover, the testing loss is upper-bounded by  LD(�  W(T)) ≤ O(Kϵ) + exp(−n2/p).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  The proof of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='1 consists of the analysis of the pruning on the signal and noise for  three stages of gradient descent: initialization, feature growing phase, and converging phase, and the  establishment of the generalization property.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' We present these analysis in detail in the following  subsections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  A special note is that the constant C showing up in the following proof of each  subsequent Lemmas is defined locally instead of globally, which means the constant C within each  Lemma is the same but may be different across different Lemma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='1  Initialization  We analyze the effect of pruning on weight-signal correlation and weight-noise correlation at the  initialization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' We first present a few supporting lemmas, and finally provide our main result of  Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='7, which shows that if the pruning is mild, then it will not hurt the max weight-signal  correlation much at the initialization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  On the other hand, the max weight-noise correlation is  reduced by a factor of √p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Assume n = Ω(K2 log Kd).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Then, with probability at least 1 − 1/d,  |{i ∈ [n] : yi = j}| = Θ(n/K)  ∀j ∈ [K].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' By Hoeffding’s inequality, with probability at least 1 − δ/2K, for a fixed j ∈ [K], we have  �����  1  n  n  �  i=1  I(yi = j) − 1  K  ����� ≤  �  log(4K/δ)  2n  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Therefore, as long as n ≥ 2K2 log(4K/δ), we have  �����  1  n  n  �  i=1  I(yi = j) − 1  K  ����� ≤  1  2K .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Taking a union bound over j ∈ [K] and making δ = 1/d yield the result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Assume pm = Ω(log d) and m = poly log d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Then, with probability 1 − 1/d, for all  j ∈ [K], k ∈ [K], we have �m  r=1(mj,r)k = Θ(pm), which implies that |Sj  signal| = Θ(pm) for all  j ∈ [K].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' When pm = Ω(log d), by multiplicative Chernoff’s bound, for a given k ∈ [K], we have  P  ������  m  �  r=1  (mj,r)k − pm  ����� ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='5pm  �  ≤ 2 exp {−Ω (pm)} .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Take a union bound over j ∈ [K], k ∈ [K], we have  P  ������  m  �  r=1  (mj,r)k − pm  ����� ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='5pm, ∀j ∈ [K], k ∈ [K]  �  ≤ 2K2 exp {−Ω (pm)} ≤ 1/d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  20  Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Assume p = 1/ poly log d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Then with probability at least 1 − 1/d, for all j ∈ [K],  r ∈ [m], �d  i=1(mj,r)i = Θ(pd).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' By multiplicative Chernoff’s bound, we have for a given j, r  P  ������  d  �  i=1  (mj,r)i − pd  ����� ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='5pd  �  ≤ 2 exp{−Ω(pd)}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Take a union bound over j, r, we have  P  ������  d  �  i=1  (mj,r)i − pd  ����� ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='5pd, ∀j ∈ [K], r ∈ [m]  �  ≤ 2Km exp{−Ω(pd)} ≤ 1/d,  where the last inequality follows from our choices of p, K, m, d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Suppose p = Ω(1/ poly log d), and m, n = poly log d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' With probability at least 1−1/d,  we have  ����ξj,r,i  ���  2  2 = Θ(σ2  npd),  ���  �  �ξj,r,i, ξi′  ���� ≤ O(σ2  n  �  pd log d),  ���  �  µk, �ξj,r,i  ���� ≤ | ⟨µ, ξi⟩ | ≤ O(σnµ  �  log d),  for all j ∈ {−1, 1}, r ∈ [m], i, i′ ∈ [n] and i ̸= i′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' From Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='4, we have with probability at least 1 − 1/d,  d  �  k=1  (mj,r)k = Θ(pd),  ∀j ∈ [K], r ∈ [m].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  For a set of Gaussian random variable g1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' , gN ∼ N(0, σ2), by Bernstein’s inequality, with prob-  ability at least 1 − δ, we have  �����  N  �  i=1  g2  i − σ2N  ����� ≲ σ2  �  N log 1  δ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Thus, by a union bound over j, r, i, with probability at least 1 − 1/d, we have  ����ξj,r,i  ���  2  2 = Θ(σ2  npd).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  For i ̸= i′, again by Bernstein’s bound, we have with probability at least 1 − δ,  ���  �  �ξj,r,i, ξi′  ���� ≤ O  �  σ2  n  �  pd log Kmn  δ  �  ,  for all j, r, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Plugging in δ = 1/d gives the result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' The proof for | ⟨µ, ξi⟩ | is similar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  21  Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Suppose we have m independent Gaussian random variables g1, g2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' , gm ∼ N(0, σ2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Then with probability 1 − δ,  max  i  gi ≥ σ  �  log  m  log 1/δ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' By the standard tail bound of Gaussian random variable, we have for every x > 0,  �σ  x − σ3  x3  � e−x2/2σ2  √  2π  ≤ P [g > x] ≤ σ  x  e−x2/2σ2  √  2π  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  We want to pick a x⋆ such that  P  �  max  i  gi ≤ x⋆  �  = (P [gi ≤ x⋆])m = (1 − P [gi ≥ x⋆])m ≤ e−m P[gi≥x⋆] ≤ δ  ⇒ P[gi ≥ x⋆] = Θ  �log(1/δ)  m  �  ⇒ x⋆ = Θ(σ  �  log(m/(log(1/δ) log m))).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='7 (Formal Restatement of Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' With probability at least 1−2/d, for all i ∈ [n],  σ0σn  �  pd ≤ max  r  �  �w(0)  j,r , ξi  �  ≤  �  2 log(Kmd)σ0σn  �  pd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Further, suppose pm ≥ Ω(log(Kd)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Then with probability 1 − 2/d, for all j ∈ [K],  σ0 ∥µj∥2 ≤  max  r∈Sj  signal  �  �w(0)  j,r , µj  �  ≤  �  2 log(8pmKd)σ0 ∥µj∥2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' We first give a proof for the second inequality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' From Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='3, we know that |Sj  signal| =  Θ(pm).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' The upper bound can be obtained by taking a union bound over r ∈ Sj  signal, j ∈ [K].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' To  prove the lower bound, applying Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='6, with probability at least 1−δ/K, we have for a given  j ∈ [K]  max  r∈Sj  signal  �  �w(0)  j,r , µj  �  ≥ σ0 ∥µj∥2  �  log  pm  log K/δ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Now, notice that we can control the constant in pm (by controlling the constant in the lower bound  of p) such that pm/ log(Kd) ≥ e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Thus, taking a union bound over j ∈ [K] and setting δ = 1/d  yield the result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  The proof of the first inequality is similar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='2  Supporting Properties for Entire Training Process  This subsection establishes a few properties (summarized in Proposition D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='10) that will be used in  the analysis of feature growing phase and converging phase of gradient descent presented in the next  two subsections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Define T ⋆ = η−1 poly(1/ϵ, µ, d−1, σ−2  n , σ−1  0 n, m, d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Denote α = Θ(log1/q(T ⋆)), β =  22  2 maxi,j,r,k  ����  �  �w(0)  j,r , µk  ���� ,  ���  �  �w(0)  j,r , ξi  ����  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' We need the following bound holds for our subsequent  analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  4m1/q max  j,r,i  ��  �w(0)  j,r , µyi  �  , Cnαµ√log d  σnpd ,  �  �w(0)  j,r , ξi  �  , 3Cnα  �  log d  pd  �  ≤ 1  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='1)  Remark D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' To see why Equation (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='1) can hold under Condition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='2, we convert everything in  terms of d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' First recall from Condition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='2 that m, n = poly(log d) and µ = Θ(σn  √  d log d) = Θ(1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  In both mild pruning and over pruning we require p ≥ Ω(1/poly log d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Since α = Θ(log1/q(T ⋆)), if  we assume T ⋆ ≤ O(poly(d)) for a moment (which we are going to justify in the next paragraph),  then α = O(log1/q(d)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Then if we set d to be large enough, we have 4m1/qCnα µ√log d  σnpd  ≤ poly log d  √  d  ≤  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Finally for the quantity 4m1/q maxj,r,i{⟨�w(0)  j,r , µyi⟩, ⟨�w(0)  j,r , ξi⟩}, by Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='2, our assumption  of K = O(log d) in Condition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='2 and our choice of σ0 = �Θ(m−4n−1µ−1) in Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='1 (or  Theorem D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='1), we can easily see that this quantity can also be made smaller than 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Now, to justify that T ⋆ ≤ O(poly(d)), we only need to justify that all the quantities T ⋆ depend on  is polynomial in d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' First of all, based on Condition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='2, n, m = poly log(d) and µ = Θ(σn  √  d log d) =  Θ(1) further implies σ−2  n  = Θ(d log2 d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Since Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='1 only requires σ0 = �Θ(m−4n−1µ−1), this  implies σ−1  0  ≤ O(poly log d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Hence σ−1  0 n = O(poly log d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Together with our assumption that  ϵ, η ≥ Ω(1/ poly(d)) (which implies 1/ϵ, 1/η ≤ O(poly(d))), we have justified that all terms involved  in T ⋆ are at most of order poly(d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Hence T ⋆ = poly(d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Remark D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Here we make remark on our assumption on ϵ and η in Condition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  For our assumption on ϵ, since the cross-entropy loss is (1) not strongly-convex and (2) achieves  its infimum at infinity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' In practice, the cross-entropy loss is minimized to a constant level, say  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' We make this assumption to avoid the pathological case where ϵ is exponentially small in  d (say ϵ = 2−d) which is unrealistic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Thus, for realistic setting, we assume ϵ ≥ Ω(1/ poly(d)) or  1/ϵ ≤ O(poly(d)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  To deal with η, the only restriction we have is η = O(1/µ2) in Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='1 and Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  However, in practice, we don’t use a learning rate that is exponentially small, say η = 2−d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Thus,  like dealing with ϵ, we assume η ≥ Ω(1/ poly(d)) or 1/η ≤ O(poly d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  We make the above assumption to simplify analysis when analyzing the magnitude of Fj(X)  for j ̸= y given sample (X, y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Proposition D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Under Condition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='2, during the training time t < T ⋆, we have  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' γ(t)  j,r,j, ζ(t)  j,r,i ≤ α,  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' ω(t)  j,r,i ≥ −β − 6Cnα  �  log d  pd .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' γ(t)  j,r,k ≥ −β − 2Cnα µ√log d  σnpd .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Notice that the lower bound has absolute value smaller than the upper bound.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Proof of Proposition D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' We use induction to prove Proposition D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  23  Induction Hypothesis:  Suppose Proposition D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='10 holds for all t < T ≤ T ⋆.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  We next show that this also holds for t = T via the following a few lemmas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Under Condition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='2, for t < T, there exists a constant C such that  �  �w(t)  j,r − �w(0)  j,r , µk  �  =  �  γ(t)  j,r,k ± Cnαµ√log d  σnpd  �  I((mj,r)k = 1),  �  �w(t)  j,r − �w(0)  j,r , ξi  �  = ζ(t)  j,r,i ± 3Cnα  �  log d  pd ,  �  �w(t)  j,r − �w(0)  j,r , ξi  �  = ω(t)  j,r,i ± 3Cnα  �  log d  pd .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' From Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='5, there exists a constant C such that with probability at least 1 − 1/d,  ���  �  �ξj,r,i, ξi′  ����  ����ξj,r,i  ���  2  2  ≤ C  �  log d  pd ,  ���  �  �ξj,r,i, µk  ����  ����ξj,r,i  ���  2  2  ≤ C µ√log d  σnpd ,  | ⟨µk, ξi⟩ |  ∥µk∥2  2  ≤ C σn  √log d  µ  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Using the signal-noise decomposition and assuming (mj,r)k = 1, we have  ���  �  �w(t)  j,r − �w(0)  j,r , µk  �  − γ(t)  j,r,k  ��� =  �����  n  �  i=1  ζ(t)  j,r,i ·  ����ξj,r,i  ���  −2  2 �  �ξj,r,i, µk  �  +  n  �  i=1  ω(t)  j,r,i  ����ξj,r,i  ���  −2  2 �  �ξj,r,i, µk  ������  ≤ C µ√log d  σnpd  n  �  i=1  ���ζ(t)  j,r,i  ��� + C µ√log d  σnpd  n  �  i=1  ���ω(t)  j,r,i  ���  ≤ 2C µ√log d  σnpd nα.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  where the second last inequality is by Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='5 and the last inequality is by induction hypothesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  To prove the second equality,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' for j = yi,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  ���  �  �w(t)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r − �w(0)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' ξi  �  − ζ(t)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i  ��� =  �������  K  �  k=1  γ(t)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='k · ⟨µk,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' ξi⟩  ∥µk∥2  2  +  �  i′̸=i  ζ(t)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i′ ·  �  �ξj,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i′,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' ξi  �  ����ξj,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i′  ���  2  2  +  n  �  i′=1  ω(t)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i′  �  �ξj,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i′,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' ξi  �  ����ξj,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i′  ���  2  2  �������  ≤ C σn  √log d  µ  K  �  k=1  |γ(t)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='k| + C  �  log d  pd  �  i′̸=i  |ζ(t)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i′| + C  �  log d  pd  n  �  i′=1  |ω(t)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i′|  = C σn  √log d  µ  Kα + 2Cnα  �  log d  pd  24  ≤ 3Cnα  �  log d  pd .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  where the last inequality is by n ≫ K and µ = Θ(σn  √  d log d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' The proof for the case of j ̸= yi is  similar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='12 (Off-diagonal Correlation Upper Bound).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Under Condition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='2, for t < T, j ̸= yi,  we have that  �  �w(t)  j,r, µyi  �  ≤  �  �w(0)  j,r , µyi  �  + Cnαµ√log d  σnpd ,  �  �w(t)  j,r, ξi  �  ≤  �  �w(0)  j,r , ξi  �  + 3Cnα  �  log d  pd ,  Fj(�  W(t)  j , xi) ≤ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' If j ̸= yi, then γ(t)  j,r,k ≤ 0 and we have that  �  �w(t)  j,r, µyi  �  ≤  �  �w(0)  j,r , µyi  �  +  �  γ(t)  j,r,yi + Cnαµ√log d  σnpd  �  I((mj,r)yi = 1)  ≤  �  �w(0)  j,r , µyi  �  + Cnαµ√log d  σnpd .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Further, we can obtain  �  �w(t)  j,r, ξi  �  ≤  �  �w(0)  j,r , ξi  �  + ω(t)  j,r,i + 3Cnα  �  log d  pd  ≤  �  �w(0)  j,r , ξi  �  + 3Cnα  �  log d  pd .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Then, we have the following bound:  Fj(�  W(t)  j , xi) =  m  �  r=1  [σ(⟨�wj,r, µyi⟩) + σ(⟨�wj,r, ξi⟩)]  ≤ m2q+1 max  j,r,i  ��  �w(0)  j,r , µyi  �  , Cnαµ√log d  σnpd ,  �  �w(0)  j,r , ξi  �  , 3Cnα  �  log d  pd  �q  ≤ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  where the first inequality is by Equation (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='13 (Diagonal Correlation Upper Bound).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Under Condition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='2, for t < T, j = yi, we  have  �  �w(t)  j,r, µj  �  ≤  �  �w(0)  j,r , µj  �  + γ(t)  j,r,j + Cnαµ√log d  σnpd ,  25  �  �w(t)  j,r, ξi  �  ≤  �  �w(0)  j,r , ξi  �  + ζ(t)  j,r,i + 3Cnα  �  log d  pd .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  If max{γ(t)  j,r,j, ζ(t)  j,r,i} ≤ m−1/q, we further have that Fj(�  W(t)  j , xi) ≤ O(1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' The two inequalities are immediate consequences of Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' If max{γ(t)  j,r,j, ζ(t)  j,r,i} ≤  m−1/q, we have  Fj(�  W(t)  j , xi) =  m  �  r=1  [σ(⟨�wj,r, µj⟩) + σ(⟨�wj,r, ξi⟩)]  ≤ 2 · 3qm max  j,r,i  �  γ(t)  j,r, ζ(t)  j,r,i,  ���  �  �w(0)  j,r , µj  ���� ,  ���  �  �w(0)  j,r , ξi  ���� , Cnαµ√log d  σnpd , 3Cnα  �  log d  pd  �q  ≤ O(1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Under Condition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='2, for t ≤ T, we have that  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' ω(t)  j,r,i ≥ −β − 6Cnα  �  log d  pd ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' γ(t)  j,r,k ≥ −β − 2Cnα µ√log d  σnpd .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' When j = yi, we have ω(t)  j,r,i = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' We only need to consider the case of j ̸= yi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' When  ω(T−1)  j,r,i  ≤ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='5β − 3Cnα  �  log d  pd , by Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='11 we have  �  �w(T−1)  j,r  , ξi  �  ≤  �  �w(0)  j,r , ξi  �  + ω(T−1)  j,r,i  + 3Cnα  �  log d  pd  ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Thus,  ω(T)  j,r,i = ω(T−1)  j,r,i  − η  n · ℓ′(T−1)  j,i  σ′ ��  �w(T−1)  j,r  , ξi  �� ����ξj,r,i  ���  2  2 I(j ̸= yi)  = ω(T−1)  j,r,i  ≥ −β − 6Cnα  �  log d  pd .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  When ω(T−1)  j,r,i  ≥ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='5β − 3Cnα  �  log d  pd , we have  ω(T)  j,r,i = ω(T−1)  j,r,i  − η  n · ℓ′(T−1)  j,i  σ′ ��  �w(T−1)  j,r  , ξi  �� ����ξj,r,i  ���  2  2 I(j ̸= yi)  ≥ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='5β − 3Cnα  �  log d  pd  − η  nσ′  �  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='5β + 3Cnα  �  log d  pd  � ����ξj,r,i  ���  2  2  ≥ −β − 6Cnα  �  log d  pd ,  26  where the last inequality is by setting η ≤ nq−1 �  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='5β + 3Cnα  �  log d  pd  �2−q  (C2σ2  nd)−1 and C2 is the  constant such that  ����ξj,r,i  ���  2  2 ≤ C2σ2  npd for all j, r, i in Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  For γ(t)  j,r,k, the proof is similar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Consider I((mj,r)k) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' When γ(t)  j,r,k ≤ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='5β − Cnα µ√log d  σnpd , by  Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='11, we have  �  �w(t)  j,r, µk  �  ≤  �  �w(0)  j,r , µk  �  + γ(t)  j,r,k + Cnαµ√log d  σnpd  ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Hence,  γ(T)  j,r,k = γ(T−1)  j,r,k  − η  n  n  �  i=1  ℓ′(T−1)  j,i  σ′ ��  �w(T−1)  j,r  , µk  ��  µ2I(yi = k)  = γ(T−1)  j,r,k  ≥ −β − 2Cnαµ√log d  σnpd .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  When γ(t)  j,r,k ≥ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='5β − Cnα µ√log d  σnpd , we have  γ(T)  j,r,k = γ(T−1)  j,r,k  − η  n  n  �  i=1  ℓ′(T−1)  j,i  σ′ ��  �w(T−1)  j,r  , µk  ��  µ2I(yi = k)  ≥ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='5β − Cnαµ√log d  σnpd  − C2  η  K σ′  �  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='5β + Cnαµ√log d  σnpd  �  µ2  ≥ −β − 2Cnαµ√log d  σnpd ,  where the first inequality follows from the fact that there are Θ( n  K ) samples such that I(yi = k),  and the last inequality follows from picking η ≤ K(0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='5β + Cnα µ√log d  σnpd )2−qµ−2q−1C−1  2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Under Condition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='2, for t ≤ T, we have γ(t)  j,r,j, ζ(t)  j,r,i ≤ α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' For yi ̸= j or r /∈ Sj  signal, γ(t)  j,r,j, ζ(t)  j,r,i = 0 ≤ α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  If yi = j, then by Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='12 we have  ���ℓ′(t)  j,i  ��� = 1 − logitj(F;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' X) =  �  i̸=j eFi(X)  �K  i=1 eFi(X) ≤  Ke  eFj(X) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='2)  Recall that  γ(t+1)  j,r,j  = γ(t)  j,r,j − I(r ∈ Sj  signal)η  n  n  �  i=1  ℓ′(t)  j,i · σ′ ��  �w(t)  j,r, µyi  ��  ∥µyi∥2  2 I(yi = j),  ζ(t+1)  j,r,i  = ζ(t)  j,r,i − η  n · ℓ′(t)  j,i · σ′ ��  �w(t)  j,r, ξi  �� ����ξj,r,i  ���  2  2 I(j = yi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  27  We first bound ζ(T)  j,r,i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Let Tj,r,i be the last time t < T that ζ(t)  j,r,i ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='5α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Then we have  ζ(T)  j,r,i = ζ(Tj,r,i)  j,r,i  − η  nℓ′(Tj,r,i)  i  σ′ ��  �w(Tj,r,i)  j,r  , ξi  ��  I(yi = j)  ����ξj,r,i  ���  2  2  �  ��  �  I1  −  �  Tj,r,i<t<T  η  nℓ′(Tj,r,i)  j,i  σ′ ��  �w(t)  j,r, ξi  ��  I(yi = j)  ����ξj,r,i  ���  2  2  �  ��  �  I2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  We bound I1, I2 separately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' We first bound I1 as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  |I1| ≤ q η  n  �  ζ(Tj,r,i)  j,r,i  + 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='5β + 3Cnα  �  log d  pd  �q−1  C2σ2  npd ≤ q2qn−1ηαq−1C2σ2  npd ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='25α,  where the first inequality follows from Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='13, the second inequality follows because β ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='1α  and 3Cnα  �  log d  pd ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='1α, and the last inequality follows because η ≤ n/(q2q+2αq−2σ2  nd).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  For Tj,r,i < t < T, by Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='11, we have that  �  �w(t)  j,r, ξi  �  ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='5α−0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='5β−3Cnα  �  log d  pd ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='25α  and  �  �w(t)  j,r, ξi  �  ≤ α + 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='5β + 3Cnα  �  log d  pd ≤ 2α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Now we bound I2 as follows  |I2| ≤  �  Tj,r,i<t<T  η  nKe exp {−Fj(X)} σ′ ��  �w(t)  j,r, ξi  ��  I(yi = j)  ����ξj,r,i  ���  2  2  ≤  �  Tj,r,i<t<T  η  nKe exp  �  −σ  ��  �w(t)  j,r, ξi  ���  σ′ ��  �w(t)  j,r, ξi  ��  I(yi = j)  ����ξj,r,i  ���  2  2  ≤ qKeη2q−1T ⋆  n  exp(−αq/4q)αq−1σ2  npd  ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='25T ⋆ exp(−αq/4q)αq−2α  ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='25α,  where the first inequality follows from Equation (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='2), the second inequality follows because  Fj(X) ≥ σ  ��  �w(t)  j,r, ξi  ��  , the fourth inequality follows by choosing η ≤ n/(qKe2q+1σ2  nd), and the  last inequality follows by choosing α = Θ(log1/q(T ⋆)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Plugging the bounds on I1, I2 finishes the proof for ζ(T)  j,r,i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  To prove γ(t)  j,r,j ≤ α, we pick η ≤ 1/(qe2q+2µ2) and the rest of the proof is similar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='14 and Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='15 imply Proposition D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='10 holds for all t ≤ T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Induction Ends  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='3  Feature Growing Phase  In this subsection, we first present a supporting lemma, and then provide our main result of  Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='17, which shows that the signal strength is relatively unaffected by pruning while the  28  noise level is reduced by a factor of √p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  During the feature growing phase of training, the output of Fj(X) = O(1) for all j ∈ [K].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Therefore, logiti(F, X) = O( 1  K ) and 1 − logiti(F, X) = Θ(1) until  �  �w(t)  j,r, µj  �  reaches m−1/q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Under the same assumption as Theorem D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='1, for T =  nη−1C4σ2−q  0  (σn  √pd)−q  C3(2C1)q−1[log d](q−1)/2 , the  following results hold:  |ζ(t)  j,r,i| = O(σ0σn  √pd) for all j ∈ [K], r ∈ [m], i ∈ [n] and t ≤ T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  |ω(t)  j,r,i| = O(σ0σn  √pd) for all j ∈ [K], r ∈ [m], i ∈ [n] and t ≤ T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Define Ψ(t) = maxj,r,i{ζ(t)  j,r,i, |ω(t)  j,r,i|}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Then we have  Ψ(t+1)  ≤ Ψ(t) + max  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i  �  �  �  �  �  η  n|ℓ′(t)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i | · σ′  �  �  �  �  �w(0)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' ξi  �  +  K  �  k=1  γ(t)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='k  ⟨µk,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' ξi⟩  ∥µk∥2  2  +  n  �  i′=1  Ψ(t)  �  �ξj,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i′,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' ξi  �  ����ξj,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i′  ���  2  2  �  �  �  ����ξj,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i  ���  2  2  �  �  �  �  �  ≤ Ψ(t) + η  nq  �  O(  �  log dσ0σn  �  pd) + K log1/q T ⋆ µσn  √log d  µ2  + O(σ2  npd) + nO(σ2  n  √pd log d)  Θ(σ2npd)  Ψ(t)  �q−1  O(σ2  npd)  ≤ Ψ(t) + η  n  �  O(  �  log dσ0σn  �  pd) + O(Ψ(t))  �q−1  O(σ2  npd),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  where the second inequality follows by |ℓ′(t)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i | and applying the bounds from Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='5, and the last  inequality follows by choosing 2K log T ⋆  σnd√p  = �O(1/  √  d) ≪ σ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Let C1, C2, C3 be the constants for the up-  per bound to hold in the big O notation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' For any T = nη−1C4σ2−q  0  (σn  √pd)−q  C3(2C1)q−1[log d](q−1)/2 = Θ( nη−1σ2−q  0  (σn  √pd)−q  [log d](q−1)/2  ),  we use induction to show that  Ψ(t) ≤ C4σ0σn  �  pd, ∀t ∈ [T].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='3)  Suppose that Equation (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='3) holds for t ∈ [T ′] for T ′ ≤ T − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Then  Ψ(T ′+1) ≤ Ψ(T ′) + η  n  �  C1  �  log dσ0σn  �  pd + C2C4σ0σn  �  pd  �q−1  C3σ2  npd  ≤ Ψ(T ′) + η  n  �  2C1  �  log dσ0σn  �  pd  �q−1  C3σ2  npd  ≤ (T ′ + 1)η  n  �  2C1  �  log dσ0σn  �  pd  �q−1  C3σ2  npd  ≤ T η  n  �  2C1  �  log dσ0σn  �  pd  �q−1  C3σ2  npd  ≤ C4σ0σn  �  pd,  where the last inequality follows by picking T =  nη−1C4σ2−q  0  (σn  √pd)−q  C3(2C1)q−1[log d](q−1)/2 = Θ( nη−1σ2−q  0  (σn  √pd)−q  [log d](q−1)/2  ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Therefore, by induction, we have Ψ(t) ≤ C4σ0σn  √pd for all t ∈ [T].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='17 (Formal Restatement of Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Under the same assumption as Theorem D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='1,  there exists time T1 =  log 2m−1/q  log(1+Θ( η  K )µqσq−2  0  ) = O(Kη−1σ2−q  0  µ−q log 2m−1/q) such that  29  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' maxr γ(T1)  j,r,j ≥ m−1/q for j ∈ [K].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' |ζ(t)  j,r,i|, |ω(t)  j,r,i| ≤ O(σ0σn  √pd) for all j ∈ [K], r ∈ [m], i ∈ [n] and t ≤ T1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' |γ(t)  j,r,k| ≤ O(σ0µ poly log d) for all j, k ∈ [K], j ̸= k, r ∈ [m] and t ≤ T1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Consider a fixed class j ∈ [K].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Denote T1 to be the last time for t ∈  �  0, nη−1C4σ2−q  0  (σn  √pd)−q  C3(2C1)q−1[log d](q−1)/2  �  satisfying maxr γ(t)  j,r ≤ m−1/q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Then for t ≤ T1, maxj,r,i ζ(t)  j,r,i, |ω(t)  j,r,i| ≤ O(σ0σp  √pd) ≤ O(m−1/q)  and maxj,r γ(t)  j,r,j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Thus, by Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='13, we obtain that Fj(�  W(t), xi) ≤ O(1), ∀yi = j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Thus,  ℓ′(t)  j,i = Θ(1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' For j ∈ Sj  signal, we have  γ(t+1)  j,r,j  = γ(t)  j,r,j − η  n  n  �  i=1  ℓ′(t)  j,i · σ′  �  �  �  �  �w(0)  j,r , µj  �  + γ(t)  j,r,j +  n  �  i′=1  ζ(t)  j,r,i  �  �ξj,r,i, µj  �  ����ξj,r,i  ���  2  2  +  n  �  i′=1  ω(t)  j,r,i  �  �ξj,r,i, µj  �  ����ξj,r,i  ���  2  2  �  �  � ∥µj∥2  2 I(yi = j)  ≥ γ(t)  j,r,j − η  n  n  �  i=1  ℓ′(t)  j,i σ′  ��  �w(0)  j,r , µj  �  + γ(t)  j,r,j − O(nσ0σnpdσnµ√log d  σ2npd  )  �  I(yi = j).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Let �γ(t)  j,r,j = γ(t)  j,r,j +  �  �w(0)  j,r , µj  �  − O(nσ0σn  √pd σnµ√log d  σ2npd  ) and A(t) = maxr �γ(t)  j,r,j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Note that by  our choice of µ, we have  nµ√log d  σnpd  = o(1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Since maxr  �  �w(0)  j,r , µj  �  ≥ Ω(σ0µ) by Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='7,  maxr  �  �w(0)  j,r , µj  �  ≥ Ω(σ0µ) − O(nσ0σnpd σnµ√log d  σ2npd  ) = Ω(σ0µ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Then we have  A(t+1) ≥ A(t) − η  n  n  �  i=1  ℓ′(t)  j,i σ′(A(t))µ2I(yi = j)  ≥ A(t) + Θ( η  K )µ2[A(t)]q−1  ≥ (1 + Θ( η  K µ2[A(t)]q−2))A(t)  ≥ (1 + Θ( η  K µqσq−2  0  ))A(t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Therefore, the sequence A(t) will exponentially grow and will reach 2m−1/q within  log 2m−1/q  log(1+Θ( η  K )µqσq−2  0  ) =  O(Kη−1σ2−q  0  µ−q log 2m−1/q) ≤ Θ( nη−1σ2−q  0  (σn  √pd)−q  [log d](q−1)/2  ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Thus, maxr γ(t)  j,r ≥ A(t)−maxj,r |  �  �w(0)  j,r , µj  �  | ≥  2m−1/q − O(σ0µ) ≥ 2 − m−1/q = m−1/q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Now we prove that under the same assumption as Theorem D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='1, for T = O(Kη−1σ2−q  0  µ−q), we  have |γ(t)  j,r,k| ≤ O(σ0µ poly log d) for all r ∈ [m], j, k ∈ [K], j ̸= k and t ≤ T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  We show that there exists a time T ′ ≥ T such that for all t ≤ T ′, maxj,r,k |γ(t)  j,r,k| ≤ O(σ0µ poly log d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Let T ′ = O(K2η−1σ2−q  0  µ−q log d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Define Φ(t) = maxr∈[m], j,k∈[K], j̸=k{|γ(t)  j,r,k|}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Since we assume T ≤ Θ( nη−1σ2−q  0  (σn  √pd)−q  [log d](q−1)/2  ), by  30  Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='16, we have ζ(t)  j,r,i, |ω(t)  j,r,i| ≤ O(σ0σn  √pd).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Φ(t+1)  ≤ Φ(t) + max  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='k,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i  �  �  �  �  �  η  n  n  �  i=1  I(yi = k)|ℓ′(t)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i |σ′  �  �  �  �  �w(0)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' µk  �  +  n  �  i′=1  ζ(t)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i′  �  �ξj,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i′,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' µk  �  ����ξj,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i′  ���  2  2  +  n  �  i′=1  ω(t)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i′  �  �ξj,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i′,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' µk  �  ����ξj,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i′  ���  2  2  �  �  � µ2  �  �  �  �  �  ≤ Φ(t) + η  K  1  K q  �  O(σ0µ  �  log d) + nO(σ0σn  �  pd)σnµ√log d  σ2npd  )  �q−1  µ2  ≤ Φ(t) + qη  K2  �  O(σ0µ  �  log d)  �q−1  µ2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  where the first inequality follows because γ(t)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='k < 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' the second inequality follows because there are  Θ(n/K) samples from a given class k and |ℓ′(t)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i | = Θ( 1  K ),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and the last inequality follows because  µ = σn  √  d log d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Now, let C be the constant such that the above holds with big O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Then, we use  induction to show that Φ(t) ≤ C2σ0µ for all t ≤ T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' We proceed as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Φ(t+1) ≤ Φ(t) + qη  K2  �  Cσ0µ  �  log d  �q−1  µ2  ≤ T qη  K2  �  Cσ0µ  �  log d  �q−1  µ2  ≤ C2σ0µpoly log d,  where the last inequality follows by picking T = C2K2η−1σ2−q  0  µ−q√log d  Cq−1  = O(K2η−1σ2−q  0  µ−q log d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='4  Converging Phase  In this subsection, we show that gradient descent can drive the training loss toward zero while  the signal in the feature is still large.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  An important intermediate step in our argument is the  development of the following gradient upper bound for multi-class cross-entropy loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  In this phase, we are going to show that  maxr γ(t)  j,r,j ≥ m1/q for all j ∈ [K].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  maxj̸=k,r∈[m] |γ(t)  j,r,k| ≤ β1 where β1 = �O(σ0µ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  maxj,r,i{ζ(t)  j,r,i, |ω(t)  j,r,i|} ≤ β2 where β2 = O(σ0σn  √pd)  Define W⋆ as follows:  w⋆  j,r = w(0)  j,r + Θ(m log(1/ϵ))µj  µ2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Based on the result from the feature growing phase,  ����  W(T1) − �  W⋆���  2  F ≤ O(Km3 log2(1/ϵ)µ−2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' We first compute  ����  W(T1) − �  W(0)���  2  F  31  =  K  �  j=1  m  �  r=1  �������  γ(T1)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='j  µj ⊙ mj,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r  µ2  +  �  k̸=j  γ(T1)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='k  µk ⊙ mj,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r  µ2  +  �  i  ζ(T1)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i  �ξj,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i  ����ξj,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i  ���  2  2  +  �  i  ω(T1)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i  �ξj,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i  ����ξj,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i  ���  2  2  �������  2  2  ≤  �  j  �  r  �  �γ(T1)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='j  1  µ +  �  k̸=j  γ(T1)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='k  1  µ +  �  i  ζ(T1)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i  1  ����ξj,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i  ���  2  +  �  i  ω(T1)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i  1  ����ξj,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i  ���  2  �  �  2  ≤  �  j  �  r  �  �O( 1  µ) + K �O(σ0) + n �O(σ0)  �2  ≤  �  j  �  r  �O( 1  µ2 )  = �O(Km 1  µ2 ),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  where the first inequality follows from triangle inequality,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' the second inequality follows from Lemma  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='17, and the last inequality follows from our choice of σ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' On the other hand,  ����  W(0) − �  W⋆���  2  F =  �  j,r  m2 log2(1ϵ) 1  µ2 = O(Km3 log2(1/ϵ) 1  µ2 ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Thus, we obtain  ����  W(T1) − �  W⋆���  2  F ≤ 4  ����  W(T1) − �  W(0)���  2  F + 4  ����  W(0) − �  W⋆���  2  F ≤ O(Km3 log2(1/ϵ) 1  µ2 ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='19 (Gradient Upper Bound).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Under Condition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='2, for t ≤ T ⋆, there exists constant  C = O(Km2/q max{µ2, σ2  npd}) such that  ���∇LS(�  W(t)) ⊙ M  ���  2  F ≤ CLS(�  W(t)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' We need to prove that |ℓ′(t)  yi,i|  ���∇F(�  W(t), xi) ⊙ M  ���  2  F ≤ C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Assume yi ̸= j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Then we obtain  ���∇Fj(�  Wj, xi) ⊙ M  ���  F ≤  �  r  ���σ′ ��  �w(t)  j,r, µyi  ��  µyi + σ′ ��  �w(t)  j,r, ξi  ��  �ξi  ���  2  ≤  �  r  σ′ ��  �w(t)  j,r, µyi  ��  ∥µyi∥2 + σ′ ��  �w(t)  j,r, ξi  �� ����ξi  ���  2  ≤ m1/q �  Fj(�  Wj, xi)  �(q−1)/q  max{µ, Cσn  �  pd}  ≤ m1/q max{µ, Cσn  �  pd},  where the first and second inequality follow from triangle inequality, the third inequality follows  from H¨older’s inequality, and the last inequality follows from Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Similarly, on the other  32  hand, if yi = j, then  ���∇Fyi(�  W) ⊙ M  ���  F ≤ m1/q �  Fyi(�  Wyi, xi)  �(q−1)/q  max{µ, Cσn  �  pd}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Therefore,  �  j̸=yi  |ℓ′(t)  j,i |  ���∇Fj(�  Wj, xi) ⊙ Mj  ���  2  F ≤  �  j̸=yi  |ℓ′(t)  j,i |m2/qO(max{µ2, σ2  npd})  = |ℓ′(t)  yi,i|m2/qO(max{µ2, σ2  npd})  ≤ Ke exp{−Fyi(xi)}m2/qO(max{µ2, σ2  npd}),  and  |ℓ′(t)  yi,i|  ���∇Fyi(�  Wyi, xi) ⊙ Myi  ���  2  F  ≤ Ke exp{−Fyi(xi)}m2/q �  Fyi(�  Wyi, xi)  �2(q−1)/q  O(max{µ2, σ2  npd},  where the inequality follows from Equation (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Thus,  K  �  j=1  |ℓ′(t)  j,i |2 ���∇Fj(�  Wj, xi) ⊙ Mj  ���  2  F  ≤ |ℓ′(t)  yi,i|  K  �  j=1  |ℓ′(t)  j,i |  ���∇Fj(�  Wj, xi) ⊙ Mj  ���  2  F  ≤ |ℓ′(t)  yi,i|Ke exp{−Fyi(xi)}m2/qO(max{µ2, σ2  npd}  ��  Fyi(�  Wyi, xi)  �(q−1)/q  + 1  �  ≤ |ℓ′(t)  yi,i|O(Km2/q max{µ2, σ2  npd}),  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='4)  where the first inequality follows because |ℓ′(t)  j,i | ≤ |ℓ′(t)  yi,i|, and the last inequality uses the fact that  exp{−x}(1 + x(q−1)/q) = O(1) for all x ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  The gradient norm can be bounded by  ���∇LS(�  W(t))  ���  2  F ≤  �  1  n  n  �  i=1  ���∇L(�  W(t),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' xi)  ���  F  �2  =  �  � 1  n  n  �  i=1  �  �  �  �  K  �  j=1  |ℓ′(t)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i |2  ���∇Fj(�  W(t)  j ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' xi)  ���  2  F  �  �  2  ≤  �  1  n  n  �  i=1  |ℓ′(t)  yi,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i|  ���∇F(�  W(t)  j ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' xi)  ���  F  �2  ≤  �  1  n  n  �  i=1  �  |ℓ′(t)  yi,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i|O(Km2/q max{µ2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' σ2nd})  �2  33  ≤ O(Km2/q max{µ2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' σ2  nd}) 1  n  n  �  i=1  |ℓ′(t)  yi,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i|  ≤ O(Km2/q max{µ2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' σ2  nd})LS(�  W(t)),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  where the first inequality uses triangle inequality,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' the second inequality follows because |ℓ′(t)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i | ≤  |ℓ′(t)  yi,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i|,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' the third inequality uses the bound (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='4), the fourth inequality uses Jensen’s inequality and  the last inequality follows because |ℓ′(t)  yi,i| ≤ ℓ(t)  i .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' For T1 ≤ t ≤ T ⋆, we have for all j ̸= yi,  �  ∇Fyi(�  W(t)  yi , xi), �  W⋆  yi  �  −  �  ∇Fj(�  W(t)  j , xi), �  W⋆  j  �  ≥ q log 2qK  ϵ  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Proof of Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' The proof of this lemma depends on the next two lemmas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' For T1 ≤ t ≤ T ⋆ and j = yi, we have  �  ∇Fj(�  W(t)  j , xi), �  W⋆  j  �  ≥ Θ(m1/q log(1/ϵ)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' By Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='17, we have  max  r  ��  �w(t)  j,r, µj  ��  = max  r  �  �  �  �  �  �  �w(0)  j,r , µj  �  + γ(t)  j,r,j +  n  �  i=1  ζ(t)  j,r,i  �  �ξj,r,i, µj  �  ����ξj,r,i  ���  2  2  +  n  �  i=1  ω(t)  j,r,i  �  �ξj,r,i, µj  �  ����ξj,r,i  ���  2  2  �  �  �  �  �  ≥ m−1/q − O(σ0µ  �  log d) − O(nσ0σn  √  dµ√log d  σnpd )  ≥ Θ(m−1/q),  where the last inequality follows by picking σ0 ≤ O(m−1n−1µ−1(log d)−1/2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' On the other hand,  ���  �  �w(t)  j,r, ξi  ���� ≤  ���  �  �w(0)  j,r , ξi  ���� + |ω(t)  j,r,i| + |ζ(t)  j,r,i| + O(n  �  log d  pd α) + O(nµ√log d  σnpd α) ≤ O(1),  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='5)  where the first inequality follows from Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='11 and the second inequality follows from Equa-  tion (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='1) and Proposition D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Therefore,  �  ∇Fj(�  W(t)  j , xi), �  W⋆  j  �  =  �  r  σ′ ��  �w(t)  j,r, µj  �� �  µj, �w⋆  j,r  �  +  �  r  σ′ ��  �w(t)  j,r, ξi  �� �  ξi, �w⋆  j,r  �  ≥  �  r  σ′ ��  �w(t)  j,r, µj  ��  Θ(m log(1/ϵ)) −  �  r  O(σ0σn  �  pd log d + σn  √log d  µ  m log(1/ϵ))  ≥ Θ(m1/q log(1/ϵ)) − O(mσ0σn  �  pd log d + σn  √log d  µ  m2 log(1/ϵ))  ≥ Θ(m1/q log(1/ϵ)),  where the last inequality follows because mσ0σn  √pd log d = o(1) and σn  √log d  µ  m2 = o(1) by our  choices of µ, σ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  34  Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' For T1 ≤ t ≤ T and j ̸= yi, we have  �  ∇Fj(�  W(t)  j , xi), �  W⋆  j  �  ≤ O(1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' First we have  �  �w(t)  j,r, µyi  �  =  �  �w(0)  j,r , µyi  �  + γ(t)  j,r,yi +  n  �  i=1  ζ(t)  j,r,i  �  �ξj,r,i, µj  �  ����ξj,r,i  ���  2  2  +  n  �  i=1  ω(t)  j,r,i  �  �ξj,r,i, µj  �  ����ξj,r,i  ���  2  2  ≤ O(σ0µ  �  log d + σ0µ poly log d + nσ0σn  �  pdσnµ√log d  σ2npd  )  ≤ O(1),  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='6)  where the first inequality follows from Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='7, Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='5 and Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='17, and the last  inequality follows from our choices of σ0, µ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Then, we have  �  ∇Fj(�  W(t)  j , xi), �  W⋆  j  �  =  �  r  σ′ ��  �w(t)  j,r, µyi  �� �  µyi, �w⋆  j,r  �  +  �  r  σ′ ��  �w(t)  j,r, ξi  �� �  ξi, �w⋆  j,r  �  ≤ mO(σ0µ  �  log d) + mO(σ0σn  �  d log d + m log(1/ϵ)σn  √log d  µ  )  ≤ O(1),  where the second inequality follows from Equation (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='6) and Equation (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='5), and the last inequality  follows from our choices of µ, σ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Applying the lower bound and upper bound from Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='21 and Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='22, we have  �  ∇Fyi(�  W(t)  yi , xi), �  W⋆  yi  �  −  �  ∇Fj(�  W(t)  j , xi), �  W⋆  j  �  ≥ Θ(m1/q log(1/ϵ)) − O(1)  ≥ q log 2qK  ϵ  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Under the same assumption as Theorem D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='1, we have  ����  W(t) − �  W⋆���  2  F −  ����  W(t+1) − �  W⋆���  2  F ≥ 5ηLS(�  W(t)) − ηϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' To simplify our notation, we define �F (t)  j (xi) =  �  ∇Fj(�  W(t)  j , xi), �  W⋆  j  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  We use the fact that the network is q-homogeneous.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  ����  W(t) − �  W⋆���  2  F −  ����  W(t+1) − �  W⋆���  2  F  = 2η  �  ∇LS(�  W(t)) ⊙ M, �  W(t) − �  W⋆�  − η2 ���∇LS(�  W(t)) ⊙ M  ���  2  F  = 2η  n  n  �  i=1  K  �  j=1  ℓ′(t)  j,i  �  qFj(�  W(t)  j ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' xi, yi) −  �  ∇Fj(�  W(t)  j , xi), �  W⋆  j  ��  − η2 ���∇LS(�  W(t)) ⊙ M  ���  2  F  35  ≥ 2qη  n  n  �  i=1  �  �log(1 +  K  �  j=1  eFj−Fyi) − log(1 +  K  �  j=1  e( �Fj− �Fyi)/q)  �  � − η2 ���∇LS(�  W(t)) ⊙ M  ���  2  F  ≥ 2qη  n  n  �  i=1  �  ℓ(�  W(t);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' xi, yi) − log(1 + Ke− log(2qK/ϵ))  �  − η2 ���∇LS(�  W(t)) ⊙ M  ���  2  F  ≥ 2qη  n  n  �  i=1  �  ℓ(�  W(t);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' xi, yi) − ϵ  2q  �  − η2 ���∇LS(�  W(t)) ⊙ M  ���  2  F  ≥ CηLS(�  W(t)) − ηϵ,  where the first inequality follows from the convexity of the cross-entropy loss with softmax, the  second inequality follows from Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='20, the third inequality follows because log(1 + x) ≤ x,  and the last inequality follows from Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='19 for some constant C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='24 (Formal Restatement of Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Under the same assumption as Theorem D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='1,  choose T2 = T1+ ∥�  W(T1)−�  W⋆∥  2  F  2ηϵ  = T1+ �O(Km3 log2(1/ϵ)µ−2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Then for any time t during this stage,  we have maxr γ(t)  j,r,j ≥ m1/q for all j ∈ [K], maxj,r,i{|ζ(t)  j,r,i|, |ω(t)  j,r,i|} ≤ 2β1, maxj̸=k,r∈[m]{|γ(t)  j,r,k|} ≤  2β2, and  1  t − T1  t  �  s=T1  LS(�  W(s)) ≤  ����  W(T1) − �  W⋆���  2  F  Cη(t − T1)  + ϵ  C .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' From Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='17, we have maxrγ(T1)  j,r,j ≥ m1/q and since γ(t) is an increasing sequence over  t, we have maxrγ(t)  j,r,j ≥ m1/q for all t ∈ [T1, T2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' We have  ����  W(s) − �  W⋆���  2  F −  ����  W(s+1) − �  W⋆���  2  F ≥ CηLS(�  W(s)) − ηϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Taking a telescopic sum from T1 to t yields  t  �  s=T1  LS(�  W(s)) ≤  ����  W(T1) − �  W⋆���  2  F + ηϵ(t − T1)  Cη  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Combining Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='18, we have  t  �  s=T1  LS(�  W(s)) ≤ O(η−1 ����  W(T1) − �  W⋆���  2  F ) = O(η−1Km3 log2(1/ϵ)µ−2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='7)  Define Ψ(t) = maxj,r,i{ζ(t)  j,r,i, |ω(t)  j,r,i|} and Φ(t) = maxj̸=k,r∈[m] |γ(t)  j,r,k| and β2 = �O(σ0µ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Now we use  induction to prove Ψ(t) ≤ 2β1 and Φ(t) ≤ 2β2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Suppose the result holds for time t ≤ t′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Then  Ψ(t+1) ≤ Ψ(t) + max  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i  �  �  �  �  �  η  n|ℓ′(t)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i | · σ′  �  �  �  �  �w(0)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' ξi  �  +  K  �  k=1  γ(t)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='k  ⟨µk,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' ξi⟩  ∥µk∥2  2  +  n  �  i′=1  Ψ(t)  �  �ξj,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i′,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' ξi  �  ����ξj,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i′  ���  2  2  �  �  �  ����ξj,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i  ���  2  2  �  �  �  �  �  36  ≤ Ψ(t) + η  nq max  i  |ℓ′(t)  yi,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i|  �  O(  �  log dσ0σn  �  pd) + K log1/q T ⋆ µσn  √log d  µ2  + O(σ2  npd) + nO(σ2  n  √pd log d)  Θ(σ2npd)  Ψ(t)  �q−1  O(σ2  npd)  ≤ Ψ(t) + η  n  n  �  i=1  |ℓ′(t)  yi,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i|  �  O(  �  log dσ0σn  �  pd) + O(Ψ(t))  �q−1  O(σ2  npd),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  where the second inequality follows by |ℓ′(t)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i | ≤ |ℓ′(t)  yi,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i| and applying the bounds from Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='5,  and the last inequality follows by choosing K log1/q T ⋆  √  d  = �O( 1  √  d) ≪ σ0σn  √pd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Unrolling the recursion  by taking a sum from T1 to t′ we have  Ψ(t′+1) (i)  ≤ Ψ(T1) + η  n  t′  �  s=T1  n  �  i=1  |ℓ′(s)  yi,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i|O(σ2  npd poly log d)βq−1  1  (ii)  ≤ Ψ(T1) + η  nO(σ2  npd poly log d)βq−1  1  t′  �  s=T1  n  �  i=1  ℓ(s)  i  = Ψ(T1) + η  nO(σ2  npd poly log d)βq−1  1  t′  �  s=T1  LS(�  W(s))  (iii)  ≤ Ψ(T1) + 1  nO(Km3µ−2σ2  npd poly log d)βq−1  1  (iv)  ≤ β1 + �O(Km3)βq−1  1  (v)  ≤ 2β1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  where (i) follows from induction hypothesis Ψ(t) ≤ 2β1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (ii) follows from the property of cross-  entropy loss with softmax |ℓ′  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i| ≤ |ℓ′  yi,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i| ≤ ℓi,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (iii) follows from Equation (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='7), (iv) follows from  our choice of µ, n, K, and (v) follows because �O(Km3)β1q−2 ≤ �O(Km3σ0σn  √pd) ≤ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Therefore,  by induction Ψ(t) ≤ 2β1 holds for time t ≤ t′ + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  On the other hand,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Φ(t′+1)  (i)  ≤ Φ(t) + max  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='k,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i  �  �  �  �  �  η  n  n  �  i=1  I(yi = k)|ℓ′(t)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i |σ′  �  �  �  �  �w(0)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' µk  �  +  n  �  i′=1  ζ(t)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i′  �  �ξj,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i′,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' µk  �  ����ξj,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i′  ���  2  2  +  n  �  i′=1  ω(t)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i′  �  �ξj,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i′,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' µk  �  ����ξj,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i′  ���  2  2  �  �  � µ2  �  �  �  �  �  (ii)  ≤ Φ(t) + Θ( η  K ) max  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i |ℓ′(t)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i |  �  O(σ0µ  �  log d) + nO(σ0σn  �  pd)σnµ√log d  σ2npd  )  �q−1  µ2  (iii)  ≤ Φ(T1) + Θ( η  K )µ2  t  �  s=T1  n  �  i=1  ℓ(s)  i  �  O(σ0µ  �  log d)  �q−1  (iv)  ≤ β2 + O(m3)βq−1  2  37  (v)  ≤ 2β2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  where (i) follows because γ(t)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='k ≤ 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' (ii) follows from Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='7 and Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='5, (iii) follows  because maxj,i |ℓ′(t)  j,i | ≤ maxi |ℓ′(t)  yi,i| ≤ maxi ℓ(t)  i  ≤ �  i ℓ(t)  i , (iv) follows from Equation (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='7), and (v)  follows because O(m3)βq−2  2  ≤ �O(m3σ0µ) ≤ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='5  Generalization Analysis  In this subsection, we show that pruning can purify the feature by reducing the variance of the  noise by a factor of p when a new sample is given.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Now the network has parameter  �w⋆  j,r = �w(0)  j,r +  K  �  k=1  γ⋆  j,r,k  µk ⊙ mj,r  µ2  +  n  �  i=1  ζ⋆  j,r,i  �ξj,r,i  ����ξj,r,i  ���  2  2  +  n  �  i=1  ω⋆  j,r,i  �ξj,r,i  ����ξj,r,i  ���  2  2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  We have  ����w⋆  j,r  ���  2 = O(σ0  √pd + µ−1 log1/q(T ⋆) + Kσ0 poly log d + nσ0σn  √pd  1  σn  √pd) = O(σ0  √pd).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='25 (Formal Restatement of Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' With probability at least 1−2Km exp  �  − (2m)−4/q  O(σ2  0σ2npd)  �  ,  max  j,r  ����w⋆  j,r, ξ  ��� ≤ (2m)−2/q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Since  �  �w⋆  j,r, ξ  �  follows a Gaussian distribution with variance O(σ2  0σ2  npd), we have  P  �����w⋆  j,r, ξ  ��� ≥ (2m)−2/q�  ≤ 2 exp  �  − (2m)−4/q  O(σ2  0σ2npd)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Applying a union bound over j ∈ [K], r ∈ [m] gives the result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Theorem D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='26 (Formal Restatement of Generalization Part of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Under the same  assumptions as Theorem D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='1, within �O(Kη−1σ2−q  0  µ−q + K2m4µ−2η−1ϵ−1) iterations, we can find  �  W⋆ such that  LS(�  W⋆) ≤ ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  LD ≤ O(Kϵ) + exp(−n2/p).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Let E be the event that Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='25 holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Then, we can divide LD(�  W⋆) into two parts:  E[ℓ(F(�  W⋆, x))] = E[I(E)ℓ(F(�  W⋆, x))]  �  ��  �  I1  + E[I(Ec)ℓ(F(�  W⋆, x))]  �  ��  �  I2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Since LS(�  W⋆) ≤ ϵ, for each class j ∈ [K] there must exist one training sample (xi, yi) ∈ S with yi =  j such that ℓ(F(�  W⋆, xi)) ≤ Kϵ ≤ 1 by pigeonhole principle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' This implies that �  j′̸=j exp(Fj′(xi) −  Fj(xi)) ≤ 2Kϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Conditioning on the event E, by Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='25, we have  |Fj(�  W⋆, x) − Fj(�  W⋆, xi)| ≤  �  r  σ(  ��w⋆  j,r, ξi  �  ) +  �  r  σ(  ��w⋆  j,r, ξ  �  )  38  ≤  �  r  (2m)−1 +  �  r  (2m)−1  ≤ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Thus, we have exp(Fj′(x) − Fj(x)) ≤ 2Kϵe2 = O(Kϵ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Next we bound the term I2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  ℓ(F(�  W⋆, x)) = log  �  �1 +  �  j′̸=y  exp(Fj′(x) − Fy(x))  �  �  ≤ log  �  �1 +  �  j′̸=y  exp(Fj′(x))  �  �  ≤  �  j′̸=y  log(1 + exp(Fj′(x)))  ≤ K +  �  j′̸=y  Fj′(x)  = K +  �  j′̸=y  σ(  ��w⋆  j′,r, µy  �  ) + σ(  ��w⋆  j′,r, ξ  �  )  ≤ K + Km(O(σ0µ  �  log d))q + �O(m(σ0σn  √  d)q) ∥ξ/σn∥q  2  ≤ 2K + ∥ξ/σn∥q  2 ,  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='8)  where the first inequality follows because Fy(x) ≥ 0, the second and third inequalities follow from  the property of log function, and the last inequality follows from our choice of σ0 ≤ �O(m−4n−1σ−1  n d−1/2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  We further have  I2 ≤  �  E[I(E)]  �  E[ℓ(F(�  W⋆, x))2]  ≤  �  P(Ec)  �  4K2 + E ∥ξ/σn∥2q  2  ≤ exp(−Cm−2/qσ−2  0 σ−2  n p−1d−1 + log(d))  ≤ exp(−n2/p),  where the first inequality follows from Cauchy-Schwarz inequality, the second inequality follows  from Equation (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='8), the third inequality follows from Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='25, and the last inequality follows  because σ0 ≤ �O(m−4n−1σ−1  n d−1/2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  E  Proof of Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='1  In this section, we show that there exists a relatively large pruning fraction (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=', small p) such that  while gradient descent is still able to drive the training error toward zero, the learned model yields  poor generalization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' We first provide a formal restatement of Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Theorem E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='1 (Formal Restatement of Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Under Condition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='2, choose initialization  variance σ0 = �Θ(m−4n−1µ−1) and learning rate η ≤ �O(1/µ2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' For ϵ > 0, if p = Θ(  1  Km log d), then  with probability at least 1−1/ log(d), there exists T = O(η−1nσq−2  0  σ−q  n (pd)−q/2+η−1ϵ−1m4nσ−2  n (pd)−1)  39  such that the following holds:  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' The training loss is below ϵ: LS(�  W(T)) ≤ ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' The model weight doesn’t learn any of its corresponding signal at all: γ(t)  j,r,j = 0 for all j ∈  [K], r ∈ [m].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' The model weights is highly correlated with the noise: maxr∈[m] ζ(T)  j,r,i ≥ Ω(m−1/q) if yi = j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Moreover, the testing loss is large:  LD(�  W(T)) ≥ Ω(log K).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  The proof of Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='1 consists of the analysis of the over-pruning for three stages of gradient  descent: initialization, feature growing phase, and converging phase, and the establishment of the  generalization property.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' We present these analysis in detail in the following subsections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='1  Initialization  Lemma E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' When m = poly log d and p = Θ(  1  Km log d), with probability 1 − O(1/ log d), for all  class j ∈ [K] we have |Sj  signal| = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' First, the probability that a given class j receives no signal is (1−p)m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' We use the inequality  that  1 + t ≥ exp {O(t)}  ∀t ∈ (−1/4, 1/4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Then the probability that |Sj  signal| = 0, ∀j ∈ [K] is given by  (1 − p)Km ≥ exp {−O (pKm)} ≥ 1 − O  �  1  log d  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='2  Feature Growing Phase  Lemma E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='3 (Formal Restatement of Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Under the same assumption as Theorem E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='1,  there exists T1 < T ⋆ such that T1 = O(η−1nσq−2  0  σ−q  n (pd)−q/2) and we have  maxr ζyi,r,i ≥ m−1/q for all i ∈ [n].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  maxj,r,i |ω(t)  j,r,i| = �O(σ0σn  √pd).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  maxj,r,k |γ(t)  j,r,k| ≤ �O(σ0µ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' First of all, recall that from Definition C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='1 we have for j = yi  �  �w(t)  j,r, ξi  �  =  �  �w(0)  j,r , ξi  �  + ζ(t)  j,r,i +  �  k̸=j  γ(t)  j,r,k  �  µk, �ξj,r,i  �  µ2  +  �  i′̸=i  ζ(t)  j,r,i  �  �ξj,r,i′, ξi  �  ����ξj,r,i′  ���  2  2  +  n  �  i′=1  ω(t)  j,r,i  �  �ξj,r,i′, ξi  �  ����ξj,r,i′  ���  2  2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  40  Let  B(t)  i  = max  j=yi,r  �  ζ(t)  j,r,i +  �  �w(0)  j,r , ξi  �  − O(n log1/q T ⋆  �  log d  pd ) − O(nσ0σn  �  pd  �  log d  pd )  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Since maxj=yi,r  �  �w(0)  j,r , ξi  �  ≥ Ω(σ0σn  √pd), we have  B(0)  i  ≥ Ω(σ0σn  �  pd) − O(n log1/q T ⋆  �  log d  pd ) − O(nσ0σn  �  pd  �  log d  pd ) ≥ Ω(σ0σn  �  pd).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Let Ti to be the last time that ζ(t)  j,r,i ≤ m−1/q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' We can compute the growth of B(t)  i  as  B(t+1)  i  ≥ B(t)  i  + Θ(ησ2  npd  n  )[B(t)  i ]q−1  ≥ B(t)  i  + Θ(ησ2  npd  n  )[B(0)  i  ]q−2B(t)  i  ≥  �  1 + Θ  �  ησq−2  0  σq  npq/2dq/2  n  ��  B(t)  i .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Therefore, B(t)  i  will reach 2m−1/q within �O(η−1nσq−2  0  σ−q  n (pd)−q/2) iterations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  On the other hand, by Proposition D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='10, we have |ω(t)  j,r,i| ≤ β+6Cnα  �  log d  pd = O(σ0σn  √pd log d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='3  Converging Phase  From the first stage we know that  �w(T1)  j,r  = �w(0)  j,r + +  �  k̸=j  γ(t)  j,r,k  µk ⊙ mj,r  µ2  +  n  �  i=1  ζ(T1)  j,r,i  �ξj,r,i  ����ξj,r,i  ���  2  2  +  n  �  i=1  ω(T1)  j,r,i  �ξj,r,i  ����ξj,r,i  ���  2  2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Now we define �  W⋆ as follows:  �w⋆  j,r = �w(0)  j,r + Θ(m log(1/ϵ))  �  ��  n  �  i=1  I(j = yi)  �ξj,r,i  ����ξj,r,i  ���  2  2  �  �� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Lemma E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Based on the result from feature growing phase,  ����  W(T1) − �  W⋆���  F ≤ O(m2n1/2 log(1/ϵ)σ−1  n (pd)−1/2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' We derive the following bound:  ����  W(T1) − �  W⋆���  F  ≤  ����  W(T1) − �  W(0)���  F +  ����  W(0) − �  W⋆���  F  41  ≤  �  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r  �  �  �  ������  �  k̸=j  γ(t)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='k  µk  µ2  ������  2  +  �������  n  �  i=1  ζ(T1)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i  �ξj,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i  ����ξj,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i  ���  2  2  �������  2  +  �������  n  �  i=1  ω(T1)  j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i  �ξj,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i  ����ξj,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='i  ���  2  2  �������  2  �  �  � + Θ(m2n1/2 log(1/ϵ)σ−1  n (pd)−1/2)  ≤ Km(O(  √  Kσ0) + O(n1/2σ−1  n (pd)−1/2 log1/q T ⋆)) + �O(m2n1/2 log(1/ϵ)σ−1  n (pd)−1/2)  ≤ �O(m2n1/2 log(1/ϵ)σ−1  n (pd)−1/2),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  where the first inequality follows from triangle inequality,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' the second inequality follows from the  expression of W(T1),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' W⋆,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' and the third inequality follows from Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='5 and the fact that  ζ(t)  j,r,i > 0 if and only if j = yi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Lemma E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' For T1 ≤ t ≤ T ⋆, we have  �  ∇Fyi(�  Wyi, xi), �  W⋆  yi  �  −  �  ∇Fj(�  Wj, xi), �  W⋆  j  �  ≥ q log 2qK  ϵ  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Lemma E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' For T1 ≤ t ≤ T ⋆ and j = yi, we have  �  ∇Fj(�  W(t)  j , xi), �  W⋆  j  �  ≥ Θ(m1/q log(1/ϵ)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' By Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='5, we have  �  �ξj,r,i, �w⋆  j,r  �  = Θ(m log(1/ϵ)) and by Lemma E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='3 for j = yi,  maxr  �  �w(t)  j,r, ξi  �  ≥ maxr ζj,r,i − maxr  �  �w(0)  j,r , ξi  �  − O(n  �  log d  d α) ≥ Θ(m−1/q).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Then we have  �  ∇Fj(�  W(t)  j , xi), �  W⋆  j  �  =  m  �  r=1  σ′ ��  �w(t)  j,r, ξi  �� �  �ξj,r,i, �w⋆  j,r  �  ≥ Θ(m1/q log(1/ϵ)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Lemma E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' For T1 ≤ t ≤ T ⋆ and j ̸= yi, we have  �  ∇Fj(�  W(t)  j , xi), �  W⋆  j  �  ≤ O(1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' We first compute  �  �w⋆  j,r, ξi  �  =  �  �w(0)  j,r , ξi  �  +Θ(m log(1/ϵ)) �n  i=1 I(j = yi)⟨�ξj,r,i,ξi⟩  ∥�ξj,r,i∥  2  2  = O(σ0σn  √pd log d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Further,  �  �w(t)  j,r, ξi  �  =  �  �w(0)  j,r , ξi  �  +  �  k̸=j  γ(t)  j,r,k  �  µk, �ξj,r,i  �  µ2  +  n  �  i=1  ζ(t)  j,r,i  �  �ξj,r,i, ξi  �  ����ξj,r,i  ���  2  2  +  n  �  i=1  ω(t)  j,r,i  �  �ξj,r,i, ξi  �  ����ξj,r,i  ���  2  2  ≤ O(σ0σn  �  pd log d),  42  where the inequality follows from Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='5 and Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Thus, we have  �  ∇Fj(�  W(t)  j , xi), �  W⋆  j  �  =  m  �  r=1  σ′ ��  �w(t)  j,r, ξi  �� �  �ξj,r,i, �w⋆  j,r  �  ≤ mO  �  σ0σn  �  pd log d  �q  ≤ O(1),  where the last inequality follows from our choice of σ0 ≤ �O(m−1/qµ−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Lemma E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Under the same assumption as Theorem E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='1, we have  ���W(t) − W⋆���  2  F −  ���W(t+1) − W⋆���  2  F ≥ CηLS(�  W(t)) − ηϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' To simplify our notation, we define �F (t)  j (xi) =  �  ∇Fj(�  W(t)  j , xi), �  W⋆  j  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' The proof is exactly  the same as the proof of Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  ����  W(t) − �  W⋆���  2  F −  ����  W(t+1) − �  W⋆���  2  F  = 2η  �  ∇LS(�  W(t)) ⊙ M, �  W(t) − �  W⋆�  − η2 ���∇LS(�  W(t)) ⊙ M  ���  2  F  = 2η  n  n  �  i=1  K  �  j=1  ℓ′(t)  j,i  �  qFj(�  W(t)  j ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' xi, yi) −  �  ∇Fj(�  W(t)  j , xi), �  W⋆  j  ��  − η2 ���∇LS(�  W(t)) ⊙ M  ���  2  F  ≥ 2qη  n  n  �  i=1  �  �log(1 +  K  �  j=1  eFj−Fyi) − log(1 +  K  �  j=1  e( �Fj− �Fyi)/q)  �  � − η2 ���∇LS(�  W(t)) ⊙ M  ���  2  F  ≥ 2qη  n  n  �  i=1  �  ℓ(�  W(t);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' xi, yi) − log(1 + Ke− log(2qK/ϵ))  �  − η2 ���∇LS(�  W(t)) ⊙ M  ���  2  F  ≥ 2qη  n  n  �  i=1  �  ℓ(�  W(t);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' xi, yi) − ϵ  2q  �  − η2 ���∇LS(�  W(t)) ⊙ M  ���  2  F  ≥ CηLS(�  W(t)) − ηϵ,  where the first inequality follows from the convexity of the cross-entropy loss with softmax, the  second inequality follows from Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='20, the third inequality follows because log(1 + x) ≤ x,  and the last inequality follows from Lemma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='19 for some constant C > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Lemma E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='9 (Formal Restatement of Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Under the same assumption as Theorem E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='1,  choose T2 = T1 +  �  ∥�  W(T1)−�  W⋆∥  2  F  2ηϵ  �  = T1 + �O(η−1ϵ−1m4nσ−2  n (pd)−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Then for any time t during  this stage we have maxj,r |ω(t)  j,r,i| = O(σ0  √pd) and  1  t − T1  t  �  s=T1  LS(�  W(s)) ≤  ����  W(T1) − �  W⋆���  2  F  Cη(t − T1)  + ϵ  C .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  43  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' We have  ����  W(s) − �  W⋆���  2  F −  ����  W(s+1) − �  W⋆���  2  F ≥ CηLS(�  W(s)) − ηϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Taking a telescopic sum from T1 to t yields  t  �  s=T1  LS(�  W(s)) ≤  ����  W(T1) − �  W⋆���  2  F + ηϵ(t − T1)  Cη  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Combining Lemma E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='4, we have  t  �  s=T1  LS(�  W(s)) ≤ O(η−1 ����  W(T1) − �  W⋆���  2  F ) = �O(η−1m4nσ−2  n (pd)−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='4  Generalization Analysis  Theorem E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='10 (Formal Restatement of the Generalization Part of Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Under the same  assumption as Theorem E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='1, within O(η−1nσq−2  0  σ−q  n (pd)−q/2+η−1ϵ−1m4nσ−2  n (pd)−1) iterations, we  can find �  W(T) such that LS(�  W(T)) ≤ ϵ, and LD(�  W(t)) ≥ Ω(log K).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' First of all, from Lemma E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='9 we know there exists t ∈ [T1, T2] such that LS(�  W(T)) ≤ ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Then, we can bound  ����w(t)  j,r  ���  2 =  �������  �w(0)  j,r +  �  k̸=j  γ(t)  j,r,k  µk  µ2 +  n  �  i=1  ζ(t)  j,r,i  �ξj,r,i  ����ξj,r,i  ���  2  2  +  n  �  i=1  ω(t)  j,r,i  �ξj,r,i  ����ξj,r,i  ���  2  2  �������  2  ≤  ����w(0)  j,r  ���  2 +  �  k̸=j  |γ(t)  j,r,k| 1  µ +  n  �  i=1  ζ(t)  j,r,i  1  ����ξj,r,i  ���  2  +  n  �  i=1  |ω(t)  j,r,i|  1  ����ξj,r,i  ���  2  ≤ O(σ0  √  d) + �O(nσ−1  n (pd)−1/2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Consider a new example (x, y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Taking a union bound over r, with probability at least 1 − d−1, we  have  ���  �  w(t)  y,r, ξ  ���� = �O(σ0σn  √  d + n(pd)−1/2),  for all r ∈ [m].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' Then,  Fy(x) =  m  �  r=1  σ  ��  �w(t)  j,r, µy  ��  + σ  ��  �w(t)  j,r, ξ  ��  ≤ m max  r  ���  �  w(t)  y,r, ξ  ����  q  ≤ m �O(σq  0σq  ndq/2 + nq(pd)−q/2)  ≤ 1,  44  where the last inequality follows because σ0 ≤ �O(m−1/qµ−1) and d ≥ �Ω(m2/qn2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  Thus, with  probability at least 1 − 1/d,  ℓ(F(�  W(t);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content=' x)) ≥ log(1 + (K − 1)e−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
+page_content='  45' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GdAyT4oBgHgl3EQffPg-/content/2301.00335v1.pdf'}
diff --git a/GtE0T4oBgHgl3EQfRQCY/content/tmp_files/2301.02205v1.pdf.txt b/GtE0T4oBgHgl3EQfRQCY/content/tmp_files/2301.02205v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..74ec76b0a183eaf117a842c658b6cab7fc6531d7
--- /dev/null
+++ b/GtE0T4oBgHgl3EQfRQCY/content/tmp_files/2301.02205v1.pdf.txt
@@ -0,0 +1,678 @@
+arXiv:2301.02205v1  [math.LO]  5 Jan 2023
+The logic with unsharp implication and negation
+Ivan Chajda and Helmut L¨anger
+Abstract
+It is well-known that intuitionistic logics can be formalized by means of Brouwe-
+rian semilattices, i.e. relatively pseudocomplemented semilattices. Then the logical
+connective implication is considered to be the relative pseudocomplement and con-
+junction is the semilattice operation meet.
+If the Brouwerian semilattice has a
+bottom element 0 then the relative pseudocomplement with respect to 0 is called
+the pseudocomplement and it is considered as the connective negation in this logic.
+Our idea is to consider an arbitrary meet-semilattice with 0 satisfying only the
+Ascending Chain Condition, which is trivially satisfied in finite semilattices, and
+introduce the connective negation x0 as the set of all maximal elements z satis-
+fying x ∧ z = 0 and the connective implication x → y as the set of all maximal
+elements z satisfying x∧z ≤ y. Such a negation and implication is “unsharp” since
+it assigns to one entry x or to two entries x and y belonging to the semilattice,
+respectively, a subset instead of an element of the semilattice. Surprisingly, this
+kind of negation and implication, respectively, still shares a number of properties
+of these connectives in intuitionistic logic, in particular the derivation rule Modus
+Ponens. Moreover, unsharp negation and unsharp implication can be characterized
+by means of five, respectively seven simple axioms. Several examples are presented.
+The concepts of a deductive system and of a filter are introduced as well as the
+congruence determined by such a filter. We finally describe certain relationships
+between these concepts.
+AMS Subject Classification: 03G10, 03G25, 03B60, 06A12, 06D20
+Keywords: Semilattice, Brouwerian semilattice, Heyting algebra, intuitionistic logic,
+unsharp negation, unsharp implication, deductive system, filter, congruence
+1
+Introduction
+Intuitionistic logic is usually algebraically formalized by means of Brouwerian semilat-
+tices, i.e. semilattices (S, ∧, ∗) where ∗ denotes relative pseudocomplementation which is
+considered as the connective implication, see [1], [2], [12], [15] and [16]. If (S, ∧, ∗) has a 0
+then x∗0 is the pseudocomplement of x usually denoted by x∗ and considered as negation
+of x in this logic. If (S, ∧, ∗, 0) is even a lattice then it is called a Heyting algebra, see [14]
+and [17]. For posets the concept of pseudocomplementation was extended and studied
+by the authors in [4] and [5].
+It is well-known that every Brouwerian lattice (or Heyting algebra) is distributive.The
+concept of relative pseudocomplementation was extended by the first author to non-
+distributive lattices under the name sectional pseudocomplementation, see [3] and [9].
+1
+
+Hence a kind of non-distributive intuitionistic logic can be created on sectionally pseu-
+docomplemented lattices.
+In their previous papers [6] and [8] the authors showed that some important logics can
+be based also on posets that need not be lattices. An example of such a logic is the
+logic of quantum mechanics based on orthomodular posets, see e.g. [6], [10], [11] and
+[18]. It is evident that in this case some logical connectives such that disjunction or
+conjunction may be only partial operations or, as pointed out by the authors in [8] and
+[7], they may be be considered in an “unsharp version”, i.e. their result need not be a
+single element but may be a subset of the poset in question. Thus also the connective
+implication is created in this way as “unsharp”. For “unsharpness” see also [13]. This
+motivated us to study a variant of intuitionistic logic based on lattices that need neither
+be relatively pseudocomplemented nor even sectionally pseudocomplemented where the
+connective implication is unsharp.
+2
+Preliminaries
+In the following we identify singletons with their unique element, i.e. we will write x
+instead of {x}. Moreover, all posets considered in the sequel are assumed to satisfy the
+Ascending Chain Condition which we will abbreviate by ACC. This implies that every
+element lies under a maximal one. Of course, every finite poset satisfies the ACC. Let
+(P, ≤) be a poset, b ∈ P and A, B ⊆ P. By Max A we will denote the set of all maximal
+elements of A. We define
+A ≤ B if a ≤ b for all a ∈ A and all b ∈ B,
+A ≤1 B if for every a ∈ A there exists some b ∈ B with a ≤ b,
+A ≈1 B if A ≤1 B and B ≤1 A.
+The relation ≤1 is a quasiorder relation on 2P and ≈1 an equivalence relation on 2P. It
+is easy to see that A ≤1 Max B provided A ⊆ B and that A ≤1 b is equivalent to A ≤ b.
+Let S = (S, ∧) be an arbitrary meet-semilattice and A, B ⊆ S. We define
+A ∧ B := {a ∧ b | a ∈ A, b ∈ B}.
+3
+Unsharp negation
+Let (S, ∧, 0) be a meet-semilattice with 0 satisfying the ACC, a ∈ S and A ⊆ S. We
+define
+a0 := Max{x ∈ S|a ∧ x = 0}.
+Hence 0 is a unary operator on the meet-semilattice (S, ∧, 0) with 0 satisfying the ACC
+which assigns to every element x ∈ S the non-void subset x0 ⊆ S. The element a is called
+sharp if a00 = a. Moreover, we define
+A0 := Max{x ∈ S|A ∧ x = 0}.
+We are going to prove the following properties of the operator 0 for every meet-semilattice
+with 0 satisfying the ACC.
+2
+
+Theorem 3.1. Let S = (S, ∧, 0) be a meet-semilattice with 0 satisfying the ACC and
+a, b ∈ S. Then the following holds:
+(i) a0 is an antichain,
+(ii) a ≤1 a00,
+(iii) a ≤ b implies b0 ≤1 a0,
+(iv) 00 = Max S,
+(v) a ∧ a0 = 0,
+(vi) if S is bounded then 00 = 1 and 10 = 0,
+(vii) a ∧ 00 ≈1 a,
+(viii) a ∧ (a ∧ b)0 ≈1 a ∧ b0.
+Proof.
+(i) This is clear.
+(ii) We have a ∈ {x ∈ S | a0 ∧ x = 0}.
+(iii) If a ≤ b then {x ∈ S | b ∧ x = 0} ⊆ {x ∈ S | a ∧ x = 0}.
+(iv) and (v) follow directly from the definition of a0.
+(vi) If S is bounded then according to (iv)
+00 = Max S = 1,
+10 = Max{x ∈ S | 1 ∧ x = 0} = Max{0} = 0.
+(vii) According to (iv) we have a ≤1 Max S = 00 and hence a ≤1 a ∧ 00 ≤ a.
+(viii) Everyone of the following statements implies the next one:
+(a ∧ b) ∧ (a ∧ b)0 = 0,
+b ∧
+�
+a ∧ (a ∧ b)0�
+= 0,
+a ∧ (a ∧ b)0 ≤1 b0,
+a ∧ (a ∧ b)0 ≤1 a ∧ b0.
+From a ∧ b ≤ b we conclude b0 ≤1 (a ∧ b)0 according to (iii) and hence a ∧ b0 ≤1
+a ∧ (a ∧ b)0.
+From (iii) of Theorem 3.1 there follows immediately x0 ∧ y0 ≤ (x ∧ y)0.
+Example 3.2. Consider the meet-semilattice visualized in Fig. 1:
+3
+
+0
+a
+b
+c
+Fig. 1
+Meet-semilattice
+We have
+a = {b, c}0 = a00,
+00 = {a, b, c},
+a ∧ (a ∧ b)0 = a ∧ 00 = a ∧ {a, b, c} = {0, a} = a ∧ {a, c} = a ∧ b0
+in accordance with (ii), (iv) and (viii) of Theorem 3.1, respectively.
+Example 3.3. Consider the modular lattice L depicted in Fig. 2:
+0
+a
+b
+c
+d
+e
+f
+g
+h
+1
+Fig. 2
+Modular lattice
+We have
+a00 = {g, h}0 = a,
+f 00 = {b, c}0 = f,
+a0 ∧ e0 = {g, h} ∧ d = d ̸= {g, h} = a0 = (a ∧ e)0.
+Hence a and f are sharp and the equality x0 ∧ y0 = (x ∧ y)0 does not hold in general. In
+L from Figure 2 we have
+e0 = d and d0 = e.
+Since e ∧ d = 0 and e ∨ d = 1, {0, d, e, 1} is a complemented lattice.
+If a0 is a singleton, it need not be a complement of a, even if the semilattice is a lattice.
+E.g., consider the four-element lattice with atoms a and b and with an additional greatest
+element 1. Then a0 = b, but a ∨ b ̸= 1, i.e., a0 is not a complement of a.
+For every cardinal number n let Mn = (Mn, ∨, ∧) denote the bounded modular lattice of
+length 2 having n atoms.
+The situation from Figure 2 can be generalized as follows.
+4
+
+Remark 3.4. Every element of a direct product of a Boolean algebra and an arbitrary
+number of lattices Mn (possibly different n) is sharp.
+This follows immediately from the fact that every element of a Boolean algebra and every
+element of the lattice Mn is sharp.
+However, if the lattice L is not a direct product of two-element lattices and various Mn
+then the assertion of Remark 3.4 need not hold, see the following example.
+Example 3.5. Consider the lattice visualized in Fig. 3:
+0
+a
+b
+c
+d
+e
+f
+g
+1
+Fig. 3
+Lattice
+We have
+a00 = {b, c}0 = f ̸= a,
+a000 = f 0 = {b, c} = a0,
+b00 = {c, f}0 = b,
+(a0 ∧ b0)00 = ({b, c} ∧ {c, f})00 = {0, c}00 = {b, f}0 = c ̸= {0, c} = a0 ∧ b0,
+(c0 ∧ f 0)00 = ({b, f} ∧ {b, c})00 = {0, b}00 = {c, f}0 = b ̸= {0, b} = e0 ∧ f 0.
+Hence a is not sharp, b is sharp and the equality (x0 ∧ y0)00 = x0 ∧ y0 does not hold in
+general.
+We are going to show that the operator 0 can be characterized by means of four simple
+conditions.
+Theorem 3.6. Let (S, ∧, 0) be a meet-semilattice with 0 satisfying the ACC and 0 a
+unary operator on S. Then the following are equivalent:
+(i) x0 = Max{y ∈ S | x ∧ y = 0} for all x ∈ S,
+(ii) the operator 0 satisfies the following conditions:
+(P1) x0 is an antichain,
+5
+
+(P2) x ∧ 00 ≈1 x,
+(P3) x ∧ x0 ≈ 0,
+(P4) x ∧ (x ∧ y)0 ≈1 x ∧ y0.
+Proof.
+(i) ⇒ (ii):
+This follows from Theorem 3.1.
+(ii) ⇒ (i):
+If x ∧ y = 0 then according to (P2) and (P4) we have
+y ≈1 y ∧ 00 = y ∧ (x ∧ y)0 = y ∧ (y ∧ x)0 ≈1 y ∧ x0 ≤1 x0
+and hence y ≤1 x0. Conversely, if y ≤1 x0 then according to (P3) we have
+x ∧ y ≤1 x ∧ x0 = 0
+and hence x ∧ y = 0. This shows that x ∧ y = 0 is equivalent to y ≤1 x0. We conclude
+Max{y ∈ S | x ∧ y = 0} = Max{y ∈ S | y ≤1 x0} = x0.
+The last equality can be seen as follows. Let z ∈ Max{y ∈ S | y ≤1 x0}. Then z ≤1 x0,
+i.e. there exists some u ∈ x0 with z ≤ u. We have u ≤1 x0. Now z < u would imply
+z /∈ Max{y ∈ S | y ≤1 x0}, a contradiction. This shows z = u ∈ x0. Conversely, assume
+z ∈ x0. Then z ≤1 x0. If z /∈ Max{y ∈ S | y ≤1 x0} then there would exist some u ∈ S
+with z < u ≤1 x0 and hence there would exist some w ∈ x0 with z < u ≤ w contradicting
+(P1). This shows z ∈ Max{y ∈ S | y ≤1 x0}.
+4
+Unsharp implication
+Now we extend the operation of relative pseudocomplementation to arbitrary meet-
+semilattices with 0 satisfying the ACC as follows: Let S = (S, ∧, 0) be a meet-semilattice
+with 0 satisfying the ACC, a, b ∈ S and A, B ⊆ S. We define
+a → b := Max{x ∈ S | a ∧ x ≤ b}.
+Thus → is a binary operator on S assigning to every pair (x, y) ∈ S2 the non-void subset
+x → y ⊆ S. It is evident that
+x0 = x → 0 for each x ∈ S.
+Moreover, we define
+A → B := Max{x ∈ S | A ∧ x ≤ B}.
+Example 4.1. The “operation table” of the operator → in the meet-semilattice of Figure 1
+looks as follows (we write abc instead of {a, b, c} and so on):
+→
+0
+a
+b
+c
+0
+abc
+abc
+abc
+abc
+a
+bc
+abc
+bc
+ab
+b
+ac
+ac
+abc
+ac
+c
+ab
+ab
+ab
+abc
+6
+
+Example 4.2. The “operation table” of the operator → in the meet-semilattice of Figure 3
+looks as follows (we write bc instead of {b, c} and so on):
+→
+0
+a
+b
+c
+d
+e
+f
+g
+1
+0
+1
+1
+1
+1
+1
+1
+1
+1
+1
+a
+bc
+1
+bc
+bc
+1
+1
+1
+1
+1
+b
+cf
+cf
+1
+cf
+cf
+1
+cf
+1
+1
+c
+bf
+bf
+bf
+1
+bf
+1
+bf
+1
+1
+d
+bc
+g
+bc
+bc
+1
+g
+1
+g
+1
+e
+0
+f
+b
+c
+f
+1
+f
+1
+1
+f
+bc
+g
+bc
+bc
+dg
+g
+1
+g
+1
+g
+0
+f
+b
+c
+f
+ef
+f
+1
+1
+1
+0
+a
+b
+c
+d
+e
+f
+g
+1
+The following properties of the binary operator → can be proved.
+Theorem 4.3. Let S = (S, ∧, 0) be a meet-semilattice with 0 satisfying the ACC and
+a, b, c ∈ S. Then the following holds:
+(i) a → b is an antichain,
+(ii) a ≤ b implies a → b = Max S,
+(iii) b ∈ Max S implies b ∈ a → b,
+(iv) b ≤1 a → b,
+(v) a ≤1 (a → b) → b,
+(vi) a ≤ b implies c → a ≤1 c → b and b → c ≤1 a → c.
+(vii) a ∧ (a → b) ≈1 a ∧ b,
+(viii) a → (b ∧ c) ≈1 (a → b) ∧ (a → c),
+(ix) (a → b) ∧ b ≈1 b,
+(x) if S is bounded then 1 → b = b,
+(xi) a ∧ (b → b) ≈1 a,
+(xii) if S is bounded then a → b = 1 if and only if a ≤ b,
+(xiii) b ≤1 a → (a ∧ b).
+Proof.
+(i) This is clear.
+(ii), (iv), (x), (xii) and (xiii) follow immediately from the definition of →.
+(iii) If b ∈ Max S then because of a∧b ≤ b we have b ∈ Max{x ∈ S | a∧x ≤ b} = a → b.
+(v) Since a ∧ x ≤ b for all x ∈ a → b we have a ∧ (a → b) ≤ b, i.e. (a → b) ∧ a ≤ b.
+7
+
+(vi) If a ≤ b then
+{x ∈ S | c ∧ x ≤ a} ⊆ {x ∈ S | c ∧ x ≤ b},
+{x ∈ S | b ∧ x ≤ c} ⊆ {x ∈ S | a ∧ x ≤ c}.
+(vii) We have a ∧ x ≤ b and hence a ∧ x ≤ a ∧ b for all x ∈ a → b and hence a ∧ b ≤1
+a ∧ (a → b) ≤ a ∧ b according to (iv).
+(viii) According to (vii) we have a → (b ∧ c) ≤1 (a → b) ∧ (a → c). Conversely, assume
+d ∈ a → b and e ∈ a → c. Then a∧d ≤ b and a∧e ≤ c and hence a∧(d∧e) ≤ b∧c
+which implies d ∧ e ≤1 a → (b ∧ c). This shows (a → b) ∧ (a → c) ≤1 a → (b ∧ c).
+(ix) We have b ≤1 a → b according to (iv) and hence b ≤1 (a → b) ∧ b ≤ b.
+(xi) According to (ii) we have a ≤1 Max S = b → b and hence a ≤1 a ∧ (b → b) ≤ a.
+From Theorem 4.3 it is evident that the binary operator → shares properties of the
+logical connective implication in intuitionistic logic despite the fact that it is unsharp,
+i.e. for x, y ∈ S the result of x → y need not be a singleton.
+Hence it extends the
+intuitionistic logic based on a Heyting algebra (L, ∨, ∧, ∗, 0) where again ∨ formalizes
+disjunction, ∧ formalizes conjunction, but now → formalizes unsharp implication and 0
+formalizes unsharp negation.
+Example 4.4. Consider the modular lattice visualized in Fig. 4:
+0
+a
+b
+c
+d
+e
+f
+1
+Fig. 4
+Modular lattice
+Then
+e ≤1 {d, e} = {e, f} → e = (d → e) → e,
+d ∧ (d → e) = d ∧ {e, f} = c = d ∧ e,
+(d → e) ∧ e = {e, f} ∧ e = {c, e} ≈1 e
+in accordance with (v), (vii) and (ix) of Theorem 4.3, respectively.
+8
+
+Remark 4.5. It is easy to see that the operation ∧ and the operator → are related by
+so-called unsharp adjointness, i.e.
+a ∧ b ≤ c if and only if a ≤1 b → c.
+Since the operation ∧ is associative, commutative and monotone, it can be considered as
+a t-norm. Thus the semilattice (S, ∧, →) endowed with the operator → is an unsharply
+residuated semilattice. Moreover, by (viii) of Theorem 4.3 we have
+a ∧ (a → b) ≈1 a ∧ b
+showing that (S, ∧, →) satisfies divisibility.
+Similarly as for the unary operator 0 we can characterize the binary operator → on a
+meet-semilattice with 0 satisfying the ACC as follows.
+Theorem 4.6. Let (S, ∧, 0) be a meet-semilattice with 0 satisfying the ACC and → a
+binary operator on S. Then the following are equivalent:
+(i) x → y = Max{z ∈ S | x ∧ z ≤ y} for all x, y ∈ S,
+(ii) The operator → satisfies the following conditions:
+(R1) x → y is an antichain,
+(R2) x ∧ (x → y) ≈1 x ∧ y,
+(R3) (x → y) ∧ y ≈1 y,
+(R4) x → (y ∧ z) ≈1 (x → y) ∧ (x → z),
+(R5) x ∧ (y → y) ≈1 x,
+(R6) y ≤ z implies x → y ≤1 x → z.
+Proof.
+(i) ⇒ (ii):
+This follows from Theorem 4.3.
+(ii) ⇒ (i):
+If x ∧ z ≤ y then according to (R3), (R5), (R4) and (R6) we have
+z ≈1 (x → z) ∧ z ≤1 x → z ≈1 (x → x) ∧ (x → z) ≈1 x → (x ∧ z) ≤1 x → y
+and hence z ≤1 x → y. Conversely, if z ≤1 x → y then according to (R2) we have
+x ∧ z ≤1 x ∧ (x → y) ≈1 x ∧ y ≤ y
+and hence x∧z ≤ y. This shows that x∧z ≤ y is equivalent to z ≤1 x → y. We conclude
+Max{z ∈ S | x ∧ z ≤ y} = Max{z ∈ S | z ≤1 x → y} = x → y.
+The last equality can be seen as follows. Let u ∈ Max{z ∈ S | z ≤1 x → y}. Then
+u ≤1 x → y, i.e. there exists some v ∈ x → y with u ≤ v. We have v ≤1 x → y.
+Now u < v would imply u /∈ Max{z ∈ S | z ≤1 x → y}, a contradiction.
+This
+shows u = v ∈ x → y.
+Conversely, assume u ∈ x → y.
+Then u ≤1 x → y.
+If
+u /∈ Max{z ∈ S | z ≤1 x → y} then there would exist some v ∈ S with u < v ≤1 x → y
+and hence there would exist some w ∈ x → y with u < v ≤ w contradicting (R1). This
+shows u ∈ Max{z ∈ S | z ≤1 x → y}.
+9
+
+Example 4.7. Consider the lattice from Figure 4. Then
+d ∧ (d → e) = d ∧ {e, f} = c = d ∧ e,
+(d → e) ∧ e = e ∧ e = e,
+d → (e ∧ f) = d → c = {e, f} ≈1 {c, e, f} = {e, f} ∧ {e, f} = (d → e) ∧ (d → f)
+in accordance with (R2), (R3) and (R4), respectively.
+5
+Deductive systems
+It is well-known that the connective implication in intuitionistic logic is closely related
+to the so-called deductive systems in the corresponding Brouwerian semilattice. In what
+follows we show that a certain modification of the concept of a deductive system plays a
+similar role for logics with unsharp implication. We define
+Definition 5.1. A deductive system of a meet-semilattice S = (S, ∧, 0) with 0 satisfying
+the ACC is a subset D of S satisfying the following conditions for x, y ∈ S:
+(D1) (Max S) ∩ D ̸= ∅,
+(D2) x ∈ D and (x → y) ∩ D ̸= ∅ imply y ∈ D.
+Recall that a filter of a meet-semilattice S = (S, ∧) is a non-empty subset F of S satisfying
+the following conditions for x, y ∈ S:
+(F1) x, y ∈ F implies x ∧ y ∈ F,
+(F2) x ∈ F and x ≤ y imply y ∈ F.
+It is clear that if S is finite then all filters of S are given by the sets [x) := {y ∈ S | x ≤ y},
+x ∈ S, and hence the poset of all filters of S is dually isomorphic to S and therefore a
+join-semilattice where [x) ∨ [y) = [x ∧ y) for all x, y ∈ S.
+For every non-empty subset A of the universe of a meet-semilattice (S, ∧) we define a
+binary relation Θ(A) on S as follows:
+(x, y) ∈ Θ(A) if there exists some a ∈ A with x ∧ a = y ∧ a.
+Although the following result is known, for the reader’s convenience we present the proof.
+Lemma 5.2. Let S = (S, ∧, 1) be a meet-semilattice with 1 and Φ ∈ Con S. Then the
+following holds:
+(i) [1]Φ is an filter of S,
+(ii) Θ([1]Φ) ⊆ Φ.
+Proof.
+(i) (F1) If a, b ∈ [1]Φ then a ∧ b ∈ [1 ∧ 1]Φ = [1]Φ.
+10
+
+(F2) If a ∈ [1]Φ, b ∈ S and a ≤ b then b = 1 ∧ b ∈ [a ∧ b]Φ = [a]Φ = [1]Φ.
+This shows that [1]Φ is a filter of S.
+(ii) If (a, b) ∈ Θ([1]Φ) then there exists some c ∈ [1]Φ with a ∧ c = b ∧ c whence
+a = a ∧ 1 Φ a ∧ c = b ∧ c Φ b ∧ 1 = b
+which shows (a, b) ∈ Φ.
+Although our definition of a deductive system differs from that known for relatively
+pseudocomplemented semilattices, we are still able to prove the following relationships
+between the concepts mentioned before.
+Theorem 5.3. Let S = (S, ∧, 0, 1) be a bounded meet-semilattice satisfying the ACC and
+D a non-empty subset of S. Then the following are equivalent:
+(i) D a deductive system of S,
+(ii) D is an filter of S,
+(iii) Θ(D) ∈ Con S and D = [1]
+�
+Θ(D)
+�
+.
+Proof.
+(i) ⇒ (ii):
+(F2) Assume a ∈ D, b ∈ S and a ≤ b.
+Then a → b = Max S because of (ii) of
+Theorem 4.3. According to (D1) we have (a → b) ∩ D = Max S ∩ D ̸= ∅ and hence
+b ∈ D by (D2).
+(F1) Let a, b ∈ D. Then by (xiii) of Theorem 4.3 we have b ≤1 a → (a ∧ b). Hence there
+exists some c ∈ a → (a ∧ b) with b ≤ c. Now (F2) implies c ∈ D and therefore
+�
+a → (a ∧ b)
+�
+∩ D ̸= ∅ from which we conclude a ∧ b ∈ D by (D2).
+(ii) ⇒ (iii):
+Evidently, Θ(D) is reflexive and symmetric. Let (a, b), (b, c) ∈ Θ(D). Then there exist
+d, e ∈ D with a ∧ d = b ∧ d and b ∧ e = c ∧ e. Because of (F1) we conclude d ∧ e ∈ D.
+Now
+a ∧ (d ∧ e) = (a ∧ d) ∧ e = (b ∧ d) ∧ e = (b ∧ e) ∧ d = (c ∧ e) ∧ d = c ∧ (d ∧ e)
+which yields (a, c) ∈ Θ(D), i.e. Θ(D) is transitive. Further, if f ∈ S then
+(a ∧ f) ∧ d = (a ∧ d) ∧ f = (b ∧ d) ∧ f = (b ∧ f) ∧ d
+showing (a ∧ f, b ∧ f) ∈ Θ(D).
+Hence Θ(D) ∈ Con S.
+If a ∈ D then because of
+a ∧ a = a = 1 ∧ a we have a ∈ [1]
+�
+Θ(D)
+�
+showing D ⊆ [1]
+�
+Θ(D)
+�
+. Conversely, assume
+a ∈ [1]
+�
+Θ(D)
+�
+. Then there exists some b ∈ D with a ∧ b = 1 ∧ b. This implies b ≤ a
+wherefrom we conclude a ∈ D by (F2) showing [1]
+�
+Θ(D)
+�
+⊆ D.
+(iii) ⇒ (i):
+11
+
+(D1) If a ∈ D then, since S satisfies the ACC, there exists some b ∈ Max S with a ≤ b
+and hence
+b = 1 ∧ b ∈ [a ∧ b]
+�
+Θ(D)
+�
+= [a]
+�
+Θ(D)
+�
+= [1]
+�
+Θ(D)
+�
+= D.
+(D2) If a ∈ D, b ∈ S and (a → b) ∩ D ̸= ∅ then there exists some c ∈ D with c ∈ a → b
+and hence a ∧ c ≤ b whence
+b = 1∧1∧b ∈ [a∧c∧b]
+�
+Θ(D)
+�
+= [a∧c]
+�
+Θ(D)
+�
+= [1∧1]
+�
+Θ(D)
+�
+= [1]
+�
+Θ(D)
+�
+= D.
+It is well known that for a filter F of a relatively pseudocomplemented semilattice we
+have (a, b) ∈ Θ(F) if and only if a → b ∈ F and b → a ∈ F. However, we can modify
+this result also for an arbitrary meet-semilattice with 0 satisfying the ACC provided our
+unsharp implication is considered.
+Proposition 5.4. Let S = (S, ∧, 0) be a meet-semilattice with 0 satisfying the ACC, F
+a filter of S and a, b ∈ S. Then the following are equivalent:
+(i) (a, b) ∈ Θ(F),
+(ii) (a → b) ∩ F ̸= ∅ and (b → a) ∩ F ̸= ∅.
+Proof.
+(i) ⇒ (ii):
+There exists some c ∈ F with a ∧ c = b ∧ c. Hence a ∧ c ≤ b and b ∧ c ≤ a and therefore
+there exists some d ∈ a → b with c ≤ d and some e ∈ b → a with c ≤ e. Because of (F2)
+we conclude d, e ∈ F showing (ii).
+(ii) ⇒ (i):
+Let c ∈ (a → b)∩F and d ∈ (b → a)∩F. Then c∧d ∈ F by (F1), a∧c ≤ b and b∧d ≤ a.
+Hence
+a ∧ (c ∧ d) = (a ∧ c) ∧ (c ∧ d) ≤ b ∧ (c ∧ d) = (b ∧ d) ∧ (c ∧ d) ≤ a ∧ (c ∧ d),
+i.e. a ∧ (c ∧ d) = b ∧ (c ∧ d) showing (i).
+Conclusion
+Although the implication within the logic based on the structure (S, ∧, 0, →) is unsharp,
+i.e. x → y may be a subset I of S which need not be a singleton, it has its logical meaning.
+Namely, we ask that x → y is the maximal element c of S satisfying x ∧ c ≤ y (where ∧
+denotes conjunction). And for each c ∈ I this is satisfied. Moreover, the elements of I
+are mutually incomparable. Thus we have no need to prefer one of them with respect to
+others. However, the expression
+x ∧ (x → y) ≤ y
+is nothing else than the derivation rule Modus Ponens (both in classical as well as in
+non-classical logic) since it properly says that the truth value of y cannot be less than
+the truth value of the conjunction x ∧ (x → y) of x and the implication x → y. Hence,
+despite of the fact of unsharpness, such a logic is sound although it is derived from an
+arbitrary meet-semilattice with 0 satisfying the ACC.
+12
+
+References
+[1] L. E. J. Brouwer, De onbetrouwbaarheid der logische principes. Tijdschrift Wijs-
+begeerte 2 (1908), 152–158.
+[2] L. E. J. Brouwer, Intuitionism and formalism. Bull. Amer. Math. Soc. 20 (1913),
+81–96.
+[3] I. Chajda, An extension of relative pseudocomplementation to non-distributive lat-
+tices. Acta Sci. Math. (Szeged) 69 (2003), 491–496.
+[4] I. Chajda, Pseudocomplemented and Stone posets. Acta Univ. Palack. Olomuc. Fac.
+Rerum Natur. Math. 51 (2012), 29–34.
+[5] I. Chajda and H. L¨anger, Algebras describing pseudocomplemented, relatively pseu-
+docomplemented and sectionally pseudocomplemented posets. Symmetry 13 (2021),
+753 (17 pp.)
+[6] I. Chajda and H. L¨anger, Implication in finite posets with pseudocomplemented
+sections. Soft Computing 26 (2022), 5945–5953.
+[7] I. Chajda and H. L¨anger, The logic of orthomodular posets of finite height. Log. J.
+IGPL 30 (2022), 143–154.
+[8] I. Chajda and H. L¨anger, Operator residuation in orthomodular posets of finite
+height. Fuzzy Sets Systems (submitted).
+[9] I. Chajda, H. L¨anger and J. Paseka, Sectionally pseudocomplemented posets. Order
+38 (2021), 527–546.
+[10] D. Fazio, A. Ledda and F. Paoli, On Finch’s conditions for the completion of ortho-
+modular posets. Found. Sci. (2020), https://doi.org/10.1007/s10699-020-09702-z.
+[11] P. D. Finch, On orthomodular posets. J. Austral. Math. Soc. 11 (1970), 57–62.
+[12] O. Frink, Pseudo-complements in semi-lattices. Duke Math. J. 29 (1962), 505–514.
+[13] R. Giuntini and H. Greuling, Toward a formal language for unsharp properties.
+Found. Phys. 19 (1989), 931–945.
+[14] A. Heyting, Die formalen Regeln der intuitionistischen Logik. Sitzungsber. Akad.
+Berlin 1930, 42–56.
+[15] P. K¨ohler, Brouwerian semilattices: the lattice of total subalgebras. Banach Center
+Publ. 9 (1982), 47–56.
+[16] A. Monteiro, Axiomes ind´ependants pour les alg`ebres de Brouwer. Rev. Un. Mat.
+Argentina 17 (1955), 149–160.
+[17] L. Monteiro, Les alg`ebres de Heyting et de Lukasiewicz trivalentes. Notre Dame J.
+Formal Logic 11 (1970), 453–466.
+[18] P. Pt´ak and S. Pulmannov´a, Orthomodular Structures as Quantum Logics. Kluwer,
+Dordrecht 1991. ISBN 0-7923-1207-4.
+13
+
+Authors’ addresses:
+Ivan Chajda
+Palack´y University Olomouc
+Faculty of Science
+Department of Algebra and Geometry
+17. listopadu 12
+771 46 Olomouc
+Czech Republic
+ivan.chajda@upol.cz
+Helmut L¨anger
+TU Wien
+Faculty of Mathematics and Geoinformation
+Institute of Discrete Mathematics and Geometry
+Wiedner Hauptstraße 8-10
+1040 Vienna
+Austria, and
+Palack´y University Olomouc
+Faculty of Science
+Department of Algebra and Geometry
+17. listopadu 12
+771 46 Olomouc
+Czech Republic
+helmut.laenger@tuwien.ac.at
+14
+
diff --git a/GtE0T4oBgHgl3EQfRQCY/content/tmp_files/load_file.txt b/GtE0T4oBgHgl3EQfRQCY/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e363b3e4a54364a2515c4e43e9bd6478837db1bc
--- /dev/null
+++ b/GtE0T4oBgHgl3EQfRQCY/content/tmp_files/load_file.txt
@@ -0,0 +1,389 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf,len=388
+page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='02205v1  [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='LO]  5 Jan 2023  The logic with unsharp implication and negation  Ivan Chajda and Helmut L¨anger  Abstract  It is well-known that intuitionistic logics can be formalized by means of Brouwe-  rian semilattices, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' relatively pseudocomplemented semilattices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Then the logical  connective implication is considered to be the relative pseudocomplement and con-  junction is the semilattice operation meet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  If the Brouwerian semilattice has a  bottom element 0 then the relative pseudocomplement with respect to 0 is called  the pseudocomplement and it is considered as the connective negation in this logic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  Our idea is to consider an arbitrary meet-semilattice with 0 satisfying only the  Ascending Chain Condition, which is trivially satisfied in finite semilattices, and  introduce the connective negation x0 as the set of all maximal elements z satis-  fying x ∧ z = 0 and the connective implication x → y as the set of all maximal  elements z satisfying x∧z ≤ y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Such a negation and implication is “unsharp” since  it assigns to one entry x or to two entries x and y belonging to the semilattice,  respectively, a subset instead of an element of the semilattice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Surprisingly, this  kind of negation and implication, respectively, still shares a number of properties  of these connectives in intuitionistic logic, in particular the derivation rule Modus  Ponens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Moreover, unsharp negation and unsharp implication can be characterized  by means of five, respectively seven simple axioms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Several examples are presented.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  The concepts of a deductive system and of a filter are introduced as well as the  congruence determined by such a filter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' We finally describe certain relationships  between these concepts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  AMS Subject Classification: 03G10, 03G25, 03B60, 06A12, 06D20  Keywords: Semilattice, Brouwerian semilattice, Heyting algebra, intuitionistic logic,  unsharp negation, unsharp implication, deductive system, filter, congruence  1  Introduction  Intuitionistic logic is usually algebraically formalized by means of Brouwerian semilat-  tices, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' semilattices (S, ∧, ∗) where ∗ denotes relative pseudocomplementation which is  considered as the connective implication, see [1], [2], [12], [15] and [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' If (S, ∧, ∗) has a 0  then x∗0 is the pseudocomplement of x usually denoted by x∗ and considered as negation  of x in this logic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' If (S, ∧, ∗, 0) is even a lattice then it is called a Heyting algebra, see [14]  and [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' For posets the concept of pseudocomplementation was extended and studied  by the authors in [4] and [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  It is well-known that every Brouwerian lattice (or Heyting algebra) is distributive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='The  concept of relative pseudocomplementation was extended by the first author to non-  distributive lattices under the name sectional pseudocomplementation, see [3] and [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  1  Hence a kind of non-distributive intuitionistic logic can be created on sectionally pseu-  docomplemented lattices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  In their previous papers [6] and [8] the authors showed that some important logics can  be based also on posets that need not be lattices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' An example of such a logic is the  logic of quantum mechanics based on orthomodular posets, see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' [6], [10], [11] and  [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' It is evident that in this case some logical connectives such that disjunction or  conjunction may be only partial operations or, as pointed out by the authors in [8] and  [7], they may be be considered in an “unsharp version”, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' their result need not be a  single element but may be a subset of the poset in question.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Thus also the connective  implication is created in this way as “unsharp”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' For “unsharpness” see also [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' This  motivated us to study a variant of intuitionistic logic based on lattices that need neither  be relatively pseudocomplemented nor even sectionally pseudocomplemented where the  connective implication is unsharp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  2  Preliminaries  In the following we identify singletons with their unique element, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' we will write x  instead of {x}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Moreover, all posets considered in the sequel are assumed to satisfy the  Ascending Chain Condition which we will abbreviate by ACC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' This implies that every  element lies under a maximal one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Of course, every finite poset satisfies the ACC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Let  (P, ≤) be a poset, b ∈ P and A, B ⊆ P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' By Max A we will denote the set of all maximal  elements of A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' We define  A ≤ B if a ≤ b for all a ∈ A and all b ∈ B,  A ≤1 B if for every a ∈ A there exists some b ∈ B with a ≤ b,  A ≈1 B if A ≤1 B and B ≤1 A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  The relation ≤1 is a quasiorder relation on 2P and ≈1 an equivalence relation on 2P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' It  is easy to see that A ≤1 Max B provided A ⊆ B and that A ≤1 b is equivalent to A ≤ b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  Let S = (S, ∧) be an arbitrary meet-semilattice and A, B ⊆ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' We define  A ∧ B := {a ∧ b | a ∈ A, b ∈ B}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  3  Unsharp negation  Let (S, ∧, 0) be a meet-semilattice with 0 satisfying the ACC, a ∈ S and A ⊆ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' We  define  a0 := Max{x ∈ S|a ∧ x = 0}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  Hence 0 is a unary operator on the meet-semilattice (S, ∧, 0) with 0 satisfying the ACC  which assigns to every element x ∈ S the non-void subset x0 ⊆ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' The element a is called  sharp if a00 = a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Moreover, we define  A0 := Max{x ∈ S|A ∧ x = 0}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  We are going to prove the following properties of the operator 0 for every meet-semilattice  with 0 satisfying the ACC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  2  Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Let S = (S, ∧, 0) be a meet-semilattice with 0 satisfying the ACC and  a, b ∈ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Then the following holds:  (i) a0 is an antichain,  (ii) a ≤1 a00,  (iii) a ≤ b implies b0 ≤1 a0,  (iv) 00 = Max S,  (v) a ∧ a0 = 0,  (vi) if S is bounded then 00 = 1 and 10 = 0,  (vii) a ∧ 00 ≈1 a,  (viii) a ∧ (a ∧ b)0 ≈1 a ∧ b0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  (i) This is clear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  (ii) We have a ∈ {x ∈ S | a0 ∧ x = 0}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  (iii) If a ≤ b then {x ∈ S | b ∧ x = 0} ⊆ {x ∈ S | a ∧ x = 0}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  (iv) and (v) follow directly from the definition of a0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  (vi) If S is bounded then according to (iv)  00 = Max S = 1,  10 = Max{x ∈ S | 1 ∧ x = 0} = Max{0} = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  (vii) According to (iv) we have a ≤1 Max S = 00 and hence a ≤1 a ∧ 00 ≤ a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  (viii) Everyone of the following statements implies the next one:  (a ∧ b) ∧ (a ∧ b)0 = 0,  b ∧  �  a ∧ (a ∧ b)0�  = 0,  a ∧ (a ∧ b)0 ≤1 b0,  a ∧ (a ∧ b)0 ≤1 a ∧ b0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  From a ∧ b ≤ b we conclude b0 ≤1 (a ∧ b)0 according to (iii) and hence a ∧ b0 ≤1  a ∧ (a ∧ b)0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  From (iii) of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='1 there follows immediately x0 ∧ y0 ≤ (x ∧ y)0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Consider the meet-semilattice visualized in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' 1:  3  0  a  b  c  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' 1  Meet-semilattice  We have  a = {b, c}0 = a00,  00 = {a, b, c},  a ∧ (a ∧ b)0 = a ∧ 00 = a ∧ {a, b, c} = {0, a} = a ∧ {a, c} = a ∧ b0  in accordance with (ii), (iv) and (viii) of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='1, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Consider the modular lattice L depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' 2:  0  a  b  c  d  e  f  g  h  1  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' 2  Modular lattice  We have  a00 = {g, h}0 = a,  f 00 = {b, c}0 = f,  a0 ∧ e0 = {g, h} ∧ d = d ̸= {g, h} = a0 = (a ∧ e)0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  Hence a and f are sharp and the equality x0 ∧ y0 = (x ∧ y)0 does not hold in general.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' In  L from Figure 2 we have  e0 = d and d0 = e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  Since e ∧ d = 0 and e ∨ d = 1, {0, d, e, 1} is a complemented lattice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  If a0 is a singleton, it need not be a complement of a, even if the semilattice is a lattice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=', consider the four-element lattice with atoms a and b and with an additional greatest  element 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Then a0 = b, but a ∨ b ̸= 1, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=', a0 is not a complement of a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  For every cardinal number n let Mn = (Mn, ∨, ∧) denote the bounded modular lattice of  length 2 having n atoms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  The situation from Figure 2 can be generalized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  4  Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Every element of a direct product of a Boolean algebra and an arbitrary  number of lattices Mn (possibly different n) is sharp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  This follows immediately from the fact that every element of a Boolean algebra and every  element of the lattice Mn is sharp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  However, if the lattice L is not a direct product of two-element lattices and various Mn  then the assertion of Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='4 need not hold, see the following example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Consider the lattice visualized in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' 3:  0  a  b  c  d  e  f  g  1  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' 3  Lattice  We have  a00 = {b, c}0 = f ̸= a,  a000 = f 0 = {b, c} = a0,  b00 = {c, f}0 = b,  (a0 ∧ b0)00 = ({b, c} ∧ {c, f})00 = {0, c}00 = {b, f}0 = c ̸= {0, c} = a0 ∧ b0,  (c0 ∧ f 0)00 = ({b, f} ∧ {b, c})00 = {0, b}00 = {c, f}0 = b ̸= {0, b} = e0 ∧ f 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  Hence a is not sharp, b is sharp and the equality (x0 ∧ y0)00 = x0 ∧ y0 does not hold in  general.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  We are going to show that the operator 0 can be characterized by means of four simple  conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Let (S, ∧, 0) be a meet-semilattice with 0 satisfying the ACC and 0 a  unary operator on S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Then the following are equivalent:  (i) x0 = Max{y ∈ S | x ∧ y = 0} for all x ∈ S,  (ii) the operator 0 satisfies the following conditions:  (P1) x0 is an antichain,  5  (P2) x ∧ 00 ≈1 x,  (P3) x ∧ x0 ≈ 0,  (P4) x ∧ (x ∧ y)0 ≈1 x ∧ y0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  (i) ⇒ (ii):  This follows from Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  (ii) ⇒ (i):  If x ∧ y = 0 then according to (P2) and (P4) we have  y ≈1 y ∧ 00 = y ∧ (x ∧ y)0 = y ∧ (y ∧ x)0 ≈1 y ∧ x0 ≤1 x0  and hence y ≤1 x0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Conversely, if y ≤1 x0 then according to (P3) we have  x ∧ y ≤1 x ∧ x0 = 0  and hence x ∧ y = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' This shows that x ∧ y = 0 is equivalent to y ≤1 x0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' We conclude  Max{y ∈ S | x ∧ y = 0} = Max{y ∈ S | y ≤1 x0} = x0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  The last equality can be seen as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Let z ∈ Max{y ∈ S | y ≤1 x0}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Then z ≤1 x0,  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' there exists some u ∈ x0 with z ≤ u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' We have u ≤1 x0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Now z < u would imply  z /∈ Max{y ∈ S | y ≤1 x0}, a contradiction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' This shows z = u ∈ x0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Conversely, assume  z ∈ x0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Then z ≤1 x0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' If z /∈ Max{y ∈ S | y ≤1 x0} then there would exist some u ∈ S  with z < u ≤1 x0 and hence there would exist some w ∈ x0 with z < u ≤ w contradicting  (P1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' This shows z ∈ Max{y ∈ S | y ≤1 x0}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  4  Unsharp implication  Now we extend the operation of relative pseudocomplementation to arbitrary meet-  semilattices with 0 satisfying the ACC as follows: Let S = (S, ∧, 0) be a meet-semilattice  with 0 satisfying the ACC, a, b ∈ S and A, B ⊆ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' We define  a → b := Max{x ∈ S | a ∧ x ≤ b}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  Thus → is a binary operator on S assigning to every pair (x, y) ∈ S2 the non-void subset  x → y ⊆ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' It is evident that  x0 = x → 0 for each x ∈ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  Moreover, we define  A → B := Max{x ∈ S | A ∧ x ≤ B}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  Example 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' The “operation table” of the operator → in the meet-semilattice of Figure 1  looks as follows (we write abc instead of {a, b, c} and so on):  →  0  a  b  c  0  abc  abc  abc  abc  a  bc  abc  bc  ab  b  ac  ac  abc  ac  c  ab  ab  ab  abc  6  Example 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' The “operation table” of the operator → in the meet-semilattice of Figure 3  looks as follows (we write bc instead of {b,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' c} and so on):  →  0  a  b  c  d  e  f  g  1  0  1  1  1  1  1  1  1  1  1  a  bc  1  bc  bc  1  1  1  1  1  b  cf  cf  1  cf  cf  1  cf  1  1  c  bf  bf  bf  1  bf  1  bf  1  1  d  bc  g  bc  bc  1  g  1  g  1  e  0  f  b  c  f  1  f  1  1  f  bc  g  bc  bc  dg  g  1  g  1  g  0  f  b  c  f  ef  f  1  1  1  0  a  b  c  d  e  f  g  1  The following properties of the binary operator → can be proved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Let S = (S, ∧, 0) be a meet-semilattice with 0 satisfying the ACC and  a, b, c ∈ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Then the following holds:  (i) a → b is an antichain,  (ii) a ≤ b implies a → b = Max S,  (iii) b ∈ Max S implies b ∈ a → b,  (iv) b ≤1 a → b,  (v) a ≤1 (a → b) → b,  (vi) a ≤ b implies c → a ≤1 c → b and b → c ≤1 a → c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  (vii) a ∧ (a → b) ≈1 a ∧ b,  (viii) a → (b ∧ c) ≈1 (a → b) ∧ (a → c),  (ix) (a → b) ∧ b ≈1 b,  (x) if S is bounded then 1 → b = b,  (xi) a ∧ (b → b) ≈1 a,  (xii) if S is bounded then a → b = 1 if and only if a ≤ b,  (xiii) b ≤1 a → (a ∧ b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  (i) This is clear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  (ii), (iv), (x), (xii) and (xiii) follow immediately from the definition of →.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  (iii) If b ∈ Max S then because of a∧b ≤ b we have b ∈ Max{x ∈ S | a∧x ≤ b} = a → b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  (v) Since a ∧ x ≤ b for all x ∈ a → b we have a ∧ (a → b) ≤ b, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' (a → b) ∧ a ≤ b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  7  (vi) If a ≤ b then  {x ∈ S | c ∧ x ≤ a} ⊆ {x ∈ S | c ∧ x ≤ b},  {x ∈ S | b ∧ x ≤ c} ⊆ {x ∈ S | a ∧ x ≤ c}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  (vii) We have a ∧ x ≤ b and hence a ∧ x ≤ a ∧ b for all x ∈ a → b and hence a ∧ b ≤1  a ∧ (a → b) ≤ a ∧ b according to (iv).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  (viii) According to (vii) we have a → (b ∧ c) ≤1 (a → b) ∧ (a → c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Conversely, assume  d ∈ a → b and e ∈ a → c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Then a∧d ≤ b and a∧e ≤ c and hence a∧(d∧e) ≤ b∧c  which implies d ∧ e ≤1 a → (b ∧ c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' This shows (a → b) ∧ (a → c) ≤1 a → (b ∧ c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  (ix) We have b ≤1 a → b according to (iv) and hence b ≤1 (a → b) ∧ b ≤ b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  (xi) According to (ii) we have a ≤1 Max S = b → b and hence a ≤1 a ∧ (b → b) ≤ a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  From Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='3 it is evident that the binary operator → shares properties of the  logical connective implication in intuitionistic logic despite the fact that it is unsharp,  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' for x, y ∈ S the result of x → y need not be a singleton.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  Hence it extends the  intuitionistic logic based on a Heyting algebra (L, ∨, ∧, ∗, 0) where again ∨ formalizes  disjunction, ∧ formalizes conjunction, but now → formalizes unsharp implication and 0  formalizes unsharp negation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  Example 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Consider the modular lattice visualized in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' 4:  0  a  b  c  d  e  f  1  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' 4  Modular lattice  Then  e ≤1 {d, e} = {e, f} → e = (d → e) → e,  d ∧ (d → e) = d ∧ {e, f} = c = d ∧ e,  (d → e) ∧ e = {e, f} ∧ e = {c, e} ≈1 e  in accordance with (v), (vii) and (ix) of Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='3, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  8  Remark 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' It is easy to see that the operation ∧ and the operator → are related by  so-called unsharp adjointness, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  a ∧ b ≤ c if and only if a ≤1 b → c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  Since the operation ∧ is associative, commutative and monotone, it can be considered as  a t-norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Thus the semilattice (S, ∧, →) endowed with the operator → is an unsharply  residuated semilattice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Moreover, by (viii) of Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='3 we have  a ∧ (a → b) ≈1 a ∧ b  showing that (S, ∧, →) satisfies divisibility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  Similarly as for the unary operator 0 we can characterize the binary operator → on a  meet-semilattice with 0 satisfying the ACC as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Let (S, ∧, 0) be a meet-semilattice with 0 satisfying the ACC and → a  binary operator on S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Then the following are equivalent:  (i) x → y = Max{z ∈ S | x ∧ z ≤ y} for all x, y ∈ S,  (ii) The operator → satisfies the following conditions:  (R1) x → y is an antichain,  (R2) x ∧ (x → y) ≈1 x ∧ y,  (R3) (x → y) ∧ y ≈1 y,  (R4) x → (y ∧ z) ≈1 (x → y) ∧ (x → z),  (R5) x ∧ (y → y) ≈1 x,  (R6) y ≤ z implies x → y ≤1 x → z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  (i) ⇒ (ii):  This follows from Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  (ii) ⇒ (i):  If x ∧ z ≤ y then according to (R3), (R5), (R4) and (R6) we have  z ≈1 (x → z) ∧ z ≤1 x → z ≈1 (x → x) ∧ (x → z) ≈1 x → (x ∧ z) ≤1 x → y  and hence z ≤1 x → y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Conversely, if z ≤1 x → y then according to (R2) we have  x ∧ z ≤1 x ∧ (x → y) ≈1 x ∧ y ≤ y  and hence x∧z ≤ y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' This shows that x∧z ≤ y is equivalent to z ≤1 x → y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' We conclude  Max{z ∈ S | x ∧ z ≤ y} = Max{z ∈ S | z ≤1 x → y} = x → y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  The last equality can be seen as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Let u ∈ Max{z ∈ S | z ≤1 x → y}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Then  u ≤1 x → y, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' there exists some v ∈ x → y with u ≤ v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' We have v ≤1 x → y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  Now u < v would imply u /∈ Max{z ∈ S | z ≤1 x → y}, a contradiction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  This  shows u = v ∈ x → y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  Conversely, assume u ∈ x → y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  Then u ≤1 x → y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  If  u /∈ Max{z ∈ S | z ≤1 x → y} then there would exist some v ∈ S with u < v ≤1 x → y  and hence there would exist some w ∈ x → y with u < v ≤ w contradicting (R1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' This  shows u ∈ Max{z ∈ S | z ≤1 x → y}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  9  Example 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Consider the lattice from Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Then  d ∧ (d → e) = d ∧ {e, f} = c = d ∧ e,  (d → e) ∧ e = e ∧ e = e,  d → (e ∧ f) = d → c = {e, f} ≈1 {c, e, f} = {e, f} ∧ {e, f} = (d → e) ∧ (d → f)  in accordance with (R2), (R3) and (R4), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  5  Deductive systems  It is well-known that the connective implication in intuitionistic logic is closely related  to the so-called deductive systems in the corresponding Brouwerian semilattice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' In what  follows we show that a certain modification of the concept of a deductive system plays a  similar role for logics with unsharp implication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' We define  Definition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' A deductive system of a meet-semilattice S = (S, ∧, 0) with 0 satisfying  the ACC is a subset D of S satisfying the following conditions for x, y ∈ S:  (D1) (Max S) ∩ D ̸= ∅,  (D2) x ∈ D and (x → y) ∩ D ̸= ∅ imply y ∈ D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  Recall that a filter of a meet-semilattice S = (S, ∧) is a non-empty subset F of S satisfying  the following conditions for x, y ∈ S:  (F1) x, y ∈ F implies x ∧ y ∈ F,  (F2) x ∈ F and x ≤ y imply y ∈ F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  It is clear that if S is finite then all filters of S are given by the sets [x) := {y ∈ S | x ≤ y},  x ∈ S, and hence the poset of all filters of S is dually isomorphic to S and therefore a  join-semilattice where [x) ∨ [y) = [x ∧ y) for all x, y ∈ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  For every non-empty subset A of the universe of a meet-semilattice (S, ∧) we define a  binary relation Θ(A) on S as follows:  (x, y) ∈ Θ(A) if there exists some a ∈ A with x ∧ a = y ∧ a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  Although the following result is known, for the reader’s convenience we present the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Let S = (S, ∧, 1) be a meet-semilattice with 1 and Φ ∈ Con S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Then the  following holds:  (i) [1]Φ is an filter of S,  (ii) Θ([1]Φ) ⊆ Φ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  (i) (F1) If a, b ∈ [1]Φ then a ∧ b ∈ [1 ∧ 1]Φ = [1]Φ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  10  (F2) If a ∈ [1]Φ, b ∈ S and a ≤ b then b = 1 ∧ b ∈ [a ∧ b]Φ = [a]Φ = [1]Φ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  This shows that [1]Φ is a filter of S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  (ii) If (a, b) ∈ Θ([1]Φ) then there exists some c ∈ [1]Φ with a ∧ c = b ∧ c whence  a = a ∧ 1 Φ a ∧ c = b ∧ c Φ b ∧ 1 = b  which shows (a, b) ∈ Φ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  Although our definition of a deductive system differs from that known for relatively  pseudocomplemented semilattices, we are still able to prove the following relationships  between the concepts mentioned before.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Let S = (S, ∧, 0, 1) be a bounded meet-semilattice satisfying the ACC and  D a non-empty subset of S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Then the following are equivalent:  (i) D a deductive system of S,  (ii) D is an filter of S,  (iii) Θ(D) ∈ Con S and D = [1]  �  Θ(D)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  (i) ⇒ (ii):  (F2) Assume a ∈ D, b ∈ S and a ≤ b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  Then a → b = Max S because of (ii) of  Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' According to (D1) we have (a → b) ∩ D = Max S ∩ D ̸= ∅ and hence  b ∈ D by (D2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  (F1) Let a, b ∈ D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Then by (xiii) of Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='3 we have b ≤1 a → (a ∧ b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Hence there  exists some c ∈ a → (a ∧ b) with b ≤ c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Now (F2) implies c ∈ D and therefore  �  a → (a ∧ b)  �  ∩ D ̸= ∅ from which we conclude a ∧ b ∈ D by (D2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  (ii) ⇒ (iii):  Evidently, Θ(D) is reflexive and symmetric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Let (a, b), (b, c) ∈ Θ(D).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Then there exist  d, e ∈ D with a ∧ d = b ∧ d and b ∧ e = c ∧ e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Because of (F1) we conclude d ∧ e ∈ D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  Now  a ∧ (d ∧ e) = (a ∧ d) ∧ e = (b ∧ d) ∧ e = (b ∧ e) ∧ d = (c ∧ e) ∧ d = c ∧ (d ∧ e)  which yields (a, c) ∈ Θ(D), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Θ(D) is transitive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Further, if f ∈ S then  (a ∧ f) ∧ d = (a ∧ d) ∧ f = (b ∧ d) ∧ f = (b ∧ f) ∧ d  showing (a ∧ f, b ∧ f) ∈ Θ(D).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  Hence Θ(D) ∈ Con S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  If a ∈ D then because of  a ∧ a = a = 1 ∧ a we have a ∈ [1]  �  Θ(D)  �  showing D ⊆ [1]  �  Θ(D)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Conversely, assume  a ∈ [1]  �  Θ(D)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Then there exists some b ∈ D with a ∧ b = 1 ∧ b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' This implies b ≤ a  wherefrom we conclude a ∈ D by (F2) showing [1]  �  Θ(D)  �  ⊆ D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  (iii) ⇒ (i):  11  (D1) If a ∈ D then, since S satisfies the ACC, there exists some b ∈ Max S with a ≤ b  and hence  b = 1 ∧ b ∈ [a ∧ b]  �  Θ(D)  �  = [a]  �  Θ(D)  �  = [1]  �  Θ(D)  �  = D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  (D2) If a ∈ D, b ∈ S and (a → b) ∩ D ̸= ∅ then there exists some c ∈ D with c ∈ a → b  and hence a ∧ c ≤ b whence  b = 1∧1∧b ∈ [a∧c∧b]  �  Θ(D)  �  = [a∧c]  �  Θ(D)  �  = [1∧1]  �  Θ(D)  �  = [1]  �  Θ(D)  �  = D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  It is well known that for a filter F of a relatively pseudocomplemented semilattice we  have (a, b) ∈ Θ(F) if and only if a → b ∈ F and b → a ∈ F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' However, we can modify  this result also for an arbitrary meet-semilattice with 0 satisfying the ACC provided our  unsharp implication is considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  Proposition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Let S = (S, ∧, 0) be a meet-semilattice with 0 satisfying the ACC, F  a filter of S and a, b ∈ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Then the following are equivalent:  (i) (a, b) ∈ Θ(F),  (ii) (a → b) ∩ F ̸= ∅ and (b → a) ∩ F ̸= ∅.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  (i) ⇒ (ii):  There exists some c ∈ F with a ∧ c = b ∧ c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Hence a ∧ c ≤ b and b ∧ c ≤ a and therefore  there exists some d ∈ a → b with c ≤ d and some e ∈ b → a with c ≤ e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Because of (F2)  we conclude d, e ∈ F showing (ii).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  (ii) ⇒ (i):  Let c ∈ (a → b)∩F and d ∈ (b → a)∩F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Then c∧d ∈ F by (F1), a∧c ≤ b and b∧d ≤ a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  Hence  a ∧ (c ∧ d) = (a ∧ c) ∧ (c ∧ d) ≤ b ∧ (c ∧ d) = (b ∧ d) ∧ (c ∧ d) ≤ a ∧ (c ∧ d),  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' a ∧ (c ∧ d) = b ∧ (c ∧ d) showing (i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  Conclusion  Although the implication within the logic based on the structure (S, ∧, 0, →) is unsharp,  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' x → y may be a subset I of S which need not be a singleton, it has its logical meaning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  Namely, we ask that x → y is the maximal element c of S satisfying x ∧ c ≤ y (where ∧  denotes conjunction).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' And for each c ∈ I this is satisfied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Moreover, the elements of I  are mutually incomparable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Thus we have no need to prefer one of them with respect to  others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' However, the expression  x ∧ (x → y) ≤ y  is nothing else than the derivation rule Modus Ponens (both in classical as well as in  non-classical logic) since it properly says that the truth value of y cannot be less than  the truth value of the conjunction x ∧ (x → y) of x and the implication x → y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Hence,  despite of the fact of unsharpness, such a logic is sound although it is derived from an  arbitrary meet-semilattice with 0 satisfying the ACC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  12  References  [1] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Brouwer, De onbetrouwbaarheid der logische principes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Tijdschrift Wijs-  begeerte 2 (1908), 152–158.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  [2] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Brouwer, Intuitionism and formalism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Bull.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Amer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' 20 (1913),  81–96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  [3] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Chajda, An extension of relative pseudocomplementation to non-distributive lat-  tices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Acta Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' (Szeged) 69 (2003), 491–496.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  [4] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Chajda, Pseudocomplemented and Stone posets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Acta Univ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Palack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Olomuc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Fac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  Rerum Natur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' 51 (2012), 29–34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  [5] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Chajda and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' L¨anger, Algebras describing pseudocomplemented, relatively pseu-  docomplemented and sectionally pseudocomplemented posets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Symmetry 13 (2021),  753 (17 pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=')  [6] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Chajda and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' L¨anger, Implication in finite posets with pseudocomplemented  sections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Soft Computing 26 (2022), 5945–5953.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  [7] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Chajda and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' L¨anger, The logic of orthomodular posets of finite height.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Log.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  IGPL 30 (2022), 143–154.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  [8] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Chajda and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' L¨anger, Operator residuation in orthomodular posets of finite  height.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Fuzzy Sets Systems (submitted).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  [9] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Chajda, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' L¨anger and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Paseka, Sectionally pseudocomplemented posets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Order  38 (2021), 527–546.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  [10] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Fazio, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Ledda and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Paoli, On Finch’s conditions for the completion of ortho-  modular posets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Found.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' (2020), https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='1007/s10699-020-09702-z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  [11] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Finch, On orthomodular posets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Austral.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' 11 (1970), 57–62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  [12] O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Frink, Pseudo-complements in semi-lattices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Duke Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' 29 (1962), 505–514.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  [13] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Giuntini and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Greuling, Toward a formal language for unsharp properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  Found.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' 19 (1989), 931–945.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  [14] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Heyting, Die formalen Regeln der intuitionistischen Logik.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Sitzungsber.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Akad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  Berlin 1930, 42–56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  [15] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' K¨ohler, Brouwerian semilattices: the lattice of total subalgebras.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Banach Center  Publ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' 9 (1982), 47–56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  [16] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Monteiro, Axiomes ind´ependants pour les alg`ebres de Brouwer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Un.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Mat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  Argentina 17 (1955), 149–160.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  [17] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Monteiro, Les alg`ebres de Heyting et de Lukasiewicz trivalentes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Notre Dame J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  Formal Logic 11 (1970), 453–466.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  [18] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Pt´ak and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Pulmannov´a, Orthomodular Structures as Quantum Logics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' Kluwer,  Dordrecht 1991.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' ISBN 0-7923-1207-4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='  13  Authors’ addresses:  Ivan Chajda  Palack´y University Olomouc  Faculty of Science  Department of Algebra and Geometry  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' listopadu 12  771 46 Olomouc  Czech Republic  ivan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='chajda@upol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='cz  Helmut L¨anger  TU Wien  Faculty of Mathematics and Geoinformation  Institute of Discrete Mathematics and Geometry  Wiedner Hauptstraße 8-10  1040 Vienna  Austria, and  Palack´y University Olomouc  Faculty of Science  Department of Algebra and Geometry  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content=' listopadu 12  771 46 Olomouc  Czech Republic  helmut.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='laenger@tuwien.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
+page_content='at  14' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE0T4oBgHgl3EQfRQCY/content/2301.02205v1.pdf'}
diff --git a/HdE0T4oBgHgl3EQfRgBm/content/tmp_files/2301.02208v1.pdf.txt b/HdE0T4oBgHgl3EQfRgBm/content/tmp_files/2301.02208v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..84d658a0cda446cba76573a4a0bd9d3f132fbd89
--- /dev/null
+++ b/HdE0T4oBgHgl3EQfRgBm/content/tmp_files/2301.02208v1.pdf.txt
@@ -0,0 +1,1183 @@
+Do Users Want Platform Moderation or Individual Control? 
+Examining the Role of Third-Person Effects and Free Speech 
+Support in Shaping Moderation Preferences 
+Shagun	Jhaver,	Amy	Zhang	
+Online	platforms	employ	commercial	content	moderators	and	use	automated	systems	to	identify	and	remove	
+the	most	blatantly	inappropriate	content	for	all	users.	They	also	provide	moderation	settings	that	let	users	
+personalize	their	preferences	for	which	posts	they	want	to	avoid	seeing.	This	study	presents	the	results	of	a	
+nationally	representative	survey	of	984	US	adults.	We	examine	how	users	would	prefer	for	three	categories	of	
+norm-violating	 content	 (hate	 speech,	 sexually	 explicit	 content,	 and	 violent	 content)	 to	 be	 regulated.	
+Specifically,	we	analyze	whether	users	prefer	platforms	to	remove	such	content	for	all	users	or	leave	it	up	to	
+each	user	to	decide	if	and	how	much	they	want	to	moderate	it.	We	explore	the	influence	of	presumed	effects	
+on	others	(PME3)	and	support	for	freedom	of	expression	on	user	attitudes,	the	two	critical	factors	identified	
+as	 relevant	 for	 social	 media	 censorship	 attitudes	 by	 prior	 literature,	 about	 this	 choice.	 We	 find	 perceived	
+negative	effects	on	others	and	free	speech	support	as	significant	predictors	of	preference	for	having	personal	
+moderation	 settings	 over	 platform-directed	 moderation	 for	 regulating	 each	 speech	 category.	 Our	 findings	
+show	that	platform	governance	initiatives	need	to	account	for	both	the	actual	and	perceived	media	effects	of	
+norm-violating	speech	categories	to	increase	user	satisfaction.	Our	analysis	also	suggests	that	people	do	not	
+see	personal	moderation	tools	as	an	infringement	on	others’	free	speech	but	as	a	means	to	assert	greater	
+agency	to	shape	their	social	media	feeds.	
+And	 then	 there	 were	 what	 I'll	 call	 the	 technolibertarians.	 For	 them,	 MUD	 rapists	 were	 of	
+course	assholes,	but	the	presence	of	assholes	on	the	system	was	a	technical	inevitability,	like	
+noise	 on	 a	 phone	 line,	 and	 best	 dealt	 with	 not	 through	 repressive	 social	 disciplinary	
+mechanisms	 but	 through	 the	 timely	 deployment	 of	 defensive	 software	 tools.	 Some	 asshole	
+blasting	violent,	graphic	language	at	you?	Don't	whine	to	the	authorities	about	it	–	hit	the	
+@gag	 command	 and	 the	 asshole's	 statements	 will	 be	 blocked	 from	 your	 screen	 (and	 only	
+yours).	It's	simple,	it's	effective,	and	it	censors	no	one.	–	Excerpt	from	“A	Rape	in	Cyberspace”	
+by	Julian	Dibbell	[7]	
+Introduction 
+With	 the	 emergence	 of	 social	 media	 sites	 and	 their	 widespread	 use	 by	 people	 to	
+communicate	 with	 one	 another,	 companies	 like	 Facebook,	 Twitter,	 and	 YouTube	 have	
+become	 the	 new	 governors	 of	 digital	 expression.	 At	 the	 same	 time,	 individuals	 who	 use	
+these	sites	can	also	actively	shape	governance	in	various	ways.	For	example,	they	may	flag	
+posts	 that	 violate	 community	 policy,	 downvote	 inappropriate	 posts,	 serve	 as	 volunteer	
+moderators,	 engage	 in	 counter-speech,	 or	 configure	 moderation	 settings	 to	 automate	
+inappropriate	 post	 removals.	 We	 are	 therefore	 moving	 towards	 a	 “pluralist	 model	 of	
+speech	regulation	[1],”	in	which	speech	must	be	regulated	in	a	multi-stakeholder	fashion	–	
+legislative	entities	enforce	online	speech	laws,	and	platform	operators	set	up	governance	
+regimes	 of	 acceptable	 content.	 However,	 users	 themselves	 can	 also	 intervene	 against	
+content	perceived	as	problematic.		
+
+This	move	to	a	pluralist	model	is	occurring	against	recent	controversies	over	platforms’	
+moderation	decisions	[32,	47]	and	growing	media,	policymakers,	and	public	calls	to	better	
+regulate	their	content	[51].	In	response,	platforms	have	begun	investing	more	resources	
+into	 improving	 how	 inappropriate	 posts	 are	 detected	 and	 removed	 from	 their	 sites.	 We	
+focus	in	this	article	on	platforms’	offering	of	personal	moderation	tools	that	let	end-users	
+configure	content	moderation	of	the	posts	they	see	to	align	with	their	content	preferences.	
+We	are	primarily	concerned	with	tools	offered	by	platforms	such	as	Instagram	and	Twitch	
+that	let	users	specify	their	sensitivity	to	specific	topical	categories	such	as	sexually	explicit	
+content	 and	 hate	 speech.	 Configuring	 such	 tools	 lets	 users	 have	 the	 moderation	 system	
+operate	in	alignment	with	their	tastes	and	thresholds.		From	the	perspective	of	platforms,	a	
+tactical	consequence	of	offering	personal	moderation	tools	is	that	the	obligation	of	making	
+hard	moderation	decisions,	the	concomitant	responsibility	of	making	mistakes	with	them,	
+and	the	cognitive	labor	of	making	the	correct	configurations	are	passed	over	to	the	users.	
+Therefore,	it	is	vital	that	we	understand	how	users	consider	the	choice	between	platform	
+versus	personal	moderation.			
+Our	 research	 responds	 to	 calls	 by	 governance	 scholars	 to	 conduct	 more	 survey-based	
+research	 to	 understand	 users’	 perspectives	 on	 moderation	 interventions	 by	 different	
+regulatory	actors	[8,	41].	So	far,	we	have	little	knowledge	of	how	end-users	perceive	being	
+given	 self-regulating	 authority	 through	 personal	 moderation	 tools.	 We	 do	 not	 know	 the	
+situations	 in	 which	 users	 prefer	 to	 have	 a	 choice	 in	 shaping	 moderation	 and	 when	 they	
+would	instead	prefer	the	platforms	manage	it	for	every	user	–	and	the	different	factors	that	
+shape	these	preferences.		
+Informed	by	the	third-person	effects	(TPE)	hypothesis,	we	fill	this	gap	by	examining	users’	
+preferences	in	the	context	of	three	norm-violating	speech	categories	that	have	been	studied	
+in	prior	literature:	(1)	Hate	speech;	(2)	Sexually	explicit	content;	and	(3)	Violent	content.	
+Previous	research	has	shown	that	perceptions	of	the	effects	of	media	messages	on	others	
+predict	censorship	attitudes	[42,	44].	We	examine	the	role	that	third-person	effects	[6]	play	
+in	 shaping	 user	 attitudes	 about	 deploying	 platform-enacted	 versus	 personal	 moderation	
+tools.		
+We	also	connect	our	findings	to	the	scholarship	on	understanding	public	attitudes	toward	
+freedom	 of	 expression	 and	 its	 consequences.	 Free	 speech	 is	 a	 core	 constitutional	 right	
+highly	valued	by	many	Americans.	However,	the	introduction	of	personal	moderation	tools	
+offers	 affordances	 that	 complicate	 the	 question	 of	 preserving	 free	 speech	 –	 users	 may	
+configure	tools	to	avoid	specific	content	categories.	Still,	others	may	continue	to	see	the	
+same	 content,	 thereby	 preventing	 infringement	 of	 online	 expressions.	 However,	 if	 most	
+users	 choose	 to	 deploy	 these	 tools,	 specific	 content	 categories	 would	 have	 significantly	
+reduced	 visibility.	 Therefore,	 we	 analyze	 how	 users’	 support	 for	 freedom	 of	 expression	
+shapes	their	notion	of	different	moderation	approaches.	
+Understanding	 the	 public	 views	 on	 the	 platform	 and	 user-enacted	 interventions	 can	
+stimulate	debates	about	the	roles	and	strategies	of	various	regulatory	actors.	It	can	also	
+speak	 to	 calls	 for	 evidence-based	 policymaking	 [30,	 40]	 by	 clarifying	 how	 the	 public	
+understands	 moderation	 practices	 and	 identifying	 the	 gaps	 between	 policy	 and	 public	
+demands	[36,	37,	41].	Given	the	rapid	introduction	of	new	moderation	strategies	by	the	
+
+platforms,	 especially	 personal	 moderation	 tools,	 independent	 academic	 assessments	 of	
+users’	 attitudes	 on	 their	 deployment	 are	 vital.	 Platforms	 can	 also	 benefit	 from	 such	
+research	 by	 understanding	 end-users'	 acceptance	 or	 rejection	 of	 various	 regulatory	
+practices	and	the	factors	that	shape	those	perspectives.	Further,	examinations	of	the	public	
+perception	of	free	speech	within	the	context	of	online	activity	may	also	shape	attempts	to	
+protect	free	speech	in	the	long	run.	
+Literature Review and Hypotheses 
+The Perceptual Component of the TPE 
+Since	Davison	[6]	first	argued	that	individuals	perceive	media’s	impact	on	the	attitudes	and	
+behaviors	of	others	to	be	greater	than	it	is	on	themselves,	many	studies	have	shown	this	
+discrepancy	to	be	consistent	across	a	range	of	contexts	[49]	such	as	political	ads	[16,	38],	
+news	 stories	 [39]	 and	 social	 media	 use	 [46].	 This	 hypothesis,	 termed	 by	 Davison	 as	 the	
+third-person	 effect	 (TPE)	 [6],	 has	 become	 a	 widely	 applied	 perspective	 to	 explain	 public	
+opinion	 on	 the	 media	 censorship	 [19-21,	 33].	 The	 TPE	 hypothesis	 has	 two	 major	
+components	–	the	perceptual	and	behavioral	components	[18].	The	perceptual	component	
+predicts	that	presumed	media	effects	on	others	(PME3)	tend	to	be	greater	than	perceived	
+media	 effects	 on	 self	 (PME1).	 In	 the	 context	 of	 social	 media	 messages’	 influence,	 the	
+perceptual	component	of	TPE	predicts	that	participants	will	consider	others	to	be	more	
+negatively	 influenced	 by	 each	 category	 of	 norm-violating	 speech	 than	 themselves.	 We,	
+therefore,	raise	the	following	hypothesis:	
+H1:	For	each	norm-violating	speech	category,	participants	will	perceive	a	greater	effect	of	
+that	speech	on	others	than	on	themselves.	
+The Behavioral Component of the TPE 
+The	behavioral	component	of	the	TPE	argues	that	when	individuals	perceive	the	greater	
+impact	of	media	messages	on	others	than	on	themselves,	they	will	take	remedial	actions	to	
+mitigate	 the	 perceived	 harmful	 effects	 [20].	 Davison	 [6]	 described	 the	 phenomenon	 of	
+censorship	 as	 one	 of	 the	 most	 interesting	 behavioral	 consequences	 of	 third-person	
+perception.	Prior	research	on	TPE	consequences	shows	that	it	leads	to	censorship	support	
+[15,	19,	44],	and	the	effects	are	particularly	salient	when	persuasive	attempts	may	include	
+socially	 undesirable	 effects	 [28].	 In	 studying	 TPE	 effects	 on	 censorship	 attitudes,	 some	
+researchers	 have	 examined	 the	 consequences	 of	 the	 other-self	 perceptual	 disparity	 in	
+media	effects	(DME	=	PME3	–	PME1).	In	contrast,	others	have	focused	on	the	perceived	
+media	impact	on	others	(PME3)	[42].	Examining	past	research	data	on	TPE	consequences,	
+Chung	 and	 Moon	 [5]	 concluded	 that	 the	 media’s	 presumed	 effect	 on	 others	 (PME3)	 is	 a	
+stronger	 predictor	 of	 censorship	 attitudes	 than	 the	 other-self	 disparity	 in	 the	 perceived	
+media	effects.	We,	therefore,	choose	PME3	as	our	primary	predictor	variable	and	raise	the	
+following	hypothesis:	
+H2:	 For	 each	 speech	 category,	 the	 perceived	 effects	 of	 that	 speech	 on	 others	 will	 be	
+positively	related	to	support	for	the	platform’s	banning	of	that	category.	
+
+Researchers	of	TPE	have	long	been	curious	about	the	potential	behaviors	that	could	result	
+from	 the	 perceived	 media	 impact	 on	 others.	 In	 addition	 to	 censorship	 support,	 prior	
+studies	have	interrogated	behavioral	outcomes	such	as	engaging	in	political	action		[10,	43,	
+50],	disseminating	opposing	information	[3,	17],	and	exposing	apparent	biases	[2,	29].	In	
+the	context	of	online	content	moderation,	Jang	and	Kim	found	that	people	with	a	greater	
+level	of	third-person	perception	were	more	likely	to	support	media	literacy	interventions	
+to	 address	 fake	 news	 [22].	 We	 add	 to	 previous	 efforts	 to	 surface	 the	 different	 types	 of	
+behavioral	 consequences	 of	 TPE	 by	 examining	 its	 impact	 on	 users’	 support	 for	 having	
+personal	 moderation	 settings	 to	 moderate	 norm-violating	 content.	 Since	 such	
+configurations	are	also	a	form	of	regulation,	prior	TPE	research	suggests	that	PME3	would	
+predict	support	for	them	[19,	42].	The	following	hypothesis	thus	can	be	raised:	
+H3:	 For	 each	 speech	 category,	 the	 perceived	 effects	 of	 that	 speech	 on	 others	 will	 be	
+positively	related	to	support	for	having	personal	moderation	tools	to	regulate	the	speech	of	
+that	category.	
+Platform-enacted	 moderation	 and	 personal	 configurations	 to	 self-moderate	 content	 are	
+different	 ways	 to	 regulate	 norm-violating	 speech.	 However,	 while	 platform-enacted	
+moderation	 censors	 content	 platform-wide,	 personal	 moderation	 tools	 allow	 users	 to	
+adjust	 whether	 and	 how	 much	 norm-violating	 speech	 they	 are	 willing	 to	 encounter	
+personally.	 Prior	 literature	 generally	 predicts	 that	 TPE	 would	 lead	 to	 support	 for	
+censorship	attitudes	[5,	19].	However,	it	does	not	guide	how	people	will	react	to	a	choice	
+between	letting	platforms	handle	a	specific	content	category	and	allowing	users	to	specify	
+their	moderation	preferences	for	that	category.	We,	therefore,	ask	the	following	research	
+question:	
+RQ1:	For	each	speech	category,	how	do	its	perceived	effects	on	others	relate	to	support	for	
+the	 platform’s	 banning	 of	 that	 category	 versus	 support	 for	 having	 personal	 moderation	
+tools	regulate	it?	
+Support for Freedom of Speech  
+Discussions	about	the	benefits	of	moderation	measures	are	always	intertwined	with	the	
+issue	of	freedom	of	speech.	In	the	United	States,	the	constitution	protects	the	right	to	free	
+expression	as	a	fundamental	human	right.	However,	platforms	are	private	parties.	Section	
+230	of	the	Communications	Decency	Act	of	1996	provides	them	the	legislative	freedom	to	
+police	their	users	as	they	see	fit	while	not	being	held	accountable	for	errors	or	oversights	
+[13,	34].	Additionally,	experts	have	shown	that	despite	Americans’	support	for	freedom	of	
+expression	 generally,	 their	 tolerance	 for	 hate	 speech	 is	 low	 	 [12,	 48,	 52].	 Thus,	 people’s	
+acceptance	of	free	speech	in	the	abstract	may	not	automatically	imply	their	tolerance	for	
+opposing	expressions	[20].	Examining	how	much	people's	support	for	free	speech	affects	
+their	 opinions	 about	 varied	 moderation	 strategies	 may	 help	 us	 better	 understand	 this	
+discrepancy	in	the	context	of	social	media	platforms.	
+Support	 for	 free	 speech	 and	 attitudes	 toward	 content	 moderation	 have	 been	 linked	 in	
+previous	studies.	For	instance,	Naab	et	al.	showed	that	people	who	commit	to	freedom	of	
+expression	are	less	likely	to	support	restrictive	actions	by	Facebook	moderators	[36].	Guo	
+
+and	 Johnson	 showed	 that	 a	 lack	 of	 support	 for	 freedom	 of	 speech	 predicts	 support	 for	
+government	 regulation	 of	 sexist	 hate	 speech	 [20].	 However,	 they	 did	 not	 find	 that	 the	
+former	 could	 predict	 supportive	 attitudes	 toward	 platform	 censorship.	 Jang	 and	 Kim	
+suggested	 that	 support	 for	 free	 expression	 decreases	 support	 for	 regulating	 fake	 news	
+despite	the	existence	of	third-person	effects	[22].	Overall,	this	body	of	research	indicates	
+that	 participants’	 support	 for	 platform	 regulation	 will	 decline	 as	 free	 speech	 support	
+increases.	We,	therefore,	raise	the	following	hypotheses:	
+H4:	 For	 each	 speech	 category,	 participants’	 support	 for	 freedom	 of	 expression	 will	 be	
+negatively	related	to	their	support	for	the	platform’s	banning	of	that	category.	
+While	prior	research	provides	guidance	on	the	expected	relationship	between	free	speech	
+support	 and	 support	 for	 platform-enacted	 moderation,	 the	 literature	 on	 personal	
+moderation	 tools	 is	 scarce.	 It	 does	 not	 offer	 any	 direct	 guidance	 on	 the	 relationship	
+between	 support	 for	 free	 speech	 and	 support	 for	 having	 personal	 moderation	 tools.	
+However,	there	is	some	prior	work	that	speaks	to	related	issues.	For	example,	Naab	et	al.	
+did	not	find	a	relationship	between	users’	commitment	to	free	speech	and	their	intention	to	
+engage	 in	 corrective	 actions	 such	 as	 rebuking	 the	 comment	 author	 or	 reporting	 the	
+comment	 [36].	 It	 is	 unclear	 whether	 that	 finding	 would	 apply	 to	 our	 context	 since	
+deploying	 personal	 moderation	 tools	 is	 a	 restrictive	 action,	 not	 a	 corrective	 action.	 Its	
+expected	 costs	 (e.g.,	 setting	 up	 once	 for	 personal	 moderation	 v/s	 reporting	 every	
+inappropriate	post;	experiencing	retaliation	when	engaging	in	counter-speech	v/s	private	
+post	removals	for	personal	moderation)	are	also	lower.	Riedl	et	al.	conducted	a	survey	that	
+showed	 that	 individuals’	 support	 for	 free	 speech	 does	 not	 increase	 their	 assumed	 self-
+responsibility	 to	 intervene	 against	 problematic	 comments	 [41].	 However,	 they	 did	 not	
+specify	to	the	survey	takers	what	type	of	responsibility	they	should	carry	out.	Besides,	in	
+our	study	context,	users	may	not	consider	personal	moderation	tools	an	obligation.		
+On	 the	 one	 hand,	 support	 for	 free	 speech	 values	 should	 reduce	 support	 for	 restrictive	
+actions	of	any	kind.	But	on	the	other	hand,	people	may	perceive	personal	moderation	tools	
+as	simply	having	a	greater	agency	to	shape	what	they	see	and	not	an	infringement	on	the	
+free	speech	of	others.	In	this	way,	personal	moderation	tools	allow	a	distinction	between	
+freedom	 of	 speech	 and	 the	 obligation	 to	 be	 heard.	 To	 clarify	 the	 direction	 of	 this	
+relationship,	we	ask	the	following	research	question:	
+RQ2:	 Does	 participants’	 support	 for	 freedom	 of	 expression	 relate	 to	 their	 support	 for	
+having	personal	moderation	tools?	
+When	faced	with	a	choice	between	letting	platforms	handle	a	certain	content	category	and	
+allowing	users	to	specify	their	moderation	preferences,	we	expect	the	latter	to	be	perceived	
+as	 more	 free	 speech	 preserving.	 It	 lets	 users	 decide	 whether	 and	 how	 many	 content	
+removals	 should	 occur	 instead	 of	 allowing	 platforms	 to	 handle	 those	 same	 decisions	
+unilaterally.	We,	therefore,	raise	the	following	hypothesis:	
+
+H5:	 For	 each	 speech	 category,	 participants’	 support	 for	 freedom	 of	 expression	 will	 be	
+related	to	greater	support	for	having	personal	moderation	tools	to	moderate	that	category	
+than	their	support	for	the	platform’s	banning	of	that	category.	
+Methods 
+Our	study	was	considered	exempt	from	review	by	the	University	of	Washington	IRB.	We	
+recruited	participants	through	Lucid,1	a	survey	company	that	provides	researchers	access	
+to	 nationally	 representative	 samples.	 Our	 inclusion	 criterion	 for	 the	 survey	 participants	
+was	all	adult	internet	users	in	the	US.	We	paid	participants	through	the	Lucid	system.		
+We	designed	our	survey	questions	to	test	the	hypotheses	identified	in	the	previous	section	
+and	adapted	survey	instruments	from	relevant	prior	literature	to	test	some	measures.	We	
+describe	these	measures	in	more	detail	below.	To	increase	the	validity	of	the	survey,	we	
+sought	feedback	on	an	early	draft	of	the	survey	questionnaire	from	other	students	at	the	
+authors’	institutions.	Nine	students	who	were	not	involved	with	the	project	responded	to	
+our	request	and	provided	feedback	on	the	wording	of	the	questions	and	survey	flow,	which	
+we	incorporated	into	the	final	survey	design.	We	also	piloted	the	survey	with	a	small	subset	
+of	 the	 sample	 (27	 participants).	 During	 this	 field	 test,	 we	 included	 this	 open-ended	
+question	at	three	different	points	in	the	survey:	“Do	you	have	any	feedback	on	any	of	the	
+questions	 so	 far?	 For	 example,	 is	 any	 question	 unclear	 or	 ambiguous?	 Please	 list	 the	
+question	and	describe	your	challenge	with	answering	it.”	At	the	end	of	the	survey,	we	also	
+asked,	“Overall,	how	can	we	improve	this	survey	from	the	perspective	of	survey	takers?		Do	
+you	have	any	other	thoughts	or	feedback	for	us?	Please	describe.”	Results	from	this	survey	
+pretest	resulted	in	another	round	of	iteration	before	our	questionnaire	reached	the	desired	
+quality.	
+Our	survey	questionnaire	consisted	of	three	blocks	containing	similar	questions	about	hate	
+speech,	sexually	explicit	content,	and	violent	posts.	To	counter	the	effects	of	the	order	of	
+presentation	 on	 survey	 results,	 we	 counterbalanced	 the	 order	 in	 which	 question	 blocks	
+related	to	the	three	content	categories	were	shown	to	the	participants.	At	the	beginning	of	
+each	block,	we	specified	the	norm-violating	category	that	the	following	questions	related	to	
+and	defined	that	category.	We	used	the	following	definitions:	
+• Hate	speech:	“Hate	speech	includes	speech	that	is	dehumanizing,	stereotyping,	or	
+insulting,	 on	 the	 basis	 of	 identity	 markers	 such	 as	 race/ethnicity,	 gender,	 sexual	
+orientation,	religion,	etc.”	
+• Violent	 content:	 “Violent	 content	 includes	 threats	 to	 commit	 violence,	 glorifying	
+violence	or	celebrating	suffering,	depictions	of	violence	that	are	gratuitous	or	gory,	
+and	animal	abuse.”		
+	
+1	https://lucidtheorem.com		
+
+• Sexually	explicit	content:	“Sexually	explicit	content	includes	content	showing	sexual	
+activity,	offering	or	requesting	sexual	activity,	female	nipples	(except	breastfeeding,	
+health,	and	acts	of	protest),	nudity	showing	genitals,	and	sexually	explicit	language.”	
+The	above	definitions	were	inspired	by	the	language	provided	by	the	Facebook	site	when	
+reporting	any	post	under	the	category	of	hate	speech,	violence,	and	nudity,	respectively.	
+We	 administered	 the	 survey	 online	 using	 the	 survey	 software	 package	 Qualtrics.	 We	
+launched	the	survey	on	November	29,	2022.	Table	1	presents	the	demographic	details	of	
+our	final	sample	after	data	cleaning	and	compares	it	with	the	demographics	of	the	adult	US	
+internet	population	[45].			
+Table	1:	Demographic	Profile	of	the	US	Survey		
+	
+Authors’	study,	US	survey	
+Nov	2022	(%)	
+American	Community	Survey,	
+US	sample	2021	(%)	
+Age:	
+	
+	
+				18-29	
+18.7	
+17.4	
+				30-49	
+40.1	
+29.5	
+				50-64	
+23.7	
+25.6	
+				65+	
+17.4	
+27.3	
+Gender:	
+	
+	
+				Male	
+48.2	
+48.6	
+				Female	
+51.8	
+51.4	
+Race/Ethnicity:	
+	
+	
+				White	
+73.5	
+68.3	
+				Black	
+12.2	
+9.3	
+				Other	
+14.3	
+22.4	
+Hispanic:	
+	
+	
+				Yes	
+4.5	
+13.7	
+Education:	
+	
+	
+				High	school	or	less	
+31.4	
+33.5	
+				Some	college	
+24.4	
+33.3	
+				College+	
+43.3	
+33.1	
+Measures 
+Perceived Influence on Self and Others 
+For	 each	 norm-violating	 speech	 category,	 we	 asked	 the	 participants	 to	 estimate	 the	
+influence	 of	 that	 category	 on	 the	 self	 and	 others.	 In	 each	 case,	 we	 asked	two	 questions:	
+“Seeing	<speech	category>	posts	on	social	media	has	a	powerful	influence	on	my	attitudes.”	
+and	 “Seeing	 <speech	 category>	 posts	 on	 social	 media	 has	 a	 powerful	 influence	 on	 my	
+behaviors.”	The	response	categories	ranged	on	a	7-point	Likert-type	scale	from	1	(strongly	
+disagree)	to	7	(strongly	agree).	These	two	items	were	averaged	to	create	a	measure	of	the	
+perceived	 influence	 of	 each	 speech	 category	 on	 the	 self	 (Hate	 speech:	 M=3.89,	 SD=1.91,	
+a=.84;	Violent	speech:	M=3.78,	SD=1.87,	a=.81;	Sexually	explicit	speech:	M=3.55,	SD=1.89,	
+
+a=.87).	 We	 asked	 another	 two	 questions	 replacing	 only	 the	 word	 “my”	 with	 “other	
+people’s”	and	averaged	the	responses	to	create	an	index	of	the	perceived	influence	of	each	
+speech	category	on	others	(Hate	speech:	M=5.28,	SD=1.46,	a=.92;	Violent	speech:	M=5.19,	
+SD=1.40,	a=.91;	Sexually	explicit	speech:	M=4.99,	SD=1.46,	a=.93).	
+Support for Freedom of Speech 
+We	used	items	developed	by	Guo	and	Johnson	to	measure	support	for	freedom	of	speech	
+[20].	 Participants	 rated	 these	 four	 statements	 on	 a	 Likert-type	 scale	 ranging	 from	 1	
+(strongly	disagree)	to	7	(strongly	agree):	(1)	In	general,	I	support	the	First	Amendment,	(2)	
+Freedom	of	expression	is	essential	to	democracy,	(3)	Democracy	works	best	when	citizens	
+communicate	 in	 an	 unregulated	 marketplace	 of	 ideas,	 and	 (4)	 Even	 extreme	 viewpoints	
+deserve	to	be	voiced	in	society.	We	included	the	First	Amendment	statement2	in	the	first	
+question	 to	 clarify	 its	 meaning.	 We	 formed	 an	 index	 for	 free	 speech	 support	 using	 the	
+means	of	these	four	items	(M=5.43,	SD=1.15,	a=.80).	
+Dependent Variables Related to Moderation 
+Support	for	platform-enacted	moderation	of	each	speech	category	was	operationalized	by	
+asking	 participants	 to	 rate	 the	 following	 statement:	 “I	 support	 social	 media	 platforms	
+taking	 down	 any	 posts	 they	 consider	 to	 be	 <speech	 category>	 so	 that	 no	 users	 can	 see	
+them.”	 The	 responses	 for	 this	 statement	 ranged	 on	 a	 7-point	 Likert-type	 scale,	 where	
+1=“strongly	disagree”	and	7=“strongly	agree.”		
+For	 operationalizing	 support	 for	 having	 personal	 moderation	 tools	 for	 each	 category,	 we	
+showed	participants	an	example	of	a	personal	moderation	feature	where	every	user	can	
+decide	the	extent	to	which	they	want	the	<speech	category>	content	filtered	out	(see	Fig.	
+1).	We	asked	participants	to	rate	their	support	for	providing	this	kind	of	setting	to	all	users	
+on	a	Likert-type	scale	ranging	from	1	(strongly	disagree)	to	7	(strongly	agree).	
+	
+2	The	First	Amendment	to	the	United	States	Constitution	states:	"Congress	shall	make	no	
+law	 respecting	 an	 establishment	 of	 religion,	 or	 prohibiting	 the	 free	 exercise	 thereof;	 or	
+abridging	the	freedom	of	speech,	or	of	the	press;	or	the	right	of	the	people	peaceably	to	
+assemble,	and	to	petition	the	Government	for	a	redress	of	grievances.”	
+
+	
+Figure	1:	Survey	question	asking	participants	to	rate	their	support	for	platforms	providing	
+personal	moderation	feature	
+In	 addition	 to	 these	 two	 measures,	 we	 also	 operationalized	 choosing	 platform-enacted	
+moderation	 v/s	 personal	 moderation	 for	 each	 speech	 category	 by	 asking	 respondents	 a	
+binary	question:	‘Given	a	choice	between	platform-wide	moderation	and	a	"Choose	your	
+moderation	settings"	feature	to	handle	<speech	category>	posts,	which	would	you	prefer	to	
+have?’	The	response	categories	included:	(1)	Platform-wide	moderation:	Platforms	should	
+have	the	power	to	remove	all	posts	they	identify	as	<speech	category>	across	the	platform	
+or	(2)	"Choose	your	moderation	settings"	feature:	Each	user	should	be	allowed	to	configure	
+the	extent	to	which	<speech	category>	posts	should	be	removed	for	them.	We	note	that	the	
+“Choose	 you	 moderation	 settings”	 feature	 enables	 a	 range	 of	 choices	 –	 from	 “no	
+moderation”	to	“a	range	of	moderation.”	Thus,	users	who	desired	neither	platform-wide	
+nor	 personal	 moderation	 to	 remove	 any	 posts	 for	 them	 could	 select	 this	 feature	 and	
+configure	it	at	the	“no	moderation”	level.		
+
+The below example shows a feature where every user can decide for themselves
+the extentto whichtheywantsexuallyexplicit contentfiltered out.
+Chooseyourmoderationsettings:
+Filteroutsexuallyexplicitpostsbasedonthelevelyouselect:
+Alittle
+Some
+More
+Alotof
+No moderation
+moderation
+moderation
+moderation
+moderation
+Onlythemostsexuallyexplicitpostswillberemovedatthislevel.
+I support platforms providing this kind of setting to all users
+O Strongly disagree
+O Disagree
+OSomewhatdisagree
+ONeitheragree nordisagree
+O Somewhatagree
+O Agree
+O Strongly agree	
+Figure	2:	Frequency	of	participants’	responses	to	survey	questions	about	support	for	platform-
+wide	and	personal	moderation,	measured	in	percentage.	
+Control Variables 
+Prior	 research	 has	 shown	 that	 socio-demographic	 variables	 are	 related	 to	 TPE	 and	 free	
+speech	and	attitude	towards	media	regulation	[19,	26,	27,	31].	Further,	social	media	use	
+has	 also	 been	 associated	 with	 individuals’	 perceptions	 of	 harmful	 content	 and	 their	
+interventions	 against	 such	 [24,	 25,	 35,	 53].	 Therefore,	 we	 controlled	 for	 age,	 education,	
+gender,	 race,	 political	 affiliation	 (1	 =	 “very	 liberal”,	 7=	 “very	 conservative”),	 and	 social	
+media	use	of	each	respondent.	We	operationalized	the	frequency	of	social	media	use	by	
+following	recommendations	by	Ernala	et	al.	[9]	and	prompting	participants	to	respond	to	
+the	question,	‘In	the	past	week,	on	average,	approximately	how	much	time	PER	DAY	have	
+you	spent	actively	using	any	social	media?	
+Results 
+Our	results	show	that	72.8%,	73.1%,	and	66.2%	of	participants	at	least	somewhat	agreed	
+that	 platforms	 should	 ban	 hate	 speech,	 violent	 content,	 and	 sexually	 explicit	 content,	
+respectively.	Further,	69.9%,	72.6%,	and	72.1%	of	participants	at	least	somewhat	agreed	
+that	 platforms	 should	 offer	 personal	 moderation	 tools	 to	 let	 end-users	 regulate	 hate	
+speech,	violent	content,	and	sexually	explicit	content,	respectively.	
+
+Statistics
+Strongly disagree
+Disagree
+Somewhatdisagree
+Personal ModerationofSexuallyExplicitContent
+I Neither agree nor disagree
+Somewhatagree
+lAgree
+IStronglyagree
+PlatformBanofSexualyExplicitContent
+Personal ModerationofViolentContent
+PlatformBanofViolentContent
+PersonalModerationofHateSpeech
+PlatformBanofHateSpeech
+0
+20
+40
+60
+80
+100
+Percentage of ParticipantsIn	line	with	research	on	the	third-person	effects,	H1	predicted	that	for	each	norm-violating	
+content	category,	participants	would	perceive	the	effects	of	that	category	on	others	to	be	
+stronger	 than	 on	 themselves.	 We	 ran	 a	 paired	 t-test	 and	 found	 the	 perceived	 effects	 on	
+others	 significantly	 stronger	 than	 on	 oneself	 for	 each	 category	 (see	 Table	 2).	 Thus,	 our	
+results	support	H1.	
+Table	2:	Mean,	standard	deviations,	standard	errors	of	participants’	perceived	effects	of	hate	
+speech,	 violent	 content,	 and	 sexually	 explicit	 content	 on	 others	 and	 self,	 and	 t-test	 results	
+comparing	perceived	effects	on	others	and	self	for	each	speech	category	(N	=	993).	***	denotes	
+p	<	.001	
+	
+	
+M	
+SD	
+SE	
+t	
+Cohen’s	d	
+Hate	speech	
+Effects	on	others	
+5.28	
+1.46	
+.05	
+25.37***	
+.805	
+Effects	on	self	
+3.89	
+1.91	
+.06	
+Violent	
+content	
+Effects	on	others	
+5.19	
+1.40	
+.05	
+25.44***	
+.807	
+Effects	on	self	
+3.77	
+1.87	
+.06	
+Sexually	
+explicit	
+content	
+Effects	on	others	
+4.99	
+1.46	
+.05	
+25.81***	
+.819	
+Effects	on	self	
+3.55	
+1.88	
+.06	
+	
+Support for Platform Ban 
+We	computed	hierarchical	linear	regression	to	test	our	hypotheses	2	and	4.	For	each	of	the	
+three	norm-violating	categories,	we	created	a	model	where	the	participant’s	support	for	
+banning	that	category	served	as	the	dependent	variable.	In	Step	1	of	the	three	regression	
+models,	we	included	the	control	variables	age,	gender,	education,	race,	political	affiliation,	
+and	social	media	use.	In	Step	2,	we	introduced	the	independent	variables	PME3	(perceived	
+effects	on	others)	for	that	category	and	support	for	free	speech	(Table	3).		
+Table	3:	Hierarchical	multiple	regression	analyses	predicting	support	for	platforms'	banning	
+of	hate	speech,	violent	content,	and	sexually	explicit	content	(N	=	983)	
+Independent	Variable	
+Support	
+for	
+platform	ban	of	
+hate	speech	(β)	
+Support	
+for	
+platform	 ban	 of	
+violent	 content	
+(β)	
+Support	
+for	
+platform	 ban	 of	
+sexually	 explicit	
+content	(β)	
+
+Step	1	
+	
+	
+	
+				Age	
+.119***	
+.055	
+.102**	
+				Gender	(Female)	
+.127***	
+.167***	
+.153***	
+				Race	(White)	
+.018	
+.013	
+-.059	
+				Educationa	
+-.008	
+.039	
+-.022	
+				Political	affiliationb	
+-.156***	
+-.09**	
+.019	
+				Social	media	usec	
+.022	
+.013	
+.019	
+				R2	
+.093***	
+.065***	
+.05***	
+Step	2	
+	
+	
+	
+				Support	for	free	speech	
+-.101***	
+-.039	
+-.006	
+				Perceived	effects	of	hate	speech	on	others	
+.476***	
+-	
+-	
+				Perceived	effects	of	violent	content	on	others	
+-	
+.397***	
+-	
+				Perceived	 effects	 of	 sexually	 explicit	 content	
+on	others	
+-	
+-	
+.391***	
+				R2	change	
+.215	
+.15***	
+.149***	
+Total	R2	
+.307***	
+.215***	
+.199***	
+**p	<	.01,	***p	<	.001	(t	test	for	β,	two-tailed;	F	test	for	R2,	two-tailed).	
+a0=	Less	than	secondary	education;	1=	Secondary	education	or	more.	
+b1=	Strong	Democrat,	7=	Strong	Republican.	
+c1=	Less	than	10	minutes	per	day,	6=	More	than	3	hours	per	day.	
+β	=	standardized	beta	from	the	full	model	(final	beta	controlling	for	all	variables	in	the	model).		
+For	 each	 norm-violating	 speech	 category,	 the	 regression	 models	 show	 significant	
+influences	of	the	participants'	perceived	effects	of	that	category	on	others	(PME3)	on	their	
+support	for	platform	ban	of	that	category	(Model	1:	hate	speech	–	β	=	.476,	p	<	.001;	Model	
+
+2:	violent	content	–	β	=	.397,	p	<	.001;	Model	3:	sexually	explicit	content	–	β	=	.391,	p	<	
+.001),	supporting	H2.		
+Greater	support	for	free	speech	significantly	negatively	influences	support	for	platform	ban	
+of	hate	speech	(β	=	-.101,	p	<	.001).	It	does	not,	however,	influence	support	for	platform	ban	
+of	violent	content	(β	=	-.039,	p	>	.05)	or	sexually	explicit	content	(β	=	-.006,	p	>	.05).	Thus,	
+H4	is	only	partially	supported.		
+Support for Personal Moderation 
+We	computed	hierarchical	linear	regression	to	test	our	hypothesis	3	and	answer	RQ	2.	For	
+each	of	the	three	norm-violating	categories,	we	created	a	model	where	the	participant’s	
+support	 for	 having	 personal	 moderation	 tools	 to	 regulate	 that	 category	 served	 as	 the	
+dependent	 variable.	 In	 Step	 1	 of	 the	 three	 regression	 models,	 we	 included	 the	 control	
+variables	age,	gender,	education,	race,	political	affiliation,	and	social	media	use.	In	Step	2,	
+we	 introduced	 the	 independent	 variables	 PME3	 (perceived	 effects	 on	 others)	 for	 that	
+category	and	support	for	free	speech	(Table	4).	
+Table	 4:	 Hierarchical	 multiple	 regression	 analyses	 predicting	 support	 for	 using	 personal	
+moderation	tools	(PMT)	to	regulate	hate	speech,	violent	content,	and	sexually	explicit	content	
+(N	=	983)	
+Independent	Variable	
+Support	
+for	
+PMT	
+to	
+regulate	
+hate	
+speech	(β)	
+Support	for	PMT	
+to	
+regulate	
+violent	 content	
+(β)	
+Support	for	PMT	
+to	
+regulate	
+sexually	 explicit	
+content	(β)	
+Step	1	
+	
+	
+	
+				Age	
+.014	
+-.017	
+-.010	
+				Gender	(Female)	
+-.016	
+.019	
+-.016	
+				Race	(White)	
+-.019	
+-.007	
+.08*	
+				Educationa	
+-.018	
+.022	
+.003	
+				Political	affiliationb	
+-.019	
+-.049	
+-.074*	
+				Social	media	usec	
+.051	
+.057	
+.086**	
+				R2	
+.009	
+.013	
+.027***	
+Step	2	
+	
+	
+	
+
+				Support	for	free	speech	
+.173***	
+.195***	
+.224***	
+				Perceived	effects	of	hate	speech	on	others	
+.224***	
+-	
+-	
+				Perceived	effects	of	violent	content	on	others	
+-	
+.187***	
+-	
+				Perceived	 effects	 of	 sexually	 explicit	 content	
+on	others	
+-	
+-	
+.225***	
+				R2	change	
+.087	
+.081	
+.111	
+Total	R2	
+.096***	
+.095***	
+.138***	
+*p	<	.05,	**p	<	.01,	***p	<	.001	(t	test	for	β,	two-tailed;	F	test	for	R2,	two-tailed).	
+a0=	Less	than	secondary	education;	1=	Secondary	education	or	more.	
+b1=	Strong	Democrat,	7=	Strong	Republican.	
+c1=	Less	than	10	minutes	per	day,	6=	More	than	3	hours	per	day.	
+β	=	standardized	beta	from	the	full	model	(final	beta	controlling	for	all	variables	in	the	model).	
+For	 each	 norm-violating	 speech	 category,	 the	 regression	 models	 show	 significant	
+influences	of	the	participants'	perceived	effects	of	that	category	on	others	(PME3)	on	their	
+support	 for	 using	 personal	 moderation	 tools	 to	 regulate	 that	 category	 (Model	 4:	 hate	
+speech	–	β	=	.224,	p	<	.001;	Model	5:	violent	content	–	β	=	.187,	p	<	.001;	Model	6:	sexually	
+explicit	content	–	β	=	.225,	p	<	.001),	supporting	H4.		
+Greater	support	for	free	speech	has	a	significant	positive	influence	on	participants’	support	
+for	 using	 personal	 moderation	 tools	 to	 regulate	 each	 norm-violating	 category	 (Model	 4:	
+hate	speech	–	β	=	.173,	p	<	.001;	Model	5:	violent	content	–	β	=	.195,	p	<	.001;	Model	6:	
+sexually	explicit	content	–	β	=	.224,	p	<	.001).	This	answers	our	RQ	2.	
+	
+
+Choosing Between Platform-wide Moderation and Personal 
+Moderation 
+	
+Figure	3:	Percentage	of	participants	preferring	platform-wide	ban	or	personal	moderation	to	
+regulate	hate	speech,	violent	content,	and	sexually	explicit	content	
+Given	 a	 choice	 between	 platform-wide	 moderation	 and	 a	 personal	 moderation	 tool	 to	
+regulate	hate	speech,	violent	content,	and	sexually	explicit	content,	52.4%,	52%,	and	55.3%	
+of	participants,	respectively,	chose	the	personal	moderation	tool.	This	finding	suggests	that	
+more	participants	prefer	autonomy	over	moderation	than	delegating	it	to	platforms	as	they	
+see	fit.	
+We	created	binomial	logistic	regression	models	to	test	our	hypothesis	5	and	answer	RQ	1.	
+For	each	of	the	three	norm-violating	categories,	we	created	a	model	where	the	participants’	
+binary	choice	between	platform-wide	moderation	and	personal	moderation	to	handle	that	
+category	served	as	the	dependent	variable.	In	Step	1	of	the	three	regression	models,	we	
+included	the	control	variables	age,	gender,	education,	race,	political	affiliation,	and	social	
+media	use.	In	Step	2,	we	introduced	the	independent	variables	PME3	(perceived	effects	on	
+others)	for	that	category	and	support	for	free	speech.	For	each	model,	we	used	the	Box-
+Tidwell	procedure	[4,	11]	to	check	the	assumption	of	linearity	in	the	logit	and	found	in	each	
+case	that	our	continuous	variable	support	for	free	speech	was	not	linearly	related	to	the	
+logit	 of	 the	 dependent	 variable.	 To	 address	 this,	 we	 split	 this	 variable	 into	 two	 ordinal	
+categories	 –	 high	 and	 low,	 recoding	 each	 entry	 for	 this	 variable	 based	 on	 whether	 it	
+exceeded	the	median	value.	Rerunning	the	Box-Tidwell	procedure	with	this	transformed	
+support	 for	 the	 free	 speech	 categorical	 variable,	 we	 found	 all	 remaining	 continuous	
+
+Statistics
+Prefer platform-wide ban
+Preferpersonalmoderation
+Sexually explicit content
+Violent content
+Hate speech
+0
+10
+20
+30
+40
+50
+60
+Percentage of Participantsindependent	variables	in	each	model	to	be	linearly	related	to	the	logit	of	the	dependent	
+variable.	We	next	present	these	models'	binomial	logistic	regression	results	(Table	5).		
+Table	 5:	 Binomial	 logistic	 regression	 analyses	 predicting	 support	 for	 using	 personal	
+moderation	tools	(PMT)	over	platform-wide	ban	to	regulate	hate	speech,	violent	content,	and	
+sexually	explicit	content	(N	=	984)	
+Independent	Variable	
+Support	
+for	
+PMT	
+over	
+platform	ban	to	
+regulate	
+hate	
+speech,	
+Odds	
+Ratio	
+Support	for	PMT	
+over	
+platform	
+ban	 to	 regulate	
+violent	 content,	
+Odds	Ratio	
+Support	for	PMT	
+over	
+platform	
+ban	 to	 regulate	
+violent	 content,	
+Odds	Ratio	
+Step	1	
+	
+	
+	
+				Age	
+.986**	
+.992	
+.994	
+				Gender	(Female)	
+.790	
+.655**	
+.674**	
+				Race	(White)	
+1.107	
+1.313	
+1.203	
+				Educationa	
+.934	
+.870	
+.981	
+				Political	affiliationb	
+1.163***	
+1.118***	
+1.074*	
+				Social	media	usec	
+.990	
+1.071	
+1.091*	
+				Nagelkerke	R2	
+.066***	
+.066***	
+.045***	
+Step	2	
+	
+	
+	
+				Support	for	free	speechd	
+2.703***	
+2.239****	
+1.969***	
+				Perceived	effects	of	hate	speech	on	others	
+.735***	
+-	
+-	
+				Perceived	effects	of	violent	content	on	others	
+-	
+.752***	
+-	
+				Perceived	 effects	 of	 sexually	 explicit	 content	
+on	others	
+-	
+-	
+.857**	
+Total	Nagelkerke	R2	
+.165***	
+.138***	
+.087***	
+*p	<	.05,	**p	<	.01,	***p	<	.001	(t	test	for	β,	two-tailed;	Omnibus	Tests	of	Model	Coefficients	for	R2).	
+
+a0=	Less	than	secondary	education;	1=	Secondary	education	or	more.	
+b1=	Strong	Democrat,	7=	Strong	Republican.	
+c1=	Less	than	10	minutes	per	day,	6=	More	than	3	hours	per	day.	
+d0=	low,	1=high.	
+odds	ratio	=	exp(β)	from	full	model.	
+For	 each	 norm-violating	 speech	 category,	 the	 regression	 models	 show	 significant	
+influences	of	the	participants'	perceived	effects	of	that	category	on	others	(PME3)	on	their	
+choice	 of	 using	 personal	 moderation	 tools	 over	 platform-enacted	 bans	 to	 regulate	 that	
+category.	Increasing	PME3	was	associated	with	a	decreased	likelihood	of	choosing	personal	
+moderation	tools	over	platform	bans	(Model	7:	hate	speech	–	exp(β)	=	.735,	p	<	.001;	Model	
+8:	violent	content	–	exp(β)	=	.752,	p	<	.001;	Model	9:	sexually	explicit	content	–	exp(β)	=	
+.857,	p	<	.01).	This	answers	our	RQ	1.		
+Higher	support	for	free	speech	has	a	significant	positive	influence	on	participants’	support	
+for	 using	 personal	 moderation	 tools	 over	 platform-enacted	 bans	 to	 regulate	 each	 norm-
+violating	 category.	 Participants	 who	 showed	 high	 support	 for	 free	 speech	 have	 2.703,	
+2.239,	and	1.969	times	higher	odds	of	choosing	personal	moderation	tools	over	platform-
+enacted	 bans	 to	 regulate	 hate	 speech,	 violent	 content,	 and	 sexually	 explicit	 content,	
+respectively.	Thus,	H5	is	supported.	
+Discussion 
+In	recent	years,	the	debates	surrounding	the	censorship	of	inappropriate	content	on	social	
+media	have	surfaced	more	and	more	due	to	the	increasing	essentiality	of	social	media	in	
+political	discourse	and	growing	controversies	over	how	platforms	regulate	[13,	14].	The	
+purpose	of	this	study	was	to	measure	public	attitudes	regarding	two	important	forms	of	
+social	media	regulation:	platform-wide	moderation,	which	lets	platforms	unilaterally	make	
+moderation	decisions	for	every	user,	and	personal	moderation,	which	empowers	users	to	
+decide	 for	 themselves	 how	 they	 would	 like	 to	 regulate	 different	 content	 categories	 by	
+adjusting	 their	 moderation	 settings.	 Third-person	 effects	 (TPE)	 are	 commonly	 used	 in	
+examining	 people’s	 attitudes	 towards	 censorship	 and	 related	 behaviors	 or	 behavioral	
+intentions	[6,	18].	The	present	research	extends	the	TPE	research	to	managing	hate	speech,	
+violent	content,	and	sexually	explicit	content	on	social	media.		
+We	 explored	 the	 presumed	 negative	 effects	 of	 each	 type	 of	 content	 on	 self	 (PME1)	 and	
+others	(PME3).	The	results	produced	strong	support	for	the	TPE	hypothesis.	As	expected,	
+participants	perceived	the	social	media	hate	speech,	violent	content,	and	sexually	explicit	
+content	to	have	a	greater	influence	on	others	than	on	themselves.	We	also	examined	how	
+PME3	and	support	for	free	speech	affected	participants’	consequent	censorial	behavior.	In	
+each	 case,	 we	 found	 that	 the	 perceived	 effects	 on	 others	 (PME3)	 predicted	 participants’	
+support	 for	 both	 platform-wide	 moderation	 and	 personal	 moderation.	 This	 is	 a	
+theoretically	 significant	 finding	 of	 this	 study	 since	 it	 helps	 advance	 TPE	 research	 by	
+
+showing	 that	 perceived	 effects	 on	 others	 play	 an	 essential	 role	 in	 triggering	 censorial	
+behavior.	Given	a	choice	between	the	platform	and	personal	moderation,	PME3	predicted	
+support	 for	 platform	 moderation	 in	 each	 case.	 This	 finding	 indicates	 that	 when	 users	
+perceive	the	adverse	effects	of	a	content	category	on	the	public,	they	desire	platforms	to	
+take	site-wide	actions	on	that	content	rather	than	regulate	it	for	themselves.		
+Further,	the	relationship	between	support	for	free	speech	and	support	for	platform-wide	
+moderation	received	only	partial	support.	While	the	connection	is	significant	and	negative	
+for	hate	speech,	it	is	not	significant	for	violent	and	sexually	explicit	content.	This	result	is	in	
+line	with	the	mixed	findings	for	free	speech	support	as	a	predictor	of	supportive	attitudes	
+towards	platform	censorship	observed	in	prior	literature	[20].	On	the	other	hand,	we	found	
+that	 support	 for	 free	 speech	 predicted	 support	 for	 the	 use	 of	 personal	 moderation	 for	
+regulating	 each	 inappropriate	 speech	 category.	 This	 suggests	 that	 people	 may	 perceive	
+personal	moderation	tools	as	not	an	infringement	on	the	free	speech	of	others	but	simply	
+having	a	greater	agency	to	shape	what	they	see.	This	is	further	bolstered	by	our	finding	that	
+given	 a	 choice	 between	 the	 platform	 and	 personal	 moderation,	 support	 for	 free	 speech	
+predicts	support	for	personal	moderation	in	each	case.		
+Other	significant	effects,	less	central	to	the	hypotheses	being	tested,	also	were	found.	We	
+found	that	age	was	positively	related	to	support	for	platform	moderation	of	hate	speech	
+and	 sexually	 explicit	 content,	 but	 not	 violent	 content.	 Females	 supported	 platform	
+moderation	of	each	speech	category	more	than	males.	Democrats	were	more	likely	than	
+Republicans	to	support	platform	moderation	of	hate	speech	and	violent	content,	but	not	
+sexually	 explicit	 content.	 Regarding	 support	 for	 personal	 moderation,	 race,	 political	
+affiliation,	and	social	media	use	were	significant	predictors	for	the	sexually	explicit	content	
+category;	however,	no	control	variables	significantly	predicted	personal	moderation	of	hate	
+speech	or	violent	content.		
+The	evidence	presented	here	has	important	implications	for	how	platforms	govern	their	
+sites.	We	show	that	part	of	the	reason	the	public	supports	moderation	of	norm-violating	
+categories	such	as	pornography	and	war	violence	is	that	it	overestimates	these	categories’	
+effects	 on	 others.	 Therefore,	 company-wide	 moderation	 decisions	 and	 public	 debates	
+concerning	 free	 speech	 and	 its	 limitations,	 must	 recognize	 and	 account	 for	 third-person	
+effects.	It	also	points	to	an	urgent	need	to	measure	the	actual	media	effects	as	opposed	to	
+the	perceived	media	effects	of	different	content	types.	We	have	noticed	that	even	during	
+our	 interview	 studies	 on	 online	 harms,	 participants	 tend	 to	 advocate	 for	 specific	
+moderation	initiatives	based	on	their	perceptions	of	what	others	might	need.	To	arrive	at	
+an	 accurate	 needs-gathering,	 scholars	 must	 focus	 on	 understanding	 the	 perspectives	 of	
+online	content	on	users	themselves	–	a	topic	on	which	they	are	an	expert	–	rather	than	the	
+abstract	others	whose	actual	needs	may	considerably	differ.		
+Several	 limitations	 of	 this	 study	 should	 be	 recognized.	 The	 survey	 design	 prohibited	 us	
+from	exploring	the	motivations	for	specific	perceptions	in	depth.	Furthermore,	we	cannot	
+make	 conclusive	 statements	 about	 causal	 relations	 as	 a	 cross-sectional	 study.	 We	 asked	
+participants	 to	 respond	 to	 questions	 about	 speech	 categories	 that	 could	 be	 broadly	
+interpreted.	We	chose	this	instead	of	presenting	a	specific	instance	of	each	speech	category	
+to	 increase	 the	 generalizability	 of	 our	 findings.	 Still,	 different	 users	 may	 have	 different	
+
+perceptions	 of	 what	 counts	 as	 hate	 speech,	 violent	 content,	 or	 sexually	 explicit	 content.	
+Prior	moderation	research	has	recognized	this	as	a	complex	challenge	in	the	social	media	
+regulation	[23].	We	provided	definitions	of	each	speech	category	in	the	survey	to	clarify	the	
+scope	 of	 each	 category	 to	 our	 participants.	 Nevertheless,	 further	 research	 on	 user	
+perceptions	 of	 stimulus-based	 designs	 that	 present	 preselected	 instances	 of	 each	 norm-
+violating	 speech	 category	 to	 participants	 would	 provide	 valuable	 insights.	 We	 did	 not	
+ground	our	survey	questions	in	a	specific	platform	to	increase	the	generalizability	of	our	
+results.	 Studies	 focused	 on	 particular	 social	 media	 sites	 can	 uncover	 whether	 attitudes	
+towards	specific	platforms	influence	users’	perceptions	of	moderation	actions.		
+References 
+[1]	 Jack	 M	 Balkin.	 2017.	 Free	 speech	 in	 the	 algorithmic	 society:	 Big	 data,	 private	
+governance,	and	new	school	speech	regulation.	UCDL	Rev.,	51	(2017),	1149.		
+[2]	 Matthew	 Barnidge	 and	 Hernando	 Rojas.	 2014.	 Hostile	 Media	 Perceptions,	 Presumed	
+Media	 Influence,	 and	 Political	 Talk:	 Expanding	 the	 Corrective	 Action	 Hypothesis.	
+International	
+Journal	
+of	
+Public	
+Opinion	
+Research,	
+26,	
+2	
+(2014),	
+135-156.	
+https://doi.org/10.1093/ijpor/edt032	
+[3]	 Uli	 Bernhard	 and	 Marco	 Dohle.	 2015.	 Corrective	 or	 Confirmative	 Actions?	 Political	
+Online	 Participation	 as	 a	 Consequence	 of	 Presumed	 Media	 Influences	 in	 Election	
+Campaigns.	Journal	of	Information	Technology	&	Politics,	12,	3	(2015/07/03	2015),	285-
+302.	https://doi.org/10.1080/19331681.2015.1048918	
+[4]	G.	E.	P.	Box	and	Paul	W.	Tidwell.	1962.	Transformation	of	the	Independent	Variables.	
+Technometrics,	
+4,	
+4	
+(1962/11/01	
+1962),	
+531-550.	
+https://www.tandfonline.com/doi/abs/10.1080/00401706.1962.10490038	
+[5]	 Sungeun	 Chung	 and	 Shin-Il	 Moon.	 2016.	 Is	 the	 Third-Person	 Effect	 Real?	 a	 Critical	
+Examination	 of	 Rationales,	 Testing	 Methods,	 and	 Previous	 Findings	 of	 the	 Third-Person	
+Effect	 on	 Censorship	 Attitudes.	 Human	 Communication	 Research,	 42,	 2	 (2016),	 312-337.	
+https://doi.org/10.1111/hcre.12078	
+[6]	W.	Phillips	Davison.	1983.	The	Third-Person	Effect	in	Communication.	Public	Opinion	
+Quarterly,	47,	1	(1983),	1-15.	https://doi.org/10.1086/268763	
+[7]	 Julian	 Dibbell.	 1994.	 A	 rape	 in	 cyberspace	 or	 how	 an	 evil	 clown,	 a	 Haitian	 trickster	
+spirit,	two	wizards,	and	a	cast	of	dozens	turned	a	database	into	a	society.	Ann.	Surv.	Am.	L.	
+(1994),	471-471.		
+[8]	Sabine	A.	Einwiller	and	Sora	Kim.	2020.	How	Online	Content	Providers	Moderate	User-
+Generated	Content	to	Prevent	Harmful	Online	Communication:	An	Analysis	of	Policies	and	
+Their	
+Implementation.	
+Policy	
+&	
+Internet,	
+12,	
+2	
+(2020),	
+184-206.	
+https://onlinelibrary.wiley.com/doi/abs/10.1002/poi3.239	
+[9]	 Sindhu	 Kiranmai	 Ernala,	 Moira	 Burke,	 Alex	 Leavitt	 and	 Nicole	 B.	 Ellison.	 2020.	 How	
+Well	 Do	 People	 Report	 Time	 Spent	 on	 Facebook?	 An	 Evaluation	 of	 Established	 Survey	
+Questions	 with	 Recommendations.	 In	 Proceedings	 of	 the	 Proceedings	 of	 the	 2020	 CHI	
+Conference	on	Human	Factors	in	Computing	Systems	(Honolulu,	HI,	USA,	2020).	Association	
+for	Computing	Machinery.	https://doi.org/10.1145/3313831.3376435	
+[10]	Lauren	Feldman,	P.	Sol	Hart,	Anthony	Leiserowitz,	Edward	Maibach	and	Connie	Roser-
+Renouf.	 2017.	 Do	 Hostile	 Media	 Perceptions	 Lead	 to	 Action?	 The	 Role	 of	 Hostile	 Media	
+
+Perceptions,	 Political	 Efficacy,	 and	 Ideology	 in	 Predicting	 Climate	 Change	 Activism.	
+Communication	
+Research,	
+44,	
+8	
+(2017),	
+1099-1124.	
+https://journals.sagepub.com/doi/abs/10.1177/0093650214565914	
+[11]	John	Fox	Applied	regression	analysis	and	generalized	linear	models.	Sage	Publications,	
+2015.	
+[12]	 James	 L.	 Gibson	 and	 Richard	 D.	 Bingham.	 1982.	 On	 the	 Conceptualization	 and	
+Measurement	of	Political	Tolerance.	American	Political	Science	Review,	76,	3	(1982),	603-
+620.	
+https://www.cambridge.org/core/article/on-the-conceptualization-and-
+measurement-of-political-tolerance/579D03FF1A6041C6DB3DD6CB1FBC98E1	
+[13]	 Tarleton	 Gillespie.	 2017.	 Governance	 of	 and	 by	 platforms.	 Sage	 handbook	 of	 social	
+media	(2017).		
+[14]	Tarleton	Gillespie	Custodians	of	the	Internet:	Platforms,	content	moderation,	and	the	
+hidden	decisions	that	shape	social	media.	Yale	University	Press,	2018.	
+[15]	Guy	J.	Golan	and	Stephen	A.	Banning.	2008.	Exploring	a	Link	Between	the	Third-Person	
+Effect	and	the	Theory	of	Reasoned	Action:Beneficial	Ads	and	Social	Expectations.	American	
+Behavioral	
+Scientist,	
+52,	
+2	
+(2008),	
+208-224.	
+https://journals.sagepub.com/doi/abs/10.1177/0002764208321352	
+[16]	Guy	J.	Golan,	Stephen	A.	Banning	and	Lisa	Lundy.	2008.	Likelihood	to	Vote,	Candidate	
+Choice,	and	the	Third-Person	Effect:Behavioral	Implications	of	Political	Advertising	in	the	
+2004	 Presidential	 Election.	 American	 Behavioral	 Scientist,	 52,	 2	 (2008),	 278-290.	
+https://journals.sagepub.com/doi/abs/10.1177/0002764208321356	
+[17]	Guy	J.	Golan	and	Joon	Soo	Lim	Third-Person	Effect	of	ISIS's	Recruitment	Propaganda:	
+Online	Political	Self-Efficacy	and	Social	Media	Activism,	2016.	
+[18]	ALBERT	GUNTHER.	1991.	What	We	Think	Others	Think:Cause	and	Consequence	in	the	
+Third-Person	
+Effect.	
+Communication	
+Research,	
+18,	
+3	
+(1991),	
+355-372.	
+https://journals.sagepub.com/doi/abs/10.1177/009365091018003004	
+[19]	Albert	C.	Gunther.	2006.	Overrating	the	X-Rating:	The	Third-Person	Perception	and	
+Support	 for	 Censorship	 of	 Pornography.	 Journal	 of	 Communication,	 45,	 1	 (2006),	 27-38.	
+https://doi.org/10.1111/j.1460-2466.1995.tb00712.x	
+[20]	Lei	Guo	and	Brett	G.	Johnson.	2020.	Third-Person	Effect	and	Hate	Speech	Censorship	
+on	
+Facebook.	
+Social	
+Media	
++	
+Society,	
+6,	
+2	
+(2020),	
+2056305120923003.	
+https://journals.sagepub.com/doi/abs/10.1177/2056305120923003	
+[21]	CYNTHIA	HOFFNER,	MARTHA	BUCHANAN,	JOEL	DAVID	ANDERSON,	LISA	A.	HUBBS,	
+STACY	K.	KAMIGAKI,	LAURA	KOWALCZYK,	ANGELA	PASTOREK,	RICHARD	S.	PLOTKIN	and	
+KELSEY	J.	SILBERG.	1999.	Support	for	Censorship	of	Television	Violence:The	Role	of	the	
+Third-Person	Effect	and	News	Exposure.	Communication	Research,	26,	6	(1999),	726-742.	
+https://journals.sagepub.com/doi/abs/10.1177/009365099026006004	
+[22]	 S.	 Mo	 Jang	 and	 Joon	 K.	 Kim.	 2018.	 Third	 person	 effects	 of	 fake	 news:	 Fake	 news	
+regulation	 and	 media	 literacy	 interventions.	 Computers	 in	 Human	 Behavior,	 80	
+(2018/03/01/	
+2018),	
+295-302.	
+https://www.sciencedirect.com/science/article/pii/S0747563217306726	
+[23]	Shagun	Jhaver,	Larry	Chan	and	Amy	Bruckman.	2018.	The	View	from	the	Other	Side:	
+The	 Border	 Between	 Controversial	 Speech	 and	 Harassment	 on	 Kotaku	 in	 Action.	 First	
+Monday,	23,	2	(2018).	http://firstmonday.org/ojs/index.php/fm/article/view/8232	
+[24]	Anja	Kalch	and	Teresa	K	Naab.	2017.	Replying,	disliking,	flagging:	How	users	engage	
+with	uncivil	and	impolite	comments	on	news	sites	(2017).		
+
+[25]	Kate	Kenski,	Kevin	Coe	and	Stephen	A.	Rains.	2020.	Perceptions	of	Uncivil	Discourse	
+Online:	An	Examination	of	Types	and	Predictors.	Communication	Research,	47,	6	(2020),	
+795-814.	https://journals.sagepub.com/doi/abs/10.1177/0093650217699933	
+[26]	 Jennifer	 L.	 Lambe.	 2002.	 Dimensions	 of	 censorship:	 Reconceptualizing	 public	
+willingness	to	censor.	Communication	Law	and	Policy,	7	(2002),	187-235.		
+[27]	Francis	L.	F.	Lee.	2009.	The	Prevention	Effect	of	Third-Person	Perception:	A	Study	on	
+the	 Perceived	 and	 Actual	 Influence	 of	 Polls.	 Mass	 Communication	 and	 Society,	 13,	 1	
+(2009/12/24	2009),	87-110.	https://doi.org/10.1080/15205430802635672	
+[28]	 Joon	 Soo	 Lim.	 2017.	 The	 Third-Person	 Effect	 of	 Online	 Advertising	 of	 Cosmetic	
+Surgery:	A	Path	Model	for	Predicting	Restrictive	Versus	Corrective	Actions.	Journalism	&	
+Mass	
+Communication	
+Quarterly,	
+94,	
+4	
+(2017),	
+972-993.	
+https://journals.sagepub.com/doi/abs/10.1177/1077699016687722	
+[29]	 Joon	 Soo	 Lim	 and	 Guy	 J.	 Golan.	 2011.	 Social	 Media	 Activism	 in	 Response	 to	 the	
+Influence	of	Political	Parody	Videos	on	YouTube.	Communication	Research,	38,	5	(2011),	
+710-727.	https://journals.sagepub.com/doi/abs/10.1177/0093650211405649	
+[30]	 Sonia	 Livingstone.	 2013.	 ‘Knowledge	 enhancement’:	 the	 risks	 and	 opportunities	 of	
+evidence-based	policy	(2013).		
+[31]	 Ven-hwei	 Lo	 and	 Chingching	 Chang.	 2006.	 Knowledge	 about	 the	 Gulf	 Wars:A	
+Theoretical	 Model	 of	 Learning	 from	 the	 News.	 Harvard	 International	 Journal	 of	
+Press/Politics,	
+11,	
+3	
+(2006),	
+135-155.	
+https://journals.sagepub.com/doi/abs/10.1177/1081180X06289582	
+[32]	J.	Nathan	Matias.	2016.	Going	dark:	Social	factors	in	collective	action	against	platform	
+operators	in	the	Reddit	blackout.	City,	2016.		
+[33]	DOUGLAS	M.	McLEOD,	WILLIAM	P.	EVELAND	and	AMY	I.	NATHANSON.	1997.	Support	
+for	Censorship	of	Violent	and	Misogynic	Rap	Lyrics:An	Analysis	of	the	Third-Person	Effect.	
+Communication	
+Research,	
+24,	
+2	
+(1997),	
+153-174.	
+https://journals.sagepub.com/doi/abs/10.1177/009365097024002003	
+[34]	Ben	Medeiros.	2017.	Platform	(Non-)Intervention	and	the	“Marketplace”	Paradigm	for	
+Speech	 Regulation.	 Social	 Media	 +	 Society,	 3,	 1	 (2017),	 2056305117691997.	
+https://journals.sagepub.com/doi/abs/10.1177/2056305117691997	
+[35]	Teresa	K	Naab,	Anja	Kalch	and	Tino	GK	Meitz.	2018.	Flagging	uncivil	user	comments:	
+Effects	of	intervention	information,	type	of	victim,	and	response	comments	on	bystander	
+behavior.	
+New	
+Media	
+&	
+Society,	
+20,	
+2	
+(2018),	
+777-795.	
+https://journals.sagepub.com/doi/abs/10.1177/1461444816670923	
+[36]	Teresa	K.	Naab,	Thorsten	Naab	and	Jonas	Brandmeier.	2021.	Uncivil	User	Comments	
+Increase	 Users’	 Intention	 to	 Engage	 in	 Corrective	 Actions	 and	 Their	 Support	 for	
+Authoritative	 Restrictive	 Actions.	 Journalism	 &	 Mass	 Communication	 Quarterly,	 98,	 2	
+(2021),	566-588.	https://journals.sagepub.com/doi/abs/10.1177/1077699019886586	
+[37]	Hye-Jin	Paek,	Jennifer	L.	Lambe	and	Douglas	M.	McLeod.	2008.	Antecedents	to	Support	
+for	Content	Restrictions.	Journalism	&	Mass	Communication	Quarterly,	85,	2	(2008),	273-
+290.	https://journals.sagepub.com/doi/abs/10.1177/107769900808500204	
+[38]	Hye-Jin	Paek,	Zhongdang	Pan,	Ye	Sun,	Joseph	Abisaid	and	Debra	Houden.	2005.	The	
+Third-Person	 Perception	 as	 Social	 Judgment:An	 Exploration	 of	 Social	 Distance	 and	
+Uncertainty	 in	 Perceived	 Effects	 of	 Political	 Attack	 Ads.	 Communication	 Research,	 32,	 2	
+(2005),	143-170.	https://journals.sagepub.com/doi/abs/10.1177/0093650204273760	
+
+[39]	Vincent	Price	and	David	Tewksbury.	1996.	Measuring	the	Third-Person	Effect	of	News:	
+The	 Impact	 of	 Question	 Order,	 Contrast	 and	 Knowledge.	 International	 Journal	 of	 Public	
+Opinion	Research,	8,	2	(1996),	120-141.	https://doi.org/10.1093/ijpor/8.2.120	
+[40]	Manuel	Puppis	and	Hilde	Van	den	Bulck.	2019.	Introduction:	Media	Policy	and	Media	
+Policy	
+Research.	
+Springer	
+International	
+Publishing,	
+City,	
+2019.	
+https://doi.org/10.1007/978-3-030-16065-4_1	
+[41]	Martin	J.	Riedl,	Teresa	K.	Naab,	Gina	M.	Masullo,	Pablo	Jost	and	Marc	Ziegele.	2021.	
+Who	 is	 responsible	 for	 interventions	 against	 problematic	 comments?	 Comparing	 user	
+attitudes	in	Germany	and	the	United	States.	Policy	&	Internet	(2021).		
+[42]	Martin	J.	Riedl,	Kelsey	N.	Whipple	and	Ryan	Wallace.	2021.	Antecedents	of	support	for	
+social	media	content	moderation	and	platform	regulation:	the	role	of	presumed	effects	on	
+self	
+and	
+others.	
+Information,	
+Communication	
+&	
+Society	
+(2021),	
+1-18.	
+https://doi.org/10.1080/1369118X.2021.1874040	
+[43]	Hernando	Rojas.	2010.	“Corrective”	Actions	in	the	Public	Sphere:	How	Perceptions	of	
+Media	and	Media	Effects	Shape	Political	Behaviors.	International	Journal	of	Public	Opinion	
+Research,	22,	3	(2010),	343-363.	https://doi.org/10.1093/ijpor/edq018	
+[44]	Hernando	Rojas,	Dhavan	V.	Shah	and	Ronald	J.	Faber.	1996.	For	the	Good	of	Others:	
+Censorship	and	the	Third-person	Effect.	International	Journal	of	Public	Opinion	Research,	8,	
+2	(1996),	163-186.	https://doi.org/10.1093/ijpor/8.2.163	
+[45]	Steven	Ruggles,	Sarah	Flood,	Ronald	Goeken,	Megan		Schouweiler	and	Matthew	Sobek.	
+2022.	IPUMS	USA,	Minneapolis,	MN.	https://doi.org/10.18128/D010.V12.0	
+[46]	Valarie	Schweisberger,	Jennifer	Billinson	and	T.	Makana	Chock.	2014.	Facebook,	the	
+Third-Person	Effect,	and	the	Differential	Impact	Hypothesis*.	Journal	of	Computer-Mediated	
+Communication,	19,	3	(2014),	403-413.	https://doi.org/10.1111/jcc4.12061	
+[47]	 Steve	 Stecklow.	 2018.	 Why	 Facebook	 is	 losing	 the	 war	 on	 hate	 speech	 in	 Myanmar.	
+Thomson	
+Reuters,	
+City,	
+2018.	
+https://www.reuters.com/investigates/special-
+report/myanmar-facebook-hate/	
+[48]	John	L	Sullivan,	James	Piereson	and	George	E	Marcus	Political	tolerance	and	American	
+democracy.	University	of	Chicago	Press,	1993.	
+[49]	 Ye	 Sun,	 Zhongdang	 Pan	 and	 Lijiang	 Shen.	 2008.	 Understanding	 the	 Third-Person	
+Perception:	Evidence	From	a	Meta-Analysis.	Journal	of	Communication,	58,	2	(2008),	280-
+300.	https://doi.org/10.1111/j.1460-2466.2008.00385.x	
+[50]	Ran	Wei,	Stella	C.	Chia	and	Ven-Hwei	Lo.	2011.	Third-person	Effect	and	Hostile	Media	
+Perception	 Influences	 on	 Voter	 Attitudes	 toward	 Polls	 in	 the	 2008	 U.S.	 Presidential	
+Election.	 International	 Journal	 of	 Public	 Opinion	 Research,	 23,	 2	 (2011),	 169-190.	
+https://doi.org/10.1093/ijpor/edq044	
+[51]	Mark	Williams,	Michelle	Butler,	Anna	Jurek-Loughrey	and	Sakir	Sezer.	2021.	Offensive	
+communications:	exploring	the	challenges	involved	in	policing	social	media.	Contemporary	
+Social	
+Science,	
+16,	
+2	
+(2021/03/15	
+2021),	
+227-240.	
+https://doi.org/10.1080/21582041.2018.1563305	
+[52]	David	A	Yalof	and	Kenneth	Dautrich	The	First	Amendment	and	the	media	in	the	court	of	
+public	opinion.	Cambridge	University	Press,	2002.	
+[53]	Marc	Ziegele,	Teresa	K	Naab	and	Pablo	Jost.	2020.	Lonely	together?	Identifying	the	
+determinants	of	collective	corrective	action	against	uncivil	comments.	New	Media	&	Society,	
+22,	
+5	
+(2020),	
+731-751.	
+https://journals.sagepub.com/doi/abs/10.1177/1461444819870130	
+
diff --git a/HdE0T4oBgHgl3EQfRgBm/content/tmp_files/load_file.txt b/HdE0T4oBgHgl3EQfRgBm/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..dd89153a32644431a68ddf7670ebcc90e9ef97df
--- /dev/null
+++ b/HdE0T4oBgHgl3EQfRgBm/content/tmp_files/load_file.txt
@@ -0,0 +1,879 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf,len=878
+page_content='Do Users Want Platform Moderation or Individual Control?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  Examining the Role of Third-Person Effects and Free Speech  Support in Shaping Moderation Preferences  Shagun Jhaver, Amy Zhang  Online platforms employ commercial content moderators and use automated systems to identify and remove  the most blatantly inappropriate content for all users.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' They also provide moderation settings that let users  personalize their preferences for which posts they want to avoid seeing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' This study presents the results of a  nationally representative survey of 984 US adults.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' We examine how users would prefer for three categories of  norm-violating  content  (hate  speech,  sexually  explicit  content,  and  violent  content)  to  be  regulated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  Specifically, we analyze whether users prefer platforms to remove such content for all users or leave it up to  each user to decide if and how much they want to moderate it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' We explore the influence of presumed effects  on others (PME3) and support for freedom of expression on user attitudes, the two critical factors identified  as  relevant  for  social  media  censorship  attitudes  by  prior  literature,  about  this  choice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' We  find  perceived  negative effects on others and free speech support as significant predictors of preference for having personal  moderation  settings  over  platform-directed  moderation  for  regulating  each  speech  category.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Our  findings  show that platform governance initiatives need to account for both the actual and perceived media effects of  norm-violating speech categories to increase user satisfaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Our analysis also suggests that people do not  see personal moderation tools as an infringement on others’ free speech but as a means to assert greater  agency to shape their social media feeds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content="  And  then  there  were  what  I'll  call  the  technolibertarians." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' For  them,  MUD  rapists  were  of  course assholes, but the presence of assholes on the system was a technical inevitability, like  noise  on  a  phone  line,  and  best  dealt  with  not  through  repressive  social  disciplinary  mechanisms  but  through  the  timely  deployment  of  defensive  software  tools.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Some  asshole  blasting violent, graphic language at you?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=" Don't whine to the authorities about it – hit the  @gag  command  and  the  asshole's  statements  will  be  blocked  from  your  screen  (and  only  yours)." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=" It's simple, it's effective, and it censors no one." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' – Excerpt from “A Rape in Cyberspace”  by Julian Dibbell [7]  Introduction  With  the  emergence  of  social  media  sites  and  their  widespread  use  by  people  to  communicate  with  one  another,  companies  like  Facebook,  Twitter,  and  YouTube  have  become  the  new  governors  of  digital  expression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' At  the  same  time,  individuals  who  use  these sites can also actively shape governance in various ways.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' For example, they may flag  posts  that  violate  community  policy,  downvote  inappropriate  posts,  serve  as  volunteer  moderators,  engage  in  counter-speech,  or  configure  moderation  settings  to  automate  inappropriate  post  removals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' We  are  therefore  moving  towards  a  “pluralist  model  of  speech regulation [1],” in which speech must be regulated in a multi-stakeholder fashion –  legislative entities enforce online speech laws, and platform operators set up governance  regimes  of  acceptable  content.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' However,  users  themselves  can  also  intervene  against  content perceived as problematic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  This move to a pluralist model is occurring against recent controversies over platforms’  moderation decisions [32, 47] and growing media, policymakers, and public calls to better  regulate their content [51].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' In response, platforms have begun investing more resources  into  improving  how  inappropriate  posts  are  detected  and  removed  from  their  sites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' We  focus in this article on platforms’ offering of personal moderation tools that let end-users  configure content moderation of the posts they see to align with their content preferences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  We are primarily concerned with tools offered by platforms such as Instagram and Twitch  that let users specify their sensitivity to specific topical categories such as sexually explicit  content  and  hate  speech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Configuring  such  tools  lets  users  have  the  moderation  system  operate in alignment with their tastes and thresholds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' From the perspective of platforms, a  tactical consequence of offering personal moderation tools is that the obligation of making  hard moderation decisions, the concomitant responsibility of making mistakes with them,  and the cognitive labor of making the correct configurations are passed over to the users.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  Therefore, it is vital that we understand how users consider the choice between platform  versus personal moderation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  Our  research  responds  to  calls  by  governance  scholars  to  conduct  more  survey-based  research  to  understand  users’  perspectives  on  moderation  interventions  by  different  regulatory actors [8, 41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' So far, we have little knowledge of how end-users perceive being  given  self-regulating  authority  through  personal  moderation  tools.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' We  do  not  know  the  situations  in  which  users  prefer  to  have  a  choice  in  shaping  moderation  and  when  they  would instead prefer the platforms manage it for every user – and the different factors that  shape these preferences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  Informed by the third-person effects (TPE) hypothesis, we fill this gap by examining users’  preferences in the context of three norm-violating speech categories that have been studied  in prior literature: (1) Hate speech;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' (2) Sexually explicit content;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' and (3) Violent content.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  Previous research has shown that perceptions of the effects of media messages on others  predict censorship attitudes [42, 44].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' We examine the role that third-person effects [6] play  in  shaping  user  attitudes  about  deploying  platform-enacted  versus  personal  moderation  tools.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  We also connect our findings to the scholarship on understanding public attitudes toward  freedom  of  expression  and  its  consequences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Free  speech  is  a  core  constitutional  right  highly valued by many Americans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' However, the introduction of personal moderation tools  offers  affordances  that  complicate  the  question  of  preserving  free  speech  –  users  may  configure tools to avoid specific content categories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Still, others may continue to see the  same  content,  thereby  preventing  infringement  of  online  expressions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' However,  if  most  users  choose  to  deploy  these  tools,  specific  content  categories  would  have  significantly  reduced  visibility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Therefore,  we  analyze  how  users’  support  for  freedom  of  expression  shapes their notion of different moderation approaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  Understanding  the  public  views  on  the  platform  and  user-enacted  interventions  can  stimulate debates about the roles and strategies of various regulatory actors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' It can also  speak  to  calls  for  evidence-based  policymaking  [30,  40]  by  clarifying  how  the  public  understands  moderation  practices  and  identifying  the  gaps  between  policy  and  public  demands [36, 37, 41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Given the rapid introduction of new moderation strategies by the  platforms,  especially  personal  moderation  tools,  independent  academic  assessments  of  users’  attitudes  on  their  deployment  are  vital.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=" Platforms  can  also  benefit  from  such  research  by  understanding  end-users'  acceptance  or  rejection  of  various  regulatory  practices and the factors that shape those perspectives." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Further, examinations of the public  perception of free speech within the context of online activity may also shape attempts to  protect free speech in the long run.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  Literature Review and Hypotheses  The Perceptual Component of the TPE  Since Davison [6] first argued that individuals perceive media’s impact on the attitudes and  behaviors of others to be greater than it is on themselves, many studies have shown this  discrepancy to be consistent across a range of contexts [49] such as political ads [16, 38],  news  stories  [39]  and  social  media  use  [46].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' This  hypothesis,  termed  by  Davison  as  the  third-person  effect  (TPE)  [6],  has  become  a  widely  applied  perspective  to  explain  public  opinion  on  the  media  censorship  [19-21,  33].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' The  TPE  hypothesis  has  two  major  components – the perceptual and behavioral components [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' The perceptual component  predicts that presumed media effects on others (PME3) tend to be greater than perceived  media  effects  on  self  (PME1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' In  the  context  of  social  media  messages’  influence,  the  perceptual component of TPE predicts that participants will consider others to be more  negatively  influenced  by  each  category  of  norm-violating  speech  than  themselves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' We,  therefore, raise the following hypothesis:  H1: For each norm-violating speech category, participants will perceive a greater effect of  that speech on others than on themselves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  The Behavioral Component of the TPE  The behavioral component of the TPE argues that when individuals perceive the greater  impact of media messages on others than on themselves, they will take remedial actions to  mitigate  the  perceived  harmful  effects  [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Davison  [6]  described  the  phenomenon  of  censorship  as  one  of  the  most  interesting  behavioral  consequences  of  third-person  perception.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Prior research on TPE consequences shows that it leads to censorship support  [15, 19, 44], and the effects are particularly salient when persuasive attempts may include  socially  undesirable  effects  [28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' In  studying  TPE  effects  on  censorship  attitudes,  some  researchers  have  examined  the  consequences  of  the  other-self  perceptual  disparity  in  media effects (DME = PME3 – PME1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' In contrast, others have focused on the perceived  media impact on others (PME3) [42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Examining past research data on TPE consequences,  Chung  and  Moon  [5]  concluded  that  the  media’s  presumed  effect  on  others  (PME3)  is  a  stronger  predictor  of  censorship  attitudes  than  the  other-self  disparity  in  the  perceived  media effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' We, therefore, choose PME3 as our primary predictor variable and raise the  following hypothesis:  H2:  For  each  speech  category,  the  perceived  effects  of  that  speech  on  others  will  be  positively related to support for the platform’s banning of that category.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  Researchers of TPE have long been curious about the potential behaviors that could result  from  the  perceived  media  impact  on  others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' In  addition  to  censorship  support,  prior  studies have interrogated behavioral outcomes such as engaging in political action  [10, 43,  50], disseminating opposing information [3, 17], and exposing apparent biases [2, 29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' In  the context of online content moderation, Jang and Kim found that people with a greater  level of third-person perception were more likely to support media literacy interventions  to  address  fake  news  [22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' We  add  to  previous  efforts  to  surface  the  different  types  of  behavioral  consequences  of  TPE  by  examining  its  impact  on  users’  support  for  having  personal  moderation  settings  to  moderate  norm-violating  content.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Since  such  configurations are also a form of regulation, prior TPE research suggests that PME3 would  predict support for them [19, 42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' The following hypothesis thus can be raised:  H3:  For  each  speech  category,  the  perceived  effects  of  that  speech  on  others  will  be  positively related to support for having personal moderation tools to regulate the speech of  that category.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  Platform-enacted  moderation  and  personal  configurations  to  self-moderate  content  are  different  ways  to  regulate  norm-violating  speech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' However,  while  platform-enacted  moderation  censors  content  platform-wide,  personal  moderation  tools  allow  users  to  adjust  whether  and  how  much  norm-violating  speech  they  are  willing  to  encounter  personally.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Prior  literature  generally  predicts  that  TPE  would  lead  to  support  for  censorship attitudes [5, 19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' However, it does not guide how people will react to a choice  between letting platforms handle a specific content category and allowing users to specify  their moderation preferences for that category.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' We, therefore, ask the following research  question:  RQ1: For each speech category, how do its perceived effects on others relate to support for  the  platform’s  banning  of  that  category  versus  support  for  having  personal  moderation  tools regulate it?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  Support for Freedom of Speech  Discussions about the benefits of moderation measures are always intertwined with the  issue of freedom of speech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' In the United States, the constitution protects the right to free  expression as a fundamental human right.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' However, platforms are private parties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Section  230 of the Communications Decency Act of 1996 provides them the legislative freedom to  police their users as they see fit while not being held accountable for errors or oversights  [13, 34].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Additionally, experts have shown that despite Americans’ support for freedom of  expression  generally,  their  tolerance  for  hate  speech  is  low    [12,  48,  52].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Thus,  people’s  acceptance of free speech in the abstract may not automatically imply their tolerance for  opposing expressions [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=" Examining how much people's support for free speech affects  their  opinions  about  varied  moderation  strategies  may  help  us  better  understand  this  discrepancy in the context of social media platforms." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  Support  for  free  speech  and  attitudes  toward  content  moderation  have  been  linked  in  previous studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' For instance, Naab et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' showed that people who commit to freedom of  expression are less likely to support restrictive actions by Facebook moderators [36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Guo  and  Johnson  showed  that  a  lack  of  support  for  freedom  of  speech  predicts  support  for  government  regulation  of  sexist  hate  speech  [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' However,  they  did  not  find  that  the  former  could  predict  supportive  attitudes  toward  platform  censorship.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Jang  and  Kim  suggested  that  support  for  free  expression  decreases  support  for  regulating  fake  news  despite the existence of third-person effects [22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Overall, this body of research indicates  that  participants’  support  for  platform  regulation  will  decline  as  free  speech  support  increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' We, therefore, raise the following hypotheses:  H4:  For  each  speech  category,  participants’  support  for  freedom  of  expression  will  be  negatively related to their support for the platform’s banning of that category.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  While prior research provides guidance on the expected relationship between free speech  support  and  support  for  platform-enacted  moderation,  the  literature  on  personal  moderation  tools  is  scarce.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' It  does  not  offer  any  direct  guidance  on  the  relationship  between  support  for  free  speech  and  support  for  having  personal  moderation  tools.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  However, there is some prior work that speaks to related issues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' For example, Naab et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  did not find a relationship between users’ commitment to free speech and their intention to  engage  in  corrective  actions  such  as  rebuking  the  comment  author  or  reporting  the  comment  [36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' It  is  unclear  whether  that  finding  would  apply  to  our  context  since  deploying  personal  moderation  tools  is  a  restrictive  action,  not  a  corrective  action.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Its  expected  costs  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=',  setting  up  once  for  personal  moderation  v/s  reporting  every  inappropriate post;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' experiencing retaliation when engaging in counter-speech v/s private  post removals for personal moderation) are also lower.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Riedl et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' conducted a survey that  showed  that  individuals’  support  for  free  speech  does  not  increase  their  assumed  self-  responsibility  to  intervene  against  problematic  comments  [41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' However,  they  did  not  specify to the survey takers what type of responsibility they should carry out.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Besides, in  our study context, users may not consider personal moderation tools an obligation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  On  the  one  hand,  support  for  free  speech  values  should  reduce  support  for  restrictive  actions of any kind.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' But on the other hand, people may perceive personal moderation tools  as simply having a greater agency to shape what they see and not an infringement on the  free speech of others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' In this way, personal moderation tools allow a distinction between  freedom  of  speech  and  the  obligation  to  be  heard.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' To  clarify  the  direction  of  this  relationship, we ask the following research question:  RQ2:  Does  participants’  support  for  freedom  of  expression  relate  to  their  support  for  having personal moderation tools?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  When faced with a choice between letting platforms handle a certain content category and  allowing users to specify their moderation preferences, we expect the latter to be perceived  as  more  free  speech  preserving.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' It  lets  users  decide  whether  and  how  many  content  removals  should  occur  instead  of  allowing  platforms  to  handle  those  same  decisions  unilaterally.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' We, therefore, raise the following hypothesis:  H5:  For  each  speech  category,  participants’  support  for  freedom  of  expression  will  be  related to greater support for having personal moderation tools to moderate that category  than their support for the platform’s banning of that category.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  Methods  Our study was considered exempt from review by the University of Washington IRB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' We  recruited participants through Lucid,1 a survey company that provides researchers access  to  nationally  representative  samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Our  inclusion  criterion  for  the  survey  participants  was all adult internet users in the US.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' We paid participants through the Lucid system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  We designed our survey questions to test the hypotheses identified in the previous section  and adapted survey instruments from relevant prior literature to test some measures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' We  describe these measures in more detail below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' To increase the validity of the survey, we  sought feedback on an early draft of the survey questionnaire from other students at the  authors’ institutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Nine students who were not involved with the project responded to  our request and provided feedback on the wording of the questions and survey flow, which  we incorporated into the final survey design.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' We also piloted the survey with a small subset  of  the  sample  (27  participants).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' During  this  field  test,  we  included  this  open-ended  question at three different points in the survey: “Do you have any feedback on any of the  questions  so  far?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' For  example,  is  any  question  unclear  or  ambiguous?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Please  list  the  question and describe your challenge with answering it.” At the end of the survey, we also  asked, “Overall, how can we improve this survey from the perspective of survey takers?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Do  you have any other thoughts or feedback for us?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Please describe.” Results from this survey  pretest resulted in another round of iteration before our questionnaire reached the desired  quality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  Our survey questionnaire consisted of three blocks containing similar questions about hate  speech, sexually explicit content, and violent posts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' To counter the effects of the order of  presentation  on  survey  results,  we  counterbalanced  the  order  in  which  question  blocks  related to the three content categories were shown to the participants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' At the beginning of  each block, we specified the norm-violating category that the following questions related to  and defined that category.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' We used the following definitions:  Hate speech: “Hate speech includes speech that is dehumanizing, stereotyping, or  insulting,  on  the  basis  of  identity  markers  such  as  race/ethnicity,  gender,  sexual  orientation, religion, etc.”  Violent  content:  “Violent  content  includes  threats  to  commit  violence,  glorifying  violence or celebrating suffering, depictions of violence that are gratuitous or gory,  and animal abuse.”  1 https://lucidtheorem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='com  Sexually explicit content: “Sexually explicit content includes content showing sexual  activity, offering or requesting sexual activity, female nipples (except breastfeeding,  health, and acts of protest), nudity showing genitals, and sexually explicit language.”  The above definitions were inspired by the language provided by the Facebook site when  reporting any post under the category of hate speech, violence, and nudity, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  We  administered  the  survey  online  using  the  survey  software  package  Qualtrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' We  launched the survey on November 29, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Table 1 presents the demographic details of  our final sample after data cleaning and compares it with the demographics of the adult US  internet population [45].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  Table 1: Demographic Profile of the US Survey  Authors’ study, US survey  Nov 2022 (%)  American Community Survey,  US sample 2021 (%)  Age:  18-29  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='7  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='4  30-49  40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='1  29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='5  50-64  23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='7  25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='6  65+  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='4  27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='3  Gender:  Male  48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='2  48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='6  Female  51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='8  51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='4  Race/Ethnicity:  White  73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='5  68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='3  Black  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='2  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='3  Other  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='3  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='4  Hispanic:  Yes  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='5  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='7  Education:  High school or less  31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='4  33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='5  Some college  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='4  33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='3  College+  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='3  33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='1  Measures  Perceived Influence on Self and Others  For  each  norm-violating  speech  category,  we  asked  the  participants  to  estimate  the  influence  of  that  category  on  the  self  and  others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' In  each  case,  we  asked two  questions:  “Seeing <speech category> posts on social media has a powerful influence on my attitudes.”  and  “Seeing  <speech  category>  posts  on  social  media  has  a  powerful  influence  on  my  behaviors.” The response categories ranged on a 7-point Likert-type scale from 1 (strongly  disagree) to 7 (strongly agree).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' These two items were averaged to create a measure of the  perceived  influence  of  each  speech  category  on  the  self  (Hate  speech:  M=3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='89,  SD=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='91,  a=.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='84;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Violent speech: M=3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='78, SD=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='87, a=.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='81;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Sexually explicit speech: M=3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='55, SD=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='89,  a=.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='87).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' We  asked  another  two  questions  replacing  only  the  word  “my”  with  “other  people’s” and averaged the responses to create an index of the perceived influence of each  speech category on others (Hate speech: M=5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='28, SD=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='46, a=.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='92;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Violent speech: M=5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='19,  SD=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='40, a=.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='91;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Sexually explicit speech: M=4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='99, SD=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='46, a=.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='93).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  Support for Freedom of Speech  We used items developed by Guo and Johnson to measure support for freedom of speech  [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Participants  rated  these  four  statements  on  a  Likert-type  scale  ranging  from  1  (strongly disagree) to 7 (strongly agree): (1) In general, I support the First Amendment, (2)  Freedom of expression is essential to democracy, (3) Democracy works best when citizens  communicate  in  an  unregulated  marketplace  of  ideas,  and  (4)  Even  extreme  viewpoints  deserve to be voiced in society.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' We included the First Amendment statement2 in the first  question  to  clarify  its  meaning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' We  formed  an  index  for  free  speech  support  using  the  means of these four items (M=5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='43, SD=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='15, a=.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='80).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  Dependent Variables Related to Moderation  Support for platform-enacted moderation of each speech category was operationalized by  asking  participants  to  rate  the  following  statement:  “I  support  social  media  platforms  taking  down  any  posts  they  consider  to  be  <speech  category>  so  that  no  users  can  see  them.”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  The  responses  for  this  statement  ranged  on  a  7-point  Likert-type  scale,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  where  1=“strongly disagree” and 7=“strongly agree.”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  For  operationalizing  support  for  having  personal  moderation  tools  for  each  category,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  we  showed participants an example of a personal moderation feature where every user can  decide the extent to which they want the <speech category> content filtered out (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' We asked participants to rate their support for providing this kind of setting to all users  on a Likert-type scale ranging from 1 (strongly disagree) to 7 (strongly agree).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  2 The First Amendment to the United States Constitution states: "Congress shall make no  law  respecting  an  establishment  of  religion,  or  prohibiting  the  free  exercise  thereof;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  or  abridging the freedom of speech, or of the press;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' or the right of the people peaceably to  assemble,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' and to petition the Government for a redress of grievances.”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  Figure 1: Survey question asking participants to rate their support for platforms providing  personal moderation feature  In  addition  to  these  two  measures,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  we  also  operationalized  choosing  platform-enacted  moderation  v/s  personal  moderation  for  each  speech  category  by  asking  respondents  a  binary question: ‘Given a choice between platform-wide moderation and a "Choose your  moderation settings" feature to handle <speech category> posts,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' which would you prefer to  have?’' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' The response categories included: (1) Platform-wide moderation: Platforms should  have the power to remove all posts they identify as <speech category> across the platform  or (2) "Choose your moderation settings" feature: Each user should be allowed to configure  the extent to which <speech category> posts should be removed for them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' We note that the  “Choose  you  moderation  settings”  feature  enables  a  range  of  choices  –  from  “no  moderation” to “a range of moderation.” Thus, users who desired neither platform-wide  nor  personal  moderation  to  remove  any  posts  for  them  could  select  this  feature  and  configure it at the “no moderation” level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  The below example shows a feature where every user can decide for themselves  the extentto whichtheywantsexuallyexplicit contentfiltered out.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  Chooseyourmoderationsettings:  Filteroutsexuallyexplicitpostsbasedonthelevelyouselect:  Alittle  Some  More  Alotof  No moderation  moderation  moderation  moderation  moderation  Onlythemostsexuallyexplicitpostswillberemovedatthislevel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  I support platforms providing this kind of setting to all users  O Strongly disagree  O Disagree  OSomewhatdisagree  ONeitheragree nordisagree  O Somewhatagree  O Agree  O Strongly agree  Figure 2: Frequency of participants’ responses to survey questions about support for platform-  wide and personal moderation, measured in percentage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  Control Variables  Prior  research  has  shown  that  socio-demographic  variables  are  related  to  TPE  and  free  speech and attitude towards media regulation [19, 26, 27, 31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Further, social media use  has  also  been  associated  with  individuals’  perceptions  of  harmful  content  and  their  interventions  against  such  [24,  25,  35,  53].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Therefore,  we  controlled  for  age,  education,  gender,  race,  political  affiliation  (1  =  “very  liberal”,  7=  “very  conservative”),  and  social  media use of each respondent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' We operationalized the frequency of social media use by  following recommendations by Ernala et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' [9] and prompting participants to respond to  the question, ‘In the past week, on average, approximately how much time PER DAY have  you spent actively using any social media?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  Results  Our results show that 72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='8%, 73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='1%, and 66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='2% of participants at least somewhat agreed  that  platforms  should  ban  hate  speech,  violent  content,  and  sexually  explicit  content,  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Further, 69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='9%, 72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='6%, and 72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='1% of participants at least somewhat agreed  that  platforms  should  offer  personal  moderation  tools  to  let  end-users  regulate  hate  speech, violent content, and sexually explicit content, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  Statistics  Strongly disagree  Disagree  Somewhatdisagree  Personal ModerationofSexuallyExplicitContent  I Neither agree nor disagree  Somewhatagree  lAgree  IStronglyagree  PlatformBanofSexualyExplicitContent  Personal ModerationofViolentContent  PlatformBanofViolentContent  PersonalModerationofHateSpeech  PlatformBanofHateSpeech  0  20  40  60  80  100  Percentage of ParticipantsIn line with research on the third-person effects,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' H1 predicted that for each norm-violating  content category,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' participants would perceive the effects of that category on others to be  stronger  than  on  themselves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' We  ran  a  paired  t-test  and  found  the  perceived  effects  on  others  significantly  stronger  than  on  oneself  for  each  category  (see  Table  2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Thus,  our  results support H1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  Table 2: Mean, standard deviations, standard errors of participants’ perceived effects of hate  speech,  violent  content,  and  sexually  explicit  content  on  others  and  self,  and  t-test  results  comparing perceived effects on others and self for each speech category (N = 993).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' *** denotes  p < .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='001  M  SD  SE  t  Cohen’s d  Hate speech  Effects on others  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='28  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='46  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='05  25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='37***  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='805  Effects on self  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='89  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='91  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='06  Violent  content  Effects on others  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='19  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='40  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='05  25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='44***  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='807  Effects on self  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='77  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='87  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='06  Sexually  explicit  content  Effects on others  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='99  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='46  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='05  25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='81***  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='819  Effects on self  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='55  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='88  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='06  Support for Platform Ban  We computed hierarchical linear regression to test our hypotheses 2 and 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' For each of the  three norm-violating categories, we created a model where the participant’s support for  banning that category served as the dependent variable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' In Step 1 of the three regression  models, we included the control variables age, gender, education, race, political affiliation,  and social media use.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' In Step 2, we introduced the independent variables PME3 (perceived  effects on others) for that category and support for free speech (Table 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content="  Table 3: Hierarchical multiple regression analyses predicting support for platforms' banning  of hate speech, violent content, and sexually explicit content (N = 983)  Independent Variable  Support  for  platform ban of  hate speech (β)  Support  for  platform  ban  of  violent  content  (β)  Support  for  platform  ban  of  sexually  explicit  content (β)  Step 1  Age  ." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='119***  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='055  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='102**  Gender (Female)  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='127***  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='167***  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='153***  Race (White)  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='018  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='013  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='059  Educationa  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='008  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='039  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='022  Political affiliationb  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='156***  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='09**  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='019  Social media usec  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='022  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='013  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='019  R2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='093***  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='065***  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='05***  Step 2  Support for free speech  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='101***  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='039  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='006  Perceived effects of hate speech on others  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='476*** Perceived effects of violent content on others .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='397*** Perceived  effects  of  sexually  explicit  content  on others .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='391***  R2 change  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='215  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='15***  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='149***  Total R2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='307***  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='215***  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='199***  **p < .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='01, ***p < .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='001 (t test for β, two-tailed;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' F test for R2, two-tailed).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  a0= Less than secondary education;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' 1= Secondary education or more.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  b1= Strong Democrat, 7= Strong Republican.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  c1= Less than 10 minutes per day, 6= More than 3 hours per day.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  β = standardized beta from the full model (final beta controlling for all variables in the model).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content="  For  each  norm-violating  speech  category,  the  regression  models  show  significant  influences of the participants' perceived effects of that category on others (PME3) on their  support for platform ban of that category (Model 1: hate speech – β = ." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='476, p < .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='001;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Model  2: violent content – β = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='397, p < .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='001;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Model 3: sexually explicit content – β = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='391, p <  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='001), supporting H2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  Greater support for free speech significantly negatively influences support for platform ban  of hate speech (β = -.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='101, p < .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' It does not, however, influence support for platform ban  of violent content (β = -.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='039, p > .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='05) or sexually explicit content (β = -.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='006, p > .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='05).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Thus,  H4 is only partially supported.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  Support for Personal Moderation  We computed hierarchical linear regression to test our hypothesis 3 and answer RQ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' For  each of the three norm-violating categories, we created a model where the participant’s  support  for  having  personal  moderation  tools  to  regulate  that  category  served  as  the  dependent  variable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' In  Step  1  of  the  three  regression  models,  we  included  the  control  variables age, gender, education, race, political affiliation, and social media use.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' In Step 2,  we  introduced  the  independent  variables  PME3  (perceived  effects  on  others)  for  that  category and support for free speech (Table 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  Table  4:  Hierarchical  multiple  regression  analyses  predicting  support  for  using  personal  moderation tools (PMT) to regulate hate speech, violent content, and sexually explicit content  (N = 983)  Independent Variable  Support  for  PMT  to  regulate  hate  speech (β)  Support for PMT  to  regulate  violent  content  (β)  Support for PMT  to  regulate  sexually  explicit  content (β)  Step 1  Age  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='014  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='017  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='010  Gender (Female)  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='016  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='019  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='016  Race (White)  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='019  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='007  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='08*  Educationa  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='018  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='022  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='003  Political affiliationb  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='019  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='049  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='074*  Social media usec  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='051  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='057  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='086**  R2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='009  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='013  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='027***  Step 2  Support for free speech  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='173***  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='195***  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='224***  Perceived effects of hate speech on others  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='224*** Perceived effects of violent content on others .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='187*** Perceived  effects  of  sexually  explicit  content  on others .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='225***  R2 change  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='087  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='081  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='111  Total R2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='096***  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='095***  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='138***  p < .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='05, **p < .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='01, ***p < .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='001 (t test for β, two-tailed;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' F test for R2, two-tailed).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  a0= Less than secondary education;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' 1= Secondary education or more.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  b1= Strong Democrat, 7= Strong Republican.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  c1= Less than 10 minutes per day, 6= More than 3 hours per day.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  β = standardized beta from the full model (final beta controlling for all variables in the model).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content="  For  each  norm-violating  speech  category,  the  regression  models  show  significant  influences of the participants' perceived effects of that category on others (PME3) on their  support  for  using  personal  moderation  tools  to  regulate  that  category  (Model  4:  hate  speech – β = ." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='224, p < .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='001;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Model 5: violent content – β = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='187, p < .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='001;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Model 6: sexually  explicit content – β = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='225, p < .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='001), supporting H4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  Greater support for free speech has a significant positive influence on participants’ support  for  using  personal  moderation  tools  to  regulate  each  norm-violating  category  (Model  4:  hate speech – β = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='173, p < .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='001;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Model 5: violent content – β = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='195, p < .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='001;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Model 6:  sexually explicit content – β = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='224, p < .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' This answers our RQ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  Choosing Between Platform-wide Moderation and Personal  Moderation  Figure 3: Percentage of participants preferring platform-wide ban or personal moderation to  regulate hate speech, violent content, and sexually explicit content  Given  a  choice  between  platform-wide  moderation  and  a  personal  moderation  tool  to  regulate hate speech, violent content, and sexually explicit content, 52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='4%, 52%, and 55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='3%  of participants, respectively, chose the personal moderation tool.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' This finding suggests that  more participants prefer autonomy over moderation than delegating it to platforms as they  see fit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  We created binomial logistic regression models to test our hypothesis 5 and answer RQ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  For each of the three norm-violating categories, we created a model where the participants’  binary choice between platform-wide moderation and personal moderation to handle that  category served as the dependent variable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' In Step 1 of the three regression models, we  included the control variables age, gender, education, race, political affiliation, and social  media use.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' In Step 2, we introduced the independent variables PME3 (perceived effects on  others) for that category and support for free speech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' For each model, we used the Box-  Tidwell procedure [4, 11] to check the assumption of linearity in the logit and found in each  case that our continuous variable support for free speech was not linearly related to the  logit  of  the  dependent  variable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' To  address  this,  we  split  this  variable  into  two  ordinal  categories  –  high  and  low,  recoding  each  entry  for  this  variable  based  on  whether  it  exceeded the median value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Rerunning the Box-Tidwell procedure with this transformed  support  for  the  free  speech  categorical  variable,  we  found  all  remaining  continuous  Statistics  Prefer platform-wide ban  Preferpersonalmoderation  Sexually explicit content  Violent content  Hate speech  0  10  20  30  40  50  60  Percentage of Participantsindependent variables in each model to be linearly related to the logit of the dependent  variable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=" We next present these models' binomial logistic regression results (Table 5)." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  Table  5:  Binomial  logistic  regression  analyses  predicting  support  for  using  personal  moderation tools (PMT) over platform-wide ban to regulate hate speech,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' violent content,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' and  sexually explicit content (N = 984)  Independent Variable  Support  for  PMT  over  platform ban to  regulate  hate  speech,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  Odds  Ratio  Support for PMT  over  platform  ban  to  regulate  violent  content,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  Odds Ratio  Support for PMT  over  platform  ban  to  regulate  violent  content,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  Odds Ratio  Step 1  Age  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='986**  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='992  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='994  Gender (Female)  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='790  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='655**  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='674**  Race (White)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='107  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='313  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='203  Educationa  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='934  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='870  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='981  Political affiliationb  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='163***  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='118***  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='074*  Social media usec  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='990  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='071  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='091*  Nagelkerke R2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='066***  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='066***  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='045***  Step 2  Support for free speechd  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='703***  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='239****  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='969***  Perceived effects of hate speech on others  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='735*** Perceived effects of violent content on others .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='752*** Perceived  effects  of  sexually  explicit  content  on others .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='857**  Total Nagelkerke R2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='165***  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='138***  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='087***  p < .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='05, **p < .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='01, ***p < .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='001 (t test for β, two-tailed;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Omnibus Tests of Model Coefficients for R2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  a0= Less than secondary education;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' 1= Secondary education or more.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  b1= Strong Democrat, 7= Strong Republican.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  c1= Less than 10 minutes per day, 6= More than 3 hours per day.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  d0= low, 1=high.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  odds ratio = exp(β) from full model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content="  For  each  norm-violating  speech  category,  the  regression  models  show  significant  influences of the participants' perceived effects of that category on others (PME3) on their  choice  of  using  personal  moderation  tools  over  platform-enacted  bans  to  regulate  that  category." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Increasing PME3 was associated with a decreased likelihood of choosing personal  moderation tools over platform bans (Model 7: hate speech – exp(β) = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='735, p < .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='001;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Model  8: violent content – exp(β) = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='752, p < .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='001;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Model 9: sexually explicit content – exp(β) =  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='857, p < .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='01).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' This answers our RQ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  Higher support for free speech has a significant positive influence on participants’ support  for  using  personal  moderation  tools  over  platform-enacted  bans  to  regulate  each  norm-  violating  category.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Participants  who  showed  high  support  for  free  speech  have  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='703,  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='239, and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='969 times higher odds of choosing personal moderation tools over platform-  enacted  bans  to  regulate  hate  speech,  violent  content,  and  sexually  explicit  content,  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Thus, H5 is supported.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  Discussion  In recent years, the debates surrounding the censorship of inappropriate content on social  media have surfaced more and more due to the increasing essentiality of social media in  political discourse and growing controversies over how platforms regulate [13, 14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' The  purpose of this study was to measure public attitudes regarding two important forms of  social media regulation: platform-wide moderation, which lets platforms unilaterally make  moderation decisions for every user, and personal moderation, which empowers users to  decide  for  themselves  how  they  would  like  to  regulate  different  content  categories  by  adjusting  their  moderation  settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Third-person  effects  (TPE)  are  commonly  used  in  examining  people’s  attitudes  towards  censorship  and  related  behaviors  or  behavioral  intentions [6, 18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' The present research extends the TPE research to managing hate speech,  violent content, and sexually explicit content on social media.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  We  explored  the  presumed  negative  effects  of  each  type  of  content  on  self  (PME1)  and  others (PME3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' The results produced strong support for the TPE hypothesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' As expected,  participants perceived the social media hate speech, violent content, and sexually explicit  content to have a greater influence on others than on themselves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' We also examined how  PME3 and support for free speech affected participants’ consequent censorial behavior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' In  each  case,  we  found  that  the  perceived  effects  on  others  (PME3)  predicted  participants’  support  for  both  platform-wide  moderation  and  personal  moderation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' This  is  a  theoretically  significant  finding  of  this  study  since  it  helps  advance  TPE  research  by  showing  that  perceived  effects  on  others  play  an  essential  role  in  triggering  censorial  behavior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Given a choice between the platform and personal moderation, PME3 predicted  support  for  platform  moderation  in  each  case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' This  finding  indicates  that  when  users  perceive the adverse effects of a content category on the public, they desire platforms to  take site-wide actions on that content rather than regulate it for themselves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  Further, the relationship between support for free speech and support for platform-wide  moderation received only partial support.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' While the connection is significant and negative  for hate speech, it is not significant for violent and sexually explicit content.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' This result is in  line with the mixed findings for free speech support as a predictor of supportive attitudes  towards platform censorship observed in prior literature [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' On the other hand, we found  that  support  for  free  speech  predicted  support  for  the  use  of  personal  moderation  for  regulating  each  inappropriate  speech  category.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' This  suggests  that  people  may  perceive  personal moderation tools as not an infringement on the free speech of others but simply  having a greater agency to shape what they see.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' This is further bolstered by our finding that  given  a  choice  between  the  platform  and  personal  moderation,  support  for  free  speech  predicts support for personal moderation in each case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  Other significant effects, less central to the hypotheses being tested, also were found.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' We  found that age was positively related to support for platform moderation of hate speech  and  sexually  explicit  content,  but  not  violent  content.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Females  supported  platform  moderation of each speech category more than males.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Democrats were more likely than  Republicans to support platform moderation of hate speech and violent content, but not  sexually  explicit  content.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Regarding  support  for  personal  moderation,  race,  political  affiliation, and social media use were significant predictors for the sexually explicit content  category;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' however, no control variables significantly predicted personal moderation of hate  speech or violent content.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  The evidence presented here has important implications for how platforms govern their  sites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' We show that part of the reason the public supports moderation of norm-violating  categories such as pornography and war violence is that it overestimates these categories’  effects  on  others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Therefore,  company-wide  moderation  decisions  and  public  debates  concerning  free  speech  and  its  limitations,  must  recognize  and  account  for  third-person  effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' It also points to an urgent need to measure the actual media effects as opposed to  the perceived media effects of different content types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' We have noticed that even during  our  interview  studies  on  online  harms,  participants  tend  to  advocate  for  specific  moderation initiatives based on their perceptions of what others might need.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' To arrive at  an  accurate  needs-gathering,  scholars  must  focus  on  understanding  the  perspectives  of  online content on users themselves – a topic on which they are an expert – rather than the  abstract others whose actual needs may considerably differ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  Several  limitations  of  this  study  should  be  recognized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' The  survey  design  prohibited  us  from exploring the motivations for specific perceptions in depth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Furthermore, we cannot  make  conclusive  statements  about  causal  relations  as  a  cross-sectional  study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' We  asked  participants  to  respond  to  questions  about  speech  categories  that  could  be  broadly  interpreted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' We chose this instead of presenting a specific instance of each speech category  to  increase  the  generalizability  of  our  findings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Still,  different  users  may  have  different  perceptions  of  what  counts  as  hate  speech,  violent  content,  or  sexually  explicit  content.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  Prior moderation research has recognized this as a complex challenge in the social media  regulation [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' We provided definitions of each speech category in the survey to clarify the  scope  of  each  category  to  our  participants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Nevertheless,  further  research  on  user  perceptions  of  stimulus-based  designs  that  present  preselected  instances  of  each  norm-  violating  speech  category  to  participants  would  provide  valuable  insights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' We  did  not  ground our survey questions in a specific platform to increase the generalizability of our  results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Studies  focused  on  particular  social  media  sites  can  uncover  whether  attitudes  towards specific platforms influence users’ perceptions of moderation actions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  References  [1]  Jack  M  Balkin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Free  speech  in  the  algorithmic  society:  Big  data,  private  governance, and new school speech regulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' UCDL Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=', 51 (2017), 1149.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  [2]  Matthew  Barnidge  and  Hernando  Rojas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Hostile  Media  Perceptions,  Presumed  Media  Influence,  and  Political  Talk:  Expanding  the  Corrective  Action  Hypothesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  International  Journal  of  Public  Opinion  Research,  26,  2  (2014),  135-156.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='1093/ijpor/edt032  [3]  Uli  Bernhard  and  Marco  Dohle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Corrective  or  Confirmative  Actions?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Political  Online  Participation  as  a  Consequence  of  Presumed  Media  Influences  in  Election  Campaigns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Journal of Information Technology & Politics, 12, 3 (2015/07/03 2015), 285-  302.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='1080/19331681.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='1048918  [4] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Box and Paul W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Tidwell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' 1962.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Transformation of the Independent Variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  Technometrics,  4,  4  (1962/11/01  1962),  531-550.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='tandfonline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='com/doi/abs/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='1080/00401706.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='1962.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='10490038  [5]  Sungeun  Chung  and  Shin-Il  Moon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Is  the  Third-Person  Effect  Real?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' a  Critical  Examination  of  Rationales,  Testing  Methods,  and  Previous  Findings  of  the  Third-Person  Effect  on  Censorship  Attitudes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Human  Communication  Research,  42,  2  (2016),  312-337.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='1111/hcre.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='12078  [6] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Phillips Davison.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' 1983.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' The Third-Person Effect in Communication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Public Opinion  Quarterly, 47, 1 (1983), 1-15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='1086/268763  [7]  Julian  Dibbell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' 1994.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' A  rape  in  cyberspace  or  how  an  evil  clown,  a  Haitian  trickster  spirit, two wizards, and a cast of dozens turned a database into a society.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Ann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Surv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Am.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  (1994), 471-471.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  [8] Sabine A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Einwiller and Sora Kim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' How Online Content Providers Moderate User-  Generated Content to Prevent Harmful Online Communication: An Analysis of Policies and  Their  Implementation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  Policy  &  Internet,  12,  2  (2020),  184-206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  https://onlinelibrary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='wiley.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='com/doi/abs/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='1002/poi3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='239  [9]  Sindhu  Kiranmai  Ernala,  Moira  Burke,  Alex  Leavitt  and  Nicole  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  Ellison.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' How  Well  Do  People  Report  Time  Spent  on  Facebook?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' An  Evaluation  of  Established  Survey  Questions  with  Recommendations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' In  Proceedings  of  the  Proceedings  of  the  2020  CHI  Conference on Human Factors in Computing Systems (Honolulu, HI, USA, 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Association  for Computing Machinery.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='1145/3313831.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='3376435  [10] Lauren Feldman, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Sol Hart, Anthony Leiserowitz, Edward Maibach and Connie Roser-  Renouf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Do  Hostile  Media  Perceptions  Lead  to  Action?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' The  Role  of  Hostile  Media  Perceptions,  Political  Efficacy,  and  Ideology  in  Predicting  Climate  Change  Activism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  Communication  Research,  44,  8  (2017),  1099-1124.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  https://journals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='sagepub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='com/doi/abs/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='1177/0093650214565914  [11] John Fox Applied regression analysis and generalized linear models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Sage Publications,  2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  [12]  James  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  Gibson  and  Richard  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  Bingham.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' 1982.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' On  the  Conceptualization  and  Measurement of Political Tolerance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' American Political Science Review, 76, 3 (1982), 603-  620.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='cambridge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='org/core/article/on-the-conceptualization-and-  measurement-of-political-tolerance/579D03FF1A6041C6DB3DD6CB1FBC98E1  [13]  Tarleton  Gillespie.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Governance  of  and  by  platforms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Sage  handbook  of  social  media (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  [14] Tarleton Gillespie Custodians of the Internet: Platforms, content moderation, and the  hidden decisions that shape social media.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Yale University Press, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  [15] Guy J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Golan and Stephen A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Banning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Exploring a Link Between the Third-Person  Effect and the Theory of Reasoned Action:Beneficial Ads and Social Expectations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' American  Behavioral  Scientist,  52,  2  (2008),  208-224.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  https://journals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='sagepub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='com/doi/abs/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='1177/0002764208321352  [16] Guy J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Golan, Stephen A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Banning and Lisa Lundy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Likelihood to Vote, Candidate  Choice, and the Third-Person Effect:Behavioral Implications of Political Advertising in the  2004  Presidential  Election.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' American  Behavioral  Scientist,  52,  2  (2008),  278-290.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  https://journals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='sagepub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='com/doi/abs/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='1177/0002764208321356  [17] Guy J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=" Golan and Joon Soo Lim Third-Person Effect of ISIS's Recruitment Propaganda:  Online Political Self-Efficacy and Social Media Activism, 2016." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  [18] ALBERT GUNTHER.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' 1991.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' What We Think Others Think:Cause and Consequence in the  Third-Person  Effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  Communication  Research,  18,  3  (1991),  355-372.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  https://journals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='sagepub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='com/doi/abs/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='1177/009365091018003004  [19] Albert C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Gunther.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Overrating the X-Rating: The Third-Person Perception and  Support  for  Censorship  of  Pornography.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Journal  of  Communication,  45,  1  (2006),  27-38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='1111/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='1460-2466.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='1995.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='tb00712.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='x  [20] Lei Guo and Brett G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Johnson.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Third-Person Effect and Hate Speech Censorship  on  Facebook.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  Social  Media  +  Society,  6,  2  (2020),  2056305120923003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  https://journals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='sagepub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='com/doi/abs/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='1177/2056305120923003  [21] CYNTHIA HOFFNER, MARTHA BUCHANAN, JOEL DAVID ANDERSON, LISA A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' HUBBS,  STACY K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' KAMIGAKI, LAURA KOWALCZYK, ANGELA PASTOREK, RICHARD S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' PLOTKIN and  KELSEY J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' SILBERG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' 1999.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Support for Censorship of Television Violence:The Role of the  Third-Person Effect and News Exposure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Communication Research, 26, 6 (1999), 726-742.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  https://journals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='sagepub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='com/doi/abs/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='1177/009365099026006004  [22]  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  Mo  Jang  and  Joon  K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  Kim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Third  person  effects  of  fake  news:  Fake  news  regulation  and  media  literacy  interventions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Computers  in  Human  Behavior,  80  (2018/03/01/  2018),  295-302.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='sciencedirect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='com/science/article/pii/S0747563217306726  [23] Shagun Jhaver, Larry Chan and Amy Bruckman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' The View from the Other Side:  The  Border  Between  Controversial  Speech  and  Harassment  on  Kotaku  in  Action.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' First  Monday, 23, 2 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' http://firstmonday.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='org/ojs/index.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='php/fm/article/view/8232  [24] Anja Kalch and Teresa K Naab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Replying, disliking, flagging: How users engage  with uncivil and impolite comments on news sites (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  [25] Kate Kenski, Kevin Coe and Stephen A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Rains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Perceptions of Uncivil Discourse  Online: An Examination of Types and Predictors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Communication Research, 47, 6 (2020),  795-814.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' https://journals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='sagepub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='com/doi/abs/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='1177/0093650217699933  [26]  Jennifer  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  Lambe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' 2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Dimensions  of  censorship:  Reconceptualizing  public  willingness to censor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Communication Law and Policy, 7 (2002), 187-235.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  [27] Francis L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Lee.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' The Prevention Effect of Third-Person Perception: A Study on  the  Perceived  and  Actual  Influence  of  Polls.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Mass  Communication  and  Society,  13,  1  (2009/12/24 2009), 87-110.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='1080/15205430802635672  [28]  Joon  Soo  Lim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' The  Third-Person  Effect  of  Online  Advertising  of  Cosmetic  Surgery: A Path Model for Predicting Restrictive Versus Corrective Actions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Journalism &  Mass  Communication  Quarterly,  94,  4  (2017),  972-993.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  https://journals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='sagepub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='com/doi/abs/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='1177/1077699016687722  [29]  Joon  Soo  Lim  and  Guy  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  Golan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Social  Media  Activism  in  Response  to  the  Influence of Political Parody Videos on YouTube.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Communication Research, 38, 5 (2011),  710-727.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' https://journals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='sagepub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='com/doi/abs/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='1177/0093650211405649  [30]  Sonia  Livingstone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' ‘Knowledge  enhancement’:  the  risks  and  opportunities  of  evidence-based policy (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  [31]  Ven-hwei  Lo  and  Chingching  Chang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Knowledge  about  the  Gulf  Wars:A  Theoretical  Model  of  Learning  from  the  News.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Harvard  International  Journal  of  Press/Politics,  11,  3  (2006),  135-155.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  https://journals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='sagepub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='com/doi/abs/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='1177/1081180X06289582  [32] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Nathan Matias.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Going dark: Social factors in collective action against platform  operators in the Reddit blackout.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' City, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  [33] DOUGLAS M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' McLEOD, WILLIAM P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' EVELAND and AMY I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' NATHANSON.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' 1997.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Support  for Censorship of Violent and Misogynic Rap Lyrics:An Analysis of the Third-Person Effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  Communication  Research,  24,  2  (1997),  153-174.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  https://journals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='sagepub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='com/doi/abs/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='1177/009365097024002003  [34] Ben Medeiros.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Platform (Non-)Intervention and the “Marketplace” Paradigm for  Speech  Regulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Social  Media  +  Society,  3,  1  (2017),  2056305117691997.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  https://journals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='sagepub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='com/doi/abs/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='1177/2056305117691997  [35] Teresa K Naab, Anja Kalch and Tino GK Meitz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Flagging uncivil user comments:  Effects of intervention information, type of victim, and response comments on bystander  behavior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  New  Media  &  Society,  20,  2  (2018),  777-795.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  https://journals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='sagepub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='com/doi/abs/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='1177/1461444816670923  [36] Teresa K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Naab, Thorsten Naab and Jonas Brandmeier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Uncivil User Comments  Increase  Users’  Intention  to  Engage  in  Corrective  Actions  and  Their  Support  for  Authoritative  Restrictive  Actions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Journalism  &  Mass  Communication  Quarterly,  98,  2  (2021), 566-588.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' https://journals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='sagepub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='com/doi/abs/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='1177/1077699019886586  [37] Hye-Jin Paek, Jennifer L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Lambe and Douglas M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' McLeod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Antecedents to Support  for Content Restrictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Journalism & Mass Communication Quarterly, 85, 2 (2008), 273-  290.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' https://journals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='sagepub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='com/doi/abs/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='1177/107769900808500204  [38] Hye-Jin Paek, Zhongdang Pan, Ye Sun, Joseph Abisaid and Debra Houden.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' The  Third-Person  Perception  as  Social  Judgment:An  Exploration  of  Social  Distance  and  Uncertainty  in  Perceived  Effects  of  Political  Attack  Ads.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Communication  Research,  32,  2  (2005), 143-170.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' https://journals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='sagepub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='com/doi/abs/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='1177/0093650204273760  [39] Vincent Price and David Tewksbury.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' 1996.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Measuring the Third-Person Effect of News:  The  Impact  of  Question  Order,  Contrast  and  Knowledge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' International  Journal  of  Public  Opinion Research, 8, 2 (1996), 120-141.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='1093/ijpor/8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='120  [40] Manuel Puppis and Hilde Van den Bulck.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Introduction: Media Policy and Media  Policy  Research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  Springer  International  Publishing,  City,  2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='1007/978-3-030-16065-4_1  [41] Martin J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Riedl, Teresa K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Naab, Gina M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Masullo, Pablo Jost and Marc Ziegele.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  Who  is  responsible  for  interventions  against  problematic  comments?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Comparing  user  attitudes in Germany and the United States.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Policy & Internet (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  [42] Martin J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Riedl, Kelsey N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Whipple and Ryan Wallace.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Antecedents of support for  social media content moderation and platform regulation: the role of presumed effects on  self  and  others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  Information,  Communication  &  Society  (2021),  1-18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='1080/1369118X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='1874040  [43] Hernando Rojas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' “Corrective” Actions in the Public Sphere: How Perceptions of  Media and Media Effects Shape Political Behaviors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' International Journal of Public Opinion  Research, 22, 3 (2010), 343-363.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='1093/ijpor/edq018  [44] Hernando Rojas, Dhavan V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Shah and Ronald J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Faber.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' 1996.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' For the Good of Others:  Censorship and the Third-person Effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' International Journal of Public Opinion Research, 8,  2 (1996), 163-186.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='1093/ijpor/8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='163  [45] Steven Ruggles, Sarah Flood, Ronald Goeken, Megan  Schouweiler and Matthew Sobek.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' IPUMS USA, Minneapolis, MN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='18128/D010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='V12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='0  [46] Valarie Schweisberger, Jennifer Billinson and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Makana Chock.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Facebook, the  Third-Person Effect, and the Differential Impact Hypothesis*.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Journal of Computer-Mediated  Communication, 19, 3 (2014), 403-413.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='1111/jcc4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='12061  [47]  Steve  Stecklow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Why  Facebook  is  losing  the  war  on  hate  speech  in  Myanmar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  Thomson  Reuters,  City,  2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='reuters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='com/investigates/special-  report/myanmar-facebook-hate/  [48] John L Sullivan, James Piereson and George E Marcus Political tolerance and American  democracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' University of Chicago Press, 1993.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  [49]  Ye  Sun,  Zhongdang  Pan  and  Lijiang  Shen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Understanding  the  Third-Person  Perception: Evidence From a Meta-Analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Journal of Communication, 58, 2 (2008), 280-  300.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='1111/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='1460-2466.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='00385.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='x  [50] Ran Wei, Stella C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Chia and Ven-Hwei Lo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Third-person Effect and Hostile Media  Perception  Influences  on  Voter  Attitudes  toward  Polls  in  the  2008  U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  Presidential  Election.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' International  Journal  of  Public  Opinion  Research,  23,  2  (2011),  169-190.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='1093/ijpor/edq044  [51] Mark Williams, Michelle Butler, Anna Jurek-Loughrey and Sakir Sezer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Offensive  communications: exploring the challenges involved in policing social media.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Contemporary  Social  Science,  16,  2  (2021/03/15  2021),  227-240.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='1080/21582041.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='1563305  [52] David A Yalof and Kenneth Dautrich The First Amendment and the media in the court of  public opinion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Cambridge University Press, 2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  [53] Marc Ziegele, Teresa K Naab and Pablo Jost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Lonely together?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' Identifying the  determinants of collective corrective action against uncivil comments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content=' New Media & Society,  22,  5  (2020),  731-751.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='  https://journals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='sagepub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='com/doi/abs/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
+page_content='1177/1461444819870130' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE0T4oBgHgl3EQfRgBm/content/2301.02208v1.pdf'}
diff --git a/HtE5T4oBgHgl3EQfWg9Q/content/tmp_files/load_file.txt b/HtE5T4oBgHgl3EQfWg9Q/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..1201af24dfbe77cade0771fc4bfc0d9d0a314dd9
--- /dev/null
+++ b/HtE5T4oBgHgl3EQfWg9Q/content/tmp_files/load_file.txt
@@ -0,0 +1,220 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf,len=219
+page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='05559v1  [quant-ph]  11 Jan 2023  Supercurrent and Electromotive force generations  by the Berry connection from many-body wave  functions  Hiroyasu Koizumi  Division of Quantum Condensed Matter Physics, Center for Computational Sciences,  University of Tsukuba, Tsukuba, Ibaraki 305-8577, Japan  E-mail: koizumi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='hiroyasu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='fn@u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='tsukuba.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='jp  January 2023  Abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='  The velocity field composed of the electromagnetic field vector potential  and the Berry connection from many-body wave functions explains supercurrent  generation, Faraday’s law for the electromotive force (EMF) generation, and other  EMF generations whose origins are not electromagnetism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' An example calculation  for the EMF from the Berry connection is performed using a model for the cuprate  superconductivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' Introduction  The Berry phase first discovered in the context of the adiabatic approximation now  prevails in various fields of physics [1, 2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='  In particular, it is now an indispensable  mathematical tool to detect topological defects in quantum wave functions [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' Recently,  the Berry connection from many-body wave functions was defined and its usefulness to  calculate supercurrent is demonstrated [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' A salient feature of such a formalism is that it  provides a vector potential directly related to the velocity field for electric current.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' In the  present work, we consider the supercurrent and electromotive force (EMF) generations  based on the same formalism [4, 5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='  The EMF is expressed using a non-irrotational ‘electric field’, Eirrot, whose origin  may not be a real electric field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' It is defined as  E =  �  C  Enon−irrot · dr  (1)  where C is a closed electric circuit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' This EMF appears due to various causes, such as  chemical reactions in batters or temperature differences in metals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='  One of the important EMF generation mechanisms is the Faraday’s law of magnetic  induction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' It is expressed as a total time-derivative of a magnetic flux of the magnetic  field B  E = − d  dt  �  S  B · dS  (2)  Supercurrent and EMF by Berry connection  2  where S is a surface whose circumference is C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' This EMF formula is often called the  “flux rule”, since  �  S B · dS is the magnetic flux through the surface S;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' it has been  claimed curious since it is composed of two different fundamental equations in classical  theory [6], i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=', the Faraday’s law of induction and the Lorentz force.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' The curiosity  is increased by the fact that one of them is an equation for fields only, and the other  includes particles and is an equation for a force on a particle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='  This peculiarity disappears in quantum theory using the vector potential A that  is more fundamental than the magnetic field B [7, 8, 9], and the wave function makes  the velocity of a particle a velocity field [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' Then, the two contributions in the “flux  rule” are connected by the duality that a U(1) phase factor added on a wave function  describes a whole system motion, and also plays the role of the vector potential when  it is transferred into the Hamiltonian [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='  In the present work, we extend the above vector potential and velocity field  approach for the electric current generation to cases where the vector potential of the  Berry connection from many-body wave functions appears [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' We show that the EMF  generation other than the electromagnetic field origin, such as those due to chemical  reactions or temperature gradients can be expressed by it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='  The organization of the present work is as follows: we explain the velocity field  appearing from the Berry connection from many-body wave functions in Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='  We reexamine the Faraday’s EMF generation formula using the velocity field from the  electromagnetic vector potential in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' We examine the EMF generation by the  Berry connection in Section 4, and an example calculation is performed for the Nernst  effect in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' Lastly, we conclude the present work by mentioning implications of  the present new theory in Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' The velocity field from the Berry connection form many-body wave  functions and supercurrent generation  The key ingredient in the present work is the Berry connection from many-body wave  functions for electrons given by  AMB  Ψ (r)=  1  ℏρ(r)Re  ��  dσ1dx2 · · ·dxNΨ∗(r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' σ1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' · · · ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' xN)(−iℏ∇)Ψ(r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' σ1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' · · · ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' xN)  �  (3)  where N is the total number of electrons in the system,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' ‘Re’ denotes the real part,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' Ψ  is the total wave function,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' xi collectively stands for the coordinate ri and the spin σi  of the ith electron,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' −iℏ∇ is the Schr¨odinger’s momentum operator for the coordinate  vector r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' and ρ(r) is the number density calculated from Ψ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' This Berry connection is  obtained by regarding r as the “adiabatic parameter”[1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='  Let us consider the electron system whose kinetic energy operator in the Schr¨odinger  Supercurrent and EMF by Berry connection  3  representation is given by  ˆT = −  N  �  j=1  ℏ2  2me  ∇2  j  (4)  where me is the electron mass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='  For convenience, we also use the following χ defined as  χ(r) = −2  � r  0  AMB  Ψ (r′) · dr′  (5)  and express the many-electron wave function Ψ as  Ψ(x1, · · · , xN) = exp  �  − i  2  N  �  j=1  χ(rj)  �  Ψ0(x1, · · · , xN)  (6)  Then, Ψ0 = Ψ exp  �  i  2  �N  j=1 χ(rj)  �  is a currentless wave function for the current  operator associated with ˆT in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' (4) since the contribution from Ψ and that from  exp  �  i  2  �N  j=1 χ(rj)  �  cancel out.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' In other words, a wave function is given as a product  of a currentless one, Ψ0, and the factor for the current exp  �  − i  2  �N  j=1 χ(rj)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' The total  wave function Ψ must be a single-valued function of coordinates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' This makes χ as an  angular variable that satisfies some periodicity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' This periodicity gives rise to non-trivial  topological integer as will be explained, shortly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='  When electromagnetic field is included, the kinetic energy operator becomes  ˆT ′ =  N  �  j=1  1  2me  (−iℏ∇j − qA)2  (7)  where q = −e is the electron charge, and A is the electromagnetic field vector potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='  The magnetic field is given by B = ∇ × A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='  In the following, we will use the same expression, Ψ, for the total wave function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='  Then, the current density for Ψ is given by  j = −eρv  (8)  with the velocity field v given by  v = e  me  �  A − ℏ  2e∇χ  �  = e  me  A + ℏ  me  AMB  Ψ  (9)  The current density in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' (8) is known to give rise to the Meissner effect if it is a  stable one due to the fact that it explicitly depends on A [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' For the stable current  case, ∇χ compensates the gauge ambiguity in A and makes v in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' (9) gauge invariant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='  If the Meissner effect is realize, the magnetic filed is expelled from the bulk of a  superconductor [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' Then, the flux quantization is observed for magnetic flux through  Supercurrent and EMF by Berry connection  4  a loop C that goes through the bulk of a ring-shaped superconductor  �  S  B · dS =  �  C  A · dr  = ℏ  2e  �  C  ∇χ · dr  = h  2ewC[χ]  (10)  where wC[χ] is the topological integer ‘winding number’ defined by  wC[χ] = 1  2π  �  C  ∇χ · dr  (11)  According to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' (9), the presence of non-zero wC[χ] means the existence of the  stable velocity field that satisfies  �  C  v · dr =  h  2me  wC[χ]  (12)  In superconductors, the quantized flux persists.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' This means that the condition  d  dtwC[χ] = 0  (13)  is realized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='  In normal metals, the time-derivative of the velocity field is often expressed as  dv  dt = −1  τ v  (14)  using a relaxation time approximation, where τ is the relaxation time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='  Combination of this with Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' (12) yields  τ d  dtwC[χ] = −wC[χ]  (15)  If the condition in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' (13) with nonzero wC[χ] is realized, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' (15) means that τ  must be ∞, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=', an infinite conductivity, or zero resistivity is realized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' The vorticity field from the vector potential A and Faraday’s flux rule  In this section, we consider the case where non-trivial AMB  Ψ  is absent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' When AMB  Ψ  is  trivial, it satisfies  ∇ × AMB  Ψ  = 0  (16)  Thus, by applying ∇× on the both sides of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' (9)  ∇ × v = e  me  B  (17)  is obtained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='  Taking the total time-derivative of the above yields  ∇ × dv  dt = e  me  ∂tB + e  me  (v · ∇)B  (18)  Supercurrent and EMF by Berry connection  5  where the total time-derivative of the field B is the Eulerian time-derivative given by  dB  dt = ∂tB + (v · ∇)B  (19)  Integrating Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' (18) over the surface S, we have  �  C  dv  dt · dr = e  me  �  S  ∂tB · dS + e  me  �  S  (v · ∇)B · dS  (20)  where the Stokes theorem is used to convert the surface integral to the line integral.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='  Noting that the electromotive force for an electron is given by  E = 1  −e  �  C  d(mev)  dt  dr  (21)  where −e is the electron charge and me is the electron mass, the following relation is  obtained  E = −  �  S  ∂tB · dS −  �  S  (v · ∇)B · dS  (22)  This is equal to the Faraday’s formula in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' (2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='  In the situation where the circuit C moves with a constant velocity v0, we have the  following relation  (v0 · ∇)B = ∇ × (B × v0) + v0(∇ · B)  = ∇ × (B × v0)  (23)  due to the fact that B satisfies ∇ · B = 0 [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='  As a consequence, the well-known EMF formula  E = −  �  S  ∂tB · dS +  �  C  (v0 × B) · dr  (24)  is obtained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' The first term in it is attributed to the Faraday’s law of induction, and  the second to the Lorentz force.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' This formula is composed of two different fundamental  equations in classical theory [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' However, in the quantum mechanical formalism, two  contributions stem from a single relation in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' (9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' The EMF generation by the Berry connection  The velocity field in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' (9) contains the vector potential AMB  Ψ  in addition to the  electromagnetic vector potential A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' Just like A, AMB  Ψ  will also give rise to the EMF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='  We now consider a general case where the Berry connection arises from a set of  states {Ψj} and given by  AMB =  �  j  pjAMB  Ψj  (25)  where pj’s are probabilities satisfy  �  j  pj = 1  (26)  and AMB  Ψj is obtained from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' (3) by replacing Ψ with Ψj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='  Supercurrent and EMF by Berry connection  6  We express AMB using the following density matrix  ˆd =  �  j  pj|Ψj⟩⟨Ψj|  (27)  where the operator ˆAMB is defined through the relation  ⟨Ψj| ˆAMB|Ψj⟩ = AMB  Ψj  (28)  From now on, we allow the time-dependence in Ψj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' When Ψj is time-dependent, AMB  Ψj  is also time-dependent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' The distribution probability pj can be also time and coordinate  dependent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='  Using the density operator ˆd and the operator ˆAMB, the vector potential from the  Berry connection is given by  AMB = tr  �  ˆd ˆAMB�  (29)  We define BMB by  BMB = ∇ × AMB  (30)  Then, the EMF from the Berry connection is given by  EMB = −ℏ  e  �  S  ∂tBMB · dS − ℏ  e  �  S  (v · ∇)BMB · dS  (31)  The first term in the right hand side can arise from the time-dependence of pj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' This  means that if pj varies with time due to chemical reactions, photo excitations, or etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='  it will give rise to the EMF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' The second term will arise if the temperature depends on  the coordinate, T(r), and pj contains the Boltzmann factor exp(−  Ej  kBT(r)), where Ej is  the energy for the state Ψj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' It also arises when pj depends on the coordinate due, for  example, to the concentration gradient of chemical spices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='  Now we consider the case where the circuit moves with a constant vector v0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' The  circuit in this case should be regarded as a region of the system which flows due to the  flow existing in the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' Such a motion may arise from a temperature gradient or  concentration gradient in the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' In this case, we have the following relation,  (v · ∇)BMB = −∇ × (v0 × BMB)  (32)  due to the fact that ∇ · BMB = ∇ · (∇ × AMB) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='  The equation (31) can be cast into the following form  EMB = −ℏ  e  �  C  �  ∂tAMB − v0 × (∇ × AMB)  �  dr  (33)  that only contains AMB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' However, the above formula may not be convenient to use due  to the fact that AMB contains topological singularities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' A convenient one may be the  following  EMB = −ℏ  e  d  dt  �  S  BMB · dS  (34)  where B in the Faraday’s law in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' (2) is replaced by BMB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='  Supercurrent and EMF by Berry connection  7  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' Nernst effect  In this section, we examine the Nernst effect observed in cuprate superconductors  [13, 14, 15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' We examine this phenomenon using Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' (34).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' A theory of superconductivity  in the cuprate predicts the appearance of spin-vortices in the CuO2 plane around doped  holes that become small polarons [16, 17, 18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' The spin-vortices generate the vector  potential  AMB = −1  2∇χ  (35)  where χ is an angular variable with period 2π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' This angular variable appears due to  the requirement that the wave function to be a single-valued function of coordinates  in the situation where itinerant motion of electrons around the small polaron hole is a  spin-twisting one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='  We can decompose χ as a sum over spin-vortices  χ =  Nh  �  j=1  χj  (36)  where χj is a contribution form the jth small polaron hole, and Nh is the total number  of holes that become small polarons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='  Each χj is characterized by its winding number  wj = 1  2π  �  Cj  ∇χj · dr  (37)  where Cj is a loop that only encircles the center of the jth spin-vortex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' We can assume  wj to be +1 or −1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' only odd integers are allowed due to the spin-twisting motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' The  numbers ±1 are favorable from the energetic point of view.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='  C(t)  v0  x  y  Ly  C(t+Δt)  v0  x0+  Δt  x0  Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' A schematic picture for the EMF appearing from the Berry connection  generated by spin-vortices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='  The Berry connection creates the vector potential  proportional to ∇χ, which creates vortices (loop currents) denoted by circles with  arrows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' We consider two loops C(t) and C(t + ∆t), where t and t + ∆t denote two  times with interval ∆t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' The loop moves with velocity v0 in the x-direction due to the  temperature gradient in that direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' A constant magnetic field is applied in the z-  direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' A voltage is generated across the y-direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' The sample exists 0 ≤ y ≤ Ly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='  The left edge of the loop at time t is x0 and that at time t + ∆t is x0 + v0∆t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='  Supercurrent and EMF by Berry connection  8  Let us consider the situation depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' We neglect the contribution from  A assuming that it is small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' The EMF generated across the sample in the y-direction  is given by  EMB = − ℏ  e  1  ∆t  ��  S(t+∆t)  BMB · dS −  �  S(t)  BMB · dS  �  = − ℏ  e  1  ∆t  ��  C(t+∆t)  AMB · dr −  �  C(t)  AMB · dr  �  = ℏ  e  1  ∆t  �  ∆C  AMB · dr  (38)  where S(t+∆t) and S(t) are surfaces in the xy-plane with circumferences C(t+∆t) and  C(t), respectively;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' ∆C is the loop encircling the area x0 ≤ x ≤ x0 + v0∆t, 0 ≤ y ≤ Ly,  with the counterclockwise direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='  We approximate  �  ∆C AMB · dr by  �  ∆C  AMB · dr = − 1  2  �  ∆C  ∇χ · dr  ≈ − 1  22π(nm − na)Lyv0∆t  (39)  where nm and na are average densities of wj = 1 (‘meron’) and wj = −1 (‘antimeron’)  vortices, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' Thus, nmLyv0∆t and naLyv0∆t are expected numbers of wj = 1  and wj = −1 vortices within the loop ∆C, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='  From Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' (38) and (38), the approximate EMB is given by  EMB ≈ hv0  2e (na − nm)Ly  (40)  Thus, the electric field generated by EMB in the y-direction is given by  Ey ≈ hv0  2e (na − nm)  (41)  In our previous work, na is denoted as nd indicting that it yields a diamagnetic  current, and nm as np indicting that it yields a paramagnetic current [17, 18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' Using nd  and np, the Nernst signal is obtained as  eN =  Ey  |∂xT| = hv0(nd − np)  2e|∂xT|  (42)  The same formula was obtained previously for the situation where spin-vortices move  by the temperature gradient [17, 18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' Here, the situation is different;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' the spin-vortices  do not move, but the electron system affected by ∇χ moves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='  Considering that the  small polaron movement is negligible at low temperature, the present situation is more  realistic than the previous one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' The temperature dependence is the same as the one  that qualitatively explains the experimental result [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='  Note that experiments indicating the presence of loop currents different from  ordinary Abrikosov vortices [19] in the cuprate [20, 21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' The present result indicates  that the observed Nernst can be explained by the presence of spin-vortex-induced loop  currents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='  Supercurrent and EMF by Berry connection  9  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' Concluding remarks  Since the EMF by the Berry connection is not the electromagnetic field origin, it may  be more appropriate to call it the Berry-connection motive force (BCMF) given by  F BMF = −eEMB = ℏ d  dt  �  S  BMB · dS  (43)  The BCMF will arise from quantum mechanical dynamics of particles other than  electrons;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' for example, from proton dynamics, through chemical reactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' The non-  trivial Berry phase effect has been predicted [22], and observed in the hydrogen transfer  reactions [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' Quantum mechanical effects are important in such reactions due to the  relatively light mass of protons [24, 25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' It is known that the EMF generated by the  proton pumps is a very important chemical process in biological systems, and the Berry-  connection motive force may play some roles in the working of the proton pumps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' It  may be also useful to invent high performance batteries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='  References  [1] Berry M V 1984 Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' Roy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' London Ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' A 391 45  [2] Bohm A, Mostafazadeh A, Koizumi H, Niu Q and Zwanziger J 2003 The Geometric Phase in  Quantum Systems (Springer)  [3] Chiu C K, Teo J C Y, Schnyder A P and Ryu S 2016 Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' 88(3) 035005 URL  https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='1103/RevModPhys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='035005  [4] Koizumi  H  2022  Physics  Letters  A  450  128367  ISSN  0375-9601  URL  https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='sciencedirect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='com/science/article/pii/S0375960122004492  [5] Koizumi H 2022 arXiv:2211.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='08759 [cond-mat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='supr-con]  [6] Feynman R P, Leighton R B and Sands M 1963 The Feynman Lectures on Physics vol 2 (Addison-  Wesley)  [7] Aharonov Y and Bohm D 1959 Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' 115 167  [8] Tonomura A, Matsuda T, Suzuki R, Fukuhara A, Osakabe N, Umezaki H, Endo J, Shinagawa K,  Sugita Y and Fujiwara H 1982 Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' 48 1443  [9] Tonomura A, Osakabe N, Matsuda T, Kawasaki T, Endo J, Yano S and Yamada H 1986 Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' 56(8) 792–795 URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='1103/PhysRevLett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='792  [10] London F 1950 Superfluids vol 1 (New York: Wiley)  [11] Koizumi H 2017 J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' Supercond.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' Nov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' Magn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' 30 3345–3349  [12] Jackson J D 1998 Classical Electrodynamics (Wiley)  [13] Xu Z A, Ong N P, Wang Y, Kakeshita T and Uchida S 2000 Nature 406 486  [14] Wang Y, Li L, Naughton M J, Gu G D, Uchida S and Ong N P 2005 Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' 95 247002  [15] Daou R, Chang J, LeBoeuf D, Cyr-Choiniere O, Laliberte F, Doiron-Leyraud N, Ramshaw  B J, Liang R, Bonn D A, Hardy W N and Taillefer L 2010 Nature 463 519–522 URL  http://dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='1038/nature08716  [16] Koizumi H 2009 J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' A 113 3997  [17] Koizumi H 2011 J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' Supercond.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' Nov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' Magn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' 24 1997  [18] Hidekata R and Koizumi H 2011 J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' Supercond.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' Nov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' Magn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' 24 2253  [19] Abrikosov A A 1957 Sov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' JETP 5 1174  [20] Xia J, Schemm E, Deutscher G, Kivelson S A, Bonn D A, Hardy W H, Liang R, Siemons W,  Koster G, Fejer M M and Kapitulnik A 2008 Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' 100 127002  [21] He R H, Hashimoto M, Karapetyan H, Koralek J D, Hinton J P, Testaud J P, Nathan V, Yoshida  Supercurrent and EMF by Berry connection  10  Y, Yao H, Tanaka K, Meevasana W, Moore R G, Lu D H, Mo S K, Ishikado M, Eisaki H, andT  P Devereaux Z H, Kivelson S A, Orenstein J, Kapitulnik A and Shen Z X  [22] Mead C A and Truhlar D 1979 J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' 70 2284  [23] Yuan D, Guan Y, Chen W, Zhao H, Yu S, Luo C, Tan Y, Xie T, Wang X, Sun  Z,  Zhang  D  H  and  Yang  X  2018  Science  362  1289–1293  ISSN  0036-8075  URL  https://science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='sciencemag.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content='org/content/362/6420/1289  [24] Kuppermann A and Schatz G C 1975 J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' 62 62 2502  [25] Elkowitz A B and Wyatt R E 1975 J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
+page_content=' 62 2504' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtE5T4oBgHgl3EQfWg9Q/content/2301.05559v1.pdf'}
diff --git a/J9FIT4oBgHgl3EQfZytY/vector_store/index.faiss b/J9FIT4oBgHgl3EQfZytY/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..41c4c308655a4e40a4253795b8c8f616e2056cb9
--- /dev/null
+++ b/J9FIT4oBgHgl3EQfZytY/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:132a6edb129b513f30724124878b926c135e78944cc50e45e3efc3f13d447c44
+size 1966125
diff --git a/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf b/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..6c065e0d6c97c93a2f17a3b60e9646162f1e01e2
--- /dev/null
+++ b/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:a7b824d81b6e36753365507f03eb135d67316ec1f345d3013dbf71afed332235
+size 197918
diff --git a/JNE2T4oBgHgl3EQfUgdI/vector_store/index.pkl b/JNE2T4oBgHgl3EQfUgdI/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..ad3b94a62e3a15e240f2f284937a1fe5e8642933
--- /dev/null
+++ b/JNE2T4oBgHgl3EQfUgdI/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:42d6a0f2c90977ccc27e01a908ef07e724adc6bcfa0aa1516f2d65ce4d90d72c
+size 78405
diff --git a/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf b/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..faabc05695e7b64116e1aad04b4be2bd5ea25c5e
--- /dev/null
+++ b/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:05d1c94bf7d6c6c8448b5f066db7b3540a2696be853c9544b2fb7b1aa2028f3c
+size 495741
diff --git a/JNE4T4oBgHgl3EQfIgz1/vector_store/index.pkl b/JNE4T4oBgHgl3EQfIgz1/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..a2bae0b9c55f01089aa612d876c85b3b6c9e4473
--- /dev/null
+++ b/JNE4T4oBgHgl3EQfIgz1/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:3ec5928f884c4aa04ab8dd36355589698be12b771a2a281d7d03efebee5869e7
+size 82483
diff --git a/JdE0T4oBgHgl3EQfiQFG/content/tmp_files/2301.02442v1.pdf.txt b/JdE0T4oBgHgl3EQfiQFG/content/tmp_files/2301.02442v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..eb9dc7a9f36a7b3147e60db8542bcc10683022dc
--- /dev/null
+++ b/JdE0T4oBgHgl3EQfiQFG/content/tmp_files/2301.02442v1.pdf.txt
@@ -0,0 +1,4330 @@
+arXiv:2301.02442v1  [math.PR]  6 Jan 2023
+Applied Probability Trust (9 January 2023)
+PDE FOR THE JOINT LAW OF THE PAIR OF A CONTINUOUS
+DIFFUSION AND ITS RUNNING MAXIMUM
+LAURE COUTIN, MONIQUE PONTIER,∗ IMT
+Abstract
+Let X be a d-dimensional diffusion and M the running supremum of its first
+component.
+In this paper,
+we show that for any t > 0, the density (with
+respect to the d + 1-dimensional Lebesgue measure) of the pair (Mt, Xt) is a
+weak solution of a Fokker-Planck partial differential equation on the closed set
+{(m, x) ∈ Rd+1, m ≥ x1}, using an integral expansion of this density.
+Keywords:
+Diffusion process, partial differential equation, running supremum
+process, joint law.
+2020 Mathematics Subject Classification: Primary 60J60
+Secondary 60G70,60H10
+1. Introduction
+The goal of this paper is to study the law of the pair (Mt, Xt) where X is a d-
+dimensional diffusion and M is the running maximum of the first component. In a
+previous work [9], using Malliavin calculus and specifically Nualart’s seminal book [21],
+we have proved that, for any t > 0 the law of Vt := (Mt, Xt) is absolutely continuous
+with respect to the Lebesgue measure with density pV (.; t), and that the support of
+this density is included in the set {(m, x) ∈ Rd+1, m ≥ x1}.
+In the present work, we prove that the density pV is a weak solution of a partial
+differential equation (PDE). Furthermore, we exhibit a boundary condition on the set
+{(m, x) ∈ Rd+1, m = x1}. This work extends the results given in [8] and in Ngom’s
+∗ Postal address: IMT, Universit´e Paul Sabatier, 31062 Toulouse cedex France
+coutin@math.univ-toulouse.fr, IMT.
+pontier@math.univ-toulouse.fr, IMT.
+1
+
+2
+AUTHOR NAMES
+thesis [20] obtained in the case where X is a L´evy process and where it is proved that
+the density is a weak solution to an integro-differential equation.
+In the literature, there exist many studies on the law of Vt. When the process X is
+a Brownian motion, one can refer to [15, 17] where an explicit expression of pV is
+given. When X is a one-dimensional linear diffusion, [11] provides an expression of
+pV using the scale function, the speed measure and the density of the law of some
+hitting times. See also [1, 4] for the particular case of Ornstein-Uhlenbeck process.
+For some applications to the local score of a biologic sequence, the case of reflected
+Brownian motion is presented in [19]. The law of the maximum Mt is studied in [2] for
+general Gaussian processes. The case of a L´evy process X is deeply investigated in the
+literature, see for instance [12, 20]. Moreover Section 2.4 in Ngom’s thesis [20] provides
+the existence and the regularity of the joint law density of the process (Mt, Xt) for a
+L´evy process X. In the case where X is a martingale (see e.g. [22, 13] or [10, 16]),
+the law of the running maximum is provided.
+Such studies concerning this running
+maximum are useful in financial area which involve hitting times, for instance for the
+pricing of barrier option. It is known that the law of hitting times is closely related to
+the one of the running maximum, see [6, 7, 23].
+As an application of our work, think
+of a firm the activity of which is characterized by a set of processes (X1, · · · , Xd). But
+one of them, e.g., X1 could be linked to an alarm, namely: when there exists s ≤ t
+such that X1
+s exceeds a threshold a, that is equivalent to Mt = sup0≤s≤t X1
+s ≥ a,
+some action is important to operate. So, the firm needs to know the law of such pair
+(Mt, Xt); more specifically the law of the stopping time τa = inf{u, X1
+u ≥ a}, is linked
+to the law of M as following: {τa ≤ t} = {Mt ≥ a}. To know the probability of such
+an alert, the law of the pair (Mt, Xt) will be useful.
+We provide an infinite expansion of the density of the law of the pair (Mt, Xt) which
+can leads to numerical approximation.
+Let (Ω, F, P) be a probability space endowed with a d-dimensional Brownian.
+Let
+X be the diffusion process with values in Rd solution of
+dXt = B(Xt)dt + A(Xt)dWt,
+t > 0
+(1)
+where X0 is a random variable independent of the Brownian motion W, with law µ0,
+and A (resp. B) is a map from Rd to the set of (d × d) matrices (resp. to Rd). Let
+
+PDE for the joint law of the pair of a continuous diffusion and its running maximum
+3
+us denote Ci
+b(Rd, Rn) the set of functions
+on Rd, which are i times differentiable,
+bounded, with bounded derivatives, taking their values in Rn. Let F = (Ft, t ≥ 0)
+be the completed right-continuous filtration defined by Ft := σ{X0, Ws, s ≤ t} ∨ N
+where N is the set of negligible sets of F.
+Under classical assumptions on A and B (cf.(4) and (5) below), then according to
+[9], for all t > 0, the law of Vt = (supu≤t X1
+t , Xt) has a density with respect to the
+Lebesgue measure on Rd+1.
+The main results and notations are given in Section 2: in the d-dimensional case,
+under a quite natural assumption (meaning Hypothesis 2.1 below) on the regularity
+of pV around the boundary of ∆, pV is a weak solution of a Fokker-Planck PDE on
+the subset of Rd+1 defined by {(m, x), m ≥ x1}. When A = Id, this assumption is
+satisfied, see Theorem 2.4. The main results are proved in Section 3 under Hypothesis
+2.1. Section 4 is devoted to prove that Hypothesis 2.1 is satisfied when A = Id. The
+main tool is an infinite expansion of pV given in Proposition 3.2. In Section 5, one-
+dimensional case, a Lamperti transformation [18] allows to get the main result for any
+A ∈ C2
+b (R, R). Finally Appendix contains some technical tools useful for the proofs of
+main results.
+2. Main results and some notations
+In this section, we give our main results, the proofs will be given later on, as it is
+mentioned in the introduction.
+2.1. Notations
+Let ∆ be the open set of RD+1 given by ∆ := {(m, x), m ∈ R, x ∈ Rd, m > x1, x =
+(x1, · · · , xd)}. From now on, we use Einstein’s convention. The infinitesimal generator
+L of the diffusion X defined in (1) is the partial differential operator on the space
+C2(Rd, R) given by:
+L = Bi∂xi + 1
+2(AAt)ij∂2
+xi,xj.
+(2)
+where At denotes the transposed matrix.
+Its adjoint operator is L∗f = 1
+2Σij∂2
+ijf − [Bi − ∂j(Σij)]∂if − [∂iBi − 1
+2∂2
+ij(Σij)]f where
+Σ := AAt. In what follows, the operators L and L∗ are extended to the space C2(Rd+1, R),
+
+4
+AUTHOR NAMES
+for Φ ∈ C2(Rd+1, R) as
+L(Φ)(m, x) = Bi(x)∂xiΦ(m, x) + 1
+2Σij(x)∂2
+xi,xjΦ(m, x),
+and L∗(Φ)(m, x) =
+1
+2Σij(x)∂2
+ijΦ(m, x) − [Bi − ∂j(Σij)](x)∂xiΦ(m, x) + [1
+2∂2
+xi,xjΣij − ∂xiBi](x)Φ(m, x).
+It can be stressed that these operators are degenerated since no derivative with respect
+to the variable m appears.
+Let A1(x) be the d dimensional vector A1(x) = (A1
+j(x), j = 1, ..., d) ∈ Rd corresponding
+to the first column of A(x), similarly Aj(x) denotes its jth line.
+Recall that M denotes the running maximum of the first component of X, meaning
+Mt = sup0≤s≤t{X1
+s} and V is the Rd+1-valued process defined by (Vt = (Mt, Xt), ∀t ≥
+0). Finally, ˜x ∈ Rd−1 denotes the vector (x2, ..., xd).
+In [9], under Assumptions (4) and (5) below, when the initial value is deterministic,
+X0 = x0 ∈ Rd, the density of Vt exists and is denoted pV (.; t, x0).
+If µ0 is the
+distribution of X0, the density of the law of Vt with respect to the Lebesgue measure
+on Rd+1 is
+pV (.; t, µ0) :=
+�
+Rd pV (.; t, x0)dµ0(x0)
+(3)
+When there is no ambiguity, the dependency in µ0 is omitted.
+Since Mt ≥ X1
+t , the support of pV (.; t, µ0) is contained in ¯∆ :=
+�
+(m, x) ∈ Rd+1|m ≥ x1�
+.
+2.2. Mains results
+The aim of this article is to show that the density pV is a weak solution of a Fokker-
+Planck PDE. The coefficients B and A are assumed to satisfy
+B ∈ C1
+b (Rd, Rd) and A ∈ C2
+b (Rd, Rd×d),
+(4)
+and that there exists a constant c > 0 such that the Euclidean norm of any vector v
+satisfies
+c∥v∥2 ≤ vtA(x)At(x)v,
+∀v, x ∈ Rd.
+(5)
+
+PDE for the joint law of the pair of a continuous diffusion and its running maximum
+5
+Our first result will be established under the following hypothesis which is a quite
+natural assumption on the regularity of pV
+in the neighbourhood of the boundary
+of ∆ since the
+set of times where the process M
+increases is included in
+the set
+{t,
+Mt = Xt} :
+Hypothesis 2.1. The density of the law of Vt = (Mt, Xt), denoted by pV (3), satisfies
+(i) the map (t, m, ˜x) �→ supu>0 pV (m, m − u, ˜x; t) belongs to L1([0, T ] × Rd, dtdmd˜x).
+(ii) for all t > 0 almost surely in (m, ˜x) ∈ Rd, limu→0+ pV (m, m − u, ˜x; t) exists and is
+denoted by pV (m, m, ˜x; t).
+Theorem 2.2. Assume that A and B fulfil (4) and (5) and that (M, X) fulfils Hy-
+pothesis 2.1.
+Then, for all initial law µ0 and F ∈ C2
+b (Rd+1, R):
+E [F(Mt, Xt)) = E
+�
+F(X1
+0, X0)
+�
++
+� t
+0
+E [L (F) (Ms, Xs)] ds
++ 1
+2
+� t
+0
+E
+�
+∂mF(X1
+s , Xs)∥A1(Xs)∥2 pV (X1
+s, Xs; s)
+pX(Xs; s)
+�
+ds.
+(6)
+Actually pX is the solution of the PDE ∂tp = L∗p,
+p(.; 0) = µ0, where
+L∗f = 1
+2Σij∂2
+ijf − [Bi − ∂j(Σij)]∂if − [∂iBi − 1
+2∂2
+ij(Σij)]f. Let aij := Σij,
+ai := [Bi − ∂j(Σij)]∂i, and a0 := ∂iBi − 1
+2∂2
+ij(Σij). Under Assumptions (4) and (5),
+the operator L∗ satisfies all the assumptions of Theorem 3.5 [14] (see (3.2) (3.3) 3.4)
+page 177). As a consequence of Theorem 3.5 line 14 pX(x; s) > 0.
+Remark 2.1. (i) When A is the identity matrix of Rd (denoted by Id) and B ∈
+C1
+b (Rd, Rd), Hypothesis 2.1 is fulfilled, see Theorem 2.4 below.
+When d = 1, using
+a Lamperti transformation [18], one proves that Hypothesis 2.1 is always fulfilled, see
+Section 5.
+(ii) This result is similar to Theorem 2.1 in [8] where the process X is a L´evy
+process. Proposition 4 in [8] gives a key of the last term in (6) with factor 1
+2. Firstly,
+roughly speaking, the local behaviour of X1
+t − X1
+s conditionally to Fs is the one of
+∥A1(Xs)∥(W 1
+t − X1
+s ). So, as in the Brownian case, the running maximum M of X1 is
+increasing as soon as it is equal to X1 and both M and X1 are increasing; it is well
+known that the Brownian process W 1 is increasing with probability 1
+2, more specifically,
+we have P{limt→s+
+W 1
+t −W 1
+s
+t−s
+= −∞} = P{limt→s+
+W 1
+t −W 1
+s
+t−s
+= +∞} = 1
+2.
+The starting point of the proof of Theorem 2.2 is the Itˆo’s formula: let F belong
+
+6
+AUTHOR NAMES
+to C2
+b (Rd+1, R). The process M is increasing, hence V = (M, X) is a semi-martingale.
+Applying Itˆo’s formula to F(V ) and taking expectation of both members,
+E [F(Vt)] = E [F(V0)] +
+� t
+0
+E [L(F)(Vs)] ds + E
+�� t
+0
+∂mF(Vs)dMs
+�
+.
+The novelty comes from the third term of the right member of the previous equation.
+The following theorem proved in Section 3 achieves the proof of Theorem 2.2.
+Theorem 2.3. Assume that A and B fulfil (4) and (5) and that (M, X) fulfils Hy-
+pothesis 2.1. For all Ψ ∈ C1
+b (Rd+1, R), let Fψ be the map
+Fψ : t �→ E
+�� t
+0 Ψ(Ms, Xs)dMs
+�
+. Then FΨ is absolutely continuous with respect to the
+Lebesgue measure and its derivative is
+˙FΨ(t) = 1
+2
+�
+Rd Ψ(m, m, ˜x)∥A1(m, ˜x)∥2pV (m, m, ˜x; t)dmd˜x.
+Remark that, as it is expressed in Theorem 2.2, this derivative can be written
+1
+2E
+�
+Ψ(X1
+t , Xt)∥A1(Xt)∥2 pV (X1
+t , Xt; t)
+pX(Xt; t)
+�
+.
+Remark 2.2. The above proposition provides an explicit formulation of the derivative
+of the function FΨ. Note that the absolute continuity of Fψ could be established as
+a direct consequence of the existence of the density of the law of the hitting time
+τa = inf{s : X1
+s ≥ a} when it exists, using the identity {τa ≤ t} = {Mt ≥ a}.
+Conversely, it could be proved that the absolute continuity of FΨ yields the existence
+of the density of the law of the hitting time τa, using a sequence of C2
+b (R, R) functions
+(Fn) approximating the indicator function 1[a,∞), namely this density satisfies fτa(t) =
+1
+2
+�
+Rd−1 pV (a, a, ˜x; t)d˜x.
+Theorem 2.4. Assume that A = Id and B satisfies Assumption (4) then, for all t > 0
+the distribution of the pair (Mt, Xt) fulfils Hypotheses 2.1. As a consequence, for all
+F ∈ C2
+b (Rd+1, R)
+E [F(Mt, Xt)] = E
+�
+F(X1
+0, X0)
+�
++
+� t
+0
+E [L (F) (Ms, Xs)] ds
++ 1
+2
+� t
+0
+E
+�
+∂mF(X1
+s , Xs)pV (X1
+s , Xs; s)
+pX(Xs; s)
+�
+ds.
+Proof. This theorem is a consequence of Theorem 2.2 and Proposition 4.1.
+□
+
+PDE for the joint law of the pair of a continuous diffusion and its running maximum
+7
+When d = 1 a Lamperti transformation leads to the following corollary:
+Corollary 1. Assume that d = 1, A and B satisfies (4) and (5), the density pV
+satisfies Hypothesis 2.1 so
+E [F(Mt, Xt)] = E [F(X0, X0)] +
+� t
+0
+E [L (F) (Ms, Xs)] ds
++ 1
+2
+� t
+0
+E
+�
+A2(Xs)∂mF(Xs, Xs)pV (Xs, Xs; s)
+pX(Xs; s)
+�
+ds.
+Remark 2.3. If pV is regular enough, and if the initial law of X0 satisfies µ0(dx) =
+f0(x)dx, then Theorem 2.2 means that pV is a weak solution in the set ∆ of ∂tp = L∗p
+where L∗f = 1
+2Σij∂2
+ijf−[Bi−∂j(Σij)]∂if−∂iBi− 1
+2∂2
+ij(Σij))f with boundary condition
+B1(m, ˜x)pV (m, m, ˜x; s) = ∂xk(Σ1,kpV )(m, m, ˜x; s) + 1
+2∂m(∥A1∥2pV )(m, m, ˜x; s). (7)
+This result is proved in Appendix A.3
+This boundary condition also appears in Proposition 4 Equation (11) of [4] (Ornstein
+Uhlenbeck process). Finally, a similar PDE is studied in Chapter 1.2 of [14] where the
+authors have established the existence of a unique strong solution of this PDE, but in
+case of a non degenerate elliptic operator.
+3.
+Proof of Theorem 2.3
+We start this section with a road map of the proof of Theorem 2.3.
+Firstly we
+compute the right derivative of the application FΨ : t �→ E[
+� t
+0 Ψ(Ms, Xs)dMs], namely
+limh→0+ Th,t with Th,t = 1
+hEP[
+� t+h
+t
+ψ(Vs)dMs]. A first step is the decomposition
+Th,t = 1
+hEP[
+� t+h
+t
+(ψ(Vs) − ψ(Vt))dMs] + 1
+hEP[ψ(Vt)(Mt+h − Mt)].
+(8)
+Since ψ ∈ C1
+b (Rd+1, R) and the process M is increasing, the first term in (8),
+is
+dominated by:
+E
+�� t+h
+t
+(ψ(Vs) − ψ(Vt))dMs
+�
+≤ ∥∇ψ∥∞E
+�
+sup
+t≤s≤t+h
+∥Vs − Vt∥(Mt+h − Mt)
+�
+.
+Lemma 3.1 states that supt≤s≤t+h ∥Xs − Xt∥p = O(
+√
+h) and Lemma 3.2 yields
+∥Mt+h − Mt∥p = o(
+√
+h) so that that this first term is an o(h).
+
+8
+AUTHOR NAMES
+Concerning the second term in (8), Mt+h − Mt can be written as sup0≤u≤h(X1
+t+h −
+X1
+t − Mt + X1
+t )+. In order to use the independence of the increments of Brownian
+motion we introduce a new process, independent of Ft, which is an approximation of
+X1
+t+u − X1
+t :
+X1
+t,u := A1
+k(Xt) ˆ
+W k
+u where ˆW k
+u := W k
+t+u − W k
+t ; Mt,h :=
+sup
+0≤u≤h
+X1
+t,u.
+(9)
+Lemma 3.4 (ii) will set E
+�
+|Mt+h − Mt − (Mt,h − Mt + X1
+t )+|
+�
+= o(h), where (x)+ =
+max(x, 0). Thus
+1
+hE[ψ(Vt)(Mt+h − Mt)] = E[ψ(Vt)(Mt,h − Mt + X1
+t )+] + o(h)
+(10)
+Remark that the law of Mt,h given Ft is the law of ∥A1(Xt)∥ sup0≤u≤h ˆW 1
+u, then using
+the function H (13), a Ft conditioning yields:
+1
+hE[ψ(Vt)(Mt+h − Mt)] =
+2
+√
+h
+E
+�
+Ψ(Vt)∥A1(Xt)∥H(
+Mt − X1
+t
+√
+h∥A1(Xt)∥
+)
+�
++ o(h).
+(11)
+Then Th,t =
+2
+√
+h E
+�
+Ψ(Vt)∥A1(Xt)∥H(
+Mt−X1
+t
+√
+h∥A1(Xt)∥)
+�
++ o(h) as it appears in Proposition
+3.1 (ii).
+In Proposition 3.2, under Hypothesis 2.1, we compute limh→0 Th;t.
+Finally in Section 3.4 we prove Fψ : t �→ E[
+� t
+0 ψ(Vs)dMs] is an absolutely continuous
+function with respect to Lebesgue measure, integral of its right derivative. Actually we
+prove that Fψ is a continuous function belonging to the Sobolev space W 1,1(I), I =
+(0, T ). This achieves the proof of Theorem 2.3.
+The main propositions to prove are
+Proposition 3.1. Let B and A fulfil (4) and (5) and let Ψ ∈ C1
+b (Rd+1, R).
+Recall
+that A1 is the vector (A1
+j, j = 1, ..., d), and ∥A1(x)∥2 = �d
+j=1(A1
+j(x))2.
+(i) for all T > 0, there exists a constant C > 0, (depending on ∥A∥∞, ∥B∥∞, ∥∇A∥∞,
+∥Ψ∥∞, ∥∇Ψ∥∞ and T ) such that ∀t ∈ [0, T ], h ∈ [0, 1],
+�����E
+�� t+h
+t
+Ψ(Vs)dMs − 2
+√
+h
+�
+Ψ(Vt)∥A1(Xt)∥H(
+Mt − X1
+t
+√
+h∥A1(Xt)∥
+)
+������� ≤ Ch∥∇Ψ∥∞,
+(12)
+(ii) for all t > 0, h ∈ [0, 1],
+lim
+h→0+
+1
+h
+�����E
+�� t+h
+t
+Ψ(Vs)dMs
+�
+− 2
+√
+hE
+�
+Ψ(Vt)∥A1(Xt)∥H(
+Mt − X1
+t
+√
+h∥A1(Xt)∥
+)
+������ = 0,
+where, denoting by ΦG the standard Gaussian cumulative distribution function,
+H(θ) :=
+� ∞
+θ
+1
+√
+2π (y − θ)e− y2
+2 dy = e− θ2
+2
+√
+2π − θΦG(−θ).
+(13)
+
+PDE for the joint law of the pair of a continuous diffusion and its running maximum
+9
+The following remark will be useful:
+Remark 3.1. The definition of H in (13) implies that
+� ∞
+0
+H(u)du = 1/4 Moreover,
+H′(θ) = −ΦG(−θ) ≤ 0, in particular H is non increasing.
+Proposition 3.2. Assume that A and B fulfil (4) and (5) and that (M, X) fulfils
+Hypothesis 2.1, then for all Ψ ∈ C1
+b (Rd+1, R), for all 0 < T and for all t ≥ 0 :
+(i)t �→ sup
+h>0
+2
+√
+h
+h
+E
+�
+Ψ(Vt)∥A1(Xt)∥H(
+Mt − X1
+t
+√
+h∥A1(Xt)∥
+)
+�
+∈ L1([0, T ], R),
+(ii) lim
+h→0+
+2
+√
+h
+h
+E
+�
+Ψ(Vt)∥A1(Xt)∥H(
+Mt − X1
+t
+√
+h∥A1(Xt)∥
+)
+�
+= 1
+2
+�
+Rd Ψ(m, m, ˜x)∥A1(m, ˜x)∥2pV (m, m, ˜x; t)dmd˜x
+As a corollary, the function t → 1
+2
+�
+Rd Ψ(m, m, ˜x)∥A1(m, ˜x)∥2pV (m, m, ˜x; t)dmd˜x be-
+longs to L1([0, T ], R).
+The proof of Proposition 3.1 will be obtained with the lemmas in the following section.
+3.1. Tools for proving Proposition 3.1
+Here we provide some estimations of the expectations
+of the increments of the
+processes X and M.
+Assumptions (4) and (5) allow us to introduce a constant K
+which denotes either max(∥A∥∞, ∥B∥∞) or max(∥A∥∞, ∥B∥∞, ∥∇A∥∞). Let Cp be
+the constant in the Burkholder-Davis-Gundy inequality (cf. Theorem B.36 in [3]).
+Lemma 3.1. Let A and B be bounded. Then, for all 0 < h ≤ 1, for all p ≥ 1 there
+exists a constant Cp,K (depending only on p and K) such that:
+sup
+t>0
+E
+�
+sup
+0≤s≤h
+∥Xt+s − Xt∥p
+�
+≤ Cp,Khp/2.
+Proof. Using the fact that (a + b)p ≤ 2p−1 [ap + bp] , a, b ≥ 0, one obtains:
+0 ≤ sup
+s≤h
+∥Xt+s − Xt∥p ≤ 2p−1
+�
+sup
+u≤h
+�
+∥
+� t+u
+t
+B(Xs)ds∥
+�p
++ sup
+u≤h
+�
+∥
+� t+u
+t
+Aj(Xs)dW j
+s ∥
+�p�
+.
+Taking expectation of both members, the Burkholder-Davis-Gundy inequality implies
+E[sup
+s≤h
+∥Xt+s−Xt∥p] ≤ 2p−1(1+Cp)E
+
+
+�� t+h
+t
+∥B(Xs)∥ds
+�p
++
+�� t+h
+t
+∥A(Xs)∥2ds
+�p/2
+ .
+
+10
+AUTHOR NAMES
+Assumption (4) on B and A yields E[sups≤h ∥Xt+s − Xt∥p] ≤ 2p−1(1 + Cp)(hpKp +
+hp/2Kp).
+□
+Lemma 3.2. Let B and A satisfy Assumptions (4) and (5). Then, for all 0 < h ≤ 1,
+for all p ≥ 1 we get:
+sup
+t>0
+E[|Mt+h − Mt|p] ≤ Cp,Khp/2 ; E[|Mt+h − Mt|p] = o(hp/2).
+(14)
+Proof. Recall Mt+h − Mt =
+�
+sup0≤u≤h(X1
+t+u − X1
+t ) + X1
+t − Mt
+�
++ recalling (x)+ =
+max(x, 0). For any a ≥ 0, one has (x − a)+ ≤ |x|1{x>a}, thus
+0 ≤ Mt+h − Mt ≤ | sup
+0≤u≤h
+(X1
+t+u − X1
+t )|1{sup0≤u≤h(X1
+t+u−X1
+t )>Mt−X1
+t }.
+Cauchy-Schwartz’s inequality yields:
+0 ≤ E [(Mt+h − Mt)p] ≤
+�
+E
+�
+| sup
+0≤u≤h
+(X1
+t+u − X1
+t )|2p
+�
+P({ sup
+0≤u≤h
+(X1
+t+u − X1
+t ) > Mt − X1
+t }).
+Replacing p by 2p in Lemma 3.1 leads to the inequality in (14) and the equality
+limh→0 sup0≤u≤h(X1
+t+u − X1
+t ) = 0 holds almost surely. According to Theorem 1.1 in
+[9]
+extended to X0 with law µ0 on Rd,
+the pair (Mt, Xt) admits a density, thus
+P{Mt − X1
+t = 0} = 0 holds almost surely. Therefore E ([Mt+h − Mt]p) is bounded by
+the product of hp/2 and a factor going to zero when h goes to 0, and this quantity is
+an o(hp/2).
+□
+For any fixed t we recall the process (Xt,u,
+u ∈ [0, h]) and the running maximum
+of its first component as follows:
+Xt,u :=
+�
+j
+Aj(Xt) ˆ
+W j
+u, Mt,h :=
+sup
+0≤u≤h
+X1
+t,u.
+(15)
+Lemma 3.3. Under Assumptions (4) and (5), for all p ≥ 1
+there exists a constant
+Cp,K such that such that for all t ≤ T , for all h ∈ [0, 1]:
+E
+�
+sup
+s≤h
+|X1
+s+t − X1
+t − X1
+t,s|p
+�
+≤ Cp,Khp.
+Proof. By definition, recalling ˆWu := Wt+u − Wt,
+u ≥ 0, we obtain
+X1
+s+t − X1
+t − X1
+t,s =
+� s
+0
+B1(Xu+t)du +
+� s
+0
+�
+A1(Xu+t) − A1(Xt)
+�
+d ˆWu.
+
+PDE for the joint law of the pair of a continuous diffusion and its running maximum
+11
+Using once again (a + b)p ≤ 2p−1(ap + bp), a, b ≥ 0, we get
+sup
+0≤s≤h
+|X1
+s+t − X1
+t − X1
+t,s|p ≤
+2p−1
+��� h
+0
+∥B1(Xu+t)∥du
+�p
++ sup
+0≤s≤h
+����
+� s
+0
+�
+A1(Xu+t) − A1(Xt)
+�
+d ˆ
+Wu
+����
+p�
+.
+Taking expectation of both sides and applying the Burkholder-Davis-Gundy inequality
+yield with Dp = 2p−1(1 + Cp):
+E
+�
+sup
+0≤s≤h
+|X1
+s+t − X1
+t − X1
+t,s|p
+�
+≤ Dp
+�
+E
+�� h
+0
+∥B1(Xu+t)∥du
+�p
++ E
+����
+� h
+0
+∥A1(Xu+t) − A1(Xt)∥2du
+����
+p/2�
+.
+The first term above is bounded by Kphp since B is bounded.
+The assumption
+that A belongs to C1
+b (Rd, Rd×d) and Jensen’s inequality imply that the second term is
+bounded by Kphp/2−1� h
+0 E∥Xu+t − Xt∥pdu thus
+E
+�
+sup
+0≤s≤h
+|X1
+s+t − X1
+t − X1
+t,s|p
+�
+≤ DpKphp/2−1
+�
+hp/2+1 +
+� h
+0
+E∥Xu+t − Xt∥pdu
+�
+.
+From Lemma 3.1 we obtain the uniform upper bound: E[∥Xu+t − Xt∥p] ≤ Cp,Kup/2
+hence
+E
+�
+sup
+s≤h
+|X1
+s+t − X1
+t − X1
+t,s|p
+�
+≤ DpKpCp,K
+p
+2 + 1
+hp.
+□
+Lemma 3.4. Under Assumptions (4) and (5), one has
+(i) ∃C > 0
+sup
+0≤t≤T ;
+0≤h≤1
+h−1E
+����Mt+h − Mt −
+�
+Mt,h − Mt + X1
+t
+�
++
+���
+�
+≤ C < ∞,
+(ii)
+lim
+h→0+ h−1E
+����Mt+h − Mt −
+�
+Mt,h − Mt + X1
+t
+�
++
+���
+�
+= 0.
+Proof. Fistly remark
+∀a ∈ R,
+��(x − a)+ − (y − a)+
+�� ≤ |x − y|
+�
+1{x>a} + 1{y>a}
+�
+,
+(16)
+and if f and g are functions on [0, T ], then
+∀s ∈ [0, T ],
+f(s) −
+sup
+0≤u≤T
+g(u) ≤ f(s) − g(s) ≤ |f(s) − g(s)| ≤ sup
+v≤T
+|f(v) − g(v)|,
+hence sups≤T f(s) − supu≤T g(u) ≤ supv≤T |f(v) − g(v)|. Here the role of f and g is
+symmetrical so sups≤T g(s) − supu≤T f(u) ≤ supv≤T |f(v) − g(v)|, and
+����sup
+s≤T
+g(s) − sup
+u≤T
+f(u)
+���� ≤ sup
+v≤T
+|f(v) − g(v)|.
+(17)
+
+12
+AUTHOR NAMES
+We now consider Mt+h − Mt =
+�
+sup0≤u≤h(X1
+u+t − X1
+t ) − Mt + X1
+t
+�
++ , using (16)
+���Mt+h − Mt −
+�
+Mt,h − Mt + X1
+t
+�
++
+��� ≤
+���� sup
+0≤u≤h
+(X1
+u+t − X1
+t ) − Mt,h
+����
+�
+1{sup0≤u≤h(X1
+u+t−X1
+t )>Mt−X1
+t } + 1{Mt,h>Mt−X1
+t }
+�
+.
+Then, for any t fixed, we apply inequality (17) to the maps g : u �→ X1
+u+t−Xt
+1 and
+f : u �→ X1
+t,u. Then
+���Mt+h − Mt −
+�
+Mt,h − Mt + X1
+t
+�
++
+��� ≤
+sup
+0≤u≤h
+��X1
+u+t − X1
+t − X1
+t,u
+��
+�
+1{sup0≤u≤h(X1
+u+t−X1
+t )>Mt−X1
+t } + 1{Mt,h>Mt−X1
+t }
+�
+.
+From Cauchy-Schwartz’s inequality and the fact that (a + b)2 ≤ 2(a2 + b2), we get
+E
+����Mt+h − Mt −
+�
+Mt,h − Mt + X1
+t
+�
++
+���
+�
+≤
+�
+2E
+�
+sup
+u≤h
+��X1
+u+t − X1
+t − X1
+t,u
+��2
+� �
+P{ sup
+0≤u≤h
+(X1
+u+t − X1
+t ) > Mt − X1
+t } + P{Mt,h > Mt − X1
+t }
+�
+.
+Lemma 3.3 with p = 2 insures that the map h �→ h−1
+�
+2E
+�
+supu≤h
+��X1
+u+t − X1
+t − X1
+t,u
+��2�
+is uniformly bounded in t. Concerning the second factor,
+• firstly the almost sure continuity with respect to h insures that the quantities
+limh→0 sup0≤u≤h(X1
+u+t − X1
+t ) and limh→0 Mt,h are equal to 0;
+• secondly the law of the pair (Mt, Xt) admits a density with respect to the Lebesgue
+measure on ¯∆ according to Theorem 1.1 [9] so P({0 = Mt − X1
+t }) = 0 and the limit of
+the second factor is equal to 0.
+This concludes the proof of the lemma.
+□
+Recall Definition (15): Xt,h = Aj(Xt)[W j
+t+h − W j
+t ], Mt,h = sup0≤u≤hX1
+t,u, h ∈ [0, 1].
+Lemma 3.5. Under Assumptions (4) and (5), with H defined in (13):
+E
+�
+(Mt,h − Mt + X1
+t )+|Ft
+�
+= 2∥A1(Xt)∥
+√
+hH
+�
+Mt − X1
+t
+∥A1(Xt)∥
+√
+h
+�
+.
+Proof. For any t fixed, conditionally to Ft the process (X1
+t,u, u ∈ [0, h]) (9) has
+the same law as (
+√
+h∥A1(Xt)∥ ˆWu, u ∈ [0, 1]) where ˆ
+W is a Brownian motion in-
+dependent of Ft, and for any h, the random variable Mt,h has the same law as
+√
+h∥A1(Xt)∥ supu≤1 ˆWu.
+Following
+[17] Section 3.1.3,
+the random variable supu≤1 ˆ
+Wu has the same law
+
+PDE for the joint law of the pair of a continuous diffusion and its running maximum
+13
+as |G| where G is a standard Gaussian variable (independent of Ft), with density
+2
+√
+2πe− z2
+2 1[0,+∞[(z). Then using the function H introduced in (13)
+E
+�
+(Mt,h − (Mt − X1
+t ))+|Ft
+�
+=
+� ∞
+0
+�
+∥A1(Xt)∥
+√
+hz − (Mt − X1
+t )
+�
++
+2
+√
+2π e− z2
+2 dz
+= 2∥A1(Xt)∥
+√
+hH(
+Mt − X1
+t
+√
+h∥A1(Xt)∥
+).
+□
+3.2. Proof of Proposition 3.1
+Let t > 0. The key of this proof is to write the quantity
+E
+�� t+h
+t
+Ψ(Vs)dMs
+�
+− 2
+√
+hE
+�
+Ψ(Vt)∥A1(Xt)∥H(
+Mt − X1
+t
+√
+h∥A1(Xt)∥
+)
+�
+as the sum of three terms,
+E
+� � t+h
+t
+(Ψ(Vs) − Ψ(Vt))dMs
+�
++ E
+�
+Ψ(Vt)
+�
+(Mt+h − Mt) − E
+�
+Mt,h − Mt + X1
+t )+|Ft
+� ��
+(18)
++ E
+�
+Ψ(Vt)E
+�
+(Mt,h − Mt + X1
+t )+ | Ft
+�
+− 2
+√
+hΨ(Vt)∥A1(Xt)∥H(
+Mt − X1
+t
+√
+h∥A1(Xt)∥
+)
+�
+.
+We now prove that each terms in sum (18) are both o(h) and O(h) uniformly in time.
+(a) Using Lemma 3.5 the third term is null.
+(b) Concerning the second term, using the fact that Ψ is bounded and Lemma 3.4 (i)
+for all t ∈ [0, T ]
+��E
+�
+Ψ(Vt)[(Mt+h − Mt) − E[(Mt,h − Mt + X1
+t )+ | Ft]
+��� ≤
+∥Ψ∥∞
+��E
+�
+Mt+h − Mt − E[(Mt,h − Mt + X1
+t )+|Ft]
+��� ≤ Ch∥Ψ∥∞,
+as it is required in (12). Moreover using Lemma 3.4 (ii)
+lim
+h→0
+1
+h
+��E
+�
+Ψ(Vt)[(Mt+h − Mt) − E[(Mt,h − Mt + X1
+t )+ | Ft]
+��� = 0.
+(c) Since ∇Ψ is bounded and the process M is increasing, the first term is bounded:
+E
+�� t+h
+t
+[Ψ(Vs) − Ψ(Vt)]dMs
+�
+≤ ∥∇Ψ∥∞E[
+sup
+t≤s≤t+h
+∥Vs − Vt∥(Mt+h − Mt)].
+
+14
+AUTHOR NAMES
+Using Cauchy-Schwarz’s inequality
+E
+�
+sup
+t≤s≤t+h
+∥Vs − Vt∥(Mt+h − Mt)
+�
+≤
+�
+E[
+sup
+t≤s≤t+h
+∥Vs − Vt∥2]E[(Mt+h − Mt)2].
+Since ∥Vs − Vt∥2 = (Ms − Mt)2 + ∥Xs − Xt∥2, we obtain
+supt≤s≤t+h ∥Vs − Vt∥2 ≤ (Mt+h − Mt)2 + supt≤s≤t+h ∥Xs − Xt∥2, hence
+E[
+sup
+t≤s≤t+h
+∥Vs−Vt∥(Mt+h−Mt)] ≤
+�
+E[(Mt+h − Mt)2] + E[
+sup
+t≤s≤t+h
+∥Xs − Xt∥]2)
+�
+E[(Mt+h − Mt)2]
+Lemmas 3.1 and 3.2 (p = 2) yield
+the fact that the first factor is an o(
+√
+h) and
+the second is an O(
+√
+h) uniformly with respect to t ≥ 0. Then E[supt≤s≤t+h ∥Vs −
+Vt∥(Mt+h − Mt)] is an o(h) and an O(h) uniformly with respect to t ≥ 0.
+□
+3.3. Proof of Proposition 3.2
+(i) Recall that A and B fulfil (4), (5) and (M, X) fulfils Hypothesis 2.1. Then, using
+the density pV of the law of the pair (Mt, Xt) we have
+E
+�
+Ψ(Vt)∥A1(Xt)∥H
+�
+Mt − X1
+t
+√
+h∥A1(Xt)∥
+��
+≤
+∥Ψ∥∞∥A∥∞
+�
+Rd+1 H
+�
+m − x1
+√
+h∥A1(x1, ˜x)∥
+�
+pV (m, x1, ˜x; t)dm dx1 d˜x.
+The change of variable x1 = m − u
+√
+h yields
+√
+h
+h E
+�
+Ψ(Vt)∥A1(Xt)∥H
+�
+Mt − X1
+t
+√
+h∥A1(Xt)∥
+��
+≤
+(19)
+∥Ψ∥∞∥A1∥∞
+�
+Rd×[0,+∞[
+H
+�
+u
+∥A1(m −
+√
+hu, ˜x)∥
+�
+pV (m, m −
+√
+hu, ˜x; t)dm d˜x du.
+Since H is decreasing (Remark 3.1) and 0 ≤ h ≤ 1, H
+�
+u
+∥A1(m−
+√
+hu,˜x)∥
+�
+≤ H(
+u
+∥A1∥∞ ) :
+�����
+√
+h
+h E
+�
+Ψ(Vt)∥A1(Xt)∥H
+�
+Mt − X1
+t
+√
+h∥A1(Xt)∥
+������� ≤
+∥Ψ∥∞∥A1∥∞
+�
+Rd×[0,+∞[
+H
+�
+u
+∥A1∥∞
+�
+sup
+r>0
+pV (m, m − r, ˜x; t)dm d˜x du.
+Applying Tonelli’s Theorem, computing the integral with respect to du in the right-
+hand with
+� ∞
+0
+H(v)dv = 1/4 (Remark 3.1), yield:
+sup
+h>0
+�����
+√
+h
+h E
+�
+Ψ(Vt)∥A1(Xt)∥H
+�
+Mt − X1
+t
+√
+h∥A1(Xt)∥
+������� ≤ 1
+4∥Ψ∥∞∥A1∥2
+∞
+�
+Rd sup
+r>0
+pV (m, m − r, ˜x; t)dm d˜x.
+
+PDE for the joint law of the pair of a continuous diffusion and its running maximum
+15
+Using Hypothesis 2.1 (i), we obtain that the map:
+t �→ sup
+h>0
+�����
+√
+h
+h E
+�
+Ψ(Vt)∥A1(Xt)∥H
+�
+Mt − X1
+t
+√
+h∥A1(Xt)∥
+�������
+belongs to L1([0, T ], R). Point (i) of Proposition 3.2 is proved.
+(ii) Concerning the proof of point (ii), firstly note that
+E
+�
+Ψ(Vt)∥A1(Xt)∥H
+�
+Mt − X1
+t
+√
+h∥A1(Xt)∥
+��
+=
+�
+Rd+1 Ψ(m, x)∥A1(x)∥H
+�
+m − x1
+√
+h∥A1(x)∥
+�
+pV (m, x; t)dm dx.
+After the change of variable x1 = m − u
+√
+h, we obtain
+√
+h
+h E
+�
+Ψ(Vt)∥A1(Xt)∥H
+�
+Mt − X1
+t
+√
+h∥A1(Xt)∥
+��
+=
+(20)
+�
+Rd×R+ Ψ(m, m − u
+√
+h, ˜x)∥A1(m − u
+√
+h, ˜x)∥H
+�
+u
+∥A1(m −
+√
+hu, ˜x)∥
+�
+pV (m, m −
+√
+hu, ˜x; t)dm d˜x du.
+Using Lebesgue’s dominated convergence Theorem, we let h go to 0 in (20) for t > 0,
+and using the fact that Ψ, A and H are continuous and Hypothesis 2.1 (ii) we obtain
+lim
+h→0
+√
+h
+h E
+�
+Ψ(Vt)∥A1(Xt)∥H
+�
+Mt − Xt
+√
+h∥A1(Xt)∥
+��
+=
+�
+Rd×[0,+∞[
+Ψ(m, m, ˜x)∥A1(m, ˜x)∥H
+�
+u
+∥A1(m, ˜x)∥
+�
+pV (m, m, ˜x; t)dm d˜x du.
+Using the change of variable z =
+u
+∥A1(m,˜x)∥, and Remark 3.1
+� ∞
+0
+H(z)dz = 1/4, yields
+lim
+h→0
+√
+h
+h E
+�
+Ψ(Vt)∥A1(Xt)∥H
+�
+Mt − X1
+t
+√
+h∥A1(Xt)∥
+��
+= 1
+4
+�
+Rd Ψ(m, m, ˜x)∥A1(m, ˜x)∥2pV (m, m,˜x; t)dm d˜x.
+□
+3.4. End of proof of Theorem 2.3
+We recall Theorem 8.2 page 204 in Brezis [5]: let f ∈ W 1,1(0, T ), then f is almost
+surely equal to an absolutely continuous function.
+As a particular case, any f ∈
+W 1,1(0, T ) ∩ C(0, T ) is absolutely continuous. Recall Fψ : t �→ E
+�� t
+0 Ψ(Vs)dMs
+�
+.
+Lemma 3.6. Assume that A and B fulfil (4) and (5) and that Ψ is a continuous
+bounded function. Then FΨ is a continuous function on R+.
+Proof. Let 0 ≤ s ≤ t. Since Ψ is bounded and M is non decreasing
+|FΨ(t) − FΨ(s)| =
+����E
+�� t
+s
+Ψ(Vu)dMu
+����� ≤ ∥Ψ∥∞E[Mt − Ms].
+The map t �→ E[Mt] being continuous, FΨ is a continuous function on R+.
+□
+
+16
+AUTHOR NAMES
+Lemma 3.7. Assume that A and B fulfil (4) and (5), (M, X) fulfils Hypothesis 2.1
+and Ψ ∈ C1
+b . Then for all T > 0, the map Fψ belongs to the Sobolev space W 1,1(]0, T [)
+and its weak derivative is
+˙FΨ(t) := 1
+2
+�
+Rd Ψ(m, ˜x)∥A1(m, ˜x)∥2pV (m, m, ˜x; t)dmd˜x
+Proof. Let g : [0, T ] → R be C1 with compact support [α, β] ⊂ (0, T ). This means
+both functions g and ˙g are continuous so bounded and that moreover g(α) = g(β) = 0.
+Note that ˙g(t) = limh→0
+g(t)−g(t−h)
+h
+,
+∀t ∈ (0, T ). Moreover,
+supt∈[0,T ] suph∈[0,1] | g(t)−g(t−h)
+h
+| ≤ ∥ ˙g∥∞. Observe that, since M is non decreasing and
+the coefficients A and B are bounded |Fψ(t)| ≤ ∥Ψ∥∞E[MT ] < ∞.
+Then, using Lebesgue’s dominated convergence Theorem
+� T
+0
+˙g(s)Fψ(s)ds =
+� T
+0
+lim
+h→0
+g(s) − g(s − h)
+h
+Fψ(s)ds = lim
+h→0
+� T
+0
+g(s) − g(s − h)
+h
+Fψ(s)ds.
+Using the change of variable u = s − h in the last integral
+� T
+0
+g(s) − g(s − h)
+h
+FΨ(s)ds = h−1
+� T
+0
+g(s)FΨ(s)ds − h−1
+� T −h
+−h
+g(u)FΨ(u + h)du
+=
+� T
+0
+g(s)FΨ(s) − FΨ(s + h)
+h
+ds−h−1
+� 0
+−h
+g(s)FΨ(s + h)ds+h−1
+� T
+T −h
+g(s)FΨ(s + h)ds.
+Recalling supp(g) = [α, β] ⊂ (0, T ), gFΨ is bounded on [0, T ] extended by 0 on [α, β]c
+so lims→0 g(s) = lims→T g(s) = 0 then h−1 � 0
+−h g(s)FΨ(s+h)ds = h−1 � T
+T −h g(s)Fψ(s+
+h)ds = 0 as soon as 0 < h ≤ T − β thus limh→0
+�
+h−1 � 0
+−h g(s)FΨ(s + h)ds
+�
+=
+limh→0
+�
+h−1 � T
+T −h g(s)Fψ(s + h)ds
+�
+= 0 Applying Lebesgue’s dominated convergence
+Theorem yields, F admits a weak derivative:
+� T
+0
+˙g(s)Fψ(s)ds = −
+� T
+0
+g(s) ˙FΨ(s)ds.
+Using Proposition 3.1 (ii)
+lim
+h→0+
+�
+−FΨ(t) − FΨ(t + h)
+h
+−
+2
+√
+h
+E
+�
+Ψ(Vt)∥A1(Xt)∥H
+�
+Mt − X1
+t
+√
+h∥A1(Xt)∥
+���
+= 0.
+Using Proposition 3.2 (ii):
+− ˙FΨ(t+) :=
+lim
+h→0,h>0
+FΨ(t) − FΨ(t + h)
+h
+= −1
+2
+�
+Rd Ψ(m, m, ˜x)∥A1(m, ˜x)∥2pV (m, m, ˜x; t)dmd˜x,
+and the points (i) of Propositions 3.1 and 3.2:
+sup
+h>0
+����
+FΨ(t) − FΨ(t + h)
+h
+���� ∈ L1([0, T ], dt),
+
+PDE for the joint law of the pair of a continuous diffusion and its running maximum
+17
+so ˙FΨ ∈ L1([0, T ], R).
+According to [5] Chap 8 section 2 page 202, FΨ belongs to W 1,1(]0, T [, R).
+□
+We now end the proof of Theorem 2.3: According to Theorem 8.2 page 204 of [5],
+Fψ is equal almost surely to an absolutely continuous function. Since FΨ is continuous
+(Lemma 3.6), the equality holds everywhere. Then FΨ is an absolutely continuous
+function and its derivative is its right derivative.
+□
+4. Case A = Id
+In this rather technical section, we firstly prove that the density of the pair (Mt, Xt)
+fulfils Hypothesis 2.1: pV (3) is continuous on the boundary of ¯∆ and is dominated by
+an integrable function:
+Proposition 4.1. Assume that B fulfils
+Assumption (4) and A = Id, then (M, X)
+fulfils Hypothesis 2.1 meaning that for all probability measure µ0 on Rd
+(i) ∀T > 0,
+sup
+(h,u)∈[0,1]×R+
+pV (b, b − hu, ˜a; t, µ0) ∈ L1([0, T ] × Rd, dtdbd˜a).
+(ii) Almost surely in (m, ˜x) ∈ Rd, ∀t > 0,
+lim
+u→0,u>0 pV (m, m − u, ˜x; t, µ0) = pV (m, m, ˜x; t, µ0).
+As a by product using Theorems 2.2 and 2.3 this proposition achieves the proof of The-
+orem 2.4. The main tool for the proof of this proposition is an integral representation
+of the density:
+Proposition 4.2. For any probability measure µ0 on Rd, for all t > 0,
+pV = p0 −
+�
+k=m,1,··· ,d
+(pk,α + pk,β)
+(21)
+where the various p are defined by (∂k is the derivative with respect to k = m, x1, ..., xd
+and Bm = B1):
+p0(m, x; t) :=
+�
+Rd pW ∗1,W (m − x1
+0, x − x0; t)µ0(dx0),
+pk,α(m, x; t) :=
+� t
+0
+�
+Rd+1 1b<mBk(a)∂kpW ∗1,W
+�
+m − a1, x − a; t − s
+�
+pV (b, a; s)dbdads,
+pk,β(m, x; t) :=
+� t
+0
+�
+R(d+1) 1b<mBk(a)∂kpW ∗1,W (b − a1, x − a; t − s)pV (m, a; s)dbdads,
+
+18
+AUTHOR NAMES
+where pW ∗1,W (., .; t) is the density of the distribution of (sups≤t W 1
+s , Wt) for t ≥ 0, see
+Appendix A.2
+4.1. Integral representation of the density: proof of Proposition 4.2
+Let t > 0 be fixed.
+Firstly, we assume that µ0 = δx0,
+x0 being fixed in Rd.
+According to Lemma 4.2 below and using the fact that B is bounded, ∀t ∈ [0, T ], the
+functions pk,γ ∈∞ L
+�
+[0, T ], L1(Rd+1)
+�
+for γ = α, β .
+Let F ∈ C1
+b (Rd+1, R) with compact support. We will prove
+EP[F(Mt, Xt)] =
+�
+Rd+1 F(m, x)
+
+p0 −
+�
+k=m,x1,...,xd
+(pk,α + pk,β)(m, x, t)
+
+ dmdx. (22)
+Using Malliavin calculus we obtain the following decomposition:
+Lemma 4.1.
+EP [F (Mt, Xt)] =
+�
+Rd+1 F (x1
+0 + b, x0 + a)pW ∗1,W (b, a; t)dbda
++
+� t
+0
+EP
+��
+Rd+1 ∂mF
+�
+X1
+s + b, Xs + a
+�
+1{Ms<X1s +b}B1(Xs)pW ∗1,W (b, a; t − s)dbda
+�
+ds
++
+� t
+0
+EP
+��
+Rd+1 ∂kF
+�
+max
+�
+Ms, X1
+s + b
+�
+, Xs + a
+�
+Bk(Xs)pW ∗1,W (b, a; t − s)dbda
+�
+ds.
+Proof. Let Z be the exponential martingale solution of
+Zt = 1 +
+� t
+0
+ZsBk(x0 + Ws)dW k
+s .
+(23)
+As previously Einstein’s convention is used. Let Q = ZP, according to Girsanov’s
+Theorem, using (23), WB :=
+�
+W k
+t −
+� t
+0 Bk(x0 + Ws)ds; k = 1, ..., d
+�
+t≥0 is a Q contin-
+uous martingale such that ⟨WB⟩t = t,
+∀t ≥ 0. That means that under Q, WB is a
+d-dimensional Brownian motion. Then the distribution of X (resp. (M, X)) under P
+is the distribution of W + x0 (resp. (W 1∗ + x0, W + x0)) under Q and
+EP [F(Mt, Xt)] = EQ
+�
+F(x1
+0 + W 1∗
+t , x0 + Wt)
+�
+= EP
+�
+F(x1
+0 + W 1∗
+t , x0 + Wt)Zt
+�
+. (24)
+Let G := F(x1
+0 + W 1∗
+t , x0 + Wt) and u := ZB(x0 + W), using (23):
+EP[F(Mt, Xt)] = EP
+�
+F(x1
+0 + W 1∗
+t , x0 + Wt)
+�
++ EP [Gδ(u)]
+(25)
+As a first step we will apply (50) (Appendix) to the second term in (25). Thus
+we have to check that the pair (G, u) ∈ D1,2 × L1,2:
+F being bounded and smooth,
+
+PDE for the joint law of the pair of a continuous diffusion and its running maximum
+19
+G ∈ D1,2; and according to Lemma A.1, the process u belongs to L1,2.
+Using (53) (τ := inf{s, W 1∗
+s
+= W 1∗
+t }) the pair (W 1∗
+t , Wt) belongs to D1,2 with Malliavin
+gradient:
+DsW 1∗
+t
+=
+�
+1[0,τ](s), 0, ....., 0
+�
+, DsW k
+t = (δj=k,
+j = 1, ..., d)1[0,t](s),
+k = 1, ..., d.
+Using the chain rule:
+⟨DG, u⟩H =
+� t
+0
+∂mF(x1
+0 + W ∗1
+t , x0 + Wt)1{W 1∗
+s <W 1∗
+t
+}B1(x0 + Ws)Zsds
++
+� t
+0
+∂kF(x1
+0 + W ∗1
+t , x0 + Wt)Bk(x0 + Ws)Zsds.
+We are now in position to apply (50) EP[Gδ(u)] = EP[⟨DG, u⟩H]:
+EP[Gδ(u)] = EP
+�� t
+0
+∂mF(x1
+0 + W 1∗
+t , x0 + Wt)1{W 1∗
+s <W 1∗
+t
+}B1(x0 + Ws)Zsds
+�
++
+EP
+�� t
+0
+∂kF(x1
+0 + W 1∗
+t , x0 + Wt)Bk(x0 + Ws)Zsds
+�
+.
+(26)
+Plugging identity (26) into right hand of (25) and using Fubini Theorem to commute
+the integrals in ds and dP, we obtain
+EP [F(Mt, Xt)] = EP
+�
+F(x1
+0 + W 1∗
+t , x0 + Wt)
+�
+(27)
++
+� t
+0
+EP
+�
+∂mF(x1
+0 + W 1∗
+t , x0 + Wt)1{W 1∗
+s <W 1∗
+t
+}ZsB1(x0 + Ws)
+�
+ds
++
+� t
+0
+EP
+�
+∂kF(x1
+0 + W 1∗
+t , x0 + Wt)ZsBk(x0 + Ws)
+�
+ds.
+As a second step we use the independence of the increments of the Brownian motion
+in order to make appear the density of (W 1∗
+t−s, Wt−s). Recall (9): ˆWt−s := Wt−Ws and
+( ˆW 1)∗
+t−s = maxs≤u≤t
+�
+W 1
+u − W 1
+s
+�
+. Then W 1∗
+t
+= max
+�
+W 1∗
+s , W 1
+s + maxs≤u≤t
+�
+W 1
+u − W 1
+s
+��
+=
+max
+�
+W 1∗
+s , W 1
+s + ( ˆW 1)∗
+t−s
+�
+so the expression (27) becomes
+EP [F(Mt, Xt)] = EP
+�
+F(x1
+0 + W 1∗
+t x0+, Wt)
+�
++
+� t
+0
+EP
+�
+∂mF
+�
+x1
+0 + W 1
+s + ( ˆ
+W 1)∗
+t−s, x0 + Ws + ˆWt−s
+�
+1{W 1∗
+s <W 1
+s +( ˆ
+W 1)∗
+t−s}ZsB1(x0 + Ws)
+�
+ds
++
+� t
+0
+EP
+�
+∂kF
+�
+max
+�
+x1
+0 + W 1∗
+s , x1
+0 + W 1
+s + ( ˆW 1)∗
+t−s
+�
+, x0 + Ws + ˆWt−s
+�
+ZsBk(x0 + Ws)
+�
+ds.
+The random vector
+�
+( ˆW 1)∗
+t−s, ˆWt−s
+�
+is independent of the σ−field Fs and has the
+same distribution as the pair (W 1∗
+t−s, Wt−s). Let pW ∗1,W (., .; t − s) be the density of its
+
+20
+AUTHOR NAMES
+law, and express the expectation with this density:
+EP [F (Mt, Xt)] =
+�
+Rd+1 F (x1
+0 + b, x0 + a)pW ∗1,W (b, a; t)dbda
++
+� t
+0
+EP
+��
+Rd+1 ∂mF �x1
+0 + W 1
+s + b, x0 + Ws + a� 1{W 1∗
+s
+<W 1
+s +b}ZsB1(x0 + Ws)pW ∗1,W (b, a; t − s)dbda
+�
+ds
++
+� t
+0
+EP
+��
+Rd+1 ∂kF
+�
+x1
+0 + max
+�
+W 1∗
+s , W 1
+s + b
+�
+, x0 + Ws + a
+�
+ZsBk(x0 + Ws)pW ∗1,W (b, a; t − s)dbda
+�
+ds.
+Using Girsanov’s Theorem for Z.P = Q, since the law of (M, X) under P is the law of
+(x1
+0 + W 1∗, x0 + W), under Q, using the equality (24):
+EP [F (Mt, Xt)] =
+�
+Rd+1 F (x1
+0 + b, x0 + a)pW ∗1,W (b, a; t)dbda
++
+� t
+0
+EP
+��
+Rd+1 ∂mF
+�
+X1
+s + b, Xs + a
+�
+1{Ms<X1s +b}B1(Xs)pW ∗1,W (b, a; t − s)dbda
+�
+ds
++
+� t
+0
+EP
+��
+Rd+1 ∂kF �max �Ms, X1
+s + b� , Xs + a� Bk(Xs)pW ∗1,W (b, a; t − s)dbda
+�
+ds.
+□
+We are now in position to achieve the proof of Proposition 4.2. Using some suitable
+translations of the variables (a, b), EP [F(Mt, Xt)] = �d
+k=0 Ik + Im. where
+I0 =
+�
+Rd+1 F(b, a)pW ∗1,W (b − x1
+0, a − x0; t)dbda,
+(28)
+Im =
+� t
+0
+EP
+��
+Rd+1 ∂mF(b, a)1{Ms<b}B1(Xs)pW ∗1,W
+�
+b − X1
+s , a − Xs; t − s
+�
+dbda
+�
+ds
+and for k = 1, ..., d,
+Ik =
+� t
+0
+EP
+��
+Rd+1 ∂kF (max (Ms, b) , a) Bk(Xs)pW ∗1,W (b − X1
+s , a − Xs; t − s)dbda
+�
+ds.
+Since B, F and its derivatives are bounded, all these integrals are finite. Using (54) in
+Appendix, the function pW ∗1,W (., .; t) is C∞ on ¯∆ = {(b, a),
+b≥a1
++,
+(a, b) ∈ Rd+1}.
+The aim is now to identify the terms p0, pk,α, pk,β, k = m, 1, · · · , d, defined in
+Proposition 4.2.
+1. Firstly we identify p0(b, a; t) as the factor of F(b, a) in the integrand of I0 :
+p0(b, a; t) = pW ∗1,W (b − x1
+0, a − x0; t).
+2. We now deal with Ik, k = 2, · · · , d. Integrating by parts with respect to ak between
+
+PDE for the joint law of the pair of a continuous diffusion and its running maximum
+21
+−∞ and ∞ in Ik for k = 2, ..., d yields
+Ik = −
+� t
+0
+EP
+��
+Rd+1 F (max (Ms, b) , a) Bk(Xs)∂kpW ∗1,W (b − X1
+s, a − Xs; t − s)dbda
+�
+ds
+= −
+� t
+0
+EP
+��
+Rd+1 1{b>Ms}F (b, a) Bk(Xs)∂kpW ∗1,W (b − X1
+s , a − Xs; t − s)dbda
+�
+ds
+−
+� t
+0
+EP
+��
+Rd+1 1{b<Ms}F (Ms, a) Bk(Xs)∂kpW ∗1,W (b − X1
+s , a − Xs; t − s)dbda
+�
+ds
+We identify −pk,α(b, a, t) inside the integral on the set (b > Ms).
+Concerning the
+integral on the set (b < Ms), we introduce the density of (Ms, Xs) and identify
+−pk,β(m, a; t) as factor of F(m, a).
+3. Finally, we identify the pm,γ and p1,γ, γ = α, β which come from the sum of Im and
+I1. Note that pW ∗1,W
+�
+b − X1
+s , a − Xs; t − s
+�
+= 0 on the set {b < a1}. Integrating by
+parts with respect to b between max
+�
+a1, Ms
+�
+and ∞ in Im yields
+Im = −
+� t
+0
+EP
+��
+Rd F
+�
+max
+�
+a1, Ms
+�
+, a
+�
+B1(Xs)pW ∗1,W
+�
+max
+�
+a1, Ms
+�
+− X1
+s , a − Xs; t − s
+�
+da
+�
+ds
+−
+� t
+0
+EP
+��
+Rd+1 1Ms<bF (b, a) B1(Xs)∂mpW ∗1,W
+�
+b − X1
+s , a − Xs; t − s
+�
+dbda
+�
+ds
+(29)
+Integrating by parts with respect to a1 between −∞ and b in I1 yields
+I1 =
+� t
+0
+EP
+��
+Rd F (max (Ms, b) , b, ˜a) B1(Xs)pW ∗1,W (b − X1
+s, b − X1
+s , ˜a − ˜Xs; t − s)dbd˜a
+�
+ds
+−
+� t
+0
+EP
+��
+Rd+1 F (max (Ms, b) , a) B1(Xs)∂1pW ∗1,W (b − X1
+s , a − Xs; t − s)dbda
+�
+ds.
+(30)
+(i) The term pm,β(b, a, t) comes from the second term in Im (29) as the factor of F(b, a):
+−
+� t
+0
+EP
+��
+Rd+1 1Ms<bF (b, a) B1(Xs)∂mpW ∗1,W
+�
+b − X1
+s , a − Xs; t − s
+�
+dbda
+�
+ds
+(ii) The terms −p1,α(b, a, t) and −p1,β(b, a; t) come from the second term in I1 (30):
+−
+� t
+0
+EP
+��
+Rd+1 F (max (b, Ms) , a) B1(Xs)∂1pW ∗1,W (b − X1
+s, a − Xs; t − s)dbda
+�
+ds.
+Inside the integral on the set (Ms < b) we identify −p1,α(b, a, t) and inside the integral
+on the set (Ms > b) we identify −p1,β(b, a; t) as the factor of F(b, a), respectively as
+
+22
+AUTHOR NAMES
+the factor of F(Ms, a).
+(iii) The term −pm,α(b, a, t) comes from the sum of first terms in I1 (30) and Im (29).
+Now we replace the variable b by a1, dbd˜a by da in the first terms of Im and I1:
+I1
+m = −
+� t
+0
+EP
+��
+Rd F �max �a1, Ms
+� , a� B1(Xs)pW ∗1,W
+�max �a1, Ms
+� − X1
+s , a − Xs; t − s� da
+�
+ds
+I1
+1 =
+� t
+0
+EP
+��
+Rd F �max �Ms, a1� , a� B1(Xs)pW ∗1,W (a1 − X1
+s , a − Xs; t − s)da
+�
+ds.
+Note that
+− pW ∗1,W
+�
+max
+�
+a1, Ms
+�
+− X1
+s, a − Xs; t − s
+�
++ pW ∗1,W (a1 − X1
+s , a − Xs; t − s)
+=
+�
+−pW ∗1,W
+�
+Ms − X1
+s, a − Xs; t − s
+�
++ pW ∗1,W
+�
+a1 − X1
+s , a − Xs; t − s
+��
+1Ms>a1
+= −
+� Ms
+a1
+∂mpW ∗1,W
+�
+b − X1
+s , a − Xs, t − s
+�
+db1Ms>a1.
+Then the sum of I1
+m and I1
+1 is:
+−
+� t
+0
+EP
+��
+Rd+1 F(Ms, a)B1(Xs)∂mpW ∗1,W
+�
+b − X1
+s, a − Xs; t − s
+�
+1Ms>b>a1dadb
+�
+ds.
+We introduce the density of the law of the pair (Ms, Xs) and we identify −pm,α(m, a; t)
+as the factor of F(m, a).
+These three steps achieve the proof of Proposition 4.2 when µ0 = δx0.
+Finally when µ0 is the law of X0, we have pV (m, w; t, µ0) =
+�
+Rd pV (m, x; t, δx0)µ0(dx0).
+Then integrating with respect to µ0 the expression obtained in (21) for pV (m, x; t, δx0)
+achieves the proof of Proposition 4.2 for any initial law µ0.
+□
+4.2.
+Proof of Proposition 4.1
+Using some idea’s used in Garroni section V.3.2 let us introduce the linear appli-
+cations on L∞([0, T ], dt, L1(Rd+1, dmdx)), k = m, 1, · · · , d:
+Ik,α[p](m, x; t) :=
+� t
+0
+�
+Rd+1 1b<mBk(a)∂kpW ∗1,W
+�
+m − a1, x − a; t − s
+�
+p(b, a; s)dbdads,
+(31)
+Ik,β[p](m, x; t) :=
+� t
+0
+�
+Rd+1 1b<mBk(a)∂kpW ∗1,W (b − a1, x − a; t − s)p(m, a; s)dbdads.
+Let us introduce the functions, defined by induction:
+p0(m, x; t, µ0) =
+�
+Rd pW 1∗,W (m − x1
+0, x − x0; t)µ0(dx0),
+pn = −
+�
+k=m,1,··· ,d
+�
+pk,α
+n
++ pk,β
+n
+�
+(32)
+
+PDE for the joint law of the pair of a continuous diffusion and its running maximum
+23
+and for k = m, 1, · · · , d, j = α, β and n ≥ 1, pk,j
+n+1(m, x; t) := Ik,j[pn](m, x; t). Let us
+denote the operator
+I := −
+�
+j=α,β;k=m,1,...,d
+Ik,j.
+(33)
+Moreover
+one remarks that this means pn+1 = I(pn) and Proposition 4.2 leads to
+pV = p0 + I(pV ). Let
+Pn :=
+n
+�
+k=0
+pk,
+n ≥ 0
+(34)
+Proposition 4.3. Assume the vector B is bounded, then for all T the sequence (Pn)n
+converges in L∞([0, T ], L1(Rd+1, dxdm)) to pV . Moreover pV = �∞
+n=0 pn.
+The proof is a consequence of the two following lemmas.
+Lemma 4.2. Let j = α, β, k = m, 1, · · · , d and T > 0 the linear applications Ik,j are
+continuous on L∞([0, T ], dt, L1(Rd+1, dmdx)) : there exists a constant C such that for
+all p ∈ L∞([0, T ], dt, L1(Rd+1, dmdx)) :
+sup
+s∈[0,t]
+∥Ik,j[p](., .; s)∥L1(Rd+1,dmdx) ≤ C
+� t
+0
+1
+√t − s sup
+u∈[0,s]
+∥p(., .; u)∥L1(Rd+1,dmdx)ds
+(35)
+As a consequence,
+sup
+s∈[0,t]
+∥I[p](., .; s)∥L1(Rd+1,dmdx) ≤ 2(d+1)C
+� t
+0
+1
+√t − s sup
+u∈[0,s]
+∥p(., .; u)∥L1(Rd+1,dmdx)ds.
+(36)
+Proof. Let T > 0, p ∈ L∞([0, T ] × L1(Rd+1, dmdx)) and t ∈ [0, T ] and let φd+1 be
+the Gaussian law density restrained to the subset {b > a1
++} (up to a constant)
+φd+1(b, b − a1, ˜a; 2t) :=
+1
+√
+2πt
+d+1 1b>a1
++e− b2+(b−a1)2+∥˜a∥2
+4t
+.
+(37)
+(i) Let j = α and k = m, 1, · · · , d, according to the definition of Ik,α and the
+boundedness of B,
+��Ik,α[p](m, x; t)
+�� ≤ ∥B∥∞
+� t
+0
+�
+Rd+1 1b<m|∂kpW ∗1,W
+�
+m − a1, x − a; t − s
+�
+p(b, a; s)|dbdads.
+
+24
+AUTHOR NAMES
+Using Lemma A.2 there exists a constant D such that for k = m, 1, · · · , d:
+|∂kpW ∗1,W (b, a; t) | ≤ D
+√
+tφd+1(b, b − a1, ˜a; 2t).
+(38)
+So
+��Ik,α[p](m, x; t)
+�� ≤ ∥B∥∞
+� t
+0
+�
+Rd+1
+D
+√t − sφd+1(m − a1, m − x1, ˜x − ˜a; t − s)|p(b, a; s)|dbdads.
+We operate an integration with respect to (m, x) using Tonelli’s theorem and omitting
+the
+indicator functions.
+Since φd+1 is the density of a Gaussian law, we get the
+following bound,
+��Ik,α[p](., .; t)
+��
+L1(Rd+1,dmdx) ≤D∥B∥∞
+� t
+0
+�
+Rd+1
+1
+√t − s|p(b, a; s)|dbdads
+≤2(d+1)/2D∥B∥∞
+� t
+0
+1
+√t − s sup
+u≤s
+∥p(., .; u)∥L1(Rd+1,dbda)ds,
+meaning inequality (35) when j = α.
+(ii) Let j = β and k = m, 1, · · · , d. According to the definition of Ik,β and the
+boundedness of B,
+��Ik,β[p](m, x; t)
+�� ≤ ∥B∥∞
+� t
+0
+�
+Rd+1 1b<m|∂kpW ∗1,W
+�
+b − a1, x − a; t − s
+�
+p(m, a; s)|dbdads.
+Using (38) yields:
+��Ik,β[p](m, x; t)
+�� ≤ ∥B∥∞
+� t
+0
+�
+Rd+1
+D
+√t − sφd+1(b−a1, b−x1, ˜x−˜a; 2(t−s))|p(m, a; s)|dbdads.
+We operate an integration with respect to x then to b using Tonelli’s theorem and
+omitting the indicator functions and using that φ is the density of a Gaussian law. So
+the bound with respect to a multiplicative constant:
+��Ik,β[p](., .; t)
+��
+L1(Rd+1,dmdx) ≤D∥B∥∞2(d+1)/2
+� t
+0
+�
+Rd+1
+1
+√t − s|p(m, a; s)|dmdads
+≤D∥B∥∞2(d+1)/2
+� t
+0
+1
+√t − s sup
+u≤s
+∥p(., .; u)∥L1(Rd+1,dmda)ds,
+meaning inequality (35) for j = β.
+Finally, estimation (36) is obtained by adding estimations (35) for j = α, β and
+k = m, 1, ..., d.
+•
+The following lemma is a consequence of (36) in Lemma 4.2:
+
+PDE for the joint law of the pair of a continuous diffusion and its running maximum
+25
+Lemma 4.3. For all n
+sup
+u≤t
+∥pn(., .; u)∥L1(Rd+1,dmdx) ≤ (2(d + 1)C)ntn/2
+Γ(1/2)n
+Γ(1 + n/2),
+(39)
+sup
+u≤t
+∥(pV − Pn)(., .; u)∥L1(Rd+1,dmdx) ≤ (2(d + 1)C)n+1t(n+1)/2 Γ(1/2)n+1
+Γ((n + 3)/2).
+(40)
+Proof. (i) For all t > 0, p0(.; t) is a density of probability, so (39) is satisfied for
+n = 0. We now assume that (39) is satisfied for n. Using pn+1 = I[pn], (36) and the
+induction e assumption:
+sup
+u≤t
+∥pn+1(., .; u)∥L1(Rd+1,dmdx) ≤ (2(d + 1)C)n+1
+Γ(1/2)n
+Γ(1 + n/2)
+� t
+0
+√
+sn
+√t − sds.
+We operate the change of variable s = tu and use
+� 1
+0 ua−1(1 − u)b−1du = Γ(a)Γ(b)
+Γ(a+b) :
+sup
+u≤t
+∥pn+1(., .; u)∥L1(Rd+1,dmdx) ≤ (2(d + 1)C)n+1t(n+1)/2
+Γ(1/2)n
+Γ(1 + n/2)
+Γ(1/2)Γ(1 + n/2)
+Γ((n + 3)/2)
+which proves (39) for all n.
+(ii) Noting that P0 = p0 and pV − p0 = I[pV ] and applying (36) to pV yield
+sup
+u≤t
+∥(pV − P0)(., .; u)∥L1(Rd+1,dmdx) ≤ 2(d + 1)Ct1/2.
+But Γ(1/2)/Γ(3/2) = 2 so (40) is satisfied for n = 0.
+We now suppose that (40) is satisfied for n. Using pV − Pn+1 =
+p0 +I(pV )−(p0+I(Pn)) = I(pV −Pn), the bound (36) and the induction assumption:
+sup
+u≤t
+∥[pV − Pn+1](., .; u)∥L1(Rd+1,dmdx) ≤ 2(d + 1)C
+� t
+0
+(2(d + 1)C)n+1 Γ(1/2)n+1
+Γ((3 + n)/2)
+√
+sn+1
+√t − sds.
+We now operate the change of variable s = tu and
+� 1
+0 ua−1(1 − u)b−1du = Γ(a)Γ(b)
+Γ(a+b)
+with a = (n + 3)/2, b = 1
+2:
+sup
+u≤t
+∥[pV − Pn+1](., .; u)∥L1(Rd+1,dmdx) ≤ (2(d + 1)C)n+2t(n+2)/2 Γ(1/2)n+2
+Γ((4 + n)/2)
+which proves (40) for n + 1 and thus for all n.
+□
+The series �
+n
+xn
+Γ(n/2+1) is convergent for any x, so Proposition 4.3 is a consequence
+of lemmas 4.2 and 4.3.
+
+26
+AUTHOR NAMES
+4.2.1. Upper Bound of pV meaning Hypothesis 2.1 (i).
+For all T > 0, x0 ∈ Rd, p ∈ L∞([0, T ], L1(Rd+1, dmdx)) the support of which being
+included in {(m, x),
+m > x1
+0, m > x1} let us denote
+N(p; t, x0) :=
+sup
+(m,x)∈Rd+1,
+m>x1,m>x1
+0
+|p(m, x; t)|
+φd+1(m − x1
+0, m − x1, ˜x − ˜x0; 2t).
+(41)
+Proposition 4.4. For all T > 0 there exists a constant CT and for all n there exists
+constants Cn = [∥B∥∞D(2(d+1))2d/2Γ(1/2)]
+n
+Γ(1+n/2)
+such that: for all x0 ∈ Rd, 0 < t ≤ T,
+(i)
+|pn(m, x; t, x0)| ≤ Cntn/2φd+1(m − x1
+0, m − x1, ˜x − ˜x0, 2t)1m>max(x1,x1
+0)
+(ii) |pV (m, x; t, x0)| ≤ CT φd+1(m − x1
+0, m − x1, ˜x − ˜x0, 2t)1m>max(x1,x1
+0)
+(iii) For all µ0 initial probability measure on Rd,
+supu>0 pV (m, m − u, ˜x, t; µ0) ∈ L1([0, T ] × Rd, dtdmd˜x).
+Remark that, actually, this point (iii) is Hypothesis 2.1 (i).
+Proof. Point (ii) is a consequence of point (i), since pV = �∞
+n=0 pn, and the series
+�
+n
+1
+Γ(1+n/2)xn admits an infinite radius of convergence (Proposition 4.3).
+We prove point (i) by induction on n using point (ii) in Lemma A.2: p0(m, x; t, x0) ≤
+e− (m−x1)2
+4t
+− ∥˜x−˜x0∥2
+4t
+−
+(m−x1
+0)2
+4t
+�
+(2π)d+1td+1
+1m>max(x1,x1
+0) = φd+1(m − x1, m − x1
+0, ˜x − ˜x0; 2t)1m>max(x1,x1
+0),
+so N(p0; t, x0) ≤ 1, which is (i) for n = 0, C0 = 1.
+We assume point (i) is true for pn, meaning N(pn; t, x0) ≤ Cntn/2. By definition
+pn+1 = I[pn], Lemma 4.4 proved below yields:
+N(pn+1; t, x0) = N(I[pn]; t, x0) ≤ 2(d + 1)2d/2∥B∥∞DCn
+� t
+0
+sn/2
+�
+2π(t − s)
+ds.
+We operate the change of variable s = tu
+N(pn+1; t, x0) ≤ 2(d + 1)2d/2∥B∥∞D
+√
+2π
+Cn(
+√
+t)n+1
+� 1
+0
+un/2
+√1 − uds
+Using
+� 1
+0
+un/2
+√1−udu = Γ((n+2)/2)Γ(1/2)
+Γ((n+3)/2)
+and Cn definition:
+N(pn+1; t, x0) ≤ Cn+1(
+√
+t)n+1,
+
+PDE for the joint law of the pair of a continuous diffusion and its running maximum
+27
+this achieves the proof of point (i) in Proposition 4.4.
+(iii) Then for all x0 ∈ Rd and using x1 = m − u,
+sup
+u>0
+pV (m, m − u, ˜x; t) ≤ CT φd+1(m − x1
+0, 0, ˜x − ˜x0; 2t) ∈ L1([0, T ] × Rd, dtdmd˜x).
+Since pV (m, x; t, µ0) =
+�
+Rd pV (m, x; t, x0)µ0(dx0) point (iii) is true.
+□
+Lemma 4.4. Let T > 0, x0 ∈ Rd, p ∈ L∞([0, T ], dt, L1(Rd+1, dmdx)) such that the
+support of p(., .; t) is included in {(m, x),
+m > x1
+0, m > x1} and for all s ∈]0, T ]
+N(p; s, x0) < ∞. Then for j = α, k = m, 1, . . . , d, the support of function Ij,k[p](.; t)
+is included in {(m, x),
+m > x1
+0, m > x1}. Moreover for all t ∈ [0, T ] we have :
+N(I[p]; t, x0) ≤ 2(d + 1)2d/2∥B∥∞D
+� t
+0
+1
+�
+2π(t − s)
+N(p; s, x0)ds,
+∀t ∈ [0, T ].
+Proof. Let T > 0, x0 ∈ Rd, p ∈ L∞([0, T ], dt, L1(Rd+1, dmdx)) such that for all
+t > 0 the support of p(.; t) is included in {(m, x),
+m > x1
+0, m > x1}.
+(i) For j = α, k = m, 1, · · · , d, using the definition of Iα,k yields:
+Ik,α[p](m, x; t) :=
+� t
+0
+�
+Rd+1 Bk(a)∂kpW ∗1,W
+�
+m − a1, x − a; t − s
+�
+1x1
+0<b<m,m>x1p(b, a; s)dbdads
+So the support of Iα,k[p](.; t) is included in {(m, x) ∈ Rd+1, m > max(x1
+0, x1)}. For
+now on, we only consider (m, x) such that m > max(x1, x1
+0).
+Let p be a function such that ∀s ∈]0, T ] N(p; x0, s) < ∞. The definition of Ik,α,
+the boundedness of B, the fact that ∂kpW ∗,W satisfies (38) and the definition (41) of
+N(p; t, x0) imply
+��Ik,α[p](m, x; t)
+�� ≤ ∥B∥∞
+� t
+0
+�
+Rd+1 N(p; s, x0)
+D
+�
+(t − s)
+1m>x11m>b>max(a1,x1
+0)
+φd+1(m − a1, m − x1, ˜x − ˜a; t − s)φd+1(b − x1
+0, b − a1, ˜a − ˜x0; s)dbdads.
+We integrate in ˜a using Lemme A.3 (ii) with u = ˜x, v = ˜a, w = ˜x0 and the fact that
+φd+1 is a Gaussian density of probability:
+��Iα,k[p](m, x; t)
+�� ≤ 2(d−1)/2∥B∥∞D
+(42)
+� t
+0
+�
+R2 N(p; s, x0)1m>b>max(a1,x1
+0)
+e− ∥˜x− ˜
+x0∥2
+4t
+�
+(2πt)d−1
+e− (m−a1)2
+4(t−s) − (m−x1)2
+4(t−s)
+�
+(2π)2(t − s)3
+e−
+(b−x1
+0)2
+4s
+− (b−a1)2
+4s
+�
+(2π)2s2
+dbda1ds.
+
+28
+AUTHOR NAMES
+Using point (i’) Lemma A.2 with u = m, v = a1, w = b, k = 1, we integrate in da1 up
+to b:
+� b
+−∞
+e− (m−a1)2
+4(t−s)
+�
+2π(t − s)
+e− (b−a1)2
+4s
+�
+(2πs)
+da1 = e
+−(m−b)2
+4t
+√
+2πt
+ΦG
+��
+s
+2t(t − s)(b − m)
+�
+where ΦG(u) =
+� u
+−∞ e−z2/2dz ≤ 1
+2e−u2/2 for u = b − m < 0 according to Lemma A.3
+(iii). This yields the bound:
+e
+−(m−b)2
+4t
+√
+2πt
+e− s(b−m)2
+4t(t−s) and
+2
+� b
+−∞
+e− (m−a1)2
+4(t−s)
+�
+2π(t − s)
+e− (b−a1)2
+4s
+�
+(2πs)
+da1 ≤ e− (m−b)2
+4t
+√
+2πt
+e− s(m−b)2
+4t(t−s) = e− (m−b)2
+4(t−s)
+√
+2πt
+.
+Plugging this inequality inside (42) yields with Cd,B = 2(d+1)/2∥B∥∞D
+��Iα,k[p](m, x; t)
+��
+Cd,B
+≤
+� t
+0
+�
+R
+N(p; s, x0)1m>b>x1
+0
+e− ∥˜x− ˜
+x0∥2
+4t
+�
+(2πt)d
+e− (m−b)2
+4(t−s) − (m−x1)2
+4(t−s)
+�
+2π(t − s)2s
+e−
+(b−x1
+0)2
+4s
+dbds.
+Omitting the indicator functions, Lemma A.3 (ii) with u = m, v = b, w = x1
+0, k = 1
+implies
+�
+b<m
+e− (m−b)2
+4(t−s) e−
+(b−x1
+0)2
+4s
+�
+2π(t − s)2πs
+db ≤
+�
+2
+2πte−
+(m−x1
+0)2
+4t
+.
+Inserting this result, we obtain
+��Iα,k[p](m, x; t)
+�� ≤
+√
+2Cd,B
+� t
+0
+N(p; s, x0) e− ∥˜x− ˜
+x0∥2
+4t
+�
+(2πt)d+1
+e−
+(m−x1
+0)2
+4t
+− (m−x1)2
+4(t−s)
+�
+2π(t − s)
+ds.
+For 0 < s < t, e− (m−x1)2
+4(t−s)
+≤ e− (m−x1)2
+4t
+, so
+��Iα,k[p](m, x; t)
+�� ≤
+√
+2Cd,B
+� t
+0
+N(p; s, x0) e− ∥˜x− ˜
+x0∥2
+4t
+�
+(2πt)d+1
+e−
+(m−x1
+0)2
+4t
+− (m−x1)2
+4t
+�
+2π(t − s)
+ds.
+Using the definition of φd+1 we identify
+��Iα,k[p](m, x; t)
+�� ≤
+√
+2Cd,B
+� t
+0
+N(p; s, x0)φd+1(m − x1
+0, m − x1, ˜x − ˜x0; 2t)
+�
+2π(t − s)
+ds
+and with the definition of N, with respect to a multiplicative constant:
+N(Iα,k[p], x0, t) ≤
+√
+2Cd,B
+� t
+0
+N(p; s, x0)
+1
+�
+2π(t − s)
+ds.
+(ii) For j = β, k = m, 1, · · · , d using the definition of Iβ,k and the fact that the support
+of p is included in {(m, x),
+m > max(x1
+0, x1)} yields Iβ,k[p](m, x; t) =
+� t
+0
+�
+Rd+1 1m>b>x1,m>x1
+0,b>a1Bk(a)∂kpW 1∗,W (b − a1, x − a, t − s)p(m, a, s)dadbds.
+
+PDE for the joint law of the pair of a continuous diffusion and its running maximum
+29
+Thus the support of Iβ,k[p](.; t) is included in {(m, x), m > max(x1, x0)}. For now on
+we only consider (m, x) satisfying m > max(x1, x1
+0). Definition of Iβ,k, the boundedness
+of B, the inequality (38) satisfied by ∂kpW ∗,W :
+|∂kpW 1∗,W (b − a1, x − a, t − s)| ≤
+D
+√t−sφd+1(b − a1, b − x1, ˜x − ˜a, 2(t − s))
+and the definition of N(p; t, x0) yield:
+��Iβ,k[p](m, x; t)
+�� ≤ ∥B∥∞D
+� t
+0
+�
+Rd+1 1m>b>x1,b>a1N(p; s, x0)
+e− (b−a1)2
+4(t−s) − (b−x1)2
+4(t−s) − ∥˜x−˜a∥2
+4(t−s)
+�
+(2π)d+1(t − s)d+2
+e−
+(m−x1
+0)2
+4s
+− (m−a1)2
+4s
+− ∥˜x0−˜a∥2
+4s
+�
+(2π)d+1sd+1
+dadbds.
+We integrate in ˜a using Lemma A.3 (ii) with u = ˜x, v = ˜a et w = ˜x0:
+��Iβ,k[p](m, x; t)
+�� ≤ Cd,B.
+(43)
+� t
+0
+�
+R2 1m>b>x1,b>a1 e− ∥˜x−˜x0∥2
+4t
+�
+(2πt)d−1 N(p; s, x0).e− (b−a1)2
+4(t−s) − (b−x1)2
+4(t−s)
+�
+(2π)2(t − s)3
+e−
+(m−x1
+0)2
+4s
+− (m−a1)2
+4s
+�
+(2π)2s2
+da1dbds.
+Using Lemma A.3 (i’) for u = b, v = a1, w = m k = 1
+� b
+−∞
+e− (b−a1)2
+4(t−s)
+�
+2π(t − s)
+e− (m−a1)2
+4s
+√
+2πs
+da1 =
+√
+2e− (b−m)2
+4t
+√
+2πt
+ΦG
+��
+t
+4s(t − s)[b − (s
+t b + t − s
+t
+m)]
+�
+= e− (b−m)2
+4t
+√
+2πt
+ΦG
+��
+t − s
+4st [b − m]
+�
+≤ e− (b−m)2
+4t
+√
+2πt
+e− t−s
+4st [b−m]2 = e− (b−m)2
+4s
+√
+2πt
+the last bound coming from Lemma A.3 (iii) since b − m < 0.
+We plugg this estimation in (43)
+��Iβ,k[p](m, x; t)
+�� ≤
+Cd,B
+� t
+0
+�
+R
+1m>b>x1 e− ∥˜x−˜x0∥2
+4t
+�
+(2πt)d N(p; s, x0)
+e− (b−x1)2
+4(t−s)
+�
+2π(t − s)2
+e−
+(m−x1
+0)2
+4s
+− (b−m)2
+4s
+√
+2πs
+dbds.
+We integrate with respect to b on R and we use Lemma A.3 (ii) with u = x1, v = b,
+w = m, k = 1:
+��Iβ,k[p](m, x; t)
+�� ≤
+√
+2Cd,B
+� t
+0
+e− (m−x1)2
+4t
+− ∥˜x−˜x0∥2
+4t
+�
+(2πt)d+1
+N(p; s, x0) e−
+(m−x1
+0)2
+4s
+�
+2π(t − s)
+ds.
+When 0 < s < t, e−
+(m−x1
+0)2
+4s
+≤ e−
+(m−x1
+0)2
+4t
+so:
+��Iβ,k[p](m, x; t)
+�� ≤
+√
+2Cd,B
+� t
+0
+e− (m−x1)2
+4t
+− ∥˜x−˜x0∥2
+4t
+−
+(m−x1
+0)2
+4t
+�
+(2πt)d+1
+N(p; s, x0)
+1
+�
+2π(t − s)
+ds.
+
+30
+AUTHOR NAMES
+Under the integral we identify the factor φd+1(m − x1
+0, m − x1, ˜x − ˜x0; 2t) so
+��Iβ,k[p](m, x; t)
+�� ≤
+√
+2Cd,Bφd+1(m − x1
+0, m − x1, ˜x − ˜x0; 2t)
+� t
+0
+N(p; s, x0)
+1
+�
+2π(t − s)
+dbds.
+Finally using the definition of N (41) we have proved
+N(Iβ,k[p], x0, t) ≤
+√
+2Cd,B
+� t
+0
+N(p; s, x0)
+1
+�
+2π(t − s)
+ds
+which achieves the proof of Lemma 4.4.
+□
+4.2.2. Proof of Hypothesis 2.1 (ii), case A = Id
+Proposition 4.5. For any µ0 probability measure on Rd, for all (m, ˜x, t) ∈ Rd×]0, T ],
+u �→ pV (m, m − u, ˜x, t) admits a limit when u goes to 0, u > 0.
+Proof. The proof is a consequence of the three following lemmas.
+Lemma 4.5. Recall that p0(m, x; t) = �
+Rd pW ∗1,W (m − x1
+0, x − x0; t)µ0(dx0).
+lim
+u→0,u>0 p0(b, b − u, ˜a; t) = p0(b, b, ˜a; t),
+∀u > 0,
+(b, ˜a) ∈ Rd, ∀t > 0.
+Proof. We have p0(b, b−u, ˜x; t) =
+�
+Rd2
+b+u−x1
+0
+√
+(2π)dtd+1 e−
+(b+u−x1
+0)2
+2t
+− ∥˜x−˜x0∥2
+2t
+1b≥x1
+0,
+u≥0µ0(dx0).
+Then, since the integrand is dominated by
+D
+√
+(2π)dtd+1 and µ0 is a probability measure,
+using Lebesgue’s dominated convergence Theorem yields:
+lim
+u→0,u>0 p0(b, b − u, ˜x; t) = p0(b, b, ˜x; t),
+∀ (b, ˜x) ∈ Rd, ∀t > 0.
+□
+Lemma 4.6. For k = m, 1, ..., d recall that
+pk,α(m, x; t) =
+� t
+0
+�
+Rd+1 1b<mBk(a)∂kpW ∗1,W (m − a1, x − a, t − s)pV (b, a; s)dbdads.
+The map u �→ pk,α(m, m − u, ˜x; t) converges to pk,α(m, m, ˜x; t) when u goes to 0+.
+Proof. The proof wil be a consequence of Lebesgue dominated theorem. First, the
+map u �→ 1b<m∂kpW ∗1,W (m − a1, m − u − a1, ˜x − ˜a; t − s)pV (b, a; s) converges to
+1b<m∂kpW ∗1,W (m − a1, ma1, ˜x − ˜a; t − s)pV (b, a; s) when u goes to 0+.
+Second it is dominated by qk,α(m, ˜x, a, b; s, x0) :=
+|Bk(a)|1b<m sup
+u>0
+��∂kpW ∗1,W (m − a1, m − u − a1, ˜x − ˜a; t − s)pV (b, a; s, x0)
+��
+
+PDE for the joint law of the pair of a continuous diffusion and its running maximum
+31
+We seek to prove that
+� T
+0
+�
+R2d+1 qk,α(m, ˜x, a, b; s, x0)dsdbdaµ0(dx0) < +∞.
+(44)
+According to estimation (38) of ∂kpW ∗1,W and estimation (ii) of Proposition 4.4, we
+obtain
+qk,α(m, ˜x, a, b; s, x0) ≤ ∥B∥∞1m>b>a1
+D
+√t − s
+�
+2π(t − s)
+d+1 exp[−(m − a1)2
+4(t − s)
+− ∥˜x − ˜a∥2
+4(t − s) ]
+CT
+√
+2πs
+d+1 exp[−(b − x1
+0)2
+4s
+− (b − a1)
+4s
+− ∥˜x0 − ˜a∥2
+4s
+].
+We integrate with respect to ˜a using Lemma A.3 (ii) for k = d + 1, u = ˜x, v = ˜a and
+w = ˜x0 :
+�
+Rd−1 qk,α(m, ˜x, a1, b; s, x1
+0)d˜a ≤ 1m>b>a1
+∥B∥∞CT D2(d−1)/2
+√t − s
+�
+2π(t − s)
+2√
+2πs
+2
+e− |˜x−˜x0∥2
+4t
+√
+2πt
+d−1
+exp[−(m − a1)2
+4(t − s)
+− (b − x1
+0)2
+4s
+− (b − a1)2
+4s
+].
+We integrate with respect to a1 between −∞ and b using Lemma A.3 (i’) for u = m,
+v = a1 and w = b
+�
+Rd 1a1<bqk,α(m, ˜x, b, a; s; x0)da ≤ 1b<m
+∥B∥∞CT D2d/2
+√t − s
+�
+2π(t − s)
+√
+2πs
+e− |˜x−˜x0∥2
+4t
+− (b−m)2
+4t
+√
+2πt
+d
+exp[−(b − x1
+0)2
+4s
+]ΦG
+��
+t
+2s(t − s)(b − [s
+t m + (t − s)
+t
+b])
+�
+.
+Note that
+�
+t
+2s(t−s)(b − [ s
+t m + (t−s)
+t
+b]) =
+�
+s
+2t(t−s)(b − m) and using Lemma A.3 (iii)
+�
+Rd qk,α(m, ˜x, b, a; s, x0)da ≤ 1b<m
+∥B∥∞CT D2d/2
+√t − s
+�
+2π(t − s)
+√
+2πs
+e− |˜x−˜x0∥2
+4t
+− (b−m)2
+4t
+√
+2πt
+d
+exp[−(b − x1
+0)2
+4s
+] exp[−
+s
+t(t − s)
+(b − m)2
+4
+].
+We observe that 1
+t +
+s
+t(t−s) =
+1
+t−s so that exp[− (b−m)2
+4t
+] exp[−
+s
+t(t−s)
+(b−m)2
+4
+] = exp[− (b−m)2
+4(t−s) ].
+We integrate with respect to b (neglecting the indicator function) using Lemma A.3
+(ii) for u = m, v = b and w = x1
+0 and exp[− (m−x1
+0)2
+4t
+] ≤ 1:
+�
+Rd+1 qk,α(m, ˜x, b, a; s, x0)dadb ≤ 1m>x1
+0
+∥B∥∞CT D2(d+1)/2
+√t − s
+e− |˜x−˜x0∥2
+4t
+√
+t
+d+1
+.
+
+32
+AUTHOR NAMES
+Since µ0 is a probability measure then
+� t
+0
+�
+R2d+1 qk,α(m, ˜x, b, a; s, x0)dadbµ0(dx0)ds <
++∞.
+This is (44) and achieves the proof of Lemma 4.6
+□
+Lemma 4.7. For k = m, 1, ..., d recall that
+pk,β(m, x; t) =
+� t
+0
+�
+Rd+1 1b<mBk(a)∂kpW ∗1,W (b − a1, x − a, t − s)pV (m, a; s)dbdads.
+The map u �→ pk,β(m, m − u, ˜x; t) converges to 0 when u goes to 0+.
+Proof. Using estimation (38) of ∂kpW ∗1,W and estimation (ii) of Proposition 4.4
+concerning pV , we dominate the integrand which defines pk,β(m, m − u, ˜x; t) by :
+qk,β(m, u, ˜x, a, b, x0, s) :=
+1m−u<b<m,a1<b
+e− (b−a1)2
+4(t−s) − (b−m+u)2
+4(t−s)
+− ∥˜x−˜a∥2
+4(t−s) −
+(m−x1
+0)2
+4s
+− (m−a1)
+4s
+− ∥˜x0−˜a∥2
+4s
+√t − s
+�
+2π(t − s)
+d+1√
+2πs
+d+1
+up to a multiplicative constant. Meaning that
+��pk,β(m, m − u, ˜x; t)
+�� ≤ ∥B∥∞
+� t
+0
+�
+R2d+1 qk,β(m, u, ˜x, a, b, x0, s)dbdadsµ0(dx0).
+(45)
+We integrate with respect to ˜a using Lemma A.3 (ii) with u = ˜x, v = ˜a and w = ˜x0
+�
+Rd−1 qk,β(m, u, ˜x, a, b, x0, s)d˜a ≤
+√
+2
+d−1 e− ∥˜x−˜x0∥2
+4t
+√
+2πt
+d−1
+e− (b−a1)2
+4(t−s) − (b−m+u)2
+4(t−s)
+−
+(m−x1
+0)2
+4s
+− (m−a1)
+4s
+√t − s
+�
+2π(t − s)
+2√
+2πs
+2
+We integrate with respect to a1 between −∞ and b using Lemma A.3 (i’) for u = b,
+v = a1 and w = m :
+�
+Rd 1b>a1qk,β(m, u, ˜x, a, b, x0, s)da ≤
+e− ∥˜x−˜x0∥2
+4t
+√
+2πt
+d
+e− (b−m)2
+4t
+− (b−m+u)2
+4(t−s)
+−
+(m−x1
+0)2
+4s
+√t − s
+�
+2π(t − s)
+√
+2πs
+ΦG
+��
+t
+s(t − s)2(b − s
+t b − t − s
+t
+m)
+�
+= e− ∥˜x−˜x0∥2
+4t
+√
+2πt
+d
+e− (b−m)2
+4t
+− (b−m+u)2
+4(t−s)
+−
+(m−x1
+0)2
+4s
+√t − s
+�
+2π(t − s)
+√
+2πs
+ΦG
+��
+t − s
+2st (b − m)
+�
+.
+Since b − m < 0, using Lemma A.3 (iii)
+�
+Rd 1b>a1qk,β(m, u, ˜x, a, b, x0, s)da ≤ e− ∥˜x−˜x0∥2
+4t
+√
+2πt
+d
+e− (b−m)2
+4t
+− (b−m+u)2
+4(t−s)
+−
+(m−x1
+0)2
+4s
+√t − s
+�
+2π(t − s)
+√
+2πs
+e− t−s
+4st (b−m)2.
+
+PDE for the joint law of the pair of a continuous diffusion and its running maximum
+33
+Note that e− (b−m)2
+4t
+e− t−s
+4st (b−m)2) = e− (b−m)2)
+4s
+. We integrate this last bound with respect
+to b between m − u and m using Lemma A.3 (i’) for the triplet (m − u, b, m) and the
+fact that s
+t (m − u) + t−s
+t m = s(m−u)+m(t−s)
+t
+�
+Rd+1 1m−u<b<m,b<a1qk,β(m, u, ˜x, a, b, x0, s)dadb ≤ e− ∥˜x−˜x0∥2
+4t
+√
+2πtd+1
+e− (m−x1
+0)2
+4s
+√t−s
+.
+�
+ΦG
+��
+t
+2s(t−s)(m − s(m−u)+m(t−s)
+t
+)
+�
+− ΦG
+��
+t
+2s(t−s)(m − u − s(m−u)+m(t−s)
+t
+)
+��
+.
+Then,
+�
+Rd+1 qk,β(m, u, ˜x, a, b, x0, s)dadb ≤
+e− ∥˜x−˜x0∥2
+4t
+√
+2πt
+d+1
+e−
+(m−x1
+0)2
+4s
+√t − s
+�
+ΦG
+��
+s
+2t(t − s)u
+�
+− ΦG
+�
+−
+�
+t − s
+2t(t − s)u
+��
+.
+Note that limu→0 ΦG
+��
+s
+2t(t−s)u
+�
+− ΦG
+�
+−
+�
+t−s
+2t(t−s)u
+�
+= 0 and
+����ΦG
+��
+s
+2t(t−s)u
+�
+− ΦG
+�
+−
+�
+t−s
+2t(t−s)u
+����� ≤ 1. Since µ is a probability measure, using
+Lebesgue dominated theorem
+lim
+u→0+
+� t
+0
+�
+R2d+1 1m−u<b<m,b<a1qk,β(m, u, ˜x, a, b, x0, s)dadbµ0(dx0)ds = 0.
+Finally estimation (45) yields limu→0+ pk,β(m, m − u, ˜x; t) = 0.
+□
+5. Cas d = 1
+Proposition 5.1. Let the real diffusion X given by dXt = B(Xt)dt+A(Xt)dWt where
+A, B fulfil (4) and (5). Then the density of probability pV satisfies Hypothesis 2.1, so
+for any initial law µ0 and F ∈ C2
+b (R2, R),
+E [F(Mt, Xt)) = E [F(X0, X0)] +
+� t
+0
+E [L (F) (Ms, Xs)] ds
++ 1
+2
+� t
+0
+E
+�
+∂mF(Xs, Xs)∥A(Xs)∥2 pV (Xs, Xs; s)
+pX(Xs; s)
+�
+ds.
+(46)
+Proof. We operate a Lamperti transformation [18]. Whithout loss of generality, A
+can be choosen positive. In case d = 1 Assumption (5): “∃c > 0 such that for any
+x ∈ R, A2(x) ≥ c” could be expressed:
+∃c > 0 such that for any x ∈ R, A(x) ≥ c.
+(47)
+
+34
+AUTHOR NAMES
+Let ϕ such that ϕ′ = 1
+A and ϕ(0) = 0, so that ϕ′ is uniformly bounded and ϕ ∈ C2(R),
+as is the function A. Moreover ϕ′ being strictly positive, ϕ is strictly increasing hence
+invertible and we denote by ϕ−1 its inverse function.
+Under the initial condition
+ϕ(0) = 0, using Itˆo formula Y = ϕ(X) satisfies
+dYt =
+�B
+A ◦ ϕ−1(Yt) − 1
+2A′ ◦ ϕ−1(Yt)
+�
+dt + dWt, Y0 = ϕ(X0).
+(48)
+Let Aϕ = 1 and Bϕ := B
+A ◦ϕ−1− 1
+2A′◦ϕ−1 which belongs to C1
+b (R) as a consequence
+of B ∈ C1
+b , A ∈ C2
+b . Obviously, ϕ′ > 0 implies that ϕ is increasing, Y ∗
+t = ϕ(X∗
+t ) =
+ϕ(Mt).
+Theorem 1.1 in [9] can be easily extended to the case where X admits an initial law
+µ0, thus the law of the pair (Y ∗
+t , Yt) admits a density with respect to the Lebesgue
+measure.
+Moreover, Lemma 2.2 in [9] sets out pV (b, a; t) =
+pY ∗,Y (ϕ(b),ϕ(a);t)
+A(b)A(a)
+. Now
+applying Theorem 2.4 to the pair (Bϕ, 1) the density pY ∗,Y satisfies Hypothesis 2.1.
+Since functions A and ϕ are continuous
+lim
+u→0+ pV (b, b − u; t) = pY ∗,Y (ϕ(b), ϕ(b); t)
+A2(b)
+that means pV satisfies Hypothesis 2.1 (ii).
+Using now (47)
+sup
+u>0
+pV (b, b − u; t) ≤ 1
+c2 sup
+u>0
+pY ∗,Y (ϕ(b), ϕ(b − u); t)
+and since ϕ is increasing, if u > 0, ϕ(b − u) < ϕ(b) and denoting v = ϕ(b) − ϕ(b − u)
+it gets v > 0, and
+sup
+u>0
+pV (b, b − u; t) ≤ 1
+c2 sup
+v>0
+pY ∗,Y (ϕ(b), ϕ(b) − v; t).
+After the change of variable m = ϕ(b) so db = A(b)dm,
+� T
+0
+�
+R
+sup
+u>0
+pY ∗,Y (ϕ(b), ϕ(b)−u; t)dbdt =
+� T
+0
+�
+R
+A(ϕ−1(m)) sup
+u>0
+pY ∗,Y (m, m−u; t)dmdt.
+Since A is bounded and pY ∗,Y satisfies Hypothesis 2.1 (i),
+� T
+0
+�
+R A(ϕ−1(m)) supu>0 pY ∗,Y (m, m − u; t)dmdt < ∞ and pV satisfies Hypothesis 2.1
+(i) and (ii).
+□
+
+PDE for the joint law of the pair of a continuous diffusion and its running maximum
+35
+6. Conclusion
+This paper establishes a PDE of which the density of the pair [Mt, Xt] running
+maximum-diffusion process is a weak solution, under a quite natural assumption on
+the regularity of pV around the boundary of ∆. This assumption is fulfilled when the
+matrix coefficient of diffusion A is the identity matrix or when the dimension d = 1.
+This PDE is degenerated then the classical results on uniqueness cannot be applied
+here. The case of non constant matrix A is an open problem. Such generalization
+could be useful in case of practical applications, as the management of barrier options,
+in models including stochastic volatility.
+Appendix A. Tools
+A.1. Malliavin calculus tools
+The material of this subsection is taken from section 1.2 in [21].
+Let H = L2([0, T ], Rd) endowed with the usual scalar product ⟨., .⟩H and the associated
+norm ∥.∥H. For all h ∈ H, W(h) :=
+� T
+0 h(t)dWt is a center Gaussian variable with
+variance equal to ∥h∥2
+H. If (h1, h2) ∈ H2, and ⟨h1, h2⟩H = 0, then, the random variables
+W(hi), i = 1, 2, are independent.
+Let S denote the class of smooth random variables F defined by:
+F = f(W(h1), ..., W(hn)), n ∈ N,
+h1, ..., hn ∈ H, f ∈ Cb(Rn).
+(49)
+Definition 1. The derivative of the smooth variable F defined in (49) is the H valued
+random variable given by DF := �n
+i=1 ∂if(W(h1), ..., W(hn))hi.
+We denote the domain of the operator D in L2(Ω) by D1,2 meaning that D1,2 is the
+closure of the class of smooth random variables S with respect to the norm
+∥F∥1,2 =
+�
+E[|F|2] + E[∥DF∥2
+H]
+�1/2 .
+Definition 2. L1,2 is the set of processes (us, s ∈ [0, T ]) which satisfy
+u ∈ L2(Ω × [0, T ], Rd) and for all s ∈ [0, T ], us belongs to D1,2 and
+∥u∥2
+L1,2 = ∥u∥2
+L2([0,T ]×Ω) + ∥Du∥2
+L2([0,T ]2×Ω) < ∞.
+
+36
+AUTHOR NAMES
+Definition 3. Let u ∈ L1,2, then the divergence δ(u) is the unique random variable
+of L2(Ω) such that E [Fδ(u)] = E [⟨DF, u⟩H] ,
+∀F ∈ S smooth random variable.
+We apply Definition 1.3.1 in [21] with u ∈ L1,2 and G ∈ D1,2:
+E [Gδ(u)] = E [⟨DG, u⟩H] .
+(50)
+Let x0 ∈ Rd. We introduce the exponential martingale
+Zx0
+t
+:= exp
+� d
+�
+k=1
+�� t
+0
+Bk(x0+Ws)dW k
+s − 1
+2
+� t
+0
+(Bk(x0+Ws))2ds
+��
+.
+(51)
+When there is no ambiguity, we will omit the exponent x0.
+Lemma A.1. Let B ∈ C1
+b (Rd, R), then for all x0 ∈ Rd the process
+(B(x0 + Ws)Zx0
+s ,
+s ∈ [0, T ]) belongs to L1,2.
+Proof. Let x0 be fixed. In this proof we omit the exponent x0. Note that Z2
+t =
+exp
+�
+2
+d
+�
+k=1
+� t
+0
+Bk(x0 + Ws)dW k
+s − 4
+2
+� t
+0
+∥B(x0 + Ws)∥2ds + 4 − 2
+2
+� t
+0
+∥B(x0 + Ws)∥2ds
+�
+≤ eT ∥B∥2
+∞ exp
+�
+2
+d
+�
+k=1
+� t
+0
+Bk(x0 + Ws)dW k
+s − 4
+2
+� t
+0
+∥B(x0 + Ws)∥2ds
+�
+.
+Then, Zt belongs to L2(Ω) for all t ∈ [0, T ] since
+sup
+t∈[0,T ]
+E(Z2
+t ) ≤ eT ∥B∥2
+∞.
+(52)
+Note that Zt = 1 + �d
+k=1
+� t
+0 Bk(x0 + Ws)ZsdW k
+s ,
+t ∈ [0, T ]. Using Lemma 2.2.1,
+Theorem 2.2.1 of [21], and the definition of L1,2, applied to the Rd+1-valued process
+Y = (W, Z) with a null drift coefficient, the matrix Σ, (d + 1, d), defined by:
+[σj,k(y), 1 ≤ j, k ≤ d] = Id, σd+1,k(y) = Bk(x1
+0 + y1, ..., xd
+0 + yd)kz,
+k = 1, ..., d,
+we obtain that Z belongs to L1,2. Since B is continuously differentiable with bounded
+derivatives, the process (B(Ws + x0)Zs,
+s ∈ [0, T ]) belongs to L1,2.
+□
+The following remark will be often used: using line -15 page 135 of [9] or Exercise
+1.2.11 p. 36 in [21]
+D1
+sW 1∗
+t
+= 1[0,τ](s) where τ := inf{s, W 1∗
+s
+= W 1∗
+t }.
+(53)
+
+PDE for the joint law of the pair of a continuous diffusion and its running maximum
+37
+A.2. Brownian motion case estimations
+Let us recall the density of distribution of the pair (W ∗,1
+t
+, W 1
+t ), where W 1 is a one-
+dimensional Brownian motion and W ∗,1 its running maximum (see e.g., Section 3.2 in
+[17] or [15]):
+pW 1∗,W 1(b, a; t) = 2 2b − a
+√
+2πt3 exp −(2b − a)2
+2t
+1b>sup(a,0).
+Thus, using the independence of the components of the process W, the law of
+(W 1∗
+t , Wt) has a density with respect to the Lebesgue measure on Rd+1 denoted by
+pW 1∗,W (.; t) :
+pW 1∗,W (b, a; t) = 2 (2b − a1)
+�
+(2π)dtd+2 e− (2b−a1)2
+2t
+−
+�d
+k=2 |ak|2
+2t
+1b≥0,b≥a1, b ∈ R, a = (a1, ..., ad) ∈ Rd.
+(54)
+Lemma A.2. (i) For all t> 0, pW ∗1,W (.; t)
+is the restriction to ¯∆ of a C∞(Rd+1)
+function and there exists a universal constant D such that for x = b, a1, a2, ...ad,
+��∂xpW ∗1,W (b, a; t)
+�� ≤
+D
+�
+(4π)dtd+2 e− b2+(b−a1)2
+4t
+−�d
+k=2
+(ak)2
+4t 1b>max(a1,0).
+(55)
+As a consequence �
+x=b,a1,...,ad
+��∂xpW ∗1,W (b, a; t − s)
+�� ∈ L1([0, t] × Rd+1, dbdads).
+(ii) p0(m, x; t, x0) ≤
+e− (m−x1)2
+4t
+− ∥˜x−˜x0∥2
+4t
+−
+(m−x1
+0)2
+4t
+�
+(2π)d+1td+1
+1m>max(x1,x1
+0)
+=
+2(d+1)/2φd+1(m − x1, m − x1
+0, ˜x − ˜x0; 2t)1m>max(x1,x1
+0),
+Proof. (i) Let pW be the density of a d dimensional Brownian motion, and the
+density of law of Wt ∀t > 0 : pW (.; t) ∈ C∞(Rd):
+pW (x; t) =
+1
+√
+2dπdtd e− �d
+k=1
+(xk)2
+2t ,
+t > 0,
+x = (x1, ..., xd) ∈ Rd.
+Its derivative with respect to x1 is
+∂x1pW (x; t) = −
+x1
+√
+2dπdtd+2 e− �d
+k=1
+(xk)2
+2t ,
+t > 0,
+x = (x1, ..., xd) ∈ Rd.
+Its second derivatives are
+∂2
+x1xkpW (x; t) =
+x1xk
+√
+2dπdtd+4 e− �d
+k=1
+(xk)2
+2t ,
+t > 0,
+x = (x1, ..., xd) ∈ Rd,
+k = 2, ..., d.
+∂2
+x1x1pW (x; t) =
+(x1)2 − t
+√
+2dπdtd+4 e− �d
+k=1
+(xk)2
+2t ,
+t > 0,
+x = (x1, ..., xd) ∈ Rd.
+
+38
+AUTHOR NAMES
+Using (2.1) page 106 of [14] we obtain the analogous of (2.2) page 107 of [14]: there
+exists a constant C such that
+|∂2
+x1x1pW (x; t)| + |∂2
+x1xkpW (x; t)| ≤ C
+t pW (x; 2t),
+k = 1, ..., d,
+t > 0,
+x ∈ Rd.
+(56)
+Recall (54)
+pW ∗1,W (b, a; t) = 2
+2b − a1
+�
+(2π)dtd+2 e− (2b−a1)2
+2t
+−�d
+k=2
+(ak)2
+2t 1b≥a1
++,
+∀(b, a) ∈ Rd+1,
+t > 0.
+We observe
+pW ∗1,W (b, a; t) = −2∂x1pW (2b − a1, a2, ..., ad; t)1b≥a1
++.
+(57)
+Then pW ∗1,W (., .; t) is the restriction to ∆ of a C∞ function.
+Moreover, using the chain rule, x being (b, a1, · · · , ad) :
+|∂xpW ∗1,W (b, a; t)| ≤ 4C
+t pW (2b − a1, a2, ..., ad; 2t)1b≥a1
++.
+(58)
+On the set {(b, a),
+b> max(0, a1)} we have
+(2b − a1)2 = (b + b − a1)2 ≥ (b)2 + (b − a1)2.
+(59)
+Plugging estimation (59) into (58) yields (55) with D = 23C.
+(ii) Recalling the definition
+p0(m, x; t, x0) = pW 1∗,W (m−x1
+0, x−x0; t) = 2m − x1 + m − x1
+0
+�
+(2π)dtd+2
+e−
+(m−x1+m−x1
+0)2
+2t
+− |˜x−˜x0∥2
+2t
+1m≥x1∨x1
+0
+we deduce the standard bound which uses xe−x2 ≤ e−x2/2 and (m − x1 + m − x1
+0)2 ≥
+(m − x1)2 + (m − x1
+0)2:
+p0(m, x; t, x0) ≤ e− (m−x1)2
+4t
+− ∥˜x−˜x0∥2
+4t
+−
+(m−x1
+0)2
+4t
+�
+(2π)d+1td+1
+1m>x1∨x1
+0
+= 2(d+1)/2φd+1(m − x1, m − x1
+0, ˜x − ˜x0; 2t)1m>x1∨x1
+0,
+□
+
+PDE for the joint law of the pair of a continuous diffusion and its running maximum
+39
+Lemma A.3. For all 0 < s < t, k ≥ 1 and all u, v, w ∈ Rk
+(i)
+∥u − v∥2
+t − s
++ ∥v − w∥2
+s
+=
+t
+s(t − s)
+����v −
+�s
+t u + t − s
+t
+w
+�����
+2
++ ∥u − w∥2
+t
+;
+(i′) k = 1,
+� b
+−∞
+e− (u−v)2
+4(t−s)
+�
+2π(t − s)
+e− (w−v)2
+4s
+√
+2πs dv =
+√
+2e− (u−w)2
+4t
+�
+2πt)
+ΦG
+��
+t
+s(t − s)[b − (s
+t u + t − s
+t
+w)]
+�
+(ii)
+�
+Rk
+e− ∥u−v∥2
+4(t−s)
+�
+(2π(t − s))k
+e− ∥w−v∥2
+4s
+�
+(2πs)k dv = 2k/2 e− ∥u−w∥2
+4t
+�
+(2πt)k
+(iii)
+For u > 0, 1 − ΦG(u) :=
+� +∞
+u
+e− z2
+2
+√
+2π dz = ΦG(−u) ≤ e− u2
+2
+2
+.
+Proof. Point (i) is proved by a development of both hands then an identification of
+the coefficients of the squared norms and scalar products: ∥u∥2, ∥v∥2, ∥w∥2, u.v, u.w, v.w.
+So we deduce (i’) as the integral of
+e−
+t
+4s(t−s)(v−( s
+t u+ t−s
+t
+w))
+2− (u−w)2
+4t
+�
+2π(t − s)
+√
+2πs
+with respect to v up to b.
+(ii) is a consequence of point (i) then an integration on Rk of the Gaussian density
+with respect to dv.
+(iii) The function u �→ ΦG(u) − e− u2
+2
+2
+is null at 0, has a null limit when u goes to
+−∞ and its derivative is u �→ − e− u2
+2
+√
+2π + u e− u2
+2
+2
+. Its derivative vanishes at
+�
+2/π and is
+negative for u ≤
+�
+2/π and positive after. Then, u �→ ΦG(u) − e− u2
+2
+2
+is negative for
+u ≤ 0.
+□
+A.3. Proof of Remark 2.3, boundary conditions of the PDE
+Here we assume that pV is regular enough. Let µ0(dx) = f0(x)dx. Using Theorem
+2.2, (6) means that:
+for all F ∈ C2
+b (Rd+1, Rd)
+�
+¯
+∆
+F (m, x)pV (m, x; t)dmdx =
+�
+Rd F (m, m, ˜x)f0(m, ˜x)dmd˜x +
+(60)
+� t
+0
+�
+¯
+∆
+LF (m, x)pV (m, x; s)dmdxds + 1
+2
+� t
+0
+�
+Rd ∥A1(m, ˜x)∥2∂mF (m, m, ˜x)pV (m, m, ˜x; s)dmd˜xds
+recalling L = Bi∂xi + 1
+2Σij∂2
+xi,xj where Σ = AAt.
+(i) Integrating by parts with respect to a convenient dxk in
+� t
+0
+�
+¯∆LF(m, x)pV (m, x; s)dmdxds and noting that the support of pV (., .; s) is ¯∆, the
+
+40
+AUTHOR NAMES
+boundary terms uniquely concern the component x1:
+� t
+0
+�
+¯∆
+LF(m, x)pV (m, x; s)dmdxds = −
+� t
+0
+�
+¯∆
+F(m, x)∂xk(BkpV )(m, x; s)dmdxds
+− 1
+2
+� t
+0
+�
+¯∆
+∂xlF(m, x)∂xk[Σk,l(m, x)pV (m, x; s)]dmdxds
++
+� t
+0
+�
+Rd
+�
+F(m, m, ˜x)B1(m, ˜x) + 1
+2∂xkF(m, m, ˜x)Σ1,k(m, ˜x)
+�
+pV (m, m, ˜x; s)dmd˜xds.
+We again operate an integration by parts on the second term above on the right hand:
+− 1
+2
+� t
+0
+�
+¯
+∆
+∂xlF (m, x)∂xkΣk,l(m, x)pV (m, x; s)]dmdxds =
+1
+2
+� t
+0
+�
+¯
+∆
+F (m, x)∂2
+xk,xl[Σk,lpV ](m, x; s)dmdxds− 1
+2
+� t
+0
+�
+Rd F (m, m, ˜x)∂xk
+�
+Σ1,kpV
+�
+(m, m, ˜x; s)dmd˜xds.
+Gathering these equalities yields
+� t
+0
+�
+¯∆
+LF(m, x)pV (m, x; s)dmdxds =
+� t
+0
+�
+¯∆
+F(m, x)L∗pV (m, x; s)dmdxds
+−1
+2
+� t
+0
+�
+Rd F(m, m, ˜x)∂xk
+�
+Σ1,kpV
+�
+(m, m, ˜x; s)dmd˜xds
+(61)
++
+� t
+0
+�
+Rd
+�
+F(m, m, ˜x)B1(m, ˜x)pV (m, m, ˜x; s) + 1
+2[∂xkFΣ1,kpV ](m, m, ˜x; s)
+�
+dmd˜xds.
+(ii) Using F ∈ C2
+b (Rd+1, R) with compact support in ∆ (so F(m, m, ˜x) = 0) we
+deduce the equality in ∆ :
+∂tpV (m, x; s) = L∗pV (m, x; s),
+∀s > 0,
+(m, x) ∈ ∆.
+(62)
+We use (60), (61) and (62) applied to F ∈ C2
+b (Rd+1, R) with compact support in ¯∆:
+0 =
+�
+Rd F(m, m, ˜x)f0(m, ˜x)dmd˜x−1
+2
+� t
+0
+�
+Rd F(m, m, ˜x)∂xk
+�
+Σ1,kpV
+�
+(m, m, ˜x; s)dmd˜xds
++
+� t
+0
+�
+Rd
+�
+F(m, m, ˜x)B1(m, ˜x)pV (m, m, ˜x; s) + 1
+2[∂xkFΣ1,kpV ](m, m, ˜x; s)
+�
+dmd˜xds
++ 1
+2
+� t
+0
+�
+Rd ∥A1(m, ˜x)∥2∂mF(m, m, ˜x)p(m, m, ˜x; s)dmd˜xds.
+(63)
+We now operate integration by parts on the last two terms:
+� t
+0
+�
+Rd
+�
+[∂xkF.Σ1,k.pV ](m, m, ˜x; s) + ∥A1(m, ˜x)∥2∂mF (m, m, ˜x)pV (m, m, ˜x; s)
+�
+dmd˜xds =
+−
+� t
+0
+�
+Rd
+�
+[F.∂xk(Σ1,kpV )](m, m, ˜x; s) + ∂m(∥A1∥2pV )(m, m, ˜x; s)
+�
+dmd˜xds
+(64)
+Plugging (64) into (63) yields the boundary condition, namely a PDE of which pV is
+a solution in the weak sense:
+B1(m, ˜x)pV (m, m, ˜x; s) = 1
+2
+�
+k≥1 ∂xk(Σ1,kpV )(m, m, ˜x; s)+
+1
+2
+�
+k≥1∂xk(Σ1,kpV )(m, m, ˜x; s) + 1
+2∂m(∥A1∥2pV )(m, m, ˜x; s)
+
+PDE for the joint law of the pair of a continuous diffusion and its running maximum
+41
+simplified as
+B1(m, ˜x)pV (m, m, ˜x; s) =
+�
+k≥1
+∂xk(Σ1,kpV )(m, m, ˜x; s) + 1
+2∂m(∥A1∥2pV )(m, m, ˜x; s)
+with the initial condition pV (m, m, ˜x; 0) = f0(m, ˜x).
+□
+Acknowledgements
+The authors would like to thank Monique JEANBLANC who gave us a valuable help
+in writing this paper. The authors would like to thank also the anonymous referees for
+their constructive comments that improved the quality of this paper.
+References
+[1] L. Alili, P. Patie, J.L. Pedersen (2005), Representations of the first hitting
+time density of an Ornstein-Uhlenbeck process, Stoch. Models 21-4 , 967-980.
+[2] J. M. Aza¨ıs, M. Wschebor (2001), On the regularity of the distribution of the
+maximum of one-parameter Gaussian processes, P.T.R.F. 119 , no. 1, 70-98.
+[3] A. Bain ans D. Crisan (2007), Fundamentals of Stochastic Filtering, Springer-
+Verlag.
+[4] C. Blanchet-Scalliet, D. Dorobantu, L. Gay (2020), Joint Law of an
+Ornstein-Uhlenbeck Process and its Supremum, J. Appl. Proba. 57 , no. 2, 541-558.
+[5] H. Brezis (2011), Functional Analysis, Sobolev Spaces and Partial Differential
+Equations, Springer-Verlag.
+[6] H. Brown, D. Hobson, L.C.G. Rogers (2001), Robust hedging of barrier
+options, Math. Finance 11, 285-314
+[7] L. Coutin and D.Dorobantu (2011), First passage time law for some L´evy
+processes with compound Poisson: existence of a density, Bernoulli 17-4, 1127-
+1135.
+[8] L. Coutin, W. Ngom, M. Pontier (2018), Joint distribution of a L´evy process
+and its running supremum, J. Appl. Proba. 55, no. 2, 488-512.
+
+42
+AUTHOR NAMES
+[9] L. Coutin, M. Pontier (2019), Existence and regularity of law density of a
+diffusion and the running maximum of the first component, Stat. and Proba.
+Letters, 153, 130-138
+[10] A.M.G. Cox, J. Obloj (2011), Robust pricing and hedging of double touch
+barrier options, SIAM J. Financial 2, 141-182 .
+[11] E. Cs`aki, A. F¨oldes, P. Salminen (1987), On the joint distribution of the
+maximum and its location for a linear diffusion, Annals IHP Proba. Stat. 23, no.
+2, 179-194.
+[12] R.A. Doney, A.E. Kyprianou (2006), Overshoots and undershoots of L´evy
+processes, Ann. Appl. Probab. 16, no. 1, 91-106.
+[13] M. Duembgen, L. C. G. Rogers, (2015) The Joint Law of the Extrema, Final
+Value and Signature of a Stopped Random Walk, Chapter in ‘Memoriam Marc Yor’,
+S´eminaire de Probabilit´es XLVII, L. N. in Mathematics 2137, 321-338.
+[14] Garroni, M. G. and Menaldi, J.-L. (1992), Green functions for second order
+parabolic integro-differential problems, Pitman Research Notes in Mathematics
+Series, Inc., NewYork, 275.
+[15] H. He, W.P. Keirstead, J. Rebholz (1998), Double lookbacks, Math. Finance,
+8, 201-228.
+[16] P. Henry-Labord`ere, J. Obloj, P. Spoida, N. Touzi (2016), The maximum
+maximum of a martingale with given n-marginals, The Annals of Applied Proba.
+26(1), 1-44.
+[17] M. Jeanblanc, M. Yor, M. Chesney (2009), Mathematical Methods for
+Financial Markets, Springer.
+[18] Lamperti J. (1964) A simple construction of certain diffusion processes, Journal
+Math Kyoto University, 4, 161-170
+[19] A. Lagnoux, S. Mercier, P. Vallois (2015), Probability that the maximum
+of the reflected Brownian motion over a finite interval [0, t] is achieved by its last
+zero before t, Electron. Commun. Probab. 20 , no. 62.
+
+PDE for the joint law of the pair of a continuous diffusion and its running maximum
+43
+[20] W. Ngom (2016), thesis: Contributions `a l’´etude de l’instant de d´efaut d’un
+processus de L´evy en observation compl`ete et incompl`ete, IMT.
+[21] D. Nualart (2006), The Malliavin calculus and related topics Second Edition,
+Springer-Verlag New-York.
+[22] L. C. G. Rogers (1993), The Joint Law of the Maximum and Terminal Value
+of a Martingale, P.T.R.F. 95(4), 451-466 December 1993.
+[23] B. Roynette, P. Vallois, A. Volpi (2008), Asymptotic behavior of the passage
+time, overshoot and undershoot for some L´evy processes, ESAIM PS 12 58–93.
+
diff --git a/JdE0T4oBgHgl3EQfiQFG/content/tmp_files/load_file.txt b/JdE0T4oBgHgl3EQfiQFG/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..340d6b2eef0b60b492a8201e3c465712c6814bbb
--- /dev/null
+++ b/JdE0T4oBgHgl3EQfiQFG/content/tmp_files/load_file.txt
@@ -0,0 +1,1296 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf,len=1295
+page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='02442v1  [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='PR]  6 Jan 2023  Applied Probability Trust (9 January 2023)  PDE FOR THE JOINT LAW OF THE PAIR OF A CONTINUOUS  DIFFUSION AND ITS RUNNING MAXIMUM  LAURE COUTIN, MONIQUE PONTIER,∗ IMT  Abstract  Let X be a d-dimensional diffusion and M the running supremum of its first  component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  In this paper,  we show that for any t > 0, the density (with  respect to the d + 1-dimensional Lebesgue measure) of the pair (Mt, Xt) is a  weak solution of a Fokker-Planck partial differential equation on the closed set  {(m, x) ∈ Rd+1, m ≥ x1}, using an integral expansion of this density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Keywords:  Diffusion process, partial differential equation, running supremum  process, joint law.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  2020 Mathematics Subject Classification: Primary 60J60  Secondary 60G70,60H10  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Introduction  The goal of this paper is to study the law of the pair (Mt, Xt) where X is a d-  dimensional diffusion and M is the running maximum of the first component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' In a  previous work [9], using Malliavin calculus and specifically Nualart’s seminal book [21],  we have proved that, for any t > 0 the law of Vt := (Mt, Xt) is absolutely continuous  with respect to the Lebesgue measure with density pV (.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t), and that the support of  this density is included in the set {(m, x) ∈ Rd+1, m ≥ x1}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  In the present work, we prove that the density pV is a weak solution of a partial  differential equation (PDE).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Furthermore, we exhibit a boundary condition on the set  {(m, x) ∈ Rd+1, m = x1}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' This work extends the results given in [8] and in Ngom’s  ∗ Postal address: IMT, Universit´e Paul Sabatier, 31062 Toulouse cedex France  coutin@math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='univ-toulouse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='fr, IMT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  pontier@math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='univ-toulouse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='fr, IMT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  1  2  AUTHOR NAMES  thesis [20] obtained in the case where X is a L´evy process and where it is proved that  the density is a weak solution to an integro-differential equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  In the literature, there exist many studies on the law of Vt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' When the process X is  a Brownian motion, one can refer to [15, 17] where an explicit expression of pV is  given.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' When X is a one-dimensional linear diffusion, [11] provides an expression of  pV using the scale function, the speed measure and the density of the law of some  hitting times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' See also [1, 4] for the particular case of Ornstein-Uhlenbeck process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  For some applications to the local score of a biologic sequence, the case of reflected  Brownian motion is presented in [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' The law of the maximum Mt is studied in [2] for  general Gaussian processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' The case of a L´evy process X is deeply investigated in the  literature, see for instance [12, 20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Moreover Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='4 in Ngom’s thesis [20] provides  the existence and the regularity of the joint law density of the process (Mt, Xt) for a  L´evy process X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' In the case where X is a martingale (see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' [22, 13] or [10, 16]),  the law of the running maximum is provided.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Such studies concerning this running  maximum are useful in financial area which involve hitting times, for instance for the  pricing of barrier option.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' It is known that the law of hitting times is closely related to  the one of the running maximum, see [6, 7, 23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  As an application of our work, think  of a firm the activity of which is characterized by a set of processes (X1, · · · , Xd).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' But  one of them, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=', X1 could be linked to an alarm, namely: when there exists s ≤ t  such that X1  s exceeds a threshold a, that is equivalent to Mt = sup0≤s≤t X1  s ≥ a,  some action is important to operate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' So, the firm needs to know the law of such pair  (Mt, Xt);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' more specifically the law of the stopping time τa = inf{u, X1  u ≥ a}, is linked  to the law of M as following: {τa ≤ t} = {Mt ≥ a}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' To know the probability of such  an alert, the law of the pair (Mt, Xt) will be useful.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  We provide an infinite expansion of the density of the law of the pair (Mt, Xt) which  can leads to numerical approximation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Let (Ω, F, P) be a probability space endowed with a d-dimensional Brownian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Let  X be the diffusion process with values in Rd solution of  dXt = B(Xt)dt + A(Xt)dWt,  t > 0  (1)  where X0 is a random variable independent of the Brownian motion W, with law µ0,  and A (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' B) is a map from Rd to the set of (d × d) matrices (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' to Rd).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Let  PDE for the joint law of the pair of a continuous diffusion and its running maximum  3  us denote Ci  b(Rd, Rn) the set of functions  on Rd, which are i times differentiable,  bounded, with bounded derivatives, taking their values in Rn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Let F = (Ft, t ≥ 0)  be the completed right-continuous filtration defined by Ft := σ{X0, Ws, s ≤ t} ∨ N  where N is the set of negligible sets of F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Under classical assumptions on A and B (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' (4) and (5) below), then according to  [9], for all t > 0, the law of Vt = (supu≤t X1  t , Xt) has a density with respect to the  Lebesgue measure on Rd+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  The main results and notations are given in Section 2: in the d-dimensional case,  under a quite natural assumption (meaning Hypothesis 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='1 below) on the regularity  of pV around the boundary of ∆, pV is a weak solution of a Fokker-Planck PDE on  the subset of Rd+1 defined by {(m, x), m ≥ x1}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' When A = Id, this assumption is  satisfied, see Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' The main results are proved in Section 3 under Hypothesis  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Section 4 is devoted to prove that Hypothesis 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='1 is satisfied when A = Id.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' The  main tool is an infinite expansion of pV given in Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' In Section 5, one-  dimensional case, a Lamperti transformation [18] allows to get the main result for any  A ∈ C2  b (R, R).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Finally Appendix contains some technical tools useful for the proofs of  main results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Main results and some notations  In this section, we give our main results, the proofs will be given later on, as it is  mentioned in the introduction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Notations  Let ∆ be the open set of RD+1 given by ∆ := {(m, x), m ∈ R, x ∈ Rd, m > x1, x =  (x1, · · · , xd)}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' From now on, we use Einstein’s convention.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' The infinitesimal generator  L of the diffusion X defined in (1) is the partial differential operator on the space  C2(Rd, R) given by:  L = Bi∂xi + 1  2(AAt)ij∂2  xi,xj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  (2)  where At denotes the transposed matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Its adjoint operator is L∗f = 1  2Σij∂2  ijf − [Bi − ∂j(Σij)]∂if − [∂iBi − 1  2∂2  ij(Σij)]f where  Σ := AAt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' In what follows, the operators L and L∗ are extended to the space C2(Rd+1, R),  4  AUTHOR NAMES  for Φ ∈ C2(Rd+1, R) as  L(Φ)(m, x) = Bi(x)∂xiΦ(m, x) + 1  2Σij(x)∂2  xi,xjΦ(m, x),  and L∗(Φ)(m, x) =  1  2Σij(x)∂2  ijΦ(m, x) − [Bi − ∂j(Σij)](x)∂xiΦ(m, x) + [1  2∂2  xi,xjΣij − ∂xiBi](x)Φ(m, x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  It can be stressed that these operators are degenerated since no derivative with respect  to the variable m appears.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Let A1(x) be the d dimensional vector A1(x) = (A1  j(x), j = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=', d) ∈ Rd corresponding  to the first column of A(x), similarly Aj(x) denotes its jth line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Recall that M denotes the running maximum of the first component of X, meaning  Mt = sup0≤s≤t{X1  s} and V is the Rd+1-valued process defined by (Vt = (Mt, Xt), ∀t ≥  0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Finally, ˜x ∈ Rd−1 denotes the vector (x2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=', xd).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  In [9], under Assumptions (4) and (5) below, when the initial value is deterministic,  X0 = x0 ∈ Rd, the density of Vt exists and is denoted pV (.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t, x0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  If µ0 is the  distribution of X0, the density of the law of Vt with respect to the Lebesgue measure  on Rd+1 is  pV (.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t, µ0) :=  �  Rd pV (.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t, x0)dµ0(x0)  (3)  When there is no ambiguity, the dependency in µ0 is omitted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Since Mt ≥ X1  t , the support of pV (.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t, µ0) is contained in ¯∆ :=  �  (m, x) ∈ Rd+1|m ≥ x1�  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Mains results  The aim of this article is to show that the density pV is a weak solution of a Fokker-  Planck PDE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' The coefficients B and A are assumed to satisfy  B ∈ C1  b (Rd, Rd) and A ∈ C2  b (Rd, Rd×d),  (4)  and that there exists a constant c > 0 such that the Euclidean norm of any vector v  satisfies  c∥v∥2 ≤ vtA(x)At(x)v,  ∀v, x ∈ Rd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  (5)  PDE for the joint law of the pair of a continuous diffusion and its running maximum  5  Our first result will be established under the following hypothesis which is a quite  natural assumption on the regularity of pV  in the neighbourhood of the boundary  of ∆ since the  set of times where the process M  increases is included in  the set  {t,  Mt = Xt} :  Hypothesis 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' The density of the law of Vt = (Mt, Xt), denoted by pV (3), satisfies  (i) the map (t, m, ˜x) �→ supu>0 pV (m, m − u, ˜x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t) belongs to L1([0, T ] × Rd, dtdmd˜x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  (ii) for all t > 0 almost surely in (m, ˜x) ∈ Rd, limu→0+ pV (m, m − u, ˜x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t) exists and is  denoted by pV (m, m, ˜x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Assume that A and B fulfil (4) and (5) and that (M, X) fulfils Hy-  pothesis 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Then, for all initial law µ0 and F ∈ C2  b (Rd+1, R):  E [F(Mt, Xt)) = E  �  F(X1  0, X0)  �  +  � t  0  E [L (F) (Ms, Xs)] ds  + 1  2  � t  0  E  �  ∂mF(X1  s , Xs)∥A1(Xs)∥2 pV (X1  s, Xs;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s)  pX(Xs;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s)  �  ds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  (6)  Actually pX is the solution of the PDE ∂tp = L∗p,  p(.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' 0) = µ0, where  L∗f = 1  2Σij∂2  ijf − [Bi − ∂j(Σij)]∂if − [∂iBi − 1  2∂2  ij(Σij)]f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Let aij := Σij,  ai := [Bi − ∂j(Σij)]∂i, and a0 := ∂iBi − 1  2∂2  ij(Σij).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Under Assumptions (4) and (5),  the operator L∗ satisfies all the assumptions of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='5 [14] (see (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='2) (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='3) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='4)  page 177).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' As a consequence of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='5 line 14 pX(x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s) > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' (i) When A is the identity matrix of Rd (denoted by Id) and B ∈  C1  b (Rd, Rd), Hypothesis 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='1 is fulfilled, see Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='4 below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  When d = 1, using  a Lamperti transformation [18], one proves that Hypothesis 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='1 is always fulfilled, see  Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  (ii) This result is similar to Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='1 in [8] where the process X is a L´evy  process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Proposition 4 in [8] gives a key of the last term in (6) with factor 1  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Firstly,  roughly speaking, the local behaviour of X1  t − X1  s conditionally to Fs is the one of  ∥A1(Xs)∥(W 1  t − X1  s ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' So, as in the Brownian case, the running maximum M of X1 is  increasing as soon as it is equal to X1 and both M and X1 are increasing;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' it is well  known that the Brownian process W 1 is increasing with probability 1  2, more specifically,  we have P{limt→s+  W 1  t −W 1  s  t−s  = −∞} = P{limt→s+  W 1  t −W 1  s  t−s  = +∞} = 1  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  The starting point of the proof of Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='2 is the Itˆo’s formula: let F belong  6  AUTHOR NAMES  to C2  b (Rd+1, R).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' The process M is increasing, hence V = (M, X) is a semi-martingale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Applying Itˆo’s formula to F(V ) and taking expectation of both members,  E [F(Vt)] = E [F(V0)] +  � t  0  E [L(F)(Vs)] ds + E  �� t  0  ∂mF(Vs)dMs  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  The novelty comes from the third term of the right member of the previous equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  The following theorem proved in Section 3 achieves the proof of Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Assume that A and B fulfil (4) and (5) and that (M, X) fulfils Hy-  pothesis 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' For all Ψ ∈ C1  b (Rd+1, R), let Fψ be the map  Fψ : t �→ E  �� t  0 Ψ(Ms, Xs)dMs  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Then FΨ is absolutely continuous with respect to the  Lebesgue measure and its derivative is  ˙FΨ(t) = 1  2  �  Rd Ψ(m, m, ˜x)∥A1(m, ˜x)∥2pV (m, m, ˜x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t)dmd˜x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Remark that, as it is expressed in Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='2, this derivative can be written  1  2E  �  Ψ(X1  t , Xt)∥A1(Xt)∥2 pV (X1  t , Xt;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t)  pX(Xt;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' The above proposition provides an explicit formulation of the derivative  of the function FΨ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Note that the absolute continuity of Fψ could be established as  a direct consequence of the existence of the density of the law of the hitting time  τa = inf{s : X1  s ≥ a} when it exists, using the identity {τa ≤ t} = {Mt ≥ a}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Conversely, it could be proved that the absolute continuity of FΨ yields the existence  of the density of the law of the hitting time τa, using a sequence of C2  b (R, R) functions  (Fn) approximating the indicator function 1[a,∞), namely this density satisfies fτa(t) =  1  2  �  Rd−1 pV (a, a, ˜x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t)d˜x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Assume that A = Id and B satisfies Assumption (4) then, for all t > 0  the distribution of the pair (Mt, Xt) fulfils Hypotheses 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' As a consequence, for all  F ∈ C2  b (Rd+1, R)  E [F(Mt, Xt)] = E  �  F(X1  0, X0)  �  +  � t  0  E [L (F) (Ms, Xs)] ds  + 1  2  � t  0  E  �  ∂mF(X1  s , Xs)pV (X1  s , Xs;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s)  pX(Xs;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s)  �  ds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' This theorem is a consequence of Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='2 and Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  □  PDE for the joint law of the pair of a continuous diffusion and its running maximum  7  When d = 1 a Lamperti transformation leads to the following corollary:  Corollary 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Assume that d = 1, A and B satisfies (4) and (5), the density pV  satisfies Hypothesis 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='1 so  E [F(Mt, Xt)] = E [F(X0, X0)] +  � t  0  E [L (F) (Ms, Xs)] ds  + 1  2  � t  0  E  �  A2(Xs)∂mF(Xs, Xs)pV (Xs, Xs;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s)  pX(Xs;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s)  �  ds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' If pV is regular enough, and if the initial law of X0 satisfies µ0(dx) =  f0(x)dx, then Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='2 means that pV is a weak solution in the set ∆ of ∂tp = L∗p  where L∗f = 1  2Σij∂2  ijf−[Bi−∂j(Σij)]∂if−∂iBi− 1  2∂2  ij(Σij))f with boundary condition  B1(m, ˜x)pV (m, m, ˜x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s) = ∂xk(Σ1,kpV )(m, m, ˜x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s) + 1  2∂m(∥A1∥2pV )(m, m, ˜x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' (7)  This result is proved in Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='3  This boundary condition also appears in Proposition 4 Equation (11) of [4] (Ornstein  Uhlenbeck process).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Finally, a similar PDE is studied in Chapter 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='2 of [14] where the  authors have established the existence of a unique strong solution of this PDE, but in  case of a non degenerate elliptic operator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Proof of Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='3  We start this section with a road map of the proof of Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Firstly we  compute the right derivative of the application FΨ : t �→ E[  � t  0 Ψ(Ms, Xs)dMs], namely  limh→0+ Th,t with Th,t = 1  hEP[  � t+h  t  ψ(Vs)dMs].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' A first step is the decomposition  Th,t = 1  hEP[  � t+h  t  (ψ(Vs) − ψ(Vt))dMs] + 1  hEP[ψ(Vt)(Mt+h − Mt)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  (8)  Since ψ ∈ C1  b (Rd+1, R) and the process M is increasing, the first term in (8),  is  dominated by:  E  �� t+h  t  (ψ(Vs) − ψ(Vt))dMs  �  ≤ ∥∇ψ∥∞E  �  sup  t≤s≤t+h  ∥Vs − Vt∥(Mt+h − Mt)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='1 states that supt≤s≤t+h ∥Xs − Xt∥p = O(  √  h) and Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='2 yields  ∥Mt+h − Mt∥p = o(  √  h) so that that this first term is an o(h).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  8  AUTHOR NAMES  Concerning the second term in (8), Mt+h − Mt can be written as sup0≤u≤h(X1  t+h −  X1  t − Mt + X1  t )+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' In order to use the independence of the increments of Brownian  motion we introduce a new process, independent of Ft, which is an approximation of  X1  t+u − X1  t :  X1  t,u := A1  k(Xt) ˆ  W k  u where ˆW k  u := W k  t+u − W k  t ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Mt,h :=  sup  0≤u≤h  X1  t,u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  (9)  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='4 (ii) will set E  �  |Mt+h − Mt − (Mt,h − Mt + X1  t )+|  �  = o(h), where (x)+ =  max(x, 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Thus  1  hE[ψ(Vt)(Mt+h − Mt)] = E[ψ(Vt)(Mt,h − Mt + X1  t )+] + o(h)  (10)  Remark that the law of Mt,h given Ft is the law of ∥A1(Xt)∥ sup0≤u≤h ˆW 1  u, then using  the function H (13), a Ft conditioning yields:  1  hE[ψ(Vt)(Mt+h − Mt)] =  2  √  h  E  �  Ψ(Vt)∥A1(Xt)∥H(  Mt − X1  t  √  h∥A1(Xt)∥  )  �  + o(h).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  (11)  Then Th,t =  2  √  h E  �  Ψ(Vt)∥A1(Xt)∥H(  Mt−X1  t  √  h∥A1(Xt)∥)  �  + o(h) as it appears in Proposition  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='1 (ii).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  In Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='2, under Hypothesis 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='1, we compute limh→0 Th;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Finally in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='4 we prove Fψ : t �→ E[  � t  0 ψ(Vs)dMs] is an absolutely continuous  function with respect to Lebesgue measure, integral of its right derivative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Actually we  prove that Fψ is a continuous function belonging to the Sobolev space W 1,1(I), I =  (0, T ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' This achieves the proof of Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  The main propositions to prove are  Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Let B and A fulfil (4) and (5) and let Ψ ∈ C1  b (Rd+1, R).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Recall  that A1 is the vector (A1  j, j = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=', d), and ∥A1(x)∥2 = �d  j=1(A1  j(x))2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  (i) for all T > 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' there exists a constant C > 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' (depending on ∥A∥∞,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' ∥B∥∞,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' ∥∇A∥∞,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  ∥Ψ∥∞,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' ∥∇Ψ∥∞ and T ) such that ∀t ∈ [0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' T ],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' h ∈ [0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' 1],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  �����E  �� t+h  t  Ψ(Vs)dMs − 2  √  h  �  Ψ(Vt)∥A1(Xt)∥H(  Mt − X1  t  √  h∥A1(Xt)∥  )  ������� ≤ Ch∥∇Ψ∥∞,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  (12)  (ii) for all t > 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' h ∈ [0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' 1],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  lim  h→0+  1  h  �����E  �� t+h  t  Ψ(Vs)dMs  �  − 2  √  hE  �  Ψ(Vt)∥A1(Xt)∥H(  Mt − X1  t  √  h∥A1(Xt)∥  )  ������ = 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  where,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' denoting by ΦG the standard Gaussian cumulative distribution function,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  H(θ) :=  � ∞  θ  1  √  2π (y − θ)e− y2  2 dy = e− θ2  2  √  2π − θΦG(−θ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  (13)  PDE for the joint law of the pair of a continuous diffusion and its running maximum  9  The following remark will be useful:  Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' The definition of H in (13) implies that  � ∞  0  H(u)du = 1/4 Moreover,  H′(θ) = −ΦG(−θ) ≤ 0, in particular H is non increasing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Assume that A and B fulfil (4) and (5) and that (M, X) fulfils  Hypothesis 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='1, then for all Ψ ∈ C1  b (Rd+1, R), for all 0 < T and for all t ≥ 0 :  (i)t �→ sup  h>0  2  √  h  h  E  �  Ψ(Vt)∥A1(Xt)∥H(  Mt − X1  t  √  h∥A1(Xt)∥  )  �  ∈ L1([0, T ], R),  (ii) lim  h→0+  2  √  h  h  E  �  Ψ(Vt)∥A1(Xt)∥H(  Mt − X1  t  √  h∥A1(Xt)∥  )  �  = 1  2  �  Rd Ψ(m, m, ˜x)∥A1(m, ˜x)∥2pV (m, m, ˜x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t)dmd˜x  As a corollary, the function t → 1  2  �  Rd Ψ(m, m, ˜x)∥A1(m, ˜x)∥2pV (m, m, ˜x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t)dmd˜x be-  longs to L1([0, T ], R).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  The proof of Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='1 will be obtained with the lemmas in the following section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Tools for proving Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='1  Here we provide some estimations of the expectations  of the increments of the  processes X and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Assumptions (4) and (5) allow us to introduce a constant K  which denotes either max(∥A∥∞, ∥B∥∞) or max(∥A∥∞, ∥B∥∞, ∥∇A∥∞).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Let Cp be  the constant in the Burkholder-Davis-Gundy inequality (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Theorem B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='36 in [3]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Let A and B be bounded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Then, for all 0 < h ≤ 1, for all p ≥ 1 there  exists a constant Cp,K (depending only on p and K) such that:  sup  t>0  E  �  sup  0≤s≤h  ∥Xt+s − Xt∥p  �  ≤ Cp,Khp/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Using the fact that (a + b)p ≤ 2p−1 [ap + bp] , a, b ≥ 0, one obtains:  0 ≤ sup  s≤h  ∥Xt+s − Xt∥p ≤ 2p−1  �  sup  u≤h  �  ∥  � t+u  t  B(Xs)ds∥  �p  + sup  u≤h  �  ∥  � t+u  t  Aj(Xs)dW j  s ∥  �p�  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Taking expectation of both members, the Burkholder-Davis-Gundy inequality implies  E[sup  s≤h  ∥Xt+s−Xt∥p] ≤ 2p−1(1+Cp)E  \uf8ee  \uf8f0  �� t+h  t  ∥B(Xs)∥ds  �p  +  �� t+h  t  ∥A(Xs)∥2ds  �p/2\uf8f9  \uf8fb .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  10  AUTHOR NAMES  Assumption (4) on B and A yields E[sups≤h ∥Xt+s − Xt∥p] ≤ 2p−1(1 + Cp)(hpKp +  hp/2Kp).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  □  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Let B and A satisfy Assumptions (4) and (5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Then, for all 0 < h ≤ 1,  for all p ≥ 1 we get:  sup  t>0  E[|Mt+h − Mt|p] ≤ Cp,Khp/2 ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' E[|Mt+h − Mt|p] = o(hp/2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  (14)  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Recall Mt+h − Mt =  �  sup0≤u≤h(X1  t+u − X1  t ) + X1  t − Mt  �  + recalling (x)+ =  max(x, 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' For any a ≥ 0, one has (x − a)+ ≤ |x|1{x>a}, thus  0 ≤ Mt+h − Mt ≤ | sup  0≤u≤h  (X1  t+u − X1  t )|1{sup0≤u≤h(X1  t+u−X1  t )>Mt−X1  t }.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Cauchy-Schwartz’s inequality yields:  0 ≤ E [(Mt+h − Mt)p] ≤  �  E  �  | sup  0≤u≤h  (X1  t+u − X1  t )|2p  �  P({ sup  0≤u≤h  (X1  t+u − X1  t ) > Mt − X1  t }).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Replacing p by 2p in Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='1 leads to the inequality in (14) and the equality  limh→0 sup0≤u≤h(X1  t+u − X1  t ) = 0 holds almost surely.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' According to Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='1 in  [9]  extended to X0 with law µ0 on Rd,  the pair (Mt, Xt) admits a density, thus  P{Mt − X1  t = 0} = 0 holds almost surely.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Therefore E ([Mt+h − Mt]p) is bounded by  the product of hp/2 and a factor going to zero when h goes to 0, and this quantity is  an o(hp/2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  □  For any fixed t we recall the process (Xt,u,  u ∈ [0, h]) and the running maximum  of its first component as follows:  Xt,u :=  �  j  Aj(Xt) ˆ  W j  u, Mt,h :=  sup  0≤u≤h  X1  t,u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  (15)  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Under Assumptions (4) and (5), for all p ≥ 1  there exists a constant  Cp,K such that such that for all t ≤ T , for all h ∈ [0, 1]:  E  �  sup  s≤h  |X1  s+t − X1  t − X1  t,s|p  �  ≤ Cp,Khp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' By definition, recalling ˆWu := Wt+u − Wt,  u ≥ 0, we obtain  X1  s+t − X1  t − X1  t,s =  � s  0  B1(Xu+t)du +  � s  0  �  A1(Xu+t) − A1(Xt)  �  d ˆWu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  PDE for the joint law of the pair of a continuous diffusion and its running maximum  11  Using once again (a + b)p ≤ 2p−1(ap + bp), a, b ≥ 0, we get  sup  0≤s≤h  |X1  s+t − X1  t − X1  t,s|p ≤  2p−1  ��� h  0  ∥B1(Xu+t)∥du  �p  + sup  0≤s≤h  ����  � s  0  �  A1(Xu+t) − A1(Xt)  �  d ˆ  Wu  ����  p�  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Taking expectation of both sides and applying the Burkholder-Davis-Gundy inequality  yield with Dp = 2p−1(1 + Cp):  E  �  sup  0≤s≤h  |X1  s+t − X1  t − X1  t,s|p  �  ≤ Dp  �  E  �� h  0  ∥B1(Xu+t)∥du  �p  + E  ����  � h  0  ∥A1(Xu+t) − A1(Xt)∥2du  ����  p/2�  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  The first term above is bounded by Kphp since B is bounded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  The assumption  that A belongs to C1  b (Rd, Rd×d) and Jensen’s inequality imply that the second term is  bounded by Kphp/2−1� h  0 E∥Xu+t − Xt∥pdu thus  E  �  sup  0≤s≤h  |X1  s+t − X1  t − X1  t,s|p  �  ≤ DpKphp/2−1  �  hp/2+1 +  � h  0  E∥Xu+t − Xt∥pdu  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  From Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='1 we obtain the uniform upper bound: E[∥Xu+t − Xt∥p] ≤ Cp,Kup/2  hence  E  �  sup  s≤h  |X1  s+t − X1  t − X1  t,s|p  �  ≤ DpKpCp,K  p  2 + 1  hp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  □  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Under Assumptions (4) and (5), one has  (i) ∃C > 0  sup  0≤t≤T ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  0≤h≤1  h−1E  ����Mt+h − Mt −  �  Mt,h − Mt + X1  t  �  +  ���  �  ≤ C < ∞,  (ii)  lim  h→0+ h−1E  ����Mt+h − Mt −  �  Mt,h − Mt + X1  t  �  +  ���  �  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Fistly remark  ∀a ∈ R,  ��(x − a)+ − (y − a)+  �� ≤ |x − y|  �  1{x>a} + 1{y>a}  �  ,  (16)  and if f and g are functions on [0, T ], then  ∀s ∈ [0, T ],  f(s) −  sup  0≤u≤T  g(u) ≤ f(s) − g(s) ≤ |f(s) − g(s)| ≤ sup  v≤T  |f(v) − g(v)|,  hence sups≤T f(s) − supu≤T g(u) ≤ supv≤T |f(v) − g(v)|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Here the role of f and g is  symmetrical so sups≤T g(s) − supu≤T f(u) ≤ supv≤T |f(v) − g(v)|, and  ����sup  s≤T  g(s) − sup  u≤T  f(u)  ���� ≤ sup  v≤T  |f(v) − g(v)|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  (17)  12  AUTHOR NAMES  We now consider Mt+h − Mt =  �  sup0≤u≤h(X1  u+t − X1  t ) − Mt + X1  t  �  + , using (16)  ���Mt+h − Mt −  �  Mt,h − Mt + X1  t  �  +  ��� ≤  ���� sup  0≤u≤h  (X1  u+t − X1  t ) − Mt,h  ����  �  1{sup0≤u≤h(X1  u+t−X1  t )>Mt−X1  t } + 1{Mt,h>Mt−X1  t }  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Then, for any t fixed, we apply inequality (17) to the maps g : u �→ X1  u+t−Xt  1 and  f : u �→ X1  t,u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Then  ���Mt+h − Mt −  �  Mt,h − Mt + X1  t  �  +  ��� ≤  sup  0≤u≤h  ��X1  u+t − X1  t − X1  t,u  ��  �  1{sup0≤u≤h(X1  u+t−X1  t )>Mt−X1  t } + 1{Mt,h>Mt−X1  t }  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  From Cauchy-Schwartz’s inequality and the fact that (a + b)2 ≤ 2(a2 + b2), we get  E  ����Mt+h − Mt −  �  Mt,h − Mt + X1  t  �  +  ���  �  ≤  �  2E  �  sup  u≤h  ��X1  u+t − X1  t − X1  t,u  ��2  � �  P{ sup  0≤u≤h  (X1  u+t − X1  t ) > Mt − X1  t } + P{Mt,h > Mt − X1  t }  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='3 with p = 2 insures that the map h �→ h−1  �  2E  �  supu≤h  ��X1  u+t − X1  t − X1  t,u  ��2�  is uniformly bounded in t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Concerning the second factor,  firstly the almost sure continuity with respect to h insures that the quantities  limh→0 sup0≤u≤h(X1  u+t − X1  t ) and limh→0 Mt,h are equal to 0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  secondly the law of the pair (Mt, Xt) admits a density with respect to the Lebesgue  measure on ¯∆ according to Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='1 [9] so P({0 = Mt − X1  t }) = 0 and the limit of  the second factor is equal to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  This concludes the proof of the lemma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  □  Recall Definition (15): Xt,h = Aj(Xt)[W j  t+h − W j  t ], Mt,h = sup0≤u≤hX1  t,u, h ∈ [0, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Under Assumptions (4) and (5), with H defined in (13):  E  �  (Mt,h − Mt + X1  t )+|Ft  �  = 2∥A1(Xt)∥  √  hH  �  Mt − X1  t  ∥A1(Xt)∥  √  h  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' For any t fixed, conditionally to Ft the process (X1  t,u, u ∈ [0, h]) (9) has  the same law as (  √  h∥A1(Xt)∥ ˆWu, u ∈ [0, 1]) where ˆ  W is a Brownian motion in-  dependent of Ft, and for any h, the random variable Mt,h has the same law as  √  h∥A1(Xt)∥ supu≤1 ˆWu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Following  [17] Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='3,  the random variable supu≤1 ˆ  Wu has the same law  PDE for the joint law of the pair of a continuous diffusion and its running maximum  13  as |G| where G is a standard Gaussian variable (independent of Ft), with density  2  √  2πe− z2  2 1[0,+∞[(z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Then using the function H introduced in (13)  E  �  (Mt,h − (Mt − X1  t ))+|Ft  �  =  � ∞  0  �  ∥A1(Xt)∥  √  hz − (Mt − X1  t )  �  +  2  √  2π e− z2  2 dz  = 2∥A1(Xt)∥  √  hH(  Mt − X1  t  √  h∥A1(Xt)∥  ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  □  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Proof of Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='1  Let t > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' The key of this proof is to write the quantity  E  �� t+h  t  Ψ(Vs)dMs  �  − 2  √  hE  �  Ψ(Vt)∥A1(Xt)∥H(  Mt − X1  t  √  h∥A1(Xt)∥  )  �  as the sum of three terms,  E  � � t+h  t  (Ψ(Vs) − Ψ(Vt))dMs  �  + E  �  Ψ(Vt)  �  (Mt+h − Mt) − E  �  Mt,h − Mt + X1  t )+|Ft  � ��  (18)  + E  �  Ψ(Vt)E  �  (Mt,h − Mt + X1  t )+ | Ft  �  − 2  √  hΨ(Vt)∥A1(Xt)∥H(  Mt − X1  t  √  h∥A1(Xt)∥  )  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  We now prove that each terms in sum (18) are both o(h) and O(h) uniformly in time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  (a) Using Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='5 the third term is null.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  (b) Concerning the second term, using the fact that Ψ is bounded and Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='4 (i)  for all t ∈ [0, T ]  ��E  �  Ψ(Vt)[(Mt+h − Mt) − E[(Mt,h − Mt + X1  t )+ | Ft]  ��� ≤  ∥Ψ∥∞  ��E  �  Mt+h − Mt − E[(Mt,h − Mt + X1  t )+|Ft]  ��� ≤ Ch∥Ψ∥∞,  as it is required in (12).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Moreover using Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='4 (ii)  lim  h→0  1  h  ��E  �  Ψ(Vt)[(Mt+h − Mt) − E[(Mt,h − Mt + X1  t )+ | Ft]  ��� = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  (c) Since ∇Ψ is bounded and the process M is increasing, the first term is bounded:  E  �� t+h  t  [Ψ(Vs) − Ψ(Vt)]dMs  �  ≤ ∥∇Ψ∥∞E[  sup  t≤s≤t+h  ∥Vs − Vt∥(Mt+h − Mt)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  14  AUTHOR NAMES  Using Cauchy-Schwarz’s inequality  E  �  sup  t≤s≤t+h  ∥Vs − Vt∥(Mt+h − Mt)  �  ≤  �  E[  sup  t≤s≤t+h  ∥Vs − Vt∥2]E[(Mt+h − Mt)2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Since ∥Vs − Vt∥2 = (Ms − Mt)2 + ∥Xs − Xt∥2, we obtain  supt≤s≤t+h ∥Vs − Vt∥2 ≤ (Mt+h − Mt)2 + supt≤s≤t+h ∥Xs − Xt∥2, hence  E[  sup  t≤s≤t+h  ∥Vs−Vt∥(Mt+h−Mt)] ≤  �  E[(Mt+h − Mt)2] + E[  sup  t≤s≤t+h  ∥Xs − Xt∥]2)  �  E[(Mt+h − Mt)2]  Lemmas 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='1 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='2 (p = 2) yield  the fact that the first factor is an o(  √  h) and  the second is an O(  √  h) uniformly with respect to t ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Then E[supt≤s≤t+h ∥Vs −  Vt∥(Mt+h − Mt)] is an o(h) and an O(h) uniformly with respect to t ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  □  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Proof of Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='2  (i) Recall that A and B fulfil (4), (5) and (M, X) fulfils Hypothesis 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Then, using  the density pV of the law of the pair (Mt, Xt) we have  E  �  Ψ(Vt)∥A1(Xt)∥H  �  Mt − X1  t  √  h∥A1(Xt)∥  ��  ≤  ∥Ψ∥∞∥A∥∞  �  Rd+1 H  �  m − x1  √  h∥A1(x1, ˜x)∥  �  pV (m, x1, ˜x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t)dm dx1 d˜x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  The change of variable x1 = m − u  √  h yields  √  h  h E  �  Ψ(Vt)∥A1(Xt)∥H  �  Mt − X1  t  √  h∥A1(Xt)∥  ��  ≤  (19)  ∥Ψ∥∞∥A1∥∞  �  Rd×[0,+∞[  H  �  u  ∥A1(m −  √  hu, ˜x)∥  �  pV (m, m −  √  hu, ˜x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t)dm d˜x du.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Since H is decreasing (Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='1) and 0 ≤ h ≤ 1, H  �  u  ∥A1(m−  √  hu,˜x)∥  �  ≤ H(  u  ∥A1∥∞ ) :  �����  √  h  h E  �  Ψ(Vt)∥A1(Xt)∥H  �  Mt − X1  t  √  h∥A1(Xt)∥  ������� ≤  ∥Ψ∥∞∥A1∥∞  �  Rd×[0,+∞[  H  �  u  ∥A1∥∞  �  sup  r>0  pV (m, m − r, ˜x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t)dm d˜x du.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Applying Tonelli’s Theorem, computing the integral with respect to du in the right-  hand with  � ∞  0  H(v)dv = 1/4 (Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='1), yield:  sup  h>0  �����  √  h  h E  �  Ψ(Vt)∥A1(Xt)∥H  �  Mt − X1  t  √  h∥A1(Xt)∥  ������� ≤ 1  4∥Ψ∥∞∥A1∥2  ∞  �  Rd sup  r>0  pV (m, m − r, ˜x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t)dm d˜x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  PDE for the joint law of the pair of a continuous diffusion and its running maximum  15  Using Hypothesis 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='1 (i), we obtain that the map:  t �→ sup  h>0  �����  √  h  h E  �  Ψ(Vt)∥A1(Xt)∥H  �  Mt − X1  t  √  h∥A1(Xt)∥  �������  belongs to L1([0, T ], R).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Point (i) of Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='2 is proved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  (ii) Concerning the proof of point (ii), firstly note that  E  �  Ψ(Vt)∥A1(Xt)∥H  �  Mt − X1  t  √  h∥A1(Xt)∥  ��  =  �  Rd+1 Ψ(m, x)∥A1(x)∥H  �  m − x1  √  h∥A1(x)∥  �  pV (m, x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t)dm dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  After the change of variable x1 = m − u  √  h, we obtain  √  h  h E  �  Ψ(Vt)∥A1(Xt)∥H  �  Mt − X1  t  √  h∥A1(Xt)∥  ��  =  (20)  �  Rd×R+ Ψ(m, m − u  √  h, ˜x)∥A1(m − u  √  h, ˜x)∥H  �  u  ∥A1(m −  √  hu, ˜x)∥  �  pV (m, m −  √  hu, ˜x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t)dm d˜x du.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Using Lebesgue’s dominated convergence Theorem, we let h go to 0 in (20) for t > 0,  and using the fact that Ψ, A and H are continuous and Hypothesis 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='1 (ii) we obtain  lim  h→0  √  h  h E  �  Ψ(Vt)∥A1(Xt)∥H  �  Mt − Xt  √  h∥A1(Xt)∥  ��  =  �  Rd×[0,+∞[  Ψ(m, m, ˜x)∥A1(m, ˜x)∥H  �  u  ∥A1(m, ˜x)∥  �  pV (m, m, ˜x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t)dm d˜x du.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Using the change of variable z =  u  ∥A1(m,˜x)∥, and Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='1  � ∞  0  H(z)dz = 1/4, yields  lim  h→0  √  h  h E  �  Ψ(Vt)∥A1(Xt)∥H  �  Mt − X1  t  √  h∥A1(Xt)∥  ��  = 1  4  �  Rd Ψ(m, m, ˜x)∥A1(m, ˜x)∥2pV (m, m,˜x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t)dm d˜x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  □  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' End of proof of Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='3  We recall Theorem 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='2 page 204 in Brezis [5]: let f ∈ W 1,1(0, T ), then f is almost  surely equal to an absolutely continuous function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  As a particular case, any f ∈  W 1,1(0, T ) ∩ C(0, T ) is absolutely continuous.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Recall Fψ : t �→ E  �� t  0 Ψ(Vs)dMs  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Assume that A and B fulfil (4) and (5) and that Ψ is a continuous  bounded function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Then FΨ is a continuous function on R+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Let 0 ≤ s ≤ t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Since Ψ is bounded and M is non decreasing  |FΨ(t) − FΨ(s)| =  ����E  �� t  s  Ψ(Vu)dMu  ����� ≤ ∥Ψ∥∞E[Mt − Ms].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  The map t �→ E[Mt] being continuous, FΨ is a continuous function on R+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  □  16  AUTHOR NAMES  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Assume that A and B fulfil (4) and (5), (M, X) fulfils Hypothesis 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='1  and Ψ ∈ C1  b .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Then for all T > 0, the map Fψ belongs to the Sobolev space W 1,1(]0, T [)  and its weak derivative is  ˙FΨ(t) := 1  2  �  Rd Ψ(m, ˜x)∥A1(m, ˜x)∥2pV (m, m, ˜x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t)dmd˜x  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Let g : [0, T ] → R be C1 with compact support [α, β] ⊂ (0, T ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' This means  both functions g and ˙g are continuous so bounded and that moreover g(α) = g(β) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Note that ˙g(t) = limh→0  g(t)−g(t−h)  h  ,  ∀t ∈ (0, T ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Moreover,  supt∈[0,T ] suph∈[0,1] | g(t)−g(t−h)  h  | ≤ ∥ ˙g∥∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Observe that, since M is non decreasing and  the coefficients A and B are bounded |Fψ(t)| ≤ ∥Ψ∥∞E[MT ] < ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Then, using Lebesgue’s dominated convergence Theorem  � T  0  ˙g(s)Fψ(s)ds =  � T  0  lim  h→0  g(s) − g(s − h)  h  Fψ(s)ds = lim  h→0  � T  0  g(s) − g(s − h)  h  Fψ(s)ds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Using the change of variable u = s − h in the last integral  � T  0  g(s) − g(s − h)  h  FΨ(s)ds = h−1  � T  0  g(s)FΨ(s)ds − h−1  � T −h  −h  g(u)FΨ(u + h)du  =  � T  0  g(s)FΨ(s) − FΨ(s + h)  h  ds−h−1  � 0  −h  g(s)FΨ(s + h)ds+h−1  � T  T −h  g(s)FΨ(s + h)ds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Recalling supp(g) = [α, β] ⊂ (0, T ), gFΨ is bounded on [0, T ] extended by 0 on [α, β]c  so lims→0 g(s) = lims→T g(s) = 0 then h−1 � 0  −h g(s)FΨ(s+h)ds = h−1 � T  T −h g(s)Fψ(s+  h)ds = 0 as soon as 0 < h ≤ T − β thus limh→0  �  h−1 � 0  −h g(s)FΨ(s + h)ds  �  =  limh→0  �  h−1 � T  T −h g(s)Fψ(s + h)ds  �  = 0 Applying Lebesgue’s dominated convergence  Theorem yields, F admits a weak derivative:  � T  0  ˙g(s)Fψ(s)ds = −  � T  0  g(s) ˙FΨ(s)ds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Using Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='1 (ii)  lim  h→0+  �  −FΨ(t) − FΨ(t + h)  h  −  2  √  h  E  �  Ψ(Vt)∥A1(Xt)∥H  �  Mt − X1  t  √  h∥A1(Xt)∥  ���  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Using Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='2 (ii):  − ˙FΨ(t+) :=  lim  h→0,h>0  FΨ(t) − FΨ(t + h)  h  = −1  2  �  Rd Ψ(m, m, ˜x)∥A1(m, ˜x)∥2pV (m, m, ˜x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t)dmd˜x,  and the points (i) of Propositions 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='1 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='2:  sup  h>0  ����  FΨ(t) − FΨ(t + h)  h  ���� ∈ L1([0, T ], dt),  PDE for the joint law of the pair of a continuous diffusion and its running maximum  17  so ˙FΨ ∈ L1([0, T ], R).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  According to [5] Chap 8 section 2 page 202, FΨ belongs to W 1,1(]0, T [, R).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  □  We now end the proof of Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='3: According to Theorem 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='2 page 204 of [5],  Fψ is equal almost surely to an absolutely continuous function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Since FΨ is continuous  (Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='6), the equality holds everywhere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Then FΨ is an absolutely continuous  function and its derivative is its right derivative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  □  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Case A = Id  In this rather technical section, we firstly prove that the density of the pair (Mt, Xt)  fulfils Hypothesis 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='1: pV (3) is continuous on the boundary of ¯∆ and is dominated by  an integrable function:  Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Assume that B fulfils  Assumption (4) and A = Id, then (M, X)  fulfils Hypothesis 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='1 meaning that for all probability measure µ0 on Rd  (i) ∀T > 0,  sup  (h,u)∈[0,1]×R+  pV (b, b − hu, ˜a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t, µ0) ∈ L1([0, T ] × Rd, dtdbd˜a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  (ii) Almost surely in (m, ˜x) ∈ Rd, ∀t > 0,  lim  u→0,u>0 pV (m, m − u, ˜x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t, µ0) = pV (m, m, ˜x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t, µ0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  As a by product using Theorems 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='2 and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='3 this proposition achieves the proof of The-  orem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' The main tool for the proof of this proposition is an integral representation  of the density:  Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' For any probability measure µ0 on Rd, for all t > 0,  pV = p0 −  �  k=m,1,··· ,d  (pk,α + pk,β)  (21)  where the various p are defined by (∂k is the derivative with respect to k = m, x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=', xd  and Bm = B1):  p0(m, x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t) :=  �  Rd pW ∗1,W (m − x1  0, x − x0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t)µ0(dx0),  pk,α(m, x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t) :=  � t  0  �  Rd+1 1b<mBk(a)∂kpW ∗1,W  �  m − a1, x − a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t − s  �  pV (b, a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s)dbdads,  pk,β(m, x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t) :=  � t  0  �  R(d+1) 1b<mBk(a)∂kpW ∗1,W (b − a1, x − a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t − s)pV (m, a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s)dbdads,  18  AUTHOR NAMES  where pW ∗1,W (.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=', .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t) is the density of the distribution of (sups≤t W 1  s , Wt) for t ≥ 0, see  Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='2  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Integral representation of the density: proof of Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='2  Let t > 0 be fixed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Firstly, we assume that µ0 = δx0,  x0 being fixed in Rd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  According to Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='2 below and using the fact that B is bounded, ∀t ∈ [0, T ], the  functions pk,γ ∈∞ L  �  [0, T ], L1(Rd+1)  �  for γ = α, β .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Let F ∈ C1  b (Rd+1, R) with compact support.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' We will prove  EP[F(Mt, Xt)] =  �  Rd+1 F(m, x)  \uf8eb  \uf8edp0 −  �  k=m,x1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=',xd  (pk,α + pk,β)(m, x, t)  \uf8f6  \uf8f8 dmdx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' (22)  Using Malliavin calculus we obtain the following decomposition:  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  EP [F (Mt, Xt)] =  �  Rd+1 F (x1  0 + b, x0 + a)pW ∗1,W (b, a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t)dbda  +  � t  0  EP  ��  Rd+1 ∂mF  �  X1  s + b, Xs + a  �  1{Ms<X1s +b}B1(Xs)pW ∗1,W (b, a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t − s)dbda  �  ds  +  � t  0  EP  ��  Rd+1 ∂kF  �  max  �  Ms, X1  s + b  �  , Xs + a  �  Bk(Xs)pW ∗1,W (b, a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t − s)dbda  �  ds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Let Z be the exponential martingale solution of  Zt = 1 +  � t  0  ZsBk(x0 + Ws)dW k  s .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  (23)  As previously Einstein’s convention is used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Let Q = ZP, according to Girsanov’s  Theorem, using (23), WB :=  �  W k  t −  � t  0 Bk(x0 + Ws)ds;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' k = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=', d  �  t≥0 is a Q contin-  uous martingale such that ⟨WB⟩t = t,  ∀t ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' That means that under Q, WB is a  d-dimensional Brownian motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Then the distribution of X (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' (M, X)) under P  is the distribution of W + x0 (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' (W 1∗ + x0, W + x0)) under Q and  EP [F(Mt, Xt)] = EQ  �  F(x1  0 + W 1∗  t , x0 + Wt)  �  = EP  �  F(x1  0 + W 1∗  t , x0 + Wt)Zt  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' (24)  Let G := F(x1  0 + W 1∗  t , x0 + Wt) and u := ZB(x0 + W), using (23):  EP[F(Mt, Xt)] = EP  �  F(x1  0 + W 1∗  t , x0 + Wt)  �  + EP [Gδ(u)]  (25)  As a first step we will apply (50) (Appendix) to the second term in (25).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Thus  we have to check that the pair (G, u) ∈ D1,2 × L1,2:  F being bounded and smooth,  PDE for the joint law of the pair of a continuous diffusion and its running maximum  19  G ∈ D1,2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' and according to Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='1, the process u belongs to L1,2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Using (53) (τ := inf{s, W 1∗  s  = W 1∗  t }) the pair (W 1∗  t , Wt) belongs to D1,2 with Malliavin  gradient:  DsW 1∗  t  =  �  1[0,τ](s), 0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=', 0  �  , DsW k  t = (δj=k,  j = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=', d)1[0,t](s),  k = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=', d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Using the chain rule:  ⟨DG, u⟩H =  � t  0  ∂mF(x1  0 + W ∗1  t , x0 + Wt)1{W 1∗  s <W 1∗  t  }B1(x0 + Ws)Zsds  +  � t  0  ∂kF(x1  0 + W ∗1  t , x0 + Wt)Bk(x0 + Ws)Zsds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  We are now in position to apply (50) EP[Gδ(u)] = EP[⟨DG, u⟩H]:  EP[Gδ(u)] = EP  �� t  0  ∂mF(x1  0 + W 1∗  t , x0 + Wt)1{W 1∗  s <W 1∗  t  }B1(x0 + Ws)Zsds  �  +  EP  �� t  0  ∂kF(x1  0 + W 1∗  t , x0 + Wt)Bk(x0 + Ws)Zsds  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  (26)  Plugging identity (26) into right hand of (25) and using Fubini Theorem to commute  the integrals in ds and dP, we obtain  EP [F(Mt, Xt)] = EP  �  F(x1  0 + W 1∗  t , x0 + Wt)  �  (27)  +  � t  0  EP  �  ∂mF(x1  0 + W 1∗  t , x0 + Wt)1{W 1∗  s <W 1∗  t  }ZsB1(x0 + Ws)  �  ds  +  � t  0  EP  �  ∂kF(x1  0 + W 1∗  t , x0 + Wt)ZsBk(x0 + Ws)  �  ds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  As a second step we use the independence of the increments of the Brownian motion  in order to make appear the density of (W 1∗  t−s, Wt−s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Recall (9): ˆWt−s := Wt−Ws and  ( ˆW 1)∗  t−s = maxs≤u≤t  �  W 1  u − W 1  s  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Then W 1∗  t  = max  �  W 1∗  s , W 1  s + maxs≤u≤t  �  W 1  u − W 1  s  ��  =  max  �  W 1∗  s , W 1  s + ( ˆW 1)∗  t−s  �  so the expression (27) becomes  EP [F(Mt, Xt)] = EP  �  F(x1  0 + W 1∗  t x0+, Wt)  �  +  � t  0  EP  �  ∂mF  �  x1  0 + W 1  s + ( ˆ  W 1)∗  t−s, x0 + Ws + ˆWt−s  �  1{W 1∗  s <W 1  s +( ˆ  W 1)∗  t−s}ZsB1(x0 + Ws)  �  ds  +  � t  0  EP  �  ∂kF  �  max  �  x1  0 + W 1∗  s , x1  0 + W 1  s + ( ˆW 1)∗  t−s  �  , x0 + Ws + ˆWt−s  �  ZsBk(x0 + Ws)  �  ds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  The random vector  �  ( ˆW 1)∗  t−s, ˆWt−s  �  is independent of the σ−field Fs and has the  same distribution as the pair (W 1∗  t−s, Wt−s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Let pW ∗1,W (.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=', .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t − s) be the density of its  20  AUTHOR NAMES  law, and express the expectation with this density:  EP [F (Mt, Xt)] =  �  Rd+1 F (x1  0 + b, x0 + a)pW ∗1,W (b, a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t)dbda  +  � t  0  EP  ��  Rd+1 ∂mF �x1  0 + W 1  s + b, x0 + Ws + a� 1{W 1∗  s  <W 1  s +b}ZsB1(x0 + Ws)pW ∗1,W (b, a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t − s)dbda  �  ds  +  � t  0  EP  ��  Rd+1 ∂kF  �  x1  0 + max  �  W 1∗  s , W 1  s + b  �  , x0 + Ws + a  �  ZsBk(x0 + Ws)pW ∗1,W (b, a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t − s)dbda  �  ds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Using Girsanov’s Theorem for Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='P = Q, since the law of (M, X) under P is the law of  (x1  0 + W 1∗, x0 + W), under Q, using the equality (24):  EP [F (Mt, Xt)] =  �  Rd+1 F (x1  0 + b, x0 + a)pW ∗1,W (b, a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t)dbda  +  � t  0  EP  ��  Rd+1 ∂mF  �  X1  s + b, Xs + a  �  1{Ms<X1s +b}B1(Xs)pW ∗1,W (b, a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t − s)dbda  �  ds  +  � t  0  EP  ��  Rd+1 ∂kF �max �Ms, X1  s + b� , Xs + a� Bk(Xs)pW ∗1,W (b, a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t − s)dbda  �  ds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  □  We are now in position to achieve the proof of Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Using some suitable  translations of the variables (a, b), EP [F(Mt, Xt)] = �d  k=0 Ik + Im.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' where  I0 =  �  Rd+1 F(b, a)pW ∗1,W (b − x1  0, a − x0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t)dbda,  (28)  Im =  � t  0  EP  ��  Rd+1 ∂mF(b, a)1{Ms<b}B1(Xs)pW ∗1,W  �  b − X1  s , a − Xs;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t − s  �  dbda  �  ds  and for k = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=', d,  Ik =  � t  0  EP  ��  Rd+1 ∂kF (max (Ms, b) , a) Bk(Xs)pW ∗1,W (b − X1  s , a − Xs;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t − s)dbda  �  ds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Since B, F and its derivatives are bounded, all these integrals are finite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Using (54) in  Appendix, the function pW ∗1,W (.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=', .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t) is C∞ on ¯∆ = {(b, a),  b≥a1  +,  (a, b) ∈ Rd+1}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  The aim is now to identify the terms p0, pk,α, pk,β, k = m, 1, · · · , d, defined in  Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Firstly we identify p0(b, a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t) as the factor of F(b, a) in the integrand of I0 :  p0(b, a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t) = pW ∗1,W (b − x1  0, a − x0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' We now deal with Ik, k = 2, · · · , d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Integrating by parts with respect to ak between  PDE for the joint law of the pair of a continuous diffusion and its running maximum  21  −∞ and ∞ in Ik for k = 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=', d yields  Ik = −  � t  0  EP  ��  Rd+1 F (max (Ms, b) , a) Bk(Xs)∂kpW ∗1,W (b − X1  s, a − Xs;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t − s)dbda  �  ds  = −  � t  0  EP  ��  Rd+1 1{b>Ms}F (b, a) Bk(Xs)∂kpW ∗1,W (b − X1  s , a − Xs;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t − s)dbda  �  ds  −  � t  0  EP  ��  Rd+1 1{b<Ms}F (Ms, a) Bk(Xs)∂kpW ∗1,W (b − X1  s , a − Xs;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t − s)dbda  �  ds  We identify −pk,α(b, a, t) inside the integral on the set (b > Ms).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Concerning the  integral on the set (b < Ms), we introduce the density of (Ms, Xs) and identify  −pk,β(m, a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t) as factor of F(m, a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Finally, we identify the pm,γ and p1,γ, γ = α, β which come from the sum of Im and  I1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Note that pW ∗1,W  �  b − X1  s , a − Xs;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t − s  �  = 0 on the set {b < a1}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Integrating by  parts with respect to b between max  �  a1, Ms  �  and ∞ in Im yields  Im = −  � t  0  EP  ��  Rd F  �  max  �  a1, Ms  �  , a  �  B1(Xs)pW ∗1,W  �  max  �  a1, Ms  �  − X1  s , a − Xs;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t − s  �  da  �  ds  −  � t  0  EP  ��  Rd+1 1Ms<bF (b, a) B1(Xs)∂mpW ∗1,W  �  b − X1  s , a − Xs;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t − s  �  dbda  �  ds  (29)  Integrating by parts with respect to a1 between −∞ and b in I1 yields  I1 =  � t  0  EP  ��  Rd F (max (Ms, b) , b, ˜a) B1(Xs)pW ∗1,W (b − X1  s, b − X1  s , ˜a − ˜Xs;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t − s)dbd˜a  �  ds  −  � t  0  EP  ��  Rd+1 F (max (Ms, b) , a) B1(Xs)∂1pW ∗1,W (b − X1  s , a − Xs;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t − s)dbda  �  ds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  (30)  (i) The term pm,β(b, a, t) comes from the second term in Im (29) as the factor of F(b, a):  −  � t  0  EP  ��  Rd+1 1Ms<bF (b, a) B1(Xs)∂mpW ∗1,W  �  b − X1  s , a − Xs;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t − s  �  dbda  �  ds  (ii) The terms −p1,α(b, a, t) and −p1,β(b, a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t) come from the second term in I1 (30):  −  � t  0  EP  ��  Rd+1 F (max (b, Ms) , a) B1(Xs)∂1pW ∗1,W (b − X1  s, a − Xs;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t − s)dbda  �  ds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Inside the integral on the set (Ms < b) we identify −p1,α(b, a, t) and inside the integral  on the set (Ms > b) we identify −p1,β(b, a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t) as the factor of F(b, a), respectively as  22  AUTHOR NAMES  the factor of F(Ms, a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  (iii) The term −pm,α(b, a, t) comes from the sum of first terms in I1 (30) and Im (29).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Now we replace the variable b by a1, dbd˜a by da in the first terms of Im and I1:  I1  m = −  � t  0  EP  ��  Rd F �max �a1, Ms  � , a� B1(Xs)pW ∗1,W  �max �a1, Ms  � − X1  s , a − Xs;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t − s� da  �  ds  I1  1 =  � t  0  EP  ��  Rd F �max �Ms, a1� , a� B1(Xs)pW ∗1,W (a1 − X1  s , a − Xs;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t − s)da  �  ds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Note that  − pW ∗1,W  �  max  �  a1, Ms  �  − X1  s, a − Xs;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t − s  �  + pW ∗1,W (a1 − X1  s , a − Xs;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t − s)  =  �  −pW ∗1,W  �  Ms − X1  s, a − Xs;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t − s  �  + pW ∗1,W  �  a1 − X1  s , a − Xs;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t − s  ��  1Ms>a1  = −  � Ms  a1  ∂mpW ∗1,W  �  b − X1  s , a − Xs, t − s  �  db1Ms>a1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Then the sum of I1  m and I1  1 is:  −  � t  0  EP  ��  Rd+1 F(Ms, a)B1(Xs)∂mpW ∗1,W  �  b − X1  s, a − Xs;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t − s  �  1Ms>b>a1dadb  �  ds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  We introduce the density of the law of the pair (Ms, Xs) and we identify −pm,α(m, a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t)  as the factor of F(m, a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  These three steps achieve the proof of Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='2 when µ0 = δx0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Finally when µ0 is the law of X0, we have pV (m, w;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t, µ0) =  �  Rd pV (m, x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t, δx0)µ0(dx0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Then integrating with respect to µ0 the expression obtained in (21) for pV (m, x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t, δx0)  achieves the proof of Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='2 for any initial law µ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  □  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Proof of Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='1  Using some idea’s used in Garroni section V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='2 let us introduce the linear appli-  cations on L∞([0, T ], dt, L1(Rd+1, dmdx)), k = m, 1, · · · , d:  Ik,α[p](m, x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t) :=  � t  0  �  Rd+1 1b<mBk(a)∂kpW ∗1,W  �  m − a1, x − a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t − s  �  p(b, a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s)dbdads,  (31)  Ik,β[p](m, x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t) :=  � t  0  �  Rd+1 1b<mBk(a)∂kpW ∗1,W (b − a1, x − a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t − s)p(m, a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s)dbdads.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Let us introduce the functions, defined by induction:  p0(m, x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t, µ0) =  �  Rd pW 1∗,W (m − x1  0, x − x0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t)µ0(dx0),  pn = −  �  k=m,1,··· ,d  �  pk,α  n  + pk,β  n  �  (32)  PDE for the joint law of the pair of a continuous diffusion and its running maximum  23  and for k = m, 1, · · · , d, j = α, β and n ≥ 1, pk,j  n+1(m, x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t) := Ik,j[pn](m, x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Let us  denote the operator  I := −  �  j=α,β;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='k=m,1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=',d  Ik,j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  (33)  Moreover  one remarks that this means pn+1 = I(pn) and Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='2 leads to  pV = p0 + I(pV ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Let  Pn :=  n  �  k=0  pk,  n ≥ 0  (34)  Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Assume the vector B is bounded, then for all T the sequence (Pn)n  converges in L∞([0, T ], L1(Rd+1, dxdm)) to pV .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Moreover pV = �∞  n=0 pn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  The proof is a consequence of the two following lemmas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Let j = α, β, k = m, 1, · · · , d and T > 0 the linear applications Ik,j are  continuous on L∞([0, T ], dt, L1(Rd+1, dmdx)) : there exists a constant C such that for  all p ∈ L∞([0, T ], dt, L1(Rd+1, dmdx)) :  sup  s∈[0,t]  ∥Ik,j[p](.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=', .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s)∥L1(Rd+1,dmdx) ≤ C  � t  0  1  √t − s sup  u∈[0,s]  ∥p(.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=', .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' u)∥L1(Rd+1,dmdx)ds  (35)  As a consequence,  sup  s∈[0,t]  ∥I[p](.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=', .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s)∥L1(Rd+1,dmdx) ≤ 2(d+1)C  � t  0  1  √t − s sup  u∈[0,s]  ∥p(.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=', .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' u)∥L1(Rd+1,dmdx)ds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  (36)  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Let T > 0, p ∈ L∞([0, T ] × L1(Rd+1, dmdx)) and t ∈ [0, T ] and let φd+1 be  the Gaussian law density restrained to the subset {b > a1  +} (up to a constant)  φd+1(b, b − a1, ˜a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' 2t) :=  1  √  2πt  d+1 1b>a1  +e− b2+(b−a1)2+∥˜a∥2  4t  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  (37)  (i) Let j = α and k = m, 1, · · · , d, according to the definition of Ik,α and the  boundedness of B,  ��Ik,α[p](m, x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t)  �� ≤ ∥B∥∞  � t  0  �  Rd+1 1b<m|∂kpW ∗1,W  �  m − a1, x − a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t − s  �  p(b, a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s)|dbdads.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  24  AUTHOR NAMES  Using Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='2 there exists a constant D such that for k = m, 1, · · · , d:  |∂kpW ∗1,W (b, a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t) | ≤ D  √  tφd+1(b, b − a1, ˜a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' 2t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  (38)  So  ��Ik,α[p](m, x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t)  �� ≤ ∥B∥∞  � t  0  �  Rd+1  D  √t − sφd+1(m − a1, m − x1, ˜x − ˜a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t − s)|p(b, a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s)|dbdads.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  We operate an integration with respect to (m, x) using Tonelli’s theorem and omitting  the  indicator functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Since φd+1 is the density of a Gaussian law, we get the  following bound,  ��Ik,α[p](.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=', .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t)  ��  L1(Rd+1,dmdx) ≤D∥B∥∞  � t  0  �  Rd+1  1  √t − s|p(b, a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s)|dbdads  ≤2(d+1)/2D∥B∥∞  � t  0  1  √t − s sup  u≤s  ∥p(.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=', .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' u)∥L1(Rd+1,dbda)ds,  meaning inequality (35) when j = α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  (ii) Let j = β and k = m, 1, · · · , d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' According to the definition of Ik,β and the  boundedness of B,  ��Ik,β[p](m, x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t)  �� ≤ ∥B∥∞  � t  0  �  Rd+1 1b<m|∂kpW ∗1,W  �  b − a1, x − a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t − s  �  p(m, a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s)|dbdads.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Using (38) yields:  ��Ik,β[p](m, x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t)  �� ≤ ∥B∥∞  � t  0  �  Rd+1  D  √t − sφd+1(b−a1, b−x1, ˜x−˜a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' 2(t−s))|p(m, a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s)|dbdads.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  We operate an integration with respect to x then to b using Tonelli’s theorem and  omitting the indicator functions and using that φ is the density of a Gaussian law.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' So  the bound with respect to a multiplicative constant:  ��Ik,β[p](.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=', .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t)  ��  L1(Rd+1,dmdx) ≤D∥B∥∞2(d+1)/2  � t  0  �  Rd+1  1  √t − s|p(m, a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s)|dmdads  ≤D∥B∥∞2(d+1)/2  � t  0  1  √t − s sup  u≤s  ∥p(.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=', .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' u)∥L1(Rd+1,dmda)ds,  meaning inequality (35) for j = β.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Finally, estimation (36) is obtained by adding estimations (35) for j = α, β and  k = m, 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=', d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' The following lemma is a consequence of (36) in Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='2:  PDE for the joint law of the pair of a continuous diffusion and its running maximum  25  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' For all n  sup  u≤t  ∥pn(.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=', .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' u)∥L1(Rd+1,dmdx) ≤ (2(d + 1)C)ntn/2  Γ(1/2)n  Γ(1 + n/2),  (39)  sup  u≤t  ∥(pV − Pn)(.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=', .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' u)∥L1(Rd+1,dmdx) ≤ (2(d + 1)C)n+1t(n+1)/2 Γ(1/2)n+1  Γ((n + 3)/2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  (40)  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' (i) For all t > 0, p0(.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t) is a density of probability, so (39) is satisfied for  n = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' We now assume that (39) is satisfied for n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Using pn+1 = I[pn], (36) and the  induction e assumption:  sup  u≤t  ∥pn+1(.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=', .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' u)∥L1(Rd+1,dmdx) ≤ (2(d + 1)C)n+1  Γ(1/2)n  Γ(1 + n/2)  � t  0  √  sn  √t − sds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  We operate the change of variable s = tu and use  � 1  0 ua−1(1 − u)b−1du = Γ(a)Γ(b)  Γ(a+b) :  sup  u≤t  ∥pn+1(.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=', .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' u)∥L1(Rd+1,dmdx) ≤ (2(d + 1)C)n+1t(n+1)/2  Γ(1/2)n  Γ(1 + n/2)  Γ(1/2)Γ(1 + n/2)  Γ((n + 3)/2)  which proves (39) for all n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  (ii) Noting that P0 = p0 and pV − p0 = I[pV ] and applying (36) to pV yield  sup  u≤t  ∥(pV − P0)(.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=', .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' u)∥L1(Rd+1,dmdx) ≤ 2(d + 1)Ct1/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  But Γ(1/2)/Γ(3/2) = 2 so (40) is satisfied for n = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  We now suppose that (40) is satisfied for n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Using pV − Pn+1 =  p0 +I(pV )−(p0+I(Pn)) = I(pV −Pn), the bound (36) and the induction assumption:  sup  u≤t  ∥[pV − Pn+1](.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=', .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' u)∥L1(Rd+1,dmdx) ≤ 2(d + 1)C  � t  0  (2(d + 1)C)n+1 Γ(1/2)n+1  Γ((3 + n)/2)  √  sn+1  √t − sds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  We now operate the change of variable s = tu and  � 1  0 ua−1(1 − u)b−1du = Γ(a)Γ(b)  Γ(a+b)  with a = (n + 3)/2, b = 1  2:  sup  u≤t  ∥[pV − Pn+1](.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=', .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' u)∥L1(Rd+1,dmdx) ≤ (2(d + 1)C)n+2t(n+2)/2 Γ(1/2)n+2  Γ((4 + n)/2)  which proves (40) for n + 1 and thus for all n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  □  The series �  n  xn  Γ(n/2+1) is convergent for any x, so Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='3 is a consequence  of lemmas 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='2 and 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  26  AUTHOR NAMES  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Upper Bound of pV meaning Hypothesis 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='1 (i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  For all T > 0, x0 ∈ Rd, p ∈ L∞([0, T ], L1(Rd+1, dmdx)) the support of which being  included in {(m, x),  m > x1  0, m > x1} let us denote  N(p;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t, x0) :=  sup  (m,x)∈Rd+1,  m>x1,m>x1  0  |p(m, x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t)|  φd+1(m − x1  0, m − x1, ˜x − ˜x0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' 2t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  (41)  Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' For all T > 0 there exists a constant CT and for all n there exists  constants Cn = [∥B∥∞D(2(d+1))2d/2Γ(1/2)]  n  Γ(1+n/2)  such that: for all x0 ∈ Rd, 0 < t ≤ T,  (i)  |pn(m, x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t, x0)| ≤ Cntn/2φd+1(m − x1  0, m − x1, ˜x − ˜x0, 2t)1m>max(x1,x1  0)  (ii) |pV (m, x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t, x0)| ≤ CT φd+1(m − x1  0, m − x1, ˜x − ˜x0, 2t)1m>max(x1,x1  0)  (iii) For all µ0 initial probability measure on Rd,  supu>0 pV (m, m − u, ˜x, t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' µ0) ∈ L1([0, T ] × Rd, dtdmd˜x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Remark that, actually, this point (iii) is Hypothesis 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='1 (i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Point (ii) is a consequence of point (i), since pV = �∞  n=0 pn, and the series  �  n  1  Γ(1+n/2)xn admits an infinite radius of convergence (Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  We prove point (i) by induction on n using point (ii) in Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='2: p0(m, x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t, x0) ≤  e− (m−x1)2  4t  − ∥˜x−˜x0∥2  4t  −  (m−x1  0)2  4t  �  (2π)d+1td+1  1m>max(x1,x1  0) = φd+1(m − x1, m − x1  0, ˜x − ˜x0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' 2t)1m>max(x1,x1  0),  so N(p0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t, x0) ≤ 1, which is (i) for n = 0, C0 = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  We assume point (i) is true for pn, meaning N(pn;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t, x0) ≤ Cntn/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' By definition  pn+1 = I[pn], Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='4 proved below yields:  N(pn+1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t, x0) = N(I[pn];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t, x0) ≤ 2(d + 1)2d/2∥B∥∞DCn  � t  0  sn/2  �  2π(t − s)  ds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  We operate the change of variable s = tu  N(pn+1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t, x0) ≤ 2(d + 1)2d/2∥B∥∞D  √  2π  Cn(  √  t)n+1  � 1  0  un/2  √1 − uds  Using  � 1  0  un/2  √1−udu = Γ((n+2)/2)Γ(1/2)  Γ((n+3)/2)  and Cn definition:  N(pn+1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t, x0) ≤ Cn+1(  √  t)n+1,  PDE for the joint law of the pair of a continuous diffusion and its running maximum  27  this achieves the proof of point (i) in Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  (iii) Then for all x0 ∈ Rd and using x1 = m − u,  sup  u>0  pV (m, m − u, ˜x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t) ≤ CT φd+1(m − x1  0, 0, ˜x − ˜x0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' 2t) ∈ L1([0, T ] × Rd, dtdmd˜x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Since pV (m, x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t, µ0) =  �  Rd pV (m, x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t, x0)µ0(dx0) point (iii) is true.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  □  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Let T > 0, x0 ∈ Rd, p ∈ L∞([0, T ], dt, L1(Rd+1, dmdx)) such that the  support of p(.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=', .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t) is included in {(m, x),  m > x1  0, m > x1} and for all s ∈]0, T ]  N(p;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s, x0) < ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Then for j = α, k = m, 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' , d, the support of function Ij,k[p](.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t)  is included in {(m, x),  m > x1  0, m > x1}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Moreover for all t ∈ [0, T ] we have :  N(I[p];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t, x0) ≤ 2(d + 1)2d/2∥B∥∞D  � t  0  1  �  2π(t − s)  N(p;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s, x0)ds,  ∀t ∈ [0, T ].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Let T > 0, x0 ∈ Rd, p ∈ L∞([0, T ], dt, L1(Rd+1, dmdx)) such that for all  t > 0 the support of p(.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t) is included in {(m, x),  m > x1  0, m > x1}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  (i) For j = α, k = m, 1, · · · , d, using the definition of Iα,k yields:  Ik,α[p](m, x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t) :=  � t  0  �  Rd+1 Bk(a)∂kpW ∗1,W  �  m − a1, x − a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t − s  �  1x1  0<b<m,m>x1p(b, a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s)dbdads  So the support of Iα,k[p](.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t) is included in {(m, x) ∈ Rd+1, m > max(x1  0, x1)}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' For  now on, we only consider (m, x) such that m > max(x1, x1  0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Let p be a function such that ∀s ∈]0, T ] N(p;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' x0, s) < ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' The definition of Ik,α,  the boundedness of B, the fact that ∂kpW ∗,W satisfies (38) and the definition (41) of  N(p;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t, x0) imply  ��Ik,α[p](m, x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t)  �� ≤ ∥B∥∞  � t  0  �  Rd+1 N(p;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s, x0)  D  �  (t − s)  1m>x11m>b>max(a1,x1  0)  φd+1(m − a1, m − x1, ˜x − ˜a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t − s)φd+1(b − x1  0, b − a1, ˜a − ˜x0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s)dbdads.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  We integrate in ˜a using Lemme A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='3 (ii) with u = ˜x, v = ˜a, w = ˜x0 and the fact that  φd+1 is a Gaussian density of probability:  ��Iα,k[p](m, x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t)  �� ≤ 2(d−1)/2∥B∥∞D  (42)  � t  0  �  R2 N(p;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s, x0)1m>b>max(a1,x1  0)  e− ∥˜x− ˜  x0∥2  4t  �  (2πt)d−1  e− (m−a1)2  4(t−s) − (m−x1)2  4(t−s)  �  (2π)2(t − s)3  e−  (b−x1  0)2  4s  − (b−a1)2  4s  �  (2π)2s2  dbda1ds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  28  AUTHOR NAMES  Using point (i’) Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='2 with u = m, v = a1, w = b, k = 1, we integrate in da1 up  to b:  � b  −∞  e− (m−a1)2  4(t−s)  �  2π(t − s)  e− (b−a1)2  4s  �  (2πs)  da1 = e  −(m−b)2  4t  √  2πt  ΦG  ��  s  2t(t − s)(b − m)  �  where ΦG(u) =  � u  −∞ e−z2/2dz ≤ 1  2e−u2/2 for u = b − m < 0 according to Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='3  (iii).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' This yields the bound:  e  −(m−b)2  4t  √  2πt  e− s(b−m)2  4t(t−s) and  2  � b  −∞  e− (m−a1)2  4(t−s)  �  2π(t − s)  e− (b−a1)2  4s  �  (2πs)  da1 ≤ e− (m−b)2  4t  √  2πt  e− s(m−b)2  4t(t−s) = e− (m−b)2  4(t−s)  √  2πt  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Plugging this inequality inside (42) yields with Cd,B = 2(d+1)/2∥B∥∞D  ��Iα,k[p](m, x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t)  ��  Cd,B  ≤  � t  0  �  R  N(p;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s, x0)1m>b>x1  0  e− ∥˜x− ˜  x0∥2  4t  �  (2πt)d  e− (m−b)2  4(t−s) − (m−x1)2  4(t−s)  �  2π(t − s)2s  e−  (b−x1  0)2  4s  dbds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Omitting the indicator functions, Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='3 (ii) with u = m, v = b, w = x1  0, k = 1  implies  �  b<m  e− (m−b)2  4(t−s) e−  (b−x1  0)2  4s  �  2π(t − s)2πs  db ≤  �  2  2πte−  (m−x1  0)2  4t  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Inserting this result, we obtain  ��Iα,k[p](m, x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t)  �� ≤  √  2Cd,B  � t  0  N(p;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s, x0) e− ∥˜x− ˜  x0∥2  4t  �  (2πt)d+1  e−  (m−x1  0)2  4t  − (m−x1)2  4(t−s)  �  2π(t − s)  ds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  For 0 < s < t, e− (m−x1)2  4(t−s)  ≤ e− (m−x1)2  4t  , so  ��Iα,k[p](m, x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t)  �� ≤  √  2Cd,B  � t  0  N(p;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s, x0) e− ∥˜x− ˜  x0∥2  4t  �  (2πt)d+1  e−  (m−x1  0)2  4t  − (m−x1)2  4t  �  2π(t − s)  ds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Using the definition of φd+1 we identify  ��Iα,k[p](m, x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t)  �� ≤  √  2Cd,B  � t  0  N(p;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s, x0)φd+1(m − x1  0, m − x1, ˜x − ˜x0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' 2t)  �  2π(t − s)  ds  and with the definition of N, with respect to a multiplicative constant:  N(Iα,k[p], x0, t) ≤  √  2Cd,B  � t  0  N(p;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s, x0)  1  �  2π(t − s)  ds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  (ii) For j = β, k = m, 1, · · · , d using the definition of Iβ,k and the fact that the support  of p is included in {(m, x),  m > max(x1  0, x1)} yields Iβ,k[p](m, x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t) =  � t  0  �  Rd+1 1m>b>x1,m>x1  0,b>a1Bk(a)∂kpW 1∗,W (b − a1, x − a, t − s)p(m, a, s)dadbds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  PDE for the joint law of the pair of a continuous diffusion and its running maximum  29  Thus the support of Iβ,k[p](.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t) is included in {(m, x), m > max(x1, x0)}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' For now on  we only consider (m, x) satisfying m > max(x1, x1  0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Definition of Iβ,k, the boundedness  of B, the inequality (38) satisfied by ∂kpW ∗,W :  |∂kpW 1∗,W (b − a1, x − a, t − s)| ≤  D  √t−sφd+1(b − a1, b − x1, ˜x − ˜a, 2(t − s))  and the definition of N(p;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t, x0) yield:  ��Iβ,k[p](m, x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t)  �� ≤ ∥B∥∞D  � t  0  �  Rd+1 1m>b>x1,b>a1N(p;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s, x0)  e− (b−a1)2  4(t−s) − (b−x1)2  4(t−s) − ∥˜x−˜a∥2  4(t−s)  �  (2π)d+1(t − s)d+2  e−  (m−x1  0)2  4s  − (m−a1)2  4s  − ∥˜x0−˜a∥2  4s  �  (2π)d+1sd+1  dadbds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  We integrate in ˜a using Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='3 (ii) with u = ˜x, v = ˜a et w = ˜x0:  ��Iβ,k[p](m, x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t)  �� ≤ Cd,B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  (43)  � t  0  �  R2 1m>b>x1,b>a1 e− ∥˜x−˜x0∥2  4t  �  (2πt)d−1 N(p;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s, x0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='e− (b−a1)2  4(t−s) − (b−x1)2  4(t−s)  �  (2π)2(t − s)3  e−  (m−x1  0)2  4s  − (m−a1)2  4s  �  (2π)2s2  da1dbds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Using Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='3 (i’) for u = b, v = a1, w = m k = 1  � b  −∞  e− (b−a1)2  4(t−s)  �  2π(t − s)  e− (m−a1)2  4s  √  2πs  da1 =  √  2e− (b−m)2  4t  √  2πt  ΦG  ��  t  4s(t − s)[b − (s  t b + t − s  t  m)]  �  = e− (b−m)2  4t  √  2πt  ΦG  ��  t − s  4st [b − m]  �  ≤ e− (b−m)2  4t  √  2πt  e− t−s  4st [b−m]2 = e− (b−m)2  4s  √  2πt  the last bound coming from Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='3 (iii) since b − m < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  We plugg this estimation in (43)  ��Iβ,k[p](m, x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t)  �� ≤  Cd,B  � t  0  �  R  1m>b>x1 e− ∥˜x−˜x0∥2  4t  �  (2πt)d N(p;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s, x0)  e− (b−x1)2  4(t−s)  �  2π(t − s)2  e−  (m−x1  0)2  4s  − (b−m)2  4s  √  2πs  dbds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  We integrate with respect to b on R and we use Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='3 (ii) with u = x1, v = b,  w = m, k = 1:  ��Iβ,k[p](m, x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t)  �� ≤  √  2Cd,B  � t  0  e− (m−x1)2  4t  − ∥˜x−˜x0∥2  4t  �  (2πt)d+1  N(p;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s, x0) e−  (m−x1  0)2  4s  �  2π(t − s)  ds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  When 0 < s < t, e−  (m−x1  0)2  4s  ≤ e−  (m−x1  0)2  4t  so:  ��Iβ,k[p](m, x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t)  �� ≤  √  2Cd,B  � t  0  e− (m−x1)2  4t  − ∥˜x−˜x0∥2  4t  −  (m−x1  0)2  4t  �  (2πt)d+1  N(p;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s, x0)  1  �  2π(t − s)  ds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  30  AUTHOR NAMES  Under the integral we identify the factor φd+1(m − x1  0, m − x1, ˜x − ˜x0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' 2t) so  ��Iβ,k[p](m, x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t)  �� ≤  √  2Cd,Bφd+1(m − x1  0, m − x1, ˜x − ˜x0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' 2t)  � t  0  N(p;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s, x0)  1  �  2π(t − s)  dbds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Finally using the definition of N (41) we have proved  N(Iβ,k[p], x0, t) ≤  √  2Cd,B  � t  0  N(p;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s, x0)  1  �  2π(t − s)  ds  which achieves the proof of Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  □  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Proof of Hypothesis 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='1 (ii), case A = Id  Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' For any µ0 probability measure on Rd, for all (m, ˜x, t) ∈ Rd×]0, T ],  u �→ pV (m, m − u, ˜x, t) admits a limit when u goes to 0, u > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' The proof is a consequence of the three following lemmas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Recall that p0(m, x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t) = �  Rd pW ∗1,W (m − x1  0, x − x0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t)µ0(dx0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  lim  u→0,u>0 p0(b, b − u, ˜a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t) = p0(b, b, ˜a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t),  ∀u > 0,  (b, ˜a) ∈ Rd, ∀t > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' We have p0(b, b−u, ˜x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t) =  �  Rd2  b+u−x1  0  √  (2π)dtd+1 e−  (b+u−x1  0)2  2t  − ∥˜x−˜x0∥2  2t  1b≥x1  0,  u≥0µ0(dx0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Then, since the integrand is dominated by  D  √  (2π)dtd+1 and µ0 is a probability measure,  using Lebesgue’s dominated convergence Theorem yields:  lim  u→0,u>0 p0(b, b − u, ˜x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t) = p0(b, b, ˜x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t),  ∀ (b, ˜x) ∈ Rd, ∀t > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  □  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' For k = m, 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=', d recall that  pk,α(m, x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t) =  � t  0  �  Rd+1 1b<mBk(a)∂kpW ∗1,W (m − a1, x − a, t − s)pV (b, a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s)dbdads.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  The map u �→ pk,α(m, m − u, ˜x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t) converges to pk,α(m, m, ˜x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t) when u goes to 0+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' The proof wil be a consequence of Lebesgue dominated theorem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' First, the  map u �→ 1b<m∂kpW ∗1,W (m − a1, m − u − a1, ˜x − ˜a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t − s)pV (b, a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s) converges to  1b<m∂kpW ∗1,W (m − a1, ma1, ˜x − ˜a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t − s)pV (b, a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s) when u goes to 0+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Second it is dominated by qk,α(m, ˜x, a, b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s, x0) :=  |Bk(a)|1b<m sup  u>0  ��∂kpW ∗1,W (m − a1, m − u − a1, ˜x − ˜a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t − s)pV (b, a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s, x0)  ��  PDE for the joint law of the pair of a continuous diffusion and its running maximum  31  We seek to prove that  � T  0  �  R2d+1 qk,α(m, ˜x, a, b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s, x0)dsdbdaµ0(dx0) < +∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  (44)  According to estimation (38) of ∂kpW ∗1,W and estimation (ii) of Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='4, we  obtain  qk,α(m, ˜x, a, b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s, x0) ≤ ∥B∥∞1m>b>a1  D  √t − s  �  2π(t − s)  d+1 exp[−(m − a1)2  4(t − s)  − ∥˜x − ˜a∥2  4(t − s) ]  CT  √  2πs  d+1 exp[−(b − x1  0)2  4s  − (b − a1)  4s  − ∥˜x0 − ˜a∥2  4s  ].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  We integrate with respect to ˜a using Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='3 (ii) for k = d + 1, u = ˜x, v = ˜a and  w = ˜x0 :  �  Rd−1 qk,α(m, ˜x, a1, b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s, x1  0)d˜a ≤ 1m>b>a1  ∥B∥∞CT D2(d−1)/2  √t − s  �  2π(t − s)  2√  2πs  2  e− |˜x−˜x0∥2  4t  √  2πt  d−1  exp[−(m − a1)2  4(t − s)  − (b − x1  0)2  4s  − (b − a1)2  4s  ].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  We integrate with respect to a1 between −∞ and b using Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='3 (i’) for u = m,  v = a1 and w = b  �  Rd 1a1<bqk,α(m, ˜x, b, a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' x0)da ≤ 1b<m  ∥B∥∞CT D2d/2  √t − s  �  2π(t − s)  √  2πs  e− |˜x−˜x0∥2  4t  − (b−m)2  4t  √  2πt  d  exp[−(b − x1  0)2  4s  ]ΦG  ��  t  2s(t − s)(b − [s  t m + (t − s)  t  b])  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Note that  �  t  2s(t−s)(b − [ s  t m + (t−s)  t  b]) =  �  s  2t(t−s)(b − m) and using Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='3 (iii)  �  Rd qk,α(m, ˜x, b, a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s, x0)da ≤ 1b<m  ∥B∥∞CT D2d/2  √t − s  �  2π(t − s)  √  2πs  e− |˜x−˜x0∥2  4t  − (b−m)2  4t  √  2πt  d  exp[−(b − x1  0)2  4s  ] exp[−  s  t(t − s)  (b − m)2  4  ].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  We observe that 1  t +  s  t(t−s) =  1  t−s so that exp[− (b−m)2  4t  ] exp[−  s  t(t−s)  (b−m)2  4  ] = exp[− (b−m)2  4(t−s) ].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  We integrate with respect to b (neglecting the indicator function) using Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='3  (ii) for u = m, v = b and w = x1  0 and exp[− (m−x1  0)2  4t  ] ≤ 1:  �  Rd+1 qk,α(m, ˜x, b, a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s, x0)dadb ≤ 1m>x1  0  ∥B∥∞CT D2(d+1)/2  √t − s  e− |˜x−˜x0∥2  4t  √  t  d+1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  32  AUTHOR NAMES  Since µ0 is a probability measure then  � t  0  �  R2d+1 qk,α(m, ˜x, b, a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s, x0)dadbµ0(dx0)ds <  +∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  This is (44) and achieves the proof of Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='6  □  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' For k = m, 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=', d recall that  pk,β(m, x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t) =  � t  0  �  Rd+1 1b<mBk(a)∂kpW ∗1,W (b − a1, x − a, t − s)pV (m, a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s)dbdads.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  The map u �→ pk,β(m, m − u, ˜x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t) converges to 0 when u goes to 0+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Using estimation (38) of ∂kpW ∗1,W and estimation (ii) of Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='4  concerning pV , we dominate the integrand which defines pk,β(m, m − u, ˜x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t) by :  qk,β(m, u, ˜x, a, b, x0, s) :=  1m−u<b<m,a1<b  e− (b−a1)2  4(t−s) − (b−m+u)2  4(t−s)  − ∥˜x−˜a∥2  4(t−s) −  (m−x1  0)2  4s  − (m−a1)  4s  − ∥˜x0−˜a∥2  4s  √t − s  �  2π(t − s)  d+1√  2πs  d+1  up to a multiplicative constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Meaning that  ��pk,β(m, m − u, ˜x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t)  �� ≤ ∥B∥∞  � t  0  �  R2d+1 qk,β(m, u, ˜x, a, b, x0, s)dbdadsµ0(dx0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  (45)  We integrate with respect to ˜a using Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='3 (ii) with u = ˜x, v = ˜a and w = ˜x0  �  Rd−1 qk,β(m, u, ˜x, a, b, x0, s)d˜a ≤  √  2  d−1 e− ∥˜x−˜x0∥2  4t  √  2πt  d−1  e− (b−a1)2  4(t−s) − (b−m+u)2  4(t−s)  −  (m−x1  0)2  4s  − (m−a1)  4s  √t − s  �  2π(t − s)  2√  2πs  2  We integrate with respect to a1 between −∞ and b using Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='3 (i’) for u = b,  v = a1 and w = m :  �  Rd 1b>a1qk,β(m, u, ˜x, a, b, x0, s)da ≤  e− ∥˜x−˜x0∥2  4t  √  2πt  d  e− (b−m)2  4t  − (b−m+u)2  4(t−s)  −  (m−x1  0)2  4s  √t − s  �  2π(t − s)  √  2πs  ΦG  ��  t  s(t − s)2(b − s  t b − t − s  t  m)  �  = e− ∥˜x−˜x0∥2  4t  √  2πt  d  e− (b−m)2  4t  − (b−m+u)2  4(t−s)  −  (m−x1  0)2  4s  √t − s  �  2π(t − s)  √  2πs  ΦG  ��  t − s  2st (b − m)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Since b − m < 0, using Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='3 (iii)  �  Rd 1b>a1qk,β(m, u, ˜x, a, b, x0, s)da ≤ e− ∥˜x−˜x0∥2  4t  √  2πt  d  e− (b−m)2  4t  − (b−m+u)2  4(t−s)  −  (m−x1  0)2  4s  √t − s  �  2π(t − s)  √  2πs  e− t−s  4st (b−m)2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  PDE for the joint law of the pair of a continuous diffusion and its running maximum  33  Note that e− (b−m)2  4t  e− t−s  4st (b−m)2) = e− (b−m)2)  4s  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' We integrate this last bound with respect  to b between m − u and m using Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='3 (i’) for the triplet (m − u, b, m) and the  fact that s  t (m − u) + t−s  t m = s(m−u)+m(t−s)  t  �  Rd+1 1m−u<b<m,b<a1qk,β(m, u, ˜x, a, b, x0, s)dadb ≤ e− ∥˜x−˜x0∥2  4t  √  2πtd+1  e− (m−x1  0)2  4s  √t−s  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  �  ΦG  ��  t  2s(t−s)(m − s(m−u)+m(t−s)  t  )  �  − ΦG  ��  t  2s(t−s)(m − u − s(m−u)+m(t−s)  t  )  ��  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Then,  �  Rd+1 qk,β(m, u, ˜x, a, b, x0, s)dadb ≤  e− ∥˜x−˜x0∥2  4t  √  2πt  d+1  e−  (m−x1  0)2  4s  √t − s  �  ΦG  ��  s  2t(t − s)u  �  − ΦG  �  −  �  t − s  2t(t − s)u  ��  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Note that limu→0 ΦG  ��  s  2t(t−s)u  �  − ΦG  �  −  �  t−s  2t(t−s)u  �  = 0 and  ����ΦG  ��  s  2t(t−s)u  �  − ΦG  �  −  �  t−s  2t(t−s)u  ����� ≤ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Since µ is a probability measure, using  Lebesgue dominated theorem  lim  u→0+  � t  0  �  R2d+1 1m−u<b<m,b<a1qk,β(m, u, ˜x, a, b, x0, s)dadbµ0(dx0)ds = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Finally estimation (45) yields limu→0+ pk,β(m, m − u, ˜x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  □  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Cas d = 1  Proposition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Let the real diffusion X given by dXt = B(Xt)dt+A(Xt)dWt where  A, B fulfil (4) and (5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Then the density of probability pV satisfies Hypothesis 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='1, so  for any initial law µ0 and F ∈ C2  b (R2, R),  E [F(Mt, Xt)) = E [F(X0, X0)] +  � t  0  E [L (F) (Ms, Xs)] ds  + 1  2  � t  0  E  �  ∂mF(Xs, Xs)∥A(Xs)∥2 pV (Xs, Xs;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s)  pX(Xs;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s)  �  ds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  (46)  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' We operate a Lamperti transformation [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Whithout loss of generality, A  can be choosen positive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' In case d = 1 Assumption (5): “∃c > 0 such that for any  x ∈ R, A2(x) ≥ c” could be expressed:  ∃c > 0 such that for any x ∈ R, A(x) ≥ c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  (47)  34  AUTHOR NAMES  Let ϕ such that ϕ′ = 1  A and ϕ(0) = 0, so that ϕ′ is uniformly bounded and ϕ ∈ C2(R),  as is the function A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Moreover ϕ′ being strictly positive, ϕ is strictly increasing hence  invertible and we denote by ϕ−1 its inverse function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Under the initial condition  ϕ(0) = 0, using Itˆo formula Y = ϕ(X) satisfies  dYt =  �B  A ◦ ϕ−1(Yt) − 1  2A′ ◦ ϕ−1(Yt)  �  dt + dWt, Y0 = ϕ(X0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  (48)  Let Aϕ = 1 and Bϕ := B  A ◦ϕ−1− 1  2A′◦ϕ−1 which belongs to C1  b (R) as a consequence  of B ∈ C1  b , A ∈ C2  b .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Obviously, ϕ′ > 0 implies that ϕ is increasing, Y ∗  t = ϕ(X∗  t ) =  ϕ(Mt).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='1 in [9] can be easily extended to the case where X admits an initial law  µ0, thus the law of the pair (Y ∗  t , Yt) admits a density with respect to the Lebesgue  measure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Moreover, Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='2 in [9] sets out pV (b, a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t) =  pY ∗,Y (ϕ(b),ϕ(a);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='t)  A(b)A(a)  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Now  applying Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='4 to the pair (Bϕ, 1) the density pY ∗,Y satisfies Hypothesis 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Since functions A and ϕ are continuous  lim  u→0+ pV (b, b − u;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t) = pY ∗,Y (ϕ(b), ϕ(b);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t)  A2(b)  that means pV satisfies Hypothesis 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='1 (ii).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Using now (47)  sup  u>0  pV (b, b − u;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t) ≤ 1  c2 sup  u>0  pY ∗,Y (ϕ(b), ϕ(b − u);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t)  and since ϕ is increasing, if u > 0, ϕ(b − u) < ϕ(b) and denoting v = ϕ(b) − ϕ(b − u)  it gets v > 0, and  sup  u>0  pV (b, b − u;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t) ≤ 1  c2 sup  v>0  pY ∗,Y (ϕ(b), ϕ(b) − v;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  After the change of variable m = ϕ(b) so db = A(b)dm,  � T  0  �  R  sup  u>0  pY ∗,Y (ϕ(b), ϕ(b)−u;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t)dbdt =  � T  0  �  R  A(ϕ−1(m)) sup  u>0  pY ∗,Y (m, m−u;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t)dmdt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Since A is bounded and pY ∗,Y satisfies Hypothesis 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='1 (i),  � T  0  �  R A(ϕ−1(m)) supu>0 pY ∗,Y (m, m − u;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t)dmdt < ∞ and pV satisfies Hypothesis 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='1  (i) and (ii).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  □  PDE for the joint law of the pair of a continuous diffusion and its running maximum  35  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Conclusion  This paper establishes a PDE of which the density of the pair [Mt, Xt] running  maximum-diffusion process is a weak solution, under a quite natural assumption on  the regularity of pV around the boundary of ∆.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' This assumption is fulfilled when the  matrix coefficient of diffusion A is the identity matrix or when the dimension d = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  This PDE is degenerated then the classical results on uniqueness cannot be applied  here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' The case of non constant matrix A is an open problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Such generalization  could be useful in case of practical applications, as the management of barrier options,  in models including stochastic volatility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Tools  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Malliavin calculus tools  The material of this subsection is taken from section 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='2 in [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Let H = L2([0, T ], Rd) endowed with the usual scalar product ⟨.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=', .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='⟩H and the associated  norm ∥.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='∥H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' For all h ∈ H, W(h) :=  � T  0 h(t)dWt is a center Gaussian variable with  variance equal to ∥h∥2  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' If (h1, h2) ∈ H2, and ⟨h1, h2⟩H = 0, then, the random variables  W(hi), i = 1, 2, are independent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Let S denote the class of smooth random variables F defined by:  F = f(W(h1), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=', W(hn)), n ∈ N,  h1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=', hn ∈ H, f ∈ Cb(Rn).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  (49)  Definition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' The derivative of the smooth variable F defined in (49) is the H valued  random variable given by DF := �n  i=1 ∂if(W(h1), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=', W(hn))hi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  We denote the domain of the operator D in L2(Ω) by D1,2 meaning that D1,2 is the  closure of the class of smooth random variables S with respect to the norm  ∥F∥1,2 =  �  E[|F|2] + E[∥DF∥2  H]  �1/2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' L1,2 is the set of processes (us, s ∈ [0, T ]) which satisfy  u ∈ L2(Ω × [0, T ], Rd) and for all s ∈ [0, T ], us belongs to D1,2 and  ∥u∥2  L1,2 = ∥u∥2  L2([0,T ]×Ω) + ∥Du∥2  L2([0,T ]2×Ω) < ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  36  AUTHOR NAMES  Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Let u ∈ L1,2, then the divergence δ(u) is the unique random variable  of L2(Ω) such that E [Fδ(u)] = E [⟨DF, u⟩H] ,  ∀F ∈ S smooth random variable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  We apply Definition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='1 in [21] with u ∈ L1,2 and G ∈ D1,2:  E [Gδ(u)] = E [⟨DG, u⟩H] .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  (50)  Let x0 ∈ Rd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' We introduce the exponential martingale  Zx0  t  := exp  � d  �  k=1  �� t  0  Bk(x0+Ws)dW k  s − 1  2  � t  0  (Bk(x0+Ws))2ds  ��  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  (51)  When there is no ambiguity, we will omit the exponent x0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Let B ∈ C1  b (Rd, R), then for all x0 ∈ Rd the process  (B(x0 + Ws)Zx0  s ,  s ∈ [0, T ]) belongs to L1,2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Let x0 be fixed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' In this proof we omit the exponent x0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Note that Z2  t =  exp  �  2  d  �  k=1  � t  0  Bk(x0 + Ws)dW k  s − 4  2  � t  0  ∥B(x0 + Ws)∥2ds + 4 − 2  2  � t  0  ∥B(x0 + Ws)∥2ds  �  ≤ eT ∥B∥2  ∞ exp  �  2  d  �  k=1  � t  0  Bk(x0 + Ws)dW k  s − 4  2  � t  0  ∥B(x0 + Ws)∥2ds  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Then, Zt belongs to L2(Ω) for all t ∈ [0, T ] since  sup  t∈[0,T ]  E(Z2  t ) ≤ eT ∥B∥2  ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  (52)  Note that Zt = 1 + �d  k=1  � t  0 Bk(x0 + Ws)ZsdW k  s ,  t ∈ [0, T ].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Using Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='1,  Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='1 of [21], and the definition of L1,2, applied to the Rd+1-valued process  Y = (W, Z) with a null drift coefficient, the matrix Σ, (d + 1, d), defined by:  [σj,k(y), 1 ≤ j, k ≤ d] = Id, σd+1,k(y) = Bk(x1  0 + y1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=', xd  0 + yd)kz,  k = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=', d,  we obtain that Z belongs to L1,2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Since B is continuously differentiable with bounded  derivatives, the process (B(Ws + x0)Zs,  s ∈ [0, T ]) belongs to L1,2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  □  The following remark will be often used: using line -15 page 135 of [9] or Exercise  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='11 p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' 36 in [21]  D1  sW 1∗  t  = 1[0,τ](s) where τ := inf{s, W 1∗  s  = W 1∗  t }.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  (53)  PDE for the joint law of the pair of a continuous diffusion and its running maximum  37  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Brownian motion case estimations  Let us recall the density of distribution of the pair (W ∗,1  t  , W 1  t ), where W 1 is a one-  dimensional Brownian motion and W ∗,1 its running maximum (see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=', Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='2 in  [17] or [15]):  pW 1∗,W 1(b, a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t) = 2 2b − a  √  2πt3 exp −(2b − a)2  2t  1b>sup(a,0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Thus, using the independence of the components of the process W, the law of  (W 1∗  t , Wt) has a density with respect to the Lebesgue measure on Rd+1 denoted by  pW 1∗,W (.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t) :  pW 1∗,W (b, a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t) = 2 (2b − a1)  �  (2π)dtd+2 e− (2b−a1)2  2t  −  �d  k=2 |ak|2  2t  1b≥0,b≥a1, b ∈ R, a = (a1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=', ad) ∈ Rd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  (54)  Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' (i) For all t> 0, pW ∗1,W (.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t)  is the restriction to ¯∆ of a C∞(Rd+1)  function and there exists a universal constant D such that for x = b, a1, a2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='ad,  ��∂xpW ∗1,W (b, a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t)  �� ≤  D  �  (4π)dtd+2 e− b2+(b−a1)2  4t  −�d  k=2  (ak)2  4t 1b>max(a1,0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  (55)  As a consequence �  x=b,a1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=',ad  ��∂xpW ∗1,W (b, a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t − s)  �� ∈ L1([0, t] × Rd+1, dbdads).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  (ii) p0(m, x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t, x0) ≤  e− (m−x1)2  4t  − ∥˜x−˜x0∥2  4t  −  (m−x1  0)2  4t  �  (2π)d+1td+1  1m>max(x1,x1  0)  =  2(d+1)/2φd+1(m − x1, m − x1  0, ˜x − ˜x0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' 2t)1m>max(x1,x1  0),  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' (i) Let pW be the density of a d dimensional Brownian motion, and the  density of law of Wt ∀t > 0 : pW (.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t) ∈ C∞(Rd):  pW (x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t) =  1  √  2dπdtd e− �d  k=1  (xk)2  2t ,  t > 0,  x = (x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=', xd) ∈ Rd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Its derivative with respect to x1 is  ∂x1pW (x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t) = −  x1  √  2dπdtd+2 e− �d  k=1  (xk)2  2t ,  t > 0,  x = (x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=', xd) ∈ Rd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Its second derivatives are  ∂2  x1xkpW (x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t) =  x1xk  √  2dπdtd+4 e− �d  k=1  (xk)2  2t ,  t > 0,  x = (x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=', xd) ∈ Rd,  k = 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=', d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  ∂2  x1x1pW (x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t) =  (x1)2 − t  √  2dπdtd+4 e− �d  k=1  (xk)2  2t ,  t > 0,  x = (x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=', xd) ∈ Rd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  38  AUTHOR NAMES  Using (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='1) page 106 of [14] we obtain the analogous of (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='2) page 107 of [14]: there  exists a constant C such that  |∂2  x1x1pW (x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t)| + |∂2  x1xkpW (x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t)| ≤ C  t pW (x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' 2t),  k = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=', d,  t > 0,  x ∈ Rd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  (56)  Recall (54)  pW ∗1,W (b, a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t) = 2  2b − a1  �  (2π)dtd+2 e− (2b−a1)2  2t  −�d  k=2  (ak)2  2t 1b≥a1  +,  ∀(b, a) ∈ Rd+1,  t > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  We observe  pW ∗1,W (b, a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t) = −2∂x1pW (2b − a1, a2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=', ad;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t)1b≥a1  +.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  (57)  Then pW ∗1,W (.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=', .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t) is the restriction to ∆ of a C∞ function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Moreover, using the chain rule, x being (b, a1, · · · , ad) :  |∂xpW ∗1,W (b, a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t)| ≤ 4C  t pW (2b − a1, a2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=', ad;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' 2t)1b≥a1  +.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  (58)  On the set {(b, a),  b> max(0, a1)} we have  (2b − a1)2 = (b + b − a1)2 ≥ (b)2 + (b − a1)2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  (59)  Plugging estimation (59) into (58) yields (55) with D = 23C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  (ii) Recalling the definition  p0(m, x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t, x0) = pW 1∗,W (m−x1  0, x−x0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t) = 2m − x1 + m − x1  0  �  (2π)dtd+2  e−  (m−x1+m−x1  0)2  2t  − |˜x−˜x0∥2  2t  1m≥x1∨x1  0  we deduce the standard bound which uses xe−x2 ≤ e−x2/2 and (m − x1 + m − x1  0)2 ≥  (m − x1)2 + (m − x1  0)2:  p0(m, x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t, x0) ≤ e− (m−x1)2  4t  − ∥˜x−˜x0∥2  4t  −  (m−x1  0)2  4t  �  (2π)d+1td+1  1m>x1∨x1  0  = 2(d+1)/2φd+1(m − x1, m − x1  0, ˜x − ˜x0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' 2t)1m>x1∨x1  0,  □  PDE for the joint law of the pair of a continuous diffusion and its running maximum  39  Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' For all 0 < s < t, k ≥ 1 and all u, v, w ∈ Rk  (i)  ∥u − v∥2  t − s  + ∥v − w∥2  s  =  t  s(t − s)  ����v −  �s  t u + t − s  t  w  �����  2  + ∥u − w∥2  t  ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  (i′) k = 1,  � b  −∞  e− (u−v)2  4(t−s)  �  2π(t − s)  e− (w−v)2  4s  √  2πs dv =  √  2e− (u−w)2  4t  �  2πt)  ΦG  ��  t  s(t − s)[b − (s  t u + t − s  t  w)]  �  (ii)  �  Rk  e− ∥u−v∥2  4(t−s)  �  (2π(t − s))k  e− ∥w−v∥2  4s  �  (2πs)k dv = 2k/2 e− ∥u−w∥2  4t  �  (2πt)k  (iii)  For u > 0, 1 − ΦG(u) :=  � +∞  u  e− z2  2  √  2π dz = ΦG(−u) ≤ e− u2  2  2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Point (i) is proved by a development of both hands then an identification of  the coefficients of the squared norms and scalar products: ∥u∥2, ∥v∥2, ∥w∥2, u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='v, u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='w, v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  So we deduce (i’) as the integral of  e−  t  4s(t−s)(v−( s  t u+ t−s  t  w))  2− (u−w)2  4t  �  2π(t − s)  √  2πs  with respect to v up to b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  (ii) is a consequence of point (i) then an integration on Rk of the Gaussian density  with respect to dv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  (iii) The function u �→ ΦG(u) − e− u2  2  2  is null at 0, has a null limit when u goes to  −∞ and its derivative is u �→ − e− u2  2  √  2π + u e− u2  2  2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Its derivative vanishes at  �  2/π and is  negative for u ≤  �  2/π and positive after.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Then, u �→ ΦG(u) − e− u2  2  2  is negative for  u ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  □  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Proof of Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='3, boundary conditions of the PDE  Here we assume that pV is regular enough.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Let µ0(dx) = f0(x)dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Using Theorem  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='2, (6) means that:  for all F ∈ C2  b (Rd+1, Rd)  �  ¯  ∆  F (m, x)pV (m, x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' t)dmdx =  �  Rd F (m, m, ˜x)f0(m, ˜x)dmd˜x +  (60)  � t  0  �  ¯  ∆  LF (m, x)pV (m, x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s)dmdxds + 1  2  � t  0  �  Rd ∥A1(m, ˜x)∥2∂mF (m, m, ˜x)pV (m, m, ˜x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s)dmd˜xds  recalling L = Bi∂xi + 1  2Σij∂2  xi,xj where Σ = AAt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  (i) Integrating by parts with respect to a convenient dxk in  � t  0  �  ¯∆LF(m, x)pV (m, x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s)dmdxds and noting that the support of pV (.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=', .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s) is ¯∆, the  40  AUTHOR NAMES  boundary terms uniquely concern the component x1:  � t  0  �  ¯∆  LF(m, x)pV (m, x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s)dmdxds = −  � t  0  �  ¯∆  F(m, x)∂xk(BkpV )(m, x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s)dmdxds  − 1  2  � t  0  �  ¯∆  ∂xlF(m, x)∂xk[Σk,l(m, x)pV (m, x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s)]dmdxds  +  � t  0  �  Rd  �  F(m, m, ˜x)B1(m, ˜x) + 1  2∂xkF(m, m, ˜x)Σ1,k(m, ˜x)  �  pV (m, m, ˜x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s)dmd˜xds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  We again operate an integration by parts on the second term above on the right hand:  − 1  2  � t  0  �  ¯  ∆  ∂xlF (m, x)∂xkΣk,l(m, x)pV (m, x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s)]dmdxds =  1  2  � t  0  �  ¯  ∆  F (m, x)∂2  xk,xl[Σk,lpV ](m, x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s)dmdxds− 1  2  � t  0  �  Rd F (m, m, ˜x)∂xk  �  Σ1,kpV  �  (m, m, ˜x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s)dmd˜xds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Gathering these equalities yields  � t  0  �  ¯∆  LF(m, x)pV (m, x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s)dmdxds =  � t  0  �  ¯∆  F(m, x)L∗pV (m, x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s)dmdxds  −1  2  � t  0  �  Rd F(m, m, ˜x)∂xk  �  Σ1,kpV  �  (m, m, ˜x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s)dmd˜xds  (61)  +  � t  0  �  Rd  �  F(m, m, ˜x)B1(m, ˜x)pV (m, m, ˜x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s) + 1  2[∂xkFΣ1,kpV ](m, m, ˜x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s)  �  dmd˜xds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  (ii) Using F ∈ C2  b (Rd+1, R) with compact support in ∆ (so F(m, m, ˜x) = 0) we  deduce the equality in ∆ :  ∂tpV (m, x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s) = L∗pV (m, x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s),  ∀s > 0,  (m, x) ∈ ∆.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  (62)  We use (60), (61) and (62) applied to F ∈ C2  b (Rd+1, R) with compact support in ¯∆:  0 =  �  Rd F(m, m, ˜x)f0(m, ˜x)dmd˜x−1  2  � t  0  �  Rd F(m, m, ˜x)∂xk  �  Σ1,kpV  �  (m, m, ˜x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s)dmd˜xds  +  � t  0  �  Rd  �  F(m, m, ˜x)B1(m, ˜x)pV (m, m, ˜x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s) + 1  2[∂xkFΣ1,kpV ](m, m, ˜x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s)  �  dmd˜xds  + 1  2  � t  0  �  Rd ∥A1(m, ˜x)∥2∂mF(m, m, ˜x)p(m, m, ˜x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s)dmd˜xds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  (63)  We now operate integration by parts on the last two terms:  � t  0  �  Rd  �  [∂xkF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='Σ1,k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='pV ](m, m, ˜x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s) + ∥A1(m, ˜x)∥2∂mF (m, m, ˜x)pV (m, m, ˜x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s)  �  dmd˜xds =  −  � t  0  �  Rd  �  [F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='∂xk(Σ1,kpV )](m, m, ˜x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s) + ∂m(∥A1∥2pV )(m, m, ˜x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s)  �  dmd˜xds  (64)  Plugging (64) into (63) yields the boundary condition, namely a PDE of which pV is  a solution in the weak sense:  B1(m, ˜x)pV (m, m, ˜x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s) = 1  2  �  k≥1 ∂xk(Σ1,kpV )(m, m, ˜x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s)+  1  2  �  k≥1∂xk(Σ1,kpV )(m, m, ˜x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s) + 1  2∂m(∥A1∥2pV )(m, m, ˜x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s)  PDE for the joint law of the pair of a continuous diffusion and its running maximum  41  simplified as  B1(m, ˜x)pV (m, m, ˜x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s) =  �  k≥1  ∂xk(Σ1,kpV )(m, m, ˜x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s) + 1  2∂m(∥A1∥2pV )(m, m, ˜x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' s)  with the initial condition pV (m, m, ˜x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' 0) = f0(m, ˜x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  □  Acknowledgements  The authors would like to thank Monique JEANBLANC who gave us a valuable help  in writing this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' The authors would like to thank also the anonymous referees for  their constructive comments that improved the quality of this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  References  [1] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Alili, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Patie, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Pedersen (2005), Representations of the first hitting  time density of an Ornstein-Uhlenbeck process, Stoch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Models 21-4 , 967-980.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  [2] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Aza¨ıs, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Wschebor (2001), On the regularity of the distribution of the  maximum of one-parameter Gaussian processes, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' 119 , no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' 1, 70-98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  [3] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Bain ans D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Crisan (2007), Fundamentals of Stochastic Filtering, Springer-  Verlag.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  [4] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Blanchet-Scalliet, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Dorobantu, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Gay (2020), Joint Law of an  Ornstein-Uhlenbeck Process and its Supremum, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Proba.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' 57 , no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' 2, 541-558.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  [5] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Brezis (2011), Functional Analysis, Sobolev Spaces and Partial Differential  Equations, Springer-Verlag.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  [6] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Brown, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Hobson, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Rogers (2001), Robust hedging of barrier  options, Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Finance 11, 285-314  [7] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Coutin and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='Dorobantu (2011), First passage time law for some L´evy  processes with compound Poisson: existence of a density, Bernoulli 17-4, 1127-  1135.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  [8] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Coutin, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Ngom, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Pontier (2018), Joint distribution of a L´evy process  and its running supremum, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Proba.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' 55, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' 2, 488-512.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  42  AUTHOR NAMES  [9] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Coutin, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Pontier (2019), Existence and regularity of law density of a  diffusion and the running maximum of the first component, Stat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' and Proba.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  Letters, 153, 130-138  [10] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Cox, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Obloj (2011), Robust pricing and hedging of double touch  barrier options, SIAM J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Financial 2, 141-182 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  [11] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Cs`aki, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' F¨oldes, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Salminen (1987), On the joint distribution of the  maximum and its location for a linear diffusion, Annals IHP Proba.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Stat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' 23, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  2, 179-194.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  [12] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Doney, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Kyprianou (2006), Overshoots and undershoots of L´evy  processes, Ann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Probab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' 16, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' 1, 91-106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  [13] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Duembgen, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Rogers, (2015) The Joint Law of the Extrema, Final  Value and Signature of a Stopped Random Walk, Chapter in ‘Memoriam Marc Yor’,  S´eminaire de Probabilit´es XLVII, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' in Mathematics 2137, 321-338.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  [14] Garroni, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' and Menaldi, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' (1992), Green functions for second order  parabolic integro-differential problems, Pitman Research Notes in Mathematics  Series, Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=', NewYork, 275.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  [15] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' He, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Keirstead, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Rebholz (1998), Double lookbacks, Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Finance,  8, 201-228.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  [16] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Henry-Labord`ere, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Obloj, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Spoida, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Touzi (2016), The maximum  maximum of a martingale with given n-marginals, The Annals of Applied Proba.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  26(1), 1-44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  [17] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Jeanblanc, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Yor, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Chesney (2009), Mathematical Methods for  Financial Markets, Springer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  [18] Lamperti J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' (1964) A simple construction of certain diffusion processes, Journal  Math Kyoto University, 4, 161-170  [19] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Lagnoux, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Mercier, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Vallois (2015), Probability that the maximum  of the reflected Brownian motion over a finite interval [0, t] is achieved by its last  zero before t, Electron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Probab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' 20 , no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' 62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  PDE for the joint law of the pair of a continuous diffusion and its running maximum  43  [20] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Ngom (2016), thesis: Contributions `a l’´etude de l’instant de d´efaut d’un  processus de L´evy en observation compl`ete et incompl`ete, IMT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  [21] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Nualart (2006), The Malliavin calculus and related topics Second Edition,  Springer-Verlag New-York.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  [22] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Rogers (1993), The Joint Law of the Maximum and Terminal Value  of a Martingale, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' 95(4), 451-466 December 1993.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content='  [23] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Roynette, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Vallois, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
+page_content=' Volpi (2008), Asymptotic behavior of the passage  time, overshoot and undershoot for some L´evy processes, ESAIM PS 12 58–93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfiQFG/content/2301.02442v1.pdf'}
diff --git a/JtFAT4oBgHgl3EQfvR6i/content/tmp_files/2301.08675v1.pdf.txt b/JtFAT4oBgHgl3EQfvR6i/content/tmp_files/2301.08675v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..9437ff9eb0f8d88bb6d877331daa884c6a8875a5
--- /dev/null
+++ b/JtFAT4oBgHgl3EQfvR6i/content/tmp_files/2301.08675v1.pdf.txt
@@ -0,0 +1,4833 @@
+Astronomy & Astrophysics manuscript no. paper
+©ESO 2023
+January 23, 2023
+Kinematic differences between multiple populations
+in Galactic globular clusters⋆,⋆⋆
+Sven Martens1, Sebastian Kamann2, Stefan Dreizler1, Fabian Göttgens1, Tim-Oliver Husser1, Marilyn Latour1, Elena
+Balakina2, Davor Krajnovi´c3, Renuka Pechetti2, and Peter M. Weilbacher3
+1 Institut für Astrophysik und Geophysik, Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
+e-mail: sven.martens@uni-goettingen.de
+2 Astrophysics Research Institute, Liverpool John Moores University, 146 Brownlow Hill, Liverpool L3 5RF, UK
+3 Leibniz-Institut für Astrophysik Potsdam (AIP), An der Sternwarte 16, 14482 Potsdam, Germany
+Received MONTH DD, YYYY; accepted MONTH DD, YYYY
+ABSTRACT
+Aims. The formation process of multiple populations in globular clusters is still up for debate. These populations are characterized by
+different light-element abundances. Kinematic differences between the populations are particularly interesting in this respect, because
+they allow us to distinguish between single-epoch formation scenarios and multi-epoch formation scenarios. We derive rotation and
+dispersion profiles for 25 globular clusters and aim to find kinematic differences between multiple populations in 21 of them to
+constrain the formation process.
+Methods. We split red-giant branch (RGB) stars in each cluster into three populations (P1, P2, P3) for the type-II clusters and two
+populations (P1 and P2) otherwise using Hubble photometry. We derive the global rotation and dispersion profiles for each cluster by
+using all stars with radial velocity measurements obtained from MUSE spectroscopy. We also derive these profiles for the individual
+populations of each cluster. Based on the rotation and dispersion profiles, we calculate the rotation strength in terms of ordered-over-
+random motion (v/σ)HL evaluated at the half-light radius of the cluster. We then consistently analyse all clusters for differences in the
+rotation strength of their populations.
+Results. We detect rotation in all but four clusters. For NGC 104, NGC 1851, NGC 2808, NGC 5286, NGC 5904, NGC 6093,
+NGC 6388, NGC 6541, NGC 7078 and NGC 7089 we also detect rotation for P1 and/or P2 stars. For NGC 2808, NGC 6093 and
+NGC 7078 we find differences in (v/σ)HL between P1 and P2 that are larger than 1σ. Whereas we find that P2 rotates faster than P1
+for NGC 6093 and NGC 7078, the opposite is true for NGC 2808. However, even for these three clusters the differences are still of
+low significance. We find that the strength of rotation of a cluster generally scales with its median relaxation time. For P1 and P2 the
+corresponding relation is very weak at best. We observe no correlation between the difference in rotation strength between P1 and
+P2 and cluster relaxation time. The stellar radial velocities derived from MUSE data that this analysis is based on are made publicly
+available.
+Key words. globular clusters: general – stars: kinematics and dynamics – techniques: imaging spectroscopy
+1. Introduction
+Classically, it is assumed that all stars in a globular cluster form
+in the same molecular cloud and therefore are identical in age
+and chemical abundances. The discovery of multiple popula-
+tions of stars within globular clusters calls this into question.
+These populations generally differ in light element abundances
+(Carretta et al. 2009), but there is no evidence of age differences
+larger than ∼ 0.1 Gyrs (Bastian & Lardo 2018; Martocchia et al.
+2018). Using these abundance differences, the stars of most clus-
+ters (type-I clusters) can be separated into at least two popula-
+tions. One population has a scaled solar metallicity, whereas the
+other populations are always enriched in some light elements
+(such as N or Na) and depleted in others (such as C or O). The
+⋆ Table 2 is only available at the CDS via anonymous ftp
+to cdsarc.u-strasbg.fr (XXXX) or via http://cdsarc.u-strasbg.fr/viz-
+bin/cat/J/A+A/XXX/Lzzz
+⋆⋆ Based on observations collected at the European Organisation
+for Astronomical Research in the Southern Hemisphere, Chile (pro-
+posal IDs 094.D-0142, 095.D-0629, 096.D-0175, 097.D-0295, 098.D-
+0148, 099.D-0019, 100.D-0161, 101.D-0268, 102.D-0270, 103.D-
+0204, 105.20CR.002)
+fraction of enriched to non-enriched stars and the strength of the
+spread in light element abundances increase with cluster mass
+(e.g. Carretta et al. 2010a; Milone et al. 2017). There is evidence
+of metallicity spreads within some globular clusters for quite
+some time (e.g. Carretta et al. 2010b). Milone et al. (2017) found
+that for these clusters (type-II clusters) the two stellar popula-
+tions are themselves split. Type-II clusters exhibit multiple sub-
+giant and red giant branches, likely due to variations in heavy-
+elements abundances. Pfeffer et al. (2021) discussed several of
+these clusters and argued that some of them are actually rem-
+nants of nuclear star clusters. The occurrence of multiple popu-
+lations is not limited to Galactic globular clusters, but they have
+also been observed in clusters of other galaxies (e.g. Mucciarelli
+et al. 2009; Milone et al. 2009; Dalessandro et al. 2016). Fur-
+thermore, Martocchia et al. (2018) found that cluster age might
+play a role in the onset of multiple populations, because they
+did not detect light-element variations in clusters younger than
+∼ 1.7 Gyr. However, by analyzing main sequence stars instead of
+red giant branch stars Cadelano et al. (2022) found evidence for
+multiple populations in the 1.5 Gyr old star cluster NGC 1783.
+Article number, page 1 of 27
+arXiv:2301.08675v1  [astro-ph.GA]  20 Jan 2023
+
+A&A proofs: manuscript no. paper
+0.5
+0.4
+0.3
+0.2
+0.1
+0.0
+0.1
+0.2
+F275W
+F814W
+0.1
+0.0
+0.1
+0.2
+0.3
+0.4
+CF275W
+2 F336W + F438W
+NGC2808
+P1 (N=371)
+P2 (N=1208)
+0.25
+0.20
+0.15
+0.10
+0.05
+0.00
+0.05
+F275W
+F814W
+0.0
+0.1
+0.2
+0.3
+CF275W
+2 F336W + F438W
+NGC1851
+P1 (N=184)
+P2 (N=357)
+P3 (N=272)
+Fig. 1. Chromosome maps for NGC 2808 and NGC 1851, where the identified populations of each cluster are labeled with different colors and
+symbols. For the type-II cluster NGC 1851 there is an additional population compared to NGC 2808.
+Several formation scenarios for multiple populations in glob-
+ular clusters have been put forward, but each scenario comes
+with its caveats (for a detailed review see Bastian & Lardo 2018).
+There are two types of formation scenarios that we discuss here
+briefly. On the one hand, multi-epoch formation scenarios pro-
+pose the formation of a second generation of stars that form
+from gas polluted by primordial stellar sources, such as asymp-
+totic giant branch stars or fast-rotating massive stars (Cottrell &
+Da Costa 1981; Renzini 2013; Decressin et al. 2007a,b). On the
+other hand, single-epoch formation scenarios suggest that some
+stars accrete material when moving through the cluster center in
+order to explain the observed spread in light-element abundances
+(Bastian et al. 2013; Gieles et al. 2018).
+The structural and kinematical differences between the mul-
+tiple populations of globular clusters today could give insights
+on the formation process of these populations. Even though kine-
+matic differences were imprinted during the birth of each cluster,
+and they diminish over time due to the interactions between stars
+during cluster evolution, at least some clusters are still expected
+to show measurable differences in their present day kinematics
+(Vesperini et al. 2013; Hénault-Brunet et al. 2015; Tiongco et al.
+2019). Differences in the concentrations of stars between pop-
+ulations at the time of formation would entail differences in ra-
+dial anisotropies over time (e.g. Richer et al. 2013; Bellini et al.
+2015). Currently, a majority of globular clusters shows a higher
+concentration of stars from the enriched population compared to
+the pristine population (e.g. Dalessandro et al. 2019).
+Hénault-Brunet et al. (2015) showed that multi-epoch and
+single-epoch formation scenarios result in very similar radial
+anisotropy profiles, as they all assume that the second popu-
+lations forms centrally concentrated relative to the first popu-
+lation. Therefore, anisotropy cannot be used to distinguish be-
+tween these two types of scenarios. However, these two forma-
+tion scenarios would entail different initial conditions for the
+kinematics of these populations of stars. For multi-epoch forma-
+tion scenarios, the rotation velocity is expected to be lower for
+the non-enriched population compared to the N-enriched popu-
+lation. On the contrary, for single-epoch formation scenarios, the
+non-enriched population is expected to have a higher rotation
+velocity than the N-enriched population (Hénault-Brunet et al.
+2015).
+Studies have been carried out to look for these differences
+in several globular clusters. In particular, Cordero et al. (2017)
+were the first to find rotational differences between multiple
+populations in a globular cluster for NGC 6205. Furthermore,
+no kinematic differences between populations have been found
+for NGC 6121 (Cordoni et al. 2020), NGC 6838 (Cordoni
+et al. 2020), NGC 6352 (Libralato et al. 2019), NGC 6205 and
+NGC 7078 (Szigeti et al. 2021). For NGC 104, Milone et al.
+(2018b) and Cordoni et al. (2020) found no differences in the ro-
+tation pattern between populations, but the latter did find that the
+enriched population exhibits stronger anisotropy than the non-
+enriched population. Cordoni et al. (2020) also found significant
+differences in the phases of the rotation curves between popula-
+tions for NGC 5904. However, Szigeti et al. (2021) could not find
+significant differences in the rotation curves of this cluster, but
+for NGC 5272 they found that the enriched population is rotat-
+ing faster than the non-enriched population. Bellini et al. (2015)
+found differences in the radial anisotropy of NGC 2808 based on
+proper motion data, but there is no analysis on radial rotation and
+dispersion profiles yet for this cluster. For NGC 6362, Dalessan-
+dro et al. (2021) found that the enriched population is rotating
+faster than the non-enriched population. Kamann et al. (2020)
+found similar results for NGC 6093 in that one of the enriched
+populations they identified is rotating significantly stronger than
+the non-enriched population. The overall lack of uniformity and
+agreement in these results emphasizes the need to further study
+the kinematic differences in multiple populations of globular
+clusters.
+In this work, we are following the approach described by
+Kamann et al. (2020) to systematically study the kinematics for
+25 galactic globular clusters and looking at differences between
+populations in 21 of them. We used radial velocities derived from
+MUSE spectroscopy in combination with radial velocities from
+Baumgardt & Hilker (2018) to extend the radial coverage of each
+globular cluster, as described in Section 2. In Section 3 we de-
+scribe our approach to split the stars of each cluster into two or
+three populations based on photometric data. We use the stel-
+lar radial velocities to create radial rotation and dispersion pro-
+files and derive parameters to characterize the global dynamics
+of each cluster and of its stellar populations. We present the re-
+sults of this analysis in Section 4 and conclude in Section 5.
+Article number, page 2 of 27
+
+Sven Martens et al.: Kinematic differences between multiple populations in Galactic globular clusters
+2. Data
+The globular clusters analyzed in this study were observed with
+the Multi Unit Spectroscopic Explorer (MUSE, Bacon et al.
+2010). MUSE is an integral field spectrograph mounted at UT4
+of the ESO Very Large Telescope (VLT) that has been in op-
+eration since 2014. It features a wide-field mode with a field of
+view of 1′×1′ at a sampling of 0.2′′ per pixel. Since 2019 MUSE
+also possesses a narrow-field mode that covers a field of view of
+7.5′′ × 7.5′′ at a sampling of 0.025” per pixel. Both modes cover
+a spectral range of 4750 Å − 9350 Å with a corresponding spec-
+tral resolution (R) of 1770 at 4750 Å and 3590 at 9350 Å. This
+analysis is based on the MUSE Galactic globular cluster survey,
+presented in Kamann et al. (2018). We are using all available
+wide-field mode data for each globular cluster.
+Basic data reduction is carried out using the official MUSE
+pipeline (Weilbacher et al. 2020). The process of extracting spec-
+tra of single stars from the resulting datacube is described in de-
+tail by Kamann et al. (2018). In short, the program PAMPELMUSE
+by Kamann et al. (2013) is used in combination with a reference
+source catalog derived from HST photometry (Sarajedini et al.
+2007; Anderson et al. 2008) to determine the position of each
+resolved star in the MUSE data and to fit the MUSE PSF as a
+function of wavelength to retrieve stellar spectra.
+As described by Husser et al. (2016), the line-of-sight ve-
+locity of each star is derived from its spectrum using cross-
+correlation and a full spectral fitting approach. By cross-
+correlating each spectrum against a set of template spectra, the
+velocity vlos,cc is derived. The value of vlos,cc is then used as an
+initial guess for the full spectral fitting method, described in de-
+tail in Husser et al. (2016). Using a Levenberg-Marquardt algo-
+rithm, the observed stellar spectra are fitted against the Göttingen
+Spectral Library (Husser et al. 2013) to derive the stellar metal-
+licity [M/H], effective temperature Teff, and radial velocity vlos,fit.
+To retain a reliable data set, we are using a set of filters on the
+line-of-sight velocities derived from MUSE spectra. We are em-
+ploying the reliability parameter Rtotal > 0.8 described in Giesers
+et al. (2019). It ensures that the value of vlos,cc is trustworthy
+and consistent with vlos,fit and that the analyzed spectrum has a
+signal-to-noise ratio of S/N > 5. Additionally, we are remov-
+ing stars that show temporal variations in their line-of-sight ve-
+locities (e.g. binaries, pulsating stars) because in such cases the
+measured velocities do not trace the gravitational potentials of
+the host clusters. We use the method described by Giesers et al.
+(2019) to derive the probability pvar that any star that was ob-
+served multiple times shows temporal variance in velocity. We
+exclude all stars with pvar > 0.5. To derive one value for the
+line-of-sight velocity for each star, we average over MUSE ve-
+locity measurements for stars that have been observed multiple
+times. The stellar coordinates and averaged radial velocities used
+for this analysis are listed in Table 2 which is only available in
+electronic form at CDS and on the Göttingen Research Online
+repository, at XXX.
+To increase the radial coverage of each cluster, we use stel-
+lar velocities from Baumgardt & Hilker (2018) in addition to the
+MUSE data. We match the Baumgardt & Hilker (2018) data to
+HST photometry from Anderson et al. (2008), but the radial ve-
+locities extend much further out than the HST data, so that most
+radial velocities are not matched, but simply added to our data
+set. Before combining, the respective systematic cluster velocity
+is subtracted from the stellar velocities to minimize systematic
+differences between data sets. If a star is included in the sam-
+ples of both MUSE and Baumgardt & Hilker (2018), we aver-
+Table 1. Overview of the number of stars per cluster and population.
+Cluster
+Nall
+NMUSE
+NP1
+NP2
+NP3
+NGC 104
+32486
+28588
+343
+1250
+–
+NGC 362
+8937
+8244
+234
+599
+22
+NGC 1851
+15182
+13250
+184
+357
+272
+NGC 1904
+5523
+4373
+–
+–
+–
+NGC 2808
+15621
+13760
+371
+1208
+–
+NGC 3201
+5206
+3917
+40
+53
+–
+NGC 5286
+7373
+6472
+264
+371
+123
+NGC 5904
+19096
+18297
+177
+587
+–
+NGC 6093
+11419
+10879
+367
+582
+–
+NGC 6218
+8053
+6156
+88
+123
+–
+NGC 6254
+15418
+14744
+135
+243
+–
+NGC 6266
+15527
+14255
+–
+–
+–
+NGC 6293
+4455
+3081
+–
+–
+–
+NGC 6388
+14711
+12528
+726
+1431
+404
+NGC 6397
+11728
+8681
+19
+50
+–
+NGC 6441
+13226
+11494
+1005
+1793
+–
+NGC 6522
+6333
+2641
+–
+–
+–
+NGC 6541
+12560
+11029
+339
+352
+–
+NGC 6624
+7815
+6012
+130
+332
+–
+NGC 6656
+17230
+11544
+122
+166
+113
+NGC 6681
+5797
+4749
+38
+249
+–
+NGC 6752
+15525
+13721
+104
+267
+–
+NGC 7078
+13770
+12899
+390
+697
+–
+NGC 7089
+12727
+12167
+264
+1086
+36
+NGC 7099
+10046
+7705
+81
+182
+–
+Notes. Nall describes the numer of stars including data from Baumgardt
+& Hilker (2018), whereas NMUSE is based solely on MUSE data.
+age the stellar velocities from both sources. As shown by Ka-
+mann et al. (2018), the stellar radial velocities from MUSE and
+Baumgardt & Hilker (2018) agree in regions where they over-
+lap. In the outer regions the completeness in terms of fraction
+of stars with a radial velocity measure is significantly smaller
+than in the center since the Baumgardt & Hilker sample only
+consists of giant branch stars. Because of energy equipartition,
+which causes mass segregation, it is possible that this affects the
+velocity dispersion in the outer regions. However, using the for-
+mula by Bianchini et al. (2016) we estimated that the difference
+between our MUSE sample and the Baumgardt & Hilker sample
+in dispersion is ≲ 0.1 km/s based on the average masses of stars
+in either sample, which is fully within the uncertainties of our
+measurements.
+3. Methods
+3.1. Population Split
+The separation into multiple populations is based on the chromo-
+some map of each globular cluster. A chromosome map, which
+was first introduced by Milone et al. (2017), is a pseudo-color
+color diagram using a combination of the HST filters F275W,
+F336W, F438W and F814W that splits the stars of a cluster into
+its populations. We use photometry from the HST UV Globular
+Cluster Survey (HUGS) from Piotto et al. (2015) and Nardiello
+et al. (2018a) to create these maps, as explained in Latour et al.
+(2019). We note that only RGB stars are included in the pop-
+ulation analysis because the chromosome maps are tailored to
+distinguish populations at this evolutionary phase.
+Article number, page 3 of 27
+
+A&A proofs: manuscript no. paper
+We need a consistent population separation because we want
+to compare the kinematics of equivalent populations between
+clusters. For type-I clusters, we use the fact that these clusters
+always consist of one population with a scaled-solar abundance
+(P1) and at least one additional population (P2) that differs in
+abundances to P1. Therefore, we follow the classification by
+Milone et al. (2017) and divide the stars of type-I clusters into
+two groups using the chromosome map. The left panel of Fig. 1
+shows our chromosome map and identified populations P1 and
+P2 for NGC 2808. Stars from P1 are always found in the lower
+part of the chromosome map around (0, 0) coordinate and, de-
+pending on the cluster, partly extend horizontally, whereas P2
+stars are located above P1 stars and extend diagonally toward
+the top left.
+Type-II clusters contain stars that are enhanced in some par-
+ticular heavy-elements, such as barium and lanthanum, possibly
+iron as well, compared to P1 and P2 stars (Marino et al. 2015).
+These metal-enhanced stars are found on the reddest part of the
+RGB in the CMD (see, e.g. Milone et al. 2017). For the Type-
+II clusters, we consider these stars as a third population (P3).
+The right panel in Fig. 1 shows our split into three populations
+for the type-II cluster NGC 1851. The position of P1 and P2 for
+NGC 1851 are similar to NGC 2808, but the third population has
+a distinct position on the upper-right region of the chromosome
+map.
+We analyze 25 globular clusters, six of which are considered
+type-II clusters. As briefly mentioned in Section 1, some type-II
+clusters might actually be the remnants of nuclear star clusters.
+However, Pfeffer et al. (2021) conclude that none of the type-
+II clusters in our sample are remnants of nuclear star clusters.
+Therefore, we treat them as globular clusters. A list of all clusters
+with the number of stars used in the analysis of the global kine-
+matics, and the number of stars per population, are shown in Ta-
+ble 1. For NGC 1904, NGC 6266, NGC 6293 and NGC 6522 the
+necessary HUGS photometric data to separate their RGB stars
+into populations are not available. In these cases, we only derive
+the global kinematic properties.
+3.2. Kinematics
+To study the kinematic differences between populations, we first
+use the radial velocities of all stars in the cluster to derive its
+global kinematics. Then we repeat the same procedure, includ-
+ing only the RGB stars assigned to specific populations. From
+the radial velocity data we create kinematic profiles and finally
+derive the ratio of ordered-over-random motion (v/σ)HL and a
+proxy for the spin parameter λR,HL. Both are evaluated at the
+half-light radius to characterize the strength of rotation for all
+clusters and each of their populations. We use a very similar ap-
+proach as described in Kamann et al. (2020), but we repeat the
+important assumptions and formulas below.
+To create kinematic profiles, we need to derive the rotational
+velocity vrot and the line-of-sight velocity dispersion σlos of each
+cluster as a function of radius. To derive these parameters, we
+employ the maximum-likelihood approach described in Kamann
+et al. (2018). We assume that the line-of-sight stellar velocities
+at any position (x, y) may be approximated by a Gaussian with
+mean vlos and standard deviation σlos. To account for the posi-
+tion of each star within the cluster with respect to the rotation
+axis of that cluster, we parameterize the line-of-sight velocities
+according to vlos(r, θ) = vrot(r) sin(θ − θ0), where r =
+�
+x2 + y2 is
+the distance from the cluster center, θ0 is the angle of the cluster
+rotation axis, and θ = atan2(y, x) is the position angle measured
+counter-clockwise from north to east.
+As described in Kamann et al. (2020), we use parametric and
+non-parametric models to analyze the stellar rotation velocities.
+For the non-parametric approach, we simply bin velocities ra-
+dially and derive the rotation velocity and velocity dispersion
+for each bin. The parametric rotation profile vrot we employ is
+characteristic for systems that have undergone violent relaxation
+(Lynden-Bell 1967; Gott 1973):
+v(r) = vsys + vrot(r) = vsys + 2vmax
+rpeakr
+r2
+peak + r2 ,
+(1)
+where vsys is the systematic velocity, vmax is the maximum ro-
+tation velocity reached at radial distance rpeak. The parametric
+dispersion profile we use is a Plummer (1911) profile
+σlos =
+σmax
+�
+1 +
+� r
+a0
+�2� 1
+4 .
+(2)
+We differ in our approach to handling non-member stars com-
+pared to Kamann et al. (2020). They used cluster membership
+probabilities that were derived from stellar metallicities and line-
+of-sight velocities, as described by Kamann et al. (2016). We
+cannot take the same approach, because we do not have metal-
+licities for the additional Baumgardt & Hilker stars. We modified
+the method of membership determination in order to have con-
+sistent membership probabilities for stars from both data sets. In
+particular, we introduce a prior on the membership probability
+for each star pi that is related to the stellar surface density of the
+cluster ρ(ri) at the radial distance ri of that star from the cluster
+center according to
+pi(r) =
+ρ(ri)
+ρ(ri) + ffg
+,
+(3)
+where ffg measures the fractional contribution of foreground
+sources to the observed source density. To describe the stellar
+surface density of each cluster, we use the LIMEPY models de-
+scribed in Gieles & Zocchi (2015), with parameters for each
+cluster as determined by de Boer et al. (2019). For NGC 6441
+and NGC 6522 de Boer et al. (2019) do not provide any param-
+eters for these models, so we chose to use King models (King
+1966) with the necessary parameters of central concentration and
+core radius taken from Harris (1996, 2010 edition). We modified
+the likelihood function Li of each star i to not solely be based on
+the likelihood of the rotation and dispersion model Lcl,i, but to
+include the membership probability pi as follows:
+Li = piLcl,i + (1 − pi)Lfg,i
+(4)
+where Lfg,i is the likelihood that star i is part of a foreground
+population. This foreground population is built from single stars
+included in a Besançon model (Robin et al. 2003) at the posi-
+tion of each cluster. The foreground likelihood for each star Lfg,i
+is then defined as the superposition of Gaussian kernels for M
+simulated stars with line-of-sight velocities vfg,j:
+Lfg,i = 1
+M
+M
+�
+j=1
+exp
+����������−
+�
+vfg,j − vlos,i
+�2
+2 · v2
+err,i
+���������� ,
+(5)
+where verr,i is the uncertainty of the measured line-of-sight ve-
+locities vlos,i.
+Article number, page 4 of 27
+
+Sven Martens et al.: Kinematic differences between multiple populations in Galactic globular clusters
+10
+1
+100
+101
+102
+0
+2
+4
+6
+OVERALL
+W
+N
+E
+S
+0
+10
+1
+100
+101
+102
+r/arcsec
+5
+10
+15
+0
+2
+4
+6
+8
+P1
+W
+N
+E
+S
+0
+r/arcsec
+2.5
+5.0
+7.5
+10.0
+12.5
+15.0
+10
+1
+100
+101
+102
+r [arcsec]
+0
+2
+4
+6
+P2
+W
+N
+E
+S
+0
+10
+1
+100
+101
+102
+r [arcsec]
+2.5
+5.0
+7.5
+10.0
+12.5
+vrot [km/s]
+r [km/s]
+NGC 2808
+Fig. 2. Rotation and dispersion profiles for NGC 2808 and each of its populations. The rotation profiles for each population are shown on the left,
+whereas the dispersion profiles are shown on the right. In the center, the angle of rotation is shown. The continuous profiles (solid lines) and binned
+profiles (symbols) shown here are each determined as fits on single stars, and the shaded area represents the 1σ uncertainty of each continuous
+profile and rotation angle. The dotted vertical line in each radial profile illustrates the half-light radius of NGC 2808.
+To maximize the likelihood of our model given the data,
+we use the Python package emcee from Foreman-Mackey et al.
+(2013), which is an implementation of the invariant Markov
+chain Monte Carlo (MCMC) ensemble sampler by Goodman &
+Weare (2010). Thinning the samples of each parameter by 16
+ensures that the final set of values for each parameter is again
+uncorrelated. We calculate the best fit parameters as the median
+of each distribution of thinned samples. In accordance with the
+standard deviation of a Gaussian, the lower and upper uncertain-
+ties of each fitted parameter are calculated using the 16th and
+84th percentile of the corresponding distribution. However, in
+some cases, the distribution of the maximum rotation velocity
+vmax may have a peak at zero and drop towards zero for larger
+values of vmax. In those cases we give an upper limit on the ro-
+tation velocity that corresponds to the 95th percentile of the dis-
+tribution and the rotation angle cannot be calculated. The actual
+fitting procedure for each cluster is performed as follows:
+1. The parametric models are fitted simultaneously to the line-
+of-sight velocities for the overall cluster including the Baum-
+gardt & Hilker data, with the systematic velocity vsys, rota-
+tion amplitude vmax, rotation angle θ0, rpeak, σmax, a0 and ffg
+as free parameters. The corresponding priors for each param-
+eter are presented in Table A.1 with the subscript ’o’. The
+priors on rpeak and a0 were chosen to exclude unphysical so-
+lutions for either small or large values of these parameters.
+2. The parametric models are fitted independently for each pop-
+ulation of that cluster with vsys, vmax, θ0, rpeak, σmax, a0 as
+free parameters. The fraction of foreground stars ffg from the
+parametric fit of the overall cluster is used to derive member-
+ship probabilities for each star that are kept fixed. The priors
+of all fitted parameters are listed in Table A.1 with the sub-
+script ’p’. The radial extent of the separation in multiple pop-
+ulations is limited by the availability of HUGS photometry
+from Piotto et al. (2015) and Nardiello et al. (2018a), which
+is why the radial coverage of the velocity and dispersion pro-
+files for each population is limited compared to the overall
+cluster. Therefore, we chose to apply strict priors on rpeak
+and a0 based on the distributions of samples from the para-
+metric fit of the overall cluster. We chose to take a similar ap-
+proach on vsys, since the systematic velocity should not vary
+between populations. Furthermore, we applied a soft prior in
+vmax, that is based on the distributions of samples from the
+parametric fit of the overall cluster for vmax and σmax, and
+the escape velocity vesc of that cluster, where we used values
+for the escape velocities from Baumgardt & Hilker (2018).
+3. The non-parametric model is fitted to the overall cluster and
+each of its populations with vsys, vmax, θ0 and σlos as free pa-
+rameters per radial bin. The priors for each parameter are
+listed in Table A.2. Again, we chose to limit the system-
+atic velocity vsys based on the results from the corresponding
+parametric fit. Additionally, we applied a prior on θ0 based
+on the value of θ0 from the corresponding parametric fit to
+ensure that the non-parametric profiles are consistent with
+the parametric profiles. We note that this approach introduces
+bias against depicting changes in the rotation axis with ra-
+dius.
+As described above, we only use the additional radial ve-
+locities from Baumgardt & Hilker (2018) in the analysis of the
+overall cluster, but not its populations, because we are unable
+to split those stars into populations. Nonetheless, the inclusion
+of this data is still important, since the strict priors on rpeak and
+a0 for the population fit are solely based on the fit of the whole
+cluster. Without the addition of that data, we would not be able
+Article number, page 5 of 27
+
+A&A proofs: manuscript no. paper
+to reliably derive these parameters for most clusters, as a result
+of the smaller radial range.
+To quantify the effect of rotation, we calculate the ratio of
+ordered-over-random (v/σ)HL motion for each population in all
+clusters. Classically, this ratio is defined as the ratio between
+the maximum rotation velocity to the central velocity dispersion.
+However, because of the weaknesses of this approach mentioned
+by Binney (2005), we follow the definition of (v/σ)HL by Cap-
+pellari et al. (2007):
+� v
+σ
+�
+HL = ⟨v2⟩
+⟨σr2⟩ =
+� rHL
+0
+ρ(r) 1
+2vrot(r)2 r dr
+� rHL
+0
+ρ(r)σ2
+los r dr
+,
+(6)
+where rHL is the half-light radius of each cluster. Emsellem et al.
+(2007) highlighted a potential shortcoming of using (v/σ)HL to
+characterize velocity fields, in that structurally different velocity
+fields can result in very similar values of (v/σ)HL. To address this
+issue, they introduced λR,HL as an alternative, which is a proxy
+for the spin parameter of the velocity field:
+λR,HL =
+⟨r|v|⟩
+⟨r
+�
+v2 + σr
+2⟩
+=
+� rHL
+0
+ρ(r) 2
+π|vrot(r)| r2 dr
+� rHL
+0
+ρ(r)
+�
+σ2
+los + 1
+2vrot(r)2 r dr
+.
+(7)
+We calculate both parameters based on the rotation and disper-
+sion profiles described in Eq. 1 and Eq. 2 for each cluster and its
+populations to quantify kinematical differences between clusters
+and populations. For these calculations, we use the values of the
+half-light radius rHL from Harris (1996, 2010 edition). For each
+cluster and all of its populations, we use the global density pro-
+files ρ(r). For some clusters, the radial rotation profiles do not
+extend beyond the half-light radius. This could introduce some
+bias to the values of (v/σ)HL and λR,HL. However, as described
+earlier, we apply a strict prior on the radial scales of the rotation
+and dispersion profiles for each population based on the overall
+profile. Therefore, when we calculate (v/σ)HL and λR,HL based
+on the MCMC results of the radial rotation and dispersion pro-
+files, we expect that any bias that may occur is correctly reflected
+in our uncertainties of these parameters. The kinematical model
+we employ to derive the rotation and dispersion profiles is not
+sensitive to structural differences between velocity fields of dif-
+ferent clusters. Therefore, we expect that (v/σ)HL and λR,HL are
+qualitatively the same for each cluster with this model.
+4. Results
+4.1. Global Kinematics
+Figure 2 shows the radial rotation and dispersion profiles for
+NGC 2808. In the top panel of this figure, the global profiles
+for the cluster are presented, where the outermost radial velocity
+data points are from the stars in the Baumgardt & Hilker (2018)
+catalog. In the lower panels of this figure, the corresponding
+profiles are shown for each population. The continuous profiles
+(solid lines) and binned profiles (symbols) shown here are each
+determined as fits on single stars, and the shaded area represents
+the 1σ uncertainty of each continuous profile and rotation angle.
+The dashed line indicates the value of the half-light radius of this
+cluster (Harris 1996, 2010 edition). The profiles for the other 24
+globular clusters and their corresponding chromosome maps are
+displayed in Figures A.1 to A.24 in the appendix. The binned
+profiles highlight again that the radial extent of our data is lim-
+ited to the center of each cluster. This could bias our ability to
+detect differences in kinematics between populations in the outer
+regions of the cluster. However, based on the work of Hénault-
+Brunet et al. (2015) we expect to find the largest differences be-
+tween populations around the half-light radius of each cluster.
+Even closer to the center, differences should still be detectable.
+Nevertheless, the extension of our work to the outskirts of the
+clusters appears as a promising opportunity for future studies.
+Overall, the binned non-parametric profiles are in good agree-
+ment with the continuous parametric profiles. The largest dis-
+crepancies between these types of profiles are found close to the
+center, where the binned profiles indicate a rise in rotation veloc-
+ity for some clusters (e.g. NGC 1904 and NGC 7089). Since the
+uncertainties of the binned rotation profiles are also the largest
+close to the center, it is uncertain whether this is a significant
+effect. We stress that the binned profiles are only used for visu-
+alization purposes and all following analyses are based on the
+parametric profiles. As mentioned in Sec. 3.2 the radial extent
+for the P1, P2 and P3 profiles is limited, which is revealed by
+the binned profiles. We used priors on the rpeak that are based
+on the parametric fit including all stars in the cluster. We use
+the parametric rotation and dispersion profiles to derive (v/σ)HL
+and λR,HL, according to Eq. 6 and Eq. 7, for each cluster and
+its populations. Both of these values are integrals of these pro-
+files up to the half-light radius of each cluster, which makes both
+parameters robust against changes in rpeak, as shown by Kamann
+et al. (2020). The fitted parameters and the values of (v/σ)HL and
+λR,HL for the populations of all clusters are listed in Table A.3.
+Since the value of vsys is close to zero for each cluster and its
+populations, it is not important for the subsequent analysis and
+is not discussed further.
+In Fig. 3 we show our values of (v/σ)HL as a function of
+the median relaxation time Trh of each cluster. The values for
+Trh are from (Harris 1996, 2010 edition), see Tab. A.3. For the
+global kinematics of the clusters, we find that there is a relation-
+ship between (v/σ)HL and the median relaxation time, in that for
+clusters with higher relaxation times we tend to get higher values
+in (v/σ)HL. In particular, for NGC 362, NGC 6397, NGC 6522
+and NGC 6681 we do not find a significant sign of rotation and
+all of them have relaxation times of log10(Trh/Gyr) < 8.95. Sim-
+ilar relations between cluster rotation and relaxation time have
+been found by Kamann et al. (2018), Bianchini et al. (2018)
+and Sollima et al. (2019). This is to be expected if we assume
+that globular clusters are imprinted at birth with the angular mo-
+mentum of their parent molecular clouds. Over time, this angu-
+lar momentum is dissipated outwards through two-body relax-
+ation. In fact, numerical simulations show that star clusters can
+be rotating shortly after their birth (Mapelli 2017; Bekki 2019)
+and that the strength of rotation declines over time (Lahén et al.
+2020). For several clusters in our sample, the relaxation times
+provided by Sollima & Baumgardt (2017) differ from those by
+Harris (1996, 2010 edition). If we use the values provided by
+Sollima & Baumgardt (2017), we find a similar relation with our
+values of (v/σ)HL but the correlation is weaker.
+We find a linear relation between (v/σ)HL and λR,HL for all clus-
+ters and populations. This is shown in Figure A.25 in the ap-
+pendix. We find that the constant of proportionality is ≈ 0.8 for
+all cases. Since our kinematic model is not sensitive to structural
+differences in the velocity field of a cluster it is expected that
+(v/σ)HL and λR,HL are qualitatively the same. In the following,
+we only use (v/σ)HL to describe the kinematics of clusters and
+populations.
+Article number, page 6 of 27
+
+Sven Martens et al.: Kinematic differences between multiple populations in Galactic globular clusters
+8.6
+8.8
+9.0
+9.2
+9.4
+log10(Trh/yr)
+0.000
+0.025
+0.050
+0.075
+0.100
+0.125
+0.150
+0.175
+(v/ )HL
+Fig. 3. Relation between rotation strength in (v/σ)HL and the median re-
+laxation time Trh of each cluster taken from Harris (1996, 2010 edition)
+4.2. Differences between P1 and P2
+To analyze P1 and P2 for differences in their kinematics, we
+compare the distributions of (v/σ)HL derived from the thinned
+MCMC samples for vmax, θ0, rpeak, σmax and a0 using Eq. 1, Eq.
+2 and Eq. 6. Figure 4 shows these distributions for all popula-
+tions of each cluster. The distributions for P1 and P2 are shown
+in green and orange, respectively. For NGC 1904, NGC 6266,
+NGC 6293, and NGC 6522, only the distribution for all stars, in
+gray, is plotted because there is no separation into populations
+for these clusters.
+For NGC 362, NGC 3201, NGC 6218, NGC 6254,
+NGC 6397, NGC 6624, NGC 6656, NGC 6681, NGC 6752 and
+NGC 7099 we find that the distributions of (v/σ)HL for P1 and
+P2 shown in Figure 4 are consistent with zero. In these cases, we
+are unable to detect rotation for either population (see Table A.3
+and the corresponding rotation profiles in the appendix). Based
+on our analysis, we find that our ability to detect rotation for any
+population depends mainly on two factors. First, the uncertain-
+ties of our analysis increase substantially for clusters with less
+than ∼ 200 stars per population (e.g. NGC 3201 and NGC 6218),
+resulting in a very broad distribution of (v/σ)HL. Second, if a
+cluster is slowly rotating ((v/σ)HL ≲ 0.05), it is challenging to
+constrain the rotation of its populations given our uncertainties.
+When both factors are present, like in the cases of NGC 6397
+and NGC 6752, our analysis only provides broad upper limits on
+the rotation strength of each population.
+For NGC 104, NGC 1851, NGC 2808, NGC 5286,
+NGC 5904, NGC 6093, NGC 6388, NGC 6541, NGC 7078 and
+NGC 7089 we are able to detect rotation for P1 or P2. All of
+these clusters fulfill the condition (v/σ)HL ≳ 0.05. NGC 6656 is
+the only other cluster in our sample that also fulfills this con-
+dition, but we are unable to detect rotation in P1 and P2 be-
+cause its populations contain fewer than 200 stars. This shows
+that the global rotation of the cluster strongly affects the rota-
+tion of the individual populations, as expected. Based on the dis-
+tributions of (v/σ)HL shown in Fig. 4, we find kinematic differ-
+ences between P1 and P2 that are significant above a 1σ-level for
+NGC 2808, NGC 6093 and NGC 7078. For NGC 6093 and NGC
+7078 we find that P2 rotates faster than P1 at a confidence level
+of 1.5σ and 2.2σ respectively, whereas P2 rotates slower than
+P1 in NGC 2808 at a confidence level of 1.8σ. For NGC 104,
+NGC 1851, NGC 5286, NGC 5904, NGC 6388, NGC 6541 and
+NGC 7089 the strength of rotation of P1 is consistent with that
+of P2.
+Furthermore, we investigated whether the strength of rota-
+tion of P1 and P2 or their difference can be related to the relax-
+ation time of the corresponding cluster. In the top and middle
+panel of Fig. 5 the values of (v/σ)HL are plotted against the re-
+laxation time of the corresponding cluster for P1 and P2. For
+both P1 and P2, the strength of rotation only depends weakly on
+the relaxation time, if there is any correlation at all. Moreover,
+we do not see a correlation between the difference of rotation
+strength between P1 and P2 with relaxation time, which is illus-
+trated in the bottom panel of Fig. 5. However, the significance of
+these results should be taken with a grain of salt, since we only
+find differences above the 1σ-level for three clusters.
+In addition, we looked into possible connections of our kine-
+matic differences with the radial concentration of P1 and P2.
+In fact, both NGC 6093 and NGC 7078 have been reported to
+contain a more centrally concentrated P1 compared to P2 ac-
+cording to Dalessandro et al. (2018) and Larsen et al. (2015),
+respectively. For both clusters, we find that P1 rotates slower
+than P2. However, Nardiello et al. (2018a) find no difference in
+concentration between P1 and P2 for NGC 7078. For NGC 104
+(Milone et al. 2018a; Cordoni et al. 2020, e.g.) and NGC 2808
+(Dalessandro et al. 2019) P2 was found to be more centrally con-
+centrated than P1. Whereas we do not find significant kinematic
+differences between P1 and P2 for NGC 104, we find that P1
+rotates faster than P2 for NGC 2808. Overall, this could hint at
+a connection between kinematic differences and the radial con-
+centration of multiple populations in globular clusters, so that a
+population more centrally concentrated would rotate less. How-
+ever, since we only find kinematic differences in three clusters
+and the information on the concentrations is only available for a
+small subset of our sample of clusters, additional data are needed
+to investigate this further. Furthermore, the observations for e.g.
+NGC 5272 (Lee & Sneden 2021), NGC 6205 (Johnson & Pila-
+chowski 2012; Cordero et al. 2017) and NGC 6362 (Dalessandro
+et al. 2019, 2021) do not support this trend in our data that more
+centrally concentrated populations rotate less.
+4.3. Additional Population in Type-II Clusters
+The distributions of (v/σ)HL for type-II clusters are also shown
+in Figure 4, where P1, P2 and P3 are shown in green, orange
+and purple respectively. For four of the six type-II clusters in
+our sample, we did not detect rotation in P3. For NGC 362,
+NGC 6656 and NGC 7089 this is most likely due to the low
+number of stars in P3 as discussed previously. For NGC 6388 P3
+is populated well, but the global rotation of the cluster is very
+low. For NGC 1851 and NGC 5286 we detect rotation in P1, P2
+and P3. For NGC 1851 we find that the distribution of (v/σ)HL
+for P3 is very similar to that of P1 and P2, whereas for NGC
+5286, there might be a hint of P3 rotating faster than P1 and P2.
+However, the observed difference in (v/σ)HL is still within the
+1σ uncertainty interval, so further data are needed to draw any
+solid conclusions. In particular, these results also do not give any
+clear hints on other formation scenarios for type-II clusters.
+4.4. Notes on Individual Clusters
+4.4.1. NGC 6093
+For NGC 6093 we observe that rpeak varies between P1 and P2
+(see Table A.3). While the values of rpeak for the whole clus-
+Article number, page 7 of 27
+
+A&A proofs: manuscript no. paper
+NGC104
+NGC1851
+NGC1904
+NGC2808
+NGC3201
+NGC362
+NGC5286
+NGC5904
+NGC6093
+NGC6218
+NGC6254
+NGC6266
+NGC6293
+NGC6388
+NGC6397
+NGC6441
+NGC6522
+NGC6541
+NGC6624
+NGC6656
+0.05
+0.15
+0.25
+NGC6681
+0.05
+0.15
+0.25
+NGC6752
+0.05
+0.15
+0.25
+NGC7078
+0.05
+0.15
+0.25
+NGC7089
+0.05
+0.15
+0.25
+NGC7099
+Number of Samples
+(v/ )HL
+Fig. 4. Distributions of samples of (v/σ)HL, which describes the strength of rotation for each cluster in this analysis. These distributions are shown
+for the overall cluster (gray) and each of its populations (P1:green, P2:orange, P3:violet). The 16th, 50th and 84th percentile for each distribution
+are shown on top of the corresponding distribution. For distributions that peak at zero, only the 95th percentile is shown to provide an upper limit
+on the rotation strength.
+ter and P1 are consistent, the distribution of samples for rpeak of
+P2 peaks at a much smaller value, which is also apparent in the
+radial rotation profile in Fig. A.8 in the appendix. Furthermore,
+the distribution of rpeak for P2 is asymmetric and there is a strong
+anti-correlation between rpeak and vmax. This causes the asymme-
+try of (v/σ)HL in Fig. 4 for P2 of this cluster. As discussed in Sec.
+4.1 the value of (v/σ)HL is generally robust to changes in rpeak.
+However, in this case the value of rpeak for P2 is very close to the
+center of that cluster, and it seems worthwhile to find out whether
+this has a significant effect on our results. If we apply a uniform
+prior on rpeak for P2, we find that the difference between P1 and
+P2 in (v/σ)HL is even larger and the asymmetry in the distribu-
+tion of (v/σ)HL vanishes. If we fix the value of rpeak for P2 to
+that obtained for the whole cluster, the asymmetry also vanishes,
+but in this case (v/σ)HL is consistent with that value for P1. This
+cluster was already analyzed for kinematic differences between
+populations based on MUSE data, with a very similar approach
+to the one presented here by Kamann et al. (2020). They did not
+find this peculiar behavior of P2 for that cluster, because they
+used a different population split than the one used here. Notably,
+they also used individual population density profiles when cal-
+culating (v/σ)HL for their populations and not the global den-
+sity profile of that cluster. Kamann et al. (2020) split the cluster
+in three populations, where our P1 is consistent with their pri-
+mordial population and our P2 includes their intermediate and
+extreme populations. If we average their values of (v/σ)HL for
+the intermediate and extreme population, the result is consistent
+with the value of (v/σ)HL they obtained for the primordial pop-
+ulation. If we consider that Kamann et al. (2020) fixed the radial
+scale of each population, our results are consistent with theirs in
+that we do not find significant kinematic differences between P1
+and P2 if the radial scale is fixed to that of the global profile.
+However, there is no physical reason for why the radial scale of
+P2 cannot be different to that of P1.
+4.4.2. NGC 2808 & NGC 7078
+For NGC 2808 and NGC 7078 we find differences above the
+1σ-level in (v/σ)HL and the rotation profiles of their popu-
+lations, whereas the dispersion profiles do not differ signifi-
+cantly. For NGC 7078 we observe that P2 rotates faster than P1.
+Qualitatively, this behavior is similar to that of NGC 6093 and
+NGC 6205, where differences of this type between similar pop-
+ulations have also been reported by Kamann et al. (2020) and
+Cordero et al. (2017) respectively. For NGC 2808 we find the
+opposite in that P1 rotates faster than P2.
+To investigate the relationship between the populations in the
+chromosome maps and their kinematic differences further for
+Article number, page 8 of 27
+
+Sven Martens et al.: Kinematic differences between multiple populations in Galactic globular clusters
+0.0
+0.1
+0.2
+0.3
+0.4
+(v/ )HL, P1
+NGC 6397
+NGC 6681
+NGC 6624
+NGC 6093
+NGC 1851
+NGC 6752
+NGC 6218
+NGC 7099
+NGC 6254
+NGC 6388
+NGC 362
+NGC 6541
+NGC 6441
+NGC 5286
+NGC 2808
+NGC 6656
+NGC 3201
+NGC 7078
+NGC 7089
+NGC 5904
+NGC 104
+0.0
+0.1
+0.2
+0.3
+(v/ )HL, P2
+8.6
+8.8
+9.0
+9.2
+9.4
+log10(Trh/yr)
+0.1
+0.0
+0.1
+(v/ )HL, P1
+(v/ )HL, P2
+Fig. 5. Relation between rotation strength in (v/σ)HL of P1 and P2 and
+the median relaxation time Trh for each cluster taken from Harris (1996,
+2010 edition), and the difference in rotation strength between P1 and P2
+as a function of median relaxation time.
+NGC 2808 and NGC 7078, we decided to reiterate the analy-
+sis with different population splits. Incidentally, the structure of
+the chromosome maps of these clusters allows us to distinguish
+between four populations (P1, P2’, P3’ and P4’) for NGC 2808
+(Milone et al. 2015; Latour et al. 2019) and three populations
+(P1, P2’ and P3’) for NGC 7078 (Nardiello et al. 2018b). Com-
+pared to Milone et al. (2015) our P2’, P3’ and P4’ in NGC 2808
+are equivalent to their populations C, D and E, while our P1’ is
+their populations A and B combined. For NGC 7078, our P2’ is
+equivalent to population B by Nardiello et al. (2018b), whereas
+our P1’ corresponds to their populations A and D and our pop-
+ulation P3’ is equal to their populations C and E. We do not
+split P1’ for both clusters and P3’ for NGC 7078 any further
+to ensure that there are still enough stars per population to get
+meaningful results from our analysis. These populations accord-
+ing to our splitting are shown in the chromosome maps in the
+upper panels of Fig. 6, whereas the distributions of (v/σ)HL for
+these populations are depicted in the lower panels of that figure.
+For NGC 2808 we find that P2’, P3’ and P4’ do not differ in their
+rotation significantly, but the difference between these three pop-
+ulations and P1’ is larger than 1σ. For NGC 7078 the value of
+(v/σ)HL of P3’ stars is consistent with that of P1’ and P2’ stars,
+but the difference between P1’ stars and P2’ is larger than 1σ.
+Therefore, we do not find a general trend of (v/σ)HL along these
+populations.
+NGC 7078 has been analyzed for kinematic differences in
+populations by Szigeti et al. (2021). They used high precision
+radial velocity data from the SDSS-IV APOGEE-2 survey for
+138 stars in NGC 7078 to measure its rotation amplitude as a
+function of position angle for the whole cluster and two popu-
+lations that were identified based on single element abundance
+changes. They derived the angular rotation profile of NGC 7078
+by splitting the cluster into two halves through the cluster center.
+This line of separation is rotated in small angular increments, and
+the difference in mean radial velocity ∆V between both halves is
+calculated at each step. If the cluster is rotating, the relation be-
+tween velocity difference ∆V and position angle relative to the
+rotation axis α is ∆V = 2vrot · sin (α). The global rotation am-
+plitude and rotation angle that they find agree with our values
+for vmax and θ0 for the whole cluster. Furthermore, they found no
+kinematic difference between their two populations, which is in
+contrast to our results. Their method may only be applied to a
+fully sampled area that is symmetric with respect to the position
+angle. To ensure that our data comply with those restrictions, we
+filter our stars to make the covered area of the cluster circular.
+If we apply their method to our filtered data for P1 and P2, we
+find rotation amplitudes and rotation angles that are consistent
+with our radial rotation curves for P1 and P2. The corresponding
+angular rotation profiles and the spatial coverage of the cluster
+are shown in Fig. A.26. In particular, we still find kinematic dif-
+ferences between P1 and P2. One striking difference between
+their data and ours is that we have 390 and 697 stars in P1 and
+P2, compared to their 33 and 49 stars in those populations. To
+investigate this further, we decreased the number of stars by ran-
+domly sampling from P1 and P2 and then applied their method
+again. Figure A.27 shows three of these angular rotation profiles
+and the spatial coverage of the cluster. We find that with so few
+stars, this method results in a wide range of fundamentally dif-
+ferent profiles, presumably because the method is very sensitive
+to single stars. Probably the uncertainties of the differential rota-
+tion profiles are underestimated because the strong correlations
+between different values in those profiles are generally not taken
+into account. Together with our much larger sample of analyzed
+stars, this could be the cause for the discrepancies between our
+results and those from Szigeti et al. (2021).
+NGC 2808 has not been analyzed for differences in its ra-
+dial rotation and dispersion profiles yet, but Bellini et al. (2015)
+found differences in the radial anisotropy profiles for this cluster,
+by using proper motion data. Given that this cluster shows kine-
+matic differences using both radial velocities and proper motion
+data, it would be very interesting to combine both data sets and
+analyze the 3D stellar velocities of this cluster for differences
+between multiple populations.
+4.4.3. NGC 104 & NGC 5904
+Neither Milone et al. (2018b), nor Cordoni et al. (2020), find
+differences in the rotation amplitude between the populations of
+NGC 104, which agrees with our results. For NGC 5904 Cordoni
+et al. (2020) do not observe any differences in rotation amplitude,
+but they do find differences in the phase of their rotation curves.
+These phase differences translate to a differing angle of rotation.
+We do not find any significant differences in rotation amplitudes
+for NGC 5904 either, but we also do not find a significant differ-
+ence in the angle of rotation between P1 and P2.
+4.5. Random Sampling of the Chromosome Map
+To further analyze the solidity of our results for NGC 2808,
+NGC 6093 and NGC 7078 and to evaluate our uncertainty es-
+timations, we randomly sampled the chromosome maps of these
+clusters to create random populations P1 and P2. To ensure com-
+parability to the original population split, we used the same num-
+ber of stars per population as in the original separations (see Ta-
+ble 1). To achieve statistically relevant results, we created 100
+Article number, page 9 of 27
+
+A&A proofs: manuscript no. paper
+0.5
+0.4
+0.3
+0.2
+0.1
+0.0
+0.1
+0.2
+F275W
+F814W
+0.1
+0.0
+0.1
+0.2
+0.3
+0.4
+CF275W
+2 F336W + F438W
+NGC2808
+P1 (N=371)
+P2 (N=428)
+P3 (N=614)
+P4 (N=166)
+0.25
+0.20
+0.15
+0.10
+0.05
+0.00
+0.05
+F275W
+F814W
+0.05
+0.00
+0.05
+0.10
+0.15
+0.20
+0.25
+CF275W
+2 F336W + F438W
+NGC7078
+P1 (N=390)
+P2 (N=332)
+P3 (N=365)
+0.05
+0.15
+0.25
+NGC2808
+Number of Samples
+(v/ )HL
+0.05
+0.15
+0.25
+NGC7078
+Number of Samples
+(v/ )HL
+Fig. 6. Top: Chromosome maps of NGC 2808 and NGC 7078, with additional population splits. For NGC 2808 the original P2 is split into three
+subpopulations (P2’, P3’ and P4’), whereas P2 of NGC 7078 is split into two subpopulations (P2’ and P3’) according to the respective morphology
+of the chromosome maps. Bottom: Distributions of samples of (v/σ)HL for NGC 2808 and NGC 7078 for the overall cluster and each of their
+newly identified populations shown atop.
+random population pairs for each cluster. We calculated the ro-
+tation and dispersion profiles and derived (v/σ)HL for each of
+these random populations, as described in Sec. 3.2. As a result,
+we calculate 100 values of (v/σ)HL for each population of each
+cluster, which are shown in the upper panels of Fig. 7. It is ap-
+parent that the distributions for P1 and P2 for each cluster have
+the same median value. This shows that, on average, we do not
+find kinematic differences when randomly sampling the chro-
+mosome map. We also find that the distributions of (v/σ)HL ob-
+tained with the random sampling are broader for smaller num-
+bers of stars per population, as expected. In the lower panels
+of Fig. 7 we show the differences of (v/σ)HL between P1 and
+P2 obtained from the random sampling. As expected, these dis-
+tributions are centered around zero. We also indicated the ob-
+served differences for NGC 2808, NGC 6093 and NGC 7078 in
+red. The observed differences lie outside the 1σ-regions of the
+distributions, which supports the solidity of our uncertainty esti-
+mations and indicates that the kinematic differences that we find
+for NGC 2808, NGC 6093 and NGC 7078 are truly connected to
+the populations defined in the chromosome maps.
+5. Conclusion & Outlook
+We created and analyzed the rotation and dispersion profiles of
+25 Galactic globular clusters in the search for kinematic differ-
+ences between different populations within each cluster. Based
+on these kinematic profiles, we derived the rotation strength in
+terms of the ratio of ordered-over-random motion (v/σ)HL, eval-
+uated at the half-light radius, for each cluster and its populations
+to quantify kinematic differences. For NGC 362, NGC 6397,
+NGC 6522 and NGC 6681 we find no significant global rotation
+when using all stars in these clusters. For NGC 104, NGC 1851,
+NGC 2808, NGC 5286, NGC5904, NGC 6093, NGC 6388,
+NGC 6541, NGC 7078 and NGC 7089 we are able to detect rota-
+tion in at least one of their populations. For three clusters we find
+differences above the 1σ level: For NGC 6093 and NGC 7078
+we find that P2 stars rotate faster than P1 stars, whereas we find
+the opposite for NGC 2808, where P1 stars rotate faster than P2
+stars.
+Our results do not give a clear hint on the formation sce-
+nario of multiple populations in globular clusters. We find sup-
+port for both multi-epoch and single-epoch formation scenarios
+in our data. For multi-epoch formation scenarios, we expect to
+find that P2 rotates faster than P1, which matches our results
+for NGC 6093 and NGC 7078. Assuming a single-epoch forma-
+Article number, page 10 of 27
+
+Sven Martens et al.: Kinematic differences between multiple populations in Galactic globular clusters
+0.0
+0.1
+0.2
+0
+10
+20
+30
+40
+Number of realizations
+NGC2808
+P1 (371)
+P2 (1208)
+0.0
+0.1
+0.2
+(v/ )HL
+NGC7078
+P1 (390)
+P2 (697)
+0.0
+0.1
+0.2
+NGC6093
+P1 (367)
+P2 (582)
+0.2
+0.0
+0.2
+0
+5
+10
+Number of realizations
+obs.
+0.2
+0.0
+0.2
+(v/ )HL, P1
+(v/ )HL, P2
+0.2
+0.0
+0.2
+Fig. 7. Top: Values of (v/σ)HL derived from randomly sampling the chromosome maps of NGC 2808, NGC 6093 and NGC 7078. The numbers of
+stars in the randomly drawn P1 and P2 are the same as the observed populations. Bottom: Differences of the randomly drawn values of (v/σ)HL
+between P1 and P2 for NGC 2808, NGC 6093 and NGC 7078. The observed differences for these clusters are shown as the red dotted line, whereas
+the black dotted line is the standard deviation of the shown distribution.
+tion scenario, it follows that P1 rotates faster than P2, which is
+what we find for NGC 2808. However, the kinematic differences
+that we find are still relatively uncertain at confidence levels of
+≲ 2σ, so further data are needed for a definitive answer. We find
+further support for both scenarios if we consider clusters with
+kinematical variations between P1 and P2 below the 1σ-level.
+While we find that the rotation strength of each cluster is pos-
+itively correlated with median relaxation time, the correlation
+between relaxation time and the rotation strength of P1 or P2 is
+weak at best, and we do not see a correlation of the kinemati-
+cal difference between P1 and P2 with relaxation time. Based on
+our analysis, neither of the two types of formation scenarios for
+multiple populations in globular clusters is favored. Bastian &
+Lardo (2018) discussed that none of the formation scenarios put
+forward to date is able to explain all the observations. It is also
+possible that the formation of multiple populations does not af-
+fect the rotation of either population in a way that we are able to
+observe. However, it would be very interesting to see what pri-
+mordial differences between P1 and P2 are consistent with the
+differences between those populations that we find.
+To get a better understanding of the formation scenarios of
+multiple populations and their kinematics in general, there are
+several problems worth addressing. For many clusters in our
+sample, we were unable to detect rotation for P1 or P2. How-
+ever, since most clusters are rotating overall, we suspect that at
+least one population should be rotating as well for most clusters.
+As mentioned in Sec. 4.1 we are generally unable to detect rota-
+tion in P1 or P2 if the overall cluster is already rotating slowly
+with (v/σ)HL ≲ 0.05 or when the number of stars per population
+is of the order of 200 stars or below. Especially the results for
+NGC 6656 and NGC 3201 could be improved significantly by in-
+creasing the number of stars per population, since these clusters
+are rotating fast enough to overcome that limitation. One way to
+tackle this issue is to determine the population tags directly from
+the spectra. An alternative would be to add additional photomet-
+ric data to be able to assign more stars to their respective popu-
+lation. This would be especially useful outside the core of each
+cluster, where radial velocity measurements of stars are avail-
+able (e.g. Baumgardt & Hilker 2018), but these stars have not
+been separated into populations yet. Leitinger et al. (in prepara-
+tion) are currently working on using ground-based photometry to
+split the populations and derive density profiles for each popula-
+tion in globular clusters. When we include their additional popu-
+lation tags for NGC 7078, we observed small changes in the dis-
+tribution of (v/σ)HL, but nothing significant since the number of
+stars per population is already comparatively large for that clus-
+ter. Nonetheless, it seems worthwhile to pursue that approach,
+since it also increases the radial range of the population data. It
+is possible that this could increase the accuracy of measurements
+of the rotation in P1 and P2 substantially. Another possibility for
+a future work would be to use density profiles per population
+to derive the rotation strength. Using data from Leitinger et al.
+(in preparation) we checked whether our results for NGC 7078
+change if we use their density profiles for P1 and P2, but we still
+find that P2 rotates faster than P1 with a difference larger than
+1σ. However, if the populations have the same rotation and dis-
+persion curves, but different concentrations, then we would ex-
+pect to find kinematic differences between them. This is because
+the observed kinematics at a given projected radius correspond
+to a different intrinsic radius relative to the cluster center. Ulti-
+mately, one needs more sophisticated models to understand all
+the details.
+Acknowledgements. SM, FG, ML, PMW and SD acknowledge funding from
+the Deutsche Forschungsgemeinschaft (grant LA 4383/4-1, DR 281/35-1 and
+KA 4537/2-1) and by the BMBF from the ErUM program through grants
+05A14MGA, 05A17MGA, 05A20MGA and 05A20BAB. SK and RP gratefully
+acknowledge funding from UKRI in the form of a Future Leaders Fellowship
+(grant no. MR/T022868/1).
+Article number, page 11 of 27
+
+A&A proofs: manuscript no. paper
+References
+Anderson, J., Sarajedini, A., Bedin, L. R., et al. 2008, AJ, 135, 2055
+Bacon, R., Accardo, M., Adjali, L., et al. 2010, in Society of Photo-Optical In-
+strumentation Engineers (SPIE) Conference Series, Vol. 7735, Ground-based
+and Airborne Instrumentation for Astronomy III, ed. I. S. McLean, S. K. Ram-
+say, & H. Takami, 773508
+Bastian, N., Lamers, H. J. G. L. M., de Mink, S. E., et al. 2013, MNRAS, 436,
+2398
+Bastian, N. & Lardo, C. 2018, ARA&A, 56, 83
+Baumgardt, H. & Hilker, M. 2018, MNRAS, 478, 1520
+Bekki, K. 2019, A&A, 622, A53
+Bellini, A., Vesperini, E., Piotto, G., et al. 2015, ApJ, 810, L13
+Bianchini, P., van de Ven, G., Norris, M. A., Schinnerer, E., & Varri, A. L. 2016,
+MNRAS, 458, 3644
+Bianchini, P., van der Marel, R. P., del Pino, A., et al. 2018, MNRAS, 481, 2125
+Binney, J. 2005, MNRAS, 363, 937
+Cadelano, M., Dalessandro, E., Salaris, M., et al. 2022, ApJ, 924, L2
+Cappellari, M., Emsellem, E., Bacon, R., et al. 2007, MNRAS, 379, 418
+Carretta, E., Bragaglia, A., Gratton, R. G., et al. 2009, A&A, 505, 117
+Carretta, E., Bragaglia, A., Gratton, R. G., et al. 2010a, A&A, 516, A55
+Carretta, E., Gratton, R. G., Lucatello, S., et al. 2010b, ApJ, 722, L1
+Cordero, M. J., Hénault-Brunet, V., Pilachowski, C. A., et al. 2017, MNRAS,
+465, 3515
+Cordoni, G., Milone, A. P., Mastrobuono-Battisti, A., et al. 2020, ApJ, 889, 18
+Cottrell, P. L. & Da Costa, G. S. 1981, ApJ, 245, L79
+Dalessandro, E., Cadelano, M., Vesperini, E., et al. 2019, ApJ, 884, L24
+Dalessandro, E., Cadelano, M., Vesperini, E., et al. 2018, ApJ, 859, 15
+Dalessandro, E., Lapenna, E., Mucciarelli, A., et al. 2016, ApJ, 829, 77
+Dalessandro, E., Raso, S., Kamann, S., et al. 2021, MNRAS, 506, 813
+de Boer, T. J. L., Gieles, M., Balbinot, E., et al. 2019, MNRAS, 485, 4906
+Decressin, T., Charbonnel, C., & Meynet, G. 2007a, A&A, 475, 859
+Decressin, T., Meynet, G., Charbonnel, C., Prantzos, N., & Ekström, S. 2007b,
+A&A, 464, 1029
+Emsellem, E., Cappellari, M., Krajnovi´c, D., et al. 2007, MNRAS, 379, 401
+Foreman-Mackey, D., Hogg, D. W., Lang, D., & Goodman, J. 2013, PASP, 125,
+306
+Gieles, M., Charbonnel, C., Krause, M. G. H., et al. 2018, MNRAS, 478, 2461
+Gieles, M. & Zocchi, A. 2015, MNRAS, 454, 576
+Giesers, B., Kamann, S., Dreizler, S., et al. 2019, A&A, 632, A3
+Goodman, J. & Weare, J. 2010, Communications in Applied Mathematics and
+Computational Science, 5, 65
+Gott, III, R. J. 1973, ApJ, 186, 481
+Harris, W. E. 1996, AJ, 112, 1487
+Husser, T.-O., Kamann, S., Dreizler, S., et al. 2016, A&A, 588, A148
+Husser, T.-O., Wende-von Berg, S., Dreizler, S., et al. 2013, A&A, 553, A6
+Hénault-Brunet, V., Gieles, M., Agertz, O., & Read, J. I. 2015, MNRAS, 450,
+1164
+Johnson, C. I. & Pilachowski, C. A. 2012, ApJ, 754, L38
+Kamann, S., Dalessandro, E., Bastian, N., et al. 2020, MNRAS, 492, 966
+Kamann, S., Husser, T.-O., Brinchmann, J., et al. 2016, A&A, 588, A149
+Kamann, S., Husser, T.-O., Dreizler, S., et al. 2018, MNRAS, 473, 5591
+Kamann, S., Wisotzki, L., & Roth, M. M. 2013, A&A, 549, A71
+King, I. R. 1966, AJ, 71, 64
+Lahén, N., Naab, T., Johansson, P. H., et al. 2020, ApJ, 904, 71
+Larsen, S. S., Baumgardt, H., Bastian, N., et al. 2015, ApJ, 804, 71
+Latour, M., Husser, T.-O., Giesers, B., et al. 2019, A&A, 631, A14
+Lee, J.-W. & Sneden, C. 2021, ApJ, 909, 167
+Libralato, M., Bellini, A., Piotto, G., et al. 2019, ApJ, 873, 109
+Lynden-Bell, D. 1967, MNRAS, 136, 101
+Mapelli, M. 2017, MNRAS, 467, 3255
+Marino, A. F., Milone, A. P., Karakas, A. I., et al. 2015, MNRAS, 450, 815
+Martocchia, S., Cabrera-Ziri, I., Lardo, C., et al. 2018, MNRAS, 473, 2688
+Martocchia, S., Niederhofer, F., Dalessandro, E., et al. 2018, MNRAS, 477, 4696
+Milone, A. P., Bedin, L. R., Piotto, G., & Anderson, J. 2009, A&A, 497, 755
+Milone, A. P., Marino, A. F., Di Criscienzo, M., et al. 2018a, MNRAS, 477, 2640
+Milone, A. P., Marino, A. F., Mastrobuono-Battisti, A., & Lagioia, E. P. 2018b,
+MNRAS, 479, 5005
+Milone, A. P., Marino, A. F., Piotto, G., et al. 2015, ApJ, 808, 51
+Milone, A. P., Piotto, G., Renzini, A., et al. 2017, MNRAS, 464, 3636
+Mucciarelli, A., Origlia, L., Ferraro, F. R., & Pancino, E. 2009, ApJ, 695, L134
+Nardiello, D., Libralato, M., Piotto, G., et al. 2018a, MNRAS, 481, 3382
+Nardiello, D., Milone, A. P., Piotto, G., et al. 2018b, MNRAS, 477, 2004
+Pfeffer, J., Lardo, C., Bastian, N., Saracino, S., & Kamann, S. 2021, MNRAS,
+500, 2514
+Piotto, G., Milone, A. P., Bedin, L. R., et al. 2015, AJ, 149, 91
+Plummer, H. C. 1911, MNRAS, 71, 460
+Renzini, A. 2013, Mem. Soc. Astron. Italiana, 84, 162
+Richer, H. B., Heyl, J., Anderson, J., et al. 2013, ApJ, 771, L15
+Robin, A. C., Reylé, C., Derrière, S., & Picaud, S. 2003, A&A, 409, 523
+Sarajedini, A., Bedin, L. R., Chaboyer, B., et al. 2007, AJ, 133, 1658
+Sollima, A. & Baumgardt, H. 2017, MNRAS, 471, 3668
+Sollima, A., Baumgardt, H., & Hilker, M. 2019, MNRAS, 485, 1460
+Szigeti, L., Mészáros, S., Szabó, G. M., et al. 2021, MNRAS, 504, 1144
+Tiongco, M. A., Vesperini, E., & Varri, A. L. 2019, MNRAS, 487, 5535
+Vesperini, E., McMillan, S. L. W., D’Antona, F., & D’Ercole, A. 2013, MNRAS,
+429, 1913
+Weilbacher, P. M., Palsa, R., Streicher, O., et al. 2020, A&A, 641, A28
+Article number, page 12 of 27
+
+Sven Martens et al.: Kinematic differences between multiple populations in Galactic globular clusters
+Appendix A: Additional Tables and Figures
+Table A.1. Priors of the parametric fit described in Sec. 3.2.
+Parameter
+Prior
+vsys,o
+U(-10 km/s, 10 km/s)
+vsys,p
+N(µ(vsys,o), σ(vsys,o))
+vmax,o
+U(0, vesc)
+vmax,p
+∝
+�N(µ(vmax,o), µ(σmax,o))
+if 0 < vmax, p < vesc
+0
+else
+θ0
+U(−π, π)
+rpeak,o
+∝
+�����������
+0
+if rpeak,o < rHL/30
+1
+if rHL/30 < rpeak,o < 5 rHL
+N(5 rHL, rHL)
+else,
+rpeak,p
+∝
+�N(µ(rpeak,o), σ(rpeak,o))
+if rpeak,p > 0
+0
+else
+σmax
+U(0, ∞)
+a0, o
+same prior as rpeak,o
+a0, p
+∝
+�N(µ(a0,o), σ(a0,o))
+if a0,p > 0
+0
+else
+ffg
+U(0, 1)
+Notes. The subscript ’o’ denotes priors for fit of the overall population,
+whereas the subscript ’p’ describes priors for each population fit.
+Table A.2. Priors of the non-parametric fit described in Sec. 3.2.
+Parameter
+Prior
+vsys
+N(µ(v∗
+sys), σ(v∗
+sys))
+vmax
+U(0, ∞)
+θ0
+N(µ(θ∗
+0), σ(θ∗
+0))
+σmax
+U(0, ∞)
+Notes. The superscript ’*’ denotes that these parameters are distribu-
+tions of samples from the parametric fit.
+Article number, page 13 of 27
+
+A&A proofs: manuscript no. paper
+10
+1
+100
+101
+102
+0
+2
+4
+6
+OVERALL
+W
+N
+E
+S
+0
+10
+1
+100
+101
+102
+r/arcsec
+2.5
+5.0
+7.5
+10.0
+12.5
+0
+2
+4
+6
+P1
+W
+N
+E
+S
+0
+r/arcsec
+5
+10
+15
+10
+1
+100
+101
+102
+r [arcsec]
+0
+2
+4
+6
+P2
+W
+N
+E
+S
+0
+10
+1
+100
+101
+102
+r [arcsec]
+5
+10
+vrot [km/s]
+r [km/s]
+NGC 104
+0.4
+0.3
+0.2
+0.1
+0.0
+0.1
+0.2
+F275W
+F814W
+0.2
+0.1
+0.0
+0.1
+0.2
+0.3
+0.4
+CF275W
+2 F336W + F438W
+Fig. A.1. Chromosome maps, rotation and dispersion profiles for NGC 104 and each of its populations. The rotation profiles for each population
+are shown on the left, whereas the dispersion profiles are shown on the right. In the center, the angle of rotation is shown.
+10
+1
+100
+101
+102
+0
+2
+4
+OVERALL
+W
+N
+E
+S
+0
+10
+1
+100
+101
+102
+r/arcsec
+2.5
+5.0
+7.5
+10.0
+0
+2
+4
+P1
+W
+N
+E
+S
+0
+r/arcsec
+2
+4
+6
+8
+0
+1
+2
+3
+4
+P2
+W
+N
+E
+S
+0
+r/arcsec
+2
+4
+6
+8
+10
+1
+100
+101
+102
+r [arcsec]
+0
+5
+10
+15
+P3
+W
+N
+E
+S
+0
+10
+1
+100
+101
+102
+r [arcsec]
+2
+4
+6
+8
+vrot [km/s]
+r [km/s]
+NGC 362
+0.25
+0.20
+0.15
+0.10
+0.05
+0.00
+0.05
+F275W
+F814W
+0.0
+0.1
+0.2
+0.3
+CF275W
+2 F336W + F438W
+Fig. A.2. Continuation of Fig. A.1 for NGC 362.
+Article number, page 14 of 27
+
+Sven Martens et al.: Kinematic differences between multiple populations in Galactic globular clusters
+10
+1
+100
+101
+102
+0
+1
+2
+3
+OVERALL
+W
+N
+E
+S
+0
+10
+1
+100
+101
+102
+r/arcsec
+5
+10
+15
+0
+1
+2
+3
+4
+P1
+W
+N
+E
+S
+0
+r/arcsec
+2.5
+5.0
+7.5
+10.0
+0
+2
+4
+P2
+W
+N
+E
+S
+0
+r/arcsec
+2
+4
+6
+8
+10
+1
+100
+101
+102
+r [arcsec]
+0
+1
+2
+3
+P3
+W
+N
+E
+S
+0
+10
+1
+100
+101
+102
+r [arcsec]
+2.5
+5.0
+7.5
+10.0
+vrot [km/s]
+r [km/s]
+NGC 1851
+0.25
+0.20
+0.15
+0.10
+0.05
+0.00
+0.05
+F275W
+F814W
+0.0
+0.1
+0.2
+0.3
+CF275W
+2 F336W + F438W
+Fig. A.3. Continuation of Fig. A.1 for NGC 1851.
+10
+1
+100
+101
+102
+r [arcsec]
+0
+1
+2
+OVERALL
+W
+N
+E
+S
+0
+10
+1
+100
+101
+102
+r [arcsec]
+5
+10
+vrot [km/s]
+r [km/s]
+NGC 1904
+Fig. A.4. Continuation of Fig. A.1 for NGC 1904.
+10
+1
+100
+101
+102
+0
+1
+2
+OVERALL
+W
+N
+E
+S
+0
+10
+1
+100
+101
+102
+r/arcsec
+3
+4
+5
+0.0
+2.5
+5.0
+7.5
+10.0
+P1
+W
+N
+E
+S
+0
+r/arcsec
+3
+4
+5
+10
+1
+100
+101
+102
+r [arcsec]
+0
+2
+4
+6
+8
+P2
+W
+N
+E
+S
+0
+10
+1
+100
+101
+102
+r [arcsec]
+2
+3
+4
+5
+vrot [km/s]
+r [km/s]
+NGC 3201
+0.5
+0.4
+0.3
+0.2
+0.1
+0.0
+F275W
+F814W
+0.05
+0.00
+0.05
+0.10
+0.15
+0.20
+0.25
+0.30
+CF275W
+2 F336W + F438W
+Fig. A.5. Continuation of Fig. A.1 for NGC 3201.
+Article number, page 15 of 27
+
+A&A proofs: manuscript no. paper
+10
+1
+100
+101
+102
+0
+2
+4
+OVERALL
+W
+N
+E
+S
+0
+10
+1
+100
+101
+102
+r/arcsec
+2.5
+5.0
+7.5
+10.0
+0
+2
+4
+6
+P1
+W
+N
+E
+S
+0
+r/arcsec
+2.5
+5.0
+7.5
+10.0
+0
+2
+4
+P2
+W
+N
+E
+S
+0
+r/arcsec
+2.5
+5.0
+7.5
+10.0
+10
+1
+100
+101
+102
+r [arcsec]
+0.0
+2.5
+5.0
+7.5
+10.0
+P3
+W
+N
+E
+S
+0
+10
+1
+100
+101
+102
+r [arcsec]
+2.5
+5.0
+7.5
+10.0
+vrot [km/s]
+r [km/s]
+NGC 5286
+0.4
+0.3
+0.2
+0.1
+0.0
+0.1
+0.2
+F275W
+F814W
+0.1
+0.0
+0.1
+0.2
+0.3
+CF275W
+2 F336W + F438W
+Fig. A.6. Continuation of Fig. A.1 for NGC 5286.
+10
+1
+100
+101
+102
+0
+1
+2
+3
+4
+OVERALL
+W
+N
+E
+S
+0
+10
+1
+100
+101
+102
+r/arcsec
+2
+4
+6
+8
+10
+0
+1
+2
+3
+4
+P1
+W
+N
+E
+S
+0
+r/arcsec
+2
+4
+6
+8
+10
+1
+100
+101
+102
+r [arcsec]
+0
+1
+2
+3
+4
+P2
+W
+N
+E
+S
+0
+10
+1
+100
+101
+102
+r [arcsec]
+2
+4
+6
+8
+vrot [km/s]
+r [km/s]
+NGC 5904
+0.2
+0.1
+0.0
+0.1
+F275W
+F814W
+0.05
+0.00
+0.05
+0.10
+0.15
+0.20
+0.25
+0.30
+0.35
+CF275W
+2 F336W + F438W
+Fig. A.7. Continuation of Fig. A.1 for NGC 5904.
+Article number, page 16 of 27
+
+Sven Martens et al.: Kinematic differences between multiple populations in Galactic globular clusters
+10
+1
+100
+101
+102
+0
+1
+2
+3
+OVERALL
+W
+N
+E
+S
+0
+10
+1
+100
+101
+102
+r/arcsec
+5
+10
+15
+0
+1
+2
+3
+4
+P1
+W
+N
+E
+S
+0
+r/arcsec
+5
+10
+10
+1
+100
+101
+102
+r [arcsec]
+0
+2
+4
+P2
+W
+N
+E
+S
+0
+10
+1
+100
+101
+102
+r [arcsec]
+5
+10
+vrot [km/s]
+r [km/s]
+NGC 6093
+0.3
+0.2
+0.1
+0.0
+0.1
+F275W
+F814W
+0.05
+0.00
+0.05
+0.10
+0.15
+0.20
+0.25
+0.30
+CF275W
+2 F336W + F438W
+Fig. A.8. Continuation of Fig. A.1 for NGC 6093.
+10
+1
+100
+101
+102
+0.0
+0.5
+1.0
+1.5
+2.0
+OVERALL
+W
+N
+E
+S
+0
+10
+1
+100
+101
+102
+r/arcsec
+2
+4
+6
+0
+2
+4
+6
+8
+P1
+W
+N
+E
+S
+0
+r/arcsec
+2
+4
+6
+10
+1
+100
+101
+102
+r [arcsec]
+0
+2
+4
+6
+P2
+W
+N
+E
+S
+0
+10
+1
+100
+101
+102
+r [arcsec]
+2
+4
+vrot [km/s]
+r [km/s]
+NGC 6218
+0.25
+0.20
+0.15
+0.10
+0.05
+0.00
+0.05
+F275W
+F814W
+0.05
+0.00
+0.05
+0.10
+0.15
+0.20
+0.25
+CF275W
+2 F336W + F438W
+Fig. A.9. Continuation of Fig. A.1 for NGC 6218.
+Article number, page 17 of 27
+
+A&A proofs: manuscript no. paper
+10
+1
+100
+101
+102
+0.0
+0.5
+1.0
+OVERALL
+W
+N
+E
+S
+0
+10
+1
+100
+101
+102
+r/arcsec
+2
+4
+6
+8
+0
+2
+4
+6
+8
+P1
+W
+N
+E
+S
+0
+r/arcsec
+2
+4
+6
+10
+1
+100
+101
+102
+r [arcsec]
+0
+2
+4
+6
+P2
+W
+N
+E
+S
+0
+10
+1
+100
+101
+102
+r [arcsec]
+2
+4
+6
+vrot [km/s]
+r [km/s]
+NGC 6254
+0.3
+0.2
+0.1
+0.0
+0.1
+F275W
+F814W
+0.05
+0.00
+0.05
+0.10
+0.15
+0.20
+0.25
+0.30
+CF275W
+2 F336W + F438W
+Fig. A.10. Continuation of Fig. A.1 for NGC 6254.
+10
+1
+100
+101
+102
+r [arcsec]
+0.0
+2.5
+5.0
+7.5
+OVERALL
+W
+N
+E
+S
+0
+10
+1
+100
+101
+102
+r [arcsec]
+5
+10
+15
+vrot [km/s]
+r [km/s]
+NGC 6266
+Fig. A.11. Continuation of Fig. A.1 for NGC 6266.
+10
+1
+100
+101
+102
+r [arcsec]
+0
+2
+4
+6
+OVERALL
+W
+N
+E
+S
+0
+10
+1
+100
+101
+102
+r [arcsec]
+2.5
+5.0
+7.5
+vrot [km/s]
+r [km/s]
+NGC 6293
+Fig. A.12. Continuation of Fig. A.1 for NGC 6293.
+Article number, page 18 of 27
+
+Sven Martens et al.: Kinematic differences between multiple populations in Galactic globular clusters
+10
+1
+100
+101
+102
+0
+2
+4
+OVERALL
+W
+N
+E
+S
+0
+10
+1
+100
+101
+102
+r/arcsec
+5
+10
+15
+20
+0
+5
+10
+P1
+W
+N
+E
+S
+0
+r/arcsec
+5
+10
+15
+0
+2
+4
+P2
+W
+N
+E
+S
+0
+r/arcsec
+5
+10
+15
+20
+10
+1
+100
+101
+102
+r [arcsec]
+0
+2
+4
+6
+8
+P3
+W
+N
+E
+S
+0
+10
+1
+100
+101
+102
+r [arcsec]
+5
+10
+15
+20
+vrot [km/s]
+r [km/s]
+NGC 6388
+1.25
+1.00
+0.75
+0.50
+0.25 0.00
+0.25
+0.50
+F275W
+F814W
+0.3
+0.2
+0.1
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+CF275W
+2 F336W + F438W
+Fig. A.13. Continuation of Fig. A.1 for NGC 6388.
+10
+1
+100
+101
+102
+0
+1
+2
+OVERALL
+W
+N
+E
+S
+0
+10
+1
+100
+101
+102
+r/arcsec
+2
+4
+6
+0.0
+2.5
+5.0
+7.5
+10.0
+P1
+W
+N
+E
+S
+0
+r/arcsec
+2
+4
+6
+10
+1
+100
+101
+102
+r [arcsec]
+0.0
+2.5
+5.0
+7.5
+10.0
+P2
+W
+N
+E
+S
+0
+10
+1
+100
+101
+102
+r [arcsec]
+2
+4
+6
+vrot [km/s]
+r [km/s]
+NGC 6397
+0.20
+0.15
+0.10
+0.05
+0.00
+F275W
+F814W
+0.05
+0.00
+0.05
+0.10
+0.15
+CF275W
+2 F336W + F438W
+Fig. A.14. Continuation of Fig. A.1 for NGC 6397.
+Article number, page 19 of 27
+
+A&A proofs: manuscript no. paper
+10
+1
+100
+101
+102
+0
+2
+4
+6
+8
+OVERALL
+W
+N
+E
+S
+0
+10
+1
+100
+101
+102
+r/arcsec
+5
+10
+15
+20
+0
+2
+4
+6
+8
+P1
+W
+N
+E
+S
+0
+r/arcsec
+5
+10
+15
+20
+10
+1
+100
+101
+102
+r [arcsec]
+0
+2
+4
+P2
+W
+N
+E
+S
+0
+10
+1
+100
+101
+102
+r [arcsec]
+5
+10
+15
+vrot [km/s]
+r [km/s]
+NGC 6441
+1.0
+0.5
+0.0
+0.5
+F275W
+F814W
+0.4
+0.2
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+CF275W
+2 F336W + F438W
+Fig. A.15. Continuation of Fig. A.1 for NGC 6441.
+10
+1
+100
+101
+102
+r [arcsec]
+0
+2
+4
+6
+OVERALL
+W
+N
+E
+S
+0
+10
+1
+100
+101
+102
+r [arcsec]
+0
+5
+10
+15
+vrot [km/s]
+r [km/s]
+NGC 6522
+Fig. A.16. Continuation of Fig. A.1 for NGC 6522.
+10
+1
+100
+101
+102
+0
+1
+2
+3
+4
+OVERALL
+W
+N
+E
+S
+0
+10
+1
+100
+101
+102
+r/arcsec
+5
+10
+15
+0
+1
+2
+3
+4
+P1
+W
+N
+E
+S
+0
+r/arcsec
+2
+4
+6
+8
+10
+1
+100
+101
+102
+r [arcsec]
+0
+2
+4
+P2
+W
+N
+E
+S
+0
+10
+1
+100
+101
+102
+r [arcsec]
+2
+4
+6
+8
+10
+vrot [km/s]
+r [km/s]
+NGC 6541
+0.3
+0.2
+0.1
+0.0
+0.1
+F275W
+F814W
+0.05
+0.00
+0.05
+0.10
+0.15
+0.20
+0.25
+0.30
+CF275W
+2 F336W + F438W
+Fig. A.17. Continuation of Fig. A.1 for NGC 6541.
+Article number, page 20 of 27
+
+Sven Martens et al.: Kinematic differences between multiple populations in Galactic globular clusters
+10
+1
+100
+101
+102
+0.0
+0.5
+1.0
+1.5
+2.0
+OVERALL
+W
+N
+E
+S
+0
+10
+1
+100
+101
+102
+r/arcsec
+2
+4
+6
+8
+10
+0
+2
+4
+6
+8
+P1
+W
+N
+E
+S
+0
+r/arcsec
+2
+4
+6
+8
+10
+1
+100
+101
+102
+r [arcsec]
+0
+2
+4
+6
+P2
+W
+N
+E
+S
+0
+10
+1
+100
+101
+102
+r [arcsec]
+2
+4
+6
+8
+vrot [km/s]
+r [km/s]
+NGC 6624
+0.6
+0.4
+0.2
+0.0
+F275W
+F814W
+0.2
+0.1
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+CF275W
+2 F336W + F438W
+Fig. A.18. Continuation of Fig. A.1 for NGC 6624.
+10
+1
+100
+101
+102
+0
+2
+4
+OVERALL
+W
+N
+E
+S
+0
+10
+1
+100
+101
+102
+r/arcsec
+2
+4
+6
+8
+10
+0
+2
+4
+6
+8
+P1
+W
+N
+E
+S
+0
+r/arcsec
+2
+4
+6
+8
+0
+2
+4
+6
+P2
+W
+N
+E
+S
+0
+r/arcsec
+2
+4
+6
+8
+10
+10
+1
+100
+101
+102
+r [arcsec]
+0
+2
+4
+6
+P3
+W
+N
+E
+S
+0
+10
+1
+100
+101
+102
+r [arcsec]
+2
+4
+6
+8
+vrot [km/s]
+r [km/s]
+NGC 6656
+0.4
+0.3
+0.2
+0.1
+0.0
+0.1
+F275W
+F814W
+0.05
+0.00
+0.05
+0.10
+0.15
+0.20
+0.25
+0.30
+CF275W
+2 F336W + F438W
+Fig. A.19. Continuation of Fig. A.1 for NGC 6656.
+Article number, page 21 of 27
+
+A&A proofs: manuscript no. paper
+10
+1
+100
+101
+102
+0
+1
+2
+3
+4
+OVERALL
+W
+N
+E
+S
+0
+10
+1
+100
+101
+102
+r/arcsec
+2.5
+5.0
+7.5
+10.0
+0
+5
+10
+P1
+W
+N
+E
+S
+0
+r/arcsec
+2
+4
+6
+8
+10
+10
+1
+100
+101
+102
+r [arcsec]
+0
+2
+4
+6
+P2
+W
+N
+E
+S
+0
+10
+1
+100
+101
+102
+r [arcsec]
+2
+4
+6
+vrot [km/s]
+r [km/s]
+NGC 6681
+0.3
+0.2
+0.1
+0.0
+F275W
+F814W
+0.0
+0.1
+0.2
+0.3
+CF275W
+2 F336W + F438W
+Fig. A.20. Continuation of Fig. A.1 for NGC 6681.
+10
+1
+100
+101
+102
+0
+1
+2
+3
+4
+OVERALL
+W
+N
+E
+S
+0
+10
+1
+100
+101
+102
+r/arcsec
+2.5
+5.0
+7.5
+10.0
+0
+5
+10
+P1
+W
+N
+E
+S
+0
+r/arcsec
+2
+4
+6
+8
+10
+1
+100
+101
+102
+r [arcsec]
+0
+2
+4
+6
+8
+P2
+W
+N
+E
+S
+0
+10
+1
+100
+101
+102
+r [arcsec]
+2
+4
+6
+8
+vrot [km/s]
+r [km/s]
+NGC 6752
+0.25
+0.20
+0.15
+0.10
+0.05
+0.00
+0.05
+F275W
+F814W
+0.05
+0.00
+0.05
+0.10
+0.15
+0.20
+0.25
+0.30
+CF275W
+2 F336W + F438W
+Fig. A.21. Continuation of Fig. A.1 for NGC 6752.
+Article number, page 22 of 27
+
+Sven Martens et al.: Kinematic differences between multiple populations in Galactic globular clusters
+10
+1
+100
+101
+102
+0
+1
+2
+3
+4
+OVERALL
+W
+N
+E
+S
+0
+10
+1
+100
+101
+102
+r/arcsec
+5
+10
+15
+0
+1
+2
+3
+P1
+W
+N
+E
+S
+0
+r/arcsec
+2.5
+5.0
+7.5
+10.0
+12.5
+10
+1
+100
+101
+102
+r [arcsec]
+0
+2
+4
+P2
+W
+N
+E
+S
+0
+10
+1
+100
+101
+102
+r [arcsec]
+5
+10
+vrot [km/s]
+r [km/s]
+NGC 7078
+0.25
+0.20
+0.15
+0.10
+0.05
+0.00
+0.05
+F275W
+F814W
+0.05
+0.00
+0.05
+0.10
+0.15
+0.20
+0.25
+CF275W
+2 F336W + F438W
+Fig. A.22. Continuation of Fig. A.1 for NGC 7078.
+10
+1
+100
+101
+102
+0
+2
+4
+OVERALL
+W
+N
+E
+S
+0
+10
+1
+100
+101
+102
+r/arcsec
+5
+10
+15
+0
+2
+4
+6
+P1
+W
+N
+E
+S
+0
+r/arcsec
+2.5
+5.0
+7.5
+10.0
+0
+2
+4
+6
+P2
+W
+N
+E
+S
+0
+r/arcsec
+5
+10
+10
+1
+100
+101
+102
+r [arcsec]
+0.0
+2.5
+5.0
+7.5
+10.0
+P3
+W
+N
+E
+S
+0
+10
+1
+100
+101
+102
+r [arcsec]
+5
+10
+15
+vrot [km/s]
+r [km/s]
+NGC 7089
+0.3
+0.2
+0.1
+0.0
+0.1
+0.2
+0.3
+F275W
+F814W
+0.1
+0.0
+0.1
+0.2
+0.3
+CF275W
+2 F336W + F438W
+Fig. A.23. Continuation of Fig. A.1 for NGC 7089.
+Article number, page 23 of 27
+
+A&A proofs: manuscript no. paper
+10
+1
+100
+101
+102
+0
+1
+2
+OVERALL
+W
+N
+E
+S
+0
+10
+1
+100
+101
+102
+r/arcsec
+2
+4
+6
+8
+0
+1
+2
+3
+P1
+W
+N
+E
+S
+0
+r/arcsec
+2
+4
+6
+10
+1
+100
+101
+102
+r [arcsec]
+0
+1
+2
+3
+P2
+W
+N
+E
+S
+0
+10
+1
+100
+101
+102
+r [arcsec]
+2
+4
+6
+vrot [km/s]
+r [km/s]
+NGC 7099
+0.175 0.150 0.125 0.100 0.075 0.050 0.0250.000
+F275W
+F814W
+0.00
+0.05
+0.10
+0.15
+CF275W
+2 F336W + F438W
+Fig. A.24. Continuation of Fig. A.1 for NGC 7099.
+0.00
+0.05
+0.10
+0.15
+0.20
+0.25
+(v/ )HL
+0.00
+0.05
+0.10
+0.15
+0.20
+0.25
+R, HL
+OVERALL
+Linear Fit: m=0.798
+0.00
+0.05
+0.10
+0.15
+0.20
+0.25
+(v/ )HL
+P1
+Linear Fit: m=0.796
+0.00
+0.05
+0.10
+0.15
+0.20
+0.25
+(v/ )HL
+P2
+Linear Fit: m=0.789
+0.00
+0.05
+0.10
+0.15
+0.20
+0.25
+(v/ )HL
+P3
+Linear Fit: m=0.796
+Fig. A.25. Derived values of λR,HL plotted against (v/σ)HL for the overall cluster and each population with a linear fit.
+40
+20
+0
+20
+40
+x [arcsec]
+40
+20
+0
+20
+40
+y [arcsec]
+0
+2
+4
+6
+Position Angle [rad]
+4
+2
+0
+2
+4
+V [km/s]
+NGC7078
+P1 (335)
+P2 (604)
+Fig. A.26. Differential rotation profile for P1 and P2 of NGC 7078, where the difference in mean radial velocity between the two subsets of stars
+is plotted against the position angle of their line of separation.
+Article number, page 24 of 27
+
+Sven Martens et al.: Kinematic differences between multiple populations in Galactic globular clusters
+40
+20
+0
+20
+40
+40
+20
+0
+20
+40
+y [arcsec]
+0
+1
+2
+3
+4
+5
+6
+15
+10
+5
+0
+5
+10
+15
+V [km/s]
+P1 (33)
+P2 (49)
+40
+20
+0
+20
+40
+40
+20
+0
+20
+40
+y [arcsec]
+0
+1
+2
+3
+4
+5
+6
+15
+10
+5
+0
+5
+10
+15
+V [km/s]
+P1 (33)
+P2 (49)
+40
+20
+0
+20
+40
+x [arcsec]
+40
+20
+0
+20
+40
+y [arcsec]
+0
+1
+2
+3
+4
+5
+6
+Position Angle [rad]
+15
+10
+5
+0
+5
+10
+15
+V [km/s]
+NGC7078
+P1 (33)
+P2 (49)
+Fig. A.27. Differential rotation profile for randomly sampled stars of P1 and P2 for NGC 7078, where the difference in mean radial velocity
+between the two subsets of stars is plotted against the position angle of their line of separation.
+Article number, page 25 of 27
+
+A&A proofs: manuscript no. paper
+Table A.3. Median and upper limits of the parameter distributions for the parametric model of each cluster.
+Cluster
+Population
+σmax [km/s]
+vmax [km/s]
+θ0 [rad]
+rpeak ["]
+a ["]
+(v/σ)HL
+λR,HL
+log10(Trh/yr)
+NGC 104
+Overall
+12.37+0.09
+−0.09
+4.75+0.14
+−0.14
+−2.34+0.03
+−0.03
+165+10
+−10
+142+6
+−5
+0.154+0.004
+−0.005
+0.117+0.004
+−0.004
+9.55
+P1
+12.4+0.5
+−0.5
+3.9+1.7
+−1.7
+−2.5+0.5
+−0.6
+165+10
+−10
+141+5
+−6
+0.13+0.05
+−0.06
+0.10+0.04
+−0.04
+–
+P2
+12.33+0.26
+−0.25
+5.5+0.9
+−0.9
+−2.45+0.18
+−0.19
+166+10
+−10
+141+6
+−6
+0.180+0.029
+−0.028
+0.136+0.021
+−0.020
+–
+NGC 362
+Overall
+8.67+0.24
+−0.23
+< 1.0
+–
+140+110
+−80
+47+6
+−6
+< 0.03
+< 0.028
+8.93
+P1
+8.1+0.5
+−0.4
+< 5
+–
+190+90
+−100
+46+6
+−6
+< 0.09
+< 0.07
+–
+P2
+8.3+0.3
+−0.3
+< 4
+–
+190+100
+−100
+45+6
+−6
+< 0.07
+< 0.06
+–
+P3
+7.5+1.5
+−1.2
+< 15
+–
+160+90
+−80
+47+6
+−6
+< 0.4
+< 0.3
+–
+NGC 1851
+Overall
+10.34+0.29
+−0.25
+1.42+0.17
+−0.16
+1.45+0.09
+−0.09
+26+8
+−6
+27.3+2.4
+−2.2
+0.062+0.014
+−0.013
+0.050+0.012
+−0.011
+8.82
+P1
+10.1+0.6
+−0.6
+2.4+1.0
+−1.1
+1.6+0.4
+−0.4
+28+7
+−8
+27.8+2.4
+−2.3
+0.10+0.05
+−0.05
+0.08+0.04
+−0.04
+–
+P2
+8.7+0.4
+−0.4
+2.3+0.8
+−0.6
+1.8+0.3
+−0.3
+29+8
+−9
+28.3+2.4
+−2.2
+0.11+0.04
+−0.03
+0.086+0.03
+−0.027
+–
+P3
+10.0+0.5
+−0.5
+2.1+0.9
+−0.8
+1.8+0.4
+−0.4
+27+8
+−8
+26.4+2.5
+−2.4
+0.09+0.04
+−0.04
+0.07+0.04
+−0.03
+–
+NGC 1904
+Overall
+7.02+0.3
+−0.28
+1.50+0.21
+−0.20
+0.26+0.14
+−0.13
+65+18
+−16
+30+5
+−4
+0.079+0.018
+−0.016
+0.064+0.016
+−0.014
+8.95
+NGC 2808
+Overall
+13.44+0.23
+−0.23
+4.02+0.23
+−0.22
+0.72+0.05
+−0.05
+69+9
+−8
+50+4
+−4
+0.123+0.009
+−0.009
+0.100+0.008
+−0.007
+9.15
+P1
+13.1+0.6
+−0.5
+5.9+1.1
+−1.0
+0.88+0.18
+−0.18
+68+9
+−9
+50+4
+−4
+0.19+0.03
+−0.03
+0.151+0.027
+−0.026
+–
+P2
+13.8+0.4
+−0.3
+3.9+0.7
+−0.6
+0.78+0.15
+−0.15
+69+9
+−9
+49+4
+−4
+0.118+0.020
+−0.019
+0.095+0.016
+−0.015
+–
+NGC 3201
+Overall
+4.68+0.07
+−0.07
+1.4+0.5
+−0.5
+1.8+0.4
+−0.4
+950+190
+−210
+970+90
+−100
+0.042+0.015
+−0.014
+0.033+0.012
+−0.011
+9.27
+P1
+4.7+0.6
+−0.5
+< 10
+–
+960+200
+−220
+960+110
+−100
+< 0.3
+< 0.24
+–
+P2
+4.4+0.5
+−0.4
+< 9
+–
+950+210
+−200
+970+110
+−100
+< 0.3
+< 0.23
+–
+NGC 5286
+Overall
+10.01+0.23
+−0.22
+4.4+1.1
+−1.0
+0.21+0.10
+−0.10
+110+40
+−30
+42+8
+−6
+0.133+0.015
+−0.015
+0.107+0.013
+−0.013
+9.11
+P1
+10.5+0.6
+−0.5
+4.9+2.8
+−2.3
+0.2+0.5
+−0.5
+110+30
+−40
+43+8
+−7
+0.14+0.06
+−0.06
+0.11+0.05
+−0.05
+–
+P2
+10.4+0.5
+−0.5
+2.7+2.3
+−1.7
+0.2+0.8
+−0.7
+120+40
+−40
+40+8
+−8
+0.08+0.05
+−0.05
+0.06+0.04
+−0.04
+–
+P3
+10.0+0.8
+−0.7
+7+4
+−3
+0.0+0.5
+−0.5
+110+40
+−30
+40+8
+−8
+0.19+0.08
+−0.09
+0.15+0.06
+−0.07
+–
+NGC 5904
+Overall
+7.80+0.08
+−0.10
+3.11+0.19
+−0.17
+0.82+0.06
+−0.06
+126+16
+−14
+176+30
+−21
+0.169+0.008
+−0.008
+0.135+0.007
+−0.007
+9.41
+P1
+7.2+0.4
+−0.4
+3.1+1.3
+−1.4
+0.3+0.5
+−0.4
+127+16
+−16
+180+30
+−30
+0.18+0.08
+−0.08
+0.15+0.06
+−0.07
+–
+P2
+7.05+0.23
+−0.21
+3.5+0.8
+−0.8
+0.45+0.22
+−0.22
+127+16
+−16
+170+30
+−30
+0.21+0.04
+−0.04
+0.17+0.03
+−0.03
+–
+NGC 6093
+Overall
+11.6+0.4
+−0.4
+2.3+0.6
+−0.3
+−0.47+0.09
+−0.09
+78+30
+−21
+21.8+2.4
+−2.3
+0.059+0.010
+−0.008
+0.046+0.008
+−0.006
+8.8
+P1
+12.3+0.7
+−0.6
+1.8+1.3
+−1.1
+−0.5+0.7
+−0.7
+90+30
+−30
+21.8+2.4
+−2.3
+0.039+0.023
+−0.022
+0.031+0.018
+−0.017
+–
+P2
+11.9+0.6
+−0.6
+3.0+0.8
+−0.7
+−0.55+0.22
+−0.22
+35+50
+−18
+19.8+2.3
+−2.4
+0.11+0.07
+−0.04
+0.09+0.06
+−0.04
+–
+NGC 6218
+Overall
+6.27+0.14
+−0.13
+0.45+0.3
+−0.25
+2.0+0.6
+−0.6
+350+230
+−220
+58+7
+−6
+0.022+0.015
+−0.013
+0.019+0.013
+−0.011
+8.87
+P1
+5.9+0.5
+−0.4
+< 9
+–
+440+210
+−200
+59+7
+−6
+< 0.29
+< 0.23
+–
+P2
+5.2+0.4
+−0.3
+< 6
+–
+460+200
+−190
+58+6
+−6
+< 0.25
+< 0.20
+–
+NGC 6254
+Overall
+6.34+0.09
+−0.08
+0.8+0.4
+−0.3
+2.37+0.3
+−0.28
+410+200
+−170
+113+13
+−11
+0.028+0.009
+−0.009
+0.022+0.007
+−0.007
+8.9
+P1
+6.5+0.4
+−0.4
+< 8
+–
+470+180
+−170
+114+13
+−13
+< 0.20
+< 0.16
+–
+P2
+5.83+0.30
+−0.26
+< 7
+–
+470+180
+−170
+114+12
+−12
+< 0.20
+< 0.15
+–
+NGC 6266
+Overall
+15.34+0.30
+−0.27
+3.8+1.6
+−1.5
+−2.60+0.11
+−0.12
+200+90
+−90
+39+3
+−3
+0.048+0.006
+−0.005
+0.037+0.005
+−0.004
+8.98
+NGC 6293
+Overall
+6.8+0.5
+−0.5
+3.5+3
+−2.1
+0.43+0.29
+−0.29
+170+120
+−150
+18+9
+−5
+0.11+0.04
+−0.03
+0.087+0.03
+−0.026
+8.94
+NGC 6388
+Overall
+17.8+0.4
+−0.3
+1.06+0.29
+−0.26
+0.84+0.26
+−0.24
+44+50
+−22
+33.7+2.6
+−2.3
+0.020+0.014
+−0.008
+0.016+0.012
+−0.007
+8.9
+P1
+17.4+0.6
+−0.6
+< 20
+–
+40+60
+−40
+34.6+2.6
+−2.4
+< 0.17
+< 0.12
+–
+P2
+18.6+0.5
+−0.5
+1.6+1.5
+−0.9
+0.2+0.6
+−0.5
+37+50
+−29
+33.5+2.6
+−2.4
+0.029+0.05
+−0.017
+0.023+0.05
+−0.014
+–
+P3
+18.9+0.9
+−0.7
+< 11
+–
+60+50
+−50
+33.4+2.6
+−2.6
+< 0.15
+< 0.12
+–
+Article number, page 26 of 27
+
+Sven Martens et al.: Kinematic differences between multiple populations in Galactic globular clusters
+Table A.3. continued.
+Cluster
+Population
+σmax [km/s]
+vmax [km/s]
+θ0 [rad]
+rpeak ["]
+a ["]
+(v/σ)HL
+λR,HL
+log10(Trh/yr)
+NGC 6397
+Overall
+6.30+0.12
+−0.12
+< 0.7
+–
+600+300
+−400
+83+7
+−7
+< 0.024
+< 0.019
+8.6
+P1
+6.2+1.2
+−1.0
+< 12
+–
+700+400
+−300
+84+7
+−7
+< 0.4
+< 0.27
+–
+P2
+5.6+0.6
+−0.5
+< 11
+–
+700+300
+−300
+83+7
+−7
+< 0.3
+< 0.23
+–
+NGC 6441
+Overall
+18.9+0.4
+−0.4
+1.3+1.0
+−0.8
+3.5+0.6
+−0.5
+150+50
+−70
+31.4+3
+−3.0
+0.010+0.006
+−0.006
+0.008+0.005
+−0.004
+9.09
+P1
+19.4+0.8
+−0.7
+< 9
+–
+180+60
+−70
+32+3
+−3
+< 0.05
+< 0.04
+–
+P2
+18.3+0.6
+−0.6
+< 5
+–
+170+70
+−70
+32+3
+−3
+< 0.029
+< 0.022
+–
+NGC 6522
+Overall
+13.7+2.4
+−1.5
+< 7
+–
+260+90
+−130
+11+4
+−4
+< 0.029
+< 0.021
+8.86
+NGC 6541
+Overall
+9.8+0.3
+−0.3
+3.4+0.6
+−0.5
+−0.19+0.07
+−0.07
+126+30
+−27
+28+3
+−3
+0.096+0.008
+−0.008
+0.073+0.007
+−0.006
+9.03
+P1
+8.8+0.4
+−0.4
+2.9+1.3
+−1.2
+−0.4+0.4
+−0.4
+135+30
+−29
+29+3
+−3
+0.09+0.03
+−0.03
+0.067+0.026
+−0.026
+–
+P2
+9.3+0.5
+−0.4
+4.0+1.5
+−1.3
+−0.07+0.27
+−0.28
+130+30
+−30
+29+3
+−3
+0.12+0.03
+−0.03
+0.089+0.026
+−0.026
+–
+NGC 6624
+Overall
+8.48+0.24
+−0.24
+1.2+0.9
+−0.7
+0.4+0.5
+−0.5
+210+70
+−100
+26+4
+−3
+0.021+0.010
+−0.011
+0.015+0.008
+−0.008
+8.71
+P1
+8.1+0.6
+−0.6
+< 9
+–
+230+90
+−80
+25+4
+−4
+< 0.12
+< 0.09
+–
+P2
+7.7+0.4
+−0.4
+< 7
+–
+240+90
+−90
+24+4
+−4
+< 0.10
+< 0.07
+–
+NGC 6656
+Overall
+9.44+0.10
+−0.10
+3.0+0.4
+−0.4
+0.25+0.10
+−0.10
+230+50
+−40
+150+14
+−13
+0.162+0.017
+−0.017
+0.134+0.014
+−0.014
+9.23
+P1
+8.6+0.6
+−0.5
+< 8
+–
+240+40
+−40
+150+15
+−14
+< 0.5
+< 0.3
+–
+P2
+9.0+0.5
+−0.5
+< 7
+–
+240+50
+−40
+150+14
+−15
+< 0.4
+< 0.28
+–
+P3
+8.6+0.6
+−0.5
+< 7
+–
+240+40
+−50
+151+14
+−15
+< 0.4
+< 0.3
+–
+NGC 6681
+Overall
+7.9+0.5
+−0.4
+< 2.2
+–
+170+70
+−100
+18+4
+−3
+< 0.04
+< 0.028
+8.65
+P1
+8.2+1.3
+−1.0
+< 12
+–
+200+90
+−90
+16+4
+−4
+< 0.20
+< 0.14
+–
+P2
+6.9+0.6
+−0.5
+< 7
+–
+210+90
+−90
+18+4
+−4
+< 0.10
+< 0.07
+–
+NGC 6752
+Overall
+8.39+0.11
+−0.11
+0.61+0.19
+−0.19
+−1.89+0.30
+−0.3
+450+170
+−150
+92+6
+−5
+0.009+0.004
+−0.003
+0.0067+0.0030
+−0.0022
+8.87
+P1
+7.9+0.6
+−0.5
+< 12
+–
+480+160
+−170
+91+6
+−6
+< 0.18
+< 0.13
+–
+P2
+7.8+0.4
+−0.4
+< 9
+–
+490+160
+−150
+92+5
+−6
+< 0.12
+< 0.09
+–
+NGC 7078
+Overall
+12.24+0.3
+−0.30
+3.21+0.27
+−0.26
+−2.26+0.06
+−0.06
+77+11
+−10
+26.6+2.3
+−2.2
+0.103+0.008
+−0.008
+0.080+0.007
+−0.006
+9.32
+P1
+11.6+0.5
+−0.5
+< 2.2
+–
+78+11
+−11
+26.4+2.1
+−2.3
+< 0.07
+< 0.06
+–
+P2
+12.8+0.5
+−0.4
+4.1+0.9
+−0.8
+−2.41+0.19
+−0.19
+78+11
+−11
+26.2+2.0
+−2.1
+0.125+0.024
+−0.024
+0.097+0.018
+−0.018
+–
+NGC 7089
+Overall
+10.91+0.24
+−0.22
+3.90+0.3
+−0.27
+2.20+0.05
+−0.05
+66+13
+−12
+47+5
+−4
+0.173+0.012
+−0.011
+0.140+0.011
+−0.010
+9.4
+P1
+11.0+0.6
+−0.5
+5.1+1.1
+−1.2
+2.11+0.22
+−0.21
+66+13
+−12
+46+5
+−5
+0.22+0.05
+−0.05
+0.18+0.04
+−0.04
+–
+P2
+11.3+0.3
+−0.3
+4.1+0.6
+−0.6
+2.26+0.13
+−0.14
+58+13
+−12
+45+5
+−4
+0.186+0.026
+−0.026
+0.152+0.022
+−0.021
+–
+P3
+13.5+2.1
+−1.7
+< 11
+–
+66+12
+−13
+47+5
+−5
+< 0.4
+< 0.3
+–
+NGC 7099
+Overall
+5.86+0.16
+−0.15
+0.53+0.17
+−0.18
+−0.8+0.3
+−0.4
+70+80
+−30
+53+8
+−7
+0.028+0.015
+−0.014
+0.021+0.012
+−0.011
+8.88
+P1
+5.3+0.5
+−0.4
+< 4
+–
+120+80
+−80
+53+8
+−8
+< 0.16
+< 0.12
+–
+P2
+5.9+0.4
+−0.3
+< 4
+–
+130+80
+−80
+50+8
+−8
+< 0.11
+< 0.08
+–
+Notes. The two measures of the rotation strength (v/σ)HL and λR,HL are derived from the parameter distribution of the parametric model, as
+described in Sec. 3.2. The median relaxation times Trh for each cluster are from Harris (1996, 2010 edition).
+Article number, page 27 of 27
+
diff --git a/JtFAT4oBgHgl3EQfvR6i/content/tmp_files/load_file.txt b/JtFAT4oBgHgl3EQfvR6i/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4e85492152130b938c2105bb6d878ff0152bd8d6
--- /dev/null
+++ b/JtFAT4oBgHgl3EQfvR6i/content/tmp_files/load_file.txt
@@ -0,0 +1,2782 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf,len=2781
+page_content='Astronomy & Astrophysics manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' paper  ©ESO 2023  January 23, 2023  Kinematic differences between multiple populations  in Galactic globular clusters⋆,⋆⋆  Sven Martens1, Sebastian Kamann2, Stefan Dreizler1, Fabian Göttgens1, Tim-Oliver Husser1, Marilyn Latour1, Elena  Balakina2, Davor Krajnovi´c3, Renuka Pechetti2, and Peter M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Weilbacher3  1 Institut für Astrophysik und Geophysik, Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany  e-mail: sven.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='martens@uni-goettingen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='de  2 Astrophysics Research Institute, Liverpool John Moores University, 146 Brownlow Hill, Liverpool L3 5RF, UK  3 Leibniz-Institut für Astrophysik Potsdam (AIP), An der Sternwarte 16, 14482 Potsdam, Germany  Received MONTH DD, YYYY;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' accepted MONTH DD, YYYY  ABSTRACT  Aims.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' The formation process of multiple populations in globular clusters is still up for debate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' These populations are characterized by  different light-element abundances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Kinematic differences between the populations are particularly interesting in this respect, because  they allow us to distinguish between single-epoch formation scenarios and multi-epoch formation scenarios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' We derive rotation and  dispersion profiles for 25 globular clusters and aim to find kinematic differences between multiple populations in 21 of them to  constrain the formation process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  Methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' We split red-giant branch (RGB) stars in each cluster into three populations (P1, P2, P3) for the type-II clusters and two  populations (P1 and P2) otherwise using Hubble photometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' We derive the global rotation and dispersion profiles for each cluster by  using all stars with radial velocity measurements obtained from MUSE spectroscopy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' We also derive these profiles for the individual  populations of each cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Based on the rotation and dispersion profiles, we calculate the rotation strength in terms of ordered-over-  random motion (v/σ)HL evaluated at the half-light radius of the cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' We then consistently analyse all clusters for differences in the  rotation strength of their populations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  Results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' We detect rotation in all but four clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' For NGC 104, NGC 1851, NGC 2808, NGC 5286, NGC 5904, NGC 6093,  NGC 6388, NGC 6541, NGC 7078 and NGC 7089 we also detect rotation for P1 and/or P2 stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' For NGC 2808, NGC 6093 and  NGC 7078 we find differences in (v/σ)HL between P1 and P2 that are larger than 1σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Whereas we find that P2 rotates faster than P1  for NGC 6093 and NGC 7078, the opposite is true for NGC 2808.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' However, even for these three clusters the differences are still of  low significance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' We find that the strength of rotation of a cluster generally scales with its median relaxation time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' For P1 and P2 the  corresponding relation is very weak at best.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' We observe no correlation between the difference in rotation strength between P1 and  P2 and cluster relaxation time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' The stellar radial velocities derived from MUSE data that this analysis is based on are made publicly  available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  Key words.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' globular clusters: general – stars: kinematics and dynamics – techniques: imaging spectroscopy  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Introduction  Classically, it is assumed that all stars in a globular cluster form  in the same molecular cloud and therefore are identical in age  and chemical abundances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' The discovery of multiple popula-  tions of stars within globular clusters calls this into question.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  These populations generally differ in light element abundances  (Carretta et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2009), but there is no evidence of age differences  larger than ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1 Gyrs (Bastian & Lardo 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Martocchia et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Using these abundance differences, the stars of most clus-  ters (type-I clusters) can be separated into at least two popula-  tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' One population has a scaled solar metallicity, whereas the  other populations are always enriched in some light elements  (such as N or Na) and depleted in others (such as C or O).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' The  ⋆ Table 2 is only available at the CDS via anonymous ftp  to cdsarc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='u-strasbg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='fr (XXXX) or via http://cdsarc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='u-strasbg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='fr/viz-  bin/cat/J/A+A/XXX/Lzzz  ⋆⋆ Based on observations collected at the European Organisation  for Astronomical Research in the Southern Hemisphere, Chile (pro-  posal IDs 094.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='D-0142, 095.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='D-0629, 096.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='D-0175, 097.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='D-0295, 098.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='D-  0148, 099.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='D-0019, 100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='D-0161, 101.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='D-0268, 102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='D-0270, 103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='D-  0204, 105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='20CR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='002)  fraction of enriched to non-enriched stars and the strength of the  spread in light element abundances increase with cluster mass  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Carretta et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2010a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Milone et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' There is evidence  of metallicity spreads within some globular clusters for quite  some time (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Carretta et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2010b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Milone et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' (2017) found  that for these clusters (type-II clusters) the two stellar popula-  tions are themselves split.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Type-II clusters exhibit multiple sub-  giant and red giant branches, likely due to variations in heavy-  elements abundances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Pfeffer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' (2021) discussed several of  these clusters and argued that some of them are actually rem-  nants of nuclear star clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' The occurrence of multiple popu-  lations is not limited to Galactic globular clusters, but they have  also been observed in clusters of other galaxies (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Mucciarelli  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2009;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Milone et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2009;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Dalessandro et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Fur-  thermore, Martocchia et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' (2018) found that cluster age might  play a role in the onset of multiple populations, because they  did not detect light-element variations in clusters younger than  ∼ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='7 Gyr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' However, by analyzing main sequence stars instead of  red giant branch stars Cadelano et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' (2022) found evidence for  multiple populations in the 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5 Gyr old star cluster NGC 1783.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  Article number, page 1 of 27  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='08675v1  [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='GA]  20 Jan 2023  A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' paper  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2  F275W  F814W  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  CF275W  2 F336W + F438W  NGC2808  P1 (N=371)  P2 (N=1208)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  F275W  F814W  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  CF275W  2 F336W + F438W  NGC1851  P1 (N=184)  P2 (N=357)  P3 (N=272)  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Chromosome maps for NGC 2808 and NGC 1851, where the identified populations of each cluster are labeled with different colors and  symbols.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' For the type-II cluster NGC 1851 there is an additional population compared to NGC 2808.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  Several formation scenarios for multiple populations in glob-  ular clusters have been put forward, but each scenario comes  with its caveats (for a detailed review see Bastian & Lardo 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  There are two types of formation scenarios that we discuss here  briefly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' On the one hand, multi-epoch formation scenarios pro-  pose the formation of a second generation of stars that form  from gas polluted by primordial stellar sources, such as asymp-  totic giant branch stars or fast-rotating massive stars (Cottrell &  Da Costa 1981;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Renzini 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Decressin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2007a,b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' On the  other hand, single-epoch formation scenarios suggest that some  stars accrete material when moving through the cluster center in  order to explain the observed spread in light-element abundances  (Bastian et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Gieles et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  The structural and kinematical differences between the mul-  tiple populations of globular clusters today could give insights  on the formation process of these populations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Even though kine-  matic differences were imprinted during the birth of each cluster,  and they diminish over time due to the interactions between stars  during cluster evolution, at least some clusters are still expected  to show measurable differences in their present day kinematics  (Vesperini et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Hénault-Brunet et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Tiongco et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Differences in the concentrations of stars between pop-  ulations at the time of formation would entail differences in ra-  dial anisotropies over time (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Richer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Bellini et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Currently, a majority of globular clusters shows a higher  concentration of stars from the enriched population compared to  the pristine population (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Dalessandro et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  Hénault-Brunet et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' (2015) showed that multi-epoch and  single-epoch formation scenarios result in very similar radial  anisotropy profiles, as they all assume that the second popu-  lations forms centrally concentrated relative to the first popu-  lation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Therefore, anisotropy cannot be used to distinguish be-  tween these two types of scenarios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' However, these two forma-  tion scenarios would entail different initial conditions for the  kinematics of these populations of stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' For multi-epoch forma-  tion scenarios, the rotation velocity is expected to be lower for  the non-enriched population compared to the N-enriched popu-  lation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' On the contrary, for single-epoch formation scenarios, the  non-enriched population is expected to have a higher rotation  velocity than the N-enriched population (Hénault-Brunet et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  Studies have been carried out to look for these differences  in several globular clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' In particular, Cordero et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' (2017)  were the first to find rotational differences between multiple  populations in a globular cluster for NGC 6205.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Furthermore,  no kinematic differences between populations have been found  for NGC 6121 (Cordoni et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2020), NGC 6838 (Cordoni  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2020), NGC 6352 (Libralato et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2019), NGC 6205 and  NGC 7078 (Szigeti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' For NGC 104, Milone et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  (2018b) and Cordoni et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' (2020) found no differences in the ro-  tation pattern between populations, but the latter did find that the  enriched population exhibits stronger anisotropy than the non-  enriched population.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Cordoni et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' (2020) also found significant  differences in the phases of the rotation curves between popula-  tions for NGC 5904.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' However, Szigeti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' (2021) could not find  significant differences in the rotation curves of this cluster, but  for NGC 5272 they found that the enriched population is rotat-  ing faster than the non-enriched population.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Bellini et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' (2015)  found differences in the radial anisotropy of NGC 2808 based on  proper motion data, but there is no analysis on radial rotation and  dispersion profiles yet for this cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' For NGC 6362, Dalessan-  dro et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' (2021) found that the enriched population is rotating  faster than the non-enriched population.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Kamann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' (2020)  found similar results for NGC 6093 in that one of the enriched  populations they identified is rotating significantly stronger than  the non-enriched population.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' The overall lack of uniformity and  agreement in these results emphasizes the need to further study  the kinematic differences in multiple populations of globular  clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  In this work, we are following the approach described by  Kamann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' (2020) to systematically study the kinematics for  25 galactic globular clusters and looking at differences between  populations in 21 of them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' We used radial velocities derived from  MUSE spectroscopy in combination with radial velocities from  Baumgardt & Hilker (2018) to extend the radial coverage of each  globular cluster, as described in Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' In Section 3 we de-  scribe our approach to split the stars of each cluster into two or  three populations based on photometric data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' We use the stel-  lar radial velocities to create radial rotation and dispersion pro-  files and derive parameters to characterize the global dynamics  of each cluster and of its stellar populations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' We present the re-  sults of this analysis in Section 4 and conclude in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  Article number, page 2 of 27  Sven Martens et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' : Kinematic differences between multiple populations in Galactic globular clusters  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Data  The globular clusters analyzed in this study were observed with  the Multi Unit Spectroscopic Explorer (MUSE, Bacon et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' MUSE is an integral field spectrograph mounted at UT4  of the ESO Very Large Telescope (VLT) that has been in op-  eration since 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' It features a wide-field mode with a field of  view of 1′×1′ at a sampling of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2′′ per pixel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Since 2019 MUSE  also possesses a narrow-field mode that covers a field of view of  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5′′ × 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5′′ at a sampling of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='025” per pixel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Both modes cover  a spectral range of 4750 Å − 9350 Å with a corresponding spec-  tral resolution (R) of 1770 at 4750 Å and 3590 at 9350 Å.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' This  analysis is based on the MUSE Galactic globular cluster survey,  presented in Kamann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' We are using all available  wide-field mode data for each globular cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  Basic data reduction is carried out using the official MUSE  pipeline (Weilbacher et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' The process of extracting spec-  tra of single stars from the resulting datacube is described in de-  tail by Kamann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' In short, the program PAMPELMUSE  by Kamann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' (2013) is used in combination with a reference  source catalog derived from HST photometry (Sarajedini et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  2007;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Anderson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2008) to determine the position of each  resolved star in the MUSE data and to fit the MUSE PSF as a  function of wavelength to retrieve stellar spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  As described by Husser et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' (2016), the line-of-sight ve-  locity of each star is derived from its spectrum using cross-  correlation and a full spectral fitting approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' By cross-  correlating each spectrum against a set of template spectra, the  velocity vlos,cc is derived.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' The value of vlos,cc is then used as an  initial guess for the full spectral fitting method, described in de-  tail in Husser et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Using a Levenberg-Marquardt algo-  rithm, the observed stellar spectra are fitted against the Göttingen  Spectral Library (Husser et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2013) to derive the stellar metal-  licity [M/H], effective temperature Teff, and radial velocity vlos,fit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  To retain a reliable data set, we are using a set of filters on the  line-of-sight velocities derived from MUSE spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' We are em-  ploying the reliability parameter Rtotal > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='8 described in Giesers  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' It ensures that the value of vlos,cc is trustworthy  and consistent with vlos,fit and that the analyzed spectrum has a  signal-to-noise ratio of S/N > 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Additionally, we are remov-  ing stars that show temporal variations in their line-of-sight ve-  locities (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' binaries, pulsating stars) because in such cases the  measured velocities do not trace the gravitational potentials of  the host clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' We use the method described by Giesers et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  (2019) to derive the probability pvar that any star that was ob-  served multiple times shows temporal variance in velocity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' We  exclude all stars with pvar > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' To derive one value for the  line-of-sight velocity for each star, we average over MUSE ve-  locity measurements for stars that have been observed multiple  times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' The stellar coordinates and averaged radial velocities used  for this analysis are listed in Table 2 which is only available in  electronic form at CDS and on the Göttingen Research Online  repository, at XXX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  To increase the radial coverage of each cluster, we use stel-  lar velocities from Baumgardt & Hilker (2018) in addition to the  MUSE data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' We match the Baumgardt & Hilker (2018) data to  HST photometry from Anderson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' (2008), but the radial ve-  locities extend much further out than the HST data, so that most  radial velocities are not matched, but simply added to our data  set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Before combining, the respective systematic cluster velocity  is subtracted from the stellar velocities to minimize systematic  differences between data sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' If a star is included in the sam-  ples of both MUSE and Baumgardt & Hilker (2018), we aver-  Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Overview of the number of stars per cluster and population.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='Cluster  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='Nall  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='NMUSE  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='NP1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='NP2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='NP3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='NGC 104  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='32486  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='28588  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='343  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1250  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='–  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='NGC 362  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='8937  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='8244  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='234  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='599  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='22  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='NGC 1851  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='15182  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='13250  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='184  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='357  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='272  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='NGC 1904  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5523  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4373  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='–  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='–  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='–  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='NGC 2808  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='15621  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='13760  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='371  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1208  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='–  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='NGC 3201  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5206  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3917  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='40  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='53  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='–  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='NGC 5286  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='7373  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='6472  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='264  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='371  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='123  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='NGC 5904  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='19096  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='18297  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='177  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='587  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='–  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='NGC 6093  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='11419  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='10879  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='367  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='582  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='–  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='NGC 6218  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='8053  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='6156  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='88  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='123  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='–  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='NGC 6254  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='15418  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='14744  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='135  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='243  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='–  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='NGC 6266  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='15527  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='14255  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='–  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='–  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='–  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='NGC 6293  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4455  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3081  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='–  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='–  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='–  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='NGC 6388  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='14711  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='12528  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='726  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1431  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='404  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='NGC 6397  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='11728  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='8681  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='19  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='50  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='–  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='NGC 6441  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='13226  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='11494  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1005  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1793  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='–  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='NGC 6522  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='6333  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2641  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='–  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='–  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='–  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='NGC 6541  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='12560  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='11029  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='339  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='352  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='–  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='NGC 6624  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='7815  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='6012  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='130  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='332  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='–  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='NGC 6656  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='17230  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='11544  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='122  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='166  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='113  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='NGC 6681  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5797  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4749  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='38  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='249  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='–  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='NGC 6752  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='15525  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='13721  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='104  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='267  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='–  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='NGC 7078  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='13770  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='12899  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='390  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='697  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='–  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='NGC 7089  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='12727  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='12167  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='264  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1086  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='36  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='NGC 7099  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='10046  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='7705  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='81  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='182  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='–  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='Notes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Nall describes the numer of stars including data from Baumgardt  & Hilker (2018), whereas NMUSE is based solely on MUSE data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  age the stellar velocities from both sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' As shown by Ka-  mann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' (2018), the stellar radial velocities from MUSE and  Baumgardt & Hilker (2018) agree in regions where they over-  lap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' In the outer regions the completeness in terms of fraction  of stars with a radial velocity measure is significantly smaller  than in the center since the Baumgardt & Hilker sample only  consists of giant branch stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Because of energy equipartition,  which causes mass segregation, it is possible that this affects the  velocity dispersion in the outer regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' However, using the for-  mula by Bianchini et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' (2016) we estimated that the difference  between our MUSE sample and the Baumgardt & Hilker sample  in dispersion is ≲ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1 km/s based on the average masses of stars  in either sample, which is fully within the uncertainties of our  measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Methods  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Population Split  The separation into multiple populations is based on the chromo-  some map of each globular cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' A chromosome map, which  was first introduced by Milone et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' (2017), is a pseudo-color  color diagram using a combination of the HST filters F275W,  F336W, F438W and F814W that splits the stars of a cluster into  its populations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' We use photometry from the HST UV Globular  Cluster Survey (HUGS) from Piotto et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' (2015) and Nardiello  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' (2018a) to create these maps, as explained in Latour et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' We note that only RGB stars are included in the pop-  ulation analysis because the chromosome maps are tailored to  distinguish populations at this evolutionary phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  Article number, page 3 of 27  A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' paper  We need a consistent population separation because we want  to compare the kinematics of equivalent populations between  clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' For type-I clusters, we use the fact that these clusters  always consist of one population with a scaled-solar abundance  (P1) and at least one additional population (P2) that differs in  abundances to P1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Therefore, we follow the classification by  Milone et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' (2017) and divide the stars of type-I clusters into  two groups using the chromosome map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' The left panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 1  shows our chromosome map and identified populations P1 and  P2 for NGC 2808.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Stars from P1 are always found in the lower  part of the chromosome map around (0, 0) coordinate and, de-  pending on the cluster, partly extend horizontally, whereas P2  stars are located above P1 stars and extend diagonally toward  the top left.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  Type-II clusters contain stars that are enhanced in some par-  ticular heavy-elements, such as barium and lanthanum, possibly  iron as well, compared to P1 and P2 stars (Marino et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  These metal-enhanced stars are found on the reddest part of the  RGB in the CMD (see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Milone et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' For the Type-  II clusters, we consider these stars as a third population (P3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  The right panel in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 1 shows our split into three populations  for the type-II cluster NGC 1851.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' The position of P1 and P2 for  NGC 1851 are similar to NGC 2808, but the third population has  a distinct position on the upper-right region of the chromosome  map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  We analyze 25 globular clusters, six of which are considered  type-II clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' As briefly mentioned in Section 1, some type-II  clusters might actually be the remnants of nuclear star clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  However, Pfeffer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' (2021) conclude that none of the type-  II clusters in our sample are remnants of nuclear star clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  Therefore, we treat them as globular clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' A list of all clusters  with the number of stars used in the analysis of the global kine-  matics, and the number of stars per population, are shown in Ta-  ble 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' For NGC 1904, NGC 6266, NGC 6293 and NGC 6522 the  necessary HUGS photometric data to separate their RGB stars  into populations are not available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' In these cases, we only derive  the global kinematic properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Kinematics  To study the kinematic differences between populations, we first  use the radial velocities of all stars in the cluster to derive its  global kinematics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Then we repeat the same procedure, includ-  ing only the RGB stars assigned to specific populations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' From  the radial velocity data we create kinematic profiles and finally  derive the ratio of ordered-over-random motion (v/σ)HL and a  proxy for the spin parameter λR,HL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Both are evaluated at the  half-light radius to characterize the strength of rotation for all  clusters and each of their populations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' We use a very similar ap-  proach as described in Kamann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' (2020), but we repeat the  important assumptions and formulas below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  To create kinematic profiles, we need to derive the rotational  velocity vrot and the line-of-sight velocity dispersion σlos of each  cluster as a function of radius.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' To derive these parameters, we  employ the maximum-likelihood approach described in Kamann  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' We assume that the line-of-sight stellar velocities  at any position (x, y) may be approximated by a Gaussian with  mean vlos and standard deviation σlos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' To account for the posi-  tion of each star within the cluster with respect to the rotation  axis of that cluster, we parameterize the line-of-sight velocities  according to vlos(r, θ) = vrot(r) sin(θ − θ0), where r =  �  x2 + y2 is  the distance from the cluster center, θ0 is the angle of the cluster  rotation axis, and θ = atan2(y, x) is the position angle measured  counter-clockwise from north to east.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  As described in Kamann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' (2020), we use parametric and  non-parametric models to analyze the stellar rotation velocities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  For the non-parametric approach, we simply bin velocities ra-  dially and derive the rotation velocity and velocity dispersion  for each bin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' The parametric rotation profile vrot we employ is  characteristic for systems that have undergone violent relaxation  (Lynden-Bell 1967;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Gott 1973):  v(r) = vsys + vrot(r) = vsys + 2vmax  rpeakr  r2  peak + r2 ,  (1)  where vsys is the systematic velocity, vmax is the maximum ro-  tation velocity reached at radial distance rpeak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' The parametric  dispersion profile we use is a Plummer (1911) profile  σlos =  σmax  �  1 +  � r  a0  �2� 1  4 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  (2)  We differ in our approach to handling non-member stars com-  pared to Kamann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' They used cluster membership  probabilities that were derived from stellar metallicities and line-  of-sight velocities, as described by Kamann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' We  cannot take the same approach, because we do not have metal-  licities for the additional Baumgardt & Hilker stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' We modified  the method of membership determination in order to have con-  sistent membership probabilities for stars from both data sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' In  particular, we introduce a prior on the membership probability  for each star pi that is related to the stellar surface density of the  cluster ρ(ri) at the radial distance ri of that star from the cluster  center according to  pi(r) =  ρ(ri)  ρ(ri) + ffg  ,  (3)  where ffg measures the fractional contribution of foreground  sources to the observed source density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' To describe the stellar  surface density of each cluster, we use the LIMEPY models de-  scribed in Gieles & Zocchi (2015), with parameters for each  cluster as determined by de Boer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' For NGC 6441  and NGC 6522 de Boer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' (2019) do not provide any param-  eters for these models, so we chose to use King models (King  1966) with the necessary parameters of central concentration and  core radius taken from Harris (1996, 2010 edition).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' We modified  the likelihood function Li of each star i to not solely be based on  the likelihood of the rotation and dispersion model Lcl,i, but to  include the membership probability pi as follows:  Li = piLcl,i + (1 − pi)Lfg,i  (4)  where Lfg,i is the likelihood that star i is part of a foreground  population.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' This foreground population is built from single stars  included in a Besançon model (Robin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2003) at the posi-  tion of each cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' The foreground likelihood for each star Lfg,i  is then defined as the superposition of Gaussian kernels for M  simulated stars with line-of-sight velocities vfg,j:  Lfg,i = 1  M  M  �  j=1  exp  ����������−  �  vfg,j − vlos,i  �2  2 · v2  err,i  ���������� ,  (5)  where verr,i is the uncertainty of the measured line-of-sight ve-  locities vlos,i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  Article number, page 4 of 27  Sven Martens et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' : Kinematic differences between multiple populations in Galactic globular clusters  10  1  100  101  102  0  2  4  6  OVERALL  W  N  E  S  0  10  1  100  101  102  r/arcsec  5  10  15  0  2  4  6  8  P1  W  N  E  S  0  r/arcsec  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  10  1  100  101  102  r [arcsec]  0  2  4  6  P2  W  N  E  S  0  10  1  100  101  102  r [arcsec]  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  vrot [km/s]  r [km/s]  NGC 2808  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Rotation and dispersion profiles for NGC 2808 and each of its populations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' The rotation profiles for each population are shown on the left,  whereas the dispersion profiles are shown on the right.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' In the center, the angle of rotation is shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' The continuous profiles (solid lines) and binned  profiles (symbols) shown here are each determined as fits on single stars, and the shaded area represents the 1σ uncertainty of each continuous  profile and rotation angle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' The dotted vertical line in each radial profile illustrates the half-light radius of NGC 2808.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  To maximize the likelihood of our model given the data,  we use the Python package emcee from Foreman-Mackey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  (2013), which is an implementation of the invariant Markov  chain Monte Carlo (MCMC) ensemble sampler by Goodman &  Weare (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Thinning the samples of each parameter by 16  ensures that the final set of values for each parameter is again  uncorrelated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' We calculate the best fit parameters as the median  of each distribution of thinned samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' In accordance with the  standard deviation of a Gaussian, the lower and upper uncertain-  ties of each fitted parameter are calculated using the 16th and  84th percentile of the corresponding distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' However, in  some cases, the distribution of the maximum rotation velocity  vmax may have a peak at zero and drop towards zero for larger  values of vmax.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' In those cases we give an upper limit on the ro-  tation velocity that corresponds to the 95th percentile of the dis-  tribution and the rotation angle cannot be calculated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' The actual  fitting procedure for each cluster is performed as follows:  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' The parametric models are fitted simultaneously to the line-  of-sight velocities for the overall cluster including the Baum-  gardt & Hilker data, with the systematic velocity vsys, rota-  tion amplitude vmax, rotation angle θ0, rpeak, σmax, a0 and ffg  as free parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' The corresponding priors for each param-  eter are presented in Table A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1 with the subscript ’o’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' The  priors on rpeak and a0 were chosen to exclude unphysical so-  lutions for either small or large values of these parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' The parametric models are fitted independently for each pop-  ulation of that cluster with vsys, vmax, θ0, rpeak, σmax, a0 as  free parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' The fraction of foreground stars ffg from the  parametric fit of the overall cluster is used to derive member-  ship probabilities for each star that are kept fixed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' The priors  of all fitted parameters are listed in Table A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1 with the sub-  script ’p’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' The radial extent of the separation in multiple pop-  ulations is limited by the availability of HUGS photometry  from Piotto et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' (2015) and Nardiello et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' (2018a), which  is why the radial coverage of the velocity and dispersion pro-  files for each population is limited compared to the overall  cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Therefore, we chose to apply strict priors on rpeak  and a0 based on the distributions of samples from the para-  metric fit of the overall cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' We chose to take a similar ap-  proach on vsys, since the systematic velocity should not vary  between populations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Furthermore, we applied a soft prior in  vmax, that is based on the distributions of samples from the  parametric fit of the overall cluster for vmax and σmax, and  the escape velocity vesc of that cluster, where we used values  for the escape velocities from Baumgardt & Hilker (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' The non-parametric model is fitted to the overall cluster and  each of its populations with vsys, vmax, θ0 and σlos as free pa-  rameters per radial bin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' The priors for each parameter are  listed in Table A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Again, we chose to limit the system-  atic velocity vsys based on the results from the corresponding  parametric fit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Additionally, we applied a prior on θ0 based  on the value of θ0 from the corresponding parametric fit to  ensure that the non-parametric profiles are consistent with  the parametric profiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' We note that this approach introduces  bias against depicting changes in the rotation axis with ra-  dius.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  As described above, we only use the additional radial ve-  locities from Baumgardt & Hilker (2018) in the analysis of the  overall cluster, but not its populations, because we are unable  to split those stars into populations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Nonetheless, the inclusion  of this data is still important, since the strict priors on rpeak and  a0 for the population fit are solely based on the fit of the whole  cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Without the addition of that data, we would not be able  Article number, page 5 of 27  A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' paper  to reliably derive these parameters for most clusters, as a result  of the smaller radial range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  To quantify the effect of rotation, we calculate the ratio of  ordered-over-random (v/σ)HL motion for each population in all  clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Classically, this ratio is defined as the ratio between  the maximum rotation velocity to the central velocity dispersion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  However, because of the weaknesses of this approach mentioned  by Binney (2005), we follow the definition of (v/σ)HL by Cap-  pellari et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' (2007):  � v  σ  �  HL = ⟨v2⟩  ⟨σr2⟩ =  � rHL  0  ρ(r) 1  2vrot(r)2 r dr  � rHL  0  ρ(r)σ2  los r dr  ,  (6)  where rHL is the half-light radius of each cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Emsellem et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  (2007) highlighted a potential shortcoming of using (v/σ)HL to  characterize velocity fields, in that structurally different velocity  fields can result in very similar values of (v/σ)HL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' To address this  issue, they introduced λR,HL as an alternative, which is a proxy  for the spin parameter of the velocity field:  λR,HL =  ⟨r|v|⟩  ⟨r  �  v2 + σr  2⟩  =  � rHL  0  ρ(r) 2  π|vrot(r)| r2 dr  � rHL  0  ρ(r)  �  σ2  los + 1  2vrot(r)2 r dr  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  (7)  We calculate both parameters based on the rotation and disper-  sion profiles described in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 1 and Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2 for each cluster and its  populations to quantify kinematical differences between clusters  and populations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' For these calculations, we use the values of the  half-light radius rHL from Harris (1996, 2010 edition).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' For each  cluster and all of its populations, we use the global density pro-  files ρ(r).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' For some clusters, the radial rotation profiles do not  extend beyond the half-light radius.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' This could introduce some  bias to the values of (v/σ)HL and λR,HL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' However, as described  earlier, we apply a strict prior on the radial scales of the rotation  and dispersion profiles for each population based on the overall  profile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Therefore, when we calculate (v/σ)HL and λR,HL based  on the MCMC results of the radial rotation and dispersion pro-  files, we expect that any bias that may occur is correctly reflected  in our uncertainties of these parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' The kinematical model  we employ to derive the rotation and dispersion profiles is not  sensitive to structural differences between velocity fields of dif-  ferent clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Therefore, we expect that (v/σ)HL and λR,HL are  qualitatively the same for each cluster with this model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Results  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Global Kinematics  Figure 2 shows the radial rotation and dispersion profiles for  NGC 2808.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' In the top panel of this figure, the global profiles  for the cluster are presented, where the outermost radial velocity  data points are from the stars in the Baumgardt & Hilker (2018)  catalog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' In the lower panels of this figure, the corresponding  profiles are shown for each population.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' The continuous profiles  (solid lines) and binned profiles (symbols) shown here are each  determined as fits on single stars, and the shaded area represents  the 1σ uncertainty of each continuous profile and rotation angle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  The dashed line indicates the value of the half-light radius of this  cluster (Harris 1996, 2010 edition).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' The profiles for the other 24  globular clusters and their corresponding chromosome maps are  displayed in Figures A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1 to A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='24 in the appendix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' The binned  profiles highlight again that the radial extent of our data is lim-  ited to the center of each cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' This could bias our ability to  detect differences in kinematics between populations in the outer  regions of the cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' However, based on the work of Hénault-  Brunet et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' (2015) we expect to find the largest differences be-  tween populations around the half-light radius of each cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  Even closer to the center, differences should still be detectable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  Nevertheless, the extension of our work to the outskirts of the  clusters appears as a promising opportunity for future studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  Overall, the binned non-parametric profiles are in good agree-  ment with the continuous parametric profiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' The largest dis-  crepancies between these types of profiles are found close to the  center, where the binned profiles indicate a rise in rotation veloc-  ity for some clusters (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' NGC 1904 and NGC 7089).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Since the  uncertainties of the binned rotation profiles are also the largest  close to the center, it is uncertain whether this is a significant  effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' We stress that the binned profiles are only used for visu-  alization purposes and all following analyses are based on the  parametric profiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' As mentioned in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2 the radial extent  for the P1, P2 and P3 profiles is limited, which is revealed by  the binned profiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' We used priors on the rpeak that are based  on the parametric fit including all stars in the cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' We use  the parametric rotation and dispersion profiles to derive (v/σ)HL  and λR,HL, according to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 6 and Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 7, for each cluster and  its populations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Both of these values are integrals of these pro-  files up to the half-light radius of each cluster, which makes both  parameters robust against changes in rpeak, as shown by Kamann  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' The fitted parameters and the values of (v/σ)HL and  λR,HL for the populations of all clusters are listed in Table A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  Since the value of vsys is close to zero for each cluster and its  populations, it is not important for the subsequent analysis and  is not discussed further.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 3 we show our values of (v/σ)HL as a function of  the median relaxation time Trh of each cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' The values for  Trh are from (Harris 1996, 2010 edition), see Tab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' For the  global kinematics of the clusters, we find that there is a relation-  ship between (v/σ)HL and the median relaxation time, in that for  clusters with higher relaxation times we tend to get higher values  in (v/σ)HL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' In particular, for NGC 362, NGC 6397, NGC 6522  and NGC 6681 we do not find a significant sign of rotation and  all of them have relaxation times of log10(Trh/Gyr) < 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Sim-  ilar relations between cluster rotation and relaxation time have  been found by Kamann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' (2018), Bianchini et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' (2018)  and Sollima et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' This is to be expected if we assume  that globular clusters are imprinted at birth with the angular mo-  mentum of their parent molecular clouds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Over time, this angu-  lar momentum is dissipated outwards through two-body relax-  ation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' In fact, numerical simulations show that star clusters can  be rotating shortly after their birth (Mapelli 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Bekki 2019)  and that the strength of rotation declines over time (Lahén et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' For several clusters in our sample, the relaxation times  provided by Sollima & Baumgardt (2017) differ from those by  Harris (1996, 2010 edition).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' If we use the values provided by  Sollima & Baumgardt (2017), we find a similar relation with our  values of (v/σ)HL but the correlation is weaker.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  We find a linear relation between (v/σ)HL and λR,HL for all clus-  ters and populations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' This is shown in Figure A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='25 in the ap-  pendix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' We find that the constant of proportionality is ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='8 for  all cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Since our kinematic model is not sensitive to structural  differences in the velocity field of a cluster it is expected that  (v/σ)HL and λR,HL are qualitatively the same.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' In the following,  we only use (v/σ)HL to describe the kinematics of clusters and  populations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  Article number, page 6 of 27  Sven Martens et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' : Kinematic differences between multiple populations in Galactic globular clusters  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='6  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='8  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  log10(Trh/yr)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='000  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='025  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='050  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='075  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='100  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='125  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='150  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='175  (v/ )HL  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Relation between rotation strength in (v/σ)HL and the median re-  laxation time Trh of each cluster taken from Harris (1996, 2010 edition)  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Differences between P1 and P2  To analyze P1 and P2 for differences in their kinematics, we  compare the distributions of (v/σ)HL derived from the thinned  MCMC samples for vmax, θ0, rpeak, σmax and a0 using Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 1, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  2 and Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Figure 4 shows these distributions for all popula-  tions of each cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' The distributions for P1 and P2 are shown  in green and orange, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' For NGC 1904, NGC 6266,  NGC 6293, and NGC 6522, only the distribution for all stars, in  gray, is plotted because there is no separation into populations  for these clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  For NGC 362, NGC 3201, NGC 6218, NGC 6254,  NGC 6397, NGC 6624, NGC 6656, NGC 6681, NGC 6752 and  NGC 7099 we find that the distributions of (v/σ)HL for P1 and  P2 shown in Figure 4 are consistent with zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' In these cases, we  are unable to detect rotation for either population (see Table A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  and the corresponding rotation profiles in the appendix).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Based  on our analysis, we find that our ability to detect rotation for any  population depends mainly on two factors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' First, the uncertain-  ties of our analysis increase substantially for clusters with less  than ∼ 200 stars per population (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' NGC 3201 and NGC 6218),  resulting in a very broad distribution of (v/σ)HL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Second, if a  cluster is slowly rotating ((v/σ)HL ≲ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05), it is challenging to  constrain the rotation of its populations given our uncertainties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  When both factors are present, like in the cases of NGC 6397  and NGC 6752, our analysis only provides broad upper limits on  the rotation strength of each population.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  For NGC 104, NGC 1851, NGC 2808, NGC 5286,  NGC 5904, NGC 6093, NGC 6388, NGC 6541, NGC 7078 and  NGC 7089 we are able to detect rotation for P1 or P2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' All of  these clusters fulfill the condition (v/σ)HL ≳ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' NGC 6656 is  the only other cluster in our sample that also fulfills this con-  dition, but we are unable to detect rotation in P1 and P2 be-  cause its populations contain fewer than 200 stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' This shows  that the global rotation of the cluster strongly affects the rota-  tion of the individual populations, as expected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Based on the dis-  tributions of (v/σ)HL shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 4, we find kinematic differ-  ences between P1 and P2 that are significant above a 1σ-level for  NGC 2808, NGC 6093 and NGC 7078.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' For NGC 6093 and NGC  7078 we find that P2 rotates faster than P1 at a confidence level  of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5σ and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2σ respectively, whereas P2 rotates slower than  P1 in NGC 2808 at a confidence level of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='8σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' For NGC 104,  NGC 1851, NGC 5286, NGC 5904, NGC 6388, NGC 6541 and  NGC 7089 the strength of rotation of P1 is consistent with that  of P2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  Furthermore, we investigated whether the strength of rota-  tion of P1 and P2 or their difference can be related to the relax-  ation time of the corresponding cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' In the top and middle  panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 5 the values of (v/σ)HL are plotted against the re-  laxation time of the corresponding cluster for P1 and P2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' For  both P1 and P2, the strength of rotation only depends weakly on  the relaxation time, if there is any correlation at all.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Moreover,  we do not see a correlation between the difference of rotation  strength between P1 and P2 with relaxation time, which is illus-  trated in the bottom panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' However, the significance of  these results should be taken with a grain of salt, since we only  find differences above the 1σ-level for three clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  In addition, we looked into possible connections of our kine-  matic differences with the radial concentration of P1 and P2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  In fact, both NGC 6093 and NGC 7078 have been reported to  contain a more centrally concentrated P1 compared to P2 ac-  cording to Dalessandro et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' (2018) and Larsen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' (2015),  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' For both clusters, we find that P1 rotates slower  than P2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' However, Nardiello et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' (2018a) find no difference in  concentration between P1 and P2 for NGC 7078.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' For NGC 104  (Milone et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2018a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Cordoni et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2020, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=') and NGC 2808  (Dalessandro et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2019) P2 was found to be more centrally con-  centrated than P1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Whereas we do not find significant kinematic  differences between P1 and P2 for NGC 104, we find that P1  rotates faster than P2 for NGC 2808.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Overall, this could hint at  a connection between kinematic differences and the radial con-  centration of multiple populations in globular clusters, so that a  population more centrally concentrated would rotate less.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' How-  ever, since we only find kinematic differences in three clusters  and the information on the concentrations is only available for a  small subset of our sample of clusters, additional data are needed  to investigate this further.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Furthermore, the observations for e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  NGC 5272 (Lee & Sneden 2021), NGC 6205 (Johnson & Pila-  chowski 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Cordero et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2017) and NGC 6362 (Dalessandro  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2019, 2021) do not support this trend in our data that more  centrally concentrated populations rotate less.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Additional Population in Type-II Clusters  The distributions of (v/σ)HL for type-II clusters are also shown  in Figure 4, where P1, P2 and P3 are shown in green, orange  and purple respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' For four of the six type-II clusters in  our sample, we did not detect rotation in P3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' For NGC 362,  NGC 6656 and NGC 7089 this is most likely due to the low  number of stars in P3 as discussed previously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' For NGC 6388 P3  is populated well, but the global rotation of the cluster is very  low.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' For NGC 1851 and NGC 5286 we detect rotation in P1, P2  and P3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' For NGC 1851 we find that the distribution of (v/σ)HL  for P3 is very similar to that of P1 and P2, whereas for NGC  5286, there might be a hint of P3 rotating faster than P1 and P2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  However, the observed difference in (v/σ)HL is still within the  1σ uncertainty interval, so further data are needed to draw any  solid conclusions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' In particular, these results also do not give any  clear hints on other formation scenarios for type-II clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Notes on Individual Clusters  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' NGC 6093  For NGC 6093 we observe that rpeak varies between P1 and P2  (see Table A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' While the values of rpeak for the whole clus-  Article number, page 7 of 27  A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' paper  NGC104  NGC1851  NGC1904  NGC2808  NGC3201  NGC362  NGC5286  NGC5904  NGC6093  NGC6218  NGC6254  NGC6266  NGC6293  NGC6388  NGC6397  NGC6441  NGC6522  NGC6541  NGC6624  NGC6656  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='25  NGC6681  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='25  NGC6752  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='25  NGC7078  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='25  NGC7089  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='25  NGC7099  Number of Samples  (v/ )HL  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Distributions of samples of (v/σ)HL, which describes the strength of rotation for each cluster in this analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' These distributions are shown  for the overall cluster (gray) and each of its populations (P1:green, P2:orange, P3:violet).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' The 16th, 50th and 84th percentile for each distribution  are shown on top of the corresponding distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' For distributions that peak at zero, only the 95th percentile is shown to provide an upper limit  on the rotation strength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  ter and P1 are consistent, the distribution of samples for rpeak of  P2 peaks at a much smaller value, which is also apparent in the  radial rotation profile in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='8 in the appendix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Furthermore,  the distribution of rpeak for P2 is asymmetric and there is a strong  anti-correlation between rpeak and vmax.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' This causes the asymme-  try of (v/σ)HL in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 4 for P2 of this cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' As discussed in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1 the value of (v/σ)HL is generally robust to changes in rpeak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  However, in this case the value of rpeak for P2 is very close to the  center of that cluster, and it seems worthwhile to find out whether  this has a significant effect on our results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' If we apply a uniform  prior on rpeak for P2, we find that the difference between P1 and  P2 in (v/σ)HL is even larger and the asymmetry in the distribu-  tion of (v/σ)HL vanishes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' If we fix the value of rpeak for P2 to  that obtained for the whole cluster, the asymmetry also vanishes,  but in this case (v/σ)HL is consistent with that value for P1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' This  cluster was already analyzed for kinematic differences between  populations based on MUSE data, with a very similar approach  to the one presented here by Kamann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' They did not  find this peculiar behavior of P2 for that cluster, because they  used a different population split than the one used here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Notably,  they also used individual population density profiles when cal-  culating (v/σ)HL for their populations and not the global den-  sity profile of that cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Kamann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' (2020) split the cluster  in three populations, where our P1 is consistent with their pri-  mordial population and our P2 includes their intermediate and  extreme populations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' If we average their values of (v/σ)HL for  the intermediate and extreme population, the result is consistent  with the value of (v/σ)HL they obtained for the primordial pop-  ulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' If we consider that Kamann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' (2020) fixed the radial  scale of each population, our results are consistent with theirs in  that we do not find significant kinematic differences between P1  and P2 if the radial scale is fixed to that of the global profile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  However, there is no physical reason for why the radial scale of  P2 cannot be different to that of P1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' NGC 2808 & NGC 7078  For NGC 2808 and NGC 7078 we find differences above the  1σ-level in (v/σ)HL and the rotation profiles of their popu-  lations, whereas the dispersion profiles do not differ signifi-  cantly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' For NGC 7078 we observe that P2 rotates faster than P1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  Qualitatively, this behavior is similar to that of NGC 6093 and  NGC 6205, where differences of this type between similar pop-  ulations have also been reported by Kamann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' (2020) and  Cordero et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' (2017) respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' For NGC 2808 we find the  opposite in that P1 rotates faster than P2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  To investigate the relationship between the populations in the  chromosome maps and their kinematic differences further for  Article number, page 8 of 27  Sven Martens et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' : Kinematic differences between multiple populations in Galactic globular clusters  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  (v/ )HL, P1  NGC 6397  NGC 6681  NGC 6624  NGC 6093  NGC 1851  NGC 6752  NGC 6218  NGC 7099  NGC 6254  NGC 6388  NGC 362  NGC 6541  NGC 6441  NGC 5286  NGC 2808  NGC 6656  NGC 3201  NGC 7078  NGC 7089  NGC 5904  NGC 104  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  (v/ )HL, P2  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='6  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='8  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  log10(Trh/yr)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1  (v/ )HL, P1  (v/ )HL, P2  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Relation between rotation strength in (v/σ)HL of P1 and P2 and  the median relaxation time Trh for each cluster taken from Harris (1996,  2010 edition), and the difference in rotation strength between P1 and P2  as a function of median relaxation time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  NGC 2808 and NGC 7078, we decided to reiterate the analy-  sis with different population splits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Incidentally, the structure of  the chromosome maps of these clusters allows us to distinguish  between four populations (P1, P2’, P3’ and P4’) for NGC 2808  (Milone et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Latour et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2019) and three populations  (P1, P2’ and P3’) for NGC 7078 (Nardiello et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2018b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Com-  pared to Milone et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' (2015) our P2’, P3’ and P4’ in NGC 2808  are equivalent to their populations C, D and E, while our P1’ is  their populations A and B combined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' For NGC 7078, our P2’ is  equivalent to population B by Nardiello et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' (2018b), whereas  our P1’ corresponds to their populations A and D and our pop-  ulation P3’ is equal to their populations C and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' We do not  split P1’ for both clusters and P3’ for NGC 7078 any further  to ensure that there are still enough stars per population to get  meaningful results from our analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' These populations accord-  ing to our splitting are shown in the chromosome maps in the  upper panels of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 6, whereas the distributions of (v/σ)HL for  these populations are depicted in the lower panels of that figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  For NGC 2808 we find that P2’, P3’ and P4’ do not differ in their  rotation significantly, but the difference between these three pop-  ulations and P1’ is larger than 1σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' For NGC 7078 the value of  (v/σ)HL of P3’ stars is consistent with that of P1’ and P2’ stars,  but the difference between P1’ stars and P2’ is larger than 1σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  Therefore, we do not find a general trend of (v/σ)HL along these  populations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  NGC 7078 has been analyzed for kinematic differences in  populations by Szigeti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' They used high precision  radial velocity data from the SDSS-IV APOGEE-2 survey for  138 stars in NGC 7078 to measure its rotation amplitude as a  function of position angle for the whole cluster and two popu-  lations that were identified based on single element abundance  changes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' They derived the angular rotation profile of NGC 7078  by splitting the cluster into two halves through the cluster center.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  This line of separation is rotated in small angular increments, and  the difference in mean radial velocity ∆V between both halves is  calculated at each step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' If the cluster is rotating, the relation be-  tween velocity difference ∆V and position angle relative to the  rotation axis α is ∆V = 2vrot · sin (α).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' The global rotation am-  plitude and rotation angle that they find agree with our values  for vmax and θ0 for the whole cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Furthermore, they found no  kinematic difference between their two populations, which is in  contrast to our results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Their method may only be applied to a  fully sampled area that is symmetric with respect to the position  angle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' To ensure that our data comply with those restrictions, we  filter our stars to make the covered area of the cluster circular.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  If we apply their method to our filtered data for P1 and P2, we  find rotation amplitudes and rotation angles that are consistent  with our radial rotation curves for P1 and P2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' The corresponding  angular rotation profiles and the spatial coverage of the cluster  are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' In particular, we still find kinematic dif-  ferences between P1 and P2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' One striking difference between  their data and ours is that we have 390 and 697 stars in P1 and  P2, compared to their 33 and 49 stars in those populations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' To  investigate this further, we decreased the number of stars by ran-  domly sampling from P1 and P2 and then applied their method  again.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Figure A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='27 shows three of these angular rotation profiles  and the spatial coverage of the cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' We find that with so few  stars, this method results in a wide range of fundamentally dif-  ferent profiles, presumably because the method is very sensitive  to single stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Probably the uncertainties of the differential rota-  tion profiles are underestimated because the strong correlations  between different values in those profiles are generally not taken  into account.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Together with our much larger sample of analyzed  stars, this could be the cause for the discrepancies between our  results and those from Szigeti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  NGC 2808 has not been analyzed for differences in its ra-  dial rotation and dispersion profiles yet, but Bellini et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' (2015)  found differences in the radial anisotropy profiles for this cluster,  by using proper motion data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Given that this cluster shows kine-  matic differences using both radial velocities and proper motion  data, it would be very interesting to combine both data sets and  analyze the 3D stellar velocities of this cluster for differences  between multiple populations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' NGC 104 & NGC 5904  Neither Milone et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' (2018b), nor Cordoni et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' (2020), find  differences in the rotation amplitude between the populations of  NGC 104, which agrees with our results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' For NGC 5904 Cordoni  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' (2020) do not observe any differences in rotation amplitude,  but they do find differences in the phase of their rotation curves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  These phase differences translate to a differing angle of rotation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  We do not find any significant differences in rotation amplitudes  for NGC 5904 either, but we also do not find a significant differ-  ence in the angle of rotation between P1 and P2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Random Sampling of the Chromosome Map  To further analyze the solidity of our results for NGC 2808,  NGC 6093 and NGC 7078 and to evaluate our uncertainty es-  timations, we randomly sampled the chromosome maps of these  clusters to create random populations P1 and P2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' To ensure com-  parability to the original population split, we used the same num-  ber of stars per population as in the original separations (see Ta-  ble 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' To achieve statistically relevant results, we created 100  Article number, page 9 of 27  A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' paper  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2  F275W  F814W  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  CF275W  2 F336W + F438W  NGC2808  P1 (N=371)  P2 (N=428)  P3 (N=614)  P4 (N=166)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  F275W  F814W  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='25  CF275W  2 F336W + F438W  NGC7078  P1 (N=390)  P2 (N=332)  P3 (N=365)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='25  NGC2808  Number of Samples  (v/ )HL  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='25  NGC7078  Number of Samples  (v/ )HL  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Top: Chromosome maps of NGC 2808 and NGC 7078, with additional population splits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' For NGC 2808 the original P2 is split into three  subpopulations (P2’, P3’ and P4’), whereas P2 of NGC 7078 is split into two subpopulations (P2’ and P3’) according to the respective morphology  of the chromosome maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Bottom: Distributions of samples of (v/σ)HL for NGC 2808 and NGC 7078 for the overall cluster and each of their  newly identified populations shown atop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  random population pairs for each cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' We calculated the ro-  tation and dispersion profiles and derived (v/σ)HL for each of  these random populations, as described in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' As a result,  we calculate 100 values of (v/σ)HL for each population of each  cluster, which are shown in the upper panels of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' It is ap-  parent that the distributions for P1 and P2 for each cluster have  the same median value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' This shows that, on average, we do not  find kinematic differences when randomly sampling the chro-  mosome map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' We also find that the distributions of (v/σ)HL ob-  tained with the random sampling are broader for smaller num-  bers of stars per population, as expected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' In the lower panels  of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 7 we show the differences of (v/σ)HL between P1 and  P2 obtained from the random sampling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' As expected, these dis-  tributions are centered around zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' We also indicated the ob-  served differences for NGC 2808, NGC 6093 and NGC 7078 in  red.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' The observed differences lie outside the 1σ-regions of the  distributions, which supports the solidity of our uncertainty esti-  mations and indicates that the kinematic differences that we find  for NGC 2808, NGC 6093 and NGC 7078 are truly connected to  the populations defined in the chromosome maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Conclusion & Outlook  We created and analyzed the rotation and dispersion profiles of  25 Galactic globular clusters in the search for kinematic differ-  ences between different populations within each cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Based  on these kinematic profiles, we derived the rotation strength in  terms of the ratio of ordered-over-random motion (v/σ)HL, eval-  uated at the half-light radius, for each cluster and its populations  to quantify kinematic differences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' For NGC 362, NGC 6397,  NGC 6522 and NGC 6681 we find no significant global rotation  when using all stars in these clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' For NGC 104, NGC 1851,  NGC 2808, NGC 5286, NGC5904, NGC 6093, NGC 6388,  NGC 6541, NGC 7078 and NGC 7089 we are able to detect rota-  tion in at least one of their populations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' For three clusters we find  differences above the 1σ level: For NGC 6093 and NGC 7078  we find that P2 stars rotate faster than P1 stars, whereas we find  the opposite for NGC 2808, where P1 stars rotate faster than P2  stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  Our results do not give a clear hint on the formation sce-  nario of multiple populations in globular clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' We find sup-  port for both multi-epoch and single-epoch formation scenarios  in our data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' For multi-epoch formation scenarios, we expect to  find that P2 rotates faster than P1, which matches our results  for NGC 6093 and NGC 7078.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Assuming a single-epoch forma-  Article number, page 10 of 27  Sven Martens et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' : Kinematic differences between multiple populations in Galactic globular clusters  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2  0  10  20  30  40  Number of realizations  NGC2808  P1 (371)  P2 (1208)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2  (v/ )HL  NGC7078  P1 (390)  P2 (697)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2  NGC6093  P1 (367)  P2 (582)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2  0  5  10  Number of realizations  obs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2  (v/ )HL, P1  (v/ )HL, P2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Top: Values of (v/σ)HL derived from randomly sampling the chromosome maps of NGC 2808, NGC 6093 and NGC 7078.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' The numbers of  stars in the randomly drawn P1 and P2 are the same as the observed populations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Bottom: Differences of the randomly drawn values of (v/σ)HL  between P1 and P2 for NGC 2808, NGC 6093 and NGC 7078.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' The observed differences for these clusters are shown as the red dotted line, whereas  the black dotted line is the standard deviation of the shown distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  tion scenario, it follows that P1 rotates faster than P2, which is  what we find for NGC 2808.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' However, the kinematic differences  that we find are still relatively uncertain at confidence levels of  ≲ 2σ, so further data are needed for a definitive answer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' We find  further support for both scenarios if we consider clusters with  kinematical variations between P1 and P2 below the 1σ-level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  While we find that the rotation strength of each cluster is pos-  itively correlated with median relaxation time, the correlation  between relaxation time and the rotation strength of P1 or P2 is  weak at best, and we do not see a correlation of the kinemati-  cal difference between P1 and P2 with relaxation time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Based on  our analysis, neither of the two types of formation scenarios for  multiple populations in globular clusters is favored.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Bastian &  Lardo (2018) discussed that none of the formation scenarios put  forward to date is able to explain all the observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' It is also  possible that the formation of multiple populations does not af-  fect the rotation of either population in a way that we are able to  observe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' However, it would be very interesting to see what pri-  mordial differences between P1 and P2 are consistent with the  differences between those populations that we find.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  To get a better understanding of the formation scenarios of  multiple populations and their kinematics in general, there are  several problems worth addressing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' For many clusters in our  sample, we were unable to detect rotation for P1 or P2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' How-  ever, since most clusters are rotating overall, we suspect that at  least one population should be rotating as well for most clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  As mentioned in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1 we are generally unable to detect rota-  tion in P1 or P2 if the overall cluster is already rotating slowly  with (v/σ)HL ≲ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05 or when the number of stars per population  is of the order of 200 stars or below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Especially the results for  NGC 6656 and NGC 3201 could be improved significantly by in-  creasing the number of stars per population, since these clusters  are rotating fast enough to overcome that limitation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' One way to  tackle this issue is to determine the population tags directly from  the spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' An alternative would be to add additional photomet-  ric data to be able to assign more stars to their respective popu-  lation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' This would be especially useful outside the core of each  cluster, where radial velocity measurements of stars are avail-  able (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Baumgardt & Hilker 2018), but these stars have not  been separated into populations yet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Leitinger et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' (in prepara-  tion) are currently working on using ground-based photometry to  split the populations and derive density profiles for each popula-  tion in globular clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' When we include their additional popu-  lation tags for NGC 7078, we observed small changes in the dis-  tribution of (v/σ)HL, but nothing significant since the number of  stars per population is already comparatively large for that clus-  ter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Nonetheless, it seems worthwhile to pursue that approach,  since it also increases the radial range of the population data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' It  is possible that this could increase the accuracy of measurements  of the rotation in P1 and P2 substantially.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Another possibility for  a future work would be to use density profiles per population  to derive the rotation strength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Using data from Leitinger et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  (in preparation) we checked whether our results for NGC 7078  change if we use their density profiles for P1 and P2, but we still  find that P2 rotates faster than P1 with a difference larger than  1σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' However, if the populations have the same rotation and dis-  persion curves, but different concentrations, then we would ex-  pect to find kinematic differences between them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' This is because  the observed kinematics at a given projected radius correspond  to a different intrinsic radius relative to the cluster center.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Ulti-  mately, one needs more sophisticated models to understand all  the details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  Acknowledgements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' SM, FG, ML, PMW and SD acknowledge funding from  the Deutsche Forschungsgemeinschaft (grant LA 4383/4-1, DR 281/35-1 and  KA 4537/2-1) and by the BMBF from the ErUM program through grants  05A14MGA, 05A17MGA, 05A20MGA and 05A20BAB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' SK and RP gratefully  acknowledge funding from UKRI in the form of a Future Leaders Fellowship  (grant no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' MR/T022868/1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  Article number, page 11 of 27  A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' paper  References  Anderson, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Sarajedini, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Bedin, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2008, AJ, 135, 2055  Bacon, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Accardo, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Adjali, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2010, in Society of Photo-Optical In-  strumentation Engineers (SPIE) Conference Series, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 7735, Ground-based  and Airborne Instrumentation for Astronomy III, ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' McLean, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Ram-  say, & H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Takami, 773508  Bastian, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Lamers, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', de Mink, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2013, MNRAS, 436,  2398  Bastian, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' & Lardo, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2018, ARA&A, 56, 83  Baumgardt, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' & Hilker, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2018, MNRAS, 478, 1520  Bekki, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2019, A&A, 622, A53  Bellini, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Vesperini, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Piotto, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2015, ApJ, 810, L13  Bianchini, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', van de Ven, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Norris, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Schinnerer, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', & Varri, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2016,  MNRAS, 458, 3644  Bianchini, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', van der Marel, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', del Pino, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2018, MNRAS, 481, 2125  Binney, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2005, MNRAS, 363, 937  Cadelano, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Dalessandro, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Salaris, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2022, ApJ, 924, L2  Cappellari, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Emsellem, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Bacon, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2007, MNRAS, 379, 418  Carretta, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Bragaglia, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Gratton, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2009, A&A, 505, 117  Carretta, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Bragaglia, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Gratton, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2010a, A&A, 516, A55  Carretta, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Gratton, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Lucatello, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2010b, ApJ, 722, L1  Cordero, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Hénault-Brunet, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Pilachowski, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2017, MNRAS,  465, 3515  Cordoni, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Milone, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Mastrobuono-Battisti, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2020, ApJ, 889, 18  Cottrell, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' & Da Costa, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 1981, ApJ, 245, L79  Dalessandro, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Cadelano, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Vesperini, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2019, ApJ, 884, L24  Dalessandro, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Cadelano, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Vesperini, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2018, ApJ, 859, 15  Dalessandro, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Lapenna, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Mucciarelli, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2016, ApJ, 829, 77  Dalessandro, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Raso, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Kamann, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2021, MNRAS, 506, 813  de Boer, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Gieles, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Balbinot, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2019, MNRAS, 485, 4906  Decressin, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Charbonnel, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', & Meynet, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2007a, A&A, 475, 859  Decressin, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Meynet, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Charbonnel, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Prantzos, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', & Ekström, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2007b,  A&A, 464, 1029  Emsellem, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Cappellari, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Krajnovi´c, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2007, MNRAS, 379, 401  Foreman-Mackey, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Hogg, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Lang, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', & Goodman, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2013, PASP, 125,  306  Gieles, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Charbonnel, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Krause, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2018, MNRAS, 478, 2461  Gieles, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' & Zocchi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2015, MNRAS, 454, 576  Giesers, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Kamann, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Dreizler, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2019, A&A, 632, A3  Goodman, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' & Weare, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2010, Communications in Applied Mathematics and  Computational Science, 5, 65  Gott, III, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 1973, ApJ, 186, 481  Harris, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 1996, AJ, 112, 1487  Husser, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='-O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Kamann, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Dreizler, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2016, A&A, 588, A148  Husser, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='-O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Wende-von Berg, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Dreizler, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2013, A&A, 553, A6  Hénault-Brunet, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Gieles, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Agertz, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', & Read, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2015, MNRAS, 450,  1164  Johnson, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' & Pilachowski, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2012, ApJ, 754, L38  Kamann, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Dalessandro, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Bastian, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2020, MNRAS, 492, 966  Kamann, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Husser, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='-O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Brinchmann, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2016, A&A, 588, A149  Kamann, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Husser, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='-O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Dreizler, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2018, MNRAS, 473, 5591  Kamann, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Wisotzki, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', & Roth, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2013, A&A, 549, A71  King, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 1966, AJ, 71, 64  Lahén, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Naab, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Johansson, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2020, ApJ, 904, 71  Larsen, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Baumgardt, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Bastian, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2015, ApJ, 804, 71  Latour, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Husser, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='-O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Giesers, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2019, A&A, 631, A14  Lee, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='-W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' & Sneden, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2021, ApJ, 909, 167  Libralato, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Bellini, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Piotto, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2019, ApJ, 873, 109  Lynden-Bell, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 1967, MNRAS, 136, 101  Mapelli, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2017, MNRAS, 467, 3255  Marino, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Milone, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Karakas, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2015, MNRAS, 450, 815  Martocchia, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Cabrera-Ziri, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Lardo, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2018, MNRAS, 473, 2688  Martocchia, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Niederhofer, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Dalessandro, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2018, MNRAS, 477, 4696  Milone, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Bedin, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Piotto, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', & Anderson, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2009, A&A, 497, 755  Milone, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Marino, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Di Criscienzo, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2018a, MNRAS, 477, 2640  Milone, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Marino, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Mastrobuono-Battisti, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', & Lagioia, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2018b,  MNRAS, 479, 5005  Milone, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Marino, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Piotto, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2015, ApJ, 808, 51  Milone, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Piotto, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Renzini, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2017, MNRAS, 464, 3636  Mucciarelli, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Origlia, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Ferraro, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', & Pancino, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2009, ApJ, 695, L134  Nardiello, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Libralato, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Piotto, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2018a, MNRAS, 481, 3382  Nardiello, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Milone, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Piotto, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2018b, MNRAS, 477, 2004  Pfeffer, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Lardo, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Bastian, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Saracino, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', & Kamann, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2021, MNRAS,  500, 2514  Piotto, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Milone, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Bedin, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2015, AJ, 149, 91  Plummer, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 1911, MNRAS, 71, 460  Renzini, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2013, Mem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Italiana, 84, 162  Richer, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Heyl, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Anderson, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2013, ApJ, 771, L15  Robin, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Reylé, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Derrière, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', & Picaud, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2003, A&A, 409, 523  Sarajedini, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Bedin, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Chaboyer, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2007, AJ, 133, 1658  Sollima, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' & Baumgardt, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2017, MNRAS, 471, 3668  Sollima, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Baumgardt, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', & Hilker, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2019, MNRAS, 485, 1460  Szigeti, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Mészáros, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Szabó, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2021, MNRAS, 504, 1144  Tiongco, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Vesperini, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', & Varri, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2019, MNRAS, 487, 5535  Vesperini, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', McMillan, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', D’Antona, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', & D’Ercole, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2013, MNRAS,  429, 1913  Weilbacher, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Palsa, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', Streicher, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 2020, A&A, 641, A28  Article number, page 12 of 27  Sven Martens et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' : Kinematic differences between multiple populations in Galactic globular clusters  Appendix A: Additional Tables and Figures  Table A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Priors of the parametric fit described in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  Parameter  Prior  vsys,o  U(-10 km/s, 10 km/s)  vsys,p  N(µ(vsys,o), σ(vsys,o))  vmax,o  U(0, vesc)  vmax,p  ∝  �N(µ(vmax,o), µ(σmax,o))  if 0 < vmax, p < vesc  0  else  θ0  U(−π, π)  rpeak,o  ∝  �����������  0  if rpeak,o < rHL/30  1  if rHL/30 < rpeak,o < 5 rHL  N(5 rHL, rHL)  else,  rpeak,p  ∝  �N(µ(rpeak,o), σ(rpeak,o))  if rpeak,p > 0  0  else  σmax  U(0, ∞)  a0, o  same prior as rpeak,o  a0, p  ∝  �N(µ(a0,o), σ(a0,o))  if a0,p > 0  0  else  ffg  U(0, 1)  Notes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' The subscript ’o’ denotes priors for fit of the overall population,  whereas the subscript ’p’ describes priors for each population fit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  Table A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Priors of the non-parametric fit described in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  Parameter  Prior  vsys  N(µ(v∗  sys), σ(v∗  sys))  vmax  U(0, ∞)  θ0  N(µ(θ∗  0), σ(θ∗  0))  σmax  U(0, ∞)  Notes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' The superscript ’*’ denotes that these parameters are distribu-  tions of samples from the parametric fit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  Article number, page 13 of 27  A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' paper  10  1  100  101  102  0  2  4  6  OVERALL  W  N  E  S  0  10  1  100  101  102  r/arcsec  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  0  2  4  6  P1  W  N  E  S  0  r/arcsec  5  10  15  10  1  100  101  102  r [arcsec]  0  2  4  6  P2  W  N  E  S  0  10  1  100  101  102  r [arcsec]  5  10  vrot [km/s]  r [km/s]  NGC 104  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2  F275W  F814W  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  CF275W  2 F336W + F438W  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Chromosome maps, rotation and dispersion profiles for NGC 104 and each of its populations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' The rotation profiles for each population  are shown on the left, whereas the dispersion profiles are shown on the right.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' In the center, the angle of rotation is shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  10  1  100  101  102  0  2  4  OVERALL  W  N  E  S  0  10  1  100  101  102  r/arcsec  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  0  2  4  P1  W  N  E  S  0  r/arcsec  2  4  6  8  0  1  2  3  4  P2  W  N  E  S  0  r/arcsec  2  4  6  8  10  1  100  101  102  r [arcsec]  0  5  10  15  P3  W  N  E  S  0  10  1  100  101  102  r [arcsec]  2  4  6  8  vrot [km/s]  r [km/s]  NGC 362  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  F275W  F814W  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  CF275W  2 F336W + F438W  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Continuation of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1 for NGC 362.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  Article number, page 14 of 27  Sven Martens et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' : Kinematic differences between multiple populations in Galactic globular clusters  10  1  100  101  102  0  1  2  3  OVERALL  W  N  E  S  0  10  1  100  101  102  r/arcsec  5  10  15  0  1  2  3  4  P1  W  N  E  S  0  r/arcsec  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  0  2  4  P2  W  N  E  S  0  r/arcsec  2  4  6  8  10  1  100  101  102  r [arcsec]  0  1  2  3  P3  W  N  E  S  0  10  1  100  101  102  r [arcsec]  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  vrot [km/s]  r [km/s]  NGC 1851  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  F275W  F814W  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  CF275W  2 F336W + F438W  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Continuation of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1 for NGC 1851.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  10  1  100  101  102  r [arcsec]  0  1  2  OVERALL  W  N  E  S  0  10  1  100  101  102  r [arcsec]  5  10  vrot [km/s]  r [km/s]  NGC 1904  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Continuation of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1 for NGC 1904.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  10  1  100  101  102  0  1  2  OVERALL  W  N  E  S  0  10  1  100  101  102  r/arcsec  3  4  5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  P1  W  N  E  S  0  r/arcsec  3  4  5  10  1  100  101  102  r [arcsec]  0  2  4  6  8  P2  W  N  E  S  0  10  1  100  101  102  r [arcsec]  2  3  4  5  vrot [km/s]  r [km/s]  NGC 3201  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  F275W  F814W  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='30  CF275W  2 F336W + F438W  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Continuation of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1 for NGC 3201.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  Article number, page 15 of 27  A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' paper  10  1  100  101  102  0  2  4  OVERALL  W  N  E  S  0  10  1  100  101  102  r/arcsec  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  0  2  4  6  P1  W  N  E  S  0  r/arcsec  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  0  2  4  P2  W  N  E  S  0  r/arcsec  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  10  1  100  101  102  r [arcsec]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  P3  W  N  E  S  0  10  1  100  101  102  r [arcsec]  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  vrot [km/s]  r [km/s]  NGC 5286  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2  F275W  F814W  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  CF275W  2 F336W + F438W  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Continuation of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1 for NGC 5286.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  10  1  100  101  102  0  1  2  3  4  OVERALL  W  N  E  S  0  10  1  100  101  102  r/arcsec  2  4  6  8  10  0  1  2  3  4  P1  W  N  E  S  0  r/arcsec  2  4  6  8  10  1  100  101  102  r [arcsec]  0  1  2  3  4  P2  W  N  E  S  0  10  1  100  101  102  r [arcsec]  2  4  6  8  vrot [km/s]  r [km/s]  NGC 5904  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1  F275W  F814W  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='30  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='35  CF275W  2 F336W + F438W  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Continuation of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1 for NGC 5904.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  Article number, page 16 of 27  Sven Martens et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' : Kinematic differences between multiple populations in Galactic globular clusters  10  1  100  101  102  0  1  2  3  OVERALL  W  N  E  S  0  10  1  100  101  102  r/arcsec  5  10  15  0  1  2  3  4  P1  W  N  E  S  0  r/arcsec  5  10  10  1  100  101  102  r [arcsec]  0  2  4  P2  W  N  E  S  0  10  1  100  101  102  r [arcsec]  5  10  vrot [km/s]  r [km/s]  NGC 6093  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1  F275W  F814W  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='30  CF275W  2 F336W + F438W  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Continuation of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1 for NGC 6093.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  10  1  100  101  102  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  OVERALL  W  N  E  S  0  10  1  100  101  102  r/arcsec  2  4  6  0  2  4  6  8  P1  W  N  E  S  0  r/arcsec  2  4  6  10  1  100  101  102  r [arcsec]  0  2  4  6  P2  W  N  E  S  0  10  1  100  101  102  r [arcsec]  2  4  vrot [km/s]  r [km/s]  NGC 6218  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  F275W  F814W  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='25  CF275W  2 F336W + F438W  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Continuation of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1 for NGC 6218.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  Article number, page 17 of 27  A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' paper  10  1  100  101  102  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  OVERALL  W  N  E  S  0  10  1  100  101  102  r/arcsec  2  4  6  8  0  2  4  6  8  P1  W  N  E  S  0  r/arcsec  2  4  6  10  1  100  101  102  r [arcsec]  0  2  4  6  P2  W  N  E  S  0  10  1  100  101  102  r [arcsec]  2  4  6  vrot [km/s]  r [km/s]  NGC 6254  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1  F275W  F814W  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='30  CF275W  2 F336W + F438W  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Continuation of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1 for NGC 6254.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  10  1  100  101  102  r [arcsec]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  OVERALL  W  N  E  S  0  10  1  100  101  102  r [arcsec]  5  10  15  vrot [km/s]  r [km/s]  NGC 6266  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Continuation of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1 for NGC 6266.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  10  1  100  101  102  r [arcsec]  0  2  4  6  OVERALL  W  N  E  S  0  10  1  100  101  102  r [arcsec]  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  vrot [km/s]  r [km/s]  NGC 6293  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Continuation of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1 for NGC 6293.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  Article number, page 18 of 27  Sven Martens et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' : Kinematic differences between multiple populations in Galactic globular clusters  10  1  100  101  102  0  2  4  OVERALL  W  N  E  S  0  10  1  100  101  102  r/arcsec  5  10  15  20  0  5  10  P1  W  N  E  S  0  r/arcsec  5  10  15  0  2  4  P2  W  N  E  S  0  r/arcsec  5  10  15  20  10  1  100  101  102  r [arcsec]  0  2  4  6  8  P3  W  N  E  S  0  10  1  100  101  102  r [arcsec]  5  10  15  20  vrot [km/s]  r [km/s]  NGC 6388  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='25  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='75  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='50  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='50  F275W  F814W  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  CF275W  2 F336W + F438W  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Continuation of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1 for NGC 6388.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  10  1  100  101  102  0  1  2  OVERALL  W  N  E  S  0  10  1  100  101  102  r/arcsec  2  4  6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  P1  W  N  E  S  0  r/arcsec  2  4  6  10  1  100  101  102  r [arcsec]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  P2  W  N  E  S  0  10  1  100  101  102  r [arcsec]  2  4  6  vrot [km/s]  r [km/s]  NGC 6397  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='00  F275W  F814W  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='15  CF275W  2 F336W + F438W  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Continuation of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1 for NGC 6397.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  Article number, page 19 of 27  A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' paper  10  1  100  101  102  0  2  4  6  8  OVERALL  W  N  E  S  0  10  1  100  101  102  r/arcsec  5  10  15  20  0  2  4  6  8  P1  W  N  E  S  0  r/arcsec  5  10  15  20  10  1  100  101  102  r [arcsec]  0  2  4  P2  W  N  E  S  0  10  1  100  101  102  r [arcsec]  5  10  15  vrot [km/s]  r [km/s]  NGC 6441  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  F275W  F814W  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  CF275W  2 F336W + F438W  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Continuation of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1 for NGC 6441.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  10  1  100  101  102  r [arcsec]  0  2  4  6  OVERALL  W  N  E  S  0  10  1  100  101  102  r [arcsec]  0  5  10  15  vrot [km/s]  r [km/s]  NGC 6522  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Continuation of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1 for NGC 6522.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  10  1  100  101  102  0  1  2  3  4  OVERALL  W  N  E  S  0  10  1  100  101  102  r/arcsec  5  10  15  0  1  2  3  4  P1  W  N  E  S  0  r/arcsec  2  4  6  8  10  1  100  101  102  r [arcsec]  0  2  4  P2  W  N  E  S  0  10  1  100  101  102  r [arcsec]  2  4  6  8  10  vrot [km/s]  r [km/s]  NGC 6541  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1  F275W  F814W  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='30  CF275W  2 F336W + F438W  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Continuation of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1 for NGC 6541.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  Article number, page 20 of 27  Sven Martens et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' : Kinematic differences between multiple populations in Galactic globular clusters  10  1  100  101  102  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  OVERALL  W  N  E  S  0  10  1  100  101  102  r/arcsec  2  4  6  8  10  0  2  4  6  8  P1  W  N  E  S  0  r/arcsec  2  4  6  8  10  1  100  101  102  r [arcsec]  0  2  4  6  P2  W  N  E  S  0  10  1  100  101  102  r [arcsec]  2  4  6  8  vrot [km/s]  r [km/s]  NGC 6624  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  F275W  F814W  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  CF275W  2 F336W + F438W  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Continuation of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1 for NGC 6624.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  10  1  100  101  102  0  2  4  OVERALL  W  N  E  S  0  10  1  100  101  102  r/arcsec  2  4  6  8  10  0  2  4  6  8  P1  W  N  E  S  0  r/arcsec  2  4  6  8  0  2  4  6  P2  W  N  E  S  0  r/arcsec  2  4  6  8  10  10  1  100  101  102  r [arcsec]  0  2  4  6  P3  W  N  E  S  0  10  1  100  101  102  r [arcsec]  2  4  6  8  vrot [km/s]  r [km/s]  NGC 6656  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1  F275W  F814W  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='30  CF275W  2 F336W + F438W  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Continuation of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1 for NGC 6656.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  Article number, page 21 of 27  A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' paper  10  1  100  101  102  0  1  2  3  4  OVERALL  W  N  E  S  0  10  1  100  101  102  r/arcsec  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  0  5  10  P1  W  N  E  S  0  r/arcsec  2  4  6  8  10  10  1  100  101  102  r [arcsec]  0  2  4  6  P2  W  N  E  S  0  10  1  100  101  102  r [arcsec]  2  4  6  vrot [km/s]  r [km/s]  NGC 6681  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  F275W  F814W  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  CF275W  2 F336W + F438W  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Continuation of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1 for NGC 6681.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  10  1  100  101  102  0  1  2  3  4  OVERALL  W  N  E  S  0  10  1  100  101  102  r/arcsec  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  0  5  10  P1  W  N  E  S  0  r/arcsec  2  4  6  8  10  1  100  101  102  r [arcsec]  0  2  4  6  8  P2  W  N  E  S  0  10  1  100  101  102  r [arcsec]  2  4  6  8  vrot [km/s]  r [km/s]  NGC 6752  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  F275W  F814W  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='30  CF275W  2 F336W + F438W  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Continuation of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1 for NGC 6752.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  Article number, page 22 of 27  Sven Martens et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' : Kinematic differences between multiple populations in Galactic globular clusters  10  1  100  101  102  0  1  2  3  4  OVERALL  W  N  E  S  0  10  1  100  101  102  r/arcsec  5  10  15  0  1  2  3  P1  W  N  E  S  0  r/arcsec  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  10  1  100  101  102  r [arcsec]  0  2  4  P2  W  N  E  S  0  10  1  100  101  102  r [arcsec]  5  10  vrot [km/s]  r [km/s]  NGC 7078  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  F275W  F814W  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='25  CF275W  2 F336W + F438W  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Continuation of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1 for NGC 7078.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  10  1  100  101  102  0  2  4  OVERALL  W  N  E  S  0  10  1  100  101  102  r/arcsec  5  10  15  0  2  4  6  P1  W  N  E  S  0  r/arcsec  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  0  2  4  6  P2  W  N  E  S  0  r/arcsec  5  10  10  1  100  101  102  r [arcsec]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  P3  W  N  E  S  0  10  1  100  101  102  r [arcsec]  5  10  15  vrot [km/s]  r [km/s]  NGC 7089  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  F275W  F814W  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  CF275W  2 F336W + F438W  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Continuation of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1 for NGC 7089.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  Article number, page 23 of 27  A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' paper  10  1  100  101  102  0  1  2  OVERALL  W  N  E  S  0  10  1  100  101  102  r/arcsec  2  4  6  8  0  1  2  3  P1  W  N  E  S  0  r/arcsec  2  4  6  10  1  100  101  102  r [arcsec]  0  1  2  3  P2  W  N  E  S  0  10  1  100  101  102  r [arcsec]  2  4  6  vrot [km/s]  r [km/s]  NGC 7099  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='175 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='150 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='125 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='100 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='075 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='050 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0250.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='000  F275W  F814W  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='15  CF275W  2 F336W + F438W  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Continuation of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1 for NGC 7099.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='25  (v/ )HL  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='25  R, HL  OVERALL  Linear Fit: m=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='798  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='25  (v/ )HL  P1  Linear Fit: m=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='796  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='25  (v/ )HL  P2  Linear Fit: m=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='789  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='25  (v/ )HL  P3  Linear Fit: m=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='796  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Derived values of λR,HL plotted against (v/σ)HL for the overall cluster and each population with a linear fit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  40  20  0  20  40  x [arcsec]  40  20  0  20  40  y [arcsec]  0  2  4  6  Position Angle [rad]  4  2  0  2  4  V [km/s]  NGC7078  P1 (335)  P2 (604)  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Differential rotation profile for P1 and P2 of NGC 7078, where the difference in mean radial velocity between the two subsets of stars  is plotted against the position angle of their line of separation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  Article number, page 24 of 27  Sven Martens et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' : Kinematic differences between multiple populations in Galactic globular clusters  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='40  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='40  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='40  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='40  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='y [arcsec]  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='V [km/s]  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='P1 (33)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='P2 (49)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='40  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='40  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='40  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='40  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='y [arcsec]  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='V [km/s]  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='P1 (33)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='P2 (49)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='40  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='40  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='x [arcsec]  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='40  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='40  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='y [arcsec]  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='Position Angle [rad]  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='V [km/s]  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='NGC7078  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='P1 (33)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='P2 (49)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Differential rotation profile for randomly sampled stars of P1 and P2 for NGC 7078, where the difference in mean radial velocity  between the two subsets of stars is plotted against the position angle of their line of separation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  Article number, page 25 of 27  A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' paper  Table A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' Median and upper limits of the parameter distributions for the parametric model of each cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  Cluster  Population  σmax [km/s]  vmax [km/s]  θ0 [rad]  rpeak ["]  a ["]  (v/σ)HL  λR,HL  log10(Trh/yr)  NGC 104  Overall  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='37+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='09  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='09  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='75+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='14  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='14  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='34+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='03  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='03  165+10  −10  142+6  −5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='154+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='004  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='005  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='117+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='004  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='004  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='55  P1  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='9+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='7  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='7  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='6  165+10  −10  141+5  −6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='13+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='06  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='10+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='04  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='04  –  P2  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='33+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='26  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='25  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='9  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='9  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='45+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='18  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='19  166+10  −10  141+6  −6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='180+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='029  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='028  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='136+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='021  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='020  –  NGC 362  Overall  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='67+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='24  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='23  < 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  –  140+110  −80  47+6  −6  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='03  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='028  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='93  P1  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  < 5  –  190+90  −100  46+6  −6  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='09  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='07  –  P2  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  < 4  –  190+100  −100  45+6  −6  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='07  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='06  –  P3  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2  < 15  –  160+90  −80  47+6  −6  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  –  NGC 1851  Overall  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='34+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='29  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='25  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='42+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='17  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='16  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='45+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='09  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='09  26+8  −6  27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3+2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='062+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='014  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='013  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='050+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='012  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='011  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='82  P1  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='6  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='6  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='6+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  28+7  −8  27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='8+2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='10+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='08+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='04  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='04  –  P2  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='7+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='8  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='8+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  29+8  −9  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3+2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='11+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='04  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='03  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='086+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='03  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='027  –  P3  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='9  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='8+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  27+8  −8  26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4+2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='09+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='04  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='07+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='04  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='03  –  NGC 1904  Overall  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='02+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='28  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='50+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='21  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='26+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='14  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='13  65+18  −16  30+5  −4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='079+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='018  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='016  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='064+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='016  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='014  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='95  NGC 2808  Overall  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='44+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='23  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='23  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='02+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='23  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='22  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='72+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  69+9  −8  50+4  −4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='123+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='009  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='009  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='100+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='008  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='007  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='15  P1  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='6  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='9+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='88+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='18  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='18  68+9  −9  50+4  −4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='19+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='03  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='03  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='151+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='027  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='026  –  P2  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='8+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='9+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='7  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='78+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='15  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='15  69+9  −9  49+4  −4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='118+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='020  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='019  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='095+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='016  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='015  –  NGC 3201  Overall  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='68+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='07  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='07  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='8+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  950+190  −210  970+90  −100  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='042+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='015  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='014  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='033+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='012  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='011  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='27  P1  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='7+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='6  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  < 10  –  960+200  −220  960+110  −100  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='24  –  P2  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  < 9  –  950+210  −200  970+110  −100  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='23  –  NGC 5286  Overall  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='01+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='23  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='22  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='21+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='10  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='10  110+40  −30  42+8  −6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='133+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='015  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='015  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='107+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='013  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='013  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='11  P1  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='6  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='9+2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='8  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  110+30  −40  43+8  −7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='14+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='06  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='06  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='11+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  –  P2  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='7+2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='8  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='7  120+40  −40  40+8  −8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='08+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='06+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='04  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='04  –  P3  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='8  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='7  7+4  −3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  110+40  −30  40+8  −8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='19+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='08  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='09  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='15+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='06  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='07  –  NGC 5904  Overall  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='80+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='08  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='10  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='11+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='19  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='17  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='82+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='06  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='06  126+16  −14  176+30  −21  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='169+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='008  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='008  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='135+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='007  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='007  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='41  P1  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  127+16  −16  180+30  −30  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='18+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='08  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='08  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='15+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='06  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='07  –  P2  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='23  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='21  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='8  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='45+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='22  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='22  127+16  −16  170+30  −30  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='21+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='04  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='17+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='03  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='03  –  NGC 6093  Overall  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='6+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='6  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='47+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='09  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='09  78+30  −21  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='8+2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='059+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='010  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='008  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='046+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='008  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='006  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='8  P1  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='7  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='8+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='7  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='7  90+30  −30  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='8+2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='039+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='023  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='022  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='031+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='018  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='017  –  P2  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='9+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='6  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='6  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='8  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='7  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='55+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='22  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='22  35+50  −18  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='8+2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='11+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='07  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='09+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='06  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='04  –  NGC 6218  Overall  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='27+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='14  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='13  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='45+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='25  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='6  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='6  350+230  −220  58+7  −6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='022+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='015  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='013  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='019+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='013  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='011  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='87  P1  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='9+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  < 9  –  440+210  −200  59+7  −6  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='29  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='23  –  P2  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  < 6  –  460+200  −190  58+6  −6  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='25  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='20  –  NGC 6254  Overall  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='34+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='09  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='08  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='8+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='37+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='28  410+200  −170  113+13  −11  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='028+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='009  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='009  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='022+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='007  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='007  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='9  P1  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  < 8  –  470+180  −170  114+13  −13  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='20  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='16  –  P2  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='83+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='30  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='26  < 7  –  470+180  −170  114+12  −12  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='20  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='15  –  NGC 6266  Overall  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='34+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='30  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='27  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='8+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='6  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='60+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='11  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='12  200+90  −90  39+3  −3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='048+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='006  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='005  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='037+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='005  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='004  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='98  NGC 6293  Overall  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='8+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5+3  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='43+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='29  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='29  170+120  −150  18+9  −5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='11+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='04  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='03  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='087+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='03  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='026  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='94  NGC 6388  Overall  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='8+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='06+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='29  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='26  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='84+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='26  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='24  44+50  −22  33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='7+2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='6  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='020+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='014  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='008  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='016+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='012  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='007  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='9  P1  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='6  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='6  < 20  –  40+60  −40  34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='6+2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='6  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='17  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='12  –  P2  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='6+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='6+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='9  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='6  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  37+50  −29  33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5+2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='6  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='029+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='017  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='023+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='014  –  P3  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='9+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='9  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='7  < 11  –  60+50  −50  33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4+2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='6  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='6  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='15  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='12  –  Article number, page 26 of 27  Sven Martens et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' : Kinematic differences between multiple populations in Galactic globular clusters  Table A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' continued.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  Cluster  Population  σmax [km/s]  vmax [km/s]  θ0 [rad]  rpeak ["]  a ["]  (v/σ)HL  λR,HL  log10(Trh/yr)  NGC 6397  Overall  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='30+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='12  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='12  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='7  –  600+300  −400  83+7  −7  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='024  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='019  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='6  P1  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  < 12  –  700+400  −300  84+7  −7  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='27  –  P2  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='6+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='6  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  < 11  –  700+300  −300  83+7  −7  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='23  –  NGC 6441  Overall  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='9+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='8  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='6  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  150+50  −70  31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4+3  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='010+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='006  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='006  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='008+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='005  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='004  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='09  P1  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='8  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='7  < 9  –  180+60  −70  32+3  −3  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='04  –  P2  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='6  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='6  < 5  –  170+70  −70  32+3  −3  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='029  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='022  –  NGC 6522  Overall  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='7+2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  < 7  –  260+90  −130  11+4  −4  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='029  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='021  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='86  NGC 6541  Overall  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='8+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='6  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='19+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='07  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='07  126+30  −27  28+3  −3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='096+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='008  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='008  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='073+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='007  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='006  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='03  P1  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='8+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='9+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  135+30  −29  29+3  −3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='09+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='03  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='03  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='067+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='026  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='026  –  P2  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='07+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='27  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='28  130+30  −30  29+3  −3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='12+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='03  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='03  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='089+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='026  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='026  –  NGC 6624  Overall  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='48+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='24  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='24  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='9  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  210+70  −100  26+4  −3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='021+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='010  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='011  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='015+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='008  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='008  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='71  P1  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='6  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='6  < 9  –  230+90  −80  25+4  −4  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='12  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='09  –  P2  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='7+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  < 7  –  240+90  −90  24+4  −4  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='10  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='07  –  NGC 6656  Overall  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='44+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='10  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='10  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='25+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='10  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='10  230+50  −40  150+14  −13  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='162+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='017  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='017  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='134+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='014  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='014  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='23  P1  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='6+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='6  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  < 8  –  240+40  −40  150+15  −14  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  –  P2  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  < 7  –  240+50  −40  150+14  −15  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='28  –  P3  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='6+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='6  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  < 7  –  240+40  −50  151+14  −15  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  –  NGC 6681  Overall  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='9+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  < 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2  –  170+70  −100  18+4  −3  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='04  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='028  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='65  P1  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  < 12  –  200+90  −90  16+4  −4  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='20  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='14  –  P2  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='9+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='6  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  < 7  –  210+90  −90  18+4  −4  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='10  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='07  –  NGC 6752  Overall  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='39+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='11  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='11  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='61+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='19  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='19  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='89+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='30  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  450+170  −150  92+6  −5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='009+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='004  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='003  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0067+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0030  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0022  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='87  P1  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='9+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='6  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  < 12  –  480+160  −170  91+6  −6  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='18  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='13  –  P2  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='8+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  < 9  –  490+160  −150  92+5  −6  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='12  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='09  –  NGC 7078  Overall  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='24+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='30  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='21+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='27  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='26  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='26+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='06  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='06  77+11  −10  26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='6+2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='103+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='008  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='008  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='080+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='007  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='006  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='32  P1  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='6+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  < 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2  –  78+11  −11  26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4+2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='07  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='06  –  P2  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='8+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='9  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='8  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='41+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='19  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='19  78+11  −11  26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2+2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='125+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='024  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='024  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='097+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='018  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='018  –  NGC 7089  Overall  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='91+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='24  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='22  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='90+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='27  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='20+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  66+13  −12  47+5  −4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='173+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='012  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='011  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='140+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='011  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='010  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  P1  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='0+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='6  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='11+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='22  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='21  66+13  −12  46+5  −5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='22+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='18+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='04  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='04  –  P2  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='6  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='6  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='26+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='13  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='14  58+13  −12  45+5  −4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='186+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='026  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='026  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='152+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='022  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='021  –  P3  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5+2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='1  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='7  < 11  –  66+12  −13  47+5  −5  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  –  NGC 7099  Overall  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='86+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='16  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='53+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='17  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='18  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='8+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  70+80  −30  53+8  −7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='028+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='015  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='014  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='021+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='012  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='011  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='88  P1  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='5  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  < 4  –  120+80  −80  53+8  −8  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='16  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='12  –  P2  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='9+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='4  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='3  < 4  –  130+80  −80  50+8  −8  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='11  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='08  –  Notes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' The two measures of the rotation strength (v/σ)HL and λR,HL are derived from the parameter distribution of the parametric model, as  described in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content=' The median relaxation times Trh for each cluster are from Harris (1996, 2010 edition).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
+page_content='  Article number, page 27 of 27' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JtFAT4oBgHgl3EQfvR6i/content/2301.08675v1.pdf'}
diff --git a/K9E3T4oBgHgl3EQfvgvP/content/tmp_files/2301.04695v1.pdf.txt b/K9E3T4oBgHgl3EQfvgvP/content/tmp_files/2301.04695v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..17c59e7b5ece08ac5270bb76a385c8c54c0ded13
--- /dev/null
+++ b/K9E3T4oBgHgl3EQfvgvP/content/tmp_files/2301.04695v1.pdf.txt
@@ -0,0 +1,975 @@
+Learning Continuous Mesh Representation with
+Spherical Implicit Surface
+Zhongpai Gao1,2
+1 MoE Key Lab of Artificial Intelligence, AI Institute, Shanghai Jiao Tong University, Shanghai, China
+2 United Imaging Intelligence, Cambridge MA, USA
+Abstract— As the most common representation for 3D shapes,
+mesh is often stored discretely with arrays of vertices and
+faces. However, 3D shapes in the real world are presented
+continuously. In this paper, we propose to learn a continuous
+representation for meshes with fixed topology, a common
+and practical setting in many faces-, hand-, and body-related
+applications. First, we split the template into multiple closed
+manifold genus-0 meshes so that each genus-0 mesh can be
+parameterized onto the unit sphere. Then we learn spherical
+implicit surface (SIS), which takes a spherical coordinate and
+a global feature or a set of local features around the coordinate
+as inputs, predicting the vertex corresponding to the coordinate
+as an output. Since the spherical coordinates are continuous,
+SIS can depict a mesh in an arbitrary resolution. SIS rep-
+resentation builds a bridge between discrete and continuous
+representation in 3D shapes. Specifically, we train SIS networks
+in a self-supervised manner for two tasks: a reconstruction
+task and a super-resolution task. Experiments show that our
+SIS representation is comparable with state-of-the-art methods
+that are specifically designed for meshes with a fixed resolution
+and significantly outperforms methods that work in arbitrary
+resolutions.
+I. INTRODUCTION
+3D shapes in the real world are continuous. While, in
+the digital world, we usually capture, store, and process
+3D shapes in a discrete way. A common representation
+of 3D shapes is triangulated mesh that structures a 3D
+shape as arrays of vertices and faces. The precision of mesh
+representation for 3D shapes is controlled by resolution (i.e.,
+number of vertices). The vertex-based mesh representation
+has been widely applied in many computer vision and
+computer graphics applications, e.g., 3D reconstruction [12],
+[29], [11], shape correspondence [15], virtual avatar [5],
+gesture synthesis [23], etc. However, the vertex-based mesh
+representation is difficult for applications that require various
+mesh resolutions. In this paper, we propose a continuous
+representation for meshes. By modeling a mesh as a function
+defined in a continuous domain, we can process the mesh in
+an arbitrary resolution as needed.
+Closed manifold genus-0 meshes are topologically equiv-
+alent to a sphere, hence this is the natural and continuous
+parameter domain for them, called spherical parameterization
+[14]. Specifically, spherical conformal parameterization [3],
+[7] that preserves the angle and hence the local geometry
+of the surface is the most important type of parameteri-
+zation since the angle structure plays an important role in
+Copyright notice: 979-8-3503-4544-5/23/$31.00 ©2023 IEEE. This work
+was supported by the National Natural Science Foundation of China
+(61901259) and China Postdoctoral Science Foundation (BX2019208).
+the computation of texture mapping, remeshing, and many
+other applications. Thus, spherical conformal parameteriza-
+tion provides a one-to-one correspondence between meshes
+and a sphere such that the spherical coordinate can be consid-
+ered as the canonical coordinate in a continuous domain for
+3D shapes. Inspired by the continuous image representation
+[6] that models an image as an implicit function of the
+continuous 2D coordinates, we model a mesh as an implicit
+function of the continuous spherical coordinates. The implicit
+function can be parameterized by a deep neural network, e.g.,
+multilayer perceptions (MLP) to map each coordinate to the
+corresponding surface position of the 3D shape. Note that,
+for a mesh that is not closed manifold genus-0, we always
+can split the mesh into multiple closed manifold genus-0
+meshes with the help of filling holes if necessary.
+This paper proposes spherical implicit surface (SIS) for
+representing mesh in a continuous manner. SIS can represent
+a mesh with an arbitrary topology. While, in this paper, we
+mainly focus on the SIS representation for a group of meshes
+with the same topology, e.g., faces, bodies, and hands. To
+share knowledge across samples instead of fitting individual
+implicit function for each mesh, we use an encoder to predict
+a global feature for each mesh. Then the implicit function
+is shared by all the meshes while it is conditioned upon
+the global feature in addition to the spherical coordinates as
+inputs. At last, the implicit function predicts the 3D position
+at the given spherical coordinate as the output. Furthermore,
+instead of using one global feature to encode the whole
+mesh, we represent a mesh by a set of local features
+distributed in spatial dimensions (i.e., 3D shape surface).
+Given a spherical coordinate, the implicit function takes the
+coordinate information and queries the local features around
+the coordinate as inputs, then predicts the 3D position at the
+given coordinate as the output. Either given the global feature
+or a set of local features of a mesh, the SIS representation can
+present the mesh in an arbitrary resolution since the spherical
+coordinates are continuous.
+To learn SIS continuous representation from the global
+feature of a mesh, we train a mesh encoder and an SIS
+decoder via a reconstruction task in a self-supervised manner.
+The mesh encoder is built by a convolutional operation
+named LSA-Conv [10] to extract the global feature of a
+mesh. To learn SIS continuous representation from a set of
+local features of a mesh, we train an SIS encoder, a feature
+fusion module, and an SIS decoder via a super-resolution
+task in a self-supervised manner. The SIS encoder takes
+arXiv:2301.04695v1  [cs.CV]  11 Jan 2023
+
+the vertex information in addition to the spherical coordi-
+nate as inputs and predicts the corresponding deep feature
+as the output. The local feature of a spherical coordinate
+in a higher resolution is assembled by the feature fusion
+module which makes use of barycentric coordinates for
+interpolation. SIS builds a bridge between the discrete and
+continuous representation in mesh and can naturally exploit
+the information provided in different resolutions. The SIS
+representation can present a mesh in an arbitrary resolution,
+thus it can be trained without resizing ground-truths and
+achieves better results than methods designed for a certain
+resolution. We evaluate our approach on the reconstruction
+and super-resolution task in two 3D shape datasets: human
+faces (COMA [27]) and human bodies (DFAUST [4]).
+The contributions of this paper are summarized in below:
+1) Taking advantage of that genus-0 meshes are topolog-
+ically equivalent to a sphere, we use spherical conformal
+parameterization to map meshes to a sphere as the continuous
+canonical coordinate for 3D shapes. Then, we introduce a
+new continuous mesh representation by modeling a mesh
+as an implicit function of the spherical coordinates, called
+spherical implicit surface (SIS).
+2) We show how this continuous representation can be
+used for reconstructing meshes. In addition to the spherical
+coordinates, the SIS representation either takes the global
+feature or a set of local features of a mesh as inputs to present
+the mesh in a continuous manner. For the input of local
+features, we introduce a feature fusion module that makes use
+of barycentric coordinates for interpolation to bridge between
+the discrete and continuous domains.
+3) Extensive experiments on COMA [27] and DFAUST
+[4] datasets show that our approach is able to generate high-
+quality meshes and demonstrate that it compares favorably
+to state-of-the-art methods designed for discrete domains and
+outperforms methods designed for continuous domains.
+II. RELATED WORK
+A. Discrete representations for 3D shapes
+Discrete representations for learning-based 3D tasks can
+be mainly categorized as: voxel-based, point-based, and
+mesh-based. Voxel presentation is a straightforward gener-
+alization of pixels to the 3D cases and has been used for
+discriminative [19], [26] and generative [8], [13] 3D tasks.
+However, voxel representations require memory that grows
+cubically with resolution. Point clouds [1], [9] and meshes
+[17], [11] have been introduced as alternative representations
+for deep learning. However, point clouds lack the connectiv-
+ity structure of the 3D shapes and usually require additional
+post-processing to generate the final 3D shape. Moreover, all
+the discrete representations are limited to the resolution (i.e.,
+number of points/vertices) that a model can produce.
+In contrast to the discrete representations, our approach
+leads to continuous surface of 3D shapes. Using deep learn-
+ing, our approach obtains a more expressive representation
+that can naturally be integrated into existing 3D shape
+generation pipelines [11], [15].
+B. Implicit Representations
+Implicit representations are continuous and differentiable
+functions that map coordinates to signal [28], e.g., images
+and 3D shapes, and are parameterized as multilayer per-
+ceptions (MLP). For images, [6] proposed local implicit
+image function (LIIF) that takes an image coordinate and
+the 2D deep features around the coordinate as inputs to
+predict the RGB value at a given coordinate so that the
+learned representation can present an image in an arbitrary
+resolution.
+For 3D shapes, recent work has investigated implicit repre-
+sentations of continuous 3D shapes that map xyz coordinates
+to a signed distance function (SDF) [24] or to an occupancy
+field [20], [25] or to a neural radiance field (NeRF) [21]. SDF
+represents a 3D shape’s surface by a continuous volumetric
+field — the distance of a point to the surface boundary and
+the sign indicates whether the region is inside or outside of
+the shape, thus it implicitly encodes a shape’s boundary as
+the zero-level-set of the learned function. Occupancy field
+is a special case of SDF and only considers the ‘sign’
+of SDF values to classify 3D points as inside or outside
+of a 3D shape. NeRF represents a scene by the volume
+density and view-dependent emitted radiance of a point and
+can produce high-fidelity appearance to render photorealistic
+novel views of complex 3D scenes. Another continuous
+representation for 3D shapes was introduced by [15], called
+template deformation (TDeform) that uses an MLP to regress
+the point-wise deformation of 3D shapes from the template
+in any resolution.
+However, for the implicit representations of SDF [24],
+occupancy field [20], and NeRF [21], the coordinates are
+defined as xyz positions in a volumetric space, which
+requires large amounts of samples from the volumetric space
+for training and needs an isosurface extraction algorithm
+for inference to extract the surface from a trained model.
+Compared to those implicit representations of 3D shapes, our
+SIS representation directly works on the surface and is more
+efficient for both training and inference. Similar to the one-
+to-one mapping from image coordinates to images, our SIS
+representation has a one-to-one mapping from the spherical
+coordinates to the surface of 3D shapes such that we only
+need to train on the samples of 3D shape vertices and infer
+a 3D shape simply by inputting the spherical coordinates.
+Even though TDeform [15] that defines the coordinates
+as the template vertices creates a one-to-one mapping from
+the template to the surface of a 3D shape, the coordinates
+are xyz positions in a volumetric space and most of the
+coordinates (except for the template vertices) do not have
+the corresponding labels, making the network difficult to be
+trained (not bijective). In contrast, our spherical coordinates
+are continuous and corresponding to the surface of 3D shapes
+everywhere (bijective). Thus, our approach is an efficient and
+effective continuous representation for 3D shapes.
+III. SPHERICAL IMPLICIT SURFACE
+In this section, we introduce spherical implicit surface
+(SIS) — our continuous representation for meshes. First, we
+
+(a) Mesh
+(b) Closed manifold   
+genus-0 meshes
+(c) Spherical conformal 
+parameterization 
+(d) Spherical coordinates 
+1
+g
+M
+2
+g
+M
+3
+g
+M
+1f
+2f
+3f
+M
+inclination 
+azimuth ˆ
+ˆ
+Fig. 1: Spherical coordinates for a mesh. The facial mesh M in (a) has multiple components and are not a closed manifold genus-0 mesh.
+It can be split into multiple genus-0 meshes: the left eye Mg2, the right eye Mg3, and the rest part Mg1 in (b). Each genus-0 mesh Mgi
+can be mapped to the unit sphere S2 by applying spherical conformal parameterization fi : S2 → Mgi from the unit sphere S2 to the
+genus-0 mesh Mgi. The unit sphere S2 can be parameterized by the normalized inclination angle ˆθ and azimuth angle ˆϕ such that we
+create a one-to-one correspondence fi : (ˆθ, ˆϕ) → Vi from the spherical coordinates to the vertices of the genus-0 mesh. The colors in
+(c) and (d) represent the corresponding vertex position on the mesh.
+apply spherical conformal parameterization to have a one-
+to-one mapping from a mesh to the unit sphere so that the
+spherical coordinate can be used as the continuous canonical
+coordinate for the mesh. Then, we describe how we can learn
+an SIS network that takes a global feature or a set of local
+features in addition to the spherical coordinates for 3D shape
+generations. At last, we introduce the loss function used to
+train our models.
+A. Spherical Coordinate
+Inspired by images where RGB values and image coor-
+dinates (i.e., xy coordinates) are one-to-one corresponding
+to each other, we seek for a one-to-one mapping between a
+canonical coordinate and meshes — a bijectve function.
+Theorem 1: The ‘uniformization theorem’ guarantees that
+there is a conformal map f : S2 → M from the unit sphere
+S2 to any genus-0 mesh M, i.e., a smooth, nondegenerate,
+and globally injective map that preserves both angles and
+orientation.
+A mesh can be defined as M = (V, F), where V =
+{v1, . . . , vN} is a set of N vertices and F ⊆ V × V × V is
+a set of triangular faces. The conformal map f : S2 → M
+can be achieved by applying spherical conformal parame-
+terization [3], [7] on a genus-0 mesh. As shown in Figure
+1, when a mesh is not a genus-0, we can always split the
+mesh M into multiple submeshes {M1, · · · , MK}, where
+M
+= {M1, . . . , MK}. We may close the holes of the
+submeshes Mi as necessary [2] so that each submesh is a
+closed manifold genus-0 mesh Mgi, where i ∈ {1, . . . , K}.
+The original submesh Mi is a subset of the genus-0 mesh
+Mgi, i.e., Mi = Mgi[Ii] where Ii is the vertex index of
+Mi in Mgi. Thus, any mesh can be formulated with one
+or multiple genus-0 meshes M = {Mg1[I1], . . . , MgK[IK]}
+where K ∈ N. Then each genus-0 submesh Mgi can find a
+conformal map fi : S2 → Mgi from the unit sphere S2
+to the genus-0 submesh Mgi. For simplicity and without
+losing generality, we assume the mesh M is already a closed
+manifold genus-0 mesh where K = 1 and I = [1, . . . , N].
+The surface of the unit sphere S2 can be parameterized
+by two numbers: its polar (inclination) angle θ measured
+from a fixed zenith direction and the azimuthal angle ϕ of
+its orthogonal projection on a reference plane that passes
+through the origin and is orthogonal to the zenith, expressed
+as
+θ = arctan
+�
+x2 + y2
+z
+∈ [0, π],
+ϕ = arctan y
+x ∈ [−π, π], (1)
+ˆθ = θ
+π ∈ [0, 1],
+ˆϕ = ϕ
+2π + 0.5 ∈ [0, 1],
+(2)
+where ˆθ and ˆϕ are the normalized inclination and azimuthal
+angle of a point on the unit sphere. Thus, we create a one-
+to-one correspondence f : (ˆθ, ˆϕ) → V from the spherical
+coordinates to the mesh vertices, i.e., vj = f(ˆθj, ˆϕj), where
+j ∈ {1, . . . , N}. As shown in Fig. 2a, the implicit function
+f that is parameterized as an MLP network can be trained
+in a supervised manner. The trained implicit function f is
+a continuous representation for the mesh, called spherical
+implicit surface (SIS) representation. During the inference
+phase, we can take (ˆθ, ˆϕ) continuously to generate the 3D
+shape in a higher resolution.
+Though an MLP networks are universal function ap-
+proximations [16], directly inputting the coordinates (ˆθ, ˆϕ)
+performs poorly at representing high-frequency variation in
+geometry and Fourier feature mapping enables an MLP
+network to learn high-frequency functions [28]. Inspired by
+
+Mesh encoder
+SIS decoder 
+LSA-Conv
+gz
+ˆ ˆ
+( , )
+� �
+v
+SIS encoder
+SIS decoder 
+ˆ ˆ
+( , )
+� �
+v
+1v
+1
+1
+ˆ ˆ
+( ,
+)
+� �
+Feature fusion 
+module
+1
+lz
+2
+lz
+3
+lz
+1
+lz
+2
+lz
+ˆlz
+1
+1
+2
+2
+3
+3
+ˆl
+l
+l
+l
+z
+z
+z
+z
+�
+�
+�
+�
+�
+�
+3
+lz
+1v
+2v
+3v
+Barycentric 
+coordinates
+(b)
+x
+Triangular face 
+lz
+Step 1
+Step 2
+(c)
+Step 3
+Random 
+subsample
+SIS representation 
+train
+inference
+Input mesh Spherical coordinates
+Continuous spherical 
+coordinates
+Reconstructed 
+mesh 
+(a)
+ˆ ˆ
+( , )
+� �
+v
+Fig. 2: Learning to generate spherical implicit surface (SIS) representation for meshes. (a) The SIS representation inputs the spherical
+coordinates and outputs the mesh vertices and is fitted to an individual mesh. (b) The SIS representation is conditioned with a global
+feature that is extracted from a mesh using a mesh encoder. (c) The SIS representation is conditioned with a local feature for each spherical
+coordinate. We input the SIS encoder a subsempled mesh whose topology is created with the help of spherical mapping and output the
+deep feature for each input vertex. A feature fusion module is introduced to ensemble the local feature for higher-resolution spherical
+coordinates based on barycentric coordinates.
+NeRF [21], we encode the spherical coordinates as
+ξ(p) = (sin(20πp), cos(20πp), . . . , sin(2L−1πp), cos(2L−1πp)), (3)
+where p = (ˆθ, ˆϕ) and L = 10 in our experiments. Though
+Fourier feature mapping ξ(·) has been used in NeRF, ap-
+plying it on our spherical coordinates is physically more
+meaningful than on the xyz coordinates used in NeRF since
+the spherical coordinates (ˆθ, ˆϕ) are defined in angles as
+presented in Eq. (1) and Fig. 1d are periodic, which is
+naturally suitable for Fourier feature mapping.
+B. Condition with Global Feature
+Instead of fitting the implicit function f to an individual
+mesh M, we propose an SIS representation that is shared by
+a group of meshes, which can be achieved by conditioning
+an observation of that mesh on the input in addition to the
+spherical coordinates. We train the model in a self-supervised
+manner via a reconstruction task. The observation of a mesh
+can be considered as a global feature zg extracted by a mesh
+encoder, as shown in Fig. 2b. During the inference phase,
+we can use the implicit function to reconstruct a mesh in an
+arbitrary resolution given its global feature. Thus, the implicit
+function (i.e., SIS decoder) can be expressed as
+v = f(zg, ˆθ, ˆϕ),
+(4)
+where zg = eng(M) and eng(·) is the mesh encoder built
+by convolutional operations and LSA-Conv [10] is used in
+our experiments.
+C. Condition with Local Feature
+To make the SIS representation more expressive, instead
+of using one global feature to encode the whole mesh, we
+
+encode a mesh by a set of local features distributed in spatial
+dimensions such that each of them stores information about
+its local area. We train the model in a self-supervised manner
+via a super-resolution task. Thus, the input is noisy sparse
+point cloud that is randomly sampled from the mesh (step 1
+in Fig. 2c). Based on the spherical mapping, we can find the
+points on the sphere corresponding to the point cloud (step
+2 in Fig. 2c). Then, we can easily and consistently build
+a topology connection for the corresponding points on the
+sphere, which is the same for the point cloud, thus we build
+a subsampled mesh (i.e., a lower resolution mesh) for the
+randomly sampled point cloud (step 3 in Fig. 2c).
+For a subsampled mesh, the SIS encoder maps each vertex
+vi to a deep feature zli. Note that, the spherical coordinates
+of the subsampled mesh can correspond to any point on the
+sphere since the SIS encoder is a continuous representation.
+The SIS decoder is also a continuous representation and
+may take spherical coordinates that are not provided in the
+subsampled mesh, i.e., spherical coordinates in a higher reso-
+lution. Thus, the SIS encoder cannot provide the deep feature
+for those higher-resolution spherical coordinates. We propose
+a feature fusion module based on barycentric coordinates to
+obtain the local feature given any spherical coordinate.
+Given a pair of spherical coordinate (ˆθ, ˆϕ), we first find
+the triangular face that contains the spherical coordinate on
+the sphere that has the same topology of the subsampled
+mesh. We denote the spherical coordinates of the triangular
+vertices on the sphere as [(ˆθ1, ˆϕ1), (ˆθ2, ˆϕ2), (ˆθ3, ˆϕ3)] and
+denote the triangular vertices of the subsampled mesh as
+[v1, v2, v3]. The deep features of the triangular vertices are
+zl1 = enl(v1), zl2 = enl(v2), and zl3 = enl(v3), where
+enl(·) is the SIS encoder. We can calculate the barycentric
+coordinates for the spherical coordinate (ˆθ, ˆϕ) relative to the
+three triangular vertices as [λ1, λ2, λ3] where �3
+i=1 λi = 1.
+Thus, based on the barycentric coordinates, we can obtain a
+coarse deep feature for the spherical coordinate (ˆθ, ˆϕ) as,
+ˆzl = λ1zl1 + λ2zl2 + λ3zl3.
+(5)
+The feature fusion module ensembles the local feature for
+the spherical coordinate (ˆθ, ˆϕ) as
+zl = ˆzl ⊕ (ˆzl − zl1) ⊕ (ˆzl − zl2) ⊕ (ˆzl − zl3) ⊕ λ.
+(6)
+At last, the implicit function (i.e., SIS decoder) can be
+expressed as
+v = f(zl, ˆθ, ˆϕ).
+(7)
+D. Loss Function Design
+Our SIS representation defines the coordinates that are
+one-to-one corresponding to the surface of 3D shapes. Thus,
+we can train the models in a self-supervised manner for each
+vertex of 3D shapes. First, the L1 reconstruction loss of
+vertices is used as
+Lrec =
+���V − ˆV
+���
+1 ,
+(8)
+where V is the ground truth vertices and ˆV is the ver-
+tices predicted by our SIS decoders. Then, Laplacian reg-
+ularization is introduced to help the mesh reconstruction.
+Laplacian term is defined as the difference between the
+vertex and the mean of its one-ring neighbors, expressed as
+Vi −
+1
+|Ni|
+�
+j∈Ni Vj where Vi is the ith vertex and Mi is
+the indices of its one-ring neighbors of Xi. We propose a
+Laplacian loss that calculates the Laplacian term difference
+between the ground truth vertices and the predicted vertices,
+expressed as
+Llap =
+�
+i∈M
+�������
+�
+�
+�Vi −
+1
+|Ni|
+�
+j∈Ni
+Vj
+�
+�
+� −
+�
+�
+� ˆ
+Vi −
+1
+|Ni|
+�
+j∈Ni
+ˆ
+Vj
+�
+�
+�
+�������1
+,
+(9)
+where M is the vertex indices of the mesh. The overall loss
+function is defined as
+L = Lrec + γLlap,
+(10)
+where γ = 0.05 in our experiments. During the inference
+phase, we can output a 3D shape simply by inputting the
+spherical coordinates with a global feature or a local feature
+to the SIS decoders.
+IV. EXPERIMENTS AND EVALUATION
+In this section, we evaluate our SIS representation on
+two different 3D shape datasets in two tasks: reconstruction
+task and super-resolution task. For the reconstruction task,
+we input meshes with fixed topology and condition the SIS
+representation with a global feature. For the super-resolution
+task, we input point clouds that are randomly downsampled
+from meshes and condition the SIS representation with a
+local feature that is assembled by a feature fusion module
+based on baryccentric coordinates.
+a) Datasets: In line with [10], we evaluate our model
+on two datasets: COMA [27] and DFAUST [4]. COMA
+is a human facial dataset that consists of 12 classes of
+extreme expressions from 12 different subjects. The dataset
+contains 20,466 3D meshes that were registered to a common
+reference template with 5,023 vertices. DFAUST is a human
+body dataset that collects over 40,000 real meshes, capturing
+129 dynamic performances from 10 subjects. The meshes
+were also registered to a common reference topology that
+has 6,890 vertices. Both two datasets are split into training
+and test set with a ratio of 9:1 and randomly select 100
+samples from the training set for validation. The test samples
+are obtained by picking consecutive frames of length 10
+uniformly at random across the sequences. All of the 3D
+meshes are standardized to have a mean of 0 and standard
+deviation of 1 to speed up the training.
+b) Training: We use Adam [18] optimizer with learning
+rate 0.001 and reduce the learning rate with decay rate 0.98
+in every epoch. The batch size is 64 and total epoch number
+is 200. Weight decay regularization is used for the network
+parameters. We implemented the models in PyTorch and
+trained on the same machine with an AMD 3700X @3.6GHz
+CPU and an NVIDIA RTX2080Ti GPU.
+c) Architecture: As shown in Fig. 2b, we adopt the
+mesh encoder from [10]. The encoder has four LSA-Conv
+layers with downsampling. The conv layers have channel
+sizes of [3, 16, 32, 64, 128] and meshes are downsampled
+with ratios of [4, 4, 4, 4]. A fully connected layer outputs the
+latent vector of 64 dimension that represents the 3D mesh.
+
+TABLE I: Comparison of reconstruction errors for the models of
+LSA-small [10], FeaStNet [30], and template deformation (TDe-
+form) [15] when latent size d = 64. For a fair comparison, we
+adjust the channel sizes to have around the same parameter size.
+
+represents the decoder can infer 3D shapes in an arbitrary
+resolution.  represents the decoder can only infer 3D shapes in a
+fixed resolution of the template. The ‘time (s)’ denotes the duration
+to infer the test sets.
+L2(mm)↓
+time (s)↓
+parm #
+DFAUST
+LSA-small [10]
+
+3.679
+3.992
+547K
+FeaStNet [30]
+
+3.769
+5.146
+548K
+TDeform [15]
+
+6.897
+4.391
+549K
+SIS (ours)
+
+4.737
+3.273
+547K
+COMA
+LSA-small [10]
+
+0.172
+5.615
+378K
+FeaStNet [30]
+
+0.208
+9.969
+378K
+TDeform [15]
+
+0.946
+5.434
+378K
+SIS (ours)
+
+0.179
+5.357
+378K
+For COMA dataset, as shown in Fig. 1, the template
+facial mesh is split into three genus-0 meshes: left eye, right
+eye, and the rest part. Thus, we need three SIS networks
+to represent the facial meshes. For DFAUST dataset, the
+template body mesh is split into six genus-0 meshes: head,
+torso, left arm, right arm, left leg, and right leg. Thus, we
+need six SIS networks to represent the body meshes. Each
+SIS network is an MLP with a skip connection in the middle
+layer. As shown in Fig. 2, the SIS encoders are conditioned
+with vertices in addition to the spherical coordinates and
+output the corresponding deep features. The SIS decoders are
+conditioned with local features in addition to the spherical
+coordinates and output the vertices of 3D shapes.
+A. Task 1: Reconstruction
+For the reconstruction task as shown in Fig. 2b, we
+compare three existing methods: LSA-Conv, FeaStNet, and
+template deformation (TDeform) when the latent space is 64.
+TDeform proposed by [15] uses the template as the canonical
+coordinate of meshes. Similar to SIS representation, the
+TDeform decoder is also built by an MLP network that
+predicts the deformation of the vertices of a mesh relative
+to the template vertices. During the inference phase, we can
+provide a higher-resolution template to predict 3D shapes
+that have the same resolution as the template. Table I shows
+the quantitative results. For a fair comparison, we adjust
+the channel sizes for each methods to have around the
+same model size. For methods that can infer 3D shapes
+in an arbitrary resolution (labeled as in Table I), our SIS
+representation outperforms TDeform in both DFAUST and
+COMA datasets. For COMA dataset, our representation even
+performs better than FeaStNet that only works in a fixed
+resolution. In terms of time comlexity, the proposed SIS is
+the most time-efficient compared with other methods since
+SIS networks are simply MLPs.
+Note that, we split both the facial template and body
+template into multiple genus-0 submeshes and each submesh
+requires an SIS network. In order to control the overall
+model size to be around the same with other methods, the
+6.514
+3.912
+2.801
+5.323
+3.321
+2.492
+2.2
+3.1
+4.0
+4.9
+5.8
+6.7
+L2 Errors (mm)
+DFAUST
+BCI
+SIS (ours)
+0.485
+0.342
+0.263
+0.369
+0.243
+0.181
+0.15
+0.22
+0.29
+0.36
+0.43
+0.50
+500
+1000
+1500
+L2 Errors (mm)
+Number of input points
+COMA
+Fig. 3: Comparison of reconstruction errors between our SIS
+representation and BCI (barycentric interpolation) for the super-
+resolution task. We train the models with 1,000 input points and
+infer the models with input points of 500, 1,000, and 1,500.
+parameter size for each SIS network is small. As shown in
+Table I, we split more parts for the body template than for
+the facial template, thus, each body part has a smaller SIS
+network and only has 5 or 6 layers with 131 channel size,
+resulting in larger errors in DFAUST dataset than COMA
+dataset compared to other methods. However, even we need
+an extra SIS network for the eyes in COMA dataset, our SIS
+representation is marginally on par (0.179 vs. 0.172) with
+LSA-small that is the current best convolutional operation de-
+signed for meshes. Even though controlling the overall model
+size to be the same with other methods is not favorable for
+our setting, our SIS representation consistently outperforms
+TDeform that uses one but deeper and larger MLP network.
+For TDeform, the input could be any xyz point in the
+volumetric space while only the points of template vertices
+are trained with labels. Thus, most of samples (except for the
+template vertices) are not trained for the implicit function of
+TDeform, i.e., undersampling occurs.
+B. Task 2: Super-resolution
+For the super-resolution task as shown in Fig. 2c, we
+randomly sample 1,000 points from a mesh as the input to
+train our models in a self-supervised manner in DFAUST and
+COMA datasets. We compare our method with a traditional
+algorithm: barycentric interpolation (BCI). BCI interpolates
+the vertex of a given spherical coordinate based on the
+barycentric coordinates that are calculated from the trian-
+gular face on the sphere. For instance, when the triangular
+vertices are [v1, v2, v3] and the barycentric coordinates are
+[λ1, λ2, λ3] where �3
+i=1 λi = 1, the interpolated vertex is
+expressed as v = λ1v1 + λ2v2 + λ3v3.
+We evaluate our approach and BCI with three different
+
+40 mm
+0 mm
+0 mm
+4 mm
+Input 
+point cloud 
+Ground truth
+Mesh
+SIS 
+(ours)
+BCI
+Input 
+point cloud 
+Ground truth
+Mesh
+SIS 
+(ours)
+BCI
+‘
+Fig. 4: Qualitative results of the super-resolution task. The per-vertex Euclidean errors produced by our SIS representation and BCI are
+visualized in colormap. The input point cloud has 1,000 points that are randomly sampled from the ground truth mesh. The left and right
+are some examples wihh varisou facial expressions and body poses from the test sets of COMA and DFAUST datasets.
+numbers of input points: 500, 1,000, and 1,500. As shown in
+Fig. 3, our SIS representation consistently outperforms BCI
+in both DFAUST and COMA datasets for all the different
+numbers of input points, which demonstrates the robustness
+of our SIS representation. The qualitative results presented
+in Fig. 4 also show that our approach produces smaller errors
+than BCI for both DFAUST and COMA datasets in various
+body poses and facial expressions.
+C. Ablation Study
+For the super-resolution task, we design a feature fusion
+module to ensemble the deep features for the local feature
+of a given spherical coordinate. To evaluate the effectiveness
+of the feature fusion module, we conduct an ablation study
+where we simply use the coarse deep feature ˆzl (Eq. 5)
+as the local feature of a given spherical coordinate without
+the feature fusion module, denoted as SIS w/o in Figure
+5. For both the COMA and DFAUST datasets, our SIS
+representation with the feature fusion module outperforms
+SIS w/o consistently with different input points. This is
+berceuse the feature fusion module considers the edges
+between the coarse deep feature with the deep features of the
+triangular vertices and provides more local structure around
+the spherical coordinate. Thus, our SIS representation with
+the feature fusion module can generate 3D shapes with more
+details.
+6.492
+3.911
+2.842
+5.323
+3.321
+2.492
+2.2
+3.1
+4.0
+4.9
+5.8
+6.7
+L2 Errors (mm)
+DFAUST
+SIS_w/o
+SIS (ours)
+0.369
+0.243
+0.181
+0.393
+0.26
+0.197
+0.15
+0.22
+0.29
+0.36
+0.43
+0.50
+500
+1000
+1500
+L2 Errors (mm)
+Number of input points
+COMA
+Fig. 5: Ablation study for of the feature fusion module in the super-
+resolution task. “SIS w/o” means we use the coarse feature in Eq. 6
+as the input of the SIS decoder without the feature fusion module.
+We train the models with 1,000 input points and infer the models
+with input points of 500, 1,000, and 1,500.
+
+F-V. CONCLUSION AND DISCUSSIONS
+A. Conclusion
+We propose to learn the continuous representation for
+meshes, which is fulfilled by our devised spherical implicit
+surface (SIS) technique. SIS builds a bridge between the
+discrete and continuous representation in mesh and can natu-
+rally exploit the information provided in different resolutions.
+To share knowledge across samples, we condition the SIS
+representation with a global feature or a set of local features
+of a mesh. We show that this continuous representation
+technique can be effectively applied for downstream tasks
+like reconstruction and super-resolution of 3D shapes.
+B. Limitations
+The SIS representation for meshes is similar to the implicit
+function for images [28]. When the resolution of a mesh
+is too low, the SIS representation may overfit to the small
+amount of training samples and cannot generalize well to
+the whole surface of the mesh. Thus, high-resolution meshes
+are more favorable to train an SIS network. Furthermore, the
+experimented datasets may not fully reflect the challenges in
+real-world scenarios.
+C. Future works
+In this work, we split a mesh template into multiple genus-
+0 submeshes and train an independent SIS network for each
+submesh. In the future, we can create a shared SIS network
+for all the submeshes to reduce the model size. Furthermore,
+currently, we simply encode the spherical coordinates with
+Fourier feature mapping. More advance coordinate encoding
+methods [22] can be integrated to our SIS representation.
+REFERENCES
+[1] P. Achlioptas, O. Diamanti, I. Mitliagkas, and L. Guibas. Learning
+representations and generative models for 3d point clouds. In ICML,
+pages 40–49. PMLR, 2018.
+[2] M. Attene.
+A lightweight approach to repairing digitized polygon
+meshes. The Visual Computer, 26(11):1393–1406, Nov 2010.
+[3] A. Baden, K. Crane, and M. Kazhdan. M¨obius Registration. Computer
+Graphics Forum, 2018.
+[4] F. Bogo, J. Romero, G. Pons-Moll, and M. J. Black. Dynamic FAUST:
+Registering human bodies in motion. In CVPR, July 2017.
+[5] C. Cao, Q. Hou, and K. Zhou.
+Displaced dynamic expression
+regression for real-time facial tracking and animation. ACM Trans.
+Graph., 33(4):43:1–43:10, July 2014.
+[6] Y. Chen, S. Liu, and X. Wang.
+Learning continuous image rep-
+resentation with local implicit image function.
+arXiv preprint
+arXiv:2012.09161, 2020.
+[7] G. P. T. Choi, Y. Leung-Liu, X. Gu, and L. M. Lui. Parallelizable
+global conformal parameterization of simply-connected surfaces via
+partial welding. SIAM Journal on Imaging Sciences, 13(3):1049–1083,
+2020.
+[8] C. B. Choy, D. Xu, J. Gwak, K. Chen, and S. Savarese. 3d-r2n2: A
+unified approach for single and multi-view 3d object reconstruction.
+In B. Leibe, J. Matas, N. Sebe, and M. Welling, editors, ECCV, pages
+628–644, Cham, 2016. Springer International Publishing.
+[9] H. Fan, H. Su, and L. J. Guibas. A point set generation network for
+3d object reconstruction from a single image. In CVPR, July 2017.
+[10] Z. Gao, J. Yan, G. Zhai, J. Zhang, Y. Yang, and X. Yang. Learning
+local neighboring structure for robust 3d shape representation.
+In
+AAAI, 2021.
+[11] Z. Gao, J. Zhang, Y. Guo, C. Ma, G. Zhai, and X. Yang.
+Semi-
+supervised 3d face representation learning from unconstrained photo
+collections. In CVPR Workshops, 2020.
+[12] K. Genova, F. Cole, A. Maschinot, A. Sarna, D. Vlasic, and W. T.
+Freeman. Unsupervised training for 3D morphable model regression.
+In CVPR, June 2018.
+[13] R. Girdhar, D. F. Fouhey, M. Rodriguez, and A. Gupta.
+Learning
+a predictable and generative vector representation for objects.
+In
+B. Leibe, J. Matas, N. Sebe, and M. Welling, editors, ECCV, pages
+484–499, Cham, 2016. Springer International Publishing.
+[14] C. Gotsman, X. Gu, and A. Sheffer.
+Fundamentals of spherical
+parameterization for 3d meshes. ACM Trans. Graph., 22(3):358–363,
+July 2003.
+[15] T. Groueix, M. Fisher, V. G. Kim, B. C. Russell, and M. Aubry.
+3D-CODED: 3D correspondences by deep deformation.
+In ECCV,
+September 2018.
+[16] K. Hornik, M. Stinchcombe, and H. White. Multilayer feedforward
+networks are universal approximators.
+Neural Networks, 2(5):359–
+366, 1989.
+[17] A. Kanazawa, S. Tulsiani, A. A. Efros, and J. Malik.
+Learning
+category-specific mesh reconstruction from image collections.
+In
+ECCV, September 2018.
+[18] D. P. Kingma and J. Ba. Adam: A method for stochastic optimization.
+arXiv preprint arXiv:1412.6980, 2014.
+[19] D. Maturana and S. Scherer.
+Voxnet: A 3d convolutional neural
+network for real-time object recognition. In IROS, pages 922–928,
+2015.
+[20] L. Mescheder, M. Oechsle, M. Niemeyer, S. Nowozin, and A. Geiger.
+Occupancy networks: Learning 3d reconstruction in function space.
+In CVPR, June 2019.
+[21] B. Mildenhall, P. P. Srinivasan, M. Tancik, J. T. Barron, R. Ramamoor-
+thi, and R. Ng. Nerf: Representing scenes as neural radiance fields for
+view synthesis. In A. Vedaldi, H. Bischof, T. Brox, and J.-M. Frahm,
+editors, ECCV, pages 405–421, Cham, 2020. Springer International
+Publishing.
+[22] T. M¨uller, A. Evans, C. Schied, and A. Keller. Instant neural graphics
+primitives with a multiresolution hash encoding. ACM Trans. Graph.,
+41(4):102:1–102:15, July 2022.
+[23] E. Ng, S. Ginosar, T. Darrell, and H. Joo.
+Body2hands: Learning
+to infer 3d hands from conversational gesture body dynamics.
+In
+Proceedings of the IEEE/CVF Conference on Computer Vision and
+Pattern Recognition, pages 11865–11874, 2021.
+[24] J. J. Park, P. Florence, J. Straub, R. Newcombe, and S. Lovegrove.
+Deepsdf: Learning continuous signed distance functions for shape
+representation. In CVPR, June 2019.
+[25] S. Peng, M. Niemeyer, L. Mescheder, M. Pollefeys, and A. Geiger.
+Convolutional occupancy networks.
+In A. Vedaldi, H. Bischof,
+T. Brox, and J.-M. Frahm, editors, ECCV, pages 523–540, Cham,
+2020. Springer International Publishing.
+[26] C. R. Qi, H. Su, M. Niessner, A. Dai, M. Yan, and L. J. Guibas.
+Volumetric and multi-view CNNs for object classification on 3d data.
+In CVPR, June 2016.
+[27] A. Ranjan, T. Bolkart, S. Sanyal, and M. J. Black. Generating 3D
+faces using convolutional mesh autoencoders. In ECCV, September
+2018.
+[28] M. Tancik, P. P. Srinivasan, B. Mildenhall, S. Fridovich-Keil,
+N. Raghavan, U. Singhal, R. Ramamoorthi, J. T. Barron, and R. Ng.
+Fourier features let networks learn high frequency functions in low
+dimensional domains. NeurIPS, 2020.
+[29] L. Tran and X. Liu. Nonlinear 3D face morphable model. In CVPR,
+June 2018.
+[30] N. Verma, E. Boyer, and J. Verbeek. FeaStNet: Feature-steered graph
+convolutions for 3D shape analysis. In CVPR, June 2018.
+
diff --git a/K9E3T4oBgHgl3EQfvgvP/content/tmp_files/load_file.txt b/K9E3T4oBgHgl3EQfvgvP/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b1c713d034ca1ab7cd9164410a11da83319a01e7
--- /dev/null
+++ b/K9E3T4oBgHgl3EQfvgvP/content/tmp_files/load_file.txt
@@ -0,0 +1,649 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf,len=648
+page_content='Learning Continuous Mesh Representation with  Spherical Implicit Surface  Zhongpai Gao1,2  1 MoE Key Lab of Artificial Intelligence, AI Institute, Shanghai Jiao Tong University, Shanghai, China  2 United Imaging Intelligence, Cambridge MA, USA  Abstract— As the most common representation for 3D shapes,  mesh is often stored discretely with arrays of vertices and  faces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' However, 3D shapes in the real world are presented  continuously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' In this paper, we propose to learn a continuous  representation for meshes with fixed topology, a common  and practical setting in many faces-, hand-, and body-related  applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' First, we split the template into multiple closed  manifold genus-0 meshes so that each genus-0 mesh can be  parameterized onto the unit sphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Then we learn spherical  implicit surface (SIS), which takes a spherical coordinate and  a global feature or a set of local features around the coordinate  as inputs, predicting the vertex corresponding to the coordinate  as an output.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Since the spherical coordinates are continuous,  SIS can depict a mesh in an arbitrary resolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' SIS rep-  resentation builds a bridge between discrete and continuous  representation in 3D shapes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Specifically, we train SIS networks  in a self-supervised manner for two tasks: a reconstruction  task and a super-resolution task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Experiments show that our  SIS representation is comparable with state-of-the-art methods  that are specifically designed for meshes with a fixed resolution  and significantly outperforms methods that work in arbitrary  resolutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' INTRODUCTION  3D shapes in the real world are continuous.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' While, in  the digital world, we usually capture, store, and process  3D shapes in a discrete way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' A common representation  of 3D shapes is triangulated mesh that structures a 3D  shape as arrays of vertices and faces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' The precision of mesh  representation for 3D shapes is controlled by resolution (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=',  number of vertices).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' The vertex-based mesh representation  has been widely applied in many computer vision and  computer graphics applications, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=', 3D reconstruction [12],  [29], [11], shape correspondence [15], virtual avatar [5],  gesture synthesis [23], etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' However, the vertex-based mesh  representation is difficult for applications that require various  mesh resolutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' In this paper, we propose a continuous  representation for meshes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' By modeling a mesh as a function  defined in a continuous domain, we can process the mesh in  an arbitrary resolution as needed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  Closed manifold genus-0 meshes are topologically equiv-  alent to a sphere, hence this is the natural and continuous  parameter domain for them, called spherical parameterization  [14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Specifically, spherical conformal parameterization [3],  [7] that preserves the angle and hence the local geometry  of the surface is the most important type of parameteri-  zation since the angle structure plays an important role in  Copyright notice: 979-8-3503-4544-5/23/$31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='00 ©2023 IEEE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' This work  was supported by the National Natural Science Foundation of China  (61901259) and China Postdoctoral Science Foundation (BX2019208).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  the computation of texture mapping, remeshing, and many  other applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Thus, spherical conformal parameteriza-  tion provides a one-to-one correspondence between meshes  and a sphere such that the spherical coordinate can be consid-  ered as the canonical coordinate in a continuous domain for  3D shapes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Inspired by the continuous image representation  [6] that models an image as an implicit function of the  continuous 2D coordinates, we model a mesh as an implicit  function of the continuous spherical coordinates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' The implicit  function can be parameterized by a deep neural network, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=',  multilayer perceptions (MLP) to map each coordinate to the  corresponding surface position of the 3D shape.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Note that,  for a mesh that is not closed manifold genus-0, we always  can split the mesh into multiple closed manifold genus-0  meshes with the help of filling holes if necessary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  This paper proposes spherical implicit surface (SIS) for  representing mesh in a continuous manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' SIS can represent  a mesh with an arbitrary topology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' While, in this paper, we  mainly focus on the SIS representation for a group of meshes  with the same topology, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=', faces, bodies, and hands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' To  share knowledge across samples instead of fitting individual  implicit function for each mesh, we use an encoder to predict  a global feature for each mesh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Then the implicit function  is shared by all the meshes while it is conditioned upon  the global feature in addition to the spherical coordinates as  inputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' At last, the implicit function predicts the 3D position  at the given spherical coordinate as the output.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Furthermore,  instead of using one global feature to encode the whole  mesh, we represent a mesh by a set of local features  distributed in spatial dimensions (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=', 3D shape surface).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  Given a spherical coordinate, the implicit function takes the  coordinate information and queries the local features around  the coordinate as inputs, then predicts the 3D position at the  given coordinate as the output.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Either given the global feature  or a set of local features of a mesh, the SIS representation can  present the mesh in an arbitrary resolution since the spherical  coordinates are continuous.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  To learn SIS continuous representation from the global  feature of a mesh, we train a mesh encoder and an SIS  decoder via a reconstruction task in a self-supervised manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  The mesh encoder is built by a convolutional operation  named LSA-Conv [10] to extract the global feature of a  mesh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' To learn SIS continuous representation from a set of  local features of a mesh, we train an SIS encoder, a feature  fusion module, and an SIS decoder via a super-resolution  task in a self-supervised manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' The SIS encoder takes  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='04695v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='CV]  11 Jan 2023  the vertex information in addition to the spherical coordi-  nate as inputs and predicts the corresponding deep feature  as the output.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' The local feature of a spherical coordinate  in a higher resolution is assembled by the feature fusion  module which makes use of barycentric coordinates for  interpolation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' SIS builds a bridge between the discrete and  continuous representation in mesh and can naturally exploit  the information provided in different resolutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' The SIS  representation can present a mesh in an arbitrary resolution,  thus it can be trained without resizing ground-truths and  achieves better results than methods designed for a certain  resolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' We evaluate our approach on the reconstruction  and super-resolution task in two 3D shape datasets: human  faces (COMA [27]) and human bodies (DFAUST [4]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  The contributions of this paper are summarized in below:  1) Taking advantage of that genus-0 meshes are topolog-  ically equivalent to a sphere, we use spherical conformal  parameterization to map meshes to a sphere as the continuous  canonical coordinate for 3D shapes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Then, we introduce a  new continuous mesh representation by modeling a mesh  as an implicit function of the spherical coordinates, called  spherical implicit surface (SIS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  2) We show how this continuous representation can be  used for reconstructing meshes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' In addition to the spherical  coordinates, the SIS representation either takes the global  feature or a set of local features of a mesh as inputs to present  the mesh in a continuous manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' For the input of local  features, we introduce a feature fusion module that makes use  of barycentric coordinates for interpolation to bridge between  the discrete and continuous domains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  3) Extensive experiments on COMA [27] and DFAUST  [4] datasets show that our approach is able to generate high-  quality meshes and demonstrate that it compares favorably  to state-of-the-art methods designed for discrete domains and  outperforms methods designed for continuous domains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' RELATED WORK  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Discrete representations for 3D shapes  Discrete representations for learning-based 3D tasks can  be mainly categorized as: voxel-based, point-based, and  mesh-based.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Voxel presentation is a straightforward gener-  alization of pixels to the 3D cases and has been used for  discriminative [19], [26] and generative [8], [13] 3D tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  However, voxel representations require memory that grows  cubically with resolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Point clouds [1], [9] and meshes  [17], [11] have been introduced as alternative representations  for deep learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' However, point clouds lack the connectiv-  ity structure of the 3D shapes and usually require additional  post-processing to generate the final 3D shape.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Moreover, all  the discrete representations are limited to the resolution (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=',  number of points/vertices) that a model can produce.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  In contrast to the discrete representations, our approach  leads to continuous surface of 3D shapes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Using deep learn-  ing, our approach obtains a more expressive representation  that can naturally be integrated into existing 3D shape  generation pipelines [11], [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Implicit Representations  Implicit representations are continuous and differentiable  functions that map coordinates to signal [28], e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=', images  and 3D shapes, and are parameterized as multilayer per-  ceptions (MLP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' For images, [6] proposed local implicit  image function (LIIF) that takes an image coordinate and  the 2D deep features around the coordinate as inputs to  predict the RGB value at a given coordinate so that the  learned representation can present an image in an arbitrary  resolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  For 3D shapes, recent work has investigated implicit repre-  sentations of continuous 3D shapes that map xyz coordinates  to a signed distance function (SDF) [24] or to an occupancy  field [20], [25] or to a neural radiance field (NeRF) [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' SDF  represents a 3D shape’s surface by a continuous volumetric  field — the distance of a point to the surface boundary and  the sign indicates whether the region is inside or outside of  the shape, thus it implicitly encodes a shape’s boundary as  the zero-level-set of the learned function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Occupancy field  is a special case of SDF and only considers the ‘sign’  of SDF values to classify 3D points as inside or outside  of a 3D shape.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' NeRF represents a scene by the volume  density and view-dependent emitted radiance of a point and  can produce high-fidelity appearance to render photorealistic  novel views of complex 3D scenes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Another continuous  representation for 3D shapes was introduced by [15], called  template deformation (TDeform) that uses an MLP to regress  the point-wise deformation of 3D shapes from the template  in any resolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  However, for the implicit representations of SDF [24],  occupancy field [20], and NeRF [21], the coordinates are  defined as xyz positions in a volumetric space, which  requires large amounts of samples from the volumetric space  for training and needs an isosurface extraction algorithm  for inference to extract the surface from a trained model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  Compared to those implicit representations of 3D shapes, our  SIS representation directly works on the surface and is more  efficient for both training and inference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Similar to the one-  to-one mapping from image coordinates to images, our SIS  representation has a one-to-one mapping from the spherical  coordinates to the surface of 3D shapes such that we only  need to train on the samples of 3D shape vertices and infer  a 3D shape simply by inputting the spherical coordinates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  Even though TDeform [15] that defines the coordinates  as the template vertices creates a one-to-one mapping from  the template to the surface of a 3D shape, the coordinates  are xyz positions in a volumetric space and most of the  coordinates (except for the template vertices) do not have  the corresponding labels, making the network difficult to be  trained (not bijective).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' In contrast, our spherical coordinates  are continuous and corresponding to the surface of 3D shapes  everywhere (bijective).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Thus, our approach is an efficient and  effective continuous representation for 3D shapes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' SPHERICAL IMPLICIT SURFACE  In this section, we introduce spherical implicit surface  (SIS) — our continuous representation for meshes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' First, we  (a) Mesh  (b) Closed manifold  genus-0 meshes  (c) Spherical conformal  parameterization  (d) Spherical coordinates  1  g  M  2  g  M  3  g  M  1f  2f  3f  M  inclination  azimuth ˆ\uf06a  ˆ\uf071  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' 1: Spherical coordinates for a mesh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' The facial mesh M in (a) has multiple components and are not a closed manifold genus-0 mesh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  It can be split into multiple genus-0 meshes: the left eye Mg2, the right eye Mg3, and the rest part Mg1 in (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Each genus-0 mesh Mgi  can be mapped to the unit sphere S2 by applying spherical conformal parameterization fi : S2 → Mgi from the unit sphere S2 to the  genus-0 mesh Mgi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' The unit sphere S2 can be parameterized by the normalized inclination angle ˆθ and azimuth angle ˆϕ such that we  create a one-to-one correspondence fi : (ˆθ, ˆϕ) → Vi from the spherical coordinates to the vertices of the genus-0 mesh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' The colors in  (c) and (d) represent the corresponding vertex position on the mesh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  apply spherical conformal parameterization to have a one-  to-one mapping from a mesh to the unit sphere so that the  spherical coordinate can be used as the continuous canonical  coordinate for the mesh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Then, we describe how we can learn  an SIS network that takes a global feature or a set of local  features in addition to the spherical coordinates for 3D shape  generations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' At last, we introduce the loss function used to  train our models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Spherical Coordinate  Inspired by images where RGB values and image coor-  dinates (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=', xy coordinates) are one-to-one corresponding  to each other, we seek for a one-to-one mapping between a  canonical coordinate and meshes — a bijectve function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  Theorem 1: The ‘uniformization theorem’ guarantees that  there is a conformal map f : S2 → M from the unit sphere  S2 to any genus-0 mesh M, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=', a smooth, nondegenerate,  and globally injective map that preserves both angles and  orientation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  A mesh can be defined as M = (V, F), where V =  {v1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' , vN} is a set of N vertices and F ⊆ V × V × V is  a set of triangular faces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' The conformal map f : S2 → M  can be achieved by applying spherical conformal parame-  terization [3], [7] on a genus-0 mesh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' As shown in Figure  1, when a mesh is not a genus-0, we can always split the  mesh M into multiple submeshes {M1, · · · , MK}, where  M  = {M1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' , MK}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' We may close the holes of the  submeshes Mi as necessary [2] so that each submesh is a  closed manifold genus-0 mesh Mgi, where i ∈ {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' , K}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  The original submesh Mi is a subset of the genus-0 mesh  Mgi, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=', Mi = Mgi[Ii] where Ii is the vertex index of  Mi in Mgi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Thus, any mesh can be formulated with one  or multiple genus-0 meshes M = {Mg1[I1], .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' , MgK[IK]}  where K ∈ N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Then each genus-0 submesh Mgi can find a  conformal map fi : S2 → Mgi from the unit sphere S2  to the genus-0 submesh Mgi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' For simplicity and without  losing generality, we assume the mesh M is already a closed  manifold genus-0 mesh where K = 1 and I = [1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' , N].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  The surface of the unit sphere S2 can be parameterized  by two numbers: its polar (inclination) angle θ measured  from a fixed zenith direction and the azimuthal angle ϕ of  its orthogonal projection on a reference plane that passes  through the origin and is orthogonal to the zenith, expressed  as  θ = arctan  �  x2 + y2  z  ∈ [0, π],  ϕ = arctan y  x ∈ [−π, π], (1)  ˆθ = θ  π ∈ [0, 1],  ˆϕ = ϕ  2π + 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='5 ∈ [0, 1],  (2)  where ˆθ and ˆϕ are the normalized inclination and azimuthal  angle of a point on the unit sphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Thus, we create a one-  to-one correspondence f : (ˆθ, ˆϕ) → V from the spherical  coordinates to the mesh vertices, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=', vj = f(ˆθj, ˆϕj), where  j ∈ {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' , N}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' 2a, the implicit function  f that is parameterized as an MLP network can be trained  in a supervised manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' The trained implicit function f is  a continuous representation for the mesh, called spherical  implicit surface (SIS) representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' During the inference  phase, we can take (ˆθ, ˆϕ) continuously to generate the 3D  shape in a higher resolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  Though an MLP networks are universal function ap-  proximations [16], directly inputting the coordinates (ˆθ, ˆϕ)  performs poorly at representing high-frequency variation in  geometry and Fourier feature mapping enables an MLP  network to learn high-frequency functions [28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Inspired by  Mesh encoder  SIS decoder  LSA-Conv  gz  ˆ ˆ  ( ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' )  � �  v  SIS encoder  SIS decoder  ˆ ˆ  ( ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' )  � �  v  1v  1  1  ˆ ˆ  ( ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  )  � �  Feature fusion  module  1  lz  2  lz  3  lz  1  lz  2  lz  ˆlz  1  1  2  2  3  3  ˆl  l  l  l  z  z  z  z  �  �  �  �  �  �  3  lz  1v  2v  3v  Barycentric  coordinates  (b)  x  Triangular face  lz  Step 1  Step 2  (c)  Step 3  Random  subsample  SIS representation  train  inference  Input mesh Spherical coordinates  Continuous spherical  coordinates  Reconstructed  mesh  (a)  ˆ ˆ  ( ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' )  � �  v  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' 2: Learning to generate spherical implicit surface (SIS) representation for meshes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' (a) The SIS representation inputs the spherical  coordinates and outputs the mesh vertices and is fitted to an individual mesh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' (b) The SIS representation is conditioned with a global  feature that is extracted from a mesh using a mesh encoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' (c) The SIS representation is conditioned with a local feature for each spherical  coordinate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' We input the SIS encoder a subsempled mesh whose topology is created with the help of spherical mapping and output the  deep feature for each input vertex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' A feature fusion module is introduced to ensemble the local feature for higher-resolution spherical  coordinates based on barycentric coordinates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  NeRF [21], we encode the spherical coordinates as  ξ(p) = (sin(20πp), cos(20πp), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' , sin(2L−1πp), cos(2L−1πp)), (3)  where p = (ˆθ, ˆϕ) and L = 10 in our experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Though  Fourier feature mapping ξ(·) has been used in NeRF, ap-  plying it on our spherical coordinates is physically more  meaningful than on the xyz coordinates used in NeRF since  the spherical coordinates (ˆθ, ˆϕ) are defined in angles as  presented in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' (1) and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' 1d are periodic, which is  naturally suitable for Fourier feature mapping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Condition with Global Feature  Instead of fitting the implicit function f to an individual  mesh M, we propose an SIS representation that is shared by  a group of meshes, which can be achieved by conditioning  an observation of that mesh on the input in addition to the  spherical coordinates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' We train the model in a self-supervised  manner via a reconstruction task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' The observation of a mesh  can be considered as a global feature zg extracted by a mesh  encoder, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' 2b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' During the inference phase,  we can use the implicit function to reconstruct a mesh in an  arbitrary resolution given its global feature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Thus, the implicit  function (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=', SIS decoder) can be expressed as  v = f(zg, ˆθ, ˆϕ),  (4)  where zg = eng(M) and eng(·) is the mesh encoder built  by convolutional operations and LSA-Conv [10] is used in  our experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Condition with Local Feature  To make the SIS representation more expressive, instead  of using one global feature to encode the whole mesh, we  encode a mesh by a set of local features distributed in spatial  dimensions such that each of them stores information about  its local area.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' We train the model in a self-supervised manner  via a super-resolution task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Thus, the input is noisy sparse  point cloud that is randomly sampled from the mesh (step 1  in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' 2c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Based on the spherical mapping, we can find the  points on the sphere corresponding to the point cloud (step  2 in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' 2c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Then, we can easily and consistently build  a topology connection for the corresponding points on the  sphere, which is the same for the point cloud, thus we build  a subsampled mesh (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=', a lower resolution mesh) for the  randomly sampled point cloud (step 3 in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' 2c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  For a subsampled mesh, the SIS encoder maps each vertex  vi to a deep feature zli.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Note that, the spherical coordinates  of the subsampled mesh can correspond to any point on the  sphere since the SIS encoder is a continuous representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  The SIS decoder is also a continuous representation and  may take spherical coordinates that are not provided in the  subsampled mesh, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=', spherical coordinates in a higher reso-  lution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Thus, the SIS encoder cannot provide the deep feature  for those higher-resolution spherical coordinates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' We propose  a feature fusion module based on barycentric coordinates to  obtain the local feature given any spherical coordinate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  Given a pair of spherical coordinate (ˆθ, ˆϕ), we first find  the triangular face that contains the spherical coordinate on  the sphere that has the same topology of the subsampled  mesh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' We denote the spherical coordinates of the triangular  vertices on the sphere as [(ˆθ1, ˆϕ1), (ˆθ2, ˆϕ2), (ˆθ3, ˆϕ3)] and  denote the triangular vertices of the subsampled mesh as  [v1, v2, v3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' The deep features of the triangular vertices are  zl1 = enl(v1), zl2 = enl(v2), and zl3 = enl(v3), where  enl(·) is the SIS encoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' We can calculate the barycentric  coordinates for the spherical coordinate (ˆθ, ˆϕ) relative to the  three triangular vertices as [λ1, λ2, λ3] where �3  i=1 λi = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  Thus, based on the barycentric coordinates, we can obtain a  coarse deep feature for the spherical coordinate (ˆθ, ˆϕ) as,  ˆzl = λ1zl1 + λ2zl2 + λ3zl3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  (5)  The feature fusion module ensembles the local feature for  the spherical coordinate (ˆθ, ˆϕ) as  zl = ˆzl ⊕ (ˆzl − zl1) ⊕ (ˆzl − zl2) ⊕ (ˆzl − zl3) ⊕ λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  (6)  At last, the implicit function (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=', SIS decoder) can be  expressed as  v = f(zl, ˆθ, ˆϕ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  (7)  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Loss Function Design  Our SIS representation defines the coordinates that are  one-to-one corresponding to the surface of 3D shapes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Thus,  we can train the models in a self-supervised manner for each  vertex of 3D shapes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' First, the L1 reconstruction loss of  vertices is used as  Lrec =  ���V − ˆV  ���  1 ,  (8)  where V is the ground truth vertices and ˆV is the ver-  tices predicted by our SIS decoders.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Then, Laplacian reg-  ularization is introduced to help the mesh reconstruction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  Laplacian term is defined as the difference between the  vertex and the mean of its one-ring neighbors, expressed as  Vi −  1  |Ni|  �  j∈Ni Vj where Vi is the ith vertex and Mi is  the indices of its one-ring neighbors of Xi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' We propose a  Laplacian loss that calculates the Laplacian term difference  between the ground truth vertices and the predicted vertices,  expressed as  Llap =  �  i∈M  �������  �  �  �Vi −  1  |Ni|  �  j∈Ni  Vj  �  �  � −  �  �  � ˆ  Vi −  1  |Ni|  �  j∈Ni  ˆ  Vj  �  �  �  �������1  ,  (9)  where M is the vertex indices of the mesh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' The overall loss  function is defined as  L = Lrec + γLlap,  (10)  where γ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='05 in our experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' During the inference  phase, we can output a 3D shape simply by inputting the  spherical coordinates with a global feature or a local feature  to the SIS decoders.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' EXPERIMENTS AND EVALUATION  In this section, we evaluate our SIS representation on  two different 3D shape datasets in two tasks: reconstruction  task and super-resolution task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' For the reconstruction task,  we input meshes with fixed topology and condition the SIS  representation with a global feature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' For the super-resolution  task, we input point clouds that are randomly downsampled  from meshes and condition the SIS representation with a  local feature that is assembled by a feature fusion module  based on baryccentric coordinates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  a) Datasets: In line with [10], we evaluate our model  on two datasets: COMA [27] and DFAUST [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' COMA  is a human facial dataset that consists of 12 classes of  extreme expressions from 12 different subjects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' The dataset  contains 20,466 3D meshes that were registered to a common  reference template with 5,023 vertices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' DFAUST is a human  body dataset that collects over 40,000 real meshes, capturing  129 dynamic performances from 10 subjects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' The meshes  were also registered to a common reference topology that  has 6,890 vertices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Both two datasets are split into training  and test set with a ratio of 9:1 and randomly select 100  samples from the training set for validation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' The test samples  are obtained by picking consecutive frames of length 10  uniformly at random across the sequences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' All of the 3D  meshes are standardized to have a mean of 0 and standard  deviation of 1 to speed up the training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  b) Training: We use Adam [18] optimizer with learning  rate 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='001 and reduce the learning rate with decay rate 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='98  in every epoch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' The batch size is 64 and total epoch number  is 200.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Weight decay regularization is used for the network  parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' We implemented the models in PyTorch and  trained on the same machine with an AMD 3700X @3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='6GHz  CPU and an NVIDIA RTX2080Ti GPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  c) Architecture: As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' 2b, we adopt the  mesh encoder from [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' The encoder has four LSA-Conv  layers with downsampling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' The conv layers have channel  sizes of [3, 16, 32, 64, 128] and meshes are downsampled  with ratios of [4, 4, 4, 4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' A fully connected layer outputs the  latent vector of 64 dimension that represents the 3D mesh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  TABLE I: Comparison of reconstruction errors for the models of  LSA-small [10], FeaStNet [30], and template deformation (TDe-  form) [15] when latent size d = 64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' For a fair comparison, we  adjust the channel sizes to have around the same parameter size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  \x13  represents the decoder can infer 3D shapes in an arbitrary  resolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' \x17 represents the decoder can only infer 3D shapes in a  fixed resolution of the template.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' The ‘time (s)’ denotes the duration  to infer the test sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  L2(mm)↓  time (s)↓  parm #  DFAUST  LSA-small [10]  \x17  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='679  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='992  547K  FeaStNet [30]  \x17  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='769  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='146  548K  TDeform [15]  \x13  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='897  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='391  549K  SIS (ours)  \x13  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='737  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='273  547K  COMA  LSA-small [10]  \x17  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='172  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='615  378K  FeaStNet [30]  \x17  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='208  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='969  378K  TDeform [15]  \x13  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='946  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='434  378K  SIS (ours)  \x13  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='179  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='357  378K  For COMA dataset, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' 1, the template  facial mesh is split into three genus-0 meshes: left eye, right  eye, and the rest part.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Thus, we need three SIS networks  to represent the facial meshes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' For DFAUST dataset, the  template body mesh is split into six genus-0 meshes: head,  torso, left arm, right arm, left leg, and right leg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Thus, we  need six SIS networks to represent the body meshes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Each  SIS network is an MLP with a skip connection in the middle  layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' 2, the SIS encoders are conditioned  with vertices in addition to the spherical coordinates and  output the corresponding deep features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' The SIS decoders are  conditioned with local features in addition to the spherical  coordinates and output the vertices of 3D shapes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Task 1: Reconstruction  For the reconstruction task as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' 2b, we  compare three existing methods: LSA-Conv, FeaStNet, and  template deformation (TDeform) when the latent space is 64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  TDeform proposed by [15] uses the template as the canonical  coordinate of meshes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Similar to SIS representation, the  TDeform decoder is also built by an MLP network that  predicts the deformation of the vertices of a mesh relative  to the template vertices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' During the inference phase, we can  provide a higher-resolution template to predict 3D shapes  that have the same resolution as the template.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Table I shows  the quantitative results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' For a fair comparison, we adjust  the channel sizes for each methods to have around the  same model size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' For methods that can infer 3D shapes  in an arbitrary resolution (labeled as \x13in Table I), our SIS  representation outperforms TDeform in both DFAUST and  COMA datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' For COMA dataset, our representation even  performs better than FeaStNet that only works in a fixed  resolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' In terms of time comlexity, the proposed SIS is  the most time-efficient compared with other methods since  SIS networks are simply MLPs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  Note that, we split both the facial template and body  template into multiple genus-0 submeshes and each submesh  requires an SIS network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' In order to control the overall  model size to be around the same with other methods, the  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='514  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='912  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='801  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='323  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='321  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='492  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='2  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='1  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='0  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='9  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='8  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='7  L2 Errors (mm)  DFAUST  BCI  SIS (ours)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='485  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='342  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='263  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='369  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='243  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='181  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='22  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='29  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='36  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='43  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='50  500  1000  1500  L2 Errors (mm)  Number of input points  COMA  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' 3: Comparison of reconstruction errors between our SIS  representation and BCI (barycentric interpolation) for the super-  resolution task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' We train the models with 1,000 input points and  infer the models with input points of 500, 1,000, and 1,500.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  parameter size for each SIS network is small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' As shown in  Table I, we split more parts for the body template than for  the facial template, thus, each body part has a smaller SIS  network and only has 5 or 6 layers with 131 channel size,  resulting in larger errors in DFAUST dataset than COMA  dataset compared to other methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' However, even we need  an extra SIS network for the eyes in COMA dataset, our SIS  representation is marginally on par (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='179 vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='172) with  LSA-small that is the current best convolutional operation de-  signed for meshes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Even though controlling the overall model  size to be the same with other methods is not favorable for  our setting, our SIS representation consistently outperforms  TDeform that uses one but deeper and larger MLP network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  For TDeform, the input could be any xyz point in the  volumetric space while only the points of template vertices  are trained with labels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Thus, most of samples (except for the  template vertices) are not trained for the implicit function of  TDeform, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=', undersampling occurs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Task 2: Super-resolution  For the super-resolution task as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' 2c, we  randomly sample 1,000 points from a mesh as the input to  train our models in a self-supervised manner in DFAUST and  COMA datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' We compare our method with a traditional  algorithm: barycentric interpolation (BCI).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' BCI interpolates  the vertex of a given spherical coordinate based on the  barycentric coordinates that are calculated from the trian-  gular face on the sphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' For instance, when the triangular  vertices are [v1, v2, v3] and the barycentric coordinates are  [λ1, λ2, λ3] where �3  i=1 λi = 1, the interpolated vertex is  expressed as v = λ1v1 + λ2v2 + λ3v3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  We evaluate our approach and BCI with three different  40 mm  0 mm  0 mm  4 mm  Input  point cloud  Ground truth  Mesh  SIS  (ours)  BCI  Input  point cloud  Ground truth  Mesh  SIS  (ours)  BCI  ‘  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' 4: Qualitative results of the super-resolution task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' The per-vertex Euclidean errors produced by our SIS representation and BCI are  visualized in colormap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' The input point cloud has 1,000 points that are randomly sampled from the ground truth mesh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' The left and right  are some examples wihh varisou facial expressions and body poses from the test sets of COMA and DFAUST datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  numbers of input points: 500, 1,000, and 1,500.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' As shown in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' 3, our SIS representation consistently outperforms BCI  in both DFAUST and COMA datasets for all the different  numbers of input points, which demonstrates the robustness  of our SIS representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' The qualitative results presented  in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' 4 also show that our approach produces smaller errors  than BCI for both DFAUST and COMA datasets in various  body poses and facial expressions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Ablation Study  For the super-resolution task, we design a feature fusion  module to ensemble the deep features for the local feature  of a given spherical coordinate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' To evaluate the effectiveness  of the feature fusion module, we conduct an ablation study  where we simply use the coarse deep feature ˆzl (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' 5)  as the local feature of a given spherical coordinate without  the feature fusion module, denoted as SIS w/o in Figure  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' For both the COMA and DFAUST datasets, our SIS  representation with the feature fusion module outperforms  SIS w/o consistently with different input points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' This is  berceuse the feature fusion module considers the edges  between the coarse deep feature with the deep features of the  triangular vertices and provides more local structure around  the spherical coordinate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Thus, our SIS representation with  the feature fusion module can generate 3D shapes with more  details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='492  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='911  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='842  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='323  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='321  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='492  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='2  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='1  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='0  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='9  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='8  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='7  L2 Errors (mm)  DFAUST  SIS_w/o  SIS (ours)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='369  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='243  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='181  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='393  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='26  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='197  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='22  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='29  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='36  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='43  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='50  500  1000  1500  L2 Errors (mm)  Number of input points  COMA  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' 5: Ablation study for of the feature fusion module in the super-  resolution task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' “SIS w/o” means we use the coarse feature in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' 6  as the input of the SIS decoder without the feature fusion module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  We train the models with 1,000 input points and infer the models  with input points of 500, 1,000, and 1,500.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  F-V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' CONCLUSION AND DISCUSSIONS  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Conclusion  We propose to learn the continuous representation for  meshes, which is fulfilled by our devised spherical implicit  surface (SIS) technique.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' SIS builds a bridge between the  discrete and continuous representation in mesh and can natu-  rally exploit the information provided in different resolutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  To share knowledge across samples, we condition the SIS  representation with a global feature or a set of local features  of a mesh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' We show that this continuous representation  technique can be effectively applied for downstream tasks  like reconstruction and super-resolution of 3D shapes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Limitations  The SIS representation for meshes is similar to the implicit  function for images [28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' When the resolution of a mesh  is too low, the SIS representation may overfit to the small  amount of training samples and cannot generalize well to  the whole surface of the mesh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Thus, high-resolution meshes  are more favorable to train an SIS network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Furthermore, the  experimented datasets may not fully reflect the challenges in  real-world scenarios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Future works  In this work, we split a mesh template into multiple genus-  0 submeshes and train an independent SIS network for each  submesh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' In the future, we can create a shared SIS network  for all the submeshes to reduce the model size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Furthermore,  currently, we simply encode the spherical coordinates with  Fourier feature mapping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' More advance coordinate encoding  methods [22] can be integrated to our SIS representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  REFERENCES  [1] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Achlioptas, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Diamanti, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Mitliagkas, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Guibas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Learning  representations and generative models for 3d point clouds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' In ICML,  pages 40–49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' PMLR, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  [2] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Attene.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  A lightweight approach to repairing digitized polygon  meshes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' The Visual Computer, 26(11):1393–1406, Nov 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  [3] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Baden, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Crane, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Kazhdan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' M¨obius Registration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Computer  Graphics Forum, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  [4] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Bogo, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Romero, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Pons-Moll, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Black.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Dynamic FAUST:  Registering human bodies in motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' In CVPR, July 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  [5] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Cao, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Hou, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Zhou.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  Displaced dynamic expression  regression for real-time facial tracking and animation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' ACM Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  Graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=', 33(4):43:1–43:10, July 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  [6] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Chen, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Liu, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Wang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  Learning continuous image rep-  resentation with local implicit image function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  arXiv preprint  arXiv:2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='09161, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  [7] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Choi, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Leung-Liu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Gu, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Lui.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Parallelizable  global conformal parameterization of simply-connected surfaces via  partial welding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' SIAM Journal on Imaging Sciences, 13(3):1049–1083,  2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  [8] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Choy, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Xu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Gwak, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Chen, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Savarese.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' 3d-r2n2: A  unified approach for single and multi-view 3d object reconstruction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  In B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Leibe, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Matas, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Sebe, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Welling, editors, ECCV, pages  628–644, Cham, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Springer International Publishing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  [9] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Fan, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Su, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Guibas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' A point set generation network for  3d object reconstruction from a single image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' In CVPR, July 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  [10] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Gao, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Yan, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Zhai, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Zhang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Yang, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Yang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Learning  local neighboring structure for robust 3d shape representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  In  AAAI, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  [11] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Gao, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Zhang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Guo, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Ma, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Zhai, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Yang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  Semi-  supervised 3d face representation learning from unconstrained photo  collections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' In CVPR Workshops, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  [12] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Genova, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Cole, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Maschinot, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Sarna, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Vlasic, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  Freeman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Unsupervised training for 3D morphable model regression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  In CVPR, June 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  [13] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Girdhar, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Fouhey, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Rodriguez, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Gupta.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  Learning  a predictable and generative vector representation for objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  In  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Leibe, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Matas, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Sebe, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Welling, editors, ECCV, pages  484–499, Cham, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Springer International Publishing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  [14] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Gotsman, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Gu, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Sheffer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  Fundamentals of spherical  parameterization for 3d meshes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' ACM Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=', 22(3):358–363,  July 2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  [15] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Groueix, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Fisher, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Kim, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Russell, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Aubry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  3D-CODED: 3D correspondences by deep deformation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  In ECCV,  September 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  [16] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Hornik, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Stinchcombe, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' White.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Multilayer feedforward  networks are universal approximators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  Neural Networks, 2(5):359–  366, 1989.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  [17] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Kanazawa, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Tulsiani, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Efros, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Malik.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  Learning  category-specific mesh reconstruction from image collections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  In  ECCV, September 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  [18] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Kingma and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Ba.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Adam: A method for stochastic optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  arXiv preprint arXiv:1412.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='6980, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  [19] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Maturana and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Scherer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  Voxnet: A 3d convolutional neural  network for real-time object recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' In IROS, pages 922–928,  2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  [20] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Mescheder, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Oechsle, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Niemeyer, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Nowozin, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Geiger.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  Occupancy networks: Learning 3d reconstruction in function space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  In CVPR, June 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  [21] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Mildenhall, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Srinivasan, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Tancik, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Barron, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Ramamoor-  thi, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Ng.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Nerf: Representing scenes as neural radiance fields for  view synthesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' In A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Vedaldi, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Bischof, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Brox, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='-M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Frahm,  editors, ECCV, pages 405–421, Cham, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Springer International  Publishing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  [22] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' M¨uller, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Evans, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Schied, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Keller.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Instant neural graphics  primitives with a multiresolution hash encoding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' ACM Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=',  41(4):102:1–102:15, July 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  [23] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Ng, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Ginosar, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Darrell, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Joo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  Body2hands: Learning  to infer 3d hands from conversational gesture body dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  In  Proceedings of the IEEE/CVF Conference on Computer Vision and  Pattern Recognition, pages 11865–11874, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  [24] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Park, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Florence, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Straub, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Newcombe, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Lovegrove.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  Deepsdf: Learning continuous signed distance functions for shape  representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' In CVPR, June 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  [25] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Peng, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Niemeyer, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Mescheder, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Pollefeys, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Geiger.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  Convolutional occupancy networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  In A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Vedaldi, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Bischof,  T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Brox, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='-M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Frahm, editors, ECCV, pages 523–540, Cham,  2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Springer International Publishing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  [26] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Qi, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Su, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Niessner, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Dai, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Yan, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Guibas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  Volumetric and multi-view CNNs for object classification on 3d data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  In CVPR, June 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  [27] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Ranjan, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Bolkart, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Sanyal, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Black.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Generating 3D  faces using convolutional mesh autoencoders.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' In ECCV, September  2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  [28] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Tancik, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Srinivasan, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Mildenhall, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Fridovich-Keil,  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Raghavan, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Singhal, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Ramamoorthi, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Barron, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Ng.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  Fourier features let networks learn high frequency functions in low  dimensional domains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' NeurIPS, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  [29] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Tran and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Liu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Nonlinear 3D face morphable model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' In CVPR,  June 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content='  [30] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Verma, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Boyer, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' Verbeek.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' FeaStNet: Feature-steered graph  convolutions for 3D shape analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
+page_content=' In CVPR, June 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E3T4oBgHgl3EQfvgvP/content/2301.04695v1.pdf'}
diff --git a/KNFQT4oBgHgl3EQfSzZL/content/tmp_files/2301.13291v1.pdf.txt b/KNFQT4oBgHgl3EQfSzZL/content/tmp_files/2301.13291v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..7d36c86f49d7cc185189ec97dcde57c9aa8bde9e
--- /dev/null
+++ b/KNFQT4oBgHgl3EQfSzZL/content/tmp_files/2301.13291v1.pdf.txt
@@ -0,0 +1,2600 @@
+Effective approach to the Antoniadis-Mottola model:
+quantum decoupling of the higher derivative terms
+Wagno Cesar e Silva ∗
+and
+Ilya L. Shapiro†
+Departamento de F´ısica, ICE, Universidade Federal de Juiz de Fora,
+36036-900, Juiz de Fora, Minas Gerais, Brazil
+Abstract
+We explore the decoupling of massive ghost mode in the 4D (four-dimensional) theory
+of the conformal factor of the metric. The model was introduced by Antoniadis and
+Mottola in [1] and can be regarded as a close analog of the fourth-derivative quantum
+gravity. The analysis of the derived one-loop nonlocal form factors includes their
+asymptotic behavior in the UV and IR limits. In the UV (high energy) domain, our
+results reproduce the Minimal Subtraction scheme-based beta functions of [1]. In
+the IR (i.e., at low energies), the diagrams with massive ghost internal lines collapse
+into tadpole-type graphs without nonlocal contributions and become irrelevant. On
+the other hand, those structures that contribute to the running of parameters of
+the action and survive in the IR, are well-correlated with the divergent part (or
+the leading in UV contributions to the form factors), coming from the effective low-
+energy theory of the conformal factor. This effective theory describes only the light
+propagating mode. Finally, we discuss whether these results may shed light on the
+possible running of the cosmological constant at low energies.
+Keywords:
+Higher derivatives, quantum gravity, massive ghosts, cosmological con-
+stant, decoupling, conformal anomaly
+1
+Introduction
+The running of the cosmological constant at low energies represents an interesting
+alternative to the numerous models of Dark Energy, as it provides the equation of state
+which is close, but not identical to the ωΛ = −1, of the cosmological constant. On the
+other hand, there is no full understanding of whether such a running is possible or not,
+such that this issue remains uncertain and is a subject of phenomenological considerations,
+as discussed in [2, 3] and many subsequent works. The main difficulty for the thorough
+∗E-mail address: wagnorion@gmail.com
+†E-mail address: ilyashapiro2003@ufjf.br
+arXiv:2301.13291v1  [hep-th]  30 Jan 2023
+
+theoretical investigation is that the traditional approach to quantum decoupling [4] implies
+calculating the nonlocal form factor (or its equivalent) and taking its low-energy limit. The
+cosmological constant acquires physical sense only in curved spacetime and, in principle,
+the corresponding form factors have to be built from covariant elements and analysed
+in curved space. According to the Appelquist-Carazzone theorem [4], heavy degrees of
+freedom decouple in the IR regime, and their loop corrections are quadratically suppressed.
+The same effect should hold in curved spacetime, leading to the corresponding decoupling
+theorems.
+The described program has been fulfilled in a series of papers [2,5–7] where the nonlocal
+form factors in the vacuum (gravitational) actions were calculated and analysed.
+The
+problem is that, these nonlocal form factors describe the decoupling, but only for the
+fourth-derivative terms in the action. Owing to covariance, the form factors depend on the
+d’Alembertian operator □. The positive powers of this operator give zero when acting on
+the cosmological constant and produce surface terms when acting on the scalar curvature
+R. Let us note that part of the mentioned papers, Refs. [6, 7], include the discussion of
+the form factors of surface terms (see [8] for the latest discussions of the mathematical
+aspects of the problem), and there may be even interesting applications of the running of
+Newton constant, related to these surface terms. However, it is unclear how one can gain
+information about the running of the cosmological constant in the traditional covariant
+framework.
+The situation changes dramatically if we perform a conformal transformation.
+For
+instance, using the parametrization
+gµν = φ2
+M 2 exp
+�¯hµν
+�
+,
+exp
+�¯hµν
+�
+= ηµν + ¯hµν + 1
+2
+¯hµλ¯hλ
+ν + 1
+3!
+¯hµλ¯hλ
+τ¯hτ
+ν + . . . ,
+(1)
+with the traceless ¯hµν and constant scale parameter M, transforms the cosmological con-
+stant term √−g into φ4 plus φ4¯hn-vertices. It is known that there is no problem to find
+nonlocal form factor and verify IR decoupling for the φ4-term in the scalar theory [9] and
+one should expect this to be equally easy in the gravitational version of the theory.
+Unfortunately, the described approach does not constitute a comprehensive solution
+of the problem of the running cosmological constant.
+In particular, it is not obvious
+that such a non-covariant running will preserve the structure of the φ4¯hn-vertices, such
+that the running can be safely attributed to the cosmological constant and not to the
+artificial scheme of reparametrization. Anyway, the running of the cosmological term in
+the 4D (four-dimensional) theory of the conformal factor of the metric is an attractive
+object of study, starting from the first proposal [10] and its realization by Antoniadis and
+Mottola [1]. The model of quantum conformal factor follows the idea to perform secondary
+quantization of the anomaly induced effective action of vacuum. This action appears as
+2
+
+a result of integrating conformal anomaly [11, 12] coming from the quantum effects of
+matter fields (see, e.g., [13] for the review or [14] for the textbook level introduction). The
+simplest realization of the anomaly induced action is a theory of a single scalar field with
+fourth derivatives, on a flat background. This procedure corresponds “switching off” the
+¯hµν-mode in the parametrization (1).
+In the paper [1] it was shown that such a model, with additional Einstein-Hilbert and
+cosmological terms, is renormalizable and, in particular, describes the running of the cos-
+mological term. The remaining question is whether this running holds in the low energy
+domain or only in the UV. Indeed, this is a general question that is quite relevant for all
+higher derivative models of quantum gravity. These models may be renormalizable [15],
+or even superrenormalizable [16] and this enables one to consistently derive the renor-
+malization group equations for the effective charges. In the 4D case, the beta functions
+are partially ambiguous [17–19], while in the six- or higher-derivative models, all beta
+functions do not depend on the gauge fixing conditions [20]. However, in which physical
+situations the corresponding running can be applied? The one-loop corrections behind the
+beta functions come from the three different types of diagrams: (i) with internal lines of
+the massless degrees of freedom (gravitons); (ii) with internal lines of massive components,
+i.e., higher derivative ghosts (or ghost-like states, ghost tachyons, etc) and normal degrees
+of freedom, typical for the superrenormalizable models;
+(iii) with mixed (massless and
+massive) internal lines. The standard approach to effective quantum gravity [21] assumes
+that only the first type of diagrams survives and gives relevant contributions in the IR.
+As with all reasonable assumptions, this one has to be verified. And, in this respect, the
+theory of quantum conformal factor [1] represents a perfect toy model. The Lagrangian
+of this theory includes non-polynomial interactions in four-derivative, two-derivative and
+zero-derivative sectors, exactly as the fourth derivative quantum gravity. This means, the
+general structure of the relevant diagrams includes all the aforementioned (i), (ii) and
+(iii)-types. Regardless the calculation of the form factors in the momentum subtraction
+scheme in the theory [1] are rather involved (as the reader may see in what follows), they
+are still alleviated compared to the ones in a full version of quantum gravity, where one has
+to face more extensive set of degrees of freedom and complicated tensor structures, typical
+for diagrammatic treatment of quantum gravity.
+In the present work we report on the derivation of nonlocal form factors in the fourth-
+derivative model of quantum conformal factor and perform the analysis of the UV and
+IR asymptotic behaviour of these quantum corrections. It is important to note that the
+effective approach to the theory of conformal factor induced by anomaly has an independent
+interest. In the recent paper [22], it was shown that this theory provides, in the effective
+approach, a propagation of a scalar mode of the gravitational field, which is not present
+3
+
+in GR. In our opinion, the investigation of quantum IR decoupling is useful for a better
+general understanding of this model in the effective framework.
+The paper is organized as follows: In sect. 2, we briefly review the four-derivative
+model for the conformal factor and present the derivation of its UV divergences using
+the heat-kernel method. The corresponding expression will be used, in what follows, as
+a reference to verify the main result in the UV. In sect. 3, we formulate the elements
+of Feynman technique, i.e., the propagator and vertices for the model, and consider the
+diagrams producing ultraviolet (UV) divergences. Furthermore, we derive the one-loop
+corrections, including the nonlocal form factors in the propagator sector. Section 4 includes
+a description of the asymptotic behavior of nonlocal contributions to the two-point function
+in the UV and IR limits. In sect. 5 we discuss the connection between the momentum
+dependence in the IR regime of the fundamental theory and the divergences in the effective
+low-energy model containing only the light (massless) mode. As usual in massless theories,
+the divergences define not only UV, but also the IR behaviour of the theory and can be
+used for comparison with the IR limit of the full theory. In Sec. 6 we present a discussion
+of the implications of the IR decoupling for the cosmological constant problems. Finally,
+in Sect. 7, we draw our conclusions and discuss the possibilities of a subsequent work. The
+three Appendices complement the main text. In the Appendix A, one can find the set of the
+Feynman diagrams used in our calculations, while in Appendix B, we collect intermediate
+formulas concerning the calculation of Feynman integrals in dimensional regularization. In
+the Appendix C we present the complete expressions of the one-loop quantum corrections
+to the three- and four-point vertices.
+The notations include the Minkowski signature (+, −, −, −). Also, to reduce the size of
+the formulas, we avoid indicating the +iϵ in the denominators of the propagators. Indeed,
+the loop calculations were performed in Euclidean signature.
+2
+The model
+Let us start with a brief review of the model which we shall use in the present work.
+The action of the model is the simplest form of the solution of the anomaly-induced action
+[11,12], with the flat fiducial metric, plus the Einstein-Hilbert and cosmological terms,
+Scf =
+�
+d4x
+�
+2b(□σ)2 − (2w + 2b + 3c)
+�
+□σ + (∂σ)2�2 + 3
+κe2σ(∂σ)2 − Λ
+κ e4σ
+�
+.
+(2)
+4
+
+Here κ = 8πG and the coefficients w, b and c are the one-loop semiclassical beta functions
+in the vacuum sector,
+w =
+1
+120(4π)2(Ns + 6Nf + 12Nv),
+b = −
+1
+360(4π)2(Ns + 11Nf + 62Nv),
+c =
+1
+180(4π)2(Ns + 6Nf − 18Nv),
+(3)
+where Ns, Nf, Nv are the multiplicities of the quantum conformal matter fields of spins
+zero, one-half and one, respectively. The trace anomaly which produces the induced part
+of the action (2) is
+⟨T µ
+µ⟩ = −
+�
+wC2 + bE4 + c □R
+�
+.
+(4)
+The coefficient c can be modified by adding a finite local term R2 to the action Sanom (see
+[13,23–25] for detailed discussion). This feature will not affect our considerations, especially
+because we will not need particular versions of the beta functions (3) and concentrate on
+the general features of the quantum theory of conformal factor based on (2).
+On top of induced part, the action includes Einstein-Hilbert and cosmological terms,
+which are not renormalized at the initial semiclassical theory, but become very relevant at
+the second stage, when we quantize the conformal factor.
+The idea that the conformal factor can be quantum, despite it emerges as an effective
+mode in the integration of matter fields, comes from Polyakov’s approach in 2D, related to
+string theory [26]. The idea of using the equivalent metric-scalar (Liouville) model as the
+basis of 2D quantum gravity was quite popular in 90-s. The use of the analogous theory
+(in curved spacetime) as a model for 4D quantum gravity was proposed in [10]. In four
+dimensions, the theory for the conformal factor can be regarded as a truncated version of
+the four-derivative quantum gravity at large distances (i.e., for the low energies, or IR),
+providing a screening mechanism for the cosmological constant [1]. An important difference
+with the 2D induced gravity is that, in 4D one can add the classical terms. Alternatively,
+one can make the Einstein-Hilbert and cosmological terms to be generated in the scheme
+of induced gravity [27], but this requires an independent scalar field and does not fit our
+purpose to construct a simplified model to explore the decoupling in a higher derivative
+quantum gravity.
+As any fourth-derivative quantum gravity model, the model of our interest has massive
+modes, which can be ghosts and tachyonic ghosts. The question of our interest is what
+happens with the contributions of these massive modes at low energies.
+5
+
+It proves useful to introduce notations similar to [1],
+θ2 ≡ (2w + 3c),
+ζ ≡
+�
+2w + 2b + 3c
+�
+,
+γ ≡ 3
+κ ,
+and
+λ ≡ Λ
+κ ,
+(5)
+such that the action (2) becomes
+Scf
+=
+�
+d4x
+�
+−θ2(□σ)2 − ζ
+�
+2(∂σ)2□σ + (∂σ)4�
++ γ e2σ(∂σ)2 − λ e4σ�
+.
+(6)
+The last two terms in (6) come from the Einstein-Hilbert and cosmological constant
+terms. In the IR, these terms dominate over the higher derivative terms and it proves
+useful to split the Lagrangian into two terms, i.e.,
+LIR = γe2σ(∂σ)2 − λe4σ
+(7)
+and
+L4der = −θ2(□σ)2 − ζ
+�
+2(∂σ)2□σ + (∂σ)4�
+.
+(8)
+Our plan is to evaluate the quantum corrections in full theory (6) and, separately, for
+the theory based on the IR-term (7). Due to the presence of higher derivative terms, the
+one-loop divergences in the full theory are obtained using the generalized Schwinger-DeWitt
+technique [17,28].
+Using the background field method, the conformal factor is decomposed into classical
+σ and quantum ρ counterparts, σ → σ + ρ. Then we obtain the bilinear in the quantum
+field forms for the two terms,
+S(2)
+4der
+=
+−
+�
+d4x
+�
+θ2(□ρ)2 + 2ζ
+�
+(∂ρ)2□σ + 2(∂µρ)(∂µσ)□ρ + (∂σ)2(∂ρ)2
++ 2(∂µρ)(∂νρ)(∂µσ)(∂νσ)
+��
+(9)
+and
+S(2)
+IR =
+�
+d4x
+�
+γe2σ�
+(∂ρ)2 + 4ρ(∂µρ)(∂µσ) + 2ρ2(∂σ)2�
+− 8λρ2e4σ�
+.
+(10)
+The Hermitian forms for the structures (9) and (10) are obtained as
+δ2S(2)
+4der
+δρ(y)δρ(z)
+=
+− 2θ2□2 + 4ζ
+�
+2(□σ)□ − 2∂µ(∂νσ)∂µ∂ν + 4(∂νσ)∂µ(∂νσ)∂µ
++ (∂σ)2□ + 2(□σ)(∂µσ)∂µ + 2(∂µσ)(∂νσ)∂µ∂ν
+�
+,
+δ2S(2)
+IR
+δρ(y)δρ(z)
+=
+− 2γe2σ�
+□ + 2(∂µσ)∂µ + 2(∂σ)2 + 2□σ
+�
+− 16λe4σ.
+(11)
+6
+
+So, for the complete model (6), we have
+δ2S(2)
+δρ(y)δρ(z) = −2θ2 ˆH,
+(12)
+where the self-adjoint four-derivative minimal operator is
+ˆH = □2 + V µν∂µ∂ν + N µ∂µ + U,
+(13)
+with the elements
+V µν = −2ζ
+θ2
+�
+2ηµν□σ − 2∂µ∂νσ + ηµν(∂σ)2 + 2(∂µσ)∂νσ
+�
++ γ
+θ2e2σηµν,
+N µ = −4ζ
+θ2
+�
+2(∂νσ)∂µ∂νσ + (□σ)∂µσ
+�
++ 2γ
+θ2 e2σ(∂µσ),
+U = 2γ
+θ2 e2σ�
+(∂σ)2 + □σ
+�
++ 8λ
+θ2 e4σ.
+(14)
+Using the standard algorithm for the fourth-order operators [17, 28], we arrive at the ex-
+pression for the divergences
+¯Γ(1)
+div = −1
+ε
+�
+d4x
+�5ζ2
+θ4
+�
+□σ + (∂σ)2�2 + γ
+θ2
+�3ζ
+θ2 + 2
+�
+(∂σ)2e2σ −
+�8λ
+θ2 − γ2
+2θ4
+�
+e4σ
+�
+,
+(15)
+where we introduce the useful notation ε = (4π)2(n − 4) and neglect the irrelevant surface
+terms. This result agrees with the previous calculations [1, 29], except for an apparent
+misprint in the sign of Eq. (4) of [29].
+In that follows, we shall confirm the expression (15) by the calculation of both divergent
+and finite nonlocal (leading logarithms) parts of the Feynman diagrams. By considering
+the minimal subtraction (MS) scheme, one can easily derive UV β-functions for the theory
+(6). In the next section, we will determine the finite parts of the one-loop diagrams that
+produce these divergences. In this case, the structure (15) will be useful in identifying the
+diagrams that are relevant for our purposes.
+For completeness, we also derived the divergences of the effective theory, based on the
+IR-term, Eq. (7), separately. The result is
+¯Γ(1)
+div, IR = −1
+ε
+�
+d4x
+�1
+2
+�
+□σ + (∂σ)2�2 − 8
+3Λ e2σ(∂σ)2 + 32
+9 Λ2e4σ
+�
+.
+(16)
+As it should be expected from the power counting, the fourth-derivative counterterms are
+required in this theory, as it is non-renormalizable. At the same time, neglecting the fourth-
+derivative terms according to the effective approach, we arrive the reference expression to
+compare with the IR limit of the full theory.
+7
+
+3
+One-loop corrections from Feynman diagrams
+In a model with higher derivatives, to explore the decoupling in the loop corrections,
+one has to separate massive and massless degrees of freedom. In many cases, this can be
+achieved by introducing auxiliary fields (see, e.g., [30]). However, in the case of the theory
+(6), this approach is not operational owing to our interest in the quantum corrections in
+the theory that have higher derivatives in both kinetic terms and the interactions. Thus,
+we shall make the separation at the level of the propagator and vertices in the Feynman
+diagrams, i.e., use the method close to the one of [31].
+The structure of the vertices and the propagator for the fundamental theory (6) can be
+calculated by using the parametrization σ → σ + ρ, where ρ is a small perturbation and
+expanding the exponential terms in the power series in ρ. Collecting the quadratic terms,
+we find that the propagator satisfies the equation
+2
+�
+θ2□2 + γ□ + 8λ
+�
+G(x, y) = iδ4(x − y).
+(17)
+Making the Fourier transform,
+G(x, y) =
+�
+d4k
+(2π)2 e−ik·(x−y) �G(k)
+(18)
+and assuming Λ ≪ γ2/θ2, we get
+�G(k) =
+i
+2[θ2k4 − γk2 + 8λ] ≃
+i
+2 θ2�
+k2 − γ
+θ2
+��
+k2 − 8
+3Λ
+�.
+(19)
+Finally, in the same approximation, the propagator can be written as
+�G(k) =
+i
+2 θ2�
+m2 − M 2)
+�
+1
+k2 − m2 −
+1
+k2 − M 2
+�
+.
+(20)
+It is easy to identify a healthy degree of freedom with the mass m2 = 8Λ/3 and a ghostly
+mode with the Planck-scale mass, M 2 = γ/θ2.
+We need to consider only those interaction vertices that are relevant for the one-loop
+corrections to the propagator. The vertices for the 3- and 4-point functions arise from
+the derivative interaction terms in the part L4der and from the higher order terms in the
+exponential expansion in LIR,
+ζ
+�
+2(∂ρ)2□ρ + (∂ρ)4�
+,
+2γ(∂ρ)2�
+ρ + ρ2�
+,
+32λ
+3
+�
+ρ3 + ρ4�
+.
+(21)
+8
+
+⇥
+(a)
+�
+(b)
+⇤
+(c)
+⇥
+(d)
+�
+(e)
+⇤
+(f)
+Figure 1: Feynman diagrams associated with the interaction vertices. The primes
+denotes derivatives acting on the propagators.
+In Fig. 1, we have presented the vertices corresponding to these interaction terms. The
+analytic expressions have the form
+V (3)
+ζ
+(p, k, q) = −4iζ
+�
+p2(k · q) + q2(k · p) + k2(p · q)
+�
+,
+V (3)
+γ (p, k, q) = 2iγ(k2 + p2 + q2),
+V (3)
+λ
+= −64iλ
+(22)
+and
+V (4)
+ζ
+(p, k, q, r) = −8iζ
+�
+(k · q)(p · r) + (k · p)(q · r) + (k · r)(p · q)
+�
+,
+V (4)
+γ (p, k, q, r) = 4iγ(k2 + p2 + q2 + r2),
+V (4)
+λ
+= −256iλ,
+(23)
+where (k · p) = kµpµ.
+Now we are in the position to determine the one-loop contributions to the self-energy
+(correction to the propagator) of the healthy (light) mode. First, consider the diagrams
+producing the UV divergences (15), derived previously using the heat-kernel method. These
+divergences are responsible for the MS-scheme based beta functions and serve as the UV
+references for the complete expressions.
+In the theory (6) the expression for the two-point function is
+G(2)
+1-loop(p, −p) ∝
+i
+(p2 − m2)
+�¯Σγ + ¯Σλ + �Σγλ + �Σλ2 + Σζ2 + Σγζ + Σγ2�
+i
+(p2 − m2).
+(24)
+We can write the general symbolic expression for the self-energy function, in the second-
+9
+
+order (in coupling constants) approximation as
+� =
++
+� 2 ⇥
+= Σlight + Σghost − 2Σmixed
+(25)
+and
+Now we are in the position to determine the one-loop contributions to the propagator of
+the healthy (or light) mode. For this we consider the self-energy diagrams that produce
+the UV divergences (16). In the theory (6) the corrections of interest for the two-point
+function are given by
+G(2)(p, �p) /
+i
+(p2 � m2)
+�¯⌃� + ¯⌃� + ⌃⇣2 + ⌃�⇣ + ⌃�2�
+i
+(p2 � m2).
+(30)
+The self-energy type corrections that are second-order in the coupling constants are given
+by
+⌃ =
++
+� 2 ⇥
+= ⌃light + ⌃ghost � 2⌃mixed
+(31)
+and
+e⌃ =
+q = 0
++
+q = 0
+�
+q = 0
+�
+q = 0
+= ⌃light
+��
+q=0 + ⌃ghost
+��
+q=0 � ⌃mixed
+��
+q=0 � ⌃mixed
+��
+m2$ M2, q=0 ,
+(32)
+where, generically,
+⌃light /
+Z
+d4k
+(2⇡)4
+i
+(k2 � m2)V (3)(p, �k, k � p)
+i
+⇥
+(k � p)2 � m2⇤V (3)(�p, k, p � k),
+(33)
+⌃ghost /
+Z
+d4k
+(2⇡)4
+i
+(k2 � M 2)V (3)(p, �k, k � p)
+i
+⇥
+(k � p)2 � M 2⇤V (3)(�p, k, p � k),
+(34)
+⌃mixed /
+Z
+d4k
+(2⇡)4
+i
+(k2 � m2)V (3)(p, �k, k � p)
+i
+⇥
+(k � p)2 � M 2⇤V (3)(�p, k, p � k),
+(35)
+while contributions that are of the first-order in the coupling constants have the following
+structure:
+¯⌃ =
++
+= ¯⌃light + ¯⌃ghost,
+(36)
+with
+¯⌃light /
+Z
+d4k
+(2⇡)4
+i
+(k2 � m2)V (4)(p, �k, k � p)
+i
+⇥
+(k � p)2 � m2⇤,
+(37)
+¯⌃ghost /
+Z
+d4k
+(2⇡)4
+i
+(k2 � M 2)V (4)(p, �k, k � p)
+i
+⇥
+(k � p)2 � M 2⇤.
+(38)
+7
+= Σlight
+��
+q=0 + Σghost
+��
+q=0 − Σmixed
+��
+q=0 − Σmixed
+��
+m2↔ M2, q=0 ,
+(26)
+where solid lines indicate light degrees of freedom while dashed lines stand for the massive
+ghosts. Furthermore,
+Σlight ∝
+�
+d4k
+(2π)4
+i
+(k2 − m2)V (3)(p, −k, k − p)
+i
+�
+(k − p)2 − m2�V (3)(−p, k, p − k),
+Σghost ∝
+�
+d4k
+(2π)4
+i
+(k2 − M 2)V (3)(p, −k, k − p)
+i
+�
+(k − p)2 − M 2�V (3)(−p, k, p − k),
+Σmixed ∝
+�
+d4k
+(2π)4
+i
+(k2 − m2)V (3)(p, −k, k − p)
+i
+�
+(k − p)2 − M 2�V (3)(−p, k, p − k), (27)
+while the contributions of the first-order in the coupling constants have the following struc-
+ture:
+¯� =
++
+= ¯Σlight + ¯Σghost ,
+(28)
+with
+¯Σlight ∝
+�
+d4k
+(2π)4
+i
+(k2 − m2)V (4)(p, k, −p, −k),
+¯Σghost ∝
+�
+d4k
+(2π)4
+i
+(k2 − M 2)V (4)(p, k, −p, −k).
+(29)
+The diagrammatic representation of the contributions to the two-point function with
+different couplings, is presented in the Appendix A. The diagrams in Fig. 2 correspond
+10
+
+to the fifth term in (24), and the last term is associated with the diagrams in Fig. 4. In
+Fig. 3 there are shown the diagrams that correspond to the term proportional to γζ. The
+diagrams for the first-order terms in the couplings γ and λ, are depicted in Figs. 5 and
+6, respectively. In addition, the third and fourth terms in (24) are associated with the
+tadpole diagrams with interaction vertices γλ shown in Fig. 7, and λ2 shown in Fig. 8.
+Let us note that each diagram here represents the sum over all the topologically equiva-
+lent diagrams with different permutations over the external momenta and with all possible
+placements of derivatives on the internal and external lines. On top of that, we omit-
+ted some tadpole-type diagrams that do not contribute to G(2)(p, −p), as they include
+derivatives of the propagator in a single spacetime point, and hence vanish.
+To evaluate the integrals in (24) we used dimensional regularization. In the model
+under consideration, this requires extending the standard list of divergent expressions [32]
+for the integrals in the spacetime of 2ω complex dimensions. The integrals proportional to
+ζ2, γζ and γ2 read, respectively, as
+Σ(2ω)
+ζ2 (p)
+=
+−
+8ζ2
+θ4(m2 − M 2)2
+�
+d2ωk
+(2π)2ω Γ(3,3)
+ζ2
+�
+2
+(k2 − m2)
+�
+(k − p)2 − M 2�
+−
+1
+(k2 − m2)
+�
+(k − p)2 − m2� −
+1
+(k2 − M 2)
+�
+(k − p)2 − M 2�
+�
+,
+(30)
+Σ(2ω)
+γζ (p)
+=
+−
+4γζ
+θ4(m2 − M 2)2
+�
+d2ωk
+(2π)2ω Γ(3,3)
+γζ
+�
+2
+(k2 − m2)
+�
+(k − p)2 − M 2�
+−
+1
+(k2 − m2)
+�
+(k − p)2 − m2� −
+1
+(k2 − M 2)
+�
+(k − p)2 − M 2�
+�
+(31)
+and
+Σ(2ω)
+γ2 (p)
+=
+−
+2γ2
+θ4(m2 − M 2)2
+�
+d2ωk
+(2π)2ω Γ(3,3)
+γ2
+�
+2
+(k2 − m2)
+�
+(k − p)2 − M 2�
+−
+1
+(k2 − m2)
+�
+(k − p)2 − m2� −
+1
+(k2 − M 2)
+�
+(k − p)2 − M 2�
+�
+,
+(32)
+where we used the following combinations of the vertex factors:
+Γ(3,3)
+ζ2
+= p4k4 − 2p2k2(p · k)2 + (p · k)4,
+Γ(3,3)
+γζ
+= p4k2 − (p2 + k2)(p · k)2 + (p · k)3 − p2k2(p · k) + k4p2,
+Γ(3,3)
+γ2
+= p4 + k4 + (p · k)2 + 2p2k2 − 2(p2 + k2)(p · k).
+(33)
+11
+
+The results of the integrations in the Euclidean space are1
+Σζ2(p)
+=
+iζ2p4
+(4π)2θ4
+�
+5
+�1
+ϵ + ln
+� µ2
+m2
+��
+− 1
+4
+�
+9A2 − 5(ab)2 − 37
+�
+−
+1
+2(ab)2c5 ln
+�1 + c
+1 − c
+�
+−
+1
+2(ab)2d5 ln
+�1 + d
+1 − d
+�
+−
+�1
+2(ab)3 + 5
+2ab
+�
+ab + a
+2 + 2
+�
++ 15a
+4
+�
+1 + 1
+4b
+�
++ 5
+�
+2 + 3
+4b + 1
+2ab
+��
+ln (1 + 4b) +
+A5
+2(ab)2 ln
+�(A + 1)2 − (ab)2
+(A − 1)2 − (ab)2
+��
+,
+(34)
+Σγζ(p)
+=
+− iγζp2
+(4π)2θ4
+�
+3
+�1
+ϵ + ln
+� µ2
+m2
+��
++
+1
+2c(ab)2
+�a
+2
+�
+2 − 1
+c2
+�
++ 1
+�
+ln
+�1 + c
+1 − c
+�
++
+1
+2d(ab)2
+�a
+2(4b + 1)
+�
+2 − 1
+d2
+�
++ 1
+�
+ln
+�1 + d
+1 − d
+�
+−
+�
+ab + a
+2 − 6
+�
+− A
+2
+�� 1
+ab − ab
+��
+1 + 1
+2b + 1
+ab
+�
+− 2
+b
+�
+1 + 1
+4b
+��
+ln
+�(A + 1)2 − (ab)2
+(A − 1)2 − (ab)2
+�
+−
+�ab
+2
+�
+ab + a
+2 + 2
+�
++ 3
+�
+1 + a
+2
+��
+1 + 1
+4b
+�
+− 1
+ab
+�
+ln (1 + 4b)
+�
+,
+(35)
+Σγ2(p)
+=
+iγ2
+(4π)2θ4
+�
+2
+�1
+ϵ + ln
+� µ2
+m2
+��
++ 3 −
+1
+2c(ab)2
+�a2
+4 − 1
+c2 + 2
+�
+ln
+�1 + c
+1 − c
+�
++
+A
+2(ab)2
+�
+ab + a
+2 − 1
+�2
+ln
+�(A + 1)2 − (ab)2
+(A − 1)2 − (ab)2
+�
+− 1
+2
+�
+ab + a
+�
+1 + 1
+4b
+�
++ 3
++ 1
+2b
+�
+1 − 2
+a
+��
+ln (1 + 4b) −
+1
+2d(ab)2
+�a2
+4 (4b + 1)2 − 1
+d2 + 2
+�
+ln
+�1 + d
+1 − d
+��
+, (36)
+where
+1
+ϵ ≡
+1
+2 − ω − γE + ln (4π),
+a = 4m2
+p2 ,
+b = M 2 − m2
+4m2
+(37)
+and γE ≈ 0.577 is the Euler-Mascheroni constant. In the limit ω → 2, the results (34),
+(35) and (36) represent divergent and finite parts.
+Note that the finite part of these
+expressions has a very complicated dependence on the external momentum.
+For these
+nonlocal structures, in the mixed sector, we used the notation
+A =
+�
+(1 + ab)2 + a.
+(38)
+Furthermore, the notations used in the light and ghost sectors, include, respectively,
+c2 =
+p2
+p2 + 4m2,
+d2 =
+p2
+p2 + 4M 2.
+(39)
+1Some intermediate details of the calculations can be found in Appendix B. The calculations were
+verified using the Package-X [33] in Mathematica [34].
+12
+
+In top of this, the relevant corrections involving the quartic vertices, are given by
+¯Σγ(p) = 2iγp2
+θ2
+Iquad
+and
+¯Σλ(p) = 64iλ
+θ2
+Iquad,
+(40)
+where the integral is
+Iquad
+=
+1
+(m2 − M 2)
+�
+d2ωk
+(2π)2ω
+�
+1
+(k2 + m2) −
+1
+(k2 + M 2)
+�
+=
+−
+1
+(4π)2
+�1
+ϵ + ln
+� µ2
+m2
+�
++ 1 −
+M 2
+(m2 − M 2) ln
+� m2
+M 2
+��
+.
+(41)
+The results (40) are tadpole-type contributions, which do not produce a nonlocal form
+factor. Therefore, these corrections are not relevant to our analysis at low energies and
+were included just of completeness. Of course, the same consideration applies to second-
+order tadpole-type corrections, which in principle contribute to divergences in the Einstein-
+Hilbert and cosmological constant sectors,
+�Σγλ(p) = − 16iγλp2
+θ4m2M 2 Iquad
+and
+�Σλ2(p) = − 512iλ2
+θ4m2M 2 Iquad,
+(42)
+with m2M 2 = 8λ/θ2. Actually, the corrections in (42) can be disregarded because tad-
+pole diagrams, such as those presented in Figs. 7 and 8, normally are eliminated using
+renormalization conditions (see, e.g., [35] or the Chapter 11 of [36] for more details).
+Let us note that here we presented only the results for the self-energy. The lower-order
+vertices were also derived and produce qualitatively the same picture. The nonlocal parts
+of these contributions follow a standard logarithmic structure, as those for propagator
+corrections. Since the corresponding formulas are relatively bulky, they are separated in
+Appendix C.
+4
+Asymptotic behavior
+In this section, we explore the asymptotic behavior of the one-loop contributions (34),
+(35), and (36). Our main interest is to verify how these expressions interpolate between the
+UV and IR regions of the fundamental theory. In this way, we have a chance to understand
+what happens to the nonlocal form factors of the contribution of loops with the massive
+degrees of freedom (massive ghosts) in the IR.
+We start with the limit p2 → ∞ that corresponds to the UV regime p2 ≫ M 2 ≫ m2.
+In this case, Eqs. (35), (34), and (36) simplify and we arrive at the expressions
+13
+
+ΣUV
+ζ2 (p2 → ∞)
+=
+iζ2p4
+(4π)2θ4
+�
+5
+�1
+ϵ − ln
+�p2
+µ2
+��
++ 3 − 15(M 2 + m2)
+p2
++ 10(m4 + m2M 2 + M 4)
+p4
+ln
+� p2
+M 2
+�
++ 35(M 2 + m2)
+6p4
++ 40M 2m2
+3p4
++ 10m6
+p4M 2 ln
+� m2
+M 2
+�
++ O
+�M 6
+p6
+��
+,
+(43)
+ΣUV
+γζ (p2 → ∞)
+=
+− iγζp2
+(4π)2θ4
+�
+3
+�1
+ϵ − ln
+�p2
+µ2
+��
++ 7 − 9(M 2 + m2)
+p2
+− 6(M 2 + m2)
+p2
+ln
+� p2
+M 2
+�
+− 6m4
+p2M 2 ln
+� m2
+M 2
+�
++ O
+�M 4
+p4
+��
+,
+(44)
+ΣUV
+γ2 (p2 → ∞)
+=
+iγ2
+(4π)2θ4
+�
+2
+�1
+ϵ + ln
+�p2
+µ2
+�
++ 2 ln
+� µ2
+M 2
+��
++ 5
++ 4m2
+M 2 ln
+� m2
+M 2
+�
++ O
+�M 2
+p2
+��
+.
+(45)
+As expected in the UV regime, the leading logarithmic terms in the form factor are pro-
+portional to the corresponding divergences. It is easy to verify that, when returning to the
+coordinate representation, the divergent part of the expressions above, together with (40)
+in the UV, correspond to the result (15), obtained from the heat-kernel technique.
+On the other hand, assuming m2 → 0, the analysis of the IR regime M 2 ≫ p2 of the
+corrections (34), (35), and (36), provides
+ΣIR
+ζ2 (M 2 ≫ p2)
+����
+m2=0
+=
+iζ2p4
+(4π)2θ4
+�
+5
+�1
+ϵ + ln
+� µ2
+M 2
+��
+− 1
+6
+�
+7 + 35p2
+2M 2 − 9p4
+2M 4
+�
++
+p4
+2M 4 ln
+�M 2
+p2
+�
++ O
+� p6
+M 6
+��
+,
+(46)
+ΣIR
+γζ(M 2 ≫ p2)
+����
+m2=0
+=
+− iγζp2
+(4π)2θ4
+�
+3
+�1
+ϵ + ln
+� µ2
+M 2
+��
+− 1
+2 + 2p2
+3M 2
+− p4
+M 4
+� 7
+20 − 1
+2 ln
+� p2
+M 2
+��
++ O
+� p6
+M 6
+��
+,
+(47)
+ΣIR
+γ2(M 2 ≫ p2)
+����
+m2=0
+=
+iγ2
+(4π)2θ4
+�
+2
+�1
+ϵ + ln
+� µ2
+M 2
+��
++ 13
+6
+p2
+M 2
+−
+p4
+2M 4
+�8
+5 + ln
+� p2
+M 2
+��
++ O
+� p6
+M 6
+��
+.
+(48)
+14
+
+The last formulas show that, in the IR limit, the divergences and momentum dependence
+do not correlate with each other, exactly as it is expected [4] (see also [2, 5, 7] for the
+semiclassical theory). We have found that this basic feature holds also for the “mixed”
+diagrams, such that the Appelquist-Carazzone theorem is valid for the fourth-derivative
+model with non-polynomial interactions. In the expressions (46) and (47), the nonlocal
+part with logarithmic form factor is suppressed by powers of M 2, whereas in (48) this is
+not the case, as the factor γ2 (remember that γ = θ2M 2) cancels this suppression in the
+terms proportional to p4. It is important to note that these nonlocal structures represent
+the contributions from the light sector alone. The one-loop diagrams with mixed (light
+and massive ghost) internal lines and (of course) the pure ghost contributions collapse and
+produce only trivial dependencies on the external momentum. All in all, we verified the
+quadratic decoupling of the heavy mode in the Feynman diagrams with the mixed contents.
+5
+One-loop corrections in the effective theory
+The last element of our investigation is the comparison between what remains from
+the logarithmic form factors of the full theory in the IR and the leading logarithms in
+the effective (initially local) theory without heavy degrees of freedom. According to the
+existing expectations [21], the two expression should demonstrate a perfect correlation.
+This result would mean, in particular, that the quantum general relativity can serve as
+a universal low-energy model in any renormalizable or superrenormalizable approach to
+quantum gravity.
+So, let us evaluate the quantum corrections to the propagator in the effective low-energy
+model of (6), containing only the light mode. We consider a scenario in which the energy
+scale is much smaller than the Planck mass. Therefore, we can assume that the EH and
+cosmological constant terms dominate over the higher derivative terms, leaving only the
+part LIR. Under these considerations, the tree-level propagator of the conformal factor
+boils down to
+�Geff(k) = −
+i
+2γ
+�
+k2 − m2�,
+(49)
+where m2 is defined in (20). The vertices are the same as those in (22) and (23). Since we
+are dealing with an effective model, we are not concerned that LIR is non-renormalizable,
+as we may ignore the higher-derivative divergences2. Thus, our interest is to explore the
+2According to the logic of the pioneer work [21] (see also [37]) the divergences in quantum gravity are
+local expressions and, therefore, have no direct relation to the long-distance regime corresponding to the
+IR limit.
+15
+
+contributions to the cosmological constant and the Einstein-Hilbert terms. These formulas
+can be compared with the structures found in the IR limit of the full theory (6).
+In the low-energy effective theory, the relevant contribution is given by
+Σeff
+γ2(p)
+=
+ip4
+(4π)2
+��1
+2 − 5
+4 a + 3
+8 a2� �1
+ϵ − ln
+� µ2
+m2
+��
++
+�
+1 − 7
+4 a + 1
+2 a2�
+− 1
+2c
+�1
+4 a2 − 1
+c2 + 2
+�
+ln
+�1 + c
+1 − c
+��
+.
+(50)
+To make the comparison more explicit, consider the particular case Λ = 0 (or, equivalently,
+p2 → ∞). Then the last expression reduces to a simpler form,
+Σeff
+γ2(p)
+���
+Λ=0
+=
+ip4
+2(4π)2
+�1
+ϵ − ln
+�p2
+µ2
+�
++ 2
+�
+.
+(51)
+Note that the nonlocal contribution to the cosmological constant sector in the IR regime
+of the “fundamental” theory (6) is correlated with the UV divergence of the result (51).
+From these results, it is also possible to establish the one-loop match between these two
+scenarios: fundamental and effective.
+For this, we introduce the relation
+ΣIR
+γ2
+=
+Σeff
+γ2 + δeff
+γ2,
+(52)
+where δeff
+γ2 is an additional term which represents, at the one-loop level, the difference
+between the correction of the fundamental theory in the low energies and the correction of
+the effective theory. Considering the collapse of the diagrams with massive ghost internal
+lines in the IR regime of the fundamental theory, as we saw in the previous section, we
+can identify that the additional term in (52) is composed of contributions arising from the
+collapse of loops in the mixed sector. These collapsed diagrams reduce to the tadpole-type
+graphs, and the remaining part, related to pure ghost loops, i.e.,
+δeff
+γ2
+=
+c(1)
+γ2, mixed + c(1)
+γ2, ghost.
+(53)
+The contribution of the tadpole-type in (53) is proportional to the mass m2, and hence
+vanishes in the simplification adopted for the IR, namely assuming c(1)
+γ2, mixed
+��
+m2=0 = 0.
+Using the results (48) and (51), we find the leading logarithmic terms in the form
+δeff
+γ2
+���
+m2=0
+=
+i
+(4π)2
+�
+2M 4 ln
+� µ2
+M 2
+�
++ 13
+6 p2M 2 − p4
+2
+�18
+5 + ln
+� µ2
+M 2
+���
+.
+(54)
+In this expression we omitted the divergent part, for simplicity. As it should be expected,
+the nonlocal part with logarithmic form factor is canceled and the IR matching condition,
+which ensure the equivalence with the result (48), is satisfied with δeff
+γ2 contains only terms
+with trivial dependencies on the external momentum.
+16
+
+6
+Implications for the cosmological constant problem
+The cosmological constant problem is one of the main unsolved issues in the present-
+day theoretical physics. The problem was formulated by Weinberg in [38] as the need
+to explain the extremely precise fine tuning between the original cosmological constant
+density in the vacuum action and the huge induced contributions. One can reformulate
+the problem in terms of the renormalization of the vacuum term [39] but this does not help
+too much in its resolution. There are also many other interesting aspects of the problem,
+related to cosmology (see, e.g., [40, 41]). Along with the main problem, in the quantum
+field theory framework we need to understand whether the cosmological constant density
+and the Newton constant are really constants or these parameters can be slowly varying
+with the energy scale, as predicted, e.g., by the four-derivative model of [1] (see also the
+examples of discussions based on the extended models [29, 42, 43]) and, of course, in the
+full fourth-derivative [17,18,44] or even higher-derivative models [20] of quantum gravity.
+As we saw in the previous sections, the naive Minimal Subtraction - based approach
+to the renormalization group for the cosmological constant term is not operational, as
+it ignores the decoupling of the massive (ghost or healthy, in some models) degrees of
+freedom. Assuming that all massive degrees of freedom have typical masses of the Planck
+order of magnitude, all the cosmological applications occur at the deep IR, where the
+Appelquist-Carazzone - type decoupling changes the beta functions. The question is what
+remains from these beta functions in the theory with both massive and massless degrees
+of freedom [44,45]?
+The result which we got for the quantum theory of conformal factor is that, in the deep
+IR, there remain the contributions (46), (47) and (48), which fit the ones of effective low-
+energy quantum theory based on the local model. This provides a positive answer to the
+aforementioned question posed in [45] and confirms the hypothesis of [21] (see also previous
+discussion based on the simplified model with two fields in [46]). Looking at the expressions
+for the IR remains of the form factors, we note that the terms without p4 or p2 factors have
+only log(µ2/M 2) factor and no momentum-dependent logarithmic terms. This confirms
+the general expectation that there cannot be physical running of the cosmological constant
+term, detectable by means of flat-space calculations, as discussed in [2] and more recently
+in [47]. Let us stress that this does not mean that the cosmological constant running is
+impossible in general, it just cannot be detected in the flat-space calculations [3].
+It is worth noting that one can observe the running of the cosmological constant term
+using the non-covariant parametrization such as (1), just as a decoupling in the beta
+function of the φ4-interaction.
+Up to a certain extent, the corresponding calculations
+were already developed in [9] and can be generalized to other theories, including quantum
+17
+
+gravity. This would be certainly an interesting way to extend the present work. However,
+it is important to be careful with the expectations to the results of such an extension, as
+there will always remain a question about the physical interpretation of the result obtained
+by means of non-covariant methods.
+7
+Conclusions and discussions
+We have considered the detailed renormalization in the theory of the conformal factor.
+Assuming a small cosmological constant, such a theory possesses two mass scales with a
+strong hierarchy between them. On top of that, the theory has non-polynomial interactions
+and is renormalizable [1].
+These features make the model qualitatively similar to the
+higher derivative quantum gravity.
+Previously, the one-loop calculations in this model
+were performed in the Minimal Subtraction scheme and we performed a more detailed
+analysis in the momentum subtraction scheme of renormalization.
+The analysis of the nonlocal form factors shows that in the UV, we meet a correspon-
+dence with the Minimal Subtraction scheme results. On the other hand, in the IR we met
+a strong deviation from this simplified scheme and, as it was anticipated, a good agreement
+with the calculation in the effective model that ignores the massive degree of freedom. One
+of the new details is that the “mixed” diagrams, with the internal lines of both small-
+mass and large-mass fields, transform into tadpoles. These diagrams contribute to the
+UV divergences, but not to the nonlocal form factors. This means, the diagrams with the
+large-mass internal lines collapse and become irrelevant in the IR. In particular, nonlocal
+structures that survive in this regime and contribute to the cosmological constant sector,
+are correlated with the UV divergent part in an effective version of the model containing
+only the light mode.
+It would be certainly interesting to extend the analysis which was presented above, for
+the models of “real” quantum gravity, i.e., the theory of quantum metric. As we mentioned
+in the Introduction, this is a technically more challenging problem because such a theory
+has gauge invariance and complicated tensor structures in the sectors of quantum metric
+and ghost. However, the results presented above show that there are very good chances to
+meet the expectation of universality of quantum general relativity as an effective theory of
+quantum gravity, at least in the fourth derivative [15] and, probably, all polynomial models
+introduced in [16], where all extra degrees of freedom have the masses of the Planck order
+of magnitude [48].
+At the same time, the situation may be more complicated in the non-local theories
+of quantum gravity [49–52] (many further references can be found in the last review).
+The most popular version of nonlocal models are free from massive degrees of freedom at
+18
+
+the tree-level. On the other hand, starting from the one-loop level, the structure of the
+propagator changes and there are infinitely many complex-energy and complex-mass ghost-
+like states with the quasi-continuous mass spectrum [53]. In this case, the universality of
+general relativity as the IR quantum gravity theory is rather uncertain. This means, there
+are still many interesting issues to explore in the area of the present work.
+The last point is that we have found a good correspondence between the IR limit of the
+theory with massless and large-mass degrees of freedom and the UV limit of the effective
+theory without the massive particles. This correspondence extends to the contributions in
+the cosmological constant sector of the gravitational action. However, these contributions
+are not momentum-dependent, confirming the general no-go statement [2] concerning the
+detection of the cosmological constant running by means of the flat-space calculations. On
+the other hand, this output does not means that such a running is impossible by itself.
+Instead, it should be interpreted as a challenge to develop new methods of effective field
+theory calculations which would be appropriate for clarifying this issue.
+Acknowledgments
+W.C.S. is grateful to CAPES for supporting his PhD project. The work of I.Sh. is
+partially supported by Conselho Nacional de Desenvolvimento Cient´ıfico e Tecnol´ogico -
+CNPq under the grant 303635/2018-5, by Funda¸c˜ao de Amparo `a Pesquisa de Minas Gerais
+- FAPEMIG under the grant PPM-00604-18.
+19
+
+Appendices
+A
+Feynman diagrams
+In this appendix, we present the set of one-loop Feynman diagrams that correspond to
+the corrections to the two-point function.
+On decoupling in higher-derivative models (draft)
+Wagno Cesar ∗
+Departamento de F´ısica, ICE, Universidade Federal de Juiz de Fora
+Contents
+1
+Appendix - Feynman diagrams
+1
+1
+Appendix - Feynman diagrams
+In this appendix, we present the set of one-loop Feynman diagrams that correspond to
+the corrections for the two-point function.
+G(2)
+⇣2 (p, �p) ⇠
+Figure 1: Diagrams for the two-point function that provide one-loop contributions to the
+renormalization of the coupling ⇣. Solid lines indicate light degrees of freedom, dashed lines
+stand for the massive ghosts, and the primes denotes derivatives acting on the propagators.
+∗E-mail address: wagnorion@gmail.com
+Figure 2: Diagrams for the two-point function that provide one-loop contributions to the
+renormalization of the coupling ζ. Solid lines indicate light degrees of freedom, dashed lines
+stand for the massive ghosts, and the primes denotes derivatives acting on the propagators.
+G(2)
+�⇣ (p, �p) ⇠
+Figure 2: Diagrams for the two-point function with the interaction vertex �⇣.
+G(2)
+�2 (p, �p) ⇠
+Figure 3: Diagrams for the two-point function with the interaction vertex �2.
+G(2)
+� (p, �p) ⇠
+Figure 4: Diagrams for the two-point function with the interaction vertex �.
+2
+Figure 3: Diagrams for the two-point function with the interaction vertex γζ.
+20
+
+G(2)
+�⇣ (p, �p) ⇠
+Figure 2: Diagrams for the two-point function with the interaction vertex �⇣.
+G(2)
+�2 (p, �p) ⇠
+Figure 3: Diagrams for the two-point function with the interaction vertex �2.
+G(2)
+� (p, �p) ⇠
+Figure 4: Diagrams for the two-point function with the interaction vertex �.
+2
+Figure 4: Diagrams for the two-point function with the interaction vertex γ2.
+G(2)
+� (p, �p) ⇠
+Figure 5: Diagrams for the two-point function with the interaction vertex �.
+G(2)
+� (p, �p) ⇠
+Figure 6: Diagrams for the two-point function with the interaction vertex �.
+G(2)
+��(p, �p) ⇠
+Figure 7: Diagrams for the two-point function with the interaction vertex ��.
+G(2)
+�2 (p, �p) ⇠
+Figure 8: Diagrams for the two-point function with the interaction vertex �2.
+3
+Figure 5: Diagrams for the two-point function with the interaction vertex γ.
+G(2)
+� (p, �p) ⇥
+Figure 6: Diagrams for the two-point function with the interaction vertex λ.
+G(2)
+� (p, �p) ⇠
+Figure 5: Diagrams for the two-point function with the interaction vertex �.
+G(2)
+� (p, �p) ⇠
+Figure 6: Diagrams for the two-point function with the interaction vertex �.
+G(2)
+��(p, �p) ⇠
+Figure 7: Diagrams for the two-point function with the interaction vertex ��.
+G(2)
+�2 (p, �p) ⇠
+Figure 8: Diagrams for the two-point function with the interaction vertex �2.
+3
+Figure 7: Diagrams for the two-point function with the interaction vertex γλ.
+G(2)
+� (p, �p) ⇠
+Figure 5: Diagrams for the two-point function with the interaction vertex �.
+G(2)
+� (p, �p) ⇠
+Figure 6: Diagrams for the two-point function with the interaction vertex �.
+G(2)
+��(p, �p) ⇠
+Figure 7: Diagrams for the two-point function with the interaction vertex ��.
+G(2)
+�2 (p, �p) ⇠
+Figure 8: Diagrams for the two-point function with the interaction vertex �2.
+3
+Figure 8: Diagrams for the two-point function with the interaction vertex λ2.
+21
+
+B
+Intermediate results for the Feynman integrals
+In this appendix, we present some intermediate results related to the calculation of
+Feynman integrals in sect. 3. By using the Feynman parametrization
+1
+ab =
+� 1
+0
+dx
+�
+(a − b)x + b
+�2,
+(55)
+and performing the following shift of integration variable k = q + px, we can rewrite the
+integrals related to the mixed sector in the expressions (30), (31) and (32), respectively, as
+Σ(2ω)
+mixed, ζ2(p)
+=
+−
+2ζ2 p4
+θ4(m2 − M 2)2
+(4ω2 − 1)
+ω(1 + ω)
+� 1
+0
+dx I4,
+(56)
+Σ(2ω)
+mixed, γζ(p)
+=
+−
+2γζ p2
+θ4(m2 − M 2)2
+(2ω − 1)
+ω
+� 1
+0
+dx
+��
+x2 − x + 1
+�
+p2I2 + I4
+�
+(57)
+and
+Σ(2ω)
+mixed, γ2(p)
+=
+−
+2γ2
+θ4(m2 − M 2)2
+� 1
+0
+dx
+�
+I4 + 1 + 4ω + 4
+�
+x2 − x
+�
+(ω + 1)
+2ω
+p2I2
++
+�
+x2 − x + 1
+�2p4I1
+�
+,
+(58)
+where
+I1 =
+�
+d2ωq
+(2π)2ω
+1
+(q2 − ∆)2 =
+i
+(4π)ω Γ(2 − ω)∆ω−2,
+(59)
+I2 =
+�
+d2ωq
+(2π)2ω
+q2
+(q2 − ∆)2 = −
+i
+(4π)ω ωΓ(1 − ω)∆ω−1,
+(60)
+I4 =
+�
+d2ωq
+(2π)2ω
+q4
+(q2 − ∆)2 =
+i
+(4π)ω ω(1 + ω)Γ(−ω)∆ω.
+(61)
+Here we define ∆ ≡ p2x(x − 1) + (M 2 − m2)x + m2. For the integrals in the other sectors,
+we have the same results as above with ∆ = ∆ghost = p2x(x − 1) + M 2 in the case of the
+ghost sector, and ∆ = ∆light = p2x(x − 1) + m2 for the light sector.
+C
+One-loop corrections to the three- and four-point vertices
+This appendix is devoted to the one-loop corrections to the vertices. In case of the
+three-point function, the relevant corrections are associated with the diagrams in Figures
+9, 10 and 11.
+22
+
+On decoupling in higher-derivative models (draft)
+Wagno Cesar ∗
+Departamento de F´ısica, ICE, Universidade Federal de Juiz de Fora
+Contents
+1
+Appendix - Feynman diagrams
+1
+1
+Appendix - Feynman diagrams
+In this appendix we present the set of Feynman diagrams associated with corrections
+for the propagator and vertices. Here we assumed the sum over the diagrams of the same
+topology, but with di↵erent permutations of the external momenta.
+�(3)
+⇣2 ⇠
+Figure 1: Diagrams for the three-point function with the interaction vertex ⇣2.
+�(4)
+⇣2 ⇠
+Figure 2: Diagrams for the four-point function with the interaction vertex ⇣2.
+∗E-mail address: wagnorion@gmail.com
+Figure 9: Diagrams for the three-point function with the interaction vertex ζ2.
+�(3)
+�⇣ ⇠
+Figure 3: Diagrams for the three-point functions with the interaction vertex �⇣.
+�(4)
+�⇣ ⇠
+Figure 4: Diagrams for the four-point functions with the interaction vertex �⇣.
+2
+Figure 10: Diagrams for the three-point function with the interaction vertex γζ.
+�(3)
+�2 ⇠
+Figure 5: Diagrams for the three-point function with the interaction vertex �2.
+�(4)
+�2 ⇠
+Figure 6: Diagrams for the four-point function with the interaction vertex �2.
+3
+Figure 11: Diagrams for the three-point function with the interaction vertex γ2.
+23
+
+In the dimensional regularization scenario, these corrections are given by following
+integrals,
+Γ(3)
+ζ2 (p, r)
+��(2ω)
+=
+−
+4ζ2
+θ4(m2 − M 2)2
+�
+d2ωk
+(2π)2ω Γ(3,4)
+ζ2
+�
+2
+(k2 − m2)
+�
+(k − p)2 − M 2�
+−
+1
+(k2 − m2)
+�
+(k − p)2 − m2� −
+1
+(k2 − M 2)
+�
+(k − p)2 − M 2�
+�
++ t- and u-channel contributions,
+(62)
+Γ(3)
+γζ (p, r)
+��(2ω)
+=
+2γζ
+θ4(m2 − M 2)2
+�
+d2ωk
+(2π)2ω
+�
+Γ(3,4)
+γζ
++ Γ(3,4)
+ζγ
+��
+2
+(k2 − m2)
+�
+(k − p)2 − M 2�
+−
+1
+(k2 − m2)
+�
+(k − p)2 − m2� −
+1
+(k2 − M 2)
+�
+(k − p)2 − M 2�
+�
++ t- and u-channel contributions
+(63)
+and
+Γ(3)
+γ2 (p, r)
+��(2ω)
+=
+−
+γ2
+θ4(m2 − M 2)2
+�
+d2ωk
+(2π)2ω Γ(3,4)
+γ2
+�
+2
+(k2 − m2)
+�
+(k − p)2 − M 2�
+−
+1
+(k2 − m2)
+�
+(k − p)2 − m2� −
+1
+(k2 − M 2)
+�
+(k − p)2 − M 2�
+�
++ t- and u-channel contributions,
+(64)
+where the combinations of the vertex factors (for the s-channel diagrams) are
+Γ(3,4)
+ζ2
+= −2
+�
+k2(p · r) − k2r2 − 2(k · p − k · r)(p · r − k · r) − p2(k · r) + r2(k · p)
+�
+×
+�
+(p · k)2 − p2k2�
+,
+Γ(3,4)
+γζ
++ Γ(3,4)
+ζγ
+= 4
+�
+(k · p)2 − k2p2��
+k2 − k · p + p2 − p · r + r2�
+− 2
+�
+k2(p · r − r2)
+−p2(k · r) − 2(k · r)(k · r − p · r) + r2(k · p) + 2(k · p)(k · r − p · r)
+�
+×
+�
+k2 − k · p + p2�
+,
+Γ(3,4)
+γ2
+= 4
+�
+k2 − (k · p) + p2��
+k2 − k · p + p2 − p · r + r2�
+.
+(65)
+Taking these integrals, we write the contributions to the three-point function as
+Γ(3)
+ζ2 (p, r)
+=
+iζ2
+(4π)2θ4
+�
+20
+�
+(p · r)2 − p2r2��1
+ϵ + ln
+� µ2
+m2
+��
++ α(3)
+ζ2 (p, r) ln (1 + 4b)
++ ξ(3)
+ζ2 (p, r) +
+�
+β(3)
+ζ2, light(p, r) ln
+�1 + c
+1 − c
+�
++ β(3)
+ζ2, ghost(p, r) ln
+�1 + d
+1 − d
+�
++ β(3)
+ζ2, mixed(p, r) ln
+�(A + 1)2 − (ab)2
+(A − 1)2 − (ab)2
+�
++ (p ↔ −r) + (p ↔ r − p)
+��
+,
+(66)
+24
+
+Γ(3)
+γζ (p, r)
+=
+−
+iγζ
+(4π)2θ4
+�
+6
+�
+p2 + r2 − (p · r)
+��1
+ϵ + ln
+� µ2
+m2
+��
++ α(3)
+γζ (p, r) ln (1 + 4b)
++ ξ(3)
+γζ (p, r) +
+�
+β(3)
+γζ, light(p, r) ln
+�1 + c
+1 − c
+�
++ β(3)
+γζ, ghost(p, r) ln
+�1 + d
+1 − d
+�
++ β(3)
+γζ, mixed(p, r) ln
+�(A + 1)2 − (ab)2
+(A − 1)2 − (ab)2
+�
++ (p ↔ −r) + (p ↔ r − p)
+��
+,
+(67)
+Γ(3)
+γ2 (p, r)
+=
+iγ2
+(4π)2θ4
+�
+12
+�1
+ϵ + ln
+� µ2
+m2
+��
++ α(3)
+γ2 (p, r) ln (1 + 4b) + ξ(3)
+γ2 (p, r)
++
+�
+β(3)
+γ2, mixed(p, r) ln
+�(A + 1)2 − (ab)2
+(A − 1)2 − (ab)2
+�
++ β(3)
+γ2, light(p, r) ln
+�1 + c
+1 − c
+�
++ β(3)
+γ2, ghost(p, r) ln
+�1 + d
+1 − d
+�
++ (p ↔ −r) + (p ↔ r − p)
+��
+,
+(68)
+where α’s, β’s and ξ’s are coefficients with polynomial dependencies on the external mo-
+menta. The full explicit form of these expressions are very bulky and we do not present
+them here. On the other hand, since they are polynomials the corresponding contributions
+are local and these explicit expression is not really important for our analysis. Remember
+that the notations a, b, A, c, d are defined in (37), (38) and (39), respectively.
+It is important that the most essential, non-local parts of the expressions have standard
+logarithmic structures, similar to those already evaluated in section 4. Therefore, it should
+be expected that the corrections above represent asymptotic behavior in the IR, similar to
+the case of the propagator corrections considered in the main part of the paper. Let us note
+that we verified and confirmed the quadratic decoupling of the heavy mode in the vertex
+terms. Furthermore, the same behavior is observed for the four-point vertex corrections.
+In this case, the diagrams of interest are depicted in Figures 12, 13 and 14.
+On decoupling in higher-derivative models (draft)
+Wagno Cesar ∗
+Departamento de F´ısica, ICE, Universidade Federal de Juiz de Fora
+Contents
+1
+Appendix - Feynman diagrams
+1
+1
+Appendix - Feynman diagrams
+In this appendix we present the set of Feynman diagrams associated with corrections
+for the propagator and vertices. Here we assumed the sum over the diagrams of the same
+topology, but with di↵erent permutations of the external momenta.
+�(3)
+⇣2 ⇠
+Figure 1: Diagrams for the three-point function with the interaction vertex ⇣2.
+�(4)
+⇣2 ⇠
+Figure 2: Diagrams for the four-point function with the interaction vertex ⇣2.
+∗E-mail address: wagnorion@gmail.com
+Figure 12: Diagrams for the four-point function with the interaction vertex ζ2.
+�(3)
+�⇣ ⇠
+Figure 3: Diagrams for the three-point functions with the interaction vertex �⇣.
+�(4)
+�⇣ ⇠
+Figure 4: Diagrams for the four-point functions with the interaction vertex �⇣.
+2
+Figure 13: Diagrams for the four-point function with the interaction vertex γζ.
+25
+
+�(3)
+�2 ⇠
+Figure 5: Diagrams for the three-point function with the interaction vertex �2.
+�(4)
+�2 ⇠
+Figure 6: Diagrams for the four-point function with the interaction vertex �2.
+3
+Figure 14: Diagrams for the four-point function with the interaction vertex γ2.
+The analytic expressions corresponding to these diagrams are
+Γ(4)
+ζ2 (p, r, q)
+��(2ω)
+=
+−
+8ζ2
+θ4(m2 − M 2)2
+�
+d2ωk
+(2π)2ω Γ(4,4)
+ζ2
+�
+2
+(k2 − m2)
+�
+(k − p)2 − M 2�
+−
+1
+(k2 − m2)
+�
+(k − p)2 − m2� −
+1
+(k2 − M 2)
+�
+(k − p)2 − M 2�
+�
++ t- and u-channel contributions,
+(69)
+Γ(4)
+γζ (p, r, q)
+��(2ω)
+=
+4γζ
+θ4(m2 − M 2)2
+�
+d2ωk
+(2π)2ω Γ(4,4)
+γζ
+�
+2
+(k2 − m2)
+�
+(k − p)2 − M 2�
+−
+1
+(k2 − m2)
+�
+(k − p)2 − m2� −
+1
+(k2 − M 2)
+�
+(k − p)2 − M 2�
+�
++ t- and u-channel contributions,
+(70)
+Γ(4)
+γ2 (p, r, q)
+��(2ω)
+=
+−
+2γ2
+θ4(m2 − M 2)2
+�
+d2ωk
+(2π)2ω Γ(4,4)
+γ2
+�
+2
+(k2 − m2)
+�
+(k − p)2 − M 2�
+−
+1
+(k2 − m2)
+�
+(k − p)2 − m2� −
+1
+(k2 − M 2)
+�
+(k − p)2 − M 2�
+�
++ t- and u-channel contributions,
+(71)
+where, for the s-channel diagrams,
+Γ(4,4)
+ζ2
+=
+�
+r2(k · q) − k2(r · q) + 2(k · q)
+�
+r · q
+�
++ q2(k · r) − 2(k · r)
+�
+k · q − r · q
+��
+×
+�
+k2�
+p2 − p · r − p · q
+�
+− p2(k · r + k · q) + 2(k · r + k · q)(p · r + p · q)
++(r2 + q2)(k · p) − 2(k · p)
+�
+k · r + k · q + p · r + p · q − r · q
+�
++ 2(k · p)2�
+,
+Γ(4,4)
+γζ
+= −2
+�
+k2(r · q) − r2(k · q) − 2(k · q)
+�
+r · q
+�
++ 2(k · r)
+�
+k · q − r · q
+�
+− q2(k · r)
+�
+×
+�
+k2 − k · r − k · q + p2 − p · r − p · q + r2 + 2(r · q) + q2�
+,
+Γ(4,4)
+γ2
+= 4
+�
+k2 − k · r − k · q + p2 − p · r − p · q + r2 + 2(r · q) + q2�
+×
+�
+k2 − k · r − k · q + r2 + r · q + q2�
+.
+(72)
+26
+
+The analytic expressions of the four-point vertex corrections involving the couplings ζ2, γζ
+and γ2 are, respectively,
+Γ(4)
+ζ2 (p, r, q)
+=
+−
+iζ2
+(4π)2θ4
+�
+20
+�
+p2(r · q) − r2(p · q) − 2(p · q)(r · q) − q2(p · r)
++ 2(p · r)
+�
+p · q − r · q
+���1
+ϵ + ln
+� µ2
+m2
+��
++ α(4)
+ζ2 (p, r, q) ln (1 + 4b)
++ β(4, s)
+ζ2, mixed(p, r, q) ln
+�(A + 1)2 − (ab)2
+(A − 1)2 − (ab)2
+�����
+p↔r+q
++ ξ(4)
+ζ2 (p, r, q)
++ β(4, s)
+ζ2, light(p, r, q) ln
+�1 + c
+1 − c
+�����
+p↔r+q
++ β(4, s)
+ζ2, ghost(p, r, q) ln
+�1 + d
+1 − d
+�����
+p↔r+q
++ β(4, t)
+ζ2, light(p, r, q) ln
+�1 + c
+1 − c
+�����
+p↔q−p
++ β(4, t)
+ζ2, ghost(p, r, q) ln
+�1 + d
+1 − d
+�����
+p↔q−p
++ β(4, t)
+ζ2, mixed(p, r, q) ln
+�(A + 1)2 − (ab)2
+(A − 1)2 − (ab)2
+�����
+p↔q−p
++ β(4, u)
+ζ2, light(p, r, q) ln
+�1 + c
+1 − c
+�����
+p↔r−p
++ β(4, u)
+ζ2, ghost(p, r, q) ln
+�1 + d
+1 − d
+�����
+p↔r−p
++ β(4, u)
+ζ2, mixed(p, r, q) ln
+�(A + 1)2 − (ab)2
+(A − 1)2 − (ab)2
+�����
+p↔r−p
+�
+,
+(73)
+Γ(4)
+γζ (p, r, q)
+=
+iγζ
+(4π)2θ4
+�
+12(p · r + p · q − r · q)
+�1
+ϵ + ln
+� µ2
+m2
+��
++ ξ(4)
+γζ (p, r, q)
++ α(4)
+γζ (p, r, q) ln (1 + 4b) + β(4, s)
+γζ, light(p, r, q) ln
+�1 + c
+1 − c
+�����
+p↔r+q
++ β(4, s)
+γζ, mixed(p, r, q) ln
+�(A + 1)2 − (ab)2
+(A − 1)2 − (ab)2
+�����
+p↔r+q
++ β(4, s)
+γζ, ghost(p, r, q) ln
+�1 + d
+1 − d
+�����
+p↔r+q
++ β(4, t)
+γζ, light(p, r, q) ln
+�1 + c
+1 − c
+�����
+p↔q−p
++ β(4, t)
+γζ, mixed(p, r, q) ln
+�(A + 1)2 − (ab)2
+(A − 1)2 − (ab)2
+�����
+p↔q−p
++ β(4, t)
+γζ, ghost(p, r, q) ln
+�1 + d
+1 − d
+�����
+p↔s−p
++ β(4, u)
+γζ, light(p, r, q) ln
+�1 + c
+1 − c
+�����
+p↔r−p
++ β(4, u)
+γζ, mixed(p, r, q) ln
+�(A + 1)2 − (ab)2
+(A − 1)2 − (ab)2
+�����
+p↔r−p
++ β(4, u)
+γζ, ghost(p, r, q) ln
+�1 + d
+1 − d
+�����
+p↔r−p
+�
+(74)
+27
+
+and
+Γ(4)
+γ2 (p, r, q)
+=
+iγ2
+(4π)2θ4
+�
+24
+�1
+ϵ + ln
+� µ2
+m2
+��
++ α(4)
+γ2 (p, r, q) ln (1 + 4b) + ξ(4)
+γ2 (p, r, q)
++ β(4, s)
+γ2, light(p, r, q) ln
+�1 + c
+1 − c
+�����
+p↔r+q
++ β(4, s)
+γ2, ghost(p, r, q) ln
+�1 + d
+1 − d
+�����
+p↔r+q
++ β(4, s)
+γ2, mixed(p, r, q) ln
+�(A + 1)2 − (ab)2
+(A − 1)2 − (ab)2
+�����
+p↔r+q
++ β(4, t)
+γ2, light(p, r, q) ln
+�1 + c
+1 − c
+�����
+p↔q−p
++ β(4, t)
+γ2, ghost(p, r, q) ln
+�1 + d
+1 − d
+�����
+p↔q−p
++ β(4, t)
+γ2, mixed(p, r, q) ln
+�(A + 1)2 − (ab)2
+(A − 1)2 − (ab)2
+�����
+p↔q−p
++ β(4, u)
+γ2, light(p, r, q) ln
+�1 + c
+1 − c
+�����
+p↔r−p
++ β(4, u)
+γ2, ghost(p, r, q) ln
+�1 + d
+1 − d
+�����
+p↔r−p
++ β(4, u)
+γ2, mixed(p, r, q) ln
+�(A + 1)2 − (ab)2
+(A − 1)2 − (ab)2
+�����
+p↔r−p
+�
+.
+(75)
+The indices in the coefficients β(4)(p, r, q) denote s−, t− and u−channel contributions.
+It is easy to note that these expressions are in a good qualitative agreement with the
+self-energy corrections and ones for the three-point vertices.
+References
+[1] I. Antoniadis and E. Mottola, Four-dimensional quantum gravity in the conformal
+sector, Phys. Rev. D45 (1992) 2013.
+[2] E.V. Gorbar and I.L. Shapiro, Renormalization group and decoupling in curved space,
+JHEP 02 (2003) 021, hep-ph/0210388.
+[3] I.L. Shapiro, J. Sol`a, On the possible running of the cosmological ’constant’, Phys.
+Lett. B682 (2009) 105, hep-th/0910.4925.
+[4] T. Appelquist and J. Carazzone, Infrared singularities and massive fields, Phys. Rev.
+D11 (1975) 2856.
+[5] E.V. Gorbar and I.L. Shapiro, Renormalization group and decoupling in curved space,
+II. The standard model and beyond, JHEP 06 (2003) 004, hep-ph/0303124.
+[6] A. Codello and O. Zanusso, On the non-local heat kernel expansion, J. Math. Phys.
+54 (2013) 013513, arXiv:1203.2034.
+28
+
+[7] S.A. Franchino-Vi˜nas, T. de Paula Netto, I.L. Shapiro, and O. Zanusso, Form factors
+and decoupling of matter fields in four-dimensional gravity, Phys. Lett. B790 (2019)
+229, arXiv:1812.00460;
+S. A. Franchino-Vi˜nas, T. de Paula Netto, and O. Zanusso, Vacuum effective ac-
+tions and mass-dependent renormalization in curved space, Universe 5 (2019) 67,
+arXiv:1902.03167.
+[8] S.A. Franchino-Vi˜nas, Resummed heat-kernel for surface contributions:
+Dirichlet
+semitransparent boundary conditions, arXiv:2208.11979.
+[9] G.B. Peixoto, E.V. Gorbar and I.L. Shapiro, On the renormalization group for the
+interacting massive scalar field theory in curved space, Class. Quant. Grav. 21 (2004)
+2281, hep-th/0311229.
+[10] S.D. Odintsov and I.L. Shapiro, Perturbative approach to induced quantum gravity,
+Class. Quant. Grav. 8 (1991), L57-60.
+[11] R.J. Riegert, A non-local action for the trace anomaly, Phys. Lett. B134 (1984) 56.
+[12] E.S. Fradkin and A.A. Tseytlin, Conformal anomaly in Weyl theory and anomaly free
+superconformal theories, Phys. Lett. B134 (1984) 187.
+[13] M.J. Duff, Twenty years of the Weyl anomaly, Class. Quant. Grav. 11 (1994) 1387,
+hep-th/9308075.
+[14] I.L. Buchbinder and I.L. Shapiro, Introduction to Quantum Field Theory with Appli-
+cations to Quantum Gravity (Oxford University Press, 2021).
+[15] K.S. Stelle, Renormalization of higher derivative quantum gravity, Phys. Rev. D16
+(1977) 953.
+[16] M. Asorey, J.L. L´opez, and I.L. Shapiro, Some remarks on high derivative quantum
+gravity, Int. Journ. Mod. Phys. A12 (1997) 5711, hep-th/9610006.
+[17] E.S. Fradkin and A.A. Tseytlin, Renormalizable asymptotically free quantum theory
+of gravity, Nucl. Phys. B201 (1982) 469.
+[18] I.G. Avramidi and A.O. Barvinsky, Asymptotic freedom In higher derivative quantum
+gravity, Phys. Lett. B159 (1985) 269.
+[19] I.L. Shapiro and A.G. Jacksenaev, Gauge dependence in higher derivative quantum
+gravity and the conformal anomaly problem, Phys. Lett. B324 (1994) 286.
+29
+
+[20] L. Modesto, L. Rachwa�l, I.L. Shapiro, Renormalization group in super-renormalizable
+quantum gravity, Eur. Phys. J. C78 (2018) 555, arXiv:1704.03988.
+[21] J.F. Donoghue, Leading quantum correction to the Newtonian potential, Phys. Rev.
+Lett. 72 (1994) 2996, gr-qc/9310024; General relativity as an effective field theory:
+The leading quantum corrections, Phys. Rev. D50 (1994) 3874, gr-qc/9405057.
+[22] E. Mottola, Scalar gravitational waves in the effective theory of gravity, JHEP 07
+(2017) 043; Erratum: JHEP 09 (2017) 107, arXiv:1606.09220.
+[23] M. Asorey, E.V. Gorbar and I.L. Shapiro, Universality and ambiguities of the confor-
+mal anomaly, Class. Quant. Grav. 21 (2004) 163, hep-th/0307187.
+[24] M. Asorey, G. de Berredo-Peixoto and I.L. Shapiro, Renormalization ambiguities and
+conformal anomaly in metric-scalar backgrounds, Phys. Rev. D74 (2006) 124011, hep-
+th/0609138.
+[25] M. Asorey, W. Cesar e Silva, I.L. Shapiro and P.R.B. do Vale, Trace anomaly and
+induced action for a metric-scalar background, arXiv:2202.00154.
+[26] A.M. Polyakov, Quantum geometry of bosonic strings, Phys. Lett. B103 (1981) 207.
+[27] I.L. Shapiro and G. Cognola, Interaction of low-energy induced gravity with quantized
+matter and phase transition induced to curvature, Phys. Rev. D51 (1995) 2775, hep-
+th/9406027.
+[28] A.O. Barvinsky and G.A. Vilkovisky, The generalized Schwinger-DeWitt technique in
+gauge theories and quantum gravity, Phys. Repts. 119 (1985) 1.
+[29] I. Antoniadis and S.D. Odintsov, Renormalization group and logarithmic corrections
+to scaling relations in the conformal sector of 4D gravity, Phys. Lett. B343 (1995) 76,
+arXiv:hep-th/9411012.
+[30] P. Creminelli, A. Nicolis, M. Papucci and E. Trincherini, Ghosts in massive gravity,
+JHEP 0509 (2005) 003, hep-th/0505147.
+[31] J. Julve and M. Tonin, Quantum gravity with higher derivative terms, Nuovo Cim.
+B46 (1978) 137.
+[32] G. Leibbrandt, Introduction to the Technique of Dimensional Regularization, Rev.
+Mod. Phys. 47 (1975) 849.
+30
+
+[33] H.H. Patel, Package-X: A Mathematica package for the analytic calculation of one-loop
+integrals, Comput. Phys. Commun. 197 (2015) 276, arXiv:1503.01469.
+[34] Wolfram Research, Inc., Mathematica, (Version 12.0, Champaign, IL, 2019).
+[35] J.C. Collins, Renormalization (Cambridge University Press, 1984).
+[36] M.E. Peskin and D.V. Schroeder, An Introduction to Quantum Field Theory (West-
+view Press, 1995).
+[37] C.P. Burgess, Quantum gravity in everyday life: General relativity as an effective field
+theory, Living Rev. Rel. 7 (2004) 5, gr-qc/0311082.
+[38] S. Weinberg, The cosmological constant problem, Rev. Mod. Phys. 61 (1989) 1.
+[39] I.L. Shapiro, J. Sol`a, Scaling behavior of the cosmological constant: Interface between
+quantum field theory and cosmology, JHEP 02 (2002) 006, hep-th/0012227.
+[40] T. Padmanabhan, Cosmological constant—the weight of the vacuum, Phys. Rep. 380
+(2003) 235, arXiv:hep-th/0212290.
+[41] V. Sahni and A.A. Starobinsky, Reconstructing Dark Energy, Int. J. Mod. Phys. D 15
+(2006) 2105, astro-ph/0610026.
+[42] I. Antoniadis, P.O. Mazur and E. Mottola, Scaling behavior of quantum four-
+geometries, Phys. Lett. B323 (1994) 284, arXiv:hep-th/9301002.
+[43] E. Elizalde, A.G. Jacksenaev, S.D. Odintsov and I.L. Shapiro, One-loop renormaliza-
+tion and asymptotic behaviour of a higher-derivative scalar theory in curved spacetime,
+Phys. Letters B328 (1994) 297, hep-th/9402154; A four-dimensional theory for quan-
+tum gravity with conformal and non-conformal explicit solutions, Class. Quant. Grav.
+12 (1995) 1385, hep-th/9412061.
+[44] G. de Berredo-Peixoto and I.L. Shapiro, Higher derivative quantum gravity with Gauss-
+Bonnet term, Phys. Rev. D71 (2005) 064005, hep-th/0412249.
+[45] I.L. Shapiro, Polemic Notes On IR Perturbative Quantum Gravity, Int. J. Mod. Phys.
+A24 (2009) 1557, arXiv:0812.3521.
+[46] T.G. Ribeiro and I.L. Shapiro Scalar model of effective field theory in curved space,
+JHEP 2019 (2019) 163, arXiv:1908.01937.
+[47] E.V. Gorbar and I,L. Shapiro, Nonlocality of quantum matter corrections and cosmo-
+logical constant running, JHEP 103 (2022) 103, arXiv:2203.09232.
+31
+
+[48] A. Accioly, B.L. Giacchini and I.L. Shapiro, On the gravitational seesaw in higher-
+derivative gravity, Eur. Phys. J. C77 (2017) 540, gr-qc/1604.07348.
+[49] N.V. Krasnikov, Nonlocal gauge theories, Theor. Math. Phys. 73 (1987) 1184.
+[50] Y.V. Kuz’min, The convergent nonlocal gravitation (in Russian), Yad. Fiz. 50 (1989)
+1630; [Sov. J. Nucl. Phys. 50 (1989) 1011].
+[51] E.T.
+Tomboulis,
+Superrenormalizable
+gauge
+and
+gravitational
+theories,
+hep-
+th/9702146;
+Nonlocal and quasilocal field theories, Phys. Rev. D92 (2015) 125037,
+arXiv:1507.00981.
+[52] L. Modesto, Super-renormalizable quantum gravity, Phys. Rev. D86 (2012) 044005,
+arXiv:1107.2403; L. Modesto and L. Rachwa�l, Super-renormalizable and finite gravi-
+tational theories, Nucl. Phys. B889 (2014) 228, arXiv:1407.8036; Nonlocal quantum
+gravity: A review, Int. J. Mod. Phys. D26 (2017) 1730020.
+[53] I.L. Shapiro, Counting ghosts in the “ghost-free” non-local gravity. Phys. Lett. B744
+(2015) 67, arXive:1502.00106.
+32
+
diff --git a/KNFQT4oBgHgl3EQfSzZL/content/tmp_files/load_file.txt b/KNFQT4oBgHgl3EQfSzZL/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..23034747d6252141591f3878864b17f279aa8249
--- /dev/null
+++ b/KNFQT4oBgHgl3EQfSzZL/content/tmp_files/load_file.txt
@@ -0,0 +1,1015 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf,len=1014
+page_content='Effective approach to the Antoniadis-Mottola model:  quantum decoupling of the higher derivative terms  Wagno Cesar e Silva ∗  and  Ilya L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Shapiro†  Departamento de F´ısica, ICE, Universidade Federal de Juiz de Fora,  36036-900, Juiz de Fora, Minas Gerais, Brazil  Abstract  We explore the decoupling of massive ghost mode in the 4D (four-dimensional) theory  of the conformal factor of the metric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' The model was introduced by Antoniadis and  Mottola in [1] and can be regarded as a close analog of the fourth-derivative quantum  gravity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' The analysis of the derived one-loop nonlocal form factors includes their  asymptotic behavior in the UV and IR limits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' In the UV (high energy) domain, our  results reproduce the Minimal Subtraction scheme-based beta functions of [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' In  the IR (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=', at low energies), the diagrams with massive ghost internal lines collapse  into tadpole-type graphs without nonlocal contributions and become irrelevant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' On  the other hand, those structures that contribute to the running of parameters of  the action and survive in the IR, are well-correlated with the divergent part (or  the leading in UV contributions to the form factors), coming from the effective low-  energy theory of the conformal factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' This effective theory describes only the light  propagating mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Finally, we discuss whether these results may shed light on the  possible running of the cosmological constant at low energies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  Keywords:  Higher derivatives, quantum gravity, massive ghosts, cosmological con-  stant, decoupling, conformal anomaly  1  Introduction  The running of the cosmological constant at low energies represents an interesting  alternative to the numerous models of Dark Energy, as it provides the equation of state  which is close, but not identical to the ωΛ = −1, of the cosmological constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' On the  other hand, there is no full understanding of whether such a running is possible or not,  such that this issue remains uncertain and is a subject of phenomenological considerations,  as discussed in [2, 3] and many subsequent works.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' The main difficulty for the thorough  ∗E-mail address: wagnorion@gmail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='com  †E-mail address: ilyashapiro2003@ufjf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='br  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='13291v1  [hep-th]  30 Jan 2023  theoretical investigation is that the traditional approach to quantum decoupling [4] implies  calculating the nonlocal form factor (or its equivalent) and taking its low-energy limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' The  cosmological constant acquires physical sense only in curved spacetime and, in principle,  the corresponding form factors have to be built from covariant elements and analysed  in curved space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' According to the Appelquist-Carazzone theorem [4], heavy degrees of  freedom decouple in the IR regime, and their loop corrections are quadratically suppressed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  The same effect should hold in curved spacetime, leading to the corresponding decoupling  theorems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  The described program has been fulfilled in a series of papers [2,5–7] where the nonlocal  form factors in the vacuum (gravitational) actions were calculated and analysed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  The  problem is that, these nonlocal form factors describe the decoupling, but only for the  fourth-derivative terms in the action.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Owing to covariance, the form factors depend on the  d’Alembertian operator □.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' The positive powers of this operator give zero when acting on  the cosmological constant and produce surface terms when acting on the scalar curvature  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Let us note that part of the mentioned papers, Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' [6, 7], include the discussion of  the form factors of surface terms (see [8] for the latest discussions of the mathematical  aspects of the problem), and there may be even interesting applications of the running of  Newton constant, related to these surface terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' However, it is unclear how one can gain  information about the running of the cosmological constant in the traditional covariant  framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  The situation changes dramatically if we perform a conformal transformation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  For  instance, using the parametrization  gµν = φ2  M 2 exp  �¯hµν  �  ,  exp  �¯hµν  �  = ηµν + ¯hµν + 1  2  ¯hµλ¯hλ  ν + 1  3!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  ¯hµλ¯hλ  τ¯hτ  ν + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' ,  (1)  with the traceless ¯hµν and constant scale parameter M, transforms the cosmological con-  stant term √−g into φ4 plus φ4¯hn-vertices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' It is known that there is no problem to find  nonlocal form factor and verify IR decoupling for the φ4-term in the scalar theory [9] and  one should expect this to be equally easy in the gravitational version of the theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  Unfortunately, the described approach does not constitute a comprehensive solution  of the problem of the running cosmological constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  In particular, it is not obvious  that such a non-covariant running will preserve the structure of the φ4¯hn-vertices, such  that the running can be safely attributed to the cosmological constant and not to the  artificial scheme of reparametrization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Anyway, the running of the cosmological term in  the 4D (four-dimensional) theory of the conformal factor of the metric is an attractive  object of study, starting from the first proposal [10] and its realization by Antoniadis and  Mottola [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' The model of quantum conformal factor follows the idea to perform secondary  quantization of the anomaly induced effective action of vacuum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' This action appears as  2  a result of integrating conformal anomaly [11, 12] coming from the quantum effects of  matter fields (see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=', [13] for the review or [14] for the textbook level introduction).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' The  simplest realization of the anomaly induced action is a theory of a single scalar field with  fourth derivatives, on a flat background.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' This procedure corresponds “switching off” the  ¯hµν-mode in the parametrization (1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  In the paper [1] it was shown that such a model, with additional Einstein-Hilbert and  cosmological terms, is renormalizable and, in particular, describes the running of the cos-  mological term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' The remaining question is whether this running holds in the low energy  domain or only in the UV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Indeed, this is a general question that is quite relevant for all  higher derivative models of quantum gravity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' These models may be renormalizable [15],  or even superrenormalizable [16] and this enables one to consistently derive the renor-  malization group equations for the effective charges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' In the 4D case, the beta functions  are partially ambiguous [17–19], while in the six- or higher-derivative models, all beta  functions do not depend on the gauge fixing conditions [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' However, in which physical  situations the corresponding running can be applied?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' The one-loop corrections behind the  beta functions come from the three different types of diagrams: (i) with internal lines of  the massless degrees of freedom (gravitons);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' (ii) with internal lines of massive components,  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=', higher derivative ghosts (or ghost-like states, ghost tachyons, etc) and normal degrees  of freedom, typical for the superrenormalizable models;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  (iii) with mixed (massless and  massive) internal lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' The standard approach to effective quantum gravity [21] assumes  that only the first type of diagrams survives and gives relevant contributions in the IR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  As with all reasonable assumptions, this one has to be verified.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' And, in this respect, the  theory of quantum conformal factor [1] represents a perfect toy model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' The Lagrangian  of this theory includes non-polynomial interactions in four-derivative, two-derivative and  zero-derivative sectors, exactly as the fourth derivative quantum gravity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' This means, the  general structure of the relevant diagrams includes all the aforementioned (i), (ii) and  (iii)-types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Regardless the calculation of the form factors in the momentum subtraction  scheme in the theory [1] are rather involved (as the reader may see in what follows), they  are still alleviated compared to the ones in a full version of quantum gravity, where one has  to face more extensive set of degrees of freedom and complicated tensor structures, typical  for diagrammatic treatment of quantum gravity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  In the present work we report on the derivation of nonlocal form factors in the fourth-  derivative model of quantum conformal factor and perform the analysis of the UV and  IR asymptotic behaviour of these quantum corrections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' It is important to note that the  effective approach to the theory of conformal factor induced by anomaly has an independent  interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' In the recent paper [22], it was shown that this theory provides, in the effective  approach, a propagation of a scalar mode of the gravitational field, which is not present  3  in GR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' In our opinion, the investigation of quantum IR decoupling is useful for a better  general understanding of this model in the effective framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  The paper is organized as follows: In sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' 2, we briefly review the four-derivative  model for the conformal factor and present the derivation of its UV divergences using  the heat-kernel method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' The corresponding expression will be used, in what follows, as  a reference to verify the main result in the UV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' In sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' 3, we formulate the elements  of Feynman technique, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=', the propagator and vertices for the model, and consider the  diagrams producing ultraviolet (UV) divergences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Furthermore, we derive the one-loop  corrections, including the nonlocal form factors in the propagator sector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Section 4 includes  a description of the asymptotic behavior of nonlocal contributions to the two-point function  in the UV and IR limits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' In sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' 5 we discuss the connection between the momentum  dependence in the IR regime of the fundamental theory and the divergences in the effective  low-energy model containing only the light (massless) mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' As usual in massless theories,  the divergences define not only UV, but also the IR behaviour of the theory and can be  used for comparison with the IR limit of the full theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' In Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' 6 we present a discussion  of the implications of the IR decoupling for the cosmological constant problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Finally,  in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' 7, we draw our conclusions and discuss the possibilities of a subsequent work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' The  three Appendices complement the main text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' In the Appendix A, one can find the set of the  Feynman diagrams used in our calculations, while in Appendix B, we collect intermediate  formulas concerning the calculation of Feynman integrals in dimensional regularization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' In  the Appendix C we present the complete expressions of the one-loop quantum corrections  to the three- and four-point vertices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  The notations include the Minkowski signature (+, −, −, −).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Also, to reduce the size of  the formulas, we avoid indicating the +iϵ in the denominators of the propagators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Indeed,  the loop calculations were performed in Euclidean signature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  2  The model  Let us start with a brief review of the model which we shall use in the present work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  The action of the model is the simplest form of the solution of the anomaly-induced action  [11,12], with the flat fiducial metric, plus the Einstein-Hilbert and cosmological terms,  Scf =  �  d4x  �  2b(□σ)2 − (2w + 2b + 3c)  �  □σ + (∂σ)2�2 + 3  κe2σ(∂σ)2 − Λ  κ e4σ  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  (2)  4  Here κ = 8πG and the coefficients w, b and c are the one-loop semiclassical beta functions  in the vacuum sector,  w =  1  120(4π)2(Ns + 6Nf + 12Nv),  b = −  1  360(4π)2(Ns + 11Nf + 62Nv),  c =  1  180(4π)2(Ns + 6Nf − 18Nv),  (3)  where Ns, Nf, Nv are the multiplicities of the quantum conformal matter fields of spins  zero, one-half and one, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' The trace anomaly which produces the induced part  of the action (2) is  ⟨T µ  µ⟩ = −  �  wC2 + bE4 + c □R  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  (4)  The coefficient c can be modified by adding a finite local term R2 to the action Sanom (see  [13,23–25] for detailed discussion).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' This feature will not affect our considerations, especially  because we will not need particular versions of the beta functions (3) and concentrate on  the general features of the quantum theory of conformal factor based on (2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  On top of induced part, the action includes Einstein-Hilbert and cosmological terms,  which are not renormalized at the initial semiclassical theory, but become very relevant at  the second stage, when we quantize the conformal factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  The idea that the conformal factor can be quantum, despite it emerges as an effective  mode in the integration of matter fields, comes from Polyakov’s approach in 2D, related to  string theory [26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' The idea of using the equivalent metric-scalar (Liouville) model as the  basis of 2D quantum gravity was quite popular in 90-s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' The use of the analogous theory  (in curved spacetime) as a model for 4D quantum gravity was proposed in [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' In four  dimensions, the theory for the conformal factor can be regarded as a truncated version of  the four-derivative quantum gravity at large distances (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=', for the low energies, or IR),  providing a screening mechanism for the cosmological constant [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' An important difference  with the 2D induced gravity is that, in 4D one can add the classical terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Alternatively,  one can make the Einstein-Hilbert and cosmological terms to be generated in the scheme  of induced gravity [27], but this requires an independent scalar field and does not fit our  purpose to construct a simplified model to explore the decoupling in a higher derivative  quantum gravity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  As any fourth-derivative quantum gravity model, the model of our interest has massive  modes, which can be ghosts and tachyonic ghosts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' The question of our interest is what  happens with the contributions of these massive modes at low energies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  5  It proves useful to introduce notations similar to [1],  θ2 ≡ (2w + 3c),  ζ ≡  �  2w + 2b + 3c  �  ,  γ ≡ 3  κ ,  and  λ ≡ Λ  κ ,  (5)  such that the action (2) becomes  Scf  =  �  d4x  �  −θ2(□σ)2 − ζ  �  2(∂σ)2□σ + (∂σ)4�  + γ e2σ(∂σ)2 − λ e4σ�  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  (6)  The last two terms in (6) come from the Einstein-Hilbert and cosmological constant  terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' In the IR, these terms dominate over the higher derivative terms and it proves  useful to split the Lagrangian into two terms, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=',  LIR = γe2σ(∂σ)2 − λe4σ  (7)  and  L4der = −θ2(□σ)2 − ζ  �  2(∂σ)2□σ + (∂σ)4�  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  (8)  Our plan is to evaluate the quantum corrections in full theory (6) and, separately, for  the theory based on the IR-term (7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Due to the presence of higher derivative terms, the  one-loop divergences in the full theory are obtained using the generalized Schwinger-DeWitt  technique [17,28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  Using the background field method, the conformal factor is decomposed into classical  σ and quantum ρ counterparts, σ → σ + ρ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Then we obtain the bilinear in the quantum  field forms for the two terms,  S(2)  4der  =  −  �  d4x  �  θ2(□ρ)2 + 2ζ  �  (∂ρ)2□σ + 2(∂µρ)(∂µσ)□ρ + (∂σ)2(∂ρ)2  + 2(∂µρ)(∂νρ)(∂µσ)(∂νσ)  ��  (9)  and  S(2)  IR =  �  d4x  �  γe2σ�  (∂ρ)2 + 4ρ(∂µρ)(∂µσ) + 2ρ2(∂σ)2�  − 8λρ2e4σ�  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  (10)  The Hermitian forms for the structures (9) and (10) are obtained as  δ2S(2)  4der  δρ(y)δρ(z)  =  − 2θ2□2 + 4ζ  �  2(□σ)□ − 2∂µ(∂νσ)∂µ∂ν + 4(∂νσ)∂µ(∂νσ)∂µ  + (∂σ)2□ + 2(□σ)(∂µσ)∂µ + 2(∂µσ)(∂νσ)∂µ∂ν  �  ,  δ2S(2)  IR  δρ(y)δρ(z)  =  − 2γe2σ�  □ + 2(∂µσ)∂µ + 2(∂σ)2 + 2□σ  �  − 16λe4σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  (11)  6  So, for the complete model (6), we have  δ2S(2)  δρ(y)δρ(z) = −2θ2 ˆH,  (12)  where the self-adjoint four-derivative minimal operator is  ˆH = □2 + V µν∂µ∂ν + N µ∂µ + U,  (13)  with the elements  V µν = −2ζ  θ2  �  2ηµν□σ − 2∂µ∂νσ + ηµν(∂σ)2 + 2(∂µσ)∂νσ  �  + γ  θ2e2σηµν,  N µ = −4ζ  θ2  �  2(∂νσ)∂µ∂νσ + (□σ)∂µσ  �  + 2γ  θ2 e2σ(∂µσ),  U = 2γ  θ2 e2σ�  (∂σ)2 + □σ  �  + 8λ  θ2 e4σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  (14)  Using the standard algorithm for the fourth-order operators [17, 28], we arrive at the ex-  pression for the divergences  ¯Γ(1)  div = −1  ε  �  d4x  �5ζ2  θ4  �  □σ + (∂σ)2�2 + γ  θ2  �3ζ  θ2 + 2  �  (∂σ)2e2σ −  �8λ  θ2 − γ2  2θ4  �  e4σ  �  ,  (15)  where we introduce the useful notation ε = (4π)2(n − 4) and neglect the irrelevant surface  terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' This result agrees with the previous calculations [1, 29], except for an apparent  misprint in the sign of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' (4) of [29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  In that follows, we shall confirm the expression (15) by the calculation of both divergent  and finite nonlocal (leading logarithms) parts of the Feynman diagrams.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' By considering  the minimal subtraction (MS) scheme, one can easily derive UV β-functions for the theory  (6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' In the next section, we will determine the finite parts of the one-loop diagrams that  produce these divergences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' In this case, the structure (15) will be useful in identifying the  diagrams that are relevant for our purposes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  For completeness, we also derived the divergences of the effective theory, based on the  IR-term, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' (7), separately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' The result is  ¯Γ(1)  div, IR = −1  ε  �  d4x  �1  2  �  □σ + (∂σ)2�2 − 8  3Λ e2σ(∂σ)2 + 32  9 Λ2e4σ  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  (16)  As it should be expected from the power counting, the fourth-derivative counterterms are  required in this theory, as it is non-renormalizable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' At the same time, neglecting the fourth-  derivative terms according to the effective approach, we arrive the reference expression to  compare with the IR limit of the full theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  7  3  One-loop corrections from Feynman diagrams  In a model with higher derivatives, to explore the decoupling in the loop corrections,  one has to separate massive and massless degrees of freedom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' In many cases, this can be  achieved by introducing auxiliary fields (see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=', [30]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' However, in the case of the theory  (6), this approach is not operational owing to our interest in the quantum corrections in  the theory that have higher derivatives in both kinetic terms and the interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Thus,  we shall make the separation at the level of the propagator and vertices in the Feynman  diagrams, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=', use the method close to the one of [31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  The structure of the vertices and the propagator for the fundamental theory (6) can be  calculated by using the parametrization σ → σ + ρ, where ρ is a small perturbation and  expanding the exponential terms in the power series in ρ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Collecting the quadratic terms,  we find that the propagator satisfies the equation  2  �  θ2□2 + γ□ + 8λ  �  G(x, y) = iδ4(x − y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  (17)  Making the Fourier transform,  G(x, y) =  �  d4k  (2π)2 e−ik·(x−y) �G(k)  (18)  and assuming Λ ≪ γ2/θ2, we get  �G(k) =  i  2[θ2k4 − γk2 + 8λ] ≃  i  2 θ2�  k2 − γ  θ2  ��  k2 − 8  3Λ  �.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  (19)  Finally, in the same approximation, the propagator can be written as  �G(k) =  i  2 θ2�  m2 − M 2)  �  1  k2 − m2 −  1  k2 − M 2  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  (20)  It is easy to identify a healthy degree of freedom with the mass m2 = 8Λ/3 and a ghostly  mode with the Planck-scale mass, M 2 = γ/θ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  We need to consider only those interaction vertices that are relevant for the one-loop  corrections to the propagator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' The vertices for the 3- and 4-point functions arise from  the derivative interaction terms in the part L4der and from the higher order terms in the  exponential expansion in LIR,  ζ  �  2(∂ρ)2□ρ + (∂ρ)4�  ,  2γ(∂ρ)2�  ρ + ρ2�  ,  32λ  3  �  ρ3 + ρ4�  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  (21)  8  ⇥  (a)  �  (b)  ⇤  (c)  ⇥  (d)  �  (e)  ⇤  (f)  Figure 1: Feynman diagrams associated with the interaction vertices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' The primes  denotes derivatives acting on the propagators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' 1, we have presented the vertices corresponding to these interaction terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' The  analytic expressions have the form  V (3)  ζ  (p, k, q) = −4iζ  �  p2(k · q) + q2(k · p) + k2(p · q)  �  ,  V (3)  γ (p, k, q) = 2iγ(k2 + p2 + q2),  V (3)  λ  = −64iλ  (22)  and  V (4)  ζ  (p, k, q, r) = −8iζ  �  (k · q)(p · r) + (k · p)(q · r) + (k · r)(p · q)  �  ,  V (4)  γ (p, k, q, r) = 4iγ(k2 + p2 + q2 + r2),  V (4)  λ  = −256iλ,  (23)  where (k · p) = kµpµ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  Now we are in the position to determine the one-loop contributions to the self-energy  (correction to the propagator) of the healthy (light) mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' First, consider the diagrams  producing the UV divergences (15), derived previously using the heat-kernel method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' These  divergences are responsible for the MS-scheme based beta functions and serve as the UV  references for the complete expressions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  In the theory (6) the expression for the two-point function is  G(2)  1-loop(p, −p) ∝  i  (p2 − m2)  �¯Σγ + ¯Σλ + �Σγλ + �Σλ2 + Σζ2 + Σγζ + Σγ2�  i  (p2 − m2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  (24)  We can write the general symbolic expression for the self-energy function, in the second-  9  order (in coupling constants) approximation as  � =  +  � 2 ⇥  = Σlight + Σghost − 2Σmixed  (25)  and  Now we are in the position to determine the one-loop contributions to the propagator of  the healthy (or light) mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' For this we consider the self-energy diagrams that produce  the UV divergences (16).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' In the theory (6) the corrections of interest for the two-point  function are given by  G(2)(p, �p) /  i  (p2 � m2)  �¯⌃� + ¯⌃� + ⌃⇣2 + ⌃�⇣ + ⌃�2�  i  (p2 � m2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  (30)  The self-energy type corrections that are second-order in the coupling constants are given  by  ⌃ =  +  � 2 ⇥  = ⌃light + ⌃ghost � 2⌃mixed  (31)  and  e⌃ =  q = 0  +  q = 0  �  q = 0  �  q = 0  = ⌃light  ��  q=0 + ⌃ghost  ��  q=0 � ⌃mixed  ��  q=0 � ⌃mixed  ��  m2$ M2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' q=0 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  (32)  where,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' generically,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  ⌃light /  Z  d4k  (2⇡)4  i  (k2 � m2)V (3)(p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' �k,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' k � p)  i  ⇥  (k � p)2 � m2⇤V (3)(�p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' k,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' p � k),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  (33)  ⌃ghost /  Z  d4k  (2⇡)4  i  (k2 � M 2)V (3)(p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' �k,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' k � p)  i  ⇥  (k � p)2 � M 2⇤V (3)(�p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' k,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' p � k),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  (34)  ⌃mixed /  Z  d4k  (2⇡)4  i  (k2 � m2)V (3)(p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' �k,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' k � p)  i  ⇥  (k � p)2 � M 2⇤V (3)(�p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' k,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' p � k),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  (35)  while contributions that are of the first-order in the coupling constants have the following  structure:  ¯⌃ =  +  = ¯⌃light + ¯⌃ghost,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  (36)  with  ¯⌃light /  Z  d4k  (2⇡)4  i  (k2 � m2)V (4)(p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' �k,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' k � p)  i  ⇥  (k � p)2 � m2⇤,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  (37)  ¯⌃ghost /  Z  d4k  (2⇡)4  i  (k2 � M 2)V (4)(p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' �k,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' k � p)  i  ⇥  (k � p)2 � M 2⇤.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  (38)  7  = Σlight  ��  q=0 + Σghost  ��  q=0 − Σmixed  ��  q=0 − Σmixed  ��  m2↔ M2, q=0 ,  (26)  where solid lines indicate light degrees of freedom while dashed lines stand for the massive  ghosts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Furthermore,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  Σlight ∝  �  d4k  (2π)4  i  (k2 − m2)V (3)(p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' −k,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' k − p)  i  �  (k − p)2 − m2�V (3)(−p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' k,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' p − k),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  Σghost ∝  �  d4k  (2π)4  i  (k2 − M 2)V (3)(p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' −k,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' k − p)  i  �  (k − p)2 − M 2�V (3)(−p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' k,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' p − k),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  Σmixed ∝  �  d4k  (2π)4  i  (k2 − m2)V (3)(p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' −k,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' k − p)  i  �  (k − p)2 − M 2�V (3)(−p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' k,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' p − k),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' (27)  while the contributions of the first-order in the coupling constants have the following struc-  ture:  ¯� =  +  = ¯Σlight + ¯Σghost ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  (28)  with  ¯Σlight ∝  �  d4k  (2π)4  i  (k2 − m2)V (4)(p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' k,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' −p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' −k),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  ¯Σghost ∝  �  d4k  (2π)4  i  (k2 − M 2)V (4)(p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' k,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' −p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' −k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  (29)  The diagrammatic representation of the contributions to the two-point function with  different couplings, is presented in the Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' The diagrams in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' 2 correspond  10  to the fifth term in (24), and the last term is associated with the diagrams in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' In  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' 3 there are shown the diagrams that correspond to the term proportional to γζ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' The  diagrams for the first-order terms in the couplings γ and λ, are depicted in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' 5 and  6, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' In addition, the third and fourth terms in (24) are associated with the  tadpole diagrams with interaction vertices γλ shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' 7, and λ2 shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  Let us note that each diagram here represents the sum over all the topologically equiva-  lent diagrams with different permutations over the external momenta and with all possible  placements of derivatives on the internal and external lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' On top of that, we omit-  ted some tadpole-type diagrams that do not contribute to G(2)(p, −p), as they include  derivatives of the propagator in a single spacetime point, and hence vanish.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  To evaluate the integrals in (24) we used dimensional regularization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' In the model  under consideration, this requires extending the standard list of divergent expressions [32]  for the integrals in the spacetime of 2ω complex dimensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' The integrals proportional to  ζ2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' γζ and γ2 read,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' respectively,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' as  Σ(2ω)  ζ2 (p)  =  −  8ζ2  θ4(m2 − M 2)2  �  d2ωk  (2π)2ω Γ(3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='3)  ζ2  �  2  (k2 − m2)  �  (k − p)2 − M 2�  −  1  (k2 − m2)  �  (k − p)2 − m2� −  1  (k2 − M 2)  �  (k − p)2 − M 2�  �  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  (30)  Σ(2ω)  γζ (p)  =  −  4γζ  θ4(m2 − M 2)2  �  d2ωk  (2π)2ω Γ(3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='3)  γζ  �  2  (k2 − m2)  �  (k − p)2 − M 2�  −  1  (k2 − m2)  �  (k − p)2 − m2� −  1  (k2 − M 2)  �  (k − p)2 − M 2�  �  (31)  and  Σ(2ω)  γ2 (p)  =  −  2γ2  θ4(m2 − M 2)2  �  d2ωk  (2π)2ω Γ(3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='3)  γ2  �  2  (k2 − m2)  �  (k − p)2 − M 2�  −  1  (k2 − m2)  �  (k − p)2 − m2� −  1  (k2 − M 2)  �  (k − p)2 − M 2�  �  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  (32)  where we used the following combinations of the vertex factors:  Γ(3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='3)  ζ2  = p4k4 − 2p2k2(p · k)2 + (p · k)4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  Γ(3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='3)  γζ  = p4k2 − (p2 + k2)(p · k)2 + (p · k)3 − p2k2(p · k) + k4p2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  Γ(3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='3)  γ2  = p4 + k4 + (p · k)2 + 2p2k2 − 2(p2 + k2)(p · k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  (33)  11  The results of the integrations in the Euclidean space are1  Σζ2(p)  =  iζ2p4  (4π)2θ4  �  5  �1  ϵ + ln  � µ2  m2  ��  − 1  4  �  9A2 − 5(ab)2 − 37  �  −  1  2(ab)2c5 ln  �1 + c  1 − c  �  −  1  2(ab)2d5 ln  �1 + d  1 − d  �  −  �1  2(ab)3 + 5  2ab  �  ab + a  2 + 2  �  + 15a  4  �  1 + 1  4b  �  + 5  �  2 + 3  4b + 1  2ab  ��  ln (1 + 4b) +  A5  2(ab)2 ln  �(A + 1)2 − (ab)2  (A − 1)2 − (ab)2  ��  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  (34)  Σγζ(p)  =  − iγζp2  (4π)2θ4  �  3  �1  ϵ + ln  � µ2  m2  ��  +  1  2c(ab)2  �a  2  �  2 − 1  c2  �  + 1  �  ln  �1 + c  1 − c  �  +  1  2d(ab)2  �a  2(4b + 1)  �  2 − 1  d2  �  + 1  �  ln  �1 + d  1 − d  �  −  �  ab + a  2 − 6  �  − A  2  �� 1  ab − ab  ��  1 + 1  2b + 1  ab  �  − 2  b  �  1 + 1  4b  ��  ln  �(A + 1)2 − (ab)2  (A − 1)2 − (ab)2  �  −  �ab  2  �  ab + a  2 + 2  �  + 3  �  1 + a  2  ��  1 + 1  4b  �  − 1  ab  �  ln (1 + 4b)  �  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  (35)  Σγ2(p)  =  iγ2  (4π)2θ4  �  2  �1  ϵ + ln  � µ2  m2  ��  + 3 −  1  2c(ab)2  �a2  4 − 1  c2 + 2  �  ln  �1 + c  1 − c  �  +  A  2(ab)2  �  ab + a  2 − 1  �2  ln  �(A + 1)2 − (ab)2  (A − 1)2 − (ab)2  �  − 1  2  �  ab + a  �  1 + 1  4b  �  + 3  + 1  2b  �  1 − 2  a  ��  ln (1 + 4b) −  1  2d(ab)2  �a2  4 (4b + 1)2 − 1  d2 + 2  �  ln  �1 + d  1 − d  ��  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' (36)  where  1  ϵ ≡  1  2 − ω − γE + ln (4π),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  a = 4m2  p2 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  b = M 2 − m2  4m2  (37)  and γE ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='577 is the Euler-Mascheroni constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' In the limit ω → 2, the results (34),  (35) and (36) represent divergent and finite parts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  Note that the finite part of these  expressions has a very complicated dependence on the external momentum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  For these  nonlocal structures, in the mixed sector, we used the notation  A =  �  (1 + ab)2 + a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  (38)  Furthermore, the notations used in the light and ghost sectors, include, respectively,  c2 =  p2  p2 + 4m2,  d2 =  p2  p2 + 4M 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  (39)  1Some intermediate details of the calculations can be found in Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' The calculations were  verified using the Package-X [33] in Mathematica [34].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  12  In top of this, the relevant corrections involving the quartic vertices, are given by  ¯Σγ(p) = 2iγp2  θ2  Iquad  and  ¯Σλ(p) = 64iλ  θ2  Iquad,  (40)  where the integral is  Iquad  =  1  (m2 − M 2)  �  d2ωk  (2π)2ω  �  1  (k2 + m2) −  1  (k2 + M 2)  �  =  −  1  (4π)2  �1  ϵ + ln  � µ2  m2  �  + 1 −  M 2  (m2 − M 2) ln  � m2  M 2  ��  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  (41)  The results (40) are tadpole-type contributions, which do not produce a nonlocal form  factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Therefore, these corrections are not relevant to our analysis at low energies and  were included just of completeness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Of course, the same consideration applies to second-  order tadpole-type corrections, which in principle contribute to divergences in the Einstein-  Hilbert and cosmological constant sectors,  �Σγλ(p) = − 16iγλp2  θ4m2M 2 Iquad  and  �Σλ2(p) = − 512iλ2  θ4m2M 2 Iquad,  (42)  with m2M 2 = 8λ/θ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Actually, the corrections in (42) can be disregarded because tad-  pole diagrams, such as those presented in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' 7 and 8, normally are eliminated using  renormalization conditions (see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=', [35] or the Chapter 11 of [36] for more details).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  Let us note that here we presented only the results for the self-energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' The lower-order  vertices were also derived and produce qualitatively the same picture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' The nonlocal parts  of these contributions follow a standard logarithmic structure, as those for propagator  corrections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Since the corresponding formulas are relatively bulky, they are separated in  Appendix C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  4  Asymptotic behavior  In this section, we explore the asymptotic behavior of the one-loop contributions (34),  (35), and (36).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Our main interest is to verify how these expressions interpolate between the  UV and IR regions of the fundamental theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' In this way, we have a chance to understand  what happens to the nonlocal form factors of the contribution of loops with the massive  degrees of freedom (massive ghosts) in the IR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  We start with the limit p2 → ∞ that corresponds to the UV regime p2 ≫ M 2 ≫ m2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  In this case, Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' (35),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' (34),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' and (36) simplify and we arrive at the expressions  13  ΣUV  ζ2 (p2 → ∞)  =  iζ2p4  (4π)2θ4  �  5  �1  ϵ − ln  �p2  µ2  ��  + 3 − 15(M 2 + m2)  p2  + 10(m4 + m2M 2 + M 4)  p4  ln  � p2  M 2  �  + 35(M 2 + m2)  6p4  + 40M 2m2  3p4  + 10m6  p4M 2 ln  � m2  M 2  �  + O  �M 6  p6  ��  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  (43)  ΣUV  γζ (p2 → ∞)  =  − iγζp2  (4π)2θ4  �  3  �1  ϵ − ln  �p2  µ2  ��  + 7 − 9(M 2 + m2)  p2  − 6(M 2 + m2)  p2  ln  � p2  M 2  �  − 6m4  p2M 2 ln  � m2  M 2  �  + O  �M 4  p4  ��  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  (44)  ΣUV  γ2 (p2 → ∞)  =  iγ2  (4π)2θ4  �  2  �1  ϵ + ln  �p2  µ2  �  + 2 ln  � µ2  M 2  ��  + 5  + 4m2  M 2 ln  � m2  M 2  �  + O  �M 2  p2  ��  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  (45)  As expected in the UV regime, the leading logarithmic terms in the form factor are pro-  portional to the corresponding divergences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' It is easy to verify that, when returning to the  coordinate representation, the divergent part of the expressions above, together with (40)  in the UV, correspond to the result (15), obtained from the heat-kernel technique.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  On the other hand,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' assuming m2 → 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' the analysis of the IR regime M 2 ≫ p2 of the  corrections (34),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' (35),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' and (36),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' provides  ΣIR  ζ2 (M 2 ≫ p2)  ����  m2=0  =  iζ2p4  (4π)2θ4  �  5  �1  ϵ + ln  � µ2  M 2  ��  − 1  6  �  7 + 35p2  2M 2 − 9p4  2M 4  �  +  p4  2M 4 ln  �M 2  p2  �  + O  � p6  M 6  ��  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  (46)  ΣIR  γζ(M 2 ≫ p2)  ����  m2=0  =  − iγζp2  (4π)2θ4  �  3  �1  ϵ + ln  � µ2  M 2  ��  − 1  2 + 2p2  3M 2  − p4  M 4  � 7  20 − 1  2 ln  � p2  M 2  ��  + O  � p6  M 6  ��  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  (47)  ΣIR  γ2(M 2 ≫ p2)  ����  m2=0  =  iγ2  (4π)2θ4  �  2  �1  ϵ + ln  � µ2  M 2  ��  + 13  6  p2  M 2  −  p4  2M 4  �8  5 + ln  � p2  M 2  ��  + O  � p6  M 6  ��  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  (48)  14  The last formulas show that, in the IR limit, the divergences and momentum dependence  do not correlate with each other, exactly as it is expected [4] (see also [2, 5, 7] for the  semiclassical theory).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' We have found that this basic feature holds also for the “mixed”  diagrams, such that the Appelquist-Carazzone theorem is valid for the fourth-derivative  model with non-polynomial interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' In the expressions (46) and (47), the nonlocal  part with logarithmic form factor is suppressed by powers of M 2, whereas in (48) this is  not the case, as the factor γ2 (remember that γ = θ2M 2) cancels this suppression in the  terms proportional to p4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' It is important to note that these nonlocal structures represent  the contributions from the light sector alone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' The one-loop diagrams with mixed (light  and massive ghost) internal lines and (of course) the pure ghost contributions collapse and  produce only trivial dependencies on the external momentum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' All in all, we verified the  quadratic decoupling of the heavy mode in the Feynman diagrams with the mixed contents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  5  One-loop corrections in the effective theory  The last element of our investigation is the comparison between what remains from  the logarithmic form factors of the full theory in the IR and the leading logarithms in  the effective (initially local) theory without heavy degrees of freedom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' According to the  existing expectations [21], the two expression should demonstrate a perfect correlation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  This result would mean, in particular, that the quantum general relativity can serve as  a universal low-energy model in any renormalizable or superrenormalizable approach to  quantum gravity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  So, let us evaluate the quantum corrections to the propagator in the effective low-energy  model of (6), containing only the light mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' We consider a scenario in which the energy  scale is much smaller than the Planck mass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Therefore, we can assume that the EH and  cosmological constant terms dominate over the higher derivative terms, leaving only the  part LIR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Under these considerations, the tree-level propagator of the conformal factor  boils down to  �Geff(k) = −  i  2γ  �  k2 − m2�,  (49)  where m2 is defined in (20).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' The vertices are the same as those in (22) and (23).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Since we  are dealing with an effective model, we are not concerned that LIR is non-renormalizable,  as we may ignore the higher-derivative divergences2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Thus, our interest is to explore the  2According to the logic of the pioneer work [21] (see also [37]) the divergences in quantum gravity are  local expressions and, therefore, have no direct relation to the long-distance regime corresponding to the  IR limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  15  contributions to the cosmological constant and the Einstein-Hilbert terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' These formulas  can be compared with the structures found in the IR limit of the full theory (6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  In the low-energy effective theory, the relevant contribution is given by  Σeff  γ2(p)  =  ip4  (4π)2  ��1  2 − 5  4 a + 3  8 a2� �1  ϵ − ln  � µ2  m2  ��  +  �  1 − 7  4 a + 1  2 a2�  − 1  2c  �1  4 a2 − 1  c2 + 2  �  ln  �1 + c  1 − c  ��  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  (50)  To make the comparison more explicit, consider the particular case Λ = 0 (or, equivalently,  p2 → ∞).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Then the last expression reduces to a simpler form,  Σeff  γ2(p)  ���  Λ=0  =  ip4  2(4π)2  �1  ϵ − ln  �p2  µ2  �  + 2  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  (51)  Note that the nonlocal contribution to the cosmological constant sector in the IR regime  of the “fundamental” theory (6) is correlated with the UV divergence of the result (51).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  From these results, it is also possible to establish the one-loop match between these two  scenarios: fundamental and effective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  For this, we introduce the relation  ΣIR  γ2  =  Σeff  γ2 + δeff  γ2,  (52)  where δeff  γ2 is an additional term which represents, at the one-loop level, the difference  between the correction of the fundamental theory in the low energies and the correction of  the effective theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Considering the collapse of the diagrams with massive ghost internal  lines in the IR regime of the fundamental theory, as we saw in the previous section, we  can identify that the additional term in (52) is composed of contributions arising from the  collapse of loops in the mixed sector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' These collapsed diagrams reduce to the tadpole-type  graphs, and the remaining part, related to pure ghost loops, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=',  δeff  γ2  =  c(1)  γ2, mixed + c(1)  γ2, ghost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  (53)  The contribution of the tadpole-type in (53) is proportional to the mass m2, and hence  vanishes in the simplification adopted for the IR, namely assuming c(1)  γ2, mixed  ��  m2=0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  Using the results (48) and (51), we find the leading logarithmic terms in the form  δeff  γ2  ���  m2=0  =  i  (4π)2  �  2M 4 ln  � µ2  M 2  �  + 13  6 p2M 2 − p4  2  �18  5 + ln  � µ2  M 2  ���  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  (54)  In this expression we omitted the divergent part, for simplicity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' As it should be expected,  the nonlocal part with logarithmic form factor is canceled and the IR matching condition,  which ensure the equivalence with the result (48), is satisfied with δeff  γ2 contains only terms  with trivial dependencies on the external momentum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  16  6  Implications for the cosmological constant problem  The cosmological constant problem is one of the main unsolved issues in the present-  day theoretical physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' The problem was formulated by Weinberg in [38] as the need  to explain the extremely precise fine tuning between the original cosmological constant  density in the vacuum action and the huge induced contributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' One can reformulate  the problem in terms of the renormalization of the vacuum term [39] but this does not help  too much in its resolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' There are also many other interesting aspects of the problem,  related to cosmology (see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=', [40, 41]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Along with the main problem, in the quantum  field theory framework we need to understand whether the cosmological constant density  and the Newton constant are really constants or these parameters can be slowly varying  with the energy scale, as predicted, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=', by the four-derivative model of [1] (see also the  examples of discussions based on the extended models [29, 42, 43]) and, of course, in the  full fourth-derivative [17,18,44] or even higher-derivative models [20] of quantum gravity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  As we saw in the previous sections, the naive Minimal Subtraction - based approach  to the renormalization group for the cosmological constant term is not operational, as  it ignores the decoupling of the massive (ghost or healthy, in some models) degrees of  freedom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Assuming that all massive degrees of freedom have typical masses of the Planck  order of magnitude, all the cosmological applications occur at the deep IR, where the  Appelquist-Carazzone - type decoupling changes the beta functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' The question is what  remains from these beta functions in the theory with both massive and massless degrees  of freedom [44,45]?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  The result which we got for the quantum theory of conformal factor is that, in the deep  IR, there remain the contributions (46), (47) and (48), which fit the ones of effective low-  energy quantum theory based on the local model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' This provides a positive answer to the  aforementioned question posed in [45] and confirms the hypothesis of [21] (see also previous  discussion based on the simplified model with two fields in [46]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Looking at the expressions  for the IR remains of the form factors, we note that the terms without p4 or p2 factors have  only log(µ2/M 2) factor and no momentum-dependent logarithmic terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' This confirms  the general expectation that there cannot be physical running of the cosmological constant  term, detectable by means of flat-space calculations, as discussed in [2] and more recently  in [47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Let us stress that this does not mean that the cosmological constant running is  impossible in general, it just cannot be detected in the flat-space calculations [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  It is worth noting that one can observe the running of the cosmological constant term  using the non-covariant parametrization such as (1), just as a decoupling in the beta  function of the φ4-interaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  Up to a certain extent, the corresponding calculations  were already developed in [9] and can be generalized to other theories, including quantum  17  gravity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' This would be certainly an interesting way to extend the present work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' However,  it is important to be careful with the expectations to the results of such an extension, as  there will always remain a question about the physical interpretation of the result obtained  by means of non-covariant methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  7  Conclusions and discussions  We have considered the detailed renormalization in the theory of the conformal factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  Assuming a small cosmological constant, such a theory possesses two mass scales with a  strong hierarchy between them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' On top of that, the theory has non-polynomial interactions  and is renormalizable [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  These features make the model qualitatively similar to the  higher derivative quantum gravity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  Previously, the one-loop calculations in this model  were performed in the Minimal Subtraction scheme and we performed a more detailed  analysis in the momentum subtraction scheme of renormalization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  The analysis of the nonlocal form factors shows that in the UV, we meet a correspon-  dence with the Minimal Subtraction scheme results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' On the other hand, in the IR we met  a strong deviation from this simplified scheme and, as it was anticipated, a good agreement  with the calculation in the effective model that ignores the massive degree of freedom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' One  of the new details is that the “mixed” diagrams, with the internal lines of both small-  mass and large-mass fields, transform into tadpoles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' These diagrams contribute to the  UV divergences, but not to the nonlocal form factors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' This means, the diagrams with the  large-mass internal lines collapse and become irrelevant in the IR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' In particular, nonlocal  structures that survive in this regime and contribute to the cosmological constant sector,  are correlated with the UV divergent part in an effective version of the model containing  only the light mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  It would be certainly interesting to extend the analysis which was presented above, for  the models of “real” quantum gravity, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=', the theory of quantum metric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' As we mentioned  in the Introduction, this is a technically more challenging problem because such a theory  has gauge invariance and complicated tensor structures in the sectors of quantum metric  and ghost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' However, the results presented above show that there are very good chances to  meet the expectation of universality of quantum general relativity as an effective theory of  quantum gravity, at least in the fourth derivative [15] and, probably, all polynomial models  introduced in [16], where all extra degrees of freedom have the masses of the Planck order  of magnitude [48].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  At the same time, the situation may be more complicated in the non-local theories  of quantum gravity [49–52] (many further references can be found in the last review).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  The most popular version of nonlocal models are free from massive degrees of freedom at  18  the tree-level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' On the other hand, starting from the one-loop level, the structure of the  propagator changes and there are infinitely many complex-energy and complex-mass ghost-  like states with the quasi-continuous mass spectrum [53].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' In this case, the universality of  general relativity as the IR quantum gravity theory is rather uncertain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' This means, there  are still many interesting issues to explore in the area of the present work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  The last point is that we have found a good correspondence between the IR limit of the  theory with massless and large-mass degrees of freedom and the UV limit of the effective  theory without the massive particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' This correspondence extends to the contributions in  the cosmological constant sector of the gravitational action.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' However, these contributions  are not momentum-dependent, confirming the general no-go statement [2] concerning the  detection of the cosmological constant running by means of the flat-space calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' On  the other hand, this output does not means that such a running is impossible by itself.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  Instead, it should be interpreted as a challenge to develop new methods of effective field  theory calculations which would be appropriate for clarifying this issue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  Acknowledgments  W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' is grateful to CAPES for supporting his PhD project.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' The work of I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='Sh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' is  partially supported by Conselho Nacional de Desenvolvimento Cient´ıfico e Tecnol´ogico -  CNPq under the grant 303635/2018-5, by Funda¸c˜ao de Amparo `a Pesquisa de Minas Gerais  FAPEMIG under the grant PPM-00604-18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  19  Appendices  A  Feynman diagrams  In this appendix, we present the set of one-loop Feynman diagrams that correspond to  the corrections to the two-point function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  On decoupling in higher-derivative models (draft)  Wagno Cesar ∗  Departamento de F´ısica, ICE, Universidade Federal de Juiz de Fora  Contents  1  Appendix - Feynman diagrams  1  1  Appendix - Feynman diagrams  In this appendix, we present the set of one-loop Feynman diagrams that correspond to  the corrections for the two-point function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  G(2)  ⇣2 (p, �p) ⇠  Figure 1: Diagrams for the two-point function that provide one-loop contributions to the  renormalization of the coupling ⇣.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Solid lines indicate light degrees of freedom, dashed lines  stand for the massive ghosts, and the primes denotes derivatives acting on the propagators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  ∗E-mail address: wagnorion@gmail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='com  Figure 2: Diagrams for the two-point function that provide one-loop contributions to the  renormalization of the coupling ζ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Solid lines indicate light degrees of freedom, dashed lines  stand for the massive ghosts, and the primes denotes derivatives acting on the propagators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  G(2)  �⇣ (p, �p) ⇠  Figure 2: Diagrams for the two-point function with the interaction vertex �⇣.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  G(2)  �2 (p, �p) ⇠  Figure 3: Diagrams for the two-point function with the interaction vertex �2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  G(2)  � (p, �p) ⇠  Figure 4: Diagrams for the two-point function with the interaction vertex �.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  2  Figure 3: Diagrams for the two-point function with the interaction vertex γζ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  20  G(2)  �⇣ (p, �p) ⇠  Figure 2: Diagrams for the two-point function with the interaction vertex �⇣.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  G(2)  �2 (p, �p) ⇠  Figure 3: Diagrams for the two-point function with the interaction vertex �2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  G(2)  � (p, �p) ⇠  Figure 4: Diagrams for the two-point function with the interaction vertex �.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  2  Figure 4: Diagrams for the two-point function with the interaction vertex γ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  G(2)  � (p, �p) ⇠  Figure 5: Diagrams for the two-point function with the interaction vertex �.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  G(2)  � (p, �p) ⇠  Figure 6: Diagrams for the two-point function with the interaction vertex �.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  G(2)  ��(p, �p) ⇠  Figure 7: Diagrams for the two-point function with the interaction vertex ��.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  G(2)  �2 (p, �p) ⇠  Figure 8: Diagrams for the two-point function with the interaction vertex �2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  3  Figure 5: Diagrams for the two-point function with the interaction vertex γ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  G(2)  � (p, �p) ⇥  Figure 6: Diagrams for the two-point function with the interaction vertex λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  G(2)  � (p, �p) ⇠  Figure 5: Diagrams for the two-point function with the interaction vertex �.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  G(2)  � (p, �p) ⇠  Figure 6: Diagrams for the two-point function with the interaction vertex �.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  G(2)  ��(p, �p) ⇠  Figure 7: Diagrams for the two-point function with the interaction vertex ��.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  G(2)  �2 (p, �p) ⇠  Figure 8: Diagrams for the two-point function with the interaction vertex �2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  3  Figure 7: Diagrams for the two-point function with the interaction vertex γλ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  G(2)  � (p, �p) ⇠  Figure 5: Diagrams for the two-point function with the interaction vertex �.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  G(2)  � (p, �p) ⇠  Figure 6: Diagrams for the two-point function with the interaction vertex �.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  G(2)  ��(p, �p) ⇠  Figure 7: Diagrams for the two-point function with the interaction vertex ��.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  G(2)  �2 (p, �p) ⇠  Figure 8: Diagrams for the two-point function with the interaction vertex �2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  3  Figure 8: Diagrams for the two-point function with the interaction vertex λ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  21  B  Intermediate results for the Feynman integrals  In this appendix, we present some intermediate results related to the calculation of  Feynman integrals in sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' By using the Feynman parametrization  1  ab =  � 1  0  dx  �  (a − b)x + b  �2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  (55)  and performing the following shift of integration variable k = q + px,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' we can rewrite the  integrals related to the mixed sector in the expressions (30),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' (31) and (32),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' respectively,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' as  Σ(2ω)  mixed,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' ζ2(p)  =  −  2ζ2 p4  θ4(m2 − M 2)2  (4ω2 − 1)  ω(1 + ω)  � 1  0  dx I4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  (56)  Σ(2ω)  mixed,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' γζ(p)  =  −  2γζ p2  θ4(m2 − M 2)2  (2ω − 1)  ω  � 1  0  dx  ��  x2 − x + 1  �  p2I2 + I4  �  (57)  and  Σ(2ω)  mixed,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' γ2(p)  =  −  2γ2  θ4(m2 − M 2)2  � 1  0  dx  �  I4 + 1 + 4ω + 4  �  x2 − x  �  (ω + 1)  2ω  p2I2  +  �  x2 − x + 1  �2p4I1  �  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  (58)  where  I1 =  �  d2ωq  (2π)2ω  1  (q2 − ∆)2 =  i  (4π)ω Γ(2 − ω)∆ω−2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  (59)  I2 =  �  d2ωq  (2π)2ω  q2  (q2 − ∆)2 = −  i  (4π)ω ωΓ(1 − ω)∆ω−1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  (60)  I4 =  �  d2ωq  (2π)2ω  q4  (q2 − ∆)2 =  i  (4π)ω ω(1 + ω)Γ(−ω)∆ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  (61)  Here we define ∆ ≡ p2x(x − 1) + (M 2 − m2)x + m2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' For the integrals in the other sectors,  we have the same results as above with ∆ = ∆ghost = p2x(x − 1) + M 2 in the case of the  ghost sector, and ∆ = ∆light = p2x(x − 1) + m2 for the light sector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  C  One-loop corrections to the three- and four-point vertices  This appendix is devoted to the one-loop corrections to the vertices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' In case of the  three-point function, the relevant corrections are associated with the diagrams in Figures  9, 10 and 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  22  On decoupling in higher-derivative models (draft)  Wagno Cesar ∗  Departamento de F´ısica, ICE, Universidade Federal de Juiz de Fora  Contents  1  Appendix - Feynman diagrams  1  1  Appendix - Feynman diagrams  In this appendix we present the set of Feynman diagrams associated with corrections  for the propagator and vertices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Here we assumed the sum over the diagrams of the same  topology, but with di↵erent permutations of the external momenta.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  �(3)  ⇣2 ⇠  Figure 1: Diagrams for the three-point function with the interaction vertex ⇣2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  �(4)  ⇣2 ⇠  Figure 2: Diagrams for the four-point function with the interaction vertex ⇣2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  ∗E-mail address: wagnorion@gmail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='com  Figure 9: Diagrams for the three-point function with the interaction vertex ζ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  �(3)  �⇣ ⇠  Figure 3: Diagrams for the three-point functions with the interaction vertex �⇣.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  �(4)  �⇣ ⇠  Figure 4: Diagrams for the four-point functions with the interaction vertex �⇣.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  2  Figure 10: Diagrams for the three-point function with the interaction vertex γζ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  �(3)  �2 ⇠  Figure 5: Diagrams for the three-point function with the interaction vertex �2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  �(4)  �2 ⇠  Figure 6: Diagrams for the four-point function with the interaction vertex �2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  3  Figure 11: Diagrams for the three-point function with the interaction vertex γ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  23  In the dimensional regularization scenario,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' these corrections are given by following  integrals,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  Γ(3)  ζ2 (p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' r)  ��(2ω)  =  −  4ζ2  θ4(m2 − M 2)2  �  d2ωk  (2π)2ω Γ(3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='4)  ζ2  �  2  (k2 − m2)  �  (k − p)2 − M 2�  −  1  (k2 − m2)  �  (k − p)2 − m2� −  1  (k2 − M 2)  �  (k − p)2 − M 2�  �  + t- and u-channel contributions,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  (62)  Γ(3)  γζ (p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' r)  ��(2ω)  =  2γζ  θ4(m2 − M 2)2  �  d2ωk  (2π)2ω  �  Γ(3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='4)  γζ  + Γ(3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='4)  ζγ  ��  2  (k2 − m2)  �  (k − p)2 − M 2�  −  1  (k2 − m2)  �  (k − p)2 − m2� −  1  (k2 − M 2)  �  (k − p)2 − M 2�  �  + t- and u-channel contributions  (63)  and  Γ(3)  γ2 (p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' r)  ��(2ω)  =  −  γ2  θ4(m2 − M 2)2  �  d2ωk  (2π)2ω Γ(3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='4)  γ2  �  2  (k2 − m2)  �  (k − p)2 − M 2�  −  1  (k2 − m2)  �  (k − p)2 − m2� −  1  (k2 − M 2)  �  (k − p)2 − M 2�  �  + t- and u-channel contributions,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  (64)  where the combinations of the vertex factors (for the s-channel diagrams) are  Γ(3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='4)  ζ2  = −2  �  k2(p · r) − k2r2 − 2(k · p − k · r)(p · r − k · r) − p2(k · r) + r2(k · p)  �  ×  �  (p · k)2 − p2k2�  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  Γ(3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='4)  γζ  + Γ(3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='4)  ζγ  = 4  �  (k · p)2 − k2p2��  k2 − k · p + p2 − p · r + r2�  − 2  �  k2(p · r − r2)  −p2(k · r) − 2(k · r)(k · r − p · r) + r2(k · p) + 2(k · p)(k · r − p · r)  �  ×  �  k2 − k · p + p2�  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  Γ(3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='4)  γ2  = 4  �  k2 − (k · p) + p2��  k2 − k · p + p2 − p · r + r2�  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  (65)  Taking these integrals,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' we write the contributions to the three-point function as  Γ(3)  ζ2 (p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' r)  =  iζ2  (4π)2θ4  �  20  �  (p · r)2 − p2r2��1  ϵ + ln  � µ2  m2  ��  + α(3)  ζ2 (p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' r) ln (1 + 4b)  + ξ(3)  ζ2 (p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' r) +  �  β(3)  ζ2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' light(p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' r) ln  �1 + c  1 − c  �  + β(3)  ζ2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' ghost(p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' r) ln  �1 + d  1 − d  �  + β(3)  ζ2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' mixed(p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' r) ln  �(A + 1)2 − (ab)2  (A − 1)2 − (ab)2  �  + (p ↔ −r) + (p ↔ r − p)  ��  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  (66)  24  Γ(3)  γζ (p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' r)  =  −  iγζ  (4π)2θ4  �  6  �  p2 + r2 − (p · r)  ��1  ϵ + ln  � µ2  m2  ��  + α(3)  γζ (p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' r) ln (1 + 4b)  + ξ(3)  γζ (p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' r) +  �  β(3)  γζ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' light(p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' r) ln  �1 + c  1 − c  �  + β(3)  γζ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' ghost(p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' r) ln  �1 + d  1 − d  �  + β(3)  γζ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' mixed(p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' r) ln  �(A + 1)2 − (ab)2  (A − 1)2 − (ab)2  �  + (p ↔ −r) + (p ↔ r − p)  ��  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  (67)  Γ(3)  γ2 (p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' r)  =  iγ2  (4π)2θ4  �  12  �1  ϵ + ln  � µ2  m2  ��  + α(3)  γ2 (p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' r) ln (1 + 4b) + ξ(3)  γ2 (p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' r)  +  �  β(3)  γ2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' mixed(p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' r) ln  �(A + 1)2 − (ab)2  (A − 1)2 − (ab)2  �  + β(3)  γ2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' light(p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' r) ln  �1 + c  1 − c  �  + β(3)  γ2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' ghost(p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' r) ln  �1 + d  1 − d  �  + (p ↔ −r) + (p ↔ r − p)  ��  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  (68)  where α’s,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' β’s and ξ’s are coefficients with polynomial dependencies on the external mo-  menta.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' The full explicit form of these expressions are very bulky and we do not present  them here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' On the other hand, since they are polynomials the corresponding contributions  are local and these explicit expression is not really important for our analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Remember  that the notations a, b, A, c, d are defined in (37), (38) and (39), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  It is important that the most essential, non-local parts of the expressions have standard  logarithmic structures, similar to those already evaluated in section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Therefore, it should  be expected that the corrections above represent asymptotic behavior in the IR, similar to  the case of the propagator corrections considered in the main part of the paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Let us note  that we verified and confirmed the quadratic decoupling of the heavy mode in the vertex  terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Furthermore, the same behavior is observed for the four-point vertex corrections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  In this case, the diagrams of interest are depicted in Figures 12, 13 and 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  On decoupling in higher-derivative models (draft)  Wagno Cesar ∗  Departamento de F´ısica, ICE, Universidade Federal de Juiz de Fora  Contents  1  Appendix - Feynman diagrams  1  1  Appendix - Feynman diagrams  In this appendix we present the set of Feynman diagrams associated with corrections  for the propagator and vertices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Here we assumed the sum over the diagrams of the same  topology, but with di↵erent permutations of the external momenta.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  �(3)  ⇣2 ⇠  Figure 1: Diagrams for the three-point function with the interaction vertex ⇣2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  �(4)  ⇣2 ⇠  Figure 2: Diagrams for the four-point function with the interaction vertex ⇣2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  ∗E-mail address: wagnorion@gmail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='com  Figure 12: Diagrams for the four-point function with the interaction vertex ζ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  �(3)  �⇣ ⇠  Figure 3: Diagrams for the three-point functions with the interaction vertex �⇣.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  �(4)  �⇣ ⇠  Figure 4: Diagrams for the four-point functions with the interaction vertex �⇣.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  2  Figure 13: Diagrams for the four-point function with the interaction vertex γζ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  25  �(3)  �2 ⇠  Figure 5: Diagrams for the three-point function with the interaction vertex �2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  �(4)  �2 ⇠  Figure 6: Diagrams for the four-point function with the interaction vertex �2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  3  Figure 14: Diagrams for the four-point function with the interaction vertex γ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  The analytic expressions corresponding to these diagrams are  Γ(4)  ζ2 (p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' q)  ��(2ω)  =  −  8ζ2  θ4(m2 − M 2)2  �  d2ωk  (2π)2ω Γ(4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='4)  ζ2  �  2  (k2 − m2)  �  (k − p)2 − M 2�  −  1  (k2 − m2)  �  (k − p)2 − m2� −  1  (k2 − M 2)  �  (k − p)2 − M 2�  �  + t- and u-channel contributions,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  (69)  Γ(4)  γζ (p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' q)  ��(2ω)  =  4γζ  θ4(m2 − M 2)2  �  d2ωk  (2π)2ω Γ(4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='4)  γζ  �  2  (k2 − m2)  �  (k − p)2 − M 2�  −  1  (k2 − m2)  �  (k − p)2 − m2� −  1  (k2 − M 2)  �  (k − p)2 − M 2�  �  + t- and u-channel contributions,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  (70)  Γ(4)  γ2 (p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' q)  ��(2ω)  =  −  2γ2  θ4(m2 − M 2)2  �  d2ωk  (2π)2ω Γ(4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='4)  γ2  �  2  (k2 − m2)  �  (k − p)2 − M 2�  −  1  (k2 − m2)  �  (k − p)2 − m2� −  1  (k2 − M 2)  �  (k − p)2 − M 2�  �  + t- and u-channel contributions,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  (71)  where,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' for the s-channel diagrams,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  Γ(4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='4)  ζ2  =  �  r2(k · q) − k2(r · q) + 2(k · q)  �  r · q  �  + q2(k · r) − 2(k · r)  �  k · q − r · q  ��  ×  �  k2�  p2 − p · r − p · q  �  − p2(k · r + k · q) + 2(k · r + k · q)(p · r + p · q)  +(r2 + q2)(k · p) − 2(k · p)  �  k · r + k · q + p · r + p · q − r · q  �  + 2(k · p)2�  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  Γ(4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='4)  γζ  = −2  �  k2(r · q) − r2(k · q) − 2(k · q)  �  r · q  �  + 2(k · r)  �  k · q − r · q  �  − q2(k · r)  �  ×  �  k2 − k · r − k · q + p2 − p · r − p · q + r2 + 2(r · q) + q2�  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  Γ(4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='4)  γ2  = 4  �  k2 − k · r − k · q + p2 − p · r − p · q + r2 + 2(r · q) + q2�  ×  �  k2 − k · r − k · q + r2 + r · q + q2�  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  (72)  26  The analytic expressions of the four-point vertex corrections involving the couplings ζ2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' γζ  and γ2 are,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' respectively,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  Γ(4)  ζ2 (p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' q)  =  −  iζ2  (4π)2θ4  �  20  �  p2(r · q) − r2(p · q) − 2(p · q)(r · q) − q2(p · r)  + 2(p · r)  �  p · q − r · q  ���1  ϵ + ln  � µ2  m2  ��  + α(4)  ζ2 (p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' q) ln (1 + 4b)  + β(4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' s)  ζ2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' mixed(p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' q) ln  �(A + 1)2 − (ab)2  (A − 1)2 − (ab)2  �����  p↔r+q  + ξ(4)  ζ2 (p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' q)  + β(4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' s)  ζ2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' light(p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' q) ln  �1 + c  1 − c  �����  p↔r+q  + β(4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' s)  ζ2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' ghost(p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' q) ln  �1 + d  1 − d  �����  p↔r+q  + β(4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' t)  ζ2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' light(p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' q) ln  �1 + c  1 − c  �����  p↔q−p  + β(4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' t)  ζ2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' ghost(p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' q) ln  �1 + d  1 − d  �����  p↔q−p  + β(4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' t)  ζ2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' mixed(p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' q) ln  �(A + 1)2 − (ab)2  (A − 1)2 − (ab)2  �����  p↔q−p  + β(4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' u)  ζ2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' light(p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' q) ln  �1 + c  1 − c  �����  p↔r−p  + β(4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' u)  ζ2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' ghost(p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' q) ln  �1 + d  1 − d  �����  p↔r−p  + β(4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' u)  ζ2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' mixed(p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' q) ln  �(A + 1)2 − (ab)2  (A − 1)2 − (ab)2  �����  p↔r−p  �  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  (73)  Γ(4)  γζ (p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' q)  =  iγζ  (4π)2θ4  �  12(p · r + p · q − r · q)  �1  ϵ + ln  � µ2  m2  ��  + ξ(4)  γζ (p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' q)  + α(4)  γζ (p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' q) ln (1 + 4b) + β(4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' s)  γζ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' light(p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' q) ln  �1 + c  1 − c  �����  p↔r+q  + β(4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' s)  γζ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' mixed(p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' q) ln  �(A + 1)2 − (ab)2  (A − 1)2 − (ab)2  �����  p↔r+q  + β(4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' s)  γζ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' ghost(p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' q) ln  �1 + d  1 − d  �����  p↔r+q  + β(4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' t)  γζ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' light(p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' q) ln  �1 + c  1 − c  �����  p↔q−p  + β(4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' t)  γζ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' mixed(p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' q) ln  �(A + 1)2 − (ab)2  (A − 1)2 − (ab)2  �����  p↔q−p  + β(4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' t)  γζ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' ghost(p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' q) ln  �1 + d  1 − d  �����  p↔s−p  + β(4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' u)  γζ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' light(p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' q) ln  �1 + c  1 − c  �����  p↔r−p  + β(4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' u)  γζ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' mixed(p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' q) ln  �(A + 1)2 − (ab)2  (A − 1)2 − (ab)2  �����  p↔r−p  + β(4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' u)  γζ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' ghost(p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' q) ln  �1 + d  1 − d  �����  p↔r−p  �  (74)  27  and  Γ(4)  γ2 (p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' q)  =  iγ2  (4π)2θ4  �  24  �1  ϵ + ln  � µ2  m2  ��  + α(4)  γ2 (p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' q) ln (1 + 4b) + ξ(4)  γ2 (p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' q)  + β(4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' s)  γ2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' light(p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' q) ln  �1 + c  1 − c  �����  p↔r+q  + β(4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' s)  γ2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' ghost(p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' q) ln  �1 + d  1 − d  �����  p↔r+q  + β(4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' s)  γ2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' mixed(p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' q) ln  �(A + 1)2 − (ab)2  (A − 1)2 − (ab)2  �����  p↔r+q  + β(4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' t)  γ2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' light(p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' q) ln  �1 + c  1 − c  �����  p↔q−p  + β(4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' t)  γ2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' ghost(p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' q) ln  �1 + d  1 − d  �����  p↔q−p  + β(4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' t)  γ2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' mixed(p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' q) ln  �(A + 1)2 − (ab)2  (A − 1)2 − (ab)2  �����  p↔q−p  + β(4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' u)  γ2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' light(p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' q) ln  �1 + c  1 − c  �����  p↔r−p  + β(4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' u)  γ2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' ghost(p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' q) ln  �1 + d  1 − d  �����  p↔r−p  + β(4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' u)  γ2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' mixed(p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' q) ln  �(A + 1)2 − (ab)2  (A − 1)2 − (ab)2  �����  p↔r−p  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  (75)  The indices in the coefficients β(4)(p, r, q) denote s−, t− and u−channel contributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  It is easy to note that these expressions are in a good qualitative agreement with the  self-energy corrections and ones for the three-point vertices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  References  [1] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Antoniadis and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Mottola, Four-dimensional quantum gravity in the conformal  sector, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' D45 (1992) 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  [2] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Gorbar and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Shapiro, Renormalization group and decoupling in curved space,  JHEP 02 (2003) 021, hep-ph/0210388.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  [3] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Shapiro, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Sol`a, On the possible running of the cosmological ’constant’, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' B682 (2009) 105, hep-th/0910.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='4925.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  [4] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Appelquist and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Carazzone, Infrared singularities and massive fields, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  D11 (1975) 2856.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  [5] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Gorbar and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Shapiro, Renormalization group and decoupling in curved space,  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' The standard model and beyond, JHEP 06 (2003) 004, hep-ph/0303124.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  [6] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Codello and O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Zanusso, On the non-local heat kernel expansion, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  54 (2013) 013513, arXiv:1203.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='2034.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  28  [7] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Franchino-Vi˜nas, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' de Paula Netto, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Shapiro, and O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Zanusso, Form factors  and decoupling of matter fields in four-dimensional gravity, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' B790 (2019)  229, arXiv:1812.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='00460;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Franchino-Vi˜nas, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' de Paula Netto, and O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Zanusso, Vacuum effective ac-  tions and mass-dependent renormalization in curved space, Universe 5 (2019) 67,  arXiv:1902.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='03167.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  [8] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Franchino-Vi˜nas, Resummed heat-kernel for surface contributions:  Dirichlet  semitransparent boundary conditions, arXiv:2208.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='11979.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  [9] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Peixoto, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Gorbar and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Shapiro, On the renormalization group for the  interacting massive scalar field theory in curved space, Class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Quant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Grav.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' 21 (2004)  2281, hep-th/0311229.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  [10] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Odintsov and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Shapiro, Perturbative approach to induced quantum gravity,  Class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Quant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Grav.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' 8 (1991), L57-60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  [11] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Riegert, A non-local action for the trace anomaly, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' B134 (1984) 56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  [12] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Fradkin and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Tseytlin, Conformal anomaly in Weyl theory and anomaly free  superconformal theories, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' B134 (1984) 187.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  [13] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Duff, Twenty years of the Weyl anomaly, Class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Quant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Grav.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' 11 (1994) 1387,  hep-th/9308075.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  [14] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Buchbinder and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Shapiro, Introduction to Quantum Field Theory with Appli-  cations to Quantum Gravity (Oxford University Press, 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  [15] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Stelle, Renormalization of higher derivative quantum gravity, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' D16  (1977) 953.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  [16] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Asorey, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' L´opez, and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Shapiro, Some remarks on high derivative quantum  gravity, Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Journ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' A12 (1997) 5711, hep-th/9610006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  [17] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Fradkin and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Tseytlin, Renormalizable asymptotically free quantum theory  of gravity, Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' B201 (1982) 469.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  [18] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Avramidi and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Barvinsky, Asymptotic freedom In higher derivative quantum  gravity, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' B159 (1985) 269.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  [19] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Shapiro and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Jacksenaev, Gauge dependence in higher derivative quantum  gravity and the conformal anomaly problem, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' B324 (1994) 286.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  29  [20] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Modesto, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Rachwa�l, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Shapiro, Renormalization group in super-renormalizable  quantum gravity, Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' C78 (2018) 555, arXiv:1704.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='03988.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  [21] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Donoghue, Leading quantum correction to the Newtonian potential, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' 72 (1994) 2996, gr-qc/9310024;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' General relativity as an effective field theory:  The leading quantum corrections, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' D50 (1994) 3874, gr-qc/9405057.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  [22] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Mottola, Scalar gravitational waves in the effective theory of gravity, JHEP 07  (2017) 043;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Erratum: JHEP 09 (2017) 107, arXiv:1606.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='09220.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  [23] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Asorey, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Gorbar and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Shapiro, Universality and ambiguities of the confor-  mal anomaly, Class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Quant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Grav.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' 21 (2004) 163, hep-th/0307187.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  [24] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Asorey, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' de Berredo-Peixoto and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Shapiro, Renormalization ambiguities and  conformal anomaly in metric-scalar backgrounds, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' D74 (2006) 124011, hep-  th/0609138.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  [25] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Asorey, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Cesar e Silva, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Shapiro and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' do Vale, Trace anomaly and  induced action for a metric-scalar background, arXiv:2202.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='00154.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  [26] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Polyakov, Quantum geometry of bosonic strings, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' B103 (1981) 207.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  [27] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Shapiro and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Cognola, Interaction of low-energy induced gravity with quantized  matter and phase transition induced to curvature, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' D51 (1995) 2775, hep-  th/9406027.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  [28] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Barvinsky and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Vilkovisky, The generalized Schwinger-DeWitt technique in  gauge theories and quantum gravity, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Repts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' 119 (1985) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  [29] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Antoniadis and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Odintsov, Renormalization group and logarithmic corrections  to scaling relations in the conformal sector of 4D gravity, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' B343 (1995) 76,  arXiv:hep-th/9411012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  [30] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Creminelli, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Nicolis, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Papucci and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Trincherini, Ghosts in massive gravity,  JHEP 0509 (2005) 003, hep-th/0505147.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  [31] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Julve and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Tonin, Quantum gravity with higher derivative terms, Nuovo Cim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  B46 (1978) 137.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  [32] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Leibbrandt, Introduction to the Technique of Dimensional Regularization, Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' 47 (1975) 849.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  30  [33] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Patel, Package-X: A Mathematica package for the analytic calculation of one-loop  integrals, Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' 197 (2015) 276, arXiv:1503.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='01469.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  [34] Wolfram Research, Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=', Mathematica, (Version 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='0, Champaign, IL, 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  [35] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Collins, Renormalization (Cambridge University Press, 1984).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  [36] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Peskin and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Schroeder, An Introduction to Quantum Field Theory (West-  view Press, 1995).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  [37] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Burgess, Quantum gravity in everyday life: General relativity as an effective field  theory, Living Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Rel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' 7 (2004) 5, gr-qc/0311082.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  [38] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Weinberg, The cosmological constant problem, Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' 61 (1989) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  [39] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Shapiro, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Sol`a, Scaling behavior of the cosmological constant: Interface between  quantum field theory and cosmology, JHEP 02 (2002) 006, hep-th/0012227.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  [40] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Padmanabhan, Cosmological constant—the weight of the vacuum, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' 380  (2003) 235, arXiv:hep-th/0212290.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  [41] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Sahni and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Starobinsky, Reconstructing Dark Energy, Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' D 15  (2006) 2105, astro-ph/0610026.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  [42] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Antoniadis, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Mazur and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Mottola, Scaling behavior of quantum four-  geometries, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' B323 (1994) 284, arXiv:hep-th/9301002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  [43] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Elizalde, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Jacksenaev, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Odintsov and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Shapiro, One-loop renormaliza-  tion and asymptotic behaviour of a higher-derivative scalar theory in curved spacetime,  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Letters B328 (1994) 297, hep-th/9402154;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' A four-dimensional theory for quan-  tum gravity with conformal and non-conformal explicit solutions, Class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Quant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Grav.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  12 (1995) 1385, hep-th/9412061.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  [44] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' de Berredo-Peixoto and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Shapiro, Higher derivative quantum gravity with Gauss-  Bonnet term, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' D71 (2005) 064005, hep-th/0412249.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  [45] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Shapiro, Polemic Notes On IR Perturbative Quantum Gravity, Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  A24 (2009) 1557, arXiv:0812.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='3521.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  [46] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Ribeiro and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Shapiro Scalar model of effective field theory in curved space,  JHEP 2019 (2019) 163, arXiv:1908.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='01937.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  [47] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Gorbar and I,L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Shapiro, Nonlocality of quantum matter corrections and cosmo-  logical constant running, JHEP 103 (2022) 103, arXiv:2203.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='09232.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  31  [48] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Accioly, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Giacchini and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Shapiro, On the gravitational seesaw in higher-  derivative gravity, Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' C77 (2017) 540, gr-qc/1604.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='07348.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  [49] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Krasnikov, Nonlocal gauge theories, Theor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' 73 (1987) 1184.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  [50] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Kuz’min, The convergent nonlocal gravitation (in Russian), Yad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Fiz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' 50 (1989)  1630;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' [Sov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' 50 (1989) 1011].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  [51] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  Tomboulis,  Superrenormalizable  gauge  and  gravitational  theories,  hep-  th/9702146;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  Nonlocal and quasilocal field theories, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' D92 (2015) 125037,  arXiv:1507.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='00981.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  [52] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Modesto, Super-renormalizable quantum gravity, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' D86 (2012) 044005,  arXiv:1107.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='2403;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Modesto and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Rachwa�l, Super-renormalizable and finite gravi-  tational theories, Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' B889 (2014) 228, arXiv:1407.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='8036;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Nonlocal quantum  gravity: A review, Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' D26 (2017) 1730020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  [53] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Shapiro, Counting ghosts in the “ghost-free” non-local gravity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content=' B744  (2015) 67, arXive:1502.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='00106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
+page_content='  32' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFQT4oBgHgl3EQfSzZL/content/2301.13291v1.pdf'}
diff --git a/L9E1T4oBgHgl3EQftAVw/content/tmp_files/2301.03372v1.pdf.txt b/L9E1T4oBgHgl3EQftAVw/content/tmp_files/2301.03372v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..676ae1f06eab61825bf52cfd1d263ee7fd492bba
--- /dev/null
+++ b/L9E1T4oBgHgl3EQftAVw/content/tmp_files/2301.03372v1.pdf.txt
@@ -0,0 +1,1099 @@
+ 
+David C. Wyld et al. (Eds): CSML, NET, BDHI, SIPO, SOEA- 2023 
+ 
+pp. 15-27, 2023. CS & IT - CSCP 2023                                                                   DOI: 10.5121/csit.2023.130102 
+ 
+MACHINE-LEARNING PREDICTION OF THE 
+COMPUTED BAND GAPS OF DOUBLE 
+PEROVSKITE MATERIALS 
+ 
+Junfei Zhang1, Yueqi Li2, and Xinbo Zhou3 
+ 
+1 School of Computing and Information Systems, The University of Melbourne, 
+Melbourne, Victoria, Australia 
+2 College of Physical Science and Technology, Xiamen University, Xiamen, 
+Fujian, China 
+3 Faculty of Information Technology, Beijing University of Technology,  
+Beijing, China 
+ 
+ABSTRACT 
+ 
+Prediction of the electronic structure of functional materials is essential for the engineering of 
+new devices. Conventional electronic structure prediction methods based on density functional 
+theory (DFT) suffer from not only high computational cost, but also limited accuracy arising from 
+the approximations of the exchange-correlation functional. Surrogate methods based on machine 
+learning have garnered much attention as a viable alternative to bypass these limitations, 
+especially in the prediction of solid-state band gaps, which motivated this research study. Herein, 
+we construct a random forest regression model for band gaps of double perovskite materials, 
+using a dataset of 1306 band gaps computed with the GLLBSC (Gritsenko, van Leeuwen, van 
+Lenthe, and Baerends solid correlation) functional. Among the 20 physical features employed, we 
+find that the bulk modulus, superconductivity temperature, and cation electronegativity exhibit the 
+highest importance scores, consistent with the physics of the underlying electronic structure. 
+Using the top 10 features, a model accuracy of 85.6% with a root mean square error of 0.64 eV is 
+obtained, comparable to previous studies. Our results are significant in the sense that they attest 
+to the potential of machine learning regressions for the rapid screening of promising candidate 
+functional materials. 
+ 
+KEYWORDS 
+ 
+Machine Learning, Random Forest Regression, Electronic Structure, Computational Material 
+Science  
+ 
+1. INTRODUCTION 
+ 
+In quantum mechanics, the energy of bound electrons becomes quantized [1], and electrons at the 
+ground state can be excited to higher energy levels by absorbing photons with the corresponding 
+wavelengths. In solid structures, the superposed electronic states form continuous energy bands. 
+In insulators and semiconductors, the band gap is the energy gap across the valence and 
+conduction band where electrons are forbidden to occupy. The magnitude of the band gap plays 
+an important role in many functional materials, such as transistors, photovoltaics, light-emitting 
+diodes, and sensors [2]. For instance, optoelectronic materials are generally wide-band gap 
+semiconductors, while thermoelectric materials are narrow-band gap semiconductors [3]. Hence, 
+accurate and efficient prediction of band gaps of solid materials is crucial for the design and 
+engineering of new devices. 
+
+16 
+       
+ 
+Computer Science & Information Technology (CS & IT) 
+ 
+One of the most widely used electronic structure methods for evaluating band gaps is density 
+functional theory (DFT) [4]. In the Kohn-Sham formalism [5], the multielectron wavefunction is 
+replaced by fictitious noninteracting states that give rise to the true electron density [6], which 
+enables the iterative solution of the single-particle Hamiltonian. However, the exchange-
+correlation energy, which contains all the quantum mechanical interactions of the electrons, does 
+not have an exact expression in terms of the electron density and as such requires an 
+approximation, such as the local density approximation (LDA) [7] or the generalized gradient 
+approximation (GGA) [8]. Such approximations have limited accuracy, most notably the 
+underestimation of the band gap of semiconductors and insulators [9]. Various approaches have 
+been proposed to address this limitation, such as the on-site Hubbard U correction [10], hybrid 
+functionals using fractional exact exchange [11], and quasiparticle methods such as the GW 
+approximation [12]. However, these methods do not always guarantee an accurate description of 
+the system, and they can be much more computationally expensive than conventional DFT [13]. 
+ 
+An alternative strategy for band gap prediction is machine learning. For example, a support 
+vector regression model was constructed for inorganic solids using experimentally measured 
+band gaps [14], thereby bypassing the limitations of DFT. Another study trained a kernel ridge 
+regression model [15] using band gaps computed with the GLLBSC (Gritsenko, van Leeuwen, 
+van Len the, and Baerends solid correlation) functional [16], which demonstrated reasonable 
+agreement with experimental values. These studies attest to the potential of machine learning 
+methods, provided that robust datasets are available for training [17]. The importance of band gap 
+prediction of functional materials and the above-mentioned limitation of DFT serves as the 
+motivation for this research study, which attests to the potential of machine learning regression 
+for band gap prediction. 
+ 
+We employ a dataset of GLLBSC-computed band gaps of 1306 double perovskites in this study. 
+Double perovskites (𝐴𝐴′𝐵𝐵′𝑋6) have double the unit cell of single perovskites (𝐴𝐵𝑋3) with 
+chemically distinct A/𝐴′ and B/𝐵′ sites [18]. A variety of physical and chemical properties can be 
+engineered by doping the cations with species of different valence states or radii [19]. Due to 
+their stable crystal structure, unique electromagnetic properties, and high catalytic activities, 
+these compounds have much potential as functional materials for environmental protection [20], 
+the chemical industry [21], photovoltaics [22], and catalysis [23]. In this regard, optimization and 
+engineering in the above-mentioned fields require a proper description of the underlying 
+electronic structure of double perovskites [24], which attests to the significance of choosing the 
+band gaps of double perovskites as our dataset.  
+ 
+Previous studies have shown that random forest regression is well-suited to capturing 
+nonlinearity, as seen across the band gap and the extracted physical features such as the highest 
+occupied energy level [25]. As such, we construct a random forest regression model for 
+predicting the band gap of double perovskite compounds, building upon a previous kernel ridge 
+regression study [15]. We find that the bulk modulus, superconductivity temperature, and cation 
+electro negativity exhibit the highest importance scores among the 20 physical descriptors 
+employed, consistent with the physics of the underlying electronic structure. A model accuracy of 
+85.6% with a root mean square error of 0.64 eV is obtained using the top 10 features, comparable 
+to previous studies [1]. 
+ 
+The succeeding part of the paper is structured as follows: The literature review is given in section 
+2; the research methodology is presented in section 3; section 4 presents the results and 
+discussion, including an evaluation of the performance of our model as well as our limitations; 
+finally, section 5 gives the concluding remarks of this work. 
+ 
+
+Computer Science & Information Technology (CS & IT)                                        17 
+ 
+ 
+2. LITERATURE REVIEW 
+ 
+This research study focuses on the prediction of the band gaps of double perovskite materials 
+using machine learning, as a surrogate method for the conventional prediction yielded by the 
+DFT. The limitation of the DFT, notably the lack of expression of the exchange-correlation 
+energy, and the potential of machine learning in solving the issue have urged computer scientists 
+to try various machine learning models for band gap prediction. This section will review recently 
+proposed machine learning models for band gap prediction. 
+ 
+2.1 Tuplewise Graph Neural Networks (TGNN) 
+ 
+Na, G. S. et al. [26] conducted a research study using modified TGNN (Tuplewise Graph Neural 
+Networks) to predict the band gap of a crystalline compound. TGNN is designed to automatically 
+generate crystal representation using crystal structures and to include the crystal-level properties 
+as an input feature. In this study, the prediction of the band gap using TGNN is shown to have 
+higher accuracy than the standard DFT. The results of two out of four datasets that the study 
+employed are of interest in our research: 1345 organic-inorganic perovskite materials of which 
+the targeting band gap is the hybrid screened exchange functional (HSE06) and 2233 materials 
+for solar cells with the targeting band gap as GLLBSC-computed band gap. Using the proposed 
+TGNN model, the experiment of the former dataset achieved an MAE of 0.045 eV and that of the 
+latter dataset achieved an MAE of 0.295 eV. 
+ 
+2.2. Alternating Conditional Expectations (ACE) 
+ 
+ACE (Alternating Conditional Expectations) is a machine learning algorithm designed to find the 
+optimal transformation between the two sets of variables, and performs well on small data sets; 
+its advantage is that the results are represented in graphic form. The limitation of ACE is that if 
+the dependence of the response variable on the predictors is slightly different than the 
+transformation that the algorithm estimated, the analytic formulas are very difficult to discover. 
+Gladkikh, V. et al. [27] conducted a study exploring the mappings between the band gap and the 
+properties of the constituent elements using ACE. The study employs a dataset containing a large 
+number of single perovskite materials (𝐴𝐵𝑋3). The best result achieved using ACE has an RMSE 
+of 0.836 eV and an MAE of 0.602 eV.  
+ 
+2.3. Kernel Ridge Regression (KRR) 
+ 
+Regonia, P.R. et al. [28] trained a KRR (Kernel Ridge Regression) model for the prediction of the 
+optical band gap of zinc oxide (𝑍𝑛𝑂). Kernel ridge regression is a variant of ridge regression that 
+is suitable for small datasets and is usually used for the prediction of the band gap of organic 
+crystal structures. The model is trained using two empirical features: the experimental time and 
+temperature conditions during 𝑍𝑛𝑂 fabrication. Quadratic features are generated to increase the 
+model's complexity and prevent the dataset's underfitting. The result presents an RMSE of 0.0849 
+eV. 
+ 
+3. METHODS 
+ 
+3.1. Random Forest Regression 
+ 
+Random forest regression is a regression method that utilizes multiple decision trees, which are 
+constructed by a simple supervised algorithm consisting of a series of if-then-else statements. The 
+randomness is manifested through random sampling of data subsets or random selection of 
+
+18 
+       
+ 
+Computer Science & Information Technology (CS & IT) 
+ 
+features. Multiple uncorrelated decision trees construct a random forest, where all trees are 
+granted free growth without any pruning. The random forest algorithm can be employed for both 
+classification and regression. For classification, the result is the outcome with the highest turnout 
+among all trees; for regression, the forest takes the average of all trees. The steps to generate a 
+random forest are as follows (Fig. 1 illustrates a flow chart of the algorithm): 
+ 
+1. From a sample with capacity N, conduct bootstrap sampling K times. The resulting K samples 
+are used as the node samples of decision trees. 
+2. Choose a constant m smaller than the dataset feature number M.  
+3. When splitting each decision tree, select m features from the original M features, choosing 
+one feature as the splitting feature of the node. The Gini index is used to calculate the 
+information gain and determine the splitting. 
+4. Repeat step 2 and step 3 for each node until no splitting can occur, when the next feature is 
+used by the parent node in the last splitting. The tree is always left unpruned to ensure free 
+growth. 
+5. Repeat steps 1-4 to generate a random forest. 
+ 
+A random forest can manage data with a high dimension of features without performing 
+dimension reduction or feature selection. This is beneficial for the dataset of this study, which 
+involves multiple atomic descriptors of double perovskites. The mutual effects of different 
+features and their significance are also quantified. Although random forest regression is 
+computationally efficient and accurate when using a large number of generated trees, the risk of 
+overfitting still exists for data with a large noise. We perform random forest regression as 
+implemented in scikit-learn, using the double_perovskites_gap dataset available in the matminer 
+package [29]. Comparing previous literature, which is normally trained using 5 to 10 atomic 
+features [30], our result is unique in the sense that we use a total of 20 atomic features to achieve 
+a more comprehensive result, of which the dimension is then reduced to 10 features. The selected 
+important features are also consistent with the underlying physics, making the results more 
+credible. 
+ 
+ 
+ 
+Figure 1. Flow chart of random forest regression 
+ 
+3.2.  Features 
+ 
+20 atomic features are obtained from the periodic_table and composition modules of the 
+Pymatgen [31] (Python Materials Genomics) package: 
+ 
+Average electronegativity 
+Average cation electronegativity 
+
+Sample Set
+(N capacity,M
+featurcs)
+Choosevariable
+Training Set 1
+Training Set2
+Training Set K
+For each variable
+Sample data
+For each tree
+Sortdata according to
+variable
+Get Gini index
+Choosethebestsplit
+Prediction 1
+Prediction 2
+Prediction K
+Average oftreepredictions
+PredictionComputer Science & Information Technology (CS & IT)                                        19 
+ 
+ 
+Average atomic radius 
+Average van der walls radius 
+Average Mendeleev number 
+Average electrical resistivity 
+Average molar volume 
+Average thermal conductivity 
+Average boiling point 
+Average melting point 
+Average critical temperature 
+Average superconduction temperature 
+Average bulk modulus 
+Average youngs modulus 
+Average Brinell hardness 
+Average rigidity modulus 
+Average mineral hardness 
+Average Vickers hardness 
+Average density of solid phase 
+Average first ionization energy 
+ 
+The dataset is first converted into a data frame, which is then processed by applying the chemical 
+composition of each compound to corresponding classes and functions in the Pymatgen package 
+to obtain the 20 features. Compositional averages are taken for atomic features of a given 
+compound, whereas molecular features are used directly. Missing values are not counted in the 
+calculation of the average. 
+ 
+4. RESULTS AND DISCUSSION 
+ 
+4.1.  Model Selection 
+ 
+Random forest regression has two parameters to be optimized: the number of estimators 
+(n_estimator) referring to the number of trees to be built before taking the maximum voting or 
+averages of predictions; and the random seed (random_state) for the random generator. Both the 
+accuracy and the computational cost of the model increase with the number of estimators [32]. 
+The cost scales as 𝑂(𝑛tree ∗ 𝑚try ∗ 𝑛 log(𝑛)), where 𝑛tree is the number of estimators, 𝑚try is 
+the number of variables to sample at each node, and 𝑛 is the number of records [33]. As such, an 
+optimal number of estimators is needed to ensure a satisfactory model performance. 
+ 
+As shown in Fig. 2, the model accuracy reaches a maximum at around 700 estimators and 
+decreases afterward, which is attributed to overfitting. As such, the n_estimator is set to 700. On 
+the other hand, the random seed determines the random sampling for the train-test split and may 
+subtly affect the accuracy due to the randomization of the training pipeline. An optimal 
+random_state value of 14 is selected. 
+ 
+The corresponding parity plot of the model prediction is shown in Fig. 3. Using a test/training 
+ratio of 0.25 and all 20 physical descriptors, the model accuracy is 85.1% with a mean absolute 
+error (MAE) of 0.47 eV, a root mean squared error (RMSE) of 0.62 eV, which is comparable to 
+the RMSE value of 0.5 eV reported in a previous kernel ridge regression study of the same 
+dataset. 
+ 
+
+20 
+       
+ 
+Computer Science & Information Technology (CS & IT) 
+ 
+ 
+ 
+Figure 2. The accuracy of the random forest regression model as a function of (a) the number of estimators 
+and (b) the random seed, using all 20 physical descriptors. 
+ 
+ 
+ 
+Figure 3. Parity plot of the predicted vs. GLLBSC-computed band gaps, obtained using all 20 physical 
+descriptors and a test/training ratio of 25/75. The parity line is shown in red. 
+ 
+4.2. Feature Selection 
+ 
+The feature importance plot is shown in Fig. 4. The top three features with the highest 
+importance scores are average bulk modulus, superconductivity temperature, and cation 
+electronegativity: 
+ 
+1) 
+Bulk modulus quantifies the elastic property of a solid or fluid under pressure, 
+specifically its resistance to compression [34]. Microscopically, bulk modulus depends on the 
+compressibility of atoms, which affects the extent of the overlap of valence atomic orbitals, and 
+therefore the band gap of the material [35]. 
+ 
+
+(a)
+(b)
+61.3
+84.25
+84.2
+84.1
+84.20
+Accuracy
+Accuracy
+64.15
+64.10
+83.8
+84.05
+83.7
+84:00
+1000
+2000
+5000
+Numberofestimators
+Randomseed8
+7
+5
+4
+m
+2
+1
+0
+0
+1
+2
+3
+4
+5
+6
+7
+8
+GLLBSCbandgap(eV)Computer Science & Information Technology (CS & IT)                                        21 
+ 
+ 
+ 
+ 
+Figure 4. Feature importance of all 20 physical descriptors, obtained from a test/training ratio of 25/75. 
+ 
+2) 
+Superconductivity is the state of matter with no electrical resistance and magnetic 
+penetrability [36]. Given that the magnitude of the band gap determines the electrical 
+conductivity, a material with a relatively small band gap is expected to more easily achieve a 
+superconducting state [37]. 
+3) 
+Electronegativity quantifies the ability of an atom to attract an electron pair in a chemical 
+bond [38]. The cation electronegativity here refers to the electronegativity difference between the 
+oxygen anions and the metal cations. A larger elemental electronegativity difference leads to a 
+larger degree of electron localization around the more electronegative element, which makes it 
+harder for electrons to leap to the conduction band [39]. 
+ 
+The low importance scores of some features, such as average electrical resistivity and molar 
+volume, indicate that the dataset contains a large amount of noise, which necessitates feature 
+selection. Table 1 summarizes the model performance using different numbers of top features. 
+The performance remains optimal up to the top 10 features, which yields an accuracy of 85.6% 
+with an RMSE of 0.64 eV. Given the marginal difference in accuracy using 20, 15, and 10 top 
+features, the remainder of the study employs the top 10 features only. 
+ 
+Table 1. The model performance obtained using different numbers of features with the highest feature 
+importance scores (MAE = mean absolute error; RMSE = root mean squared error;  
+NRMSE = normalized RMSE). 
+ 
+Number of top features 
+20 
+15 
+10 
+5 
+3 
+1 
+Accuracy (%) 
+85.1 
+85.5 
+85.6 
+82.3 
+82.4 
+65.2 
+MAE (eV) 
+0.47 
+0.46 
+0.46 
+0.56 
+0.57 
+1.12 
+RMSE (eV) 
+0.62 
+0.62 
+0.64 
+0.79 
+0.81 
+1.43 
+NRMSE 
+0.08 
+0.07 
+0.08 
+0.10 
+0.10 
+0.17 
+ 
+
+avg bulk modulus
+avgsuperconductivitytemperature
+avg cation electronegativity
+avg electronegativity
+avg boiling point
+avg critical temperature
+avg Vickers hardness
+avg Mendeleev number
+avg thermal conductivity
+avg Youngs modulus
+avg rigidity modulus
+avg mineral hardness
+avg density of solid phase
+avg first ionization energy
+avg van der Waals radius
+avg melting point
+avg Brinell hardness
+avg atomic radius
+avg molar volume
+avg electrical resistivity
+0.0000.0250.0500.0750.1000.125
+0.1500.1750.20022 
+       
+ 
+Computer Science & Information Technology (CS & IT) 
+ 
+The corresponding importance scores and parity plots are shown in Figs. 5 & 6, respectively. The 
+model constructed using the top 10 features exhibits the least deviation of the data points from 
+the parity line. Moreover, the models overall tend to show a larger underestimation for larger 
+band gap values, which can potentially be attributed to the limited accuracy of the GLLBSC 
+functional itself [40]. 
+ 
+ 
+ 
+Figure 5. Feature importance scores for models constructed using a number of features with the highest 
+importance scores. 
+ 
+4.3. Testing and Training Set partition 
+ 
+Table 2 summarizes the model performance as a function of the different test-to-training set 
+partitions, ranging from 10/90 to 75/25. As expected, the test set accuracy decreases with the 
+number of training set data points. The corresponding parity plots in Fig. 7 also demonstrate a 
+larger extent of deviation from the parity line as the proportion of the training set decreases. 
+Based on these results, we validate that the test/training ratio of 25/75 is sufficient in providing 
+satisfactory accuracy (85.6%) and reasonable RMSE (0.64 eV). 
+ 
+Table 2. Model performance obtained with different test-to-training set partitions. 
+ 
+Test/training set ratio 
+10/90 
+20/80 
+25/75 
+40/60 
+50/50 
+75/25 
+Number of test set data points 
+131 
+262 
+327 
+523 
+653 
+980 
+Number of training set data points 
+1175 
+1044 
+979 
+783 
+653 
+326 
+Test set accuracy (%) 
+87.9 
+86.8 
+85.6 
+82.6 
+82.5 
+76.2 
+MAE (eV) 
+0.41 
+0.45 
+0.46 
+0.5 
+0.53 
+0.67 
+RMSE (eV) 
+0.57 
+0.63 
+0.64 
+0.7 
+0.74 
+0.88 
+NRMSE 
+0.07 
+0.08 
+0.08 
+0.08 
+0.09 
+0.11 
+ 
+ 
+
+Top 20
+Top 15
+Top 10
+avg bulk modulus
+avg bulk modulus
+sninpow xinq 6Ae
+avg superconductivity temperature
+avg cation electronegativity
+avg superconductivity temperature
+avg superconductivity temperature
+avg electronegativity
+avg electronegativity
+avg critical temperature
+avg boilling point
+avg Vickers hardness
+avg boiling point
+avg critical temperature
+avg cation electronegativity
+avg Mendeleev number
+avg Vickers hardness
+avg electronegativity
+avg Youngs modulus
+avg Mendeleev number
+avg thermal conductivity
+avg Vickers hardness
+avg min
+neralhardness
+avg density of solid phase
+avg Youngs modulus
+avg first ionization
+avg critical temperature
+avg van der Waals radius
+avg rigidity modulus
+avg melting point
+avg density of solid phase
+avg Youngs modulus
+avg Brinell hardness
+avg first ionization energy
+avg atomic radius
+avg Mendeleev number
+avg molar volume
+avg mineral hardness
+avg electrical resistivity
+avg van der Waals radius
+avg thermal conductivity
+0.00D.02D.05.07.10D.12.15.175.200
+0.00D.025.05.075.10D.125.15D.175.200
+0.00
+0.05
+0.10
+0.15
+0.20
+Top 5
+ dol
+avg superconductivity temperature
+avg superconductivity temperature
+avg bulk modulus
+avg boiling point
+avg bulk modulus
+avg cation electronegativity
+avg cation electronegativity
+avg electronegativity
+0.000.050.100.150.200.250.30
+0.00 0.05 0.10 0.15 0.20 0
+0.25 0.30 0.35 0.40Computer Science & Information Technology (CS & IT)                                        23 
+ 
+ 
+ 
+ 
+Figure 6. Parity plots of the predicted vs. GLLBSC-computed band gaps obtained using different numbers 
+of features with the highest importance scores. The parity line is shown in red. 
+ 
+ 
+ 
+Figure 7. Parity plots of the predicted vs. GLLBSC-computed band gaps obtained using different test-to-
+training set partitions. The parity line is shown in red. 
+
+Top 20
+Top 15
+8
+(eV)
+7
+deb
+5
+band
+4
+4
+Predicted 
+3
+2
+N
+-
+1
+5
+8
+1
+2
+5
+6
+7
+8
+GLLBSCbandgap (eV)
+GLLBSC band gap (eV)
+Top 10
+Top 5
+8
+8
+7
+deb
+6
+band
+4
+4
+Predicted
+Predicted b
+3
+2
+N
+0
+0
+2
+3
+4
+5
+6
+8
+.
+2
+3
+4
+GLLBSC E
+band_gap (ev)
+GLLBSC band gap (eV)
+6
+:
+Top 3
+Top 1
+8
+(eV)
+7
+gap
+Iband
+5
+4
+Predicted
+Predicted 
+3
+N
+2
+5
+8
+2
+4
+5
+GLLBSC band gap (eV)
+GLLBSC band gap (eV)test/training=1o/90
+test/training=20/80
+8
+7
+ Predicted band gap (evV)
+gap
+5
+band
+4
+4
+Predicted
+3
+2
+N
+1
+1
+0
+0
+0
+1
+3
+5
+6
+1
+2
+3
+4
+5
+6
+8
+GLLBSC band gap (eV)
+test/training=25/75
+test/training=40/60
+8
+B
+7
+ gap (eV)
+6
+5
+band
+5
+ band
+4
+4
+Predicted
+Predicted 
+3
+2
+-
+0
+1
+2
+3
+4
+5
+8
+1
+2
+3
+4
+GLLBSC band gap (eV)
+6
+:
+GLLBSC band gap (eV)
+test/training=50/50
+test/training=75/25
+8
+8
+ Predicted band gap (evV)
+deb
+5
+band
+4
+4
+Predicted
+3
+m
+N
+N
+2
+.
+5
+8
+6
+8
+GLLBSC band gap (eV)
+GLLBSC band gap (eV)24 
+       
+ 
+Computer Science & Information Technology (CS & IT) 
+ 
+4.4.  Model Performances 
+ 
+Table 3 summarizes the result of previous studies. The best performance yields in KRR by P. R. 
+Regonia et al. [28] with an RMSE of 0.09. Our random forest regression model is comparable to 
+linear regression and XBGoost by G. S. Na et al. [26] and has a lower MAE than ACE and ET by 
+V. Gladkikh et al. [27]. 
+ 
+Table 3. Results of the models for band gap prediction (TGNN = tuplewise graph neural networks; 
+XGBoost = extreme gradient boosting; ACE = alternating conditional expectations; ET = extremely 
+randomized trees; KRR = kernel ridge regression; ANN = alternating conditional expectations; GBR = 
+gradient boosting regression). 
+ 
+Model 
+Study 
+Material 
+type 
+Number 
+of 
+materials 
+Band gap 
+Accuracy 
+(%) 
+MAE 
+(eV) 
+RMSE 
+(eV) 
+Random 
+forest 
+J. Zhang et al.  
+Double 
+perovskites 
+1306 
+GLLBSC 
+85.6 
+0.46 
+0.64 
+TGNN 
+G. S. Na et al. 
+[26] 
+Materials 
+for 
+solar 
+cells 
+2233 
+GLLBSC 
+- 
+0.30 
+- 
+Linear 
+regression 
+G. S. Na et al. 
+[26] 
+Materials 
+for 
+solar 
+cells 
+2233 
+GLLBSC 
+ 
+- 
+0.44 
+- 
+XGBoost 
+G. S. Na et al. 
+[26] 
+Materials 
+for 
+solar 
+cells 
+2233 
+GLLBSC 
+- 
+0.44 
+- 
+ACE 
+V. Gladkikh 
+et al. [27] 
+Single 
+perovskites 
+- 
+HSE 
+- 
+0.60 
+0.84 
+ET 
+V. Gladkikh 
+et al. [27] 
+Single 
+perovskites 
+- 
+HSE 
+- 
+0.54 
+0.75 
+KRR 
+P. 
+R. 
+Regonia 
+et 
+al. [28] 
+ZnO 
+quantum 
+dots 
+- 
+Optical 
+band gap 
+98.0 
+- 
+0.09 
+ANN 
+P. 
+R. 
+Regonia 
+et 
+al. [28] 
+ZnO 
+quantum 
+dots 
+- 
+Optical 
+band gap 
+97.8 
+- 
+0.09 
+GBR 
+M. Guo et al. 
+[8] 
+Binary 
+compounds 
+4096 
+DFT-
+calculated 
+band gap 
+ 
+81.0 
+- 
+0.26 
+ 
+4.5. Limitations and Recommendations 
+ 
+This study is limited by the relatively small sample size. We use 1306 data to generate all the 
+results, which may reduce the power of the study and cause a large margin of error. Future 
+research studies can focus on using larger datasets, which we suppose will improve the model 
+fitting. In this study, the missing values are filled by the mean value of that feature. This 
+preprocessing step can be taken more carefully by trying various means to deal with the missing 
+values. Another limitation of the study is that we lack a more interpretable understanding of 
+random forest regression in statistical learning theory. A single decision tree is interpretable 
+because it follows several decision steps, whereas a forest lacks this step-by-step interpretability. 
+Hence, using interpretability tools such as the RF Visualization Toolkits [41] to generate a 
+“Decision Path View” may help to understand the forest. This is essential since the feature’s 
+importance is related to the underlying physics.  
+
+Computer Science & Information Technology (CS & IT)                                        25 
+ 
+ 
+5. CONCLUSION 
+ 
+Despite the widespread use of first-principles methods based on density functional theory (DFT) 
+in materials science, it remains computationally costly and limited in its accuracy due to the 
+approximation of the exchange-correlation functional. In this regard, machine learning presents a 
+viable alternative for the rapid prediction of materials’ electronic properties while retaining 
+reasonable fidelity to DFT. This study has implemented random forest regression for the 
+prediction of the band gap of double perovskite compounds employing a dataset of 1306 
+GLLBSC-computed band gaps. Among the 20 physical descriptors, average bulk modulus, 
+superconductivity temperature, and cation electronegativity exhibited the highest importance 
+scores, which provide a physically interpretable description in terms of the underlying electronic 
+structure. Optimal model performance is obtained with the top 10 features and a test/training 
+partition of 25/75, yielding a model accuracy of 85.6% and RMSE of 0.64 eV comparable to 
+previous studies. Our results highlight the potential of machine learning regression for rapid and 
+physically interpretable prediction of the electronic properties of functional materials. 
+ 
+ACKNOWLEDGMENTS 
+ 
+This work was supported by Touch Education Technology Inc. We acknowledge scientific and 
+editorial support from the Project Lead, J. S. Lim of Harvard University; technical support from 
+the Project Support C. Zhang; and administrative support from C. Ding of Touch Education 
+Technology Inc. 
+ 
+This work was led by J.Z. with support from Y.L. and X.Z. J.Z. performed machine learning, 
+literature review, and drafted the manuscript. Y.L. performed parameter optimization, 
+visualization, and literature review. X.Z. assisted with literature review and writing. 
+ 
+REFERENCES 
+ 
+[1] 
+M. Guo, X. Xu & H. Xie, “Predicting the band gap of binary compounds from machine-learning 
+regression methods,” 2021.  
+[2] 
+B. R. Sutherland, “Solar Materials Find Their Band Gap,” Joule, vol. 4, pp. 984–985, 2020. 
+[3] 
+J. Zhang, L. Yang, M. Qu, D. Qi & K. H. L. Zhang, “Wide Bandgap Oxide Semiconductors: from 
+Materials Physics to Optoelectronic Devices,” Advanced Materials, vol. 33, 2021. 
+[4] 
+D. Bagayoko, “Understanding density functional theory (DFT) and completing it in practice,” AIP 
+Advances, vol. 4, 2014. 
+[5] 
+R. Jestädt, M. Ruggenthaler, M. J. T. Oliveira, A. Rubio & H. Appel, “Light-matter interactions 
+within the Ehrenfest–Maxwell–Pauli–Kohn–Sham framework: fundamentals, implementation, and 
+nano-optical applications”, Advances in Physics, vol. 68, issue 4, pp. 225-333, 2019. 
+[6] 
+M. Kuisma, J. Ojanen, J. Enkovaara & T. T. Rantala, “Kohn-Sham potential with discontinuity for 
+band gap materials,” Physical Review B - Condensed Matter and Materials Physics, vol. 82, 2010. 
+[7] 
+X. Hai, J. Tahir-Kheli & W. A. Goddard, “Accurate band gaps for semiconductors from density 
+functional theory,” Journal of Physical Chemistry Letters, vol. 2, pp. 212–217, 2011. 
+[8] 
+R. Peverati, Y. Zhao & D. G. Truhlar, “Generalized Gradient Approximation That Recovers the 
+Second-Order Density-Gradient Expansion with Optimized Across-the-Board Performance,” The 
+Journal of Physical Chemistry Letters, vol. 2, issue 16, pp. 1991-1997, 2011. 
+[9] 
+J. S. Lim, D. Saldana-Greco & A. M. Rappe, “Improved pseudopotential transferability for magnetic 
+and electronic properties of binary manganese oxides from DFT+U+J calculations,” Physical Review 
+B, vol. 94, 2016. 
+[10]  E. Ahmed & K. Senthilkumar, “First-principle investigation of defect-associated LVM and structural 
+parameter dependency in response to the ground state on-site Hubbard correction of w-ZnO,” Journal 
+of Raman Spectroscopy, vol. 53, issue 6, pp. 1166-1178, 2022. 
+
+26 
+       
+ 
+Computer Science & Information Technology (CS & IT) 
+ 
+[11] C. Franchini, R. Podloucky, J. Paier, M. Marsman & G. Kresse, “Ground-state properties of 
+multivalent manganese oxides: Density functional and hybrid density functional calculations,” 
+Physical Review B - Condensed Matter and Materials Physics, vol. 75, 2007. 
+[12] M. J. van Setten, F. Weigend & F. Evers, “The GW-method for quantum chemistry applications: 
+Theory and implementation,” Journal of Chemical Theory and Computation, vol. 9, pp. 232–246, 
+2013. 
+[13] D. Bagayoko, “Understanding density functional theory (DFT) and completing it in practice,” AIP 
+Advances, vol. 4, 2014. 
+[14] Y. Zhuo, A. Mansouri Tehrani & J. Brgoch, “Predicting the Band Gaps of Inorganic Solids by 
+Machine Learning,” Journal of Physical Chemistry Letters, vol. 9, pp. 1668–1673, 2018. 
+[15]  
+ A. C. Rajan, A. Mishra, S. Satsangi, R. Vaish, H. Mizuseki, K. Lee, K. A. Singh, “Machine-
+learning-assisted accurate band gap predictions of functionalized mxene,” Chemistry of Materials, vol. 
+30, pp. 4031–4038, 2018. 
+[16]  O. Gritsenko, N. van Leeuwen, E. van Lenthe & E. J. Baerends, “Self-consistent approximation to the 
+Kohn-Sham exchange potential,” PHYSICAL REVIEW A, vol. 51, pp. 1944-1954, 1995. 
+[17]  J. Schmidt, M. R. G. Marques, S. Botti & M. A. L. Marques, “Recent advances and applications of 
+machine learning in solid-state materials science,” npj Computational Materials, vol. 5, 2019. 
+[18]  
+T. Saha-Dasgupta, “Double perovskites with 3d and 4d/5d transition metals: Compounds with 
+promises,” Materials Research Express, vol. 7, 2019. 
+[19] E. Grabowska, “Selected perovskite oxides: Characterization, preparation and photocatalytic 
+properties-A review,” Applied Catalysis B: Environmental, vol. 186, pp. 97–126, 2016. 
+[20]  A. Dey, J. Ye, A. De, E. Debroye, A. Ha, E. Bladt, A. Kshirsagar, Z. Wang, J. Yin, Y. Wang, L. 
+Quan, F. Yan, M. Gao, X. Li, J. Shamsi, T. Debnath, M. Cao, M. Scheel, S. Kumar, J. Steele, M. 
+Gerhard, L. Chouhan, K. Xu, X. Wu, Y. Li, Y. Zhang, A. Dutta, C. Han, I. Vincon, A. Rogach, A. 
+Nag, A. Samanta, B. Korgel, C. Shih, D. Gamelin, D. Son, H. Zeng, H. Zhong, H. Sun, H. Demir, I. 
+Scheblykin, I. Mora-Seró, I. Stolarczyk, J. Zhang, J. Feldmann, J. Hofkens, J. Luther, J. Pérez-Prieto, 
+L. Li, L. Manna, M. Bodnarchuk, M. Kovalenko, M. Roeffaers, N. Pradhan, O. Mohammed, O. Bakr, 
+P. Yang, P. Müller-Buschbaum, P. Kamat, Q. Bao, Q. Zhang, R. Krahne, R. Galian, S. Stranks, S. 
+Bals, V. Biju, W. Tisdale, Y. Yan, R. Hoye & L. Polavarapu, “State of the Art and Prospects for 
+Halide Perovskite Nanocrystals,” ACS Nano, vol. 15, pp. 10775–10981, 2021. 
+[21] P. Chen, Y. Bai, S. Wang, M. Lyu, J. Yun & L. Wang, “In Situ Growth of 2D Perovskite Capping 
+Layer for Stable and Efficient Perovskite Solar Cells,” Advanced Functional Materials, vol. 28, 2018. 
+[22]  C. Wu, Q. Zhang, Y. Liu, W. Luo, X. Guo, Z. Huang, H. Ting, W. Sun, X. Zhong, S. Wei, S. Wang, 
+Z. Chen, L. Xiao, “The Dawn of Lead-Free Perovskite Solar Cell: Highly Stable Double Perovskite 
+Cs2AgBiBr6 Film,” Advanced Science, vol. 5, 2018. 
+[23] H. Wang, J. Want, Y. Pi, Q. Shao, Y. Tan & X. Huang, “Double Perovskite LaFexNi1−xO3 
+Nanorods Enable Efficient Oxygen Evolution Electrocatalysis,” Angewandte Chemie, vol. 131, pp. 
+2338–2342, 2019. 
+[24] K. Du, W. Meng, X. Wang, Y. Yan & D. B. Mitzi, “Bandgap Engineering of Lead‐Free Double 
+Perovskite Cs2AgBiBr6 through Trivalent Metal Alloying,” Angewandte Chemie, vol. 129, pp. 
+8270–8274, 2017. 
+[25] Z. Guo & B. Lin, “Machine learning stability and band gap of lead-free halide double perovskite 
+materials for perovskite solar cells,” Solar Energy, vol. 228, pp. 689–699, 2021. 
+[26] G. S. Na, S. Jang, Y. L. Lee & H. Chang, “Tuplewise Material Representation Based Machine 
+Learning for Accurate Band Gap Prediction,” The Journal of Physical Chemistry A, vol. 124, issue 50, 
+pp. 10616-10623, 2020. 
+[27] V. Gladkikh, D. Y. Kim, A. Hajibabaei, A. Jana, C. W. Myung & K. S. Kim, “Machine Learning for 
+Predicting the Band Gaps of ABX3 Perovskites from Elemental Properties,” The Journal of Physical 
+Chemistry C, vol. 124, issue 16, pp. 8905-8918, 2020. 
+[28] P. R. Regonia, C. M. Pelicano, R. Tani, A. Ishizumi, H. Yanagi & K. Ikeda, “Predicting the band gap 
+of ZnO quantum dots via supervised machine learning models,” Optik, vol. 207, 2020. 
+[29] L. Ward, A. Dunn, A. Faghaninia, N. Zimmermann, S. Bajaj, Q. Wang, J. Montoya, J. Chen, K. 
+Bystrom, M. Dylla, K. Chard, M. Asta, K. Persson, G. Snyder, I. Foster, A. Jain, “Matminer: An open 
+source toolkit for materials data mining,” Computational Materials Science, vol. 152, pp. 60–69, 2018. 
+[30] L. Zhang & W. Hu, “High-Throughput Calculation and Machine Learning of Two-Dimensional 
+Halide Perovskite Materials: Formation Energy and Band Gap,” 2022. 
+
+Computer Science & Information Technology (CS & IT)                                        27 
+ 
+ 
+[31] S. Ong, W. Richards, A. Jain, G. Hautier, M. Kocher, S. Cholia, D. Gunter, V. Chevrier, K. Persson, 
+G. Ceder, “Python Materials Genomics (pymatgen): A robust, open-source python library for 
+materials analysis. Computational Materials Science, vol. 68, pp. 314–319, 2013. 
+[32] P. Probst, M. N. Wright & A. L. Boulesteix, “Hyperparameters and tuning strategies for random 
+forest,” Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery, vol. 9, 2019. 
+[33] X. Solé, S. Solé, A. Ramisa & C. Torras, “Evaluation of Random Forests on large-scale classification 
+problems using a Bag-of-Visual-Words representation,” 2014.  
+[34] A. Furmanchuk, A. Agrawal & A. Choudhary, “Predictive analytics for crystalline materials: bulk 
+modulus,” RSC Advances, vol. 6, issue 97, pp. 95246-95251, 2016.  
+[35] K Li, C. Kang & D. Xue, “Electronegativity calculation of bulk modulus and band gap of ternary 
+ZnO-based alloys,” Materials Research Bulletin, vol. 47, pp. 2902–2905, 2012. 
+[36] S. Saha, S. di Cataldo, M. Amsler, W. von der Linden & L. Boeri, “High-temperature conventional 
+superconductivity in the boron-carbon system: Material trends,” Physical Review B, vol. 102, 2020. 
+[37] K. B. Thapa, S. Srivastava & S. Tiwari, “Enlarged Photonic Band Gap in Heterostructure of Metallic 
+Photonic and Superconducting Photonic Crystals,” J Supercond Nov Magn, vol. 23, pp. 517–525, 
+2010. 
+[38] P. Politzer, J. S. Murray, “Electronegativity—a perspective,” J Mol Model, vol. 24, issue 214, 2018. 
+[39] K. Dagenais, M. Chamberlin & C. Constantin, “Modeling Energy Band Gap as a Function of Optical 
+Electronegativity for Binary Oxides,” Journal of Young Investigators, vol. 25, issue 3, pp. 73-78, 
+2013. 
+[40] F. Tran, S. Ehsan & P. Blaha, “Assessment of the GLLB-SC potential for solid-state properties and 
+attempts for improvement,” Physical Review Materials, vol. 2, 2018. 
+[41] M. Haddouchi & A. Berrado, “A survey of methods and tools used for interpreting Random Forest,” 
+1st International Conference on Smart Systems and Data Science (ICSSD), 2019, pp. 1-6. 
+ 
+AUTHORS AND CO-AUTHORS 
+ 
+Junfei Zhang is the author of this paper. She is currently pursuing a Bachelor of 
+Science degree at The University of Melbourne, Melbourne, Victoria, Australia. She is 
+actively conducting computer science related research studies. Her research interest 
+includes machine learning, computer vision, and quantum algorithms. She is currently 
+studying Computer Science at The University of Copenhagen, Copenhagen, Denmark as 
+an exchange student at the time of publication. 
+ 
+ 
+Yueqi Li is the co-author of this paper. She is pursuing B.S. Physics in College of 
+Physical Science and Technology, Xiamen University, China. Her main areas of 
+research interest are Biophysics and Machine learning. 
+ 
+ 
+ 
+Xinbo Zhou is the co-author of this paper. She is a junior student in the Faculty of 
+Information Technology at Beijing University of Technology 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+© 2023 By AIRCC Publishing Corporation. This article is published under the Creative 
+Commons Attribution (CC BY) license. 
+
diff --git a/L9E1T4oBgHgl3EQftAVw/content/tmp_files/load_file.txt b/L9E1T4oBgHgl3EQftAVw/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..9cf92143cabaa03333ea9f3efc0b3270a10b63d5
--- /dev/null
+++ b/L9E1T4oBgHgl3EQftAVw/content/tmp_files/load_file.txt
@@ -0,0 +1,1052 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf,len=1051
+page_content='David C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Wyld et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' (Eds): CSML, NET, BDHI, SIPO, SOEA- 2023  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 15-27, 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' CS & IT - CSCP 2023                                                                   DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='5121/csit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='130102  MACHINE-LEARNING PREDICTION OF THE COMPUTED BAND GAPS OF DOUBLE PEROVSKITE MATERIALS  Junfei Zhang1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Yueqi Li2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' and Xinbo Zhou3  1 School of Computing and Information Systems,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' The University of Melbourne,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Melbourne,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Victoria,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Australia 2 College of Physical Science and Technology,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Xiamen University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Xiamen,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Fujian,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' China 3 Faculty of Information Technology,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Beijing University of Technology,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Beijing,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' China  ABSTRACT  Prediction of the electronic structure of functional materials is essential for the engineering of new devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Conventional electronic structure prediction methods based on density functional theory (DFT) suffer from not only high computational cost, but also limited accuracy arising from the approximations of the exchange-correlation functional.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Surrogate methods based on machine learning have garnered much attention as a viable alternative to bypass these limitations, especially in the prediction of solid-state band gaps, which motivated this research study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Herein, we construct a random forest regression model for band gaps of double perovskite materials, using a dataset of 1306 band gaps computed with the GLLBSC (Gritsenko, van Leeuwen, van Lenthe, and Baerends solid correlation) functional.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Among the 20 physical features employed, we find that the bulk modulus, superconductivity temperature, and cation electronegativity exhibit the highest importance scores, consistent with the physics of the underlying electronic structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Using the top 10 features, a model accuracy of 85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='6% with a root mean square error of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='64 eV is obtained, comparable to previous studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Our results are significant in the sense that they attest to the potential of machine learning regressions for the rapid screening of promising candidate functional materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='  KEYWORDS  Machine Learning, Random Forest Regression, Electronic Structure, Computational Material Science  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' INTRODUCTION  In quantum mechanics, the energy of bound electrons becomes quantized [1], and electrons at the ground state can be excited to higher energy levels by absorbing photons with the corresponding wavelengths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' In solid structures, the superposed electronic states form continuous energy bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' In insulators and semiconductors, the band gap is the energy gap across the valence and conduction band where electrons are forbidden to occupy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' The magnitude of the band gap plays an important role in many functional materials, such as transistors, photovoltaics, light-emitting diodes, and sensors [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' For instance, optoelectronic materials are generally wide-band gap semiconductors, while thermoelectric materials are narrow-band gap semiconductors [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Hence, accurate and efficient prediction of band gaps of solid materials is crucial for the design and engineering of new devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='  16  Computer Science & Information Technology (CS & IT)  One of the most widely used electronic structure methods for evaluating band gaps is density functional theory (DFT) [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' In the Kohn-Sham formalism [5], the multielectron wavefunction is replaced by fictitious noninteracting states that give rise to the true electron density [6], which enables the iterative solution of the single-particle Hamiltonian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' However, the exchange- correlation energy, which contains all the quantum mechanical interactions of the electrons, does not have an exact expression in terms of the electron density and as such requires an approximation, such as the local density approximation (LDA) [7] or the generalized gradient approximation (GGA) [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Such approximations have limited accuracy, most notably the underestimation of the band gap of semiconductors and insulators [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Various approaches have been proposed to address this limitation, such as the on-site Hubbard U correction [10], hybrid functionals using fractional exact exchange [11], and quasiparticle methods such as the GW approximation [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' However, these methods do not always guarantee an accurate description of the system, and they can be much more computationally expensive than conventional DFT [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='  An alternative strategy for band gap prediction is machine learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' For example, a support vector regression model was constructed for inorganic solids using experimentally measured band gaps [14], thereby bypassing the limitations of DFT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Another study trained a kernel ridge regression model [15] using band gaps computed with the GLLBSC (Gritsenko, van Leeuwen, van Len the, and Baerends solid correlation) functional [16], which demonstrated reasonable agreement with experimental values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' These studies attest to the potential of machine learning methods, provided that robust datasets are available for training [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' The importance of band gap prediction of functional materials and the above-mentioned limitation of DFT serves as the motivation for this research study, which attests to the potential of machine learning regression for band gap prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='  We employ a dataset of GLLBSC-computed band gaps of 1306 double perovskites in this study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Double perovskites (𝐴𝐴′𝐵𝐵′𝑋6) have double the unit cell of single perovskites (𝐴𝐵𝑋3) with chemically distinct A/𝐴′ and B/𝐵′ sites [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' A variety of physical and chemical properties can be engineered by doping the cations with species of different valence states or radii [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Due to their stable crystal structure, unique electromagnetic properties, and high catalytic activities, these compounds have much potential as functional materials for environmental protection [20], the chemical industry [21], photovoltaics [22], and catalysis [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' In this regard, optimization and engineering in the above-mentioned fields require a proper description of the underlying electronic structure of double perovskites [24], which attests to the significance of choosing the band gaps of double perovskites as our dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='  Previous studies have shown that random forest regression is well-suited to capturing nonlinearity, as seen across the band gap and the extracted physical features such as the highest occupied energy level [25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' As such, we construct a random forest regression model for predicting the band gap of double perovskite compounds, building upon a previous kernel ridge regression study [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' We find that the bulk modulus, superconductivity temperature, and cation electro negativity exhibit the highest importance scores among the 20 physical descriptors employed, consistent with the physics of the underlying electronic structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' A model accuracy of 85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='6% with a root mean square error of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='64 eV is obtained using the top 10 features, comparable to previous studies [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='  The succeeding part of the paper is structured as follows: The literature review is given in section 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' the research methodology is presented in section 3;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' section 4 presents the results and discussion, including an evaluation of the performance of our model as well as our limitations;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' finally, section 5 gives the concluding remarks of this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='  Computer Science & Information Technology (CS & IT)                                        17  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' LITERATURE REVIEW  This research study focuses on the prediction of the band gaps of double perovskite materials using machine learning, as a surrogate method for the conventional prediction yielded by the DFT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' The limitation of the DFT, notably the lack of expression of the exchange-correlation energy, and the potential of machine learning in solving the issue have urged computer scientists to try various machine learning models for band gap prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' This section will review recently proposed machine learning models for band gap prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='1 Tuplewise Graph Neural Networks (TGNN)  Na, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' [26] conducted a research study using modified TGNN (Tuplewise Graph Neural Networks) to predict the band gap of a crystalline compound.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' TGNN is designed to automatically generate crystal representation using crystal structures and to include the crystal-level properties as an input feature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' In this study, the prediction of the band gap using TGNN is shown to have higher accuracy than the standard DFT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' The results of two out of four datasets that the study employed are of interest in our research: 1345 organic-inorganic perovskite materials of which the targeting band gap is the hybrid screened exchange functional (HSE06) and 2233 materials for solar cells with the targeting band gap as GLLBSC-computed band gap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Using the proposed TGNN model, the experiment of the former dataset achieved an MAE of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='045 eV and that of the latter dataset achieved an MAE of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='295 eV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Alternating Conditional Expectations (ACE)  ACE (Alternating Conditional Expectations) is a machine learning algorithm designed to find the optimal transformation between the two sets of variables, and performs well on small data sets;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' its advantage is that the results are represented in graphic form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' The limitation of ACE is that if the dependence of the response variable on the predictors is slightly different than the transformation that the algorithm estimated, the analytic formulas are very difficult to discover.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Gladkikh, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' [27] conducted a study exploring the mappings between the band gap and the properties of the constituent elements using ACE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' The study employs a dataset containing a large number of single perovskite materials (𝐴𝐵𝑋3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' The best result achieved using ACE has an RMSE of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='836 eV and an MAE of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='602 eV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Kernel Ridge Regression (KRR)  Regonia, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' [28] trained a KRR (Kernel Ridge Regression) model for the prediction of the optical band gap of zinc oxide (𝑍𝑛𝑂).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Kernel ridge regression is a variant of ridge regression that is suitable for small datasets and is usually used for the prediction of the band gap of organic crystal structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' The model is trained using two empirical features: the experimental time and temperature conditions during 𝑍𝑛𝑂 fabrication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=" Quadratic features are generated to increase the model's complexity and prevent the dataset's underfitting." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' The result presents an RMSE of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='0849 eV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' METHODS  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Random Forest Regression  Random forest regression is a regression method that utilizes multiple decision trees, which are constructed by a simple supervised algorithm consisting of a series of if-then-else statements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' The randomness is manifested through random sampling of data subsets or random selection of  18  Computer Science & Information Technology (CS & IT)  features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Multiple uncorrelated decision trees construct a random forest, where all trees are granted free growth without any pruning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' The random forest algorithm can be employed for both classification and regression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' For classification, the result is the outcome with the highest turnout among all trees;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' for regression, the forest takes the average of all trees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' The steps to generate a random forest are as follows (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 1 illustrates a flow chart of the algorithm):  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' From a sample with capacity N, conduct bootstrap sampling K times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' The resulting K samples are used as the node samples of decision trees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Choose a constant m smaller than the dataset feature number M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' When splitting each decision tree, select m features from the original M features, choosing one feature as the splitting feature of the node.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' The Gini index is used to calculate the information gain and determine the splitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Repeat step 2 and step 3 for each node until no splitting can occur, when the next feature is used by the parent node in the last splitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' The tree is always left unpruned to ensure free growth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Repeat steps 1-4 to generate a random forest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='  A random forest can manage data with a high dimension of features without performing dimension reduction or feature selection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' This is beneficial for the dataset of this study, which involves multiple atomic descriptors of double perovskites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' The mutual effects of different features and their significance are also quantified.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Although random forest regression is computationally efficient and accurate when using a large number of generated trees, the risk of overfitting still exists for data with a large noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' We perform random forest regression as implemented in scikit-learn, using the double_perovskites_gap dataset available in the matminer package [29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Comparing previous literature, which is normally trained using 5 to 10 atomic features [30], our result is unique in the sense that we use a total of 20 atomic features to achieve a more comprehensive result, of which the dimension is then reduced to 10 features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' The selected important features are also consistent with the underlying physics, making the results more credible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='  Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Flow chart of random forest regression  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Features  20 atomic features are obtained from the periodic_table and composition modules of the Pymatgen [31] (Python Materials Genomics) package:  Average electronegativity  Average cation electronegativity  Sample Set (N capacity,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='M featurcs) Choosevariable Training Set 1 Training Set2 Training Set K For each variable Sample data For each tree Sortdata according to variable Get Gini index Choosethebestsplit Prediction 1 Prediction 2 Prediction K Average oftreepredictions PredictionComputer Science & Information Technology (CS & IT)                                        ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='19  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='Average atomic radius Average van der walls radius Average Mendeleev number Average electrical resistivity Average molar volume Average thermal conductivity Average boiling point Average melting point Average critical temperature Average superconduction temperature Average bulk modulus Average youngs modulus Average Brinell hardness Average rigidity modulus Average mineral hardness Average Vickers hardness Average density of solid phase Average first ionization energy  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='The dataset is first converted into a data frame,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' which is then processed by applying the chemical composition of each compound to corresponding classes and functions in the Pymatgen package to obtain the 20 features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Compositional averages are taken for atomic features of a given compound, whereas molecular features are used directly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Missing values are not counted in the calculation of the average.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' RESULTS AND DISCUSSION  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Model Selection  Random forest regression has two parameters to be optimized: the number of estimators (n_estimator) referring to the number of trees to be built before taking the maximum voting or averages of predictions;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' and the random seed (random_state) for the random generator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Both the accuracy and the computational cost of the model increase with the number of estimators [32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' The cost scales as 𝑂(𝑛tree ∗ 𝑚try ∗ 𝑛 log(𝑛)), where 𝑛tree is the number of estimators, 𝑚try is the number of variables to sample at each node, and 𝑛 is the number of records [33].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' As such, an optimal number of estimators is needed to ensure a satisfactory model performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='  As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 2, the model accuracy reaches a maximum at around 700 estimators and decreases afterward, which is attributed to overfitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' As such, the n_estimator is set to 700.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' On the other hand, the random seed determines the random sampling for the train-test split and may subtly affect the accuracy due to the randomization of the training pipeline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' An optimal random_state value of 14 is selected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='  The corresponding parity plot of the model prediction is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Using a test/training ratio of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='25 and all 20 physical descriptors, the model accuracy is 85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='1% with a mean absolute error (MAE) of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='47 eV, a root mean squared error (RMSE) of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='62 eV, which is comparable to the RMSE value of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='5 eV reported in a previous kernel ridge regression study of the same dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='  20  Computer Science & Information Technology (CS & IT)  Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' The accuracy of the random forest regression model as a function of (a) the number of estimators and (b) the random seed, using all 20 physical descriptors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='  Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Parity plot of the predicted vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' GLLBSC-computed band gaps, obtained using all 20 physical descriptors and a test/training ratio of 25/75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' The parity line is shown in red.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Feature Selection  The feature importance plot is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' The top three features with the highest importance scores are average bulk modulus, superconductivity temperature, and cation electronegativity:  1) Bulk modulus quantifies the elastic property of a solid or fluid under pressure, specifically its resistance to compression [34].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Microscopically, bulk modulus depends on the compressibility of atoms, which affects the extent of the overlap of valence atomic orbitals, and therefore the band gap of the material [35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='  (a) (b) 61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='3 84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='25 84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='2 84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='1 84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='20 Accuracy Accuracy 64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='15 64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='10 83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='8 84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='05 83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='7 84:00 1000 2000 5000 Numberofestimators Randomseed8 7 5 4 m 2 1 0 0 1 2 3 4 5 6 7 8 GLLBSCbandgap(eV)Computer Science & Information Technology (CS & IT)                                        21  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Feature importance of all 20 physical descriptors, obtained from a test/training ratio of 25/75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='  2) Superconductivity is the state of matter with no electrical resistance and magnetic penetrability [36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Given that the magnitude of the band gap determines the electrical conductivity, a material with a relatively small band gap is expected to more easily achieve a superconducting state [37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 3) Electronegativity quantifies the ability of an atom to attract an electron pair in a chemical bond [38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' The cation electronegativity here refers to the electronegativity difference between the oxygen anions and the metal cations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' A larger elemental electronegativity difference leads to a larger degree of electron localization around the more electronegative element, which makes it harder for electrons to leap to the conduction band [39].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='  The low importance scores of some features, such as average electrical resistivity and molar volume, indicate that the dataset contains a large amount of noise, which necessitates feature selection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Table 1 summarizes the model performance using different numbers of top features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' The performance remains optimal up to the top 10 features, which yields an accuracy of 85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='6% with an RMSE of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='64 eV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Given the marginal difference in accuracy using 20, 15, and 10 top features, the remainder of the study employs the top 10 features only.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='  Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' The model performance obtained using different numbers of features with the highest feature importance scores (MAE = mean absolute error;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' RMSE = root mean squared error;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' NRMSE = normalized RMSE).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='  Number of top features  20  15  10  5  3  1  Accuracy (%)  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='1  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='5  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='6  82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='3  82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='4  65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='2  MAE (eV)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='47  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='46  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='46  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='56  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='57  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='12  RMSE (eV)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='62  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='62  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='64  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='79  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='81  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='43  NRMSE  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='08  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='07  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='08  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='17  avg bulk modulus avgsuperconductivitytemperature avg cation electronegativity avg electronegativity avg boiling point avg critical temperature avg Vickers hardness avg Mendeleev number avg thermal conductivity avg Youngs modulus avg rigidity modulus avg mineral hardness avg density of solid phase avg first ionization energy avg van der Waals radius avg melting point avg Brinell hardness avg atomic radius avg molar volume avg electrical resistivity 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='0000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='0250.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='0500.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='0750.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='1000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='125 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='1500.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='1750.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='20022  Computer Science & Information Technology (CS & IT)  The corresponding importance scores and parity plots are shown in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 5 & 6, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' The model constructed using the top 10 features exhibits the least deviation of the data points from the parity line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Moreover, the models overall tend to show a larger underestimation for larger band gap values, which can potentially be attributed to the limited accuracy of the GLLBSC functional itself [40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='  Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Feature importance scores for models constructed using a number of features with the highest importance scores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Testing and Training Set partition  Table 2 summarizes the model performance as a function of the different test-to-training set partitions, ranging from 10/90 to 75/25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' As expected, the test set accuracy decreases with the number of training set data points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' The corresponding parity plots in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 7 also demonstrate a larger extent of deviation from the parity line as the proportion of the training set decreases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Based on these results, we validate that the test/training ratio of 25/75 is sufficient in providing satisfactory accuracy (85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='6%) and reasonable RMSE (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='64 eV).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='  Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Model performance obtained with different test-to-training set partitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='  Test/training set ratio 10/90 20/80 25/75 40/60 50/50 75/25 Number of test set data points 131 262 327 523 653 980 Number of training set data points 1175 1044 979 783 653 326 Test set accuracy (%) 87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='9 86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='8 85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='6 82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='6 82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='5 76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='2 MAE (eV) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='41 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='45 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='46 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='53 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='67 RMSE (eV) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='57 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='63 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='64 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='74 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='88 NRMSE 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='07 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='08 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='08 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='08 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='09 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='Top ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='20 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='Top ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='15 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='Top ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='avg ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='bulk ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='modulus ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='avg ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='bulk ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='modulus ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='sninpow ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='xinq ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='6Ae ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='avg ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='superconductivity ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='temperature ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='avg ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='cation ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='electronegativity ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='avg ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='superconductivity ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='temperature ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='avg ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='superconductivity ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='temperature ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='avg ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='electronegativity ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='avg ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='electronegativity ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='avg ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='critical ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='temperature ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='avg ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='boilling ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='point ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='avg ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='Vickers ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='hardness ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='avg ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='boiling ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='point ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='avg ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='critical ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='temperature ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='avg ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='cation ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='electronegativity ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='avg ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='Mendeleev ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='number ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='avg ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='Vickers ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='hardness ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='avg ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='electronegativity ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='avg ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='Youngs ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='modulus ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='avg ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='Mendeleev ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='number ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='avg ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='thermal ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='conductivity ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='avg ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='Vickers ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='hardness ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='avg ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='min ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='neralhardness ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='avg ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='density ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='of ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='solid ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='phase ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='avg ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='Youngs ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='modulus ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='avg ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='first ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='ionization ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='avg ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='critical ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='temperature ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='avg ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='van ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='der ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='Waals ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='radius ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='avg ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='rigidity ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='modulus ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='avg ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='melting ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='point ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='avg ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='density ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='of ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='solid ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='phase ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='avg ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='Youngs ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='modulus ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='avg ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='Brinell ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='hardness ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='avg ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='first ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='ionization ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='energy ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='avg ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='atomic ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='radius ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='avg ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='Mendeleev ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='number ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='avg ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='molar ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='volume ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='avg ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='mineral ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='hardness ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='avg ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='electrical ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='resistivity ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='avg ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='van ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='der ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='Waals ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='radius ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='avg ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='thermal ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='conductivity ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='00D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='02D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='07.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='10D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='175.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='200 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='00D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='025.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='075.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='10D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='125.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='15D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='175.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='200 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='20 Top 5 dol avg superconductivity temperature avg superconductivity temperature avg bulk modulus avg boiling point avg bulk modulus avg cation electronegativity avg cation electronegativity avg electronegativity 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='050.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='150.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='200.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='250.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='30 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='20 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='30 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='35 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='40Computer Science & Information Technology (CS & IT)                                        23  Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Parity plots of the predicted vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' GLLBSC-computed band gaps obtained using different numbers of features with the highest importance scores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' The parity line is shown in red.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='  Figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Parity plots of the predicted vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' GLLBSC-computed band gaps obtained using different test-to- training set partitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' The parity line is shown in red.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='  Top 20  Top 15  8  (eV)  7  deb  5  band  4  4  Predicted  3  2  N 1  5  8  1  2  5  6  7  8  GLLBSCbandgap (eV)  GLLBSC band gap (eV)  Top 10  Top 5  8  8  7  deb  6  band  4  4  Predicted  Predicted b  3  2  N  0  0  2  3  4  5  6  8  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='GLLBSC E  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='band_gap (ev)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='GLLBSC band gap (eV)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=':  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='Top 3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='Top 1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='(eV)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='gap  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='Iband  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='Predicted  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='Predicted  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='N  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='GLLBSC band gap (eV)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='GLLBSC band gap (eV)test/training=1o/90  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='test/training=20/80  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='Predicted band gap (evV)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='gap  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='band  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='Predicted  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='N  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='GLLBSC band gap (eV)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='test/training=25/75  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='test/training=40/60  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='B  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='gap (eV)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='band  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='band  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='Predicted  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='Predicted  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='2 0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='GLLBSC band gap (eV)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=':  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='GLLBSC band gap (eV)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='test/training=50/50  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='test/training=75/25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='Predicted band gap (evV)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='deb  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='band  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='Predicted  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='m  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='N  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='N  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='  5  8  6  8  GLLBSC band gap (eV)  GLLBSC band gap (eV)24  Computer Science & Information Technology (CS & IT)  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Model Performances  Table 3 summarizes the result of previous studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' The best performance yields in KRR by P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Regonia et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' [28] with an RMSE of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='09.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Our random forest regression model is comparable to linear regression and XBGoost by G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Na et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' [26] and has a lower MAE than ACE and ET by V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Gladkikh et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='  Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Results of the models for band gap prediction (TGNN = tuplewise graph neural networks;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' XGBoost = extreme gradient boosting;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' ACE = alternating conditional expectations;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' ET = extremely randomized trees;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' KRR = kernel ridge regression;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' ANN = alternating conditional expectations;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' GBR = gradient boosting regression).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='  Model Study Material type Number of materials Band gap Accuracy (%) MAE (eV) RMSE (eV) Random forest J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Double perovskites 1306 GLLBSC 85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='46 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='64 TGNN G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Na et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' [26] Materials for solar cells 2233 GLLBSC - 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='30 - Linear regression G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Na et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' [26] Materials for solar cells 2233 GLLBSC  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='44  XGBoost G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Na et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' [26] Materials for solar cells 2233 GLLBSC  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='44  ACE V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Gladkikh et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' [27] Single perovskites  HSE  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='60 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='84 ET V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Gladkikh et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' [27] Single perovskites  HSE  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='54 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='75 KRR P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Regonia et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' [28] ZnO quantum dots  Optical band gap 98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='09 ANN P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Regonia et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' [28] ZnO quantum dots  Optical band gap 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='09 GBR M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Guo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' [8] Binary compounds 4096 DFT  calculated band gap  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='26  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Limitations and Recommendations  This study is limited by the relatively small sample size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' We use 1306 data to generate all the results, which may reduce the power of the study and cause a large margin of error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Future research studies can focus on using larger datasets, which we suppose will improve the model fitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' In this study, the missing values are filled by the mean value of that feature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' This preprocessing step can be taken more carefully by trying various means to deal with the missing values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Another limitation of the study is that we lack a more interpretable understanding of random forest regression in statistical learning theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' A single decision tree is interpretable because it follows several decision steps, whereas a forest lacks this step-by-step interpretability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Hence, using interpretability tools such as the RF Visualization Toolkits [41] to generate a “Decision Path View” may help to understand the forest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' This is essential since the feature’s importance is related to the underlying physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='  Computer Science & Information Technology (CS & IT)                                        25  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' CONCLUSION  Despite the widespread use of first-principles methods based on density functional theory (DFT) in materials science, it remains computationally costly and limited in its accuracy due to the approximation of the exchange-correlation functional.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' In this regard, machine learning presents a viable alternative for the rapid prediction of materials’ electronic properties while retaining reasonable fidelity to DFT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' This study has implemented random forest regression for the prediction of the band gap of double perovskite compounds employing a dataset of 1306 GLLBSC-computed band gaps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Among the 20 physical descriptors, average bulk modulus, superconductivity temperature, and cation electronegativity exhibited the highest importance scores, which provide a physically interpretable description in terms of the underlying electronic structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Optimal model performance is obtained with the top 10 features and a test/training partition of 25/75, yielding a model accuracy of 85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='6% and RMSE of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='64 eV comparable to previous studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Our results highlight the potential of machine learning regression for rapid and physically interpretable prediction of the electronic properties of functional materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='  ACKNOWLEDGMENTS  This work was supported by Touch Education Technology Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' We acknowledge scientific and editorial support from the Project Lead, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Lim of Harvard University;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' technical support from the Project Support C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Zhang;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' and administrative support from C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Ding of Touch Education Technology Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='  This work was led by J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' with support from Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' performed machine learning, literature review, and drafted the manuscript.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' performed parameter optimization, visualization, and literature review.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' assisted with literature review and writing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='  REFERENCES  [1] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Guo, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Xu & H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Xie, “Predicting the band gap of binary compounds from machine-learning regression methods,” 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' [2] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Sutherland, “Solar Materials Find Their Band Gap,” Joule, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 4, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 984–985, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' [3] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Zhang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Yang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Qu, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Qi & K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Zhang, “Wide Bandgap Oxide Semiconductors: from Materials Physics to Optoelectronic Devices,” Advanced Materials, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 33, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' [4] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Bagayoko, “Understanding density functional theory (DFT) and completing it in practice,” AIP Advances, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 4, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' [5] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Jestädt, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Ruggenthaler, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Oliveira, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Rubio & H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Appel, “Light-matter interactions within the Ehrenfest–Maxwell–Pauli–Kohn–Sham framework: fundamentals, implementation, and nano-optical applications”, Advances in Physics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 68, issue 4, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 225-333, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' [6] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Kuisma, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Ojanen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Enkovaara & T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Rantala, “Kohn-Sham potential with discontinuity for band gap materials,” Physical Review B - Condensed Matter and Materials Physics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 82, 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' [7] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Hai, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Tahir-Kheli & W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Goddard, “Accurate band gaps for semiconductors from density functional theory,” Journal of Physical Chemistry Letters, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 212–217, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' [8] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Peverati, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Zhao & D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Truhlar, “Generalized Gradient Approximation That Recovers the Second-Order Density-Gradient Expansion with Optimized Across-the-Board Performance,” The Journal of Physical Chemistry Letters, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 2, issue 16, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 1991-1997, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='  [9] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Lim, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Saldana-Greco & A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Rappe, “Improved pseudopotential transferability for magnetic and electronic properties of binary manganese oxides from DFT+U+J calculations,” Physical Review B, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 94, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' [10]  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Ahmed & K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Senthilkumar, “First-principle investigation of defect-associated LVM and structural parameter dependency in response to the ground state on-site Hubbard correction of w-ZnO,” Journal of Raman Spectroscopy, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 53, issue 6, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 1166-1178, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='  26  Computer Science & Information Technology (CS & IT)  [11] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Franchini, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Podloucky, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Paier, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Marsman & G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Kresse, “Ground-state properties of multivalent manganese oxides: Density functional and hybrid density functional calculations,” Physical Review B - Condensed Matter and Materials Physics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 75, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' [12] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' van Setten, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Weigend & F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Evers, “The GW-method for quantum chemistry applications: Theory and implementation,” Journal of Chemical Theory and Computation, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 9, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 232–246, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' [13] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Bagayoko, “Understanding density functional theory (DFT) and completing it in practice,” AIP Advances, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 4, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' [14] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Zhuo, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Mansouri Tehrani & J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Brgoch, “Predicting the Band Gaps of Inorganic Solids by Machine Learning,” Journal of Physical Chemistry Letters, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 9, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 1668–1673, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' [15] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Rajan, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Mishra, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Satsangi, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Vaish, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Mizuseki, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Lee, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Singh, “Machine- learning-assisted accurate band gap predictions of functionalized mxene,” Chemistry of Materials, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 30, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 4031–4038, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' [16]  O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Gritsenko, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' van Leeuwen, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' van Lenthe & E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Baerends, “Self-consistent approximation to the Kohn-Sham exchange potential,” PHYSICAL REVIEW A, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 51, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 1944-1954, 1995.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' [17]  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Schmidt, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Marques, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Botti & M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Marques, “Recent advances and applications of machine learning in solid-state materials science,” npj Computational Materials, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 5, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='  [18] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Saha-Dasgupta, “Double perovskites with 3d and 4d/5d transition metals: Compounds with promises,” Materials Research Express, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 7, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' [19] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Grabowska, “Selected perovskite oxides: Characterization, preparation and photocatalytic properties-A review,” Applied Catalysis B: Environmental, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 186, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 97–126, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' [20]  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Dey, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Ye, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' De, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Debroye, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Ha, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Bladt, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Kshirsagar, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Wang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Yin, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Wang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Quan, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Yan, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Gao, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Li, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Shamsi, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Debnath, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Cao, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Scheel, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Kumar, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Steele, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Gerhard, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Chouhan, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Xu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Wu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Li, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Zhang, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Dutta, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Han, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Vincon, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Rogach, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Nag, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Samanta, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Korgel, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Shih, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Gamelin, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Son, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Zeng, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Zhong, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Sun, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Demir, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Scheblykin, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Mora-Seró, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Stolarczyk, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Zhang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Feldmann, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Hofkens, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Luther, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Pérez-Prieto, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Li, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Manna, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Bodnarchuk, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Kovalenko, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Roeffaers, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Pradhan, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Mohammed, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Bakr, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Yang, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Müller-Buschbaum, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Kamat, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Bao, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Zhang, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Krahne, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Galian, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Stranks, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Bals, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Biju, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Tisdale, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Yan, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Hoye & L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Polavarapu, “State of the Art and Prospects for Halide Perovskite Nanocrystals,” ACS Nano, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 15, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 10775–10981, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' [21] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Chen, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Bai, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Wang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Lyu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Yun & L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Wang, “In Situ Growth of 2D Perovskite Capping Layer for Stable and Efficient Perovskite Solar Cells,” Advanced Functional Materials, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 28, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='  [22]  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Wu, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Zhang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Liu, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Luo, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Guo, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Huang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Ting, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Sun, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Zhong, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Wei, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Wang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Chen, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Xiao, “The Dawn of Lead-Free Perovskite Solar Cell: Highly Stable Double Perovskite Cs2AgBiBr6 Film,” Advanced Science, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 5, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' [23] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Wang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Want, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Pi, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Shao, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Tan & X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Huang, “Double Perovskite LaFexNi1−xO3 Nanorods Enable Efficient Oxygen Evolution Electrocatalysis,” Angewandte Chemie, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 131, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 2338–2342, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' [24] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Du, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Meng, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Wang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Yan & D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Mitzi, “Bandgap Engineering of Lead‐Free Double Perovskite Cs2AgBiBr6 through Trivalent Metal Alloying,” Angewandte Chemie, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 129, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 8270–8274, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' [25] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Guo & B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Lin, “Machine learning stability and band gap of lead-free halide double perovskite materials for perovskite solar cells,” Solar Energy, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 228, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 689–699, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' [26] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Na, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Jang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Lee & H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Chang, “Tuplewise Material Representation Based Machine Learning for Accurate Band Gap Prediction,” The Journal of Physical Chemistry A, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 124, issue 50, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 10616-10623, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' [27] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Gladkikh, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Kim, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Hajibabaei, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Jana, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Myung & K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Kim, “Machine Learning for Predicting the Band Gaps of ABX3 Perovskites from Elemental Properties,” The Journal of Physical Chemistry C, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 124, issue 16, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 8905-8918, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' [28] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Regonia, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Pelicano, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Tani, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Ishizumi, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Yanagi & K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Ikeda, “Predicting the band gap of ZnO quantum dots via supervised machine learning models,” Optik, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 207, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='  [29] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Ward, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Dunn, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Faghaninia, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Zimmermann, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Bajaj, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Wang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Montoya, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Chen, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Bystrom, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Dylla, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Chard, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Asta, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Persson, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Snyder, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Foster, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Jain, “Matminer: An open source toolkit for materials data mining,” Computational Materials Science, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 152, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 60–69, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' [30] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Zhang & W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Hu, “High-Throughput Calculation and Machine Learning of Two-Dimensional Halide Perovskite Materials: Formation Energy and Band Gap,” 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='  Computer Science & Information Technology (CS & IT)                                        27  [31] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Ong, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Richards, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Jain, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Hautier, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Kocher, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Cholia, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Gunter, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Chevrier, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Persson, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Ceder, “Python Materials Genomics (pymatgen): A robust, open-source python library for materials analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Computational Materials Science, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 68, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 314–319, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' [32] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Probst, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Wright & A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Boulesteix, “Hyperparameters and tuning strategies for random forest,” Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 9, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' [33] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Solé, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Solé, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Ramisa & C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Torras, “Evaluation of Random Forests on large-scale classification problems using a Bag-of-Visual-Words representation,” 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' [34] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Furmanchuk, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Agrawal & A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Choudhary, “Predictive analytics for crystalline materials: bulk modulus,” RSC Advances, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 6, issue 97, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 95246-95251, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' [35] K Li, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Kang & D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Xue, “Electronegativity calculation of bulk modulus and band gap of ternary ZnO-based alloys,” Materials Research Bulletin, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 47, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 2902–2905, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' [36] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Saha, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' di Cataldo, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Amsler, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' von der Linden & L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Boeri, “High-temperature conventional superconductivity in the boron-carbon system: Material trends,” Physical Review B, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 102, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' [37] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Thapa, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Srivastava & S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Tiwari, “Enlarged Photonic Band Gap in Heterostructure of Metallic Photonic and Superconducting Photonic Crystals,” J Supercond Nov Magn, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 23, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 517–525, 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' [38] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Politzer, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Murray, “Electronegativity—a perspective,” J Mol Model, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 24, issue 214, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='  [39] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Dagenais, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Chamberlin & C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Constantin, “Modeling Energy Band Gap as a Function of Optical Electronegativity for Binary Oxides,” Journal of Young Investigators, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 25, issue 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 73-78, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' [40] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Tran, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Ehsan & P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Blaha, “Assessment of the GLLB-SC potential for solid-state properties and attempts for improvement,” Physical Review Materials, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 2, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' [41] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Haddouchi & A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Berrado, “A survey of methods and tools used for interpreting Random Forest,” 1st International Conference on Smart Systems and Data Science (ICSSD), 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' 1-6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='  AUTHORS AND CO AUTHORS  Junfei Zhang is the author of this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' She is currently pursuing a Bachelor of Science degree at The University of Melbourne, Melbourne, Victoria, Australia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' She is actively conducting computer science related research studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Her research interest includes machine learning, computer vision, and quantum algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' She is currently studying Computer Science at The University of Copenhagen, Copenhagen, Denmark as an exchange student at the time of publication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='  Yueqi Li is the co-author of this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' She is pursuing B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Physics in College of Physical Science and Technology, Xiamen University, China.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' Her main areas of research interest are Biophysics and Machine learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content='  Xinbo Zhou is the co-author of this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' She is a junior student in the Faculty of Information Technology at Beijing University of Technology  © 2023 By AIRCC Publishing Corporation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
+page_content=' This article is published under the Creative Commons Attribution (CC BY) license.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E1T4oBgHgl3EQftAVw/content/2301.03372v1.pdf'}
diff --git a/LNE2T4oBgHgl3EQfAwaK/content/tmp_files/2301.03595v1.pdf.txt b/LNE2T4oBgHgl3EQfAwaK/content/tmp_files/2301.03595v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..bb26ec7927da25be2d923c6d366fd4e052e67327
--- /dev/null
+++ b/LNE2T4oBgHgl3EQfAwaK/content/tmp_files/2301.03595v1.pdf.txt
@@ -0,0 +1,615 @@
+White-box Inference Attacks against Centralized Machine Learning and
+Federated Learning
+Jingyi Ge
+College of Information Science and Technology, Donghua University,201620,Shanghai, China
+2222138@mail.dhu.edu.cn
+Abstract.
+With the development of information science and technology, various industries have generated
+massive amounts of data, and machine learning is widely used in the analysis of big data. However, if the
+privacy of machine learning applications’ customers cannot be guaranteed, it will cause security threats
+and losses to users' personal privacy information and service providers. Therefore, the issue of privacy
+protection of machine learning has received wide attention. For centralized machine learning models, we
+evaluate the impact of different neural network layers, gradient, gradient norm, and fine-tuned models on
+member inference attack performance with prior knowledge; For the federated learning model, we
+discuss the location of the attacker in the target model and its attack mode. The results show that the
+centralized machine learning model shows more serious member information leakage in all aspects, and
+the accuracy of the attacker in the central parameter server is significantly higher than the local Inference
+attacks as participants.
+Key words: machine learning, federated learning, white-box inference attacks, stochastic gradient
+descent.
+1 Introduction
+1.1 Introduction
+Machine learning is the technical core of the vigorous development of contemporary
+artificial intelligence and the basic way of computer intelligence.In machine learning, users
+can get output results with arbitrary input through general algorithms. Machine learning will
+collect and learn previous data in this way, and improve the algorithm of the computer itself,
+so as to effectively optimize the performance of computer programs.
+Machine learning is widely used in the analysis and processing of big data because of its
+superior information processing ability, such as medical diagnosis, weather prediction,
+economic research, mine engineering, and so on.
+
+However, the model training calculation process, the activation function and so on. Training
+data privacy: In machine learning, the sample data includes some personalized identifiable
+information (Personality Identifiable Information, PII), which can represent user attributes,
+such as email address, address, surname and other user identity attributes. Privacy (3) predict
+conclusion: machine model will directly calculate the prediction of
+users, the predicted
+information may be input the privacy information, such as medical diagnosis model can
+predict the probability of patients with a disease, the predicted personal information may be
+used for malicious diagnosis service providers.If the privacy rights in machine learning
+applications cannot be guaranteed and pose a threat to the security of users' personal privacy
+information, it is not only for the users using the service, but also for the service providers.
+1.2 Research status quo
+With the expansion of the application of information science and technology, the research
+has also made vigorous progress in depth and breadth, and the research of privacy-related
+issues has produced numerous achievements and insights in machine learning and deep
+learning algorithms.
+Attack strategy. Shokri[2]These are the first researchers to propose member reasoning
+attacks. When the black box frame of the target for the internal logic function and operation
+process, they let the attacker trained on the shadow models , shadow model has similar
+distribution and architecture with the target, so its behavior on the training data and the
+target model on the training data behavior more or less similar, can effectively achieve the
+attack effect. The output statistical characteristics (such as entropy) can be used to perform
+member inference. In the face of limited access and insufficient samples in black-box
+inference attacks, we use the fast attack for high-precision member inference, Peng[4]et al
+launched a new member inference attack method, based on principal component (PCA)
+member reasoning attack (PCA-based attack), the low migration of the previous
+experimental model is effectively improved, and this member reasoning attack can be
+member reasoning attack without the target model information.
+Fredrikson[5] designed the inversion attack (Model Inversion) technology firstly, they
+used the attacker as the central parameter server of the federated learning model, with the
+maximum
+posterior
+probability
+and
+model
+prediction
+confidence
+as
+the
+attack
+mechanism.Thereafter, Fredrikson’s[6] model reversal attack is improved. In order to apply
+their attack to the non-linear target model, and the target is regarded as the parameter input,
+the loss function is optimized by using the reconstruction attack. The improved reversal
+
+attack can effectively handle the discrete data. Hitaj[7]et al's research applied reversal
+attacks to attackers as federated learning participants, who reconstruct the input samples of
+participants in the model of the model by simulating data samples overlapping the target
+distribution using a generative adversarial network (GAN). The restoration of a certain
+category of pictures is realized on the multilayer neural network. This is an expansion and
+deepening of the attack proposed by Fredrikson et al.
+Ateniese[12] et al made usage of an attack according to property, they launched a known
+target model intrinsic function calculation process and training mode under the premise of
+inferred machine learning participants sample data and some original model data of the
+specific properties of the correlation inference attack, and named the attack attribute
+(Property) inference attack, and in the speech data set inferred accent information
+identification task reflects the effectiveness of the attack.Their attribute inference attack is
+captured by Ganju[13]et al realized the expanded application in the fully connected network.
+Blanchard[15] et al set the malicious participants[16] as the attacker, with the central
+parameter server using the linear aggregation method as the attack target, found that the
+target transmission of messages fabricated according to the local model, or even arbitrary
+data and target transmission, can achieve the training intervention of the model.Experiments
+show that when a large number of participants in the distributed learning model hide or
+malicious participants who are prone to leak information, even less capable attackers can
+hijack the target model and implement Byzantine attacks.
+Defense strategy. Dwork[19]et al first put forward the concept and technology of
+differential privacy defense technology. They used noise to intervene the output of the
+model, which blurred the attack effect of attackers targeting the model output, making it
+impossible for attackers to identify multiple target data sets, and making it difficult to make
+a correct judgment on the membership of the data points.Shokri[20] used the stochastic
+gradient descent (SGD) optimization method, the differential privacy protection technology
+in the process of distributed machine learning, but their privacy protection method need to
+randomly selected on the gradient greater than set threshold met ε - differential privacy
+Laplace noise, and strict privacy budget controls each privacy consumption until exhausted,
+shut off data access rights, this method is difficult for practice.
+In summary, Machine learning has hidden privacy information security risks in terms of
+model construction and input application, Many scholars' research on federated learning,
+distributed learning and other environments has accelerated the rapid development of
+machine learning technology, We use a white-box inference attack model as a means of
+
+comparing the training characteristics of centralized machine learning models and federated
+learning models, And to explore the corresponding risks generated, To refine the study of
+machine learning privacy risks, To supplement the offensive and defensive strategies in the
+field of centralized machine learning, Finally, the infinite possibilities for the future
+applications of machine learning models in various scenarios are explored.
+1.3 Study content and chapter arrangement
+Come in for Nasr[25] et al’s study for the privacy risk of deep learning, this paper used a
+white box member reasoning attack simulation experiment, aimed to explore in the machine
+deep learning environment, centralized machine learning and federal learning setting, for the
+level of information leakage and affect the level of the model, and will compare the two
+learning mechanism characteristics. This paper will be respectively for centralized machine
+learning and federated learning model member inference attack, using stochastic gradient
+descent optimizer, model gradient vector as an important attack index, the final simulation
+results can show the white box member inference attack model for the two target model
+membership inference accuracy, namely the current learning model in what leaked their own
+training data.Our evaluation directions include: supervised attacks and unsupervised attacks,
+inference attacks on the model and its newer versions, passive member reasoning attacks,
+and active member inference attacks. The experimental results evaluate the model
+performance based on the member inference attack accuracy score and the True / False
+positive (ROC) curve.
+The first part of this paper introduces the privacy rights in machine learning and the existing
+attack and defense strategies for machine learning. The second part of the related
+knowledge, the list of the discussed problems and simulation experiments of the background
+knowledge and the function basis and its definition. The third part, the model and algorithm,
+shows the workflow and fundamentals of the white-box member inference attack model used
+in this paper.The fourth part of white box inference attack performance evaluation
+introduces the experimental related work setting and process, model attack performance
+evaluation index and attack simulation results for centralized machine learning model and
+federated learning model.
+2 Related knowledge
+
+2.1 Member Reasoning Attack
+The degree of privacy information leakage of a certain model can be defined as: the
+attacking party can get one or some private data through this mode. The former shows an
+increased utility, while the latter reflects a privacy loss. This paper uses white-box member
+inference attacks to quantify this privacy leakage.
+Generally speaking, the purpose of an algorithm for member inference attacks is to reason
+about the identity of a particular data (a member instance or a non-member instance) in the
+target training set.In practice, attackers with different training premises use member
+inference attacks to infer the membership of a given data to the target model dataset.Part of
+the data belonging to the target model data set is observed and used by the attackers to infer
+more relevant information of the target data set. Therefore, under the attack mode of member
+reasoning, the important private information of the training data is likely to be displayed
+through the leakage degree of the target model.
+This paper uses the way of member reasoning attack to obtain more visual and valuable
+machine learning model mechanism and vulnerabilities, the results can reflect the
+information leakage degree and privacy security of the machine model in the learning
+process.
+2.2 Shadow training techniques and white-box reasoning attacks
+Shadow training technique (Shadow Training Technique). When the attacker cannot
+obtain the internal algorithm, the attack feature data cannot be obtained, so the attacker can
+only start with the output constantly updated by the target model of the neural network layer
+at any input.Shokri[2]In order to effectively conduct member reasoning attacks, et al. used
+shadow training techniques to deal with such situations.
+White-box membership inference attack. In this environment, the attacker can observe not
+only the model output f (x; W), but also the period operation and all parameters involved in
+the training process, including all hidden layer output hi (x), so the attacker with white box
+permission can effectively expand the attack environment of the attacker with black box
+permission.
+2.3 Supervised attacks and unsupervised attacks
+Supervised and unsupervised learning depends on whether an attacker has prior knowledge
+such as a part of the target dataset or a sample codistributed with the target sample.When
+have this knowledge, we will use the way of supervision let the attack model on the known
+
+data to build the attack model, that is to let the reasoning model directly learning attack data
+points and target model members of the membership, in such supervised learning mode to
+build the reasoning attack became a supervised attack.
+However, when the attacker does not have knowledge and pre-training conditions on the
+internal structure and sample distribution of the target model, we choose to build an
+unsupervised attack model, predict more information about the target data set according to
+the underlying output of the target model, and develop member inference attacks.
+2.4 Stochastic Gradient Descent (SGD) optimizer
+Stochastic gradient descent (SGD) algorithm is one of the deep learning optimizers, and it is
+also a relatively basic neural network optimization method.The algorithm repeatedly update
+model parameters W as the gradient drop, by calculating the loss function value gradient,
+iterative weight and bias, reduce the empirical expectation on the training set D, make it tend
+to zero, so that the model parameters constantly approaching the expression of the real data,
+as shown in formula (1), for stochastic gradient descent (SGD) algorithm working principle,
+which is the classification model f loss function.
+min
+��� ���(���, ���) ~���[���(���(���; ���), ���)]
+(1)
+Stochastic gradient descent algorithm will leave marks for the parameter loss function
+gradient of each trained sample, which is the basis of reasoning attack, the white box
+inference attack model and use of stochastic gradient descent optimization algorithm, these
+sample markers can make the model gradient vector of all parameters on the attack of the
+target easy to be observed, which becomes our important attack index.
+2.5 Passive attack and active attack
+Passive or active white-box member inference attack mode depends on whether the attacker
+passively receives the update parameter gradient of the observation model or actively
+influences the training process of the target model.
+Active attack (global attacker and local attacker). In the active attack mode, the attacker
+will participate in the target model training process, and obtain the corresponding training set
+member information through the active influence of their training parameters, based on
+which the reasoning attack is implemented.Due to the structural characteristics of federated
+learning, active attacks are often applied to them. The central parameter server will distribute
+the parameters before the start of each training, collect the local model parameters uploaded
+
+by each participant and aggregate and update the global models, and each training stage can
+contribute to the attacker's attack.
+��� ← ��� + ��� ���������
+������
+(2)
+2.6 Centralized learning
+In this environment setting, all data are trained in the central parameter server set, which
+includes public general data as well as some private data. The attack model is able to
+observe the complete independent learning model and the training results of each output.
+Fig 1 Centralized machine learning.
+In the experimental study of this paper, training with the new dataset d to get model updates,
+These fine-tuning (Fine-tuning) models are often caused by the effects of those private data,
+In the following training sessions, The attacker can observe the fine-tuning of the new
+independent model f and its training results, Member inference for the new dataset d,
+besides, The attacker will also make inference attacks on the two versions of the data set
+before and after the fine update. To get more member information on your private data,
+Restore the important privacy involved.
+2.7 Federated Learning
+In order to achieve a certain accuracy and have stronger reference value, machine learning
+needs to cover enough large dimension training samples, but in practical application, data
+
+participant2
+participant 3
+participant1
+Zparticipant N
+attackercollection not only need high density sample transmission, also exacerbated the privacy
+information crisis, because the larger the base data often contains more important
+information in the field of information, this undoubtedly enhances the privacy risk. Under
+the federated learning framework, the central parameter server each participant in federated
+learning training has their own training set, they download global parameters in the
+beginning, and training in the local model, they do local update and upload back to the
+central parameter server, parameter server processing N participants of the update average,
+data aggregation sharing save the latest parameter version of the global model. Participants'
+sharing content is limited to parameters rather than specific data.
+Fig 2 Privacy risks of centralized machine learning.
+3 Models and algorithms used
+3.1 White-box membership inference attack model
+For the two types of attackers classified according to having or without background
+knowledge, we trained the attack model to perform the attack in different ways.We
+performed attack simulation experiments using the Alexnet model trained on the CIFAR-100
+dataset as input of the attack model, and the following white-box member inference attack
+model.
+
+participant2
+Malicious participants
+participant1
+participantN3.2 Principles and algorithms
+In the white-box inference attack model we use, the tag components are built on a fully
+connected network. Aggregate all local weights received from the previous layer, form
+inputs to nonlinear functions, form the output values of each module of the convolutional
+layer, and optimize model convergence.The white box reasoning attack model recombines
+the output of each submodule component, combines the output of all feature extraction
+components through the encoder components, the encoder output constitutes the attack
+output of the model, the output is divided into "members" and "non-members", we put the
+accuracy of the model for the unknown stronghold (predicted members, non-members) as
+our basis to judge the attack performance of the model.
+4 Experiments of the white-box membership inference attack
+4.1 Experimental setup
+The equipment prepared for the experiment is the Intel core i7-8650U CPU memory 16.0GB
+of the computer, the experimental language Python.The experiment uses Pytorch to
+complete the neural network, which is easy to define, which helps us to easily and quickly
+establish relatively small projects.
+Attack Model. ReLU activation function is defined as formula (5), where yi is the model
+output as a non-saturated activation function, its unilateral inhibition ability to the output can
+solve a certain "gradient disappearance" problem, and effectively improve the model
+convergence speed to help effectively realize non-linear activation transformation.
+Otherwise, ReLU activation function can sparse the model well, and such sparsity facilitates
+experimental fitting to the data.
+��� ������ = ������,
+������ > 0
+0,
+������ ≤ 0
+(6)
+Performance evaluation indicators. For the white-box model used in this paper, we used
+two —— centralized machine learning and federated model —— with centralized
+performance evaluation indicators to form a more comprehensive evaluation system, to help
+improve the learning characteristics of the two learning models and the differentiation of
+member information leakage level.
+
+Table 1 Parameter Control Table.
+parameter
+Parameter name
+f
+object model
+h
+Attack model
+W
+Target model parameters
+D, D’
+Member and non-member datasets
+Pr
+Precision--Recall Rate
+γ
+Adverse update rate
+4.2 Analysis of the simulation experiment results
+Deep learning has two main training algorithms. In this paper, we first show the simulation
+results analysis of the centralized machine learning, and then provide the simulation results
+and analysis of the federated learning objective model.
+Simulation results analysis of white-box membership inference attacks for centralized
+machine learning. For the attack of centralized machine learning model, this paper will
+evaluate the white box attack model from the following dimensions: based on the attack
+model's understanding of target training mode, sample distribution, attack and defense
+mechanism, starting from the two presets of supervised attack and unsupervised attack.In
+supervised attacks, the output of different layers from the trained attacker attack model and
+the gradient of the classification model; in unsupervised attacks, we use shadow training
+techniques; and in a special case, we update multiple versions of the target model
+simultaneously.
+Supervised attacks. In the context of supervised attacks, we train the target and attack
+models using a pre-trained CIFAR100 dataset. Therefore, the white-box inference attack
+model understands the subset and sample distribution of the target, and can start the member
+reasoning attack from the gradient and number of layers of the target model.
+Table 2 Shows the member inference attack accuracy for the outputs of different layers of the
+CIFAR1000-Alexnet centralized learning model
+output layer
+Member prediction accuracy
+The bottom third layer
+72.88%
+
+The penultimate layer
+74.06%
+The final layer
+74.61%
+When the training of the target model enters the last few layers, it will contain a lot of
+training information from its previous layers, which makes the more data information the
+model stores and covers more parameters, which is one of the reasons why the output of the
+final layer of the target model leaks more membership information.
+Since the deep neural network contains large-scale parameter data beyond the dimensions
+that the target model is correctly generalized, the parameter gradient in the target model will
+show differences that attackers can easily distinguish between.
+We used the CIFAR00 dataset to train the Densenet model with model parameter scale
+25.62M and parameter scale 1.7M two models as the target model.
+The experiment also performs distribution statistics for the gradient norm of membership of
+the output of each output class of the target CIFAR100-Alexnet centralized machine learning
+model.
+
+2000
+member
+non-member
+1500
+Gradient norm
+1000
+500
+20
+40
+60
+80
+100
+Output classFig5 Gradient norm distribution of output members and non-members of each target CIFAR100-Alexnet
+centralized machine learning model[25].
+Since the gradient distribution of members of CIFAR100-Densenet and non-members of
+CIFAR100-Densenet model is more different than that of CIFAR100-Resnet model, the
+attack accuracy on Densenet architecture is better both from model output and model
+gradient perspective.
+Table 3 Attack models attack the three target models with different architectures trained on the CIFAR100
+dataset, respectively for the output of the model and the member inference accuracy of the gradient.
+object model
+Attack accuracy
+Dataset
+Model architecture
+target outputs
+target gradients
+CIFAR100
+Alexnet
+74.61%
+75.09%
+CIFAR100
+Resnet
+62.20%
+64.34%
+CIFAR100
+Densenet
+67.72%
+74.31%
+Unsupervised attacks. In order to assign members of the target model to non-member
+examples, according to the gradient model value, we give the spectral clustering algorithm
+with "member" cluster sample, and the other samples we preset as "non-member" to
+facilitate the distribution of members and non-member samples to determine the member
+inference accuracy of unsupervised attacks.
+Fine-tuned models. Such attack observation was chosen because we want to expand the attack
+model from one to multiple to improve its performance. And in fact, model fine-tuning is
+often influenced by important private data.
+Table 4 Attack Accuracy of attacking fine-tuned models trained on the CIFAR100 dataset in centralized machine
+learning.
+Dataset
+Model architecture
+Non-member in Dataset D
+Non-member in Dataset DΔ
+CIFAR
+100
+Alexnet
+75.38%
+71.36%
+CIFAR
+100
+DenseNet
+74.61%
+71.50%
+Passive attack. The experiment will make the Alexnet model trained on the CIFAR100
+dataset as the most target model, and set the position of the attacker to the central parameter
+
+server.First, our attack starts with the training phase of the model.Attacks follow five
+discontinuous training sessions against the target model, from 5 to 300.
+Table 5 Attack accuracy of passive global attacker’s attacking different training stages of the Alexnet federated
+learning model trained on the CIFAR100 dataset.
+Training stage
+Attack accuracy
+5 10 15 20 25
+57.32%
+10 20 30 40 50
+76.47%
+50 100 150 200
+79.50%
+100 150 200 250 300
+84.89%
+Active attack. Due to the federated learning mode, the central parameter server for each
+update data aggregation will negatively affect the reasoning accuracy of attack model, so in
+order to get more training set data information of target participants, we use the same attack
+model, preset global attacker active isolation target training participants, intervention in his
+training process, to hinder its data upload and receive.
+Table 6 The attack accuracy of passive and active white-box members for target models (four participants)
+trained on the CIFAR100 dataset at different locations under the federated learning architecture.
+Target model
+Global attacker
+Local attacker
+Dataset
+Model
+architecture
+Passive
+Active
+Passive
+CIFAR100
+Alexnet
+84.98%
+88.52%
+72.88%
+CIFAR100
+Densenet
+77.43%
+82.90%
+71.98%
+Active global attacker in the implementation of the attack, will actively block part of the
+central parameter server issued parameters, which makes the target participants not only
+cannot share with the central parameter server, also and other participants smooth
+aggregation, which strengthens the attack model gradient superposition of the local SDG
+algorithm, causing the target local model internal members and non-member example
+become easier to identify.
+
+5 Conclusion
+In contrast to the leakage of training and learning information and related privacy
+vulnerabilities in the training and learning characteristics of the internal member samples of
+centralized machine learning and federated learning models, we use different pre-trained
+attack models to distinguish their access to and knowledge of the internal function, training
+patterns, learning methods, distribution, and training set information of the target model.
+Experimental data show we use the white box members of the inference attack evaluation
+results: under the premise of using such attack model for attack, training late centralized
+machine learning model in all aspects show greater members of information leakage, neural
+network layer, gradient two attack indicators showed similar attack results, and for the latter,
+as a global model of passive attacker members of the reasoning accuracy will be
+significantly higher than the participants of the local attack architecture.
+Federal machine learning broke the traditional centralized machine learning centralized data
+control deadlock, to personal local data privacy security issues provides new ideas, through
+the data communication and sharing bridge, improve the efficiency of the machine learning
+model, accuracy and high reference value, in the era of all Internet, machine learning
+technology inspired wide attention and innovation, based on attack and defensive research,
+spawned multi-dimensional application of attack strategy[28]. And for the powerful attack
+ability of white-box membership inference attacks, there are now some adversarial defense
+strategies[28]Still helpless about it means that information security in personally sensitive
+areas is still an urgent issue for users using related technology products, because it can even
+lead to serious property losses, which undoubtedly poses great obstacles to the use of
+machine learning in daily life.
+Reasoning in this paper, the field of machine learning white box members against sensitive
+sectors in order to improve information security and user privacy information security
+protection problems to provide important insights and discuss, for the big data age of
+machine learning is widely used in everyday life and prosperity and development of solid
+foundation, to speed up the steps of 5 g era, it can better popularize machine learning
+technology to all aspects of social life, so that the general public can enjoy the convenience
+and have less worries.In addition, more loopholes and learning features of machine learning
+are waiting for us to explore and further study.
+
+6 References
+[1] SHOKRI R, STRONATI M. SONG C, et al. Membership inference attacks against
+machine learning models[C]//IEEE Symposium on Security and Privacy.2017:3-18.
+[2] Salem A, Zhang Y, Humbert M, et al.Ml-leaks:Model and data independent membership
+inference
+attacks
+and
+defenses
+on
+machine
+learning
+models[J].arXiv
+preprint
+arXiv:1806.01246,2018.
+[3] FREDRIKSON M, LANTZ E, JHA S, et al. Privacy in pharmacogenetics: An end-to-end
+case study of personalized warfarin dosing[C]//USENIX Security.2014:17-32.
+[4] FREDRIKSON M, JHA S, RISTENPART T. Model inversion attacks that exploit
+confidence information and basic countermeasures[C]//Proceedings of ACM SIGSAC.
+2015:1322-1333.
+[5] ZHU L, HAN S. Deep leakage from gradients[C]//Advances in Neural Information
+Processing Systems. 2019:17-31.
+[6] JUUTI M, SZYLLER S, MARCHAL S, et al. PRADA: protecting against DNN model
+stealing attacks[C]//IEEE European Symposium on Security and Privacy.2019:512-527.
+[7] ATENIESE G, MANCINI L V, SPOGNARDI A, et al. Hacking smart machines with
+smarter ones: How to extract meaningful data from machine learning classifiers[J].
+International Journal of Security and Networks, 2015, 10(3): 137-150.
+[8] ATENIESE G, MANCINI L V, SPOGNARDI A, et al. Hacking smart machines with
+smarter ones: How to extract meaningful data from machine learning classifiers[J].
+International Journal of Security and Networks, 2015, 10(3): 137-150.
+[9] MELIS L, SONG C, DE CRISTOFARO E, et al. Exploiting unintended feature leakage
+in collaborative learning[C]//IEEE Symposium on Security and Privacy. 2019:691-706.
+[10] BLANCHARD P, EL MHAMDI E M, GUERRAOUI R, et al. Machine learning with
+adversaries: Byzantine tolerant gradient descent[C]//Neural Information Processing
+Systems.2017:118-128.
+[2] BONAWITZ K, EICHNER H, GRIESKAMP W, et al. Towards federated learning at
+scale: System design[C]//IEEE CVPR Workshop.2019:3310-3319.
+[11] FUNG C, YOON C J M, BESCHASTNIKH I. The limitations of federated learning in
+sybil settings[C]//International Symposium on Research in Attacks. 2020:301-316.
+[12] DWORK C, ROTH A. The algorithmic foundations of differential privacy[J].
+Foundations and Trends in Theoretical Computer Science, 2014, 9(3/4):211-407.
+[13] GEYER R C, KLEIN T, NABI M. Differentially private federated learning: A client
+level perspective[J]. arXiv preprint, 2017:1712.07557.
+
+[14] BHOWMICK A, DUCHI J, FREUDIGER J, et al. Protection against reconstruction and
+its applications in private federated learning[J]. arXiv preprint, 2018:1812.00984.
+[15] NASR M, SHOKRI R, HOUMANSADR A. Comprehensive privacy analysis of deep
+learning: Passive and active white-box inference attacks against centralized and
+federated learning[C] // 2019 IEEE Symposium on Security and Privacy (SP). IEEE,
+2019 : 739 - 753.
+[16] SZEGEDY C, ZAREMBA W, SUTSKEVER I, et al. Intriguing properties of neural
+networks[J]. arXiv preprint arXiv: 1312. 6199, 2013.
+[17] Ping Zhao, Hongbo Jiang, John C. S. Lui, Chen Wang, Fanzi Zeng, Fu Xiao, and
+Zhetao Li. P3-LOC: A Privacy-Preserving Paradigm-Driven Framework for Indoor
+Localization. IEEE/ACM Transactions on Networking (ToN), vol. 26, no. 6, pp.
+2856-2869, 2018.
+[18] Hongbo Jiang, Yuanmeng Wang, Ping Zhao, Zhu Xiao. A Utility-Aware General
+Framework with Quantifiable Privacy Preservation for Destination Prediction in LBSs.
+IEEE/ACM Transactions on Networking (ToN), vol. 29, no. 5, pp. 2228-2241, 2021.
+[19] Ping Zhao, Jiaxin Sun, and Guanglin Zhang. DAML: Practical Secure Protocol for Data
+Aggregation based on Machine Learning. ACM Transactions on Sensor Networks, vol.
+16, no. 4, pp. 1-18, 2020.
+[20] Ping Zhao, Wuwu Liu, Guanglin Zhang, Zongpeng Li, and Lin Wang. Preserving
+Privacy in WiFi Localization with Plausible Dummy Locations. IEEE Transactions on
+Vehicular Technology, vol. 69, no. 10, pp. 11909-11925, 2020.
+[21]
+Guanglin
+Zhang,
+Anqi
+Zhang,
+Ping
+Zhao,
+and
+Jiaxin
+Sun.
+Lightweight
+Privacy-Preserving Scheme in WiFi Fingerprint-Based Indoor Localization. IEEE
+Systems Journal, vol. 14, no. 3, pp. 4638-4647, 2020.
+[22] Ping Zhao, Jie Li, Fanzi Zeng, Fu Xiao, Chen Wang, Hongbo Jiang. ILLIA: Enabling
+k-Anonymity-based
+Privacy
+Preserving
+against
+Location
+Injection
+Attacks
+in
+continuous LBS Query. IEEE Internet of Things Journal, vol. 5, no. 2, pp. 1033–1042,
+2018.
+[23] Ping Zhao, Hongbo Jiang, Jie Li, Fanzi Zeng, Xiao Zhu, Kun Xie, and Guanglin Zhang.
+Synthesizing Privacy Preserving Traces: Enhancing Plausibility with Social Networks.
+IEEE/ACM Transactions on Networking (ToN), vol. 27, no. 6, pp. 2391 – 2404, 2019.
+[24] Ping Zhao, Jiawei Tao, Guanglin Zhang. Deep Reinforcement Learning-based Joint
+Optimization of Delay and Privacy in Multiple-User MEC Systems. IEEE Transactions
+on Cloud Computing, DOI: 10.1109/TCC.2022.3140231, 2022.
+
+[25] Ping Zhao, Hongbo Jiang, Jie Li, Zhu Xiao, Daibo Liu, Ju Ren, Deke Guo. Garbage in,
+Garbage
+out:
+Poisoning
+Attacks
+Disguised
+with
+Plausible
+Mobility
+in
+Data
+Aggregation. IEEE Transactions on Network Science and Engineering (TNSE), vol. 8,
+no. 3, pp. 2679-2693, 2021.
+[26] Ping Zhao, Xiaohui Zhao, Daiyu Huang, H. Huang. Privacy-Preserving Scheme against
+Location Data Poisoning Attacks in Mobile-Edge Computing. IEEE Transactions on
+Computational Social Systems, vol. 7, no. 3, pp. 818-826, 2020.
+[27] Ping Zhao, Chen Wang, and Hongbo Jiang. On the Performance of k -Anonymity
+against Inference Attacks with Background Information. IEEE Internet of Things
+Journal, vol. 6, no. 1, pp. 808–819, 2018.
+[28] Guanglin Zhang, Sifan Ni, and Ping Zhao. Enhancing Privacy Preservation in Speech
+Data Publishing. IEEE Internet of Things Journal, vol. 7, no. 8, pp. 7357-7367, 2020.
+[29] Guanglin Zhang, Anqi Zhang, Ping Zhao. LocMIA: Membership Inference Attacks
+against Aggregated Location Data. IEEE Internet of Things Journal, vol. 7, no. 12, pp.
+11778-11788, 2020.
+[30] Guanglin Zhang, Sifan Ni and Ping Zhao. Learning-based Joint Optimization of
+Energy-Delay and Privacy in Multiple-User Edge-Cloud Collaboration MEC Systems.
+IEEE Internet of Things Journal, doi: 10.1109/JIOT.2021.3088607, 2021.
+[31] P. Zhao, Z. Cao, J. Jiang and F. Gao, "Practical Private Aggregation in Federated
+Learning Against Inference Attack," in IEEE Internet of Things Journal, 2022, doi:
+10.1109/JIOT.2022.3201231.
+[32] Hongbo Jiang, Yu Zhang, Zhu Xiao, Ping Zhao and Arun Iyengar. An Empirical Study
+of Travel Behavior Using Private Car Trajectory Data. IEEE Transactions on Network
+Science and Engineering, vol. 8, no. 1, pp. 53-64, 2021.
+
diff --git a/LNE2T4oBgHgl3EQfAwaK/content/tmp_files/load_file.txt b/LNE2T4oBgHgl3EQfAwaK/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4274d8ea2792e1ee2db9c5c013f076e7fbe106dc
--- /dev/null
+++ b/LNE2T4oBgHgl3EQfAwaK/content/tmp_files/load_file.txt
@@ -0,0 +1,370 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf,len=369
+page_content='White-box Inference Attacks against Centralized Machine Learning and  Federated Learning  Jingyi Ge  College of Information Science and Technology, Donghua University,201620,Shanghai, China  2222138@mail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='dhu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='cn  Abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  With the development of information science and technology, various industries have generated  massive amounts of data, and machine learning is widely used in the analysis of big data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=" However, if the  privacy of machine learning applications’ customers cannot be guaranteed, it will cause security threats  and losses to users' personal privacy information and service providers." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' Therefore, the issue of privacy  protection of machine learning has received wide attention.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' For centralized machine learning models, we  evaluate the impact of different neural network layers, gradient, gradient norm, and fine-tuned models on  member inference attack performance with prior knowledge;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' For the federated learning model, we  discuss the location of the attacker in the target model and its attack mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' The results show that the  centralized machine learning model shows more serious member information leakage in all aspects, and  the accuracy of the attacker in the central parameter server is significantly higher than the local Inference  attacks as participants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  Key words: machine learning, federated learning, white-box inference attacks, stochastic gradient  descent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  1 Introduction  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='1 Introduction  Machine learning is the technical core of the vigorous development of contemporary  artificial intelligence and the basic way of computer intelligence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='In machine learning, users  can get output results with arbitrary input through general algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' Machine learning will  collect and learn previous data in this way, and improve the algorithm of the computer itself,  so as to effectively optimize the performance of computer programs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  Machine learning is widely used in the analysis and processing of big data because of its  superior information processing ability, such as medical diagnosis, weather prediction,  economic research, mine engineering, and so on.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  However, the model training calculation process, the activation function and so on.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' Training  data privacy: In machine learning, the sample data includes some personalized identifiable  information (Personality Identifiable Information, PII), which can represent user attributes,  such as email address, address, surname and other user identity attributes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' Privacy (3) predict  conclusion: machine model will directly calculate the prediction of  users, the predicted  information may be input the privacy information, such as medical diagnosis model can  predict the probability of patients with a disease, the predicted personal information may be  used for malicious diagnosis service providers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content="If the privacy rights in machine learning  applications cannot be guaranteed and pose a threat to the security of users' personal privacy  information, it is not only for the users using the service, but also for the service providers." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='2 Research status quo  With the expansion of the application of information science and technology, the research  has also made vigorous progress in depth and breadth, and the research of privacy-related  issues has produced numerous achievements and insights in machine learning and deep  learning algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  Attack strategy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' Shokri[2]These are the first researchers to propose member reasoning  attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' When the black box frame of the target for the internal logic function and operation  process, they let the attacker trained on the shadow models , shadow model has similar  distribution and architecture with the target, so its behavior on the training data and the  target model on the training data behavior more or less similar, can effectively achieve the  attack effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' The output statistical characteristics (such as entropy) can be used to perform  member inference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' In the face of limited access and insufficient samples in black-box  inference attacks, we use the fast attack for high-precision member inference, Peng[4]et al  launched a new member inference attack method, based on principal component (PCA)  member reasoning attack (PCA-based attack), the low migration of the previous  experimental model is effectively improved, and this member reasoning attack can be  member reasoning attack without the target model information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  Fredrikson[5] designed the inversion attack (Model Inversion) technology firstly, they  used the attacker as the central parameter server of the federated learning model, with the  maximum  posterior  probability  and  model  prediction  confidence  as  the  attack  mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='Thereafter, Fredrikson’s[6] model reversal attack is improved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' In order to apply  their attack to the non-linear target model, and the target is regarded as the parameter input,  the loss function is optimized by using the reconstruction attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' The improved reversal  attack can effectively handle the discrete data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=" Hitaj[7]et al's research applied reversal  attacks to attackers as federated learning participants, who reconstruct the input samples of  participants in the model of the model by simulating data samples overlapping the target  distribution using a generative adversarial network (GAN)." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' The restoration of a certain  category of pictures is realized on the multilayer neural network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' This is an expansion and  deepening of the attack proposed by Fredrikson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  Ateniese[12] et al made usage of an attack according to property,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' they launched a known  target model intrinsic function calculation process and training mode under the premise of  inferred machine learning participants sample data and some original model data of the  specific properties of the correlation inference attack,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' and named the attack attribute  (Property) inference attack,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' and in the speech data set inferred accent information  identification task reflects the effectiveness of the attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='Their attribute inference attack is  captured by Ganju[13]et al realized the expanded application in the fully connected network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  Blanchard[15] et al set the malicious participants[16] as the attacker, with the central  parameter server using the linear aggregation method as the attack target, found that the  target transmission of messages fabricated according to the local model, or even arbitrary  data and target transmission, can achieve the training intervention of the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='Experiments  show that when a large number of participants in the distributed learning model hide or  malicious participants who are prone to leak information, even less capable attackers can  hijack the target model and implement Byzantine attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  Defense strategy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' Dwork[19]et al first put forward the concept and technology of  differential privacy defense technology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' They used noise to intervene the output of the  model, which blurred the attack effect of attackers targeting the model output, making it  impossible for attackers to identify multiple target data sets, and making it difficult to make  a correct judgment on the membership of the data points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='Shokri[20] used the stochastic  gradient descent (SGD) optimization method, the differential privacy protection technology  in the process of distributed machine learning, but their privacy protection method need to  randomly selected on the gradient greater than set threshold met ε - differential privacy  Laplace noise, and strict privacy budget controls each privacy consumption until exhausted,  shut off data access rights, this method is difficult for practice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  In summary,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' Machine learning has hidden privacy information security risks in terms of  model construction and input application,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=" Many scholars' research on federated learning," metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  distributed learning and other environments has accelerated the rapid development of  machine learning technology,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' We use a white-box inference attack model as a means of  comparing the training characteristics of centralized machine learning models and federated  learning models,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' And to explore the corresponding risks generated,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' To refine the study of  machine learning privacy risks,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' To supplement the offensive and defensive strategies in the  field of centralized machine learning,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' Finally,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' the infinite possibilities for the future  applications of machine learning models in various scenarios are explored.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='3 Study content and chapter arrangement  Come in for Nasr[25] et al’s study for the privacy risk of deep learning, this paper used a  white box member reasoning attack simulation experiment, aimed to explore in the machine  deep learning environment, centralized machine learning and federal learning setting, for the  level of information leakage and affect the level of the model, and will compare the two  learning mechanism characteristics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' This paper will be respectively for centralized machine  learning and federated learning model member inference attack, using stochastic gradient  descent optimizer, model gradient vector as an important attack index, the final simulation  results can show the white box member inference attack model for the two target model  membership inference accuracy, namely the current learning model in what leaked their own  training data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='Our evaluation directions include: supervised attacks and unsupervised attacks,  inference attacks on the model and its newer versions, passive member reasoning attacks,  and active member inference attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' The experimental results evaluate the model  performance based on the member inference attack accuracy score and the True / False  positive (ROC) curve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  The first part of this paper introduces the privacy rights in machine learning and the existing  attack and defense strategies for machine learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' The second part of the related  knowledge, the list of the discussed problems and simulation experiments of the background  knowledge and the function basis and its definition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' The third part, the model and algorithm,  shows the workflow and fundamentals of the white-box member inference attack model used  in this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='The fourth part of white box inference attack performance evaluation  introduces the experimental related work setting and process, model attack performance  evaluation index and attack simulation results for centralized machine learning model and  federated learning model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  2 Related knowledge  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='1 Member Reasoning Attack  The degree of privacy information leakage of a certain model can be defined as: the  attacking party can get one or some private data through this mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' The former shows an  increased utility, while the latter reflects a privacy loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' This paper uses white-box member  inference attacks to quantify this privacy leakage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  Generally speaking, the purpose of an algorithm for member inference attacks is to reason  about the identity of a particular data (a member instance or a non-member instance) in the  target training set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='In practice, attackers with different training premises use member  inference attacks to infer the membership of a given data to the target model dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='Part of  the data belonging to the target model data set is observed and used by the attackers to infer  more relevant information of the target data set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' Therefore, under the attack mode of member  reasoning, the important private information of the training data is likely to be displayed  through the leakage degree of the target model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  This paper uses the way of member reasoning attack to obtain more visual and valuable  machine learning model mechanism and vulnerabilities, the results can reflect the  information leakage degree and privacy security of the machine model in the learning  process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='2 Shadow training techniques and white-box reasoning attacks  Shadow training technique (Shadow Training Technique).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' When the attacker cannot  obtain the internal algorithm, the attack feature data cannot be obtained, so the attacker can  only start with the output constantly updated by the target model of the neural network layer  at any input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='Shokri[2]In order to effectively conduct member reasoning attacks, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' used  shadow training techniques to deal with such situations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  White-box membership inference attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' In this environment, the attacker can observe not  only the model output f (x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' W), but also the period operation and all parameters involved in  the training process, including all hidden layer output hi (x), so the attacker with white box  permission can effectively expand the attack environment of the attacker with black box  permission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='3 Supervised attacks and unsupervised attacks  Supervised and unsupervised learning depends on whether an attacker has prior knowledge  such as a part of the target dataset or a sample codistributed with the target sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='When  have this knowledge, we will use the way of supervision let the attack model on the known  data to build the attack model, that is to let the reasoning model directly learning attack data  points and target model members of the membership, in such supervised learning mode to  build the reasoning attack became a supervised attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  However, when the attacker does not have knowledge and pre-training conditions on the  internal structure and sample distribution of the target model, we choose to build an  unsupervised attack model, predict more information about the target data set according to  the underlying output of the target model, and develop member inference attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='4 Stochastic Gradient Descent (SGD) optimizer  Stochastic gradient descent (SGD) algorithm is one of the deep learning optimizers, and it is  also a relatively basic neural network optimization method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='The algorithm repeatedly update  model parameters W as the gradient drop, by calculating the loss function value gradient,  iterative weight and bias, reduce the empirical expectation on the training set D, make it tend  to zero, so that the model parameters constantly approaching the expression of the real data,  as shown in formula (1), for stochastic gradient descent (SGD) algorithm working principle,  which is the classification model f loss function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  min  ��� ���(���, ���) ~���[���(���(���;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' ���), ���)]  (1)  Stochastic gradient descent algorithm will leave marks for the parameter loss function  gradient of each trained sample, which is the basis of reasoning attack, the white box  inference attack model and use of stochastic gradient descent optimization algorithm, these  sample markers can make the model gradient vector of all parameters on the attack of the  target easy to be observed, which becomes our important attack index.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='5 Passive attack and active attack  Passive or active white-box member inference attack mode depends on whether the attacker  passively receives the update parameter gradient of the observation model or actively  influences the training process of the target model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  Active attack (global attacker and local attacker).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' In the active attack mode, the attacker  will participate in the target model training process, and obtain the corresponding training set  member information through the active influence of their training parameters, based on  which the reasoning attack is implemented.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='Due to the structural characteristics of federated  learning, active attacks are often applied to them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=" The central parameter server will distribute  the parameters before the start of each training, collect the local model parameters uploaded  by each participant and aggregate and update the global models, and each training stage can  contribute to the attacker's attack." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  ��� ← ��� + ��� ���������  ������  (2)  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='6 Centralized learning  In this environment setting, all data are trained in the central parameter server set, which  includes public general data as well as some private data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' The attack model is able to  observe the complete independent learning model and the training results of each output.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  Fig 1 Centralized machine learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  In the experimental study of this paper, training with the new dataset d to get model updates,  These fine-tuning (Fine-tuning) models are often caused by the effects of those private data,  In the following training sessions, The attacker can observe the fine-tuning of the new  independent model f and its training results, Member inference for the new dataset d,  besides, The attacker will also make inference attacks on the two versions of the data set  before and after the fine update.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' To get more member information on your private data,  Restore the important privacy involved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='7 Federated Learning  In order to achieve a certain accuracy and have stronger reference value,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' machine learning  needs to cover enough large dimension training samples,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' but in practical application,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' data  participant2  participant 3  participant1  Zparticipant N  attackercollection not only need high density sample transmission,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' also exacerbated the privacy  information crisis,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' because the larger the base data often contains more important  information in the field of information,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' this undoubtedly enhances the privacy risk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' Under  the federated learning framework, the central parameter server each participant in federated  learning training has their own training set, they download global parameters in the  beginning, and training in the local model, they do local update and upload back to the  central parameter server, parameter server processing N participants of the update average,  data aggregation sharing save the latest parameter version of the global model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=" Participants'  sharing content is limited to parameters rather than specific data." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  Fig 2 Privacy risks of centralized machine learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  3 Models and algorithms used  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='1 White-box membership inference attack model  For the two types of attackers classified according to having or without background  knowledge, we trained the attack model to perform the attack in different ways.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='We  performed attack simulation experiments using the Alexnet model trained on the CIFAR-100  dataset as input of the attack model, and the following white-box member inference attack  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  participant2  Malicious participants  participant1  participantN3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='2 Principles and algorithms  In the white-box inference attack model we use, the tag components are built on a fully  connected network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' Aggregate all local weights received from the previous layer, form  inputs to nonlinear functions, form the output values of each module of the convolutional  layer, and optimize model convergence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='The white box reasoning attack model recombines  the output of each submodule component, combines the output of all feature extraction  components through the encoder components, the encoder output constitutes the attack  output of the model, the output is divided into "members" and "non-members", we put the  accuracy of the model for the unknown stronghold (predicted members, non-members) as  our basis to judge the attack performance of the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  4 Experiments of the white-box membership inference attack  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='1 Experimental setup  The equipment prepared for the experiment is the Intel core i7-8650U CPU memory 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='0GB  of the computer, the experimental language Python.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='The experiment uses Pytorch to  complete the neural network, which is easy to define, which helps us to easily and quickly  establish relatively small projects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  Attack Model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' ReLU activation function is defined as formula (5), where yi is the model  output as a non-saturated activation function, its unilateral inhibition ability to the output can  solve a certain "gradient disappearance" problem, and effectively improve the model  convergence speed to help effectively realize non-linear activation transformation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  Otherwise, ReLU activation function can sparse the model well, and such sparsity facilitates  experimental fitting to the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  ��� ������ = ������,  ������ > 0  0,  ������ ≤ 0  (6)  Performance evaluation indicators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' For the white-box model used in this paper, we used  two —— centralized machine learning and federated model —— with centralized  performance evaluation indicators to form a more comprehensive evaluation system, to help  improve the learning characteristics of the two learning models and the differentiation of  member information leakage level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  Table 1 Parameter Control Table.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  parameter  Parameter name  f  object model  h  Attack model  W  Target model parameters  D, D’  Member and non-member datasets  Pr  Precision--Recall Rate  γ  Adverse update rate  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='2 Analysis of the simulation experiment results  Deep learning has two main training algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' In this paper, we first show the simulation  results analysis of the centralized machine learning, and then provide the simulation results  and analysis of the federated learning objective model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  Simulation results analysis of white-box membership inference attacks for centralized  machine learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=" For the attack of centralized machine learning model, this paper will  evaluate the white box attack model from the following dimensions: based on the attack  model's understanding of target training mode, sample distribution, attack and defense  mechanism, starting from the two presets of supervised attack and unsupervised attack." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='In  supervised attacks, the output of different layers from the trained attacker attack model and  the gradient of the classification model;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' in unsupervised attacks, we use shadow training  techniques;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' and in a special case, we update multiple versions of the target model  simultaneously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  Supervised attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' In the context of supervised attacks, we train the target and attack  models using a pre-trained CIFAR100 dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' Therefore, the white-box inference attack  model understands the subset and sample distribution of the target, and can start the member  reasoning attack from the gradient and number of layers of the target model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  Table 2 Shows the member inference attack accuracy for the outputs of different layers of the  CIFAR1000-Alexnet centralized learning model  output layer  Member prediction accuracy  The bottom third layer  72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='88%  The penultimate layer  74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='06%  The final layer  74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='61%  When the training of the target model enters the last few layers, it will contain a lot of  training information from its previous layers, which makes the more data information the  model stores and covers more parameters, which is one of the reasons why the output of the  final layer of the target model leaks more membership information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  Since the deep neural network contains large-scale parameter data beyond the dimensions  that the target model is correctly generalized, the parameter gradient in the target model will  show differences that attackers can easily distinguish between.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  We used the CIFAR00 dataset to train the Densenet model with model parameter scale  25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='62M and parameter scale 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='7M two models as the target model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  The experiment also performs distribution statistics for the gradient norm of membership of  the output of each output class of the target CIFAR100-Alexnet centralized machine learning  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  2000  member  non-member  1500  Gradient norm  1000  500  20  40  60  80  100  Output classFig5 Gradient norm distribution of output members and non-members of each target CIFAR100-Alexnet  centralized machine learning model[25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  Since the gradient distribution of members of CIFAR100-Densenet and non-members of  CIFAR100-Densenet model is more different than that of CIFAR100-Resnet model, the  attack accuracy on Densenet architecture is better both from model output and model  gradient perspective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  Table 3 Attack models attack the three target models with different architectures trained on the CIFAR100  dataset, respectively for the output of the model and the member inference accuracy of the gradient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  object model  Attack accuracy  Dataset  Model architecture  target outputs  target gradients  CIFAR100  Alexnet  74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='61%  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='09%  CIFAR100  Resnet  62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='20%  64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='34%  CIFAR100  Densenet  67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='72%  74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='31%  Unsupervised attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' In order to assign members of the target model to non-member  examples, according to the gradient model value, we give the spectral clustering algorithm  with "member" cluster sample, and the other samples we preset as "non-member" to  facilitate the distribution of members and non-member samples to determine the member  inference accuracy of unsupervised attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  Fine-tuned models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' Such attack observation was chosen because we want to expand the attack  model from one to multiple to improve its performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' And in fact, model fine-tuning is  often influenced by important private data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  Table 4 Attack Accuracy of attacking fine-tuned models trained on the CIFAR100 dataset in centralized machine  learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  Dataset  Model architecture  Non-member in Dataset D  Non-member in Dataset DΔ  CIFAR  100  Alexnet  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='38%  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='36%  CIFAR  100  DenseNet  74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='61%  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='50%  Passive attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' The experiment will make the Alexnet model trained on the CIFAR100  dataset as the most target model, and set the position of the attacker to the central parameter  server.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='First, our attack starts with the training phase of the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='Attacks follow five  discontinuous training sessions against the target model, from 5 to 300.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  Table 5 Attack accuracy of passive global attacker’s attacking different training stages of the Alexnet federated  learning model trained on the CIFAR100 dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  Training stage  Attack accuracy  5 10 15 20 25  57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='32%  10 20 30 40 50  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='47%  50 100 150 200  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='50%  100 150 200 250 300  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='89%  Active attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' Due to the federated learning mode, the central parameter server for each  update data aggregation will negatively affect the reasoning accuracy of attack model, so in  order to get more training set data information of target participants, we use the same attack  model, preset global attacker active isolation target training participants, intervention in his  training process, to hinder its data upload and receive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  Table 6 The attack accuracy of passive and active white-box members for target models (four participants)  trained on the CIFAR100 dataset at different locations under the federated learning architecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  Target model  Global attacker  Local attacker  Dataset  Model  architecture  Passive  Active  Passive  CIFAR100  Alexnet  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='98%  88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='52%  72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='88%  CIFAR100  Densenet  77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='43%  82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='90%  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='98%  Active global attacker in the implementation of the attack, will actively block part of the  central parameter server issued parameters, which makes the target participants not only  cannot share with the central parameter server, also and other participants smooth  aggregation, which strengthens the attack model gradient superposition of the local SDG  algorithm, causing the target local model internal members and non-member example  become easier to identify.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  5 Conclusion  In contrast to the leakage of training and learning information and related privacy  vulnerabilities in the training and learning characteristics of the internal member samples of  centralized machine learning and federated learning models, we use different pre-trained  attack models to distinguish their access to and knowledge of the internal function, training  patterns, learning methods, distribution, and training set information of the target model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  Experimental data show we use the white box members of the inference attack evaluation  results: under the premise of using such attack model for attack,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' training late centralized  machine learning model in all aspects show greater members of information leakage,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' neural  network layer,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' gradient two attack indicators showed similar attack results,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' and for the latter,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  as a global model of passive attacker members of the reasoning accuracy will be  significantly higher than the participants of the local attack architecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  Federal machine learning broke the traditional centralized machine learning centralized data  control deadlock,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' to personal local data privacy security issues provides new ideas,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' through  the data communication and sharing bridge,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' improve the efficiency of the machine learning  model,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' accuracy and high reference value,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' in the era of all Internet,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' machine learning  technology inspired wide attention and innovation,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' based on attack and defensive research,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  spawned multi-dimensional application of attack strategy[28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' And for the powerful attack  ability of white-box membership inference attacks, there are now some adversarial defense  strategies[28]Still helpless about it means that information security in personally sensitive  areas is still an urgent issue for users using related technology products, because it can even  lead to serious property losses, which undoubtedly poses great obstacles to the use of  machine learning in daily life.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  Reasoning in this paper,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' the field of machine learning white box members against sensitive  sectors in order to improve information security and user privacy information security  protection problems to provide important insights and discuss,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' for the big data age of  machine learning is widely used in everyday life and prosperity and development of solid  foundation,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' to speed up the steps of 5 g era,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' it can better popularize machine learning  technology to all aspects of social life,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' so that the general public can enjoy the convenience  and have less worries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='In addition, more loopholes and learning features of machine learning  are waiting for us to explore and further study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  6 References  [1] SHOKRI R, STRONATI M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' SONG C, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' Membership inference attacks against  machine learning models[C]//IEEE Symposium on Security and Privacy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='2017:3-18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  [2] Salem A, Zhang Y, Humbert M, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='Ml-leaks:Model and data independent membership  inference  attacks  and  defenses  on  machine  learning  models[J].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='arXiv  preprint  arXiv:1806.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='01246,2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  [3] FREDRIKSON M, LANTZ E, JHA S, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' Privacy in pharmacogenetics: An end-to-end  case study of personalized warfarin dosing[C]//USENIX Security.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='2014:17-32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  [4] FREDRIKSON M, JHA S, RISTENPART T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' Model inversion attacks that exploit  confidence information and basic countermeasures[C]//Proceedings of ACM SIGSAC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  2015:1322-1333.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  [5] ZHU L, HAN S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' Deep leakage from gradients[C]//Advances in Neural Information  Processing Systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' 2019:17-31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  [6] JUUTI M, SZYLLER S, MARCHAL S, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' PRADA: protecting against DNN model  stealing attacks[C]//IEEE European Symposium on Security and Privacy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='2019:512-527.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  [7] ATENIESE G, MANCINI L V, SPOGNARDI A, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' Hacking smart machines with  smarter ones: How to extract meaningful data from machine learning classifiers[J].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  International Journal of Security and Networks, 2015, 10(3): 137-150.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  [8] ATENIESE G, MANCINI L V, SPOGNARDI A, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' Hacking smart machines with  smarter ones: How to extract meaningful data from machine learning classifiers[J].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  International Journal of Security and Networks, 2015, 10(3): 137-150.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  [9] MELIS L, SONG C, DE CRISTOFARO E, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' Exploiting unintended feature leakage  in collaborative learning[C]//IEEE Symposium on Security and Privacy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' 2019:691-706.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  [10] BLANCHARD P, EL MHAMDI E M, GUERRAOUI R, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' Machine learning with  adversaries: Byzantine tolerant gradient descent[C]//Neural Information Processing  Systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='2017:118-128.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  [2] BONAWITZ K, EICHNER H, GRIESKAMP W, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' Towards federated learning at  scale: System design[C]//IEEE CVPR Workshop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='2019:3310-3319.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  [11] FUNG C, YOON C J M, BESCHASTNIKH I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' The limitations of federated learning in  sybil settings[C]//International Symposium on Research in Attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' 2020:301-316.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  [12] DWORK C, ROTH A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' The algorithmic foundations of differential privacy[J].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  Foundations and Trends in Theoretical Computer Science, 2014, 9(3/4):211-407.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  [13] GEYER R C, KLEIN T, NABI M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' Differentially private federated learning: A client  level perspective[J].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' arXiv preprint, 2017:1712.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='07557.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  [14] BHOWMICK A, DUCHI J, FREUDIGER J, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' Protection against reconstruction and  its applications in private federated learning[J].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' arXiv preprint, 2018:1812.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='00984.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  [15] NASR M, SHOKRI R, HOUMANSADR A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' Comprehensive privacy analysis of deep  learning: Passive and active white-box inference attacks against centralized and  federated learning[C] // 2019 IEEE Symposium on Security and Privacy (SP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' IEEE,  2019 : 739 - 753.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  [16] SZEGEDY C, ZAREMBA W, SUTSKEVER I, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' Intriguing properties of neural  networks[J].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' arXiv preprint arXiv: 1312.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' 6199, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  [17] Ping Zhao, Hongbo Jiang, John C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' Lui, Chen Wang, Fanzi Zeng, Fu Xiao, and  Zhetao Li.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' P3-LOC: A Privacy-Preserving Paradigm-Driven Framework for Indoor  Localization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' IEEE/ACM Transactions on Networking (ToN), vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' 26, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' 6, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  2856-2869, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  [18] Hongbo Jiang, Yuanmeng Wang, Ping Zhao, Zhu Xiao.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' A Utility-Aware General  Framework with Quantifiable Privacy Preservation for Destination Prediction in LBSs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  IEEE/ACM Transactions on Networking (ToN), vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' 29, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' 5, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' 2228-2241, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  [19] Ping Zhao, Jiaxin Sun, and Guanglin Zhang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' DAML: Practical Secure Protocol for Data  Aggregation based on Machine Learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' ACM Transactions on Sensor Networks, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  16, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' 4, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' 1-18, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  [20] Ping Zhao, Wuwu Liu, Guanglin Zhang, Zongpeng Li, and Lin Wang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' Preserving  Privacy in WiFi Localization with Plausible Dummy Locations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' IEEE Transactions on  Vehicular Technology, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' 69, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' 10, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' 11909-11925, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  [21]  Guanglin  Zhang,  Anqi  Zhang,  Ping  Zhao,  and  Jiaxin  Sun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  Lightweight  Privacy-Preserving Scheme in WiFi Fingerprint-Based Indoor Localization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' IEEE  Systems Journal, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' 14, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' 4638-4647, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  [22] Ping Zhao, Jie Li, Fanzi Zeng, Fu Xiao, Chen Wang, Hongbo Jiang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' ILLIA: Enabling  k-Anonymity-based  Privacy  Preserving  against  Location  Injection  Attacks  in  continuous LBS Query.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' IEEE Internet of Things Journal, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' 5, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' 1033–1042,  2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  [23] Ping Zhao, Hongbo Jiang, Jie Li, Fanzi Zeng, Xiao Zhu, Kun Xie, and Guanglin Zhang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  Synthesizing Privacy Preserving Traces: Enhancing Plausibility with Social Networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  IEEE/ACM Transactions on Networking (ToN), vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' 27, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' 6, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' 2391 – 2404, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  [24] Ping Zhao, Jiawei Tao, Guanglin Zhang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' Deep Reinforcement Learning-based Joint  Optimization of Delay and Privacy in Multiple-User MEC Systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' IEEE Transactions  on Cloud Computing, DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='1109/TCC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='3140231, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  [25] Ping Zhao, Hongbo Jiang, Jie Li, Zhu Xiao, Daibo Liu, Ju Ren, Deke Guo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' Garbage in,  Garbage  out:  Poisoning  Attacks  Disguised  with  Plausible  Mobility  in  Data  Aggregation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' IEEE Transactions on Network Science and Engineering (TNSE), vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' 8,  no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' 2679-2693, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  [26] Ping Zhao, Xiaohui Zhao, Daiyu Huang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' Huang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' Privacy-Preserving Scheme against  Location Data Poisoning Attacks in Mobile-Edge Computing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' IEEE Transactions on  Computational Social Systems, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' 7, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' 818-826, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  [27] Ping Zhao, Chen Wang, and Hongbo Jiang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' On the Performance of k -Anonymity  against Inference Attacks with Background Information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' IEEE Internet of Things  Journal, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' 6, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' 808–819, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  [28] Guanglin Zhang, Sifan Ni, and Ping Zhao.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' Enhancing Privacy Preservation in Speech  Data Publishing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' IEEE Internet of Things Journal, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' 7, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' 8, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' 7357-7367, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  [29] Guanglin Zhang, Anqi Zhang, Ping Zhao.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' LocMIA: Membership Inference Attacks  against Aggregated Location Data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' IEEE Internet of Things Journal, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' 7, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' 12, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  11778-11788, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  [30] Guanglin Zhang, Sifan Ni and Ping Zhao.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' Learning-based Joint Optimization of  Energy-Delay and Privacy in Multiple-User Edge-Cloud Collaboration MEC Systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  IEEE Internet of Things Journal, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='1109/JIOT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='3088607, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  [31] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' Zhao, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' Cao, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' Jiang and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' Gao, "Practical Private Aggregation in Federated  Learning Against Inference Attack," in IEEE Internet of Things Journal, 2022, doi:  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='1109/JIOT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='3201231.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content='  [32] Hongbo Jiang, Yu Zhang, Zhu Xiao, Ping Zhao and Arun Iyengar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' An Empirical Study  of Travel Behavior Using Private Car Trajectory Data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' IEEE Transactions on Network  Science and Engineering, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' 8, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
+page_content=' 53-64, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LNE2T4oBgHgl3EQfAwaK/content/2301.03595v1.pdf'}
diff --git a/LNE3T4oBgHgl3EQfYAr5/content/2301.04485v1.pdf b/LNE3T4oBgHgl3EQfYAr5/content/2301.04485v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..092fc81627575215ce5335ba2ea345e6aedd2fbb
--- /dev/null
+++ b/LNE3T4oBgHgl3EQfYAr5/content/2301.04485v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:5120cf73f08584d2b16e476806f68d8a9c4a9488ebb26918fb33c4564fa86a1e
+size 19771350
diff --git a/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf b/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..68e4e7412c32800f3d265ac33dcedeb358a6619d
--- /dev/null
+++ b/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:0cc8394ab1d870e9ae23c47e69024c04bfc297163b275b71eb824aa470ec756b
+size 1032614
diff --git a/LdAzT4oBgHgl3EQfyv4r/vector_store/index.pkl b/LdAzT4oBgHgl3EQfyv4r/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..dbe5c92c5bfc8f14cae9bb8d1f3ecc00e10bfb05
--- /dev/null
+++ b/LdAzT4oBgHgl3EQfyv4r/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:32d09b028fa776b25437eb576940c0c1886b56f09d1097a9be87ee54e216d242
+size 248298
diff --git a/N9FJT4oBgHgl3EQf0S3d/content/tmp_files/2301.11647v1.pdf.txt b/N9FJT4oBgHgl3EQf0S3d/content/tmp_files/2301.11647v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..39a62e43dffacbe5d7592b6b56771326e8c8d6d2
--- /dev/null
+++ b/N9FJT4oBgHgl3EQf0S3d/content/tmp_files/2301.11647v1.pdf.txt
@@ -0,0 +1,4415 @@
+Learning the Dynamics of Sparsely Observed Interacting Systems
+Linus Bleistein 1 2 3 Adeline Fermanian 4 5 6 Anne-Sophie Jannot 1 7 Agathe Guilloux 1
+Abstract
+We address the problem of learning the dynamics of an unknown non-parametric system linking a target and a
+feature time series. The feature time series is measured on a sparse and irregular grid, while we have access to
+only a few points of the target time series. Once learned, we can use these dynamics to predict values of the
+target from the previous values of the feature time series. We frame this task as learning the solution map of a
+controlled differential equation (CDE). By leveraging the rich theory of signatures, we are able to cast this non-
+linear problem as a high-dimensional linear regression. We provide an oracle bound on the prediction error which
+exhibits explicit dependencies on the individual-specific sampling schemes. Our theoretical results are illustrated
+by simulations which show that our method outperforms existing algorithms for recovering the full time series
+while being computationally cheap. We conclude by demonstrating its potential on real-world epidemiological
+data.
+1. Introduction
+Time series are ubiquitous in many areas such as finance, economics, robotics, agriculture, and healthcare. One is typically
+interested in modelling the evolution of a target quantity through time, which is known to be affected by a set of time-
+evolving features. For example, pollution levels in a city are driven by quantities such as temperature, pressure, traffic,
+or economic activity measured through time. Mathematically, one wishes to model the evolution of a quantity yt ∈ Rp,
+p ≥ 1, as a function of some time evolving features xt ∈ Rd, d ≥ 1, for t ∈ [0, 1]. In other words, the goal is to learn the
+dynamics that link the target to the features.
+Such an interaction is typically modelled via differential equations, which are a common choice of model in natural
+sciences (Zwillinger, 1989). In this article, we assume that there exists a function G : Rp × Rd → Rp such that
+yt = y0 +
+� t
+0
+G(ys, xs)ds
+(1)
+or equivalently
+dyt = G(yt, xt)dt,
+y0 ∈ Rp.
+The value yt depends on the trajectory of the features time series xs up to time t. Learning the dynamics of the system can
+be framed as learning the solution map of (1), i.e., a function Ψ which, given a time t, an initial point y0 ∈ Rp, and the
+history of the path up to time t, denoted by x[0,t] = (xs)s∈[0,t], outputs the value of y at time t.
+If we know Ψ, we gain access to the values of y at any point in time provided we know the values of x up to this point
+; this encompasses many tasks such as forecasting or interpolating between points of y. We specifically have in mind
+applications where we have an easy access to x but a limited one to y.
+This problem is extremely common in healthcare. For example, in obstetrics, the lactic acidosis (LA) of the fetus, which
+is a proxy for fetal distress, is a quantity of high medical interest for predicting complications in the first hours after birth.
+1Inria Paris, F-75015 Paris, France 2Centre de Recherche des Cordeliers, INSERM, Universit´e de Paris, Sorbonne Universit´e, F-
+75006 Paris, France 3LaMME, UEVE and UMR 8071, Paris Saclay University, F-91042, Evry, France 4MINES ParisTech, PSL Research
+University, CBIO, F-75006 Paris, France 5INSERM, U900, F-75005 Paris, France 6Institut Curie, PSL Research University, F-75005
+Paris, France 7AP-HP. Correspondence to: Linus Bleistein <linus.bleistein@inria.fr>.
+arXiv:2301.11647v1  [stat.ML]  27 Jan 2023
+
+Learning the Dynamics of Sparsely Observed Interacting Systems
+This biomarker cannot be measured during pregnancy but only at birth because the measurement is highly invasive. Some
+vitals such as heart rate and fetal movement are however easy to measure during pregnancy. In this case, x is the non-
+invasive measurements made during pregnancy, while y is the invasive measurement of LA at birth. Predicting the value
+of y at any time t (both before and at birth) would allow for early diagnosis. Similarly, after surgery, patients are often
+monitored to detect hemorrhage. While some vitals such as heart rate of saturation are monitored in continuous time,
+haemoglobin—which is highly predictive of hemorrhage—is only measured by blood samples taken a few times a day,
+which can significantly delay hemorrhage diagnostic.
+Irregular data.
+In practice, the functions x and y are measured on discrete grids and take the form of time series. These
+often present a lot of heterogeneity, both within and across individuals.
+(i) For every individual, the time between any two measurements can vary, and thus individuals may not be recorded on
+the same grid.
+(ii) The number of total sampling points might vary between individuals.
+(iii) Each measurement in time might be corrupted by measurement noise.
+Mathematically, we consider n pairs of functions {(x1, y1), . . . , (xn, yn)}. Each xi deterministically produces a specific
+yi through the Ordinary Differential Equation (ODE) (1). We call xi the feature path and yi the target path. Both xi and
+yi are only observed at a finite set of times specific to every individual. We denote by
+Di =
+�
+ti
+1, . . . , ti
+ki
+�
+,
+i = 1, . . . , n,
+the sampling grid of xi and by ¯Di the sampling grid of yi. We stress that both the number of sampling times ki and the
+sampling times ti
+1, . . . , ti
+ki themselves are individual specific, as described in (i) and (ii). Moreover, the observations are
+corrupted by additive noise, such that we observe
+Xi
+t = xi
+t + ξi
+t
+for all t ∈ Di, and similarly Y i
+t = yi
+t + εi
+t for every t ∈ ¯Di, where the ξi
+t and εi
+t are sub-gaussian i.i.d. random vectors.
+Each input may therefore be written as a matrix Xi = (Xi
+t)t∈Di ∈ Rki×d which we call the feature time series. Similarly,
+the quantity of interest is a matrix Yi = (Y i
+t )t∈ ¯
+Di ∈ Rmi×p (where mi is the length of ¯Di) and is called the target time
+series. The grid ¯Di is assumed to be a subset of Di: in our setup yi is hard to sample and therefore measured at only a few
+points (and sometimes only one) while xi is easy to access and measured at high frequency. Our goal is to approximate the
+dynamics linking x and y from the irregular, heterogeneous, and fuzzy data Xi and Yi.
+Such heterogeneity is difficult to handle by classical machine learning algorithms such as Long short-term memory net-
+works (LSTM, Hochreiter & Schmidhuber, 1997) which assume that the data is regularly sampled. Some more recent
+approaches (Rubanova et al., 2019; De Brouwer et al., 2019; Kidger et al., 2020) have adapted these models by introduc-
+ing continuously evolving hidden states to account for the irregular spacing between observation times.
+We build upon the approach of Neural Controlled Differential Equations (Neural CDE, Kidger et al., 2020; Morrill et al.,
+2021b), which have proven to be very successful for time series classification and online prediction tasks (Morrill et al.,
+2021a). The key idea of Neural CDE is that under some fairly mild assumptions, any general ordinary differential equation
+of the form (1) can be rewritten as
+yt = y0 +
+� t
+0
+F(ys)dxs,
+(2)
+where F : Rp → Rp×d is a matrix-valued vector field, such that the right-hand-side of (2) is a matrix-vector product (see,
+e.g., Fermanian et al., 2021, Proposition 2, for a proof). The function x is often called the driver of the CDE. In a Neural
+CDE setting, the driver x is a continuous interpolation of the feature times series, y corresponds to a continuously-evolving
+state, and F is chosen to be a neural network. This network is then trained such that the values of (yt) can be used as
+features for classification or regression tasks. While Neural CDE have been shown to outperform other architectures with
+limited memory usage, their training time is considerable and no statistical guarantees exist.
+
+Learning the Dynamics of Sparsely Observed Interacting Systems
+Model.
+We model the interactions between the target and the feature paths through a CDE of the form (2). This modelling
+choice encapsulates a broad variety of settings, since the vector field F can be any (regular enough) function. A priori, the
+solution map Ψ of this CDE is a complex function of time and the history of x up to t; however, by linearizing the model,
+we are able to approximate Ψ by a simple scalar product between a deterministic transformation of the history of x, called
+the signature of x at order N ≥ 1 and denoted by SN(x[0,t]), and a time independent matrix θ∗
+N. Informally, we have
+Ψ
+�
+x[0,t], t
+�
+≈ SN
+�
+x[0,t]
+�⊤θ∗
+N.
+Two striking features of this linearized model are (i) that θ∗
+N can be learned on any time horizon [0, t] since it is independant
+of time, and (ii) that once it has been learned, the model can be called at any time t.
+Contributions.
+Our contributions are threefold. First, we frame the task of learning the interactions between two time
+series as learning the flow of a CDE, which can be linearized in the signature space. While the connection between CDEs
+and signatures is well-known, this is the first time CDEs are used as a statistical model. We then leverage this linearization
+to derive statistical guarantees on the prediction error with an explicit dependence on both sampling irregularities and the
+noise affecting measurements. To our knowledge, this is the first bound of this type for signature-based models, allowing for
+better understanding of the dependencies between prediction performance and sampling roughness. Finally, the resulting
+algorithm, called SigLasso, is shown to be computationally cheap and competitive compared to existing baselines on a wide
+range of simulated data and a real-world example of hospitalization growth rate prediction during the Covid pandemic.
+Related works.
+Signatures originated as a prominent tool in stochastic analysis (Chen, 1958; Lyons et al., 2007; Friz
+& Victoir, 2010) and have proven to be a powerful feature extraction method in machine learning in various domains
+such as healthcare (Morrill et al., 2020b; Wang et al., 2020), human action recognition (Yang et al., 2022), or financial
+modelling (Lyons et al., 2014; Buehler et al., 2020). Their appealing properties include a capacity to handle irregular data,
+to capture dependence between coordinates, and their links with the theory of CDE. We refer to Lyons & McLeod (2022)
+for a recent survey on their use cases. However, the statistical properties of signatures based algorithms have received little
+attention so far, with a few notable exceptions (Papavasiliou & Ladroue, 2011; Lemercier et al., 2021; Fermanian, 2022).
+On the other hand, the interplay between dynamical systems and machine learning has received considerable attention in
+the recent years. A first line of work has focused on approximating the solution of ODE and Partial Differential Equations
+(PDE) with neural networks (Lagaris et al., 1998; Han et al., 2018; Zubov et al., 2021) and directly learning dynamical
+systems (Long et al., 2018; Fattahi et al., 2019). Recent approaches have been interested in combining deep learning
+algorithms with physical knowledge (Greydanus et al., 2019; Brunton et al., 2020; Willard et al., 2020). Finally, dynamical
+systems, seen as continuous versions of neural network architectures, have also been a great source of inspiration for
+analysing and designing machine learning algorithms in the recent years (Chen et al., 2018; Fermanian et al., 2021;
+Marion et al., 2022). We refer to Kidger (2022) for an extensive review.
+Our problem also bears close resemblance to frameworks encountered in sequence-to-sequence learning (Sutskever et al.,
+2014; Gehring et al., 2017) and functional regression (Ramsay & Dalzell, 1991; Marx & Eilers, 1999).
+Overview.
+Section 2 introduces the CDE model for interacting systems, the mathematical context and the learning proce-
+dure. Our main theoretical result is presented in Section 3. We conclude by an empirical study on synthetic and real-world
+data in Section 4. All proofs are postponed to the appendix and the code to reproduce the experiments is available on our
+Github.
+2. Model and assumptions
+2.1. A CDE-based model on the dynamics
+We start by describing our assumptions on the feature and target paths, which are linked by Equation (2). To correctly
+define the integral of Equation (2), we need to impose some conditions on the xi and on F. Note that we consider that the
+xi are defined on [0, 1] but our results extend easily to any compact time interval [a, b].
+Assumption 1. All paths (xi)1≤i≤n are continuous and there exists 0 < L < 1 such that, for all i = 1, . . . , n,
+��xi��
+1-var,[0,1] = sup
+D
+�
+k
+��xi
+tk+1 − xi
+tk
+�� ≤ L,
+
+Learning the Dynamics of Sparsely Observed Interacting Systems
+where ∥·∥ is the Euclidean norm and the supremum is taken over all finite dissections D = {0 = t1 < · · · < tk = 1}.
+We write C1-var
+L
+([0, 1], Rd) for the set of continuous paths of total variation bounded by L. Outside the statistical context,
+when referring to general paths, we will drop the superscripts i and simply write x and y to alleviate notations.
+We assume that the target path y is the solution of the ODE (1). This modelization choice means that the evolution of y
+is governed by a dynamical system whose dynamics itself are allowed to vary with the current value of the feature path.
+Observe that this model can be seen as a generalized form of a non-autonomous system (Lyons et al., 2007), which we
+recover by taking xt = t. Since Equation (1) can be rewritten as a CDE, the starting point of our work is to assume that
+the true dynamics of the data follow such a CDE, as stated in the following assumption.
+Assumption 2. There exists a smooth vector field F : Rp → Rp×d such that, for all i = 1, . . . , n, yi is the solution of the
+CDE (2) driven by xi with initial condition yi
+0 = y0 ∈ Rp homogeneous amongst individuals.
+By “smooth” we mean that each coordinate of F is infinitely differentiable, that is, is C∞. The vector field F and the initial
+condition y0 are common to all individuals, which can be seen as homogeneity assumptions on our sample. On the other
+hand, since every individual i has her own feature path xi, the target paths yi are individual specific. In other words, there
+exists a solution map Ψ that depends only on y0 and F and is such that, for any t ∈ [0, 1], Ψ(xi
+[0,t], t) = yi
+t.
+The vector field F encapsulates the common physical dynamics governing the evolution of yi, which are affected by the
+changes in xi. Note that there is no parametric model on F (although some strong smoothness requirements will be needed)
+contrarily to functional or traditional time series models (Ramsay & Silverman, 2005; Morris, 2015).
+2.2. Linearizing the CDE with signatures
+Before defining the Taylor expansion of the CDE (2), which will allow us to linearize the solution map Ψ, we need to
+introduce the notion of signature, which have emerged as a powerful tool to model time series (Levin et al., 2013; Kidger
+et al., 2019).
+From now on, for any feature path x with values in Rd, we denote by x(j) its jth coordinate, for j = 1, . . . , d.
+Definition 2.1. Let x ∈ C1-var
+L
+([0, 1], Rd). Take a word of length k from the alphabet {1, . . . , d}, that is, an element
+I = (i1, . . . , ik) ∈ {1, . . . , d}k. For all t ∈ [0, 1], the signature coefficient associated to this word is the scalar
+SI�
+x[0,t]
+�
+=
+�
+· · ·
+�
+0<u1<···<uk<t
+dx(i1)
+u1 · · · dx(ik)
+uk .
+Signatures encode geometric properties of paths and have numerous appealing properties as a feature set for time series.
+In the following, we draw on their connection with Taylor expansions of CDEs.
+We introduce a series of notation on signature coefficients, grouping them by the length k of the words. For any k ∈ N and
+t ∈ [0, 1], the signature of order k of x[0,t] is
+Xk,[0,t] =
+�
+SI(x[0,t])
+�
+I∈{1,...,d}k ∈ Rdk,
+where the words (i1, . . . , ik) are in lexicographic order. We then denote the full signature by
+S(x[0,t]) =
+�
+1, X1
+[0,t], . . . , Xk
+[0,t], . . .
+�
+and, for any N ≥ 1, the signature truncated at order N by
+SN(x[0,t]) =
+�
+1, X1
+[0,t], . . . , XN
+[0,t]
+�⊤.
+The size of the signature truncated at order N grows exponentially with N, since, for d ≥ 2, it is equal to
+sd(N) = 1 + d + d2 + · · · + dN = dN+1 − 1
+d − 1
+.
+When computing signatures, it is common practice to add time as a coordinate to the path (Fermanian, 2021), that is,
+consider the path (t, xt)⊤. From now on, we assume that the first dimension of x always corresponds to time, so that
+d ≥ 2.
+We are now ready to define the Taylor expansion of a CDE.
+
+Learning the Dynamics of Sparsely Observed Interacting Systems
+Definition 2.2. Let N ≥ 1. The Taylor expansion of order N of the solution y of Equation (2) is defined by
+yN,t = y0 +
+N
+�
+k=1
+�
+I∈{1,...,d}k
+SI �
+x[0,t]
+�
+× ΦI
+F (y0) ,
+(3)
+where ΦI
+F(·) ∈ Rp is the differential product of the vector field F along I, whose definition is postponed to Appendix A.3.
+The differential products ΦI
+F(y0) are essentially a combination of multiplication and summation of derivatives of the
+different components of F, evaluated at y0.
+The Taylor expansion crucially allows to write the solution map as a product between a time-varying term (the signature
+of the feature path) and a constant-over-time term (the differential product). This is similar to a regular Taylor expansion;
+we discuss this analogy in Appendix A.4. Note that Equation (3) may also be written as a matrix-vector product
+yN,t
+⊤ = SN(x[0,t])⊤θ∗
+N ∈ Rp,
+(4)
+where θ∗
+N ∈ Rsd(N)×p is a matrix collecting all differential products ΦI
+F(y0) up to order N and the offset y0. Since θ∗
+N
+depends neither on x nor on t, the Taylor expansion of y at order N is simply a linear function of the truncated signature.
+For this expansion to become exact in the sens of pointwise convergence, we need quite strong regularity assumption on
+F. This is the price to pay for the non-parametric nature of our model.
+Assumption 3. The vector field F has fast decaying derivatives. In other words, defining
+Λk(F) =
+sup
+I∈{1,...,d}k
+��ΦI
+F (y0)
+�� ,
+we assume that �∞
+k=0 dkΛk(F)/k! < ∞.
+Let y be the solution of the CDE (2), and let (yN,t)t∈[0,1] be its N-th Taylor expansion. Under Assumptions 1, 2, and 3,
+we then have, for any t ∈ [0, 1],
+��yt − yN,t
+��
+−→
+N→+∞ 0.
+(5)
+We refer the reader to Friz & Victoir (2008) and Fermanian et al. (2021, Proposition 4) for more details on this result.
+While we impose relatively strong regularity assumptions on the vector field F, the assumptions on x are mild (see As-
+sumption 1). Therefore, our assumptions, while enforcing a fairly high amount of regularity on the dynamical structure,
+still accommodate most of the real world data. Also note that Fermanian et al. (2021) give conditions under which As-
+sumption 3 is satisfied when F is a layer of a neural network with smooth activation functions.
+2.3. The learning problem
+We go back to the statistical learning problem.
+Recall that in practice, we do not observe the continuous paths
+{(x1, y1), . . . , (xn, yn)} but their discretized and fuzzy counterparts {(X1, Y1), . . . , (Xn, Yn)} measured on a set of
+individual grids D = {D1, . . . , Dn} and ¯D = { ¯D1, . . . , ¯Dn}. We allow for high data heterogeneity: two individuals can
+be sampled at very different frequencies and at different time-points, and therefore have different observation grids.
+The meshsize of a sampling grid D, denoted by |D| is defined as the largest gap between two successive sampling times,
+that is,
+|D| = max
+ti∈D |ti+1 − ti|.
+Its cardinality, denoted by #D, is the number of sampling points in D. We make the following assumption on the sampling
+procedure.
+Assumption 4. For all i = 1, . . . , n,
+0 ∈ Di,
+#Di ≥ 2,
+and
+¯Di ⊂ Di.
+
+Learning the Dynamics of Sparsely Observed Interacting Systems
+ 
+ 
+Figure 1: The workflow of our model. Starting from the left, the first panel describes our modelling hypothesis: the target
+and feature time series are linked through an unknown CDE. The second panel shows the observed data. The third panel
+shows how every observation of the target is mapped to the signature of the corresponding path, how to construct the
+dataset SD
+N, Y from this data and finally how to learn the SigLasso estimator.
+This assumption essentially means that the measurements on all individuals start at 0 and that the sampling grid of Yi is
+coarser than the sampling grid of Xi. We also let |D| = maxi|Di| be the biggest gap between two successive sampling
+times within the whole set of individual grids and #D =
+n�
+i=1
+#Di the total number of sampling points of the feature time
+series. We recall that the random vectors ξi
+t, t ∈ Di, are the noises affecting the measurements of xi. The random vectors
+εi
+t affect the measurements of yi. We end with assumptions on the law of these measurement noises.
+Assumption 5 (Noise on the feature time series). The noises (ξi
+t)i∈{1,...,n},t∈Di are i.i.d. vξ-subgaussian random vectors.
+Assumption 6 (Noise on the target time series). The noises (εi
+t)i∈{1,...,n},t∈ ¯
+Di are i.i.d. vε-subgaussian random vectors
+and independent from (ξi
+t)i∈{1,...,n},t∈Di.
+The goal of the learning procedure is to learn the solution map Ψ, in order to infer the value of y at any time t, given
+observations of x up to time t. We have seen previously that this problem boils down to estimating the matrix θ∗
+N via
+Equation (4). The truncation order N ≥ 1 is an hyperparameter and will be selected by cross-validation.
+Single target measurement.
+For the sake of simplicity, we first present the case where Y i is measured only at the end
+of the observation period, as in the example of LA measurements in obstetrics. In this case, for all i = 1, . . . , n, we have
+mi = 1 such that M = n,
+Di = (ti
+1, . . . , ti
+ki),
+and
+¯Di = (ti
+ki).
+Then Yi ∈ Rp, and we denote by
+Y =
+�Y1, . . . , Yn�⊤ ∈ Rn×p
+the matrix containing all target measurements. Since we do not have access to the feature paths xi but only to the discrete
+measurements Xi, we compute the signature of its linear interpolation normalized by its total variation, sampled up to
+final time ti
+ki, and denote by SD
+N ∈ Rn×sd(N) the matrix of stacked signatures. Note that signatures of piecewise linear
+functions are fast to compute with packages such as signatory (Kidger & Lyons, 2020) or iisignature (Reizenstein
+& Graham, 2020). The complexity to compute the signature truncated at order N of the ith feature time series is of the
+order O(#DidN). Finally, we approximate θ∗
+N ∈ Rsd(N)×p by solving the optimisation problem
+min
+θ∈Rsd(N)×p
+1
+2n
+��Y − SD
+Nθ
+��2
+F + Ω(θ),
+(6)
+where Ω : Rsd(N)×p → R+ is a regularization term and ∥·∥F is the Frobenius norm. We have reduced the complex
+problem of learning the solution map Ψ to a simple penalized linear regression in the signature space. This linear model
+on the signature is close to the one studied by Levin et al. (2013); Lyons et al. (2014); Fermanian (2022).
+
+1.5
+2.5 
+1.0
+o.
+1.0
+2.0 
+1.5
+0.5 
+0.5
+1.0 
+0.0 
+.....
+0.5 
+0.0
+...
+..
+0.5
+0.0 
+...
+0.5
+1.0
+0.5
+1.5
+1.0 
+1.0
+1.5
+2.0
+0.0 
+0.25
+0.5
+0.75
+1.0 
+0.0 
+0.25
+0.5 
+0.75
+1.0 
+0.0
+0.25
+0.5 
+0.75
+1.0 
+Time1.0
+0.5
+......
+.......
+0.0 
+.O..
+.....
+0.5
+....
+1.0
+0.0 
+0.2 
+0.4 
+0.6
+0.8 
+1.0
+Time
+4
+3
+2
+1
+0.0
+0.2
+0.4 
+0.6
+0.8
+1.0
+TimeT
+M
+TMW7
+............
+6
+5
+.....
+2
+2
+3
+2
+0.0
+0.25 
+0.5 
+0.75
+1.0 
+0.0 
+0.25
+ 0.5 
+0.75
+1.0 
+0.0 
+0.25 
+0.5
+0.75
+1.0 
+Time1.0
+1.0
+1.0
+.
+:
+:
+0.5
+0.5
+0.5
+..
+.
+0.0
+0.0
+0.0
+..
+..
++
+0.5
+0.5
+0.5
+:
+1.0
+1.0
+1.0 
+1.5
+1.5
+1.5
+0.0 
+0.2 
+0.4
+0.6
+0.8
+1.0
+0.0
+0.2
+0.4 
+0.6
+0.8
+1.0
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0Learning the Dynamics of Sparsely Observed Interacting Systems
+Multiple target measurements.
+We also cover the case when # ¯Di > 1, that is, the target is measured at multiple times
+for every individual, as in the example of hemorrhage detection. In this case, we have Yi ∈ Rmi×p and we stack the
+different measurement matrices Yi to obtain a matrix Y of size M × p, where M = m1 + · · · + mn. For any i = 1, . . . , n
+and every t ∈ ¯Di, we predict Y i
+t using the signature of the linear interpolation of the normalized (Xi
+0, . . . , Xi
+t). In this
+manner, we will be able to predict Y i
+t at every point where Xi
+t is sampled. The exact workflow of our model is described
+in Figure 1.
+3. Theoretical guarantees
+3.1. Mathematical setup
+We consider a general multiple target measurements setting. To simplify the exposure of our results, we consider an
+univariate target path, i.e., p = 1. In this case, the true parameter θ∗
+N is a vector of size sd(N) and not a matrix. The
+general case p ≥ 1, which our algorithm handles as running p Lasso regressions in parallel, is considered in the Appendix
+B, were we prove all results in this setting. In addition, to lighten the presentation of the oracle inequality, we also
+focus in this section on the case of ω-Lipschitz feature paths, that is, for every i = 1, . . . , n and for all s, t ∈ [0, 1],
+��xi
+t − xi
+s
+�� ≤ ω|t − s|. We stress that our results are valid for continuous paths of bounded variations. We let y ∈ RM
+be the matrix collecting all unobserved values of the target paths at measurement times such that y = E
+�
+Y
+�
+, where the
+expectation is taken over the noises εi
+t, and define �θN,M as
+�θN,M ∈ arg min
+θ∈Rsd(N)
+1
+2M
+��Y − SD
+Nθ
+��2
+2 + Ω(θ).
+(7)
+For δ ∈ (0, 1), we define the set
+Aξ(δ) =
+�
+max
+��ξi
+t
+�� ≤ vξ
+√
+d + vξ
+�
+1
+C log #D
+δ
+�
+(8)
+where the maximum is taken on all i = 1, . . . , n and t ∈ Di, and C is a universal constant. This set is of probability greater
+than 1 − δ under Assumption 5 (see Appendix A.5). Similarly, for k ≥ 0 and ¯δ ∈ (0, 1), let
+Ck(¯δ) =
+�
+vε log(2Ndk/¯δ)
+and define
+Aε(¯δ) =
+N
+�
+k=0
+���ε⊤SD
+·,[k]
+��
+∞ ≤ M
+1
+2 Ck(¯δ)
+k!
+�
+,
+where SD
+·,[k] is the sub-matrix of size M × dk of SD
+N associated to the signature coefficients of order k, and ε ∈ RM is a
+vector of i.i.d. noise terms satisfying Assumption 6 (see Appendix B.2). Under Assumptions 5 and 6, Aξ(δ) ∩ Aε(¯δ) is of
+probability at least (1 − δ)(1 − ¯δ). Let
+Ω(θ) =
+N
+�
+k=0
+Ck(¯δ)
+k!
+√
+M
+��θ[k]
+��
+1,
+(9)
+where θ[k] is the subvector of size dk that collects all elements of θ associated to words of size k (see Appendix B.2).
+This penalization can be implemented by rescaling the feature matrix SD
+N and solving a standard ℓ1-penalized regression
+problem (see Appendix C.1). Our result extends to more general penalties by adapting existing techniques from Chesneau
+& Hebiri (2008) for the group-lasso, or Lederer et al. (2019) for the hierarchical lasso.
+3.2. Main results
+The error made when learning θ∗
+N by �θN,M comes from three different sources.
+1. Truncating the signature used in the regression at depth N ≥ 1 results in a truncation bias.
+
+Learning the Dynamics of Sparsely Observed Interacting Systems
+Table 1: Performance of SigLasso, GRU and Neural CDE in different simulation settings, averaged over 10 iterations. In
+every setting, n = 50, # ¯Di = 5 for all i = 1, . . . , n (and therefore M = 250).
+L2 error
+MSE on last point
+Setting
+SigLasso
+GRU
+Neural CDE
+SigLasso
+GRU
+Neural CDE
+Well-specified
+0.13 ± 0.07
+1.05 ± 0.42
+0.61 ± 0.38
+0.73 ± 0.56
+3.32 ± 1.60
+1.46 ± 1.20
+Ill-specified
+0.15 ± 0.02
+0.24 ± 0.11
+0.29 ± 0.15
+0.09 ± 0.05
+0.19 ± 0.09
+0.22 ± 0.15
+OU
+0.01 ± 0.02
+0.05 ± 0.06
+0.17 ± 0.12
+0.018 ± 0.025
+0.014 ± 0.020
+0.013 ± 0.016
+Tumor growth
+0.16 ± 0.02
+0.66 ± 0.09
+5.29 ± 1.38
+0.35 ± 0.12
+2.00 ± 0.38
+8.76 ± 9.26
+2. Discretization of the feature path and the noise affecting each measurement point induce a discretization error. In
+particular, there is a trade-off between sampling frequency and variance of the noise.
+3. The measurement error on yi and the finite-sample setting induce a classical estimation error.
+The following lemmas bound each of those errors. We first bound the variance of the estimator with arguments borrowed
+from Bickel et al. (2009).
+Lemma 3.1. Under Assumptions 1 and 2, on the set Aε(¯δ) ∩ Aξ(δ), the prediction error
+1
+2M
+��y − SD
+N �θN,M
+��2
+2
+is bounded above by
+1
+2M
+��y − SD
+Nθ∗
+N
+��2
+2 + 2CN(¯δ)
+√
+M
+N
+�
+k=0
+dkΛk(F)
+k!
+.
+See Appendix B.2 for a proof. This inequality decomposes the error into a bias and a variance term. We denote the
+signature matrix of the unobserved paths xi by SN ∈ RM×sd(N).
+As for the bias term, notice that one can write
+1
+2M
+��y − SD
+Nθ∗
+N
+��2
+2 ≤ 1
+M ∥y − SNθ∗
+N∥2
+2
+�
+��
+�
+Truncation bias
++ 1
+M
+��SNθ∗
+N − SD
+Nθ∗
+N
+��2
+2
+�
+��
+�
+Discretization error
+.
+Bounding each of these terms corresponds to, respectively, Lemmas 3.2 and 3.3. We stress that the truncation bias is of a
+different nature than the discretization error since it depends on a choice of hyperparameter while the latter is inherent to
+the data at hand.
+Lemma 3.2. Under Assumptions 1 and 2, for any N ≥ 1,
+1
+M ∥y − SNθ∗
+N∥2
+2 ≤
+�
+dN+1ΛN+1(F)
+(N + 1)!
+�2
+.
+Under Assumption 3, the right-hand-side decays exponentially fast with N. This lemma is an immediate consequence of
+Fermanian et al. (2021) (see Appendix B.3). We now turn to the error induced by the discretization of the feature path.
+Lemma 3.3. Under Assumptions 1, 4, and 5, on the set Aξ(δ), one has
+1
+M
+��(SN − SD
+N)θ∗
+N
+��2
+2 ≤ CD,N(δ)
+N
+�
+k=0
+dkΛk(F)2
+k!2
+,
+where CD,N(δ) is equal to
+(2eLN!)2
+�
+ω|D| + vξ
+√
+d + vξ
+�
+1
+C log #D
+δ
+�2
+and C is a universal constant.
+
+Learning the Dynamics of Sparsely Observed Interacting Systems
+This lemma relies on a fine analysis of the distance between two signature layers. The dependence of CD,N(δ) on sampling
+mechanisms and noise is of particular interest. First, the term ω|D| refers to the longest time between two observations
+amongst individuals. Not sampling an individual during a long period of time causes a loss in information, which is
+bounded by the Lipschitz control ω of the feature path.
+The remaining part of CD,N(δ) is a consequence of the noises ξi
+t affecting the measurement points of the feature time series
+and does not vanish with n. The emergence of such a bias is a well studied phenomenon in errors-in-variable models, and
+cannot be corrected without precise knowledge of the noise’s variance (Loh & Wainwright, 2011). Note that if we assume
+that the feature paths are measured without noise (i.e., vξ = 0), the right-hand-side collapses to a discretization error term
+proportional to |D|2 and tends to 0 as |D| → 0. The proof of this Lemma is given in Appendix B.5.
+From Lemmas 3.1 to 3.3 and the definitions of Aξ and Aε finally we get the following oracle inequality. The proof is given
+in Appendix B.6.
+Theorem 3.4 (An oracle inequality for learning with signatures). Under Assumptions 1, 2, 4, 5, and 6, with probability at
+least (1 − δ)(1 − ¯δ), the prediction error is bounded above by
+1
+2M
+���y − SD
+N �θN,M
+���
+2
+2 ≤
+�
+dN+1ΛN+1(F)
+(N + 1)!
+�2
+(10)
++ CD,N(δ)
+N
+�
+k=0
+dkΛk(F)2
+k!2
+(11)
++ 2CN(¯δ)
+√
+M
+N
+�
+k=0
+dkΛk(F)
+k!
+.
+(12)
+All terms depend on the regularity of the vector field F via the constants Λk(F): the bigger these constants, the faster the
+vector field F may vary, making the CDE harder to predict. The convergence speed in 1/
+√
+M is classical. Also note that
+our bound is non-asymptotic and is valid for any M ≥ 1.
+The dependence of the bound on N is highly non-trivial and requires an in-depth analysis of the regularity of F in order to
+bound Λk(F), which is out of the scope of this paper. The asymptotic behaviour of this oracle inequality is discussed in
+Appendix B.7.
+4. Experiments
+We study the performance of SigLasso obtained by solving the optimization problem (7), where Ω(θ) is defined by Equa-
+tion (9). All details are given in Appendix C.
+4.1. Simulations
+We consider several settings of data generation. First, in the well-specified setting, the data is generated from a model with
+regular feature paths x (piecewise polynomials) and target paths y wich are solutions to the CDE dyt = tanh(Ayt)dxt,
+where A is a randomly drawn matrix. In the ill-specified setting, the target y is equal to yt = log ∥ �10
+h=1 xt−h∥ for any
+t ∈ [0, 1]. In the third setting, called OU setting, the feature paths are realizations of Brownian motions and the target paths
+are Ornstein-Uhlenbeck processes (Borodin & Salminen, 2012) driven by the feature paths. The last setting corresponds
+to the tumor growth model from Simeoni et al. (2004). The feature path represents the concentration of a treatment drug,
+generated as the squared value of the smooth paths used in the well-specified setting, and the target path y, the weight of
+the tumor, is governed by a system of differential equations given in Appendix C.6.
+We compare SigLasso to a GRU and Neural CDE (Kidger et al., 2020). We measure the performance of the models with
+two metrics on a test set: the mean squared error for predicting the last observation point of the target paths and the L2
+error for predicting the full path on a fine grid.
+The results are shown in Table 1 and Figure 2. In Figure 2 we consider the well-specified setting and vary the number
+of sampling points of the target paths between 1 and 20. In Table 1 it is fixed to 5 but the simulation settings change.
+Sampling of both the target and the feature time series is highly irregular. SigLasso outperforms Neural CDE and GRU
+
+Learning the Dynamics of Sparsely Observed Interacting Systems
+2.5
+5.0
+7.5
+10.0
+12.5
+15.0
+17.5
+20.0
+Number of sampling points of Y
+0.00
+0.25
+0.50
+0.75
+1.00
+1.25
+1.50
+1.75
+2.00
+L2 recontruction error on test set
+SigLasso
+GRU
+Neural CDE
+Figure 2: L2 reconstruction error of SigLasso, GRU and Neural CDE in the well-specified setting, for varying number of
+target samples.
+2021-04-07
+2021-04-19
+2021-05-01
+2021-05-13
+2021-05-25
+2021-06-06
+2021-06-18
+2021-06-30
+Days
+−0.10
+−0.08
+−0.06
+−0.04
+−0.02
+0.00
+0.02
+0.04
+Growth rate
+Ground truth
+Figure 3: Interpolation (left of dotted line) and prediction (right of dotted line) of HGR in region ˆIle de France for SigLasso.
+The lighter the blue, the smaller the horizon h.
+models in generalizing from a few learning points of the target to its full trajectory in all settings. An additional byproduct
+of SigLasso’s simple form is its training speed: its is approximately 10 times faster than GRU and 100 times faster than
+Neural CDE, including cross-validation to select N and regularization strength (see Appendix C.8).
+4.2. Forecasting the growth rate of hospitalizations in France during the Covid-19 pandemic
+Forecasting hospitalizations in real time during the Covid-19 pandemic is a notably difficult task. In this experiment,
+we train our model to learn the dynamics linking population data related to mobility, vaccination, and weather, and the
+hospitalization growth rate (HGR) in each of the 9 metropolitan regions of France based on the data of Paireau et al. (2022).
+The feature time series is specific to each region and 12-dimensional. We consider prediction horizons h = 1, . . . , 14,
+meaning that we predict the hospital saturation at time t using the history of the feature time series up to t − h. Using our
+notations, we have for each region d = 12, p = 1, n = 1. The target is sampled every day during the training period left of
+the dotted line in Figure 3. The model is then asked to predict the HGR on the days right of the dotted line.
+Both GRU and SigLasso learn smooth and precise dynamics, which generalize well above the learning horizon and yield
+similar prediction performance (see Appendix C.7). Neural CDE and the original method proposed by Paireau et al. (2022)
+perform poorly. Figure 3 shows an example of reconstruction and prediction of HGR obtained with SigLasso.
+5. Conclusion
+We have introduced a novel CDE-based model for interacting systems. Drawing on the theory of signatures, we derive
+an oracle bound that depends explicitly on the roughness of the data sampling. We illustrate the high performance of our
+approach on synthetic and real-world data.
+The obtained theoretical guarantees rely on strong regularity assumptions on the vector field F. The exact approximation
+properties of this class of vector field are a very interesting direction for future work. Considering other penalties that take
+into account the underlying structure of θ∗
+N would also be an interesting extension of our work.
+
+Learning the Dynamics of Sparsely Observed Interacting Systems
+References
+Bickel, P. J., Ritov, Y., and Tsybakov, A. B. Simultaneous analysis of lasso and dantzig selector. The Annals of Statistics,
+37(4):1705–1732, 2009.
+Borodin, A. N. and Salminen, P. Handbook of Brownian Motion-Facts and Formulae. Birkh¨auser, Basel, 2012.
+Brunton, S. L., Noack, B. R., and Koumoutsakos, P.
+Machine learning for fluid mechanics.
+Annual review of fluid
+mechanics, 52:477–508, 2020.
+Buehler, H., Horvath, B., Lyons, T., Arribas, I. P., and Wood, B. A data-driven market simulator for small data environ-
+ments. arXiv preprint arXiv:2006.14498, 2020.
+Chen, K.-T. Integration of paths—a faithful representation of paths by non-commutative formal power series. Transactions
+of the American Mathematical Society, 89:395–407, 1958.
+Chen, R. T. Q., Rubanova, Y., Bettencourt, J., and Duvenaud, D. K. Neural ordinary differential equations. In Bengio,
+S., Wallach, H., Larochelle, H., Grauman, K., Cesa-Bianchi, N., and Garnett, R. (eds.), Advances in Neural Information
+Processing Systems, volume 31, pp. 6572–6583. Curran Associates, Inc., 2018.
+Chesneau, C. and Hebiri, M. Some theoretical results on the grouped variables lasso. Mathematical Methods of Statistics,
+17(4):317–326, 2008.
+De Brouwer, E., Simm, J., Arany, A., and Moreau, Y. GRU-ODE-Bayes: Continuous modeling of sporadically-observed
+time series. In Wallach, H., Larochelle, H., Beygelzimer, A., d'Alch´e-Buc, F., Fox, E., and Garnett, R. (eds.), Advances
+in Neural Information Processing Systems, volume 32, pp. 7379–7390. Curran Associates, Inc., 2019.
+Fattahi, S., Matni, N., and Sojoudi, S. Learning sparse dynamical systems from a single sample trajectory. In 2019 IEEE
+58th Conference on Decision and Control (CDC), pp. 2682–2689. IEEE, 2019.
+Fermanian, A. Embedding and learning with signatures. Computational Statistics & Data Analysis, 157:107148, 2021.
+Fermanian, A. Functional linear regression with truncated signatures. Journal of Multivariate Analysis, 192:105031, 2022.
+Fermanian, A., Marion, P., Vert, J.-P., and Biau, G. Framing RNN as a kernel method: A neural ODE approach. In
+Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P., and Vaughan, J. W. (eds.), Advances in Neural Information
+Processing Systems, volume 34, pp. 3121–3134. Curran Associates, Inc., 2021.
+Friz, P. and Victoir, N. Euler estimates for rough differential equations. Journal of Differential Equations, 244:388–412,
+2008.
+Friz, P. K. and Victoir, N. B. Multidimensional Stochastic Processes as Rough Paths: Theory and Applications, volume
+120 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge, 2010.
+Gehring, J., Auli, M., Grangier, D., Yarats, D., and Dauphin, Y. N. Convolutional sequence to sequence learning. In
+Precup, D. and Teh, Y. W. (eds.), Proceedings of the 34th International Conference on Machine Learning, volume 70,
+pp. 1243–1252. PMLR, 2017.
+Greydanus, S., Dzamba, M., and Yosinski, J. Hamiltonian neural networks. In Wallach, H., Larochelle, H., Beygelzimer,
+A., d'Alch´e-Buc, F., Fox, E., and Garnett, R. (eds.), Advances in Neural Information Processing Systems, volume 32.
+Curran Associates, Inc., 2019.
+Han, J., Jentzen, A., and E, W. Solving high-dimensional partial differential equations using deep learning. Proceedings
+of the National Academy of Sciences, 115(34):8505–8510, 2018.
+Hochreiter, S. and Schmidhuber, J. Long short-term memory. Neural Computation, 9:1735–1780, 1997.
+Kidger, P. On neural differential equations. arXiv preprint arXiv:2202.02435, 2022.
+Kidger, P. and Lyons, T. Signatory: differentiable computations of the signature and logsignature transforms, on both cpu
+and gpu. In International Conference on Learning Representations, 2020.
+
+Learning the Dynamics of Sparsely Observed Interacting Systems
+Kidger, P., Bonnier, P., Perez Arribas, I., Salvi, C., and Lyons, T. Deep signature transforms. In Wallach, H., Larochelle, H.,
+Beygelzimer, A., d'Alch´e-Buc, F., Fox, E., and Garnett, R. (eds.), Advances in Neural Information Processing Systems,
+volume 32, pp. 3099–3109. Curran Associates, Inc., 2019.
+Kidger, P., Morrill, J., Foster, J., and Lyons, T. Neural controlled differential equations for irregular time series. In
+Larochelle, H., Ranzato, M., Hadsell, R., Balcan, M. F., and Lin, H. (eds.), Advances in Neural Information Processing
+Systems, volume 33, pp. 6696–6707. Curran Associates, Inc., 2020.
+Lagaris, I. E., Likas, A., and Fotiadis, D. I. Artificial neural networks for solving ordinary and partial differential equations.
+IEEE transactions on neural networks, 9(5):987–1000, 1998.
+Lederer, J., Yu, L., and Gaynanova, I. Oracle inequalities for high-dimensional prediction. Bernoulli, 25(2):1225–1255,
+2019.
+Lemercier, M., Salvi, C., Damoulas, T., Bonilla, E., and Lyons, T. Distribution regression for sequential data. In Banerjee,
+A. and Fukumizu, K. (eds.), Proceedings of The 24th International Conference on Artificial Intelligence and Statistics,
+volume 130, pp. 3754–3762. PMLR, 2021.
+Levin, D., Lyons, T., and Ni, H. Learning from the past, predicting the statistics for the future, learning an evolving system.
+arXiv preprint arXiv:1309.0260, 2013.
+Loh, P.-l. and Wainwright, M. J. High-dimensional regression with noisy and missing data: Provable guarantees with
+non-convexity. In Shawe-Taylor, J., Zemel, R., Bartlett, P., Pereira, F., and Weinberger, K. (eds.), Advances in Neural
+Information Processing Systems, volume 24. Curran Associates, Inc., 2011.
+Long, Z., Lu, Y., Ma, X., and Dong, B. PDE-net: Learning PDEs from data. In Dy, J. and Krause, A. (eds.), Proceedings
+of the 35th International Conference on Machine Learning, volume 80, pp. 3208–3216. PMLR, 2018.
+Lyons, T. and McLeod, A. D. Signature methods in machine learning. arXiv preprint arXiv:2206.14674, 2022.
+Lyons, T., Caruana, M., and L´evy, T. Differential Equations driven by Rough Paths, volume 1908 of Lecture Notes in
+Mathematics. Springer, Berlin, 2007.
+Lyons, T., Ni, H., and Oberhauser, H. A feature set for streams and an application to high-frequency financial tick data. In
+Proceedings of the 2014 International Conference on Big Data Science and Computing, pp. 5. ACM, 2014.
+Marion, P., Fermanian, A., Biau, G., and Vert, J.-P.
+Scaling resnets in the large-depth regime.
+arXiv preprint
+arXiv:2206.06929, 2022.
+Marx, B. D. and Eilers, P. H. Generalized linear regression on sampled signals and curves: a P-spline approach. Techno-
+metrics, 41:1–13, 1999.
+Morrill, J., Fermanian, A., Kidger, P., and Lyons, T. A generalised signature method for multivariate time series feature
+extraction. arXiv preprint arXiv:2006.00873, 2020a.
+Morrill, J., Kidger, P., Yang, L., and Lyons, T. Neural controlled differential equations for online prediction tasks. arXiv
+preprint arXiv:2106.11028, 2021a.
+Morrill, J., Salvi, C., Kidger, P., and Foster, J. Neural rough differential equations for long time series. In Meila, M. and
+Zhang, T. (eds.), Proceedings of the 38th International Conference on Machine Learning, volume 139, pp. 7829–7838.
+PMLR, 2021b.
+Morrill, J. H., Kormilitzin, A., Nevado-Holgado, A. J., Swaminathan, S., Howison, S. D., and Lyons, T. J. Utilization
+of the signature method to identify the early onset of sepsis from multivariate physiological time series in critical care
+monitoring. Critical Care Medicine, 48:e976–e981, 2020b.
+Morris, J. S. Functional regression. Annual Review of Statistics and Its Application, 2:321–359, 2015.
+Paireau, J., Andronico, A., Hoz´e, N., Layan, M., Crepey, P., Roumagnac, A., Lavielle, M., Bo¨elle, P.-Y., and Cauchemez,
+S. An ensemble model based on early predictors to forecast covid-19 health care demand in france. Proceedings of the
+National Academy of Sciences, 119(18):e2103302119, 2022.
+
+Learning the Dynamics of Sparsely Observed Interacting Systems
+Papavasiliou, A. and Ladroue, C. Parameter estimation for rough differential equations. The Annals of Statistics, 39(4):
+2047–2073, 2011.
+Pedregosa, F., Varoquaux, G., Gramfort, A., Michel, V., Thirion, B., Grisel, O., Blondel, M., Prettenhofer, P., Weiss, R.,
+Dubourg, V., Vanderplas, J., Passos, A., Cournapeau, D., Brucher, M., Perrot, M., and Duchesnay, E. Scikit-learn:
+Machine learning in Python. Journal of Machine Learning Research, 12:2825–2830, 2011.
+Ramsay, J. O. and Dalzell, C. Some tools for functional data analysis. Journal of the Royal Statistical Society. Series B
+(Methodological), 53:539–561, 1991.
+Ramsay, J. O. and Silverman, B. W. Functional Data Analysis. 2nd Edition. Springer, New York, 2005.
+Reizenstein, J. F. and Graham, B.
+Algorithm 1004: The iisignature library: Efficient calculation of iterated-integral
+signatures and log signatures. ACM Transactions on Mathematical Software, 46(1):1–21, 2020.
+Rubanova, Y., Chen, R. T. Q., and Duvenaud, D. K. Latent ordinary differential equations for irregularly-sampled time
+series. In Wallach, H., Larochelle, H., Beygelzimer, A., d'Alch´e-Buc, F., Fox, E., and Garnett, R. (eds.), Advances in
+Neural Information Processing Systems, volume 32, pp. 5320–5330. Curran Associates, Inc., 2019.
+Simeoni, M., Magni, P., Cammia, C., De Nicolao, G., Croci, V., Pesenti, E., Germani, M., Poggesi, I., and Rocchetti, M.
+Predictive pharmacokinetic-pharmacodynamic modeling of tumor growth kinetics in xenograft models after administra-
+tion of anticancer agents. Cancer research, 64(3):1094–1101, 2004.
+Sutskever, I., Vinyals, O., and Le, Q. V.
+Sequence to sequence learning with neural networks.
+In Ghahramani, Z.,
+Welling, M., Cortes, C., Lawrence, N., and Weinberger, K. (eds.), Advances in Neural Information Processing Systems,
+volume 27. Curran Associates, Inc., 2014.
+Vershynin, R. Introduction to the non-asymptotic analysis of random matrices. arXiv preprint arXiv:1011.3027, 2010.
+Vershynin, R. High-dimensional probability: An introduction with applications in data science, volume 47. Cambridge
+university press, 2018.
+Wang, B., Wu, Y., Taylor, N., Lyons, T., Liakata, M., Nevado-Holgado, A. J., and Saunders, K. E. Learning to detect
+bipolar disorder and borderline personality disorder with language and speech in non-clinical interviews. Interspeech
+2020, pp. 437–441, 2020.
+Willard, J., Jia, X., Xu, S., Steinbach, M., and Kumar, V. Integrating physics-based modeling with machine learning: A
+survey. arXiv preprint arXiv:2003.04919, 2020.
+Yang, W., Lyons, T., Ni, H., Schmid, C., and Jin, L. Developing the path signature methodology and its application to
+landmark-based human action recognition. In Yin, G. and Zariphopoulou, T. (eds.), Stochastic Analysis, Filtering, and
+Stochastic Optimization: A Commemorative Volume to Honor Mark H.A. Davis’s Contributions, pp. 431–464. Springer,
+2022.
+Zubov, K., McCarthy, Z., Ma, Y., Calisto, F., Pagliarino, V., Azeglio, S., Bottero, L., Luj´an, E., Sulzer, V., Bharambe, A.,
+et al. NeuralPDE: Automating physics-informed neural networks (PINNs) with error approximations. arXiv preprint
+arXiv:2107.09443, 2021.
+Zwillinger, D. Handbook of differential equations. Academic Press, Inc., London, 1989.
+
+Learning the Dynamics of Sparsely Observed Interacting Systems
+Supplementary Material
+A. Mathematical details
+A.1. The Riemann-Stieltjes integral
+We fitst recall two key properties on the Riemann-Stieljes integral. For a general presentation of the Riemann-Stieltjes
+integral, we refer to Friz & Victoir (2010).
+Proposition A.1. Let x ∈ C1-var
+L
+([0, 1], Rd) and y : [0, 1] → Rd be a continuous path. Then
+����
+� t
+0
+ysdxs
+���� ≤ ∥y∥∞,[0,t] ∥x∥1-var,[0,t]
+We refer the reader to Friz & Victoir (2010, Proposition 2.2) for a proof.
+Proposition A.2 (Integration by parts). Let x, y ∈ C1-var
+L
+([0, 1], Rd). Then
+� t
+s
+yudxu +
+� t
+s
+xudyu = ytxt − ysxs
+See Friz & Victoir (2010, Proposition 2.4) for a proof.
+A.2. The truncated tensor algebra
+This section introduces notations and definitions on the space in which signatures are defined, namely, the tensor algebra.
+While for the exposition of our main results, the truncated signature of a path x ∈ C1-var
+L
+([0, 1], Rd) at depth N ≥ 1 can
+be assimilated to an element of Rsd(N), it is often useful to place ourselves in the tensor algebra to obtain finer bounds or
+technical results.
+Let x ∈ C1-var
+L
+([0, 1], Rd) be a path of bounded variation. For a word I = (i1, . . . , ik) ∈ {1, . . . , d}k of size k, the
+signature coefficient SI(x[0,1]) can be seen as an element of the k-th tensor product of Rd with itself, denoted by
+�
+Rd�⊗k.
+For instance, the coefficients of order k = 1 can be written as a vector and the coefficients of order k = 2 as a matrix, and
+so on, i.e.,
+X1
+[0,1] =
+�
+���
+� 1
+0 dx(1)
+s
+...
+� 1
+0 dx(d)
+s
+�
+���
+and
+X2
+[0,1] =
+�
+���
+� 1
+0 dx(1)
+s dx(1)
+s
+. . .
+� 1
+0 dx(1)
+s dx(d)
+s
+...
+...
+� 1
+0 dx(d)
+s dx(1)
+s
+. . .
+� 1
+0 dx(d)
+s dx(d)
+s
+�
+��� .
+We now define a norm on (Rd)⊗k. Let a ∈ (Rd)⊗k and (e1, . . . , ed) be the canonical basis of Rd. Then (ei1 ⊗ · · · ⊗
+eik)(i1,...,ik)∈{1,...,d}k is a basis of (Rd)⊗k. We can thus write a as a = (aI)I∈{1,...,d}k. For every k ≥ 0, the vector space
+(Rd)⊗k is naturally endowed with the norm
+∥a∥2
+(Rd)⊗k =
+�
+I∈{1,...,d}k
+�
+aI�2.
+Remark that this norm satisfies for any x ∈ (Rd)⊗k and y ∈ (Rd)⊗m,
+∥x ⊗ y∥(Rd)⊗(k+m) = ∥x∥(Rd)⊗k ∥y∥(Rd)⊗m .
+(13)
+We refer to Fermanian et al. (2021) for further deails. The signature truncated at depth N ≥ 1 collects elements from
+R,
+�
+Rd�⊗2, . . . ,
+�
+Rd�⊗N. It can thus be seen as an element of the truncated tensor algebra
+TN(Rd) = R ⊕
+�
+Rd�⊗2 ⊕ · · · ⊕
+�
+Rd�⊗N.
+
+Learning the Dynamics of Sparsely Observed Interacting Systems
+Let a = (a0, . . . , aN) ∈ TN(Rd), where every ak ∈ (Rd)⊗k. We define the norm
+∥a∥TN(Rd) =
+� N
+�
+k=0
+∥ak∥2
+(Rd)⊗k
+�1/2
+.
+To clarify, if we consider the truncated signature of x at depth N ≥ 1, which is an element of TN(Rd), then
+��SN(x[0,t])
+��
+TN(Rd) =
+� N
+�
+k=0
+���Xk
+[0,t]
+���
+2
+(Rd)⊗k
+�1/2
+=
+� N
+�
+k=0
+�
+I∈{1,...,d}k
+SI(x[0,t])2�1/2
+.
+Note that this norm is exactly equivalent to the Euclidian norm of Rsd(N), which is the space we consider in the exposition
+of our main results for the sake of simplicity.
+We are now ready to define the tensor product on the truncated tensor algebra. For two elements a = (a0, . . . , aN) and
+b = (b0, . . . , bN) both in TN(Rd), we define
+a ⊗ b = (c0, . . . , cj, . . . , cN),
+where cj =
+j
+�
+k=0
+ak ⊗ bj−k.
+For any k = 0, . . . , N, we let πk : TN(Rd) → (Rd)⊗k be the canonical projection of TN(Rd) onto (Rd)⊗k. More
+precisely, for every a = (a0, . . . , aN) ∈ TN(Rd),
+πk(a) = ak
+We also define the canonical projection Πk : TN(Rd) → Tk(Rd) defined by
+Πk(a) = (a0, . . . , ak) .
+A.3. The differential product
+We first define the differential product, in order to give a precise statement of Assumption 3.
+Definition A.3. Let F, G : Rp → Rp be two smooth vector fields, i.e., each of their components is C∞. Denote by J(·)
+the Jacobian matrix. The differential product F ⋆ G : Rp → Rp is the smooth vector field defined for any h ∈ Rp
+(F ⋆ G)(h) =
+e
+�
+j=1
+∂G
+∂hj
+(h)Fj(h) = J(G)(h)F(h).
+The differential product is not associative. We therefore use the convention to evaluate it from right to left, that is,
+F 1 ⋆ F 2 ⋆ F 3 = F 1 ⋆
+�
+F 2 ⋆ F 3�
+.
+Let F : Rp → Rp×d be a smooth vector field. We write F 1, . . . , F d the columns of F. Every F i, for i = 1, . . . , d, can
+thus be seen as a map from Rp to Rp. Recall that y0 ∈ Rp is the initial condition of the CDE defined in Assumption 2. Let
+I = (i1, . . . , ik) ∈ {1, . . . , d}k. We now define
+ΦI
+F(y0) =
+�
+F i1 ⋆ · · · ⋆ F ik�
+(y0) ∈ Rp.
+We refer to Fermanian et al. (2021) for greater details on the differential product. We now define for all k ≥ 1
+Λk(F) =
+sup
+1≤i1,...,ik≤d
+��ΦI
+F(y0)
+�� ∈ R,
+(14)
+and use the convention Λ0(F) = ∥y0∥. Remark that Assumption 3 implies that
+dN+1ΛN+1(F)
+(N + 1)!
+−→
+N→+∞ 0.
+
+Learning the Dynamics of Sparsely Observed Interacting Systems
+As an immediate consequence, the truncation bias
+�
+dN+1ΛN+1(F)
+(N + 1)!
+�2
+introduced in Lemma 3.2, vanishes as N grows.
+A.4. Analogy with the Taylor extension
+The definition of the Taylor expansion of a CDE exposed in the previous subsection is technical. However, it can simply
+be thought of as a generalization of the the classical Taylor expansion of a C∞ function f : R → R. Recall that in this
+case, the Taylor expansion at 0 evaluated at t ∈ R of order N ∈ N writes as a power series
+f(t) ≈ f(0) + f ′(0)
+1!
+t + · · · + f (N)(0)
+N!
+tN.
+(15)
+Every element of this power series is a product of two terms: the derivatives of f encode some information about the
+regularity of f at the initial point 0 and do not depend on t, while the polynomial terms tk allow this linearized form to
+evolve with time t. Remark that these polynomial terms do not depend on f.
+Similarly, Equation (3) is also a sum of products of two terms. On the one hand, the evolving nature of the system,
+instead of being handled by the polynomial terms tk, are now captured by the signature coefficients SI(x[0,t]). As the
+polynomial terms, they do not depend on F. On the other hand, the information about the initial value of the system at
+time t = 0 and the dynamics of F are summarized by the differential product ΦI
+F (y0), which play the same role as the
+successive derivatives in Equation (15). To capture the multivariate nature of the paths, the Taylor expansion is summed
+over multi-indexes, or words, I = (i1, . . . , ik) ∈ {1, . . . , d}k of size k for k ∈ N.
+A.5. Properties of subgaussian random vectors
+We start with the definition of a subgaussian random variable, see Vershynin (2010) for more details.
+Definition A.4. A real-valued random variable X is said to be σ2-subgaussian if for all t > 0
+P(X > t) ≤ exp(−t2/σ2),
+or, equivalently, if for all t ∈ R
+E(etX) ≤ exp(−ct2σ2),
+where c is an universal constant. A random vector Z is subgaussian if, for any vector c of norm 1, ⟨Z, c⟩ is subgaussian.
+The norm of a sequence of d subgaussian random variables concentrates around
+√
+d, as stated by the following lemma.
+Lemma A.5. Let X1, . . . , Xn be a sequence of i.i.d. σ2-subgaussian random variables. Let X = (X1, . . . , Xd) ∈ Rd.
+There exists a universal constant C such that for all t > 0
+P(∥X∥2 ≥ t + σ
+√
+d) ≤ exp(−Ct2/σ2).
+Proof. We refer to Vershynin (2018, Theorem 3.1.1) for a proof.
+We can use this lemma to bound the maximum of n sequences of d subgaussian random variables with high probability.
+Lemma A.6. Let X1, . . . , Xn be a sequence of i.i.d. σ2-subgaussian random variables, such that for all i = 1, . . . , n,
+Xi = (Xi1, . . . , Xid). Then there exists a universal constant such that for all δ ∈ (0, 1)
+P
+�
+max
+i=1,...,n ∥Xi∥ ≤ σ
+√
+d + σ
+�
+1
+C log(n/δ)
+�
+≥ 1 − δ.
+
+Learning the Dynamics of Sparsely Observed Interacting Systems
+Proof. Using Lemma A.5 and a union bound, we have
+P
+�
+max
+i=1,...,n ∥Xi∥ ≥ σ
+√
+d + σ
+�
+1
+C log(n/δ)
+�
+= P
+�
+n
+�
+i=1
+�
+∥Xi∥2 ≥ σ
+√
+d + σ
+�
+1
+C log(n/δ)
+��
+≤
+n
+�
+i=1
+P
+�
+∥Xi∥2 ≥ σ
+√
+d + σ
+�
+1
+C log(n/δ)
+�
+≤ δ,
+which yields the desired inequality.
+Notice that the universal constant is identical between both lemmas. As a consequence of this last lemma, under Assump-
+tion 5, the set
+Aξ(δ) =
+�
+max
+i=1,...,n,t∈Di
+��ξi
+t
+�� ≤ vξ
+√
+d + vξ
+�
+1
+C log(#D/δ)
+�
+(16)
+where #D =
+n�
+i=1
+#Di is of probability at least 1 − δ.
+We also need the following lemma.
+Lemma A.7. Let X1, . . . , Xn be a sequence of i.i.d. σ2-subgaussian random variables. Let Z1, . . . , Zn be random vari-
+ables such that for all i = 1, . . . , n, |Zi| ≤ α almost surely. Then
+n�
+i=1
+XiZi is nσ2α2-subgaussian.
+Proof. We use the characterization of subgaussian random variables by their characteristic function. For all t > 0,
+E
+�
+et �n
+i=1 XiZi
+�
+= E
+�
+n
+�
+i=1
+E
+�
+etXiZi | Z1, . . . , Zn
+��
+≤ E
+�
+n
+�
+i=1
+E
+�
+etXi�
+≤ E
+�
+ect2nα2σ2�
+.
+This finally yields that
+E
+�
+et � XiZi
+�
+≤ E
+�
+ect2nα2σ2�
+,
+which concludes the proof.
+B. Proofs
+B.1. Preliminary notations
+Let (E, ∥·∥E) be a normed vector space and x : [0, 1] → E. The supremum norm of x is defined for all t ∈ [0, 1] as
+∥x∥∞,[0,t] = sup
+s∈[0,t]
+∥xs∥E .
+When referring to the total variation ∥x∥1-var,[0,1] of a path x : [0, 1] → Rd over the whole domain, depending on the
+mathematical context, we will sometimes drop the time subscript and simply write ∥x∥1-var.
+When referring to a matrix A = (Aij) ∈ Rn×p, we define classicaly the infinite and Frobenius norms by
+∥A∥∞ =
+max
+i=1,...,n
+j=1,...,p
+|Aij|
+and
+∥A∥F =
+�
+�
+�
+�
+�
+i=1,...,n
+j=1,...,p
+|Aij|2.
+We now introduce some notations to take advantage of the structure of θ∗
+N. The true parameter of the Taylor expansion of
+the model CDE, defined in Equation (4), can be written in block notation as
+
+Learning the Dynamics of Sparsely Observed Interacting Systems
+θ∗
+N =
+�
+�������������������������������������
+θ∗
+[0],1
+· · ·
+θ∗
+[0],p
+θ∗
+[1],1
+· · ·
+θ∗
+[1],p
+θ∗
+[2],1
+· · ·
+θ∗
+[2],p
+...
+θ∗
+[N],1
+· · ·
+θ∗
+[N],p
+�
+�������������������������������������
+∈ Rsd(N)×p,
+where
+θ∗
+[k],ℓ ∈ Rdk×1, k = 0, . . . , N, ℓ = 1, . . . , p.
+(17)
+Every column of θ∗
+N corresponds to a dimension of the target, while blocks of lines correspond to signatures layers. Thus
+for every k = 0, . . . , N and ℓ = 1, . . . , p, θ∗
+[k],ℓ is a column vector of size dk.
+Similarly, for a general θ ∈ Rsd(N)×p and the SigLasso estimator �θN,M, we will refere to the blocks forming these matrices
+as respectively θ[k],ℓ and �θ[k],ℓ, for k = 0, . . . , N and ℓ = 1, . . . p.
+Likewise, the signature feature matrix SD
+N ∈ RM×sd(N) can be written in block notation as
+SD
+N =
+�
+1
+SD
+·,[1]
+SD
+·,[2]
+· · ·
+SD
+·,[N]
+�
+=
+�
+��
+1
+SD
+1,[1]
+SD
+1,[2]
+SD
+1,[N]
+...
+...
+...
+· · ·
+...
+1
+SD
+n,[1]
+SD
+n,[2]
+SD
+n,[N]
+�
+�� ,
+where for any k = 1, . . . , N, SD
+·,[k] ∈ RM×dk and, for every individual i = 1, . . . , n, SD
+i,[k] ∈ Rmi×dk (recall that mi is
+the number of measurements of the target path yi). More precisely, given her target sampling grid ¯Di = (¯ti
+1, . . . , ¯ti
+mi), the
+individual-specific signature block of depth k is equal to
+SD
+i,[k] =
+�
+���
+1
+S(1)(Xi
+[0,¯ti
+1])
+· · ·
+S(d,...,d)(Xi
+[0,¯ti
+1])
+...
+...
+...
+1
+S(1)(Xi
+[0,¯timi])
+· · ·
+S(d,...,d)(Xi
+[0,¯ti
+mi])
+�
+��� ,
+where the path t → Xi
+t is a linear interpolation of the observed time series Xi. The same notations will be used for the
+true signature feature matrix SN. We use the bracket notation [·] both in θ∗
+N and SD
+N to emphasise that both the columns of
+the feature matrix and the lines of learned parameter correspond to words of the alphabet {1, . . . , d}.
+The unobserved matrix of true values of the target writes as
+
+Learning the Dynamics of Sparsely Observed Interacting Systems
+y =
+�
+��
+y1
+...
+yn
+�
+�� =
+�
+��
+y1
+1
+· · ·
+y1
+p
+...
+...
+yn
+1
+· · ·
+yn
+p
+�
+�� =
+�
+��������������
+y1
+1,¯t1
+1
+· · ·
+y1
+p,¯t1
+1
+...
+...
+y1
+1,¯t1m1
+· · ·
+y1
+p,¯t1m1
+...
+...
+yn
+1,¯tn
+1
+· · ·
+yn
+p,¯tn
+1
+...
+...
+yn
+1,¯tn
+mn
+· · ·
+yn
+p,¯tn
+mn
+�
+��������������
+∈ RM×p
+(18)
+and the measurement matrix Y ∈ RM×p can be written in a similar fashion as
+Y =
+�
+��
+Y1
+...
+Yn
+�
+�� =
+�
+��
+Y1
+1
+· · ·
+Y1
+p
+...
+...
+Yn
+1
+· · ·
+Yn
+p
+�
+�� =
+�
+��������������
+Y 1
+1,¯t1
+1
+· · ·
+Y 1
+p,¯t1
+1
+...
+...
+Y 1
+1,¯t1m1
+· · ·
+Y 1
+p,¯t1m1
+...
+...
+Y n
+1,¯tn
+1
+· · ·
+Y n
+p,¯tn
+1
+...
+...
+Y n
+1,¯tn
+mn
+· · ·
+Y n
+p,¯tn
+mn
+�
+��������������
+=
+�
+��������������
+y1
+1,¯t1
+1 + ε1
+1,¯t1
+1
+· · ·
+y1
+p,¯t1
+1 + ε1
+p,¯t1
+1
+...
+...
+y1
+1,¯t1m1 + ε1
+1,¯t1m1
+· · ·
+y1
+p,¯t1m1 + ε1
+p,¯t1m1
+...
+...
+yn
+1,¯tn
+1 + εn
+1,¯tn
+1
+· · ·
+yn
+p,¯tn
+1 + εn
+p,¯tn
+1
+...
+...
+yn
+1,¯tn
+mn + εn
+1,¯tn
+mn
+· · ·
+yn
+p,¯tn
+mn + εn
+p,¯tn
+mn
+�
+��������������
+(19)
+B.2. Proof of Lemma 3.1
+Using the definition of Λk, we get the following proposition which allows to obtain an explicit dependence of the oracle
+bound on the regularity of F.
+Proposition B.1. Let θ∗
+N be defined as in Equation (4). Then
+∥θ∗
+N∥2
+F ≤
+N
+�
+k=0
+dkΛk(F)2,
+and, for all k = 0, . . . , N and ℓ = 1, . . . , p,
+��θ∗
+[k],ℓ
+��
+1 ≤ dkΛk(F).
+Proof. By definition,
+∥θ∗
+N∥2
+F =
+N
+�
+k=0
+�
+1≤i1,...,ik≤d
+��F i1 ⋆ · · · ⋆ F ik(y0)
+��2
+2 .
+Since for all (i1, . . . , ik) ∈ {1, . . . , d}k,
+��F i1 ⋆ · · · ⋆ F ik(y0)
+��2
+2 ≤ Λk(F)2,
+we get
+N
+�
+k=0
+�
+1≤i1,...,ik≤d
+��F i1 ⋆ · · · ⋆ F ik(y0)
+��2
+2 ≤
+N
+�
+k=0
+�
+1≤i1,...,ik≤d
+Λk(F)2
+≤
+N
+�
+k=0
+dkΛk(F)2.
+
+Learning the Dynamics of Sparsely Observed Interacting Systems
+We now turn to the second inequality. For k = 0, the inequality holds by definition. For k = 1, . . . , N and ℓ = 1, . . . , p,
+by definition of the ℓ1 norm,
+���θ∗
+[k],·
+���
+1 =
+�
+1≤i1,...,ik≤d
+��ΦI
+F(y0)
+��
+1 ,
+This yields
+���θ∗
+[k],·
+���
+1 ≤ dkΛk(F)
+and thus
+���θ∗
+[k],ℓ
+���
+1 ≤ dkΛk(F)
+for ℓ = 1, . . . , p.
+The following lemma is needed to leverage classical proof techniques to bound the prediction error of the Lasso estimator.
+Lemma B.2. Let x ∈ C1-var
+L
+([0, 1], Rd). Then conditionally on Aξ(δ), for a given signature layer k ≥ 1, the maximum
+among all signature coefficients and individuals is bounded from above, that is
+���SD
+·,[k]
+���
+∞ ≤ 1
+k!.
+Proof. It is well known (see, e.g., Fermanian, 2022, Proposition 3) that if Xk is the signature of a path x ∈ C1-var
+L
+([0, 1], Rd),
+then
+��Xk��
+(Rd)⊗k ≤ ∥x∥k
+1-var
+k!
+.
+As a consequence, for every word I of size k, one gets
+��SI(x))
+�� ≤ ∥x∥k
+1-var
+k!
+.
+The matrix SD
+N is constructed by taking signatures of linear interpolations of the Xis normalized by their total variation. It
+therefore contains only signatures of paths of total variation bounded by 1. Taking the maximum on I ∈ {1, . . . , d}k and
+individuals i = 1, . . . , n, we get
+���SD
+·,[k]
+���
+∞ ≤ 1
+k!.
+This final inequality being stated, we can now go back to the proof of Lemma 3.1. We prove it in full generality for p ≥ 1.
+In this proof, we make extensive use of the notations introduced in Subsection B.1 and refer the reader to it if a notation is
+unclear.
+Proof. In all the proof, we place ourselves on the set Aξ(δ) defined by Equation (8), which ensures that the matrix SD
+N,
+seen as a random quantity, is well defined. Recall that we have two sources of randomness: the feature noises ξi
+t on the
+Xis and the target noises εi
+t on the Yis. The feature noises appear only in SD
+N and make it a random quantity. For SD
+N to
+be well-defined, we then need the total variation of the linear interpolation of the feature time series Xi to be finite. This
+holds on the set Aξ(δ) since all noises are then bounded.
+Recall that we have defined �θN,M as
+�θN,M ∈
+arg min
+θ∈Rsd(N)×p
+1
+2M
+��Y − SD
+Nθ
+��2
+F + Ω(θ).
+Note that
+1
+2M
+��Y − SD
+Nθ
+��2
+F + Ω(θ) =
+p
+�
+ℓ=1
+1
+2M
+��Yℓ − SD
+Nθ[·],ℓ
+��2
+2 + Ω(θ[·],ℓ)
+
+Learning the Dynamics of Sparsely Observed Interacting Systems
+where Yℓ ∈ RM is the ℓ-th column of the target measurement matrix defined in Equation (19). The quantity θ[·],ℓ ∈ Rsd(N)
+is the ℓ-th column of the parameter matrix defined in Equation (17).
+By definition, for any θ ∈ Rsd(N), we have
+���Yℓ − SD
+N �θ[·],ℓ
+���
+2
+2 ≤
+��Yℓ − SD
+Nθ
+��2
+2 + Ω(θ) − Ω(�θ[·],ℓ).
+Moreover, letting εℓ = (ε1
+ℓ,¯t1
+1, . . . , εn
+ℓ,¯tn
+mn )⊤ ∈ RM be a vector of i.i.d. noises (see Equation (19)), we have Yℓ = yℓ + εℓ.
+The Pythagorean theorem then yields for any θ ∈ Rsd(N),
+��Yℓ − SD
+Nθ
+��2
+2 =
+��yℓ − SD
+Nθ
+��2
+2 + ∥εℓ∥2 + 2⟨εℓ, yℓ − SD
+Nθ⟩.
+Putting these two equations together, we obtain
+1
+2M
+���yℓ − SD
+N �θ[·],ℓ
+���
+2
+2 ≤
+1
+2M
+��yℓ − SD
+Nθ
+��2
+2 + 1
+M ⟨εℓ, SD
+N(�θ[·],ℓ − θ)⟩ + Ω(θ) − Ω(�θ[·],ℓ).
+(20)
+We now work at each layer of the signature matrix SD
+N. Towards that end, we rewrite
+SD
+N
+��θ[·],ℓ − θ
+�
+=
+N
+�
+k=0
+SD
+·,[k]
+��θ[k],ℓ − θ[k]
+�
+,
+and bound
+�
+εℓ, SD
+N(�θ[·],ℓ − θℓ)
+�
+=
+N
+�
+k=0
+�
+εℓ, SD
+·,[k](�θ[k],ℓ) − θ[k])
+�
+≤
+N
+�
+k=0
+∥ε⊤
+ℓ SD
+·,[k]∥∞∥�θ[k],ℓ − θ[k]∥1
+by ℓ1 − ℓ∞ norms duality. We fix k and study the term ∥ε⊤
+ℓ SD
+·,[k]∥∞. Lemma B.2 ensures that each of the words of the
+signature layer of depth k is bounded by 1/k!. As a consequence, by Lemma A.7, under Assumption 6, every element of
+the vector ε⊤
+ℓ SD
+·,[k] is vεM/k!2-subgaussian. It follows that, for any real number µ > 0,
+P
+�
+∥ε⊤
+ℓ SD
+·,[k]∥∞ > µ
+�
+≤ 2dk exp
+�
+− (k!)2µ2
+vεM
+�
+.
+We furthermore place ourselves on Aε(¯δ) defined by
+Aε(¯δ) =
+p�
+ℓ=1
+N
+�
+k=0
+�
+∥ε⊤
+ℓ SD
+·,[k]∥∞ ≤ 1
+k!
+�
+vεM log(2pNdk/¯δ)
+�
+.
+We have just seen that, under Assumption 6 (and still conditionally on Aξ(δ)), one has P(Aε(¯δ)) ≥ 1 − ¯δ. Putting together
+all terms in Equation (20) and plugging the definition of Ω given in Equation (9), we obtain that, on the set Aε(¯δ) ∩ Aξ(δ),
+for all θ ∈ Rsd(N)×p,
+1
+2M
+���y − SD
+N �θN,M
+���
+2
+F ≤
+1
+2M
+��y − SD
+Nθ
+��2
+F
++
+p
+�
+ℓ=1
+N
+�
+k=0
+� 1
+M ∥ε⊤
+ℓ SD
+·,[k]∥∞∥�θ[k],ℓ − θ[k],ℓ∥1 + Ck(¯δ)
+k!
+√
+M
+�
+∥θ[k],ℓ∥1 − ∥�θ[k],ℓ∥1
+��
+≤
+1
+2M
+��y − SD
+Nθ
+��2
+F
++
+p
+�
+ℓ=1
+N
+�
+k=0
+1
+k!
+√
+M
+�
+vε log(2pNdk/¯δ)
+�
+∥�θ[k],ℓ − θ[k],ℓ∥1 + ∥θ[k],ℓ∥1 − ∥�θ[k],ℓ∥1
+�
+.
+Choosing θ = θ∗
+N, by the triangular inequality,
+∥�θ[k],ℓ − θ∗
+[k],ℓ∥1 + ∥θ∗
+[k],ℓ∥1 − ∥�θ[k],ℓ∥1 ≤ 2∥θ∗
+[k],ℓ∥1,
+
+Learning the Dynamics of Sparsely Observed Interacting Systems
+which finally gives us
+1
+2M
+���y − SD
+N �θN,M
+���
+2
+F ≤
+1
+2M
+��y − SD
+Nθ∗
+N
+��2
+F +
+2
+√
+M
+�
+vε log(2pNdN/¯δ)
+p
+�
+ℓ=1
+N
+�
+k=0
+∥θ∗
+[k],ℓ∥1
+k!
+≤
+1
+2M
+��y − SD
+Nθ∗
+N
+��2
+F + 2p
+√
+M
+�
+vε log(2pNdN/¯δ)
+N
+�
+k=0
+dkΛk(F)
+k!
+=
+1
+2M
+��y − SD
+Nθ∗
+N
+��2
+F + 2pCN(¯δ)
+√
+M
+N
+�
+k=0
+dkΛk(F)
+k!
+,
+where the last inequality comes from Proposition B.1. To conclude the proof, we just need to compute the probability of
+the set Aξ(δ) ∩ Aε(¯δ). It is an immediate consequence of Lemma A.6 that P(Aξ(δ)) ≥ 1 − δ, and we have seen that
+P(Aε(¯δ)|Aξ(δ)) ≥ 1 − ¯δ, which yields that
+P(Aξ(δ) ∩ Aε(¯δ)) ≥ (1 − ¯δ)(1 − δ).
+B.3. Proof of Lemma 3.2
+This proof relies on bouding the remainder of the Taylor expansion of the CDE.
+Proof. For every i = 1, . . . , n and a given point ti ∈ ¯Di, one has, using the upper bound of the approximation error of a
+CDE by its Taylor expansion provided by Fermanian et al. (2021, Proposition 4)
+���yi
+ti − SN(xi
+[0,ti])θ∗
+N
+��� ≤ dN+1ΛN+1(F)
+(N + 1)!
+.
+This immediately gives
+1
+M ∥y − SNθ∗
+N∥2
+F = 1
+M
+n
+�
+i=1
+�
+ti∈ ¯
+Di
+���yi
+ti − SN(xi
+[0,ti])θ∗
+N
+���
+2
+≤ 1
+M
+M
+�
+i=1
+�dN+1ΛN+1(F)
+(N + 1)!
+�2
+=
+�dN+1ΛN+1(F)
+(N + 1)!
+�2
+,
+which concludes the proof.
+B.4. A layer-wise bound on the signature
+We now prove that signature layers are locally Lipschitz mappings. We start with the following proposition.
+Proposition B.3. Let x ∈ C1-var
+L
+([0, 1], Rd). Then for all t ∈ [0, 1], the path t �→ Xk
+[0,t] has 1-variation
+��Xk��
+1-var,[0,t] ≤ Lk
+k! .
+Proof. By definition of the total variation,
+��Xk��
+1-var,[0,t] = sup
+D
+m
+�
+i=1
+���Xk
+[0,ti+1] − Xk
+[0,ti]
+���
+(Rd)⊗k = sup
+D
+m
+�
+i=1
+���Xk
+[ti,ti+1]
+���
+(Rd)⊗k ,
+since Xk
+[0,t] =
+� t
+0 dxu1 ⊗ · · · ⊗ dxuk, and where the supremum is taken over finite dissections D = {0 = t1, . . . , tm = 1}
+of [0, 1]. Notice that the signature layer of depth k is here written as an element of (Rd)⊗k, which is more convenient for
+this proof. Then
+sup
+D
+m
+�
+i=1
+���Xk
+[ti,ti+1]
+���
+(Rd)⊗k ≤ sup
+D
+m
+�
+i=1
+∥x∥k
+1-var,[ti,ti+1]
+k!
+≤ 1
+k! sup
+D
+� m
+�
+i=1
+∥x∥1-var,[ti,ti+1]
+�k
+= 1
+k! sup
+D
+∥x∥k
+1-var,[0,1] ≤ Lk
+k! ,
+where the second inequality follows from the multinomial theorem and the last equality comes from the fact that for all
+s < u < t, ∥x∥1-var,[s,u] + ∥x∥1-var,[u,t] = ∥x∥1-var,[s,t]. This ends our proof.
+
+Learning the Dynamics of Sparsely Observed Interacting Systems
+We now state a bound on the difference between the k-th layer of the signatures of two different paths.
+Theorem B.4. Let x, z ∈ C1-var([0, 1], Rd). Then for all k ≥ 2, the difference in supremum norm between the paths
+t → Xk
+[0,t] and t → Zk
+[0,t] is bounded by
+��Xk − Zk��
+∞,[0,t] ≤ 2Lk−1
+k−1
+�
+j=1
+1
+j! ∥x − z∥∞,[0,t] ≤ 2eLk−1 ∥x − z∥∞,[0,t]
+and
+���X1
+[0,t] − Z1
+[0,t]
+��� ≤ 2 ∥x − z∥∞,[0,t] .
+Proof. Our proof works by induction. Let x, z ∈ C1-var
+L
+([0, 1], Rd), and for t ∈ [0, 1] denote by Xk
+[0,t] resp. Zk
+[0,t] the k-th
+layer of the signature of x resp. z. For k = 1 and t ∈ [0, 1], remark that
+X1
+[0,t] − Z1
+[0,t] =
+� t
+0
+d(xu − zu) = xt − zt − (x0 − z0)
+such that
+���X1
+[0,t] − Z1
+[0,t]
+��� ≤ ∥x − z∥∞,[0,t] + ∥x0 − z0∥ ≤ 2 ∥x − z∥∞,[0,t] .
+Consider now k ≥ 2. We have
+Xk
+[0,t] − Zk
+[0,t] =
+� t
+0
+Xk−1
+[0,s] ⊗ dxs −
+� t
+0
+Zk−1
+[0,s] ⊗ dzs =
+� t
+0
+Xk−1
+[0,s] ⊗ d(xs − zs + zs) −
+� t
+0
+Zk−1
+[0,s] ⊗ dzs,
+and thus
+Xk
+[0,t] − Zk
+[0,t] =
+� t
+0
+Xk−1
+[0,s] ⊗ d(xs − zs) +
+� t
+0
+�
+Xk−1
+[0,s] − Zk−1
+[0,s]
+�
+⊗ dzs.
+We now bound each of these terms separately. First,
+����
+� t
+0
+�
+Xk−1
+[0,s] − Zk−1
+[0,s]
+�
+⊗ dzs
+����
+(Rd)⊗k
+≤
+��Xk−1 − Zk−1��
+∞,[0,t] ∥z∥1-var,[0,t] ≤
+��Xk−1 − Zk−1��
+∞,[0,t] L.
+Moving to the first integral, integration by parts yields
+� t
+0
+Xk−1
+[0,s] ⊗ d(xs − zs) = Xk
+[0,t] ⊗ (xt − zt) − Xk
+[0,0] ⊗ (x0 − z0) −
+� t
+0
+(xs − zs) ⊗ dXk−1
+[0,s].
+We stress that Proposition (A.2) applies since the integral over the tensor product is taken coordinate-wise. Since Xk−1
+[0,0] = 0,
+we are left with
+� t
+0
+Xk−1
+[0,s] ⊗ d(xs − zs) = Xk
+[0,t] ⊗ (xt − zt) −
+� t
+0
+(xs − zs) ⊗ dXk−1
+[0,s].
+Using Lemma B.3 and submultiplicativity of the tensor norms, this can thus be bounded by
+����
+� t
+0
+Xk−1
+[0,s] ⊗ d(xs − zs)
+����
+(Rd)⊗k ≤
+���Xk−1
+[0,t]
+���
+(Rd)⊗(k−1) ∥x − z∥∞,[0,t] + ∥x − z∥∞,[0,t]
+��Xk−1��
+1-var,[0,t]
+= 2Lk−1
+(k − 1)! ∥x − z∥∞,[0,t] .
+Finally, we are left with
+��Xk − Zk��
+∞,[0,t] ≤ 2Lk−1
+(k − 1)! ∥x − z∥∞,[0,t] +
+��Xk−1 − Zk−1��
+∞,[0,t] L,
+which can be recursively bounded by
+��Xk − Zk��
+∞,[0,t] ≤ 2Lk−1 ∥x − z∥∞,[0,t]
+k−1
+�
+j=1
+1
+j! ≤ 2Lk−1e ∥x − z∥∞,[0,t] .
+
+Learning the Dynamics of Sparsely Observed Interacting Systems
+Note that this inequality implies that if z is chosen as the linear interpolation of a discretization of x on a grid D, and if the
+grid gets finer, all signature layers converge at speed ∥x − z∥∞,[0,t] but the multiplicative constant increases with depth (if
+L ≥ 1). Figure 4 illustrates this phenomenon.
+50
+100
+150
+200
+Number of sampling points of X
+100
+101
+102
+||SN(x)
+SN(X)||
+N=3
+N=4
+N=5
+N=6
+50
+100
+150
+200
+Number of sampling points of X
+101
+102
+||SN(x)
+SN(X)||
+N=3
+N=4
+N=5
+N=6
+50
+100
+150
+200
+Number of sampling points of X
+102
+||SN(x)
+SN(X)||
+N=3
+N=4
+N=5
+N=6
+Figure 4: Difference between the signature of a continuous path x and the signature of its discretized and noisy counterpart
+X, without noise on the discretization points (left), with noise of variance vξ = 0.082 (middle) and with noise of variance
+vξ = 0.52. For every number of sampling points, we average the distance between the two signature over 50 randomly
+chosen discretizations of the interval [0, 1]. The discretized path is generated as in the well-specified setting (see Appendix
+C.4).
+B.5. Proof of Lemma 3.3
+First, recall that for a generic path x : [0, 1] → Rd, a modulus of continuity is a continuous function ωx : R≥0 → R≥0
+vanishing at 0 such that for all t, s ∈ [0, 1]
+∥xt − xs∥ ≤ ωx(|t − s|).
+Also recall that by Heine’s theorem, we can define such a modulus of continuity for every continuous mapping [0, 1] to Rd.
+We start by giving a general lemma that bounds the difference between the signature layers of a path and its discretized
+version. Its proof is based on the results of the previous section.
+Lemma B.5. Let x ∈ C1-var
+L
+([0, 1], Rd) and ωx : R≥0 → R≥0 its modulus of continuity. Let xD : [0, 1] → Rd be the path
+obtained by linear interpolation of the discretization of x on a grid D corrupted by additive noise ξ. Let Xk
+[0,t] and Xk,D
+[0,t]
+be their respective k-th layers of signature. Then for all t ∈ [0, 1] and k ≥ 2
+��Xk − Xk,D��
+∞,[0,1] ≤ 2Lk−1
+k−1
+�
+j=1
+1
+j!
+�
+max
+0≤s≤|D| ωx(s) + max
+t∈D ∥ξt∥
+�
+,
+and for k = 1
+��X1 − X1,D��
+∞,[0,1] ≤ 2
+�
+max
+0≤s≤|D| ωx(s) + max
+t∈D ∥ξt∥
+�
+.
+Proof. Theorem B.4 yields for k ≥ 2
+��Xk − Xk,D��
+∞,[0,1] ≤ 2Lk−1
+k−1
+�
+j=1
+1
+j!
+��x − xD��
+∞,[0,t]
+Now, remark that
+��x − xD��
+∞,[0,1] ≤ ∥x − ˜x∥∞,[0,1] + max
+t∈D ∥ξt∥
+(21)
+
+Learning the Dynamics of Sparsely Observed Interacting Systems
+from the triangular inequality, where ˜x is the piecewise linear path obtained by linear interpolation of x0, xt1, . . . , xtj.
+Now, since the paths x and ˜x coincide on 0, t1, . . . , tj, we have
+∥x − ˜x∥∞,[0,1] =
+max
+i=0,...,j−1 ∥x − ˜x∥∞,[ti,ti+1] ≤
+max
+i=0,...,j−1 ωx
+�
+|ti+1 − ti|
+�
+=
+max
+0≤s≤|D| ωx(s).
+This gets us
+��Xk − Xk,D��
+∞,[0,1] ≤ 2Lk−1
+k−1
+�
+j=1
+1
+j!
+�
+max
+0≤s≤|D| ωx(s) + max
+t∈D ∥ξt∥
+�
+.
+For the case k = 1, we immediately get
+��X1 − X1,D��
+∞,[0,1] ≤ 2
+�
+max
+0≤s≤|D| ωx(s) + max
+t∈D ∥ξt∥
+�
+using the same technique as above.
+This result is illustrated in Figure 4. One can notice that as predicted by our theoretical bounds, the convergence of signature
+of high order happens at the same rate than the convergence of signatures of lower order. However, the multiplicative
+constant controlling the tightness of the bound increases with N, leading to a slower convergence when N increases.
+Strong noise hinders the convergence of the signature of the discretized path since in this case, the noise’s variance is
+independent of the number of sampling points : adding more sampling points means adding more noise. There thus
+are two trade-offs when learning with signatures. A first trade-off is between sampling frequency and order: with paths
+sampled at low resolution, one should prefer lower order signatures, which trade model complexity against precise features.
+A second trade-off is between sampling and noise: if the feature time series are very noisy, the precision of the features
+increases up to a certain point, past which noise prevails.
+With this result in hand, we can now prove Lemma 3.3.
+Proof. We restrict ourselves to the ω-Lipschitz case. In this case, ωx(s) = ωs, and Lemma B.5 becomes
+��Xk − Xk,D��
+∞,[0,1] ≤ 2Lk−1
+k−1
+�
+j=0
+1
+j!
+�
+ω|D| + max
+t∈D ∥ξt∥
+�
+≤ 2eLk−1�
+ω|D| + max
+t∈D ∥ξt∥
+�
+This results holds for a single path on the time interval [0, t]. Now moving to the feature matrices, we have
+1
+M
+��(SN − SD
+N)θ∗
+N
+��2
+F ≤ 1
+M
+n
+�
+i=1
+N
+�
+k=0
+���(Si,[k] − SD
+i,[k])θ∗
+[k],·
+���
+2
+F
+≤ 1
+M
+n
+�
+i=1
+�
+t∈ ¯
+Di
+N
+�
+k=0
+dkΛk(F)2�
+2eLk−1�
+ω|Di| +
+max
+t′∈D,t′≤t ∥ξt′∥
+��2
+≤ 4e2�
+ω|D| +
+max
+t′∈D,t′≤t ∥ξt′∥
+��2
+L2
+N
+�
+k=0
+dkΛk(F)2
+k!2
+× k!2
+≤ 4e2N!2�
+ω|D| +
+max
+t′∈D,t′≤t ∥ξt′∥
+��2
+L2
+N
+�
+k=0
+dkΛk(F)2
+k!2
+.
+On the set Aξ(δ), one has
+max
+i=1,...,n,t∈Di
+��ξi
+t
+�� ≤ vξ
+√
+d + vξ
+�
+C−1 log(δ−1#D).
+(22)
+
+Learning the Dynamics of Sparsely Observed Interacting Systems
+Writing
+CD,N(δ) = 4e2L2N!2�
+ω|D| + vξ
+√
+d + vξ
+�
+C−1 log(δ−1#D)
+�2
+One finally gets with probability 1 − δ that
+1
+M
+��(SN − SD
+N)θ∗
+N
+��2
+F ≤ CD,N(δ)
+N
+�
+k=0
+dkΛk(F)2
+k!2
+.
+B.6. Proof of the main Theorem
+We finally combine all Lemmas to obtain the desired oracle bound.
+Proof. First, we have from Lemma 3.1 that on Aε(¯δ),
+1
+2M
+���y − SD
+N �θN,M
+���
+2
+F ≤
+1
+2M
+��y − SD
+Nθ∗
+N
+��2
+F + 2pCN(¯δ)
+√
+M
+N
+�
+k=0
+dkΛk(F)
+k!
+.
+The first term of the right-hand side of this inequality is bounded by
+1
+2M
+��y − SD
+Nθ∗
+N
+��2
+F ≤ 1
+M ∥y − SNθ∗
+N∥2
+F + 1
+M
+��SNθ∗
+N − SD
+Nθ∗
+N
+��2
+F .
+By Lemma 3.2 and Lemma 3.3, this can in turn be bounded on Aε(¯δ) ∩ Aξ(δ) by
+1
+2M
+��y − SD
+Nθ∗
+N
+��2
+F ≤
+�
+dN+1ΛN+1(F)
+(N + 1)!
+�2
++ CD,N(δ)
+N
+�
+k=0
+dkΛk(F)2
+k!2
+Combining all the pieces, this finally gives us, on Aε(¯δ) ∩ Aξ(δ),
+1
+2M
+���y − SD
+N �θN,M
+���
+2
+F ≤
+�
+dN+1ΛN+1(F)
+(N + 1)!
+�2
++ CD,N(δ)
+N
+�
+k=0
+dkΛk(F)2
+k!2
++ 2pCN(¯δ)
+√
+M
+N
+�
+k=0
+dkΛk(F)
+k!
+.
+B.7. Asymptotics
+We briefly discuss the asymptotic behaviour of the upper bound of the oracle inequality.
+Sampling coarseness D.
+In the noiseless case, CD,N → 0 as |D| → 0. This means that the discretization bias of our
+estimator vanishes as the sampling gets finer. However, in the noisy case - that is, when vξ > 0 - our estimator is durably
+biased. This is consistent with the literature on learning with fussy features (Loh & Wainwright, 2011).
+
+Learning the Dynamics of Sparsely Observed Interacting Systems
+Truncation depth N.
+A natural question is whether the bias of our estimator vanishes as N → ∞. If we have perfect
+sampling, i.e. the limit case where D = 0 and vξ = 0, our bound on the prediction error becomes on Aε(¯δ)
+1
+2M
+���y − SD
+N �θN,M
+���
+2
+F ≤
+�
+dN+1ΛN+1(F)
+(N + 1)!
+�2
++ 2pCN(¯δ)
+√
+M
+N
+�
+k=0
+dkΛk(F)
+k!
+.
+The first term of this bound vanishes as an immediate consequence of Assumption 3, while the second term is a statistical
+error term that behaves like
+√
+log(NdN)
+√
+M
+. In order to obtain an assymptotical convergence, we thus need that N log(dN) =
+o(M).
+In the more realistic setting where |D| > 0, the discretization bias behaves like LN−1N!|D|. It is thus sufficient to assume
+that |D| = o(1/N!). If vξ > 0, our estimator is durably biased due to the measurement noise, and this bias increases with
+N → ∞. This is due to a ”propagation of chaos” phenomenon: the difference between the unobserved feature path and
+the interpolated feature time series is amplified by taking the successive iterated integrals that define the signature. This
+advocates for using simple, low-order signature models in the presence of noise, as the gain in precision obtained when
+taking higher N and reducing the truncation bias will at some point be lost because of the amplified noise.
+Dimension p of the target path.
+Our oracle bound only depends on p through the statistical error term. This term is
+proportional to p√log p, which is expected in multitask regression.
+Dimension d of the feature path.
+Our oracle bound exhibits multiple dependencies in d. First, the truncation bias grows
+polynomially with d. Similarly, the discretization bias also depends polynomially on d. Finally, the statistical error term is
+proportional to log d times a polynomial term.
+C. Algorithms, experiments, and supplementary results
+C.1. Implementation details
+Recall that the SigLasso estimator �θN,M is defined as
+�θN,M ∈
+arg min
+θ∈Rsd(N)×p
+1
+2M
+��Y − SD
+Nθ
+��2
+F + Ω(θ),
+where
+Ω(θ) =
+N
+�
+k=0
+M
+1
+2 Ck(¯δ)
+k!
+��θ[k],·
+��
+1 ,
+and
+Ck(¯δ) =
+�
+vε log(2pNdk/¯δ)
+for ¯δ ∈ [0, 1]. Our goal is first to rewrite the penalty Ω(θ) as
+Ω(θ) = C
+N
+�
+k=0
+λk
+��θ[k],·
+��
+1 ,
+such that training will only require to scale each layer of θ and to crossvalidate the multiplicative constant C. Since for
+k ≥ 1,
+Ck(¯δ) =
+√
+k ×
+�
+vε(¯δ/k + log(pN)/k + log d) ≤
+√
+k ×
+�
+vε(¯δ + log(pN) + log d),
+
+Learning the Dynamics of Sparsely Observed Interacting Systems
+we let λk =
+√
+k
+k! .
+We now show that the minimization problem with layer-specific penalty can be written as a standard regression problem
+with ℓ1 penalization by rescaling the feature matrix, that is, multiplying SD
+N by a well-chosen diagonal matrix. Consider
+the ℓ1-penalized problem
+min
+θ∈Rsd(N)×p
+1
+2M
+��Y − SD
+Nθ
+��2
+F + C
+N
+�
+k=0
+λk
+��θ[k],·
+��
+1 ,
+where C > 0 controls the strength of the penalization.
+Making the change of variable
+˜θ = diag(1, λ1, . . . , λ1
+�
+��
+�
+d repetitions
+, λ2, . . . , λ2
+�
+��
+�
+d2 repetitions
+, . . . , λk, . . . , λk
+�
+��
+�
+dN repetitions
+)θ,
+which is equivalent to
+θ = diag(1, 1/λ1, . . . , 1/λ1, . . . , 1/λk, . . . , 1/λk)˜θ,
+and denoting by W this last weight matrix, we get the equivalent minimization problem
+min
+˜θ∈Rsd(N)×p
+1
+2M
+���Y − SD
+NW ˜θ
+���
+2
+F + C
+N
+�
+k=0
+���˜θ[k],·
+���
+1 .
+We can thus obtain the SigLasso estimator by (i) multiplying the feature matrix SD
+N by W and solving the associated
+ℓ1-penalized problem (ii) multiplying the obtained solution by W.
+The Learn-And-Reconstruct algorithm is the generic algorithm used in our work. It is applicable for a wide variety of tasks
+such as missing values inference, trajectory reconstruction, forecasting and many more. It is described in Algorithm 1.
+Algorithm 1 Learn-and-Reconstruct Algorithm. The algorithm infers for every individual in the test set a reconstructed
+time series ˆY i
+t .
+1. Learn the dynamics
+Input: train dataset of normalized paths (X1, Y1), . . . , (Xn, Yn) sampled on (D1, ¯D1), . . . , (Dn, ¯Dn).
+Construct the feature matrix SD
+N and the target vector Y
+for i = 1 to n do
+for t in ¯Di do
+SD
+N ← Append SN(Xi
+[0,t])
+Y ← Append Y i
+t
+end for
+end for
+Compute ˆθN,M by solving (6) with Y, SD
+N using coordinate descent.
+2. Reconstruct trajectories
+Input: test dataset ˜X1, . . . , ˜Xn sampled on ˜D1, . . . , ˜Dn.
+for i = 1 to n do
+for t in ˜Di do
+ˆY i
+t = ˆθN,MSN( ˜Xi
+[0,t])
+end for
+end for
+C.2. Assessing feature importance
+We two metrics used to asses the importance of the different dimensions of the feature path.
+Given a truncation depth N and a dimension i ∈ {1, . . . , d}, we define its pure feature importance (PFI) as the sum of the
+norm of the coefficients (or vectors in the case the target is multivariate) of �θN,M that are associated to signatures taken on
+
+Learning the Dynamics of Sparsely Observed Interacting Systems
+the words I1 = (i), I2 = (i, i), and so forth until IN = (i, . . . , i). Mathematically,
+PFI(i) = 1
+N
+� ��θI1��
+2 +
+��θI2��
+2 + · · · +
+��θIN ��
+2
+�
+.
+Since signatures also capture interactions between dimensions of the feature path, we also define the cross feature impor-
+tance (CFI) as the sum of norms of the coefficients (or vectors) of �θN,M that are associated to signatures coefficients of
+words of length ≤ N in which the letter i appears. Mathematically,
+CFI(i) =
+1
+sd(N) − sd−1(N)
+�
+I s.t. i ∈ I
+��θI��
+2 .
+For a given truncation depth N, note that there are sd(N) − sd−1(N) =
+N
+�
+k=0
+dk −
+N
+�
+k=0
+(d − 1)k terms in the last sum, which
+justifies our choice of normalization.
+C.3. Details on model implementation and evaluation
+SigLasso.
+The SigLasso model is implemented using the CVLasso class in scikit-learn (Pedregosa et al., 2011).
+This implementation optimises the objective function using coordinate descent and features automatic cross-validation of
+the penalty strength. We use iisignature (Reizenstein & Graham, 2020) to compute the signature of the feature time
+series. Every time series is standardized prior to this through division by its own total variation, as suggested by Morrill
+et al. (2020a). The depth of the signature is a hyperparameter chosen between 2 and 9 or 6 depending on the experiment.
+An intercept is added.
+GRU.
+The GRU is of width 128 and systematically trained with 100 epoches using a learning rate of 0.001.
+Neural CDE.
+We use the implementation of Neural CDE provided by torchcde (Kidger et al., 2020). We use the
+original vector field described in the documentation of this package, with the small tweak that we use a smoother non-
+linearity (tanh instead of ReLU). We observed that using the rk4 solver instead of dopri5 significantly accelerates the
+training time of the Neural CDE without affecting the model’s performances. The learning rate is hand-tuned to either
+0.001 or 0.0001 depending on the experiment. We train the model for 100 epochs and asses its convergence by using a
+standard stopping criteria.
+Metrics. The MSE is computed in a classical fashion. To compute the integrate MSE, we compute the L2 distance between
+the piecewise constant interpolations of the true yt and the predicted �yt.
+C.4. Details on the well specified model
+Generation of the training data.
+We generate a two-dimensional feature path by interpolating for every dimension 15
+points in [0, 1], each of them being draw randomly for a normal distribution N(0, 1). The interpolation is done with
+Hermite cubic splines with backward differences using the package torchcde (Kidger et al., 2020). Time is added as a
+supplementary channel, which is a standard practice when learning with signatures and Neural CDEs. These paths are then
+downsampled by randomly drawing sampling points for the target and the feature time series specific to every individual.
+The target path is the solution of a CDE of the form
+dyt = σ
+�
+Ayt
+�
+dxt
+where σ : Rp → Rp is the hyperbolic tangent, A ∈ Rd×p is a matrix drawn randomly from N(0, Id×p) and xt is the
+feature path constructed as above. The solution of this CDE is computed using torchcde.
+Generation of the test data.
+We generate the test data in the same way than the training data. However, this data is not
+downsampled as we wish to assess the generalization capacities of our model—i.e., is our model capable of approximating
+the dynamics and extrapolating to continuous feature paths.
+
+Learning the Dynamics of Sparsely Observed Interacting Systems
+C.5. Details on Ornstein-Uhlenbeck experiment
+We take (xt)t∈[0,1] to be a 1-dimensional Brownian motion with variance σ2 = 0.1, and generate (yt) as a 1-dimensional
+Ornstein-Uhlenbeck process driven by (xt), that is, for all t ∈ [0, 1]
+dyt = θ(µ − yt)dt + dxt.
+Simulation of (yt) is done using a standard Euler-Maruyama simulation scheme. We let θ = 3 and µ = 1. The training
+data is then downsampled as in the well specified experiment.
+C.6. Details on the tumor growth experiment
+We consider the following tumor growth model taken from (Simeoni et al., 2004). Let x ∈ C1−var([0, 1], R). The weight
+y ∈ C([0, 1], R+) under the concentration of a treatment drug x is governed by the differential system
+du1
+t =
+��
+λ0u1
+t
+�
+1 + (λ0
+λ1
+yt)ψ��−1/ψ
+− k2xtu1
+t
+�
+dt
+du2
+t =
+�
+k2xtu1
+t − k1u2
+t
+�
+dt
+du3
+t =
+�
+k1(u2
+t − u3
+t)
+�
+dt
+du4
+t =
+�
+k1(u3
+t − u4
+t)
+�
+dt
+yt = u1
+t + u2
+t + u3
+t + u4
+t
+with initial condition (u1
+0, u2
+0, u3
+0, u4
+0, y0) = (2, 0, 0, 0, 2) and parameters (k1, k2, λ0, λ1, ψ) = (10, 0.5, 0.9, 0.7, 20). The
+concentration (xt) is chosen to be the squared value of the paths used for the well-specified experiment. Notice that this
+system is non-linear w.r.t. x. Indeed, writing dyt = G(yt, xt)dt, one has, for α ∈ R, G(yt, αxt) ̸= αG(yt, xt). The
+training data is then downsampled as in the well specified experiment.
+C.7. Details on the French Covid experiment
+We illustrate the performance of our method and competitors on French Covid data from 2021-03-31 to 2021-07-07 avail-
+able on Gitlab. Hospital data was obtained from the SI-VIC database, the national inpatient surveillance system.
+Target path.
+Following Paireau et al. (2022), we chose the predict the growth rate of incident hospitalisations in each
+of the 9 metropolitan regions of France. The exponential growth rate was computed from raw data using a 2 days rolling
+window and then smoothed using local polynomial regression as in Paireau et al. (2022). Mathematically, our target time
+series is the R-valued growth rate, and we fit a different model for every of the 12 regions. It is displayed for all 12 regions
+in Figure 6.
+Feature path.
+As in Paireau et al. (2022), we consider a set of 12 time-dependant predictors of different types summa-
+rized in Table 2 and plotted in Figure 5. Both SIDEP (”Syst`eme d’Information de D´epistage Populationnel”) and VAC-SI
+datasets are publicly available. The mobility data was obtained from Google. The mobility-related predictors describe
+travel trends for different kind of public spaces such as such as shops and leisure spaces, food stores and pharmacies,
+parks, public transport stations, workplaces and residential areas. The meteorological data was obtained from M´et´eo
+France.
+Models.
+SigLasso (weighted and unweighted), NCDE and GRU algorithms were trained on the period from 2021-03-31
+to 2021-06-23 and tested on the period from 2021-06-24 to 2021-07-07. We included a history of 10 days at each point
+and performed prediction for different horizons ranging from 1 to 14. In others words, at horizon h, features values from
+day t − h − 10 to day t − h to were used to compute the prediction at time t. All feature time series are normalized to have
+total variation equal to 1.
+Architectural details.
+The GRU has width 128 and is trained for 100 epochs with a learning rate of 0.0001. The NCDE
+is trained for 30 epochs with a learning rate of 0.001. It has 2 hidden layers of width 128, an intermediate Tanh(·) non-
+
+Learning the Dynamics of Sparsely Observed Interacting Systems
+2021-03-14
+2021-04-13
+2021-05-13
+2021-06-12
+2021-07-12
+Date
+0.05
+0.10
+0.15
+0.20
+0.25
+0.30
+0.35
+prop_pos_symp
+ARA
+BFC
+BRE
+CVL
+GES
+HDF
+IDF
+NOR
+NAQ
+OCC
+PDL
+PAC
+2021-03-14
+2021-04-13
+2021-05-13
+2021-06-12
+2021-07-12
+Date
+10
+0
+10
+20
+30
+40
+grocery_and_pharmacy
+2021-03-14
+2021-04-13
+2021-05-13
+2021-06-12
+2021-07-12
+Date
+25
+0
+25
+50
+75
+100
+125
+150
+parks
+2021-03-14
+2021-04-13
+2021-05-13
+2021-06-12
+2021-07-12
+Date
+40
+30
+20
+10
+0
+10
+20
+30
+transit_stations
+2021-03-14
+2021-04-13
+2021-05-13
+2021-06-12
+2021-07-12
+Date
+40
+30
+20
+10
+0
+workplaces
+ARA
+BFC
+BRE
+CVL
+GES
+HDF
+IDF
+NOR
+NAQ
+OCC
+PDL
+PAC
+2021-03-14
+2021-04-13
+2021-05-13
+2021-06-12
+2021-07-12
+Date
+0.0
+2.5
+5.0
+7.5
+10.0
+12.5
+15.0
+17.5
+residential
+2021-03-14
+2021-04-13
+2021-05-13
+2021-06-12
+2021-07-12
+Date
+0
+20
+40
+60
+80
+IPTCC
+2021-03-14
+2021-04-13
+2021-05-13
+2021-06-12
+2021-07-12
+Date
+5.0
+7.5
+10.0
+12.5
+15.0
+17.5
+20.0
+22.5
+25.0
+temperature
+2021-03-14
+2021-04-13
+2021-05-13
+2021-06-12
+2021-07-12
+Date
+55
+60
+65
+70
+75
+80
+85
+rel_humidity
+ARA
+BFC
+BRE
+CVL
+GES
+HDF
+IDF
+NOR
+NAQ
+OCC
+PDL
+PAC
+2021-03-14
+2021-04-13
+2021-05-13
+2021-06-12
+2021-07-12
+Date
+4
+6
+8
+10
+12
+14
+abs_humidity
+2021-03-14
+2021-04-13
+2021-05-13
+2021-06-12
+2021-07-12
+Date
+0.10
+0.05
+0.00
+0.05
+0.10
+P_r
+2021-03-14
+2021-04-13
+2021-05-13
+2021-06-12
+2021-07-12
+Date
+0.05
+0.10
+0.15
+0.20
+0.25
+0.30
+0.35
+0.40
+couv_complet
+Figure 5: The 12 different feature time series used to forecast the hospitalization growth rate. Every different color
+corresponds to a given region of France.
+
+Learning the Dynamics of Sparsely Observed Interacting Systems
+Predictor
+Type
+Source
+Description
+prop pos symp
+Epidemiological
+SIDEP databas
+proportion of positive tests among symptomatics
+P r
+Epidemiological
+SIDEP database
+growth rate of positive tests
+couv-complet
+Epidemiological
+VAC-SI database
+proportion of vaccinated
+grocery and pharmacy
+Mobility
+Google
+visits to grocery and pharmacy stores
+parks
+Mobility
+Google
+visits to parks
+transit stations
+Mobility
+Google
+visits visits to transit stations
+workplaces
+Mobility
+Google
+visits to workplaces
+residential
+Mobility
+Google
+visits to residential places
+IPTCC
+Meteorological
+M´et´eo France
+Index PREDICT of climatic transmissivity
+temperature
+Meteorological
+M´et´eo France
+temperature
+rel humidity
+Meteorological
+M´et´eo France
+relative humidity
+abs humidity
+Meteorological
+M´et´eo France
+absolute humidity
+Table 2: The set of time-dependant predictors used to predict the hospital admission growth rate. See Figure 5 for a
+vizualisation of all different features across regions through time.
+2021-03-01
+2021-03-15
+2021-04-01
+2021-04-15
+2021-05-01
+2021-05-15
+2021-06-01
+2021-06-15
+2021-07-01
+Date
+0.15
+0.10
+0.05
+0.00
+Hospitalization growth rate
+ARA
+BFC
+BRE
+CVL
+GES
+HDF
+IDF
+NOR
+NAQ
+OCC
+PDL
+PAC
+Figure 6: Hospitalization growth rate through time during the full period for the 12 different regions of France.
+
+Learning the Dynamics of Sparsely Observed Interacting Systems
+2021-04-07
+2021-04-19
+2021-05-01
+2021-05-13
+2021-05-25
+2021-06-06
+2021-06-18
+2021-06-30
+−0.06
+−0.04
+−0.02
+0.00
+0.02
+Growth rate
+ARA
+2021-04-07
+2021-04-19
+2021-05-01
+2021-05-13
+2021-05-25
+2021-06-06
+2021-06-18
+2021-06-30
+Days
+−0.10
+−0.08
+−0.06
+−0.04
+−0.02
+0.00
+GES
+2021-04-07
+2021-04-19
+2021-05-01
+2021-05-13
+2021-05-25
+2021-06-06
+2021-06-18
+2021-06-30
+−0.06
+−0.04
+−0.02
+0.00
+NAQ
+2021-04-07
+2021-04-19
+2021-05-01
+2021-05-13
+2021-05-25
+2021-06-06
+2021-06-18
+2021-06-30
+−0.10
+−0.08
+−0.06
+−0.04
+−0.02
+0.00
+0.02
+Growth rate
+BFC
+2021-04-07
+2021-04-19
+2021-05-01
+2021-05-13
+2021-05-25
+2021-06-06
+2021-06-18
+2021-06-30
+Days
+−0.08
+−0.06
+−0.04
+−0.02
+0.00
+HDF
+2021-04-07
+2021-04-19
+2021-05-01
+2021-05-13
+2021-05-25
+2021-06-06
+2021-06-18
+2021-06-30
+−0.06
+−0.04
+−0.02
+0.00
+0.02
+OCC
+2021-04-07
+2021-04-19
+2021-05-01
+2021-05-13
+2021-05-25
+2021-06-06
+2021-06-18
+2021-06-30
+−0.15
+−0.10
+−0.05
+0.00
+Growth rate
+BRE
+2021-04-07
+2021-04-19
+2021-05-01
+2021-05-13
+2021-05-25
+2021-06-06
+2021-06-18
+2021-06-30
+Days
+−0.08
+−0.06
+−0.04
+−0.02
+0.00
+IDF
+2021-04-07
+2021-04-19
+2021-05-01
+2021-05-13
+2021-05-25
+2021-06-06
+2021-06-18
+2021-06-30
+−0.06
+−0.04
+−0.02
+0.00
+PDL
+2021-04-07
+2021-04-19
+2021-05-01
+2021-05-13
+2021-05-25
+2021-06-06
+2021-06-18
+2021-06-30
+−0.10
+−0.08
+−0.06
+−0.04
+−0.02
+0.00
+0.02
+Growth rate
+CVL
+2021-04-07
+2021-04-19
+2021-05-01
+2021-05-13
+2021-05-25
+2021-06-06
+2021-06-18
+2021-06-30
+Days
+−0.06
+−0.04
+−0.02
+0.00
+0.02
+NOR
+2021-04-07
+2021-04-19
+2021-05-01
+2021-05-13
+2021-05-25
+2021-06-06
+2021-06-18
+2021-06-30
+−0.06
+−0.04
+−0.02
+0.00
+PAC
+Figure 7: Interpolation (left of dotted line) and prediction (right of dotted line) of hospitalization growth rate for all 12
+french regions using weighted SigLasso.
+linearity and a final linear readout. This architecture is identical to the one proposed in (Kidger, 2022). Penalty strenght of
+the SigLasso is crossvalided using the internal implementation LassoCV of scikit-learn (Pedregosa et al., 2011).
+All details, in particular the features used for each individual prediction, can be found in Paireau et al. (2022).
+We refer to the supplementary information file of Paireau et al. (2022) and our code for more details.
+Results.
+Figure 12 displays the RMSE (on all regions) of NCDE, SigLasso, GRU, and the Ensemble method for all
+prediction horizons h = 1, . . . , 14. Figures 7, 8, 10 and 9 display the obtained interpolation for weighted and unweighted
+SigLasso, GRU and NCDE at different horizons (corresponding to different line colors in winter matplotlib palette). The
+lighter the blue, the smaller the time horizon: the lightest curve corresponds to a time horizon equal to h = 1. Truth is in
+red.
+C.8. Additional results
+We give in Table 3 some additional results on the experiments described above.
+Table 3: Training time of SigLasso, GRU and Neural CDE in different simulation settings, averaged over 10 iterations. In
+every setting, n = 50, # ¯Di = 5 for all i = 1, . . . , n (and therefore M = 250).
+Training time (s)
+SigLasso
+GRU
+Neural CDE
+Well-specified
+0.37 ± 0.23
+269 ± 109
+1754 ± 587
+OU
+0.057 ± 0.005
+27 ± 0.44
+216 ± 2.7
+Tumor growth
+0.056 ± 0.007
+31 ± 3.5
+250 ± 14
+
+Learning the Dynamics of Sparsely Observed Interacting Systems
+2021-04-07
+2021-04-19
+2021-05-01
+2021-05-13
+2021-05-25
+2021-06-06
+2021-06-18
+2021-06-30
+−0.08
+−0.06
+−0.04
+−0.02
+0.00
+0.02
+Growth rate
+ARA
+2021-04-07
+2021-04-19
+2021-05-01
+2021-05-13
+2021-05-25
+2021-06-06
+2021-06-18
+2021-06-30
+Days
+−0.10
+−0.08
+−0.06
+−0.04
+−0.02
+0.00
+GES
+2021-04-07
+2021-04-19
+2021-05-01
+2021-05-13
+2021-05-25
+2021-06-06
+2021-06-18
+2021-06-30
+−0.06
+−0.04
+−0.02
+0.00
+NAQ
+2021-04-07
+2021-04-19
+2021-05-01
+2021-05-13
+2021-05-25
+2021-06-06
+2021-06-18
+2021-06-30
+−0.10
+−0.08
+−0.06
+−0.04
+−0.02
+0.00
+0.02
+Growth rate
+BFC
+2021-04-07
+2021-04-19
+2021-05-01
+2021-05-13
+2021-05-25
+2021-06-06
+2021-06-18
+2021-06-30
+Days
+−0.08
+−0.06
+−0.04
+−0.02
+0.00
+HDF
+2021-04-07
+2021-04-19
+2021-05-01
+2021-05-13
+2021-05-25
+2021-06-06
+2021-06-18
+2021-06-30
+−0.08
+−0.06
+−0.04
+−0.02
+0.00
+0.02
+OCC
+2021-04-07
+2021-04-19
+2021-05-01
+2021-05-13
+2021-05-25
+2021-06-06
+2021-06-18
+2021-06-30
+−0.15
+−0.10
+−0.05
+0.00
+Growth rate
+BRE
+2021-04-07
+2021-04-19
+2021-05-01
+2021-05-13
+2021-05-25
+2021-06-06
+2021-06-18
+2021-06-30
+Days
+−0.08
+−0.06
+−0.04
+−0.02
+0.00
+IDF
+2021-04-07
+2021-04-19
+2021-05-01
+2021-05-13
+2021-05-25
+2021-06-06
+2021-06-18
+2021-06-30
+−0.06
+−0.04
+−0.02
+0.00
+PDL
+2021-04-07
+2021-04-19
+2021-05-01
+2021-05-13
+2021-05-25
+2021-06-06
+2021-06-18
+2021-06-30
+−0.10
+−0.08
+−0.06
+−0.04
+−0.02
+0.00
+0.02
+Growth rate
+CVL
+2021-04-07
+2021-04-19
+2021-05-01
+2021-05-13
+2021-05-25
+2021-06-06
+2021-06-18
+2021-06-30
+Days
+−0.06
+−0.04
+−0.02
+0.00
+0.02
+NOR
+2021-04-07
+2021-04-19
+2021-05-01
+2021-05-13
+2021-05-25
+2021-06-06
+2021-06-18
+2021-06-30
+−0.06
+−0.04
+−0.02
+0.00
+0.02
+PAC
+Figure 8: Interpolation (left of dotted line) and prediction (right of dotted line) of hospitalization growth rate for all 12
+french regions using unweighted SigLasso.
+2021-04-07
+2021-04-19
+2021-05-01
+2021-05-13
+2021-05-25
+2021-06-06
+2021-06-18
+2021-06-30
+−0.10
+−0.05
+0.00
+0.05
+0.10
+Growth rate
+ARA
+2021-04-07
+2021-04-19
+2021-05-01
+2021-05-13
+2021-05-25
+2021-06-06
+2021-06-18
+2021-06-30
+Days
+−0.10
+−0.05
+0.00
+0.05
+0.10
+GES
+2021-04-07
+2021-04-19
+2021-05-01
+2021-05-13
+2021-05-25
+2021-06-06
+2021-06-18
+2021-06-30
+−0.10
+−0.05
+0.00
+0.05
+0.10
+NAQ
+2021-04-07
+2021-04-19
+2021-05-01
+2021-05-13
+2021-05-25
+2021-06-06
+2021-06-18
+2021-06-30
+−0.10
+−0.05
+0.00
+0.05
+0.10
+Growth rate
+BFC
+2021-04-07
+2021-04-19
+2021-05-01
+2021-05-13
+2021-05-25
+2021-06-06
+2021-06-18
+2021-06-30
+Days
+−0.10
+−0.05
+0.00
+0.05
+0.10
+HDF
+2021-04-07
+2021-04-19
+2021-05-01
+2021-05-13
+2021-05-25
+2021-06-06
+2021-06-18
+2021-06-30
+−0.10
+−0.05
+0.00
+0.05
+0.10
+OCC
+2021-04-07
+2021-04-19
+2021-05-01
+2021-05-13
+2021-05-25
+2021-06-06
+2021-06-18
+2021-06-30
+−0.10
+−0.05
+0.00
+0.05
+0.10
+Growth rate
+BRE
+2021-04-07
+2021-04-19
+2021-05-01
+2021-05-13
+2021-05-25
+2021-06-06
+2021-06-18
+2021-06-30
+Days
+−0.10
+−0.05
+0.00
+0.05
+0.10
+IDF
+2021-04-07
+2021-04-19
+2021-05-01
+2021-05-13
+2021-05-25
+2021-06-06
+2021-06-18
+2021-06-30
+−0.10
+−0.05
+0.00
+0.05
+0.10
+PDL
+2021-04-07
+2021-04-19
+2021-05-01
+2021-05-13
+2021-05-25
+2021-06-06
+2021-06-18
+2021-06-30
+−0.10
+−0.05
+0.00
+0.05
+0.10
+Growth rate
+CVL
+2021-04-07
+2021-04-19
+2021-05-01
+2021-05-13
+2021-05-25
+2021-06-06
+2021-06-18
+2021-06-30
+Days
+−0.10
+−0.05
+0.00
+0.05
+0.10
+NOR
+2021-04-07
+2021-04-19
+2021-05-01
+2021-05-13
+2021-05-25
+2021-06-06
+2021-06-18
+2021-06-30
+−0.10
+−0.05
+0.00
+0.05
+0.10
+PAC
+Figure 9: Interpolation (left of dotted line) and prediction (right of dotted line) of hospitalization growth rate for all 12
+french regions using NCDE.
+
+Learning the Dynamics of Sparsely Observed Interacting Systems
+2021-04-07
+2021-04-19
+2021-05-01
+2021-05-13
+2021-05-25
+2021-06-06
+2021-06-18
+2021-06-30
+−0.08
+−0.06
+−0.04
+−0.02
+0.00
+0.02
+Growth rate
+ARA
+2021-04-07
+2021-04-19
+2021-05-01
+2021-05-13
+2021-05-25
+2021-06-06
+2021-06-18
+2021-06-30
+Days
+−0.10
+−0.08
+−0.06
+−0.04
+−0.02
+0.00
+GES
+2021-04-07
+2021-04-19
+2021-05-01
+2021-05-13
+2021-05-25
+2021-06-06
+2021-06-18
+2021-06-30
+−0.08
+−0.06
+−0.04
+−0.02
+0.00
+NAQ
+2021-04-07
+2021-04-19
+2021-05-01
+2021-05-13
+2021-05-25
+2021-06-06
+2021-06-18
+2021-06-30
+−0.10
+−0.08
+−0.06
+−0.04
+−0.02
+0.00
+0.02
+0.04
+Growth rate
+BFC
+2021-04-07
+2021-04-19
+2021-05-01
+2021-05-13
+2021-05-25
+2021-06-06
+2021-06-18
+2021-06-30
+Days
+−0.08
+−0.06
+−0.04
+−0.02
+0.00
+0.02
+HDF
+2021-04-07
+2021-04-19
+2021-05-01
+2021-05-13
+2021-05-25
+2021-06-06
+2021-06-18
+2021-06-30
+−0.08
+−0.06
+−0.04
+−0.02
+0.00
+0.02
+OCC
+2021-04-07
+2021-04-19
+2021-05-01
+2021-05-13
+2021-05-25
+2021-06-06
+2021-06-18
+2021-06-30
+−0.15
+−0.10
+−0.05
+0.00
+Growth rate
+BRE
+2021-04-07
+2021-04-19
+2021-05-01
+2021-05-13
+2021-05-25
+2021-06-06
+2021-06-18
+2021-06-30
+Days
+−0.08
+−0.06
+−0.04
+−0.02
+0.00
+IDF
+2021-04-07
+2021-04-19
+2021-05-01
+2021-05-13
+2021-05-25
+2021-06-06
+2021-06-18
+2021-06-30
+−0.08
+−0.06
+−0.04
+−0.02
+0.00
+PDL
+2021-04-07
+2021-04-19
+2021-05-01
+2021-05-13
+2021-05-25
+2021-06-06
+2021-06-18
+2021-06-30
+−0.10
+−0.08
+−0.06
+−0.04
+−0.02
+0.00
+0.02
+Growth rate
+CVL
+2021-04-07
+2021-04-19
+2021-05-01
+2021-05-13
+2021-05-25
+2021-06-06
+2021-06-18
+2021-06-30
+Days
+−0.08
+−0.06
+−0.04
+−0.02
+0.00
+0.02
+NOR
+2021-04-07
+2021-04-19
+2021-05-01
+2021-05-13
+2021-05-25
+2021-06-06
+2021-06-18
+2021-06-30
+−0.08
+−0.06
+−0.04
+−0.02
+0.00
+PAC
+Figure 10: Interpolation (left of dotted line) and prediction (right of dotted line) of hospitalization growth rate for all 12
+french regions using GRU.
+2021−03−26
+2021−04−07
+2021−04−18
+2021−04−30
+2021−05−12
+2021−05−24
+2021−06−05
+2021−06−17
+2021−06−28
+2021−07−10
+−0.3
+−0.2
+−0.1
+0.0
+0.1
+0.2
+0.3
+Growth rate
+ARA
+2021−03−26
+2021−04−07
+2021−04−18
+2021−04−30
+2021−05−12
+2021−05−24
+2021−06−05
+2021−06−17
+2021−06−28
+2021−07−10
+Days
+−0.3
+−0.2
+−0.1
+0.0
+0.1
+0.2
+0.3
+GES
+2021−03−26
+2021−04−07
+2021−04−18
+2021−04−30
+2021−05−12
+2021−05−24
+2021−06−05
+2021−06−17
+2021−06−28
+2021−07−10
+−0.3
+−0.2
+−0.1
+0.0
+0.1
+0.2
+0.3
+NAQ
+2021−03−26
+2021−04−07
+2021−04−18
+2021−04−30
+2021−05−12
+2021−05−24
+2021−06−05
+2021−06−17
+2021−06−28
+2021−07−10
+−0.3
+−0.2
+−0.1
+0.0
+0.1
+0.2
+0.3
+Growth rate
+BFC
+2021−03−26
+2021−04−07
+2021−04−18
+2021−04−30
+2021−05−12
+2021−05−24
+2021−06−05
+2021−06−17
+2021−06−28
+2021−07−10
+Days
+−0.3
+−0.2
+−0.1
+0.0
+0.1
+0.2
+0.3
+HDF
+2021−03−26
+2021−04−07
+2021−04−18
+2021−04−30
+2021−05−12
+2021−05−24
+2021−06−05
+2021−06−17
+2021−06−28
+2021−07−10
+−0.3
+−0.2
+−0.1
+0.0
+0.1
+0.2
+0.3
+OCC
+2021−03−26
+2021−04−07
+2021−04−18
+2021−04−30
+2021−05−12
+2021−05−24
+2021−06−05
+2021−06−17
+2021−06−28
+2021−07−10
+−0.3
+−0.2
+−0.1
+0.0
+0.1
+0.2
+0.3
+Growth rate
+BRE
+2021−03−26
+2021−04−07
+2021−04−18
+2021−04−30
+2021−05−12
+2021−05−24
+2021−06−05
+2021−06−17
+2021−06−28
+2021−07−10
+Days
+−0.3
+−0.2
+−0.1
+0.0
+0.1
+0.2
+0.3
+IDF
+2021−03−26
+2021−04−07
+2021−04−18
+2021−04−30
+2021−05−12
+2021−05−24
+2021−06−05
+2021−06−17
+2021−06−28
+2021−07−10
+−0.3
+−0.2
+−0.1
+0.0
+0.1
+0.2
+0.3
+PDL
+2021−03−26
+2021−04−07
+2021−04−18
+2021−04−30
+2021−05−12
+2021−05−24
+2021−06−05
+2021−06−17
+2021−06−28
+2021−07−10
+−0.3
+−0.2
+−0.1
+0.0
+0.1
+0.2
+0.3
+Growth rate
+CVL
+2021−03−26
+2021−04−07
+2021−04−18
+2021−04−30
+2021−05−12
+2021−05−24
+2021−06−05
+2021−06−17
+2021−06−28
+2021−07−10
+Days
+−0.3
+−0.2
+−0.1
+0.0
+0.1
+0.2
+0.3
+NOR
+2021−03−26
+2021−04−07
+2021−04−18
+2021−04−30
+2021−05−12
+2021−05−24
+2021−06−05
+2021−06−17
+2021−06−28
+2021−07−10
+−0.3
+−0.2
+−0.1
+0.0
+0.1
+0.2
+0.3
+PAC
+Figure 11: Interpolation (left of dotted line) and prediction (right of dotted line) of hospitalization growth rate for all 12
+french regions using ensemble methods (Paireau et al., 2022).
+
+Learning the Dynamics of Sparsely Observed Interacting Systems
+2
+4
+6
+8
+10
+12
+14
+Horizon of prediction
+100
+101
+RMSE
+SigLasso
+SigLasso (weighted)
+GRU
+NCDE
+Ensemble
+2
+4
+6
+8
+10
+12
+14
+Horizon of prediction
+100
+101
+SigLasso
+SigLasso (weighted)
+GRU
+NCDE
+Ensemble
+Figure 12: RMSE accross all regions on the training period (left) and the testing period (right) for the ensemble methode
+(Paireau et al., 2022), NCDE, GRU, and SigLasso (weighted and unweighted). See Figure 13 for a zoom-in on GRU and
+SigLasso performances.
+2
+4
+6
+8
+10
+12
+14
+Horizon of prediction
+5 × 10−1
+6 × 10−1
+RMSE
+SigLasso
+SigLasso (weighted)
+GRU
+2
+4
+6
+8
+10
+12
+14
+Horizon of prediction
+4.4 × 10−1
+4.6 × 10−1
+4.8 × 10−1
+5 × 10−1
+5.2 × 10−1
+SigLasso
+SigLasso (weighted)
+GRU
+Figure 13: RMSE accross all regions on the training period (left) and the testing period (right) for GRU and SigLasso
+(weighted and unweighted).
+
diff --git a/N9FJT4oBgHgl3EQf0S3d/content/tmp_files/load_file.txt b/N9FJT4oBgHgl3EQf0S3d/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..dbe2db1aef711d46865fbc1176f75e62de0a5b35
--- /dev/null
+++ b/N9FJT4oBgHgl3EQf0S3d/content/tmp_files/load_file.txt
@@ -0,0 +1,2579 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf,len=2578
+page_content='Learning the Dynamics of Sparsely Observed Interacting Systems  Linus Bleistein 1 2 3 Adeline Fermanian 4 5 6 Anne-Sophie Jannot 1 7 Agathe Guilloux 1  Abstract  We address the problem of learning the dynamics of an unknown non-parametric system linking a target and a  feature time series.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' The feature time series is measured on a sparse and irregular grid, while we have access to  only a few points of the target time series.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Once learned, we can use these dynamics to predict values of the  target from the previous values of the feature time series.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' We frame this task as learning the solution map of a  controlled differential equation (CDE).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' By leveraging the rich theory of signatures, we are able to cast this non-  linear problem as a high-dimensional linear regression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' We provide an oracle bound on the prediction error which  exhibits explicit dependencies on the individual-specific sampling schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Our theoretical results are illustrated  by simulations which show that our method outperforms existing algorithms for recovering the full time series  while being computationally cheap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' We conclude by demonstrating its potential on real-world epidemiological  data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Introduction  Time series are ubiquitous in many areas such as finance, economics, robotics, agriculture, and healthcare.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' One is typically  interested in modelling the evolution of a target quantity through time, which is known to be affected by a set of time-  evolving features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' For example, pollution levels in a city are driven by quantities such as temperature, pressure, traffic,  or economic activity measured through time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Mathematically, one wishes to model the evolution of a quantity yt ∈ Rp,  p ≥ 1, as a function of some time evolving features xt ∈ Rd, d ≥ 1, for t ∈ [0, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' In other words, the goal is to learn the  dynamics that link the target to the features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Such an interaction is typically modelled via differential equations, which are a common choice of model in natural  sciences (Zwillinger, 1989).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' In this article, we assume that there exists a function G : Rp × Rd → Rp such that  yt = y0 +  � t  0  G(ys, xs)ds  (1)  or equivalently  dyt = G(yt, xt)dt,  y0 ∈ Rp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  The value yt depends on the trajectory of the features time series xs up to time t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Learning the dynamics of the system can  be framed as learning the solution map of (1), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', a function Ψ which, given a time t, an initial point y0 ∈ Rp, and the  history of the path up to time t, denoted by x[0,t] = (xs)s∈[0,t], outputs the value of y at time t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  If we know Ψ, we gain access to the values of y at any point in time provided we know the values of x up to this point  ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' this encompasses many tasks such as forecasting or interpolating between points of y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' We specifically have in mind  applications where we have an easy access to x but a limited one to y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  This problem is extremely common in healthcare.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' For example, in obstetrics, the lactic acidosis (LA) of the fetus, which  is a proxy for fetal distress, is a quantity of high medical interest for predicting complications in the first hours after birth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  1Inria Paris, F-75015 Paris, France 2Centre de Recherche des Cordeliers, INSERM, Universit´e de Paris, Sorbonne Universit´e, F-  75006 Paris, France 3LaMME, UEVE and UMR 8071, Paris Saclay University, F-91042, Evry, France 4MINES ParisTech, PSL Research  University, CBIO, F-75006 Paris, France 5INSERM, U900, F-75005 Paris, France 6Institut Curie, PSL Research University, F-75005  Paris, France 7AP-HP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Correspondence to: Linus Bleistein <linus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='bleistein@inria.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='fr>.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='11647v1  [stat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='ML]  27 Jan 2023  Learning the Dynamics of Sparsely Observed Interacting Systems  This biomarker cannot be measured during pregnancy but only at birth because the measurement is highly invasive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Some  vitals such as heart rate and fetal movement are however easy to measure during pregnancy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' In this case, x is the non-  invasive measurements made during pregnancy, while y is the invasive measurement of LA at birth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Predicting the value  of y at any time t (both before and at birth) would allow for early diagnosis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Similarly, after surgery, patients are often  monitored to detect hemorrhage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' While some vitals such as heart rate of saturation are monitored in continuous time,  haemoglobin—which is highly predictive of hemorrhage—is only measured by blood samples taken a few times a day,  which can significantly delay hemorrhage diagnostic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Irregular data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  In practice, the functions x and y are measured on discrete grids and take the form of time series.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' These  often present a lot of heterogeneity, both within and across individuals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  (i) For every individual, the time between any two measurements can vary, and thus individuals may not be recorded on  the same grid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  (ii) The number of total sampling points might vary between individuals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  (iii) Each measurement in time might be corrupted by measurement noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Mathematically, we consider n pairs of functions {(x1, y1), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , (xn, yn)}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Each xi deterministically produces a specific  yi through the Ordinary Differential Equation (ODE) (1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' We call xi the feature path and yi the target path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Both xi and  yi are only observed at a finite set of times specific to every individual.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' We denote by  Di =  �  ti  1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , ti  ki  �  ,  i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , n,  the sampling grid of xi and by ¯Di the sampling grid of yi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' We stress that both the number of sampling times ki and the  sampling times ti  1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , ti  ki themselves are individual specific, as described in (i) and (ii).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Moreover, the observations are  corrupted by additive noise, such that we observe  Xi  t = xi  t + ξi  t  for all t ∈ Di, and similarly Y i  t = yi  t + εi  t for every t ∈ ¯Di, where the ξi  t and εi  t are sub-gaussian i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' random vectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Each input may therefore be written as a matrix Xi = (Xi  t)t∈Di ∈ Rki×d which we call the feature time series.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Similarly,  the quantity of interest is a matrix Yi = (Y i  t )t∈ ¯  Di ∈ Rmi×p (where mi is the length of ¯Di) and is called the target time  series.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' The grid ¯Di is assumed to be a subset of Di: in our setup yi is hard to sample and therefore measured at only a few  points (and sometimes only one) while xi is easy to access and measured at high frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Our goal is to approximate the  dynamics linking x and y from the irregular, heterogeneous, and fuzzy data Xi and Yi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Such heterogeneity is difficult to handle by classical machine learning algorithms such as Long short-term memory net-  works (LSTM, Hochreiter & Schmidhuber, 1997) which assume that the data is regularly sampled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Some more recent  approaches (Rubanova et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' De Brouwer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Kidger et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', 2020) have adapted these models by introduc-  ing continuously evolving hidden states to account for the irregular spacing between observation times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  We build upon the approach of Neural Controlled Differential Equations (Neural CDE, Kidger et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Morrill et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=',  2021b), which have proven to be very successful for time series classification and online prediction tasks (Morrill et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=',  2021a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' The key idea of Neural CDE is that under some fairly mild assumptions, any general ordinary differential equation  of the form (1) can be rewritten as  yt = y0 +  � t  0  F(ys)dxs,  (2)  where F : Rp → Rp×d is a matrix-valued vector field, such that the right-hand-side of (2) is a matrix-vector product (see,  e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Fermanian et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', 2021, Proposition 2, for a proof).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' The function x is often called the driver of the CDE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' In a Neural  CDE setting, the driver x is a continuous interpolation of the feature times series, y corresponds to a continuously-evolving  state, and F is chosen to be a neural network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' This network is then trained such that the values of (yt) can be used as  features for classification or regression tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' While Neural CDE have been shown to outperform other architectures with  limited memory usage, their training time is considerable and no statistical guarantees exist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Learning the Dynamics of Sparsely Observed Interacting Systems  Model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  We model the interactions between the target and the feature paths through a CDE of the form (2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' This modelling  choice encapsulates a broad variety of settings, since the vector field F can be any (regular enough) function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' A priori, the  solution map Ψ of this CDE is a complex function of time and the history of x up to t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' however, by linearizing the model,  we are able to approximate Ψ by a simple scalar product between a deterministic transformation of the history of x, called  the signature of x at order N ≥ 1 and denoted by SN(x[0,t]), and a time independent matrix θ∗  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Informally, we have  Ψ  �  x[0,t], t  �  ≈ SN  �  x[0,t]  �⊤θ∗  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Two striking features of this linearized model are (i) that θ∗  N can be learned on any time horizon [0, t] since it is independant  of time, and (ii) that once it has been learned, the model can be called at any time t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Contributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Our contributions are threefold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' First, we frame the task of learning the interactions between two time  series as learning the flow of a CDE, which can be linearized in the signature space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' While the connection between CDEs  and signatures is well-known, this is the first time CDEs are used as a statistical model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' We then leverage this linearization  to derive statistical guarantees on the prediction error with an explicit dependence on both sampling irregularities and the  noise affecting measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' To our knowledge, this is the first bound of this type for signature-based models, allowing for  better understanding of the dependencies between prediction performance and sampling roughness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Finally, the resulting  algorithm, called SigLasso, is shown to be computationally cheap and competitive compared to existing baselines on a wide  range of simulated data and a real-world example of hospitalization growth rate prediction during the Covid pandemic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Related works.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Signatures originated as a prominent tool in stochastic analysis (Chen, 1958;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Lyons et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', 2007;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Friz  & Victoir, 2010) and have proven to be a powerful feature extraction method in machine learning in various domains  such as healthcare (Morrill et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', 2020b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', 2020), human action recognition (Yang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', 2022), or financial  modelling (Lyons et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Buehler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Their appealing properties include a capacity to handle irregular data,  to capture dependence between coordinates, and their links with the theory of CDE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' We refer to Lyons & McLeod (2022)  for a recent survey on their use cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' However, the statistical properties of signatures based algorithms have received little  attention so far, with a few notable exceptions (Papavasiliou & Ladroue, 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Lemercier et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Fermanian, 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  On the other hand, the interplay between dynamical systems and machine learning has received considerable attention in  the recent years.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' A first line of work has focused on approximating the solution of ODE and Partial Differential Equations  (PDE) with neural networks (Lagaris et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', 1998;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Han et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Zubov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', 2021) and directly learning dynamical  systems (Long et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Fattahi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Recent approaches have been interested in combining deep learning  algorithms with physical knowledge (Greydanus et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Brunton et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Willard et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Finally, dynamical  systems, seen as continuous versions of neural network architectures, have also been a great source of inspiration for  analysing and designing machine learning algorithms in the recent years (Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Fermanian et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Marion et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' We refer to Kidger (2022) for an extensive review.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Our problem also bears close resemblance to frameworks encountered in sequence-to-sequence learning (Sutskever et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=',  2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Gehring et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', 2017) and functional regression (Ramsay & Dalzell, 1991;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Marx & Eilers, 1999).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Overview.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Section 2 introduces the CDE model for interacting systems, the mathematical context and the learning proce-  dure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Our main theoretical result is presented in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' We conclude by an empirical study on synthetic and real-world  data in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' All proofs are postponed to the appendix and the code to reproduce the experiments is available on our  Github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Model and assumptions  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' A CDE-based model on the dynamics  We start by describing our assumptions on the feature and target paths, which are linked by Equation (2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' To correctly  define the integral of Equation (2), we need to impose some conditions on the xi and on F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Note that we consider that the  xi are defined on [0, 1] but our results extend easily to any compact time interval [a, b].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Assumption 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' All paths (xi)1≤i≤n are continuous and there exists 0 < L < 1 such that, for all i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , n,  ��xi��  1-var,[0,1] = sup  D  �  k  ��xi  tk+1 − xi  tk  �� ≤ L,  Learning the Dynamics of Sparsely Observed Interacting Systems  where ∥·∥ is the Euclidean norm and the supremum is taken over all finite dissections D = {0 = t1 < · · · < tk = 1}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  We write C1-var  L  ([0, 1], Rd) for the set of continuous paths of total variation bounded by L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Outside the statistical context,  when referring to general paths, we will drop the superscripts i and simply write x and y to alleviate notations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  We assume that the target path y is the solution of the ODE (1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' This modelization choice means that the evolution of y  is governed by a dynamical system whose dynamics itself are allowed to vary with the current value of the feature path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Observe that this model can be seen as a generalized form of a non-autonomous system (Lyons et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', 2007), which we  recover by taking xt = t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Since Equation (1) can be rewritten as a CDE, the starting point of our work is to assume that  the true dynamics of the data follow such a CDE, as stated in the following assumption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Assumption 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' There exists a smooth vector field F : Rp → Rp×d such that, for all i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , n, yi is the solution of the  CDE (2) driven by xi with initial condition yi  0 = y0 ∈ Rp homogeneous amongst individuals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  By “smooth” we mean that each coordinate of F is infinitely differentiable, that is, is C∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' The vector field F and the initial  condition y0 are common to all individuals, which can be seen as homogeneity assumptions on our sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' On the other  hand, since every individual i has her own feature path xi, the target paths yi are individual specific.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' In other words, there  exists a solution map Ψ that depends only on y0 and F and is such that, for any t ∈ [0, 1], Ψ(xi  [0,t], t) = yi  t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  The vector field F encapsulates the common physical dynamics governing the evolution of yi, which are affected by the  changes in xi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Note that there is no parametric model on F (although some strong smoothness requirements will be needed)  contrarily to functional or traditional time series models (Ramsay & Silverman, 2005;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Morris, 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Linearizing the CDE with signatures  Before defining the Taylor expansion of the CDE (2), which will allow us to linearize the solution map Ψ, we need to  introduce the notion of signature, which have emerged as a powerful tool to model time series (Levin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Kidger  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  From now on, for any feature path x with values in Rd, we denote by x(j) its jth coordinate, for j = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Let x ∈ C1-var  L  ([0, 1], Rd).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Take a word of length k from the alphabet {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , d}, that is, an element  I = (i1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , ik) ∈ {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , d}k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' For all t ∈ [0, 1], the signature coefficient associated to this word is the scalar  SI�  x[0,t]  �  =  �  · ·  �  0<u1<···<uk<t  dx(i1)  u1 · · · dx(ik)  uk .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Signatures encode geometric properties of paths and have numerous appealing properties as a feature set for time series.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  In the following, we draw on their connection with Taylor expansions of CDEs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  We introduce a series of notation on signature coefficients, grouping them by the length k of the words.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' For any k ∈ N and  t ∈ [0, 1], the signature of order k of x[0,t] is  Xk,[0,t] =  �  SI(x[0,t])  �  I∈{1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=',d}k ∈ Rdk,  where the words (i1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , ik) are in lexicographic order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' We then denote the full signature by  S(x[0,t]) =  �  1, X1  [0,t], .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , Xk  [0,t], .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  �  and, for any N ≥ 1, the signature truncated at order N by  SN(x[0,t]) =  �  1, X1  [0,t], .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , XN  [0,t]  �⊤.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  The size of the signature truncated at order N grows exponentially with N, since, for d ≥ 2, it is equal to  sd(N) = 1 + d + d2 + · · · + dN = dN+1 − 1  d − 1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  When computing signatures, it is common practice to add time as a coordinate to the path (Fermanian, 2021), that is,  consider the path (t, xt)⊤.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' From now on, we assume that the first dimension of x always corresponds to time, so that  d ≥ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  We are now ready to define the Taylor expansion of a CDE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Learning the Dynamics of Sparsely Observed Interacting Systems  Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Let N ≥ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' The Taylor expansion of order N of the solution y of Equation (2) is defined by  yN,t = y0 +  N  �  k=1  �  I∈{1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=',d}k  SI �  x[0,t]  �  × ΦI  F (y0) ,  (3)  where ΦI  F(·) ∈ Rp is the differential product of the vector field F along I, whose definition is postponed to Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  The differential products ΦI  F(y0) are essentially a combination of multiplication and summation of derivatives of the  different components of F, evaluated at y0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  The Taylor expansion crucially allows to write the solution map as a product between a time-varying term (the signature  of the feature path) and a constant-over-time term (the differential product).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' This is similar to a regular Taylor expansion;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  we discuss this analogy in Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Note that Equation (3) may also be written as a matrix-vector product  yN,t  ⊤ = SN(x[0,t])⊤θ∗  N ∈ Rp,  (4)  where θ∗  N ∈ Rsd(N)×p is a matrix collecting all differential products ΦI  F(y0) up to order N and the offset y0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Since θ∗  N  depends neither on x nor on t, the Taylor expansion of y at order N is simply a linear function of the truncated signature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  For this expansion to become exact in the sens of pointwise convergence, we need quite strong regularity assumption on  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' This is the price to pay for the non-parametric nature of our model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Assumption 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' The vector field F has fast decaying derivatives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' In other words, defining  Λk(F) =  sup  I∈{1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=',d}k  ��ΦI  F (y0)  �� ,  we assume that �∞  k=0 dkΛk(F)/k!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' < ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Let y be the solution of the CDE (2), and let (yN,t)t∈[0,1] be its N-th Taylor expansion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Under Assumptions 1, 2, and 3,  we then have, for any t ∈ [0, 1],  ��yt − yN,t  ��  −→  N→+∞ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  (5)  We refer the reader to Friz & Victoir (2008) and Fermanian et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' (2021, Proposition 4) for more details on this result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  While we impose relatively strong regularity assumptions on the vector field F, the assumptions on x are mild (see As-  sumption 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Therefore, our assumptions, while enforcing a fairly high amount of regularity on the dynamical structure,  still accommodate most of the real world data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Also note that Fermanian et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' (2021) give conditions under which As-  sumption 3 is satisfied when F is a layer of a neural network with smooth activation functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' The learning problem  We go back to the statistical learning problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Recall that in practice, we do not observe the continuous paths  {(x1, y1), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , (xn, yn)} but their discretized and fuzzy counterparts {(X1, Y1), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , (Xn, Yn)} measured on a set of  individual grids D = {D1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , Dn} and ¯D = { ¯D1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , ¯Dn}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' We allow for high data heterogeneity: two individuals can  be sampled at very different frequencies and at different time-points, and therefore have different observation grids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  The meshsize of a sampling grid D, denoted by |D| is defined as the largest gap between two successive sampling times,  that is,  |D| = max  ti∈D |ti+1 − ti|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Its cardinality, denoted by #D, is the number of sampling points in D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' We make the following assumption on the sampling  procedure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Assumption 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' For all i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , n,  0 ∈ Di,  #Di ≥ 2,  and  ¯Di ⊂ Di.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Learning the Dynamics of Sparsely Observed Interacting Systems  Figure 1: The workflow of our model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Starting from the left, the first panel describes our modelling hypothesis: the target  and feature time series are linked through an unknown CDE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' The second panel shows the observed data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' The third panel  shows how every observation of the target is mapped to the signature of the corresponding path, how to construct the  dataset SD  N, Y from this data and finally how to learn the SigLasso estimator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  This assumption essentially means that the measurements on all individuals start at 0 and that the sampling grid of Yi is  coarser than the sampling grid of Xi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' We also let |D| = maxi|Di| be the biggest gap between two successive sampling  times within the whole set of individual grids and #D =  n�  i=1  #Di the total number of sampling points of the feature time  series.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' We recall that the random vectors ξi  t, t ∈ Di, are the noises affecting the measurements of xi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' The random vectors  εi  t affect the measurements of yi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' We end with assumptions on the law of these measurement noises.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Assumption 5 (Noise on the feature time series).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' The noises (ξi  t)i∈{1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=',n},t∈Di are i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' vξ-subgaussian random vectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Assumption 6 (Noise on the target time series).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' The noises (εi  t)i∈{1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=',n},t∈ ¯  Di are i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' vε-subgaussian random vectors  and independent from (ξi  t)i∈{1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=',n},t∈Di.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  The goal of the learning procedure is to learn the solution map Ψ, in order to infer the value of y at any time t, given  observations of x up to time t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' We have seen previously that this problem boils down to estimating the matrix θ∗  N via  Equation (4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' The truncation order N ≥ 1 is an hyperparameter and will be selected by cross-validation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Single target measurement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  For the sake of simplicity, we first present the case where Y i is measured only at the end  of the observation period, as in the example of LA measurements in obstetrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' In this case, for all i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , n, we have  mi = 1 such that M = n,  Di = (ti  1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , ti  ki),  and  ¯Di = (ti  ki).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Then Yi ∈ Rp, and we denote by  Y =  �Y1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , Yn�⊤ ∈ Rn×p  the matrix containing all target measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Since we do not have access to the feature paths xi but only to the discrete  measurements Xi, we compute the signature of its linear interpolation normalized by its total variation, sampled up to  final time ti  ki, and denote by SD  N ∈ Rn×sd(N) the matrix of stacked signatures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Note that signatures of piecewise linear  functions are fast to compute with packages such as signatory (Kidger & Lyons, 2020) or iisignature (Reizenstein  & Graham, 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' The complexity to compute the signature truncated at order N of the ith feature time series is of the  order O(#DidN).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Finally, we approximate θ∗  N ∈ Rsd(N)×p by solving the optimisation problem  min  θ∈Rsd(N)×p  1  2n  ��Y − SD  Nθ  ��2  F + Ω(θ),  (6)  where Ω : Rsd(N)×p → R+ is a regularization term and ∥·∥F is the Frobenius norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' We have reduced the complex  problem of learning the solution map Ψ to a simple penalized linear regression in the signature space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' This linear model  on the signature is close to the one studied by Levin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' (2013);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Lyons et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' (2014);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Fermanian (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  o.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='.  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='75  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='75  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='75  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  Time1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='5  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='.  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='.  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='5  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='.  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  Time  4  3  2  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  TimeT  M  TMW7  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='.  6  5  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  2  2  3  2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='75  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='75  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='75  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  Time1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  :  :  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='5  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='.  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='.  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='.  +  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='5  :  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0Learning the Dynamics of Sparsely Observed Interacting Systems  Multiple target measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  We also cover the case when # ¯Di > 1, that is, the target is measured at multiple times  for every individual, as in the example of hemorrhage detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' In this case, we have Yi ∈ Rmi×p and we stack the  different measurement matrices Yi to obtain a matrix Y of size M × p, where M = m1 + · · · + mn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' For any i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , n  and every t ∈ ¯Di, we predict Y i  t using the signature of the linear interpolation of the normalized (Xi  0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , Xi  t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' In this  manner, we will be able to predict Y i  t at every point where Xi  t is sampled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' The exact workflow of our model is described  in Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Theoretical guarantees  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Mathematical setup  We consider a general multiple target measurements setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' To simplify the exposure of our results, we consider an  univariate target path, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', p = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' In this case, the true parameter θ∗  N is a vector of size sd(N) and not a matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' The  general case p ≥ 1, which our algorithm handles as running p Lasso regressions in parallel, is considered in the Appendix  B, were we prove all results in this setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' In addition, to lighten the presentation of the oracle inequality, we also  focus in this section on the case of ω-Lipschitz feature paths, that is, for every i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , n and for all s, t ∈ [0, 1],  ��xi  t − xi  s  �� ≤ ω|t − s|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' We stress that our results are valid for continuous paths of bounded variations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' We let y ∈ RM  be the matrix collecting all unobserved values of the target paths at measurement times such that y = E  �  Y  �  , where the  expectation is taken over the noises εi  t, and define �θN,M as  �θN,M ∈ arg min  θ∈Rsd(N)  1  2M  ��Y − SD  Nθ  ��2  2 + Ω(θ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  (7)  For δ ∈ (0, 1), we define the set  Aξ(δ) =  �  max  ��ξi  t  �� ≤ vξ  √  d + vξ  �  1  C log #D  δ  �  (8)  where the maximum is taken on all i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , n and t ∈ Di, and C is a universal constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' This set is of probability greater  than 1 − δ under Assumption 5 (see Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Similarly, for k ≥ 0 and ¯δ ∈ (0, 1), let  Ck(¯δ) =  �  vε log(2Ndk/¯δ)  and define  Aε(¯δ) =  N  �  k=0  ���ε⊤SD  ,[k]  ��  ∞ ≤ M  1  2 Ck(¯δ)  k!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  �  ,  where SD  ,[k] is the sub-matrix of size M × dk of SD  N associated to the signature coefficients of order k, and ε ∈ RM is a  vector of i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' noise terms satisfying Assumption 6 (see Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Under Assumptions 5 and 6, Aξ(δ) ∩ Aε(¯δ) is of  probability at least (1 − δ)(1 − ¯δ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Let  Ω(θ) =  N  �  k=0  Ck(¯δ)  k!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  √  M  ��θ[k]  ��  1,  (9)  where θ[k] is the subvector of size dk that collects all elements of θ associated to words of size k (see Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  This penalization can be implemented by rescaling the feature matrix SD  N and solving a standard ℓ1-penalized regression  problem (see Appendix C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Our result extends to more general penalties by adapting existing techniques from Chesneau  & Hebiri (2008) for the group-lasso, or Lederer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' (2019) for the hierarchical lasso.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Main results  The error made when learning θ∗  N by �θN,M comes from three different sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Truncating the signature used in the regression at depth N ≥ 1 results in a truncation bias.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Learning the Dynamics of Sparsely Observed Interacting Systems  Table 1: Performance of SigLasso, GRU and Neural CDE in different simulation settings, averaged over 10 iterations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' In  every setting, n = 50, # ¯Di = 5 for all i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , n (and therefore M = 250).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  L2 error  MSE on last point  Setting  SigLasso  GRU  Neural CDE  SigLasso  GRU  Neural CDE  Well-specified  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='13 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='07  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='05 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='42  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='61 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='38  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='73 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='56  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='32 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='60  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='46 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='20  Ill-specified  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='15 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='24 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='11  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='29 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='09 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='19 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='09  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='22 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='15  OU  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='01 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='05 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='06  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='17 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='12  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='018 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='025  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='014 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='020  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='013 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='016  Tumor growth  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='16 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='66 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='09  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='29 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='38  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='35 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='12  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='00 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='38  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='76 ± 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='26  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Discretization of the feature path and the noise affecting each measurement point induce a discretization error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' In  particular, there is a trade-off between sampling frequency and variance of the noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' The measurement error on yi and the finite-sample setting induce a classical estimation error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  The following lemmas bound each of those errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' We first bound the variance of the estimator with arguments borrowed  from Bickel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Under Assumptions 1 and 2, on the set Aε(¯δ) ∩ Aξ(δ), the prediction error  1  2M  ��y − SD  N �θN,M  ��2  2  is bounded above by  1  2M  ��y − SD  Nθ∗  N  ��2  2 + 2CN(¯δ)  √  M  N  �  k=0  dkΛk(F)  k!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  See Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2 for a proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' This inequality decomposes the error into a bias and a variance term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' We denote the  signature matrix of the unobserved paths xi by SN ∈ RM×sd(N).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  As for the bias term, notice that one can write  1  2M  ��y − SD  Nθ∗  N  ��2  2 ≤ 1  M ∥y − SNθ∗  N∥2  2  �  ��  �  Truncation bias  + 1  M  ��SNθ∗  N − SD  Nθ∗  N  ��2  2  �  ��  �  Discretization error  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Bounding each of these terms corresponds to, respectively, Lemmas 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' We stress that the truncation bias is of a  different nature than the discretization error since it depends on a choice of hyperparameter while the latter is inherent to  the data at hand.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Under Assumptions 1 and 2, for any N ≥ 1,  1  M ∥y − SNθ∗  N∥2  2 ≤  �  dN+1ΛN+1(F)  (N + 1)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  �2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Under Assumption 3, the right-hand-side decays exponentially fast with N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' This lemma is an immediate consequence of  Fermanian et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' (2021) (see Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' We now turn to the error induced by the discretization of the feature path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Under Assumptions 1, 4, and 5, on the set Aξ(δ), one has  1  M  ��(SN − SD  N)θ∗  N  ��2  2 ≤ CD,N(δ)  N  �  k=0  dkΛk(F)2  k!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2  ,  where CD,N(δ) is equal to  (2eLN!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' )2  �  ω|D| + vξ  √  d + vξ  �  1  C log #D  δ  �2  and C is a universal constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Learning the Dynamics of Sparsely Observed Interacting Systems  This lemma relies on a fine analysis of the distance between two signature layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' The dependence of CD,N(δ) on sampling  mechanisms and noise is of particular interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' First, the term ω|D| refers to the longest time between two observations  amongst individuals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Not sampling an individual during a long period of time causes a loss in information, which is  bounded by the Lipschitz control ω of the feature path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  The remaining part of CD,N(δ) is a consequence of the noises ξi  t affecting the measurement points of the feature time series  and does not vanish with n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' The emergence of such a bias is a well studied phenomenon in errors-in-variable models, and  cannot be corrected without precise knowledge of the noise’s variance (Loh & Wainwright, 2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Note that if we assume  that the feature paths are measured without noise (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', vξ = 0), the right-hand-side collapses to a discretization error term  proportional to |D|2 and tends to 0 as |D| → 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' The proof of this Lemma is given in Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  From Lemmas 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='1 to 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='3 and the definitions of Aξ and Aε finally we get the following oracle inequality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' The proof is given  in Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='4 (An oracle inequality for learning with signatures).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Under Assumptions 1, 2, 4, 5, and 6, with probability at  least (1 − δ)(1 − ¯δ), the prediction error is bounded above by  1  2M  ���y − SD  N �θN,M  ���  2  2 ≤  �  dN+1ΛN+1(F)  (N + 1)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  �2  (10)  + CD,N(δ)  N  �  k=0  dkΛk(F)2  k!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2  (11)  + 2CN(¯δ)  √  M  N  �  k=0  dkΛk(F)  k!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  (12)  All terms depend on the regularity of the vector field F via the constants Λk(F): the bigger these constants, the faster the  vector field F may vary, making the CDE harder to predict.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' The convergence speed in 1/  √  M is classical.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Also note that  our bound is non-asymptotic and is valid for any M ≥ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  The dependence of the bound on N is highly non-trivial and requires an in-depth analysis of the regularity of F in order to  bound Λk(F), which is out of the scope of this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' The asymptotic behaviour of this oracle inequality is discussed in  Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Experiments  We study the performance of SigLasso obtained by solving the optimization problem (7), where Ω(θ) is defined by Equa-  tion (9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' All details are given in Appendix C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Simulations  We consider several settings of data generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' First, in the well-specified setting, the data is generated from a model with  regular feature paths x (piecewise polynomials) and target paths y wich are solutions to the CDE dyt = tanh(Ayt)dxt,  where A is a randomly drawn matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' In the ill-specified setting, the target y is equal to yt = log ∥ �10  h=1 xt−h∥ for any  t ∈ [0, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' In the third setting, called OU setting, the feature paths are realizations of Brownian motions and the target paths  are Ornstein-Uhlenbeck processes (Borodin & Salminen, 2012) driven by the feature paths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' The last setting corresponds  to the tumor growth model from Simeoni et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' The feature path represents the concentration of a treatment drug,  generated as the squared value of the smooth paths used in the well-specified setting, and the target path y, the weight of  the tumor, is governed by a system of differential equations given in Appendix C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  We compare SigLasso to a GRU and Neural CDE (Kidger et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' We measure the performance of the models with  two metrics on a test set: the mean squared error for predicting the last observation point of the target paths and the L2  error for predicting the full path on a fine grid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  The results are shown in Table 1 and Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' In Figure 2 we consider the well-specified setting and vary the number  of sampling points of the target paths between 1 and 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' In Table 1 it is fixed to 5 but the simulation settings change.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Sampling of both the target and the feature time series is highly irregular.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' SigLasso outperforms Neural CDE and GRU  Learning the Dynamics of Sparsely Observed Interacting Systems  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='5  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='5  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='5  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='5  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  Number of sampling points of Y  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='50  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='75  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='00  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='25  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='50  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='75  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='00  L2 recontruction error on test set  SigLasso  GRU  Neural CDE  Figure 2: L2 reconstruction error of SigLasso, GRU and Neural CDE in the well-specified setting, for varying number of  target samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  2021-04-07  2021-04-19  2021-05-01  2021-05-13  2021-05-25  2021-06-06  2021-06-18  2021-06-30  Days  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='10  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='08  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='06  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='04  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='04  Growth rate  Ground truth  Figure 3: Interpolation (left of dotted line) and prediction (right of dotted line) of HGR in region ˆIle de France for SigLasso.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  The lighter the blue, the smaller the horizon h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  models in generalizing from a few learning points of the target to its full trajectory in all settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' An additional byproduct  of SigLasso’s simple form is its training speed: its is approximately 10 times faster than GRU and 100 times faster than  Neural CDE, including cross-validation to select N and regularization strength (see Appendix C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Forecasting the growth rate of hospitalizations in France during the Covid-19 pandemic  Forecasting hospitalizations in real time during the Covid-19 pandemic is a notably difficult task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' In this experiment,  we train our model to learn the dynamics linking population data related to mobility, vaccination, and weather, and the  hospitalization growth rate (HGR) in each of the 9 metropolitan regions of France based on the data of Paireau et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  The feature time series is specific to each region and 12-dimensional.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' We consider prediction horizons h = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , 14,  meaning that we predict the hospital saturation at time t using the history of the feature time series up to t − h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Using our  notations, we have for each region d = 12, p = 1, n = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' The target is sampled every day during the training period left of  the dotted line in Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' The model is then asked to predict the HGR on the days right of the dotted line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Both GRU and SigLasso learn smooth and precise dynamics, which generalize well above the learning horizon and yield  similar prediction performance (see Appendix C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Neural CDE and the original method proposed by Paireau et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' (2022)  perform poorly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Figure 3 shows an example of reconstruction and prediction of HGR obtained with SigLasso.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Conclusion  We have introduced a novel CDE-based model for interacting systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Drawing on the theory of signatures, we derive  an oracle bound that depends explicitly on the roughness of the data sampling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' We illustrate the high performance of our  approach on synthetic and real-world data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  The obtained theoretical guarantees rely on strong regularity assumptions on the vector field F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' The exact approximation  properties of this class of vector field are a very interesting direction for future work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Considering other penalties that take  into account the underlying structure of θ∗  N would also be an interesting extension of our work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Learning the Dynamics of Sparsely Observed Interacting Systems  References  Bickel, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Ritov, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', and Tsybakov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Simultaneous analysis of lasso and dantzig selector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' The Annals of Statistics,  37(4):1705–1732, 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Borodin, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' and Salminen, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Handbook of Brownian Motion-Facts and Formulae.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Birkh¨auser, Basel, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Brunton, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Noack, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', and Koumoutsakos, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Machine learning for fluid mechanics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Annual review of fluid  mechanics, 52:477–508, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Buehler, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Horvath, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Lyons, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Arribas, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', and Wood, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' A data-driven market simulator for small data environ-  ments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' arXiv preprint arXiv:2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='14498, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Chen, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='-T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Integration of paths—a faithful representation of paths by non-commutative formal power series.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Transactions  of the American Mathematical Society, 89:395–407, 1958.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Chen, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Rubanova, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Bettencourt, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', and Duvenaud, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Neural ordinary differential equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' In Bengio,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Wallach, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Larochelle, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Grauman, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Cesa-Bianchi, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', and Garnett, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' (eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' ), Advances in Neural Information  Processing Systems, volume 31, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' 6572–6583.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Curran Associates, Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Chesneau, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' and Hebiri, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Some theoretical results on the grouped variables lasso.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Mathematical Methods of Statistics,  17(4):317–326, 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  De Brouwer, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Simm, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Arany, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', and Moreau, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' GRU-ODE-Bayes: Continuous modeling of sporadically-observed  time series.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' In Wallach, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Larochelle, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Beygelzimer, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=", d'Alch´e-Buc, F." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Fox, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', and Garnett, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' (eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' ), Advances  in Neural Information Processing Systems, volume 32, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' 7379–7390.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Curran Associates, Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Fattahi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Matni, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', and Sojoudi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Learning sparse dynamical systems from a single sample trajectory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' In 2019 IEEE  58th Conference on Decision and Control (CDC), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' 2682–2689.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' IEEE, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Fermanian, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Embedding and learning with signatures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Computational Statistics & Data Analysis, 157:107148, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Fermanian, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Functional linear regression with truncated signatures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Journal of Multivariate Analysis, 192:105031, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Fermanian, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Marion, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Vert, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='-P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', and Biau, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Framing RNN as a kernel method: A neural ODE approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' In  Ranzato, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Beygelzimer, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Dauphin, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Liang, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', and Vaughan, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' (eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' ), Advances in Neural Information  Processing Systems, volume 34, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' 3121–3134.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Curran Associates, Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Friz, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' and Victoir, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Euler estimates for rough differential equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Journal of Differential Equations, 244:388–412,  2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Friz, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' and Victoir, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Multidimensional Stochastic Processes as Rough Paths: Theory and Applications, volume  120 of Cambridge Studies in Advanced Mathematics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Cambridge University Press, Cambridge, 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Gehring, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Auli, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Grangier, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Yarats, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', and Dauphin, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Convolutional sequence to sequence learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' In  Precup, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' and Teh, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' (eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' ), Proceedings of the 34th International Conference on Machine Learning, volume 70,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' 1243–1252.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' PMLR, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Greydanus, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Dzamba, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', and Yosinski, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Hamiltonian neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' In Wallach, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Larochelle, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Beygelzimer,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=", d'Alch´e-Buc, F." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Fox, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', and Garnett, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' (eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' ), Advances in Neural Information Processing Systems, volume 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Curran Associates, Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Han, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Jentzen, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', and E, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Solving high-dimensional partial differential equations using deep learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Proceedings  of the National Academy of Sciences, 115(34):8505–8510, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Hochreiter, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' and Schmidhuber, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Long short-term memory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Neural Computation, 9:1735–1780, 1997.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Kidger, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' On neural differential equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' arXiv preprint arXiv:2202.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='02435, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Kidger, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' and Lyons, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Signatory: differentiable computations of the signature and logsignature transforms, on both cpu  and gpu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' In International Conference on Learning Representations, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Learning the Dynamics of Sparsely Observed Interacting Systems  Kidger, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Bonnier, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Perez Arribas, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Salvi, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', and Lyons, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Deep signature transforms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' In Wallach, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Larochelle, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=',  Beygelzimer, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=", d'Alch´e-Buc, F." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Fox, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', and Garnett, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' (eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' ), Advances in Neural Information Processing Systems,  volume 32, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' 3099–3109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Curran Associates, Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Kidger, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Morrill, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Foster, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', and Lyons, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Neural controlled differential equations for irregular time series.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' In  Larochelle, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Ranzato, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Hadsell, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Balcan, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', and Lin, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' (eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' ), Advances in Neural Information Processing  Systems, volume 33, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' 6696–6707.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Curran Associates, Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Lagaris, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Likas, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', and Fotiadis, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Artificial neural networks for solving ordinary and partial differential equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  IEEE transactions on neural networks, 9(5):987–1000, 1998.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Lederer, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Yu, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', and Gaynanova, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Oracle inequalities for high-dimensional prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Bernoulli, 25(2):1225–1255,  2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Lemercier, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Salvi, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Damoulas, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Bonilla, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', and Lyons, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Distribution regression for sequential data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' In Banerjee,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' and Fukumizu, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' (eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' ), Proceedings of The 24th International Conference on Artificial Intelligence and Statistics,  volume 130, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' 3754–3762.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' PMLR, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Levin, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Lyons, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', and Ni, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Learning from the past, predicting the statistics for the future, learning an evolving system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  arXiv preprint arXiv:1309.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0260, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Loh, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='-l.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' and Wainwright, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' High-dimensional regression with noisy and missing data: Provable guarantees with  non-convexity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' In Shawe-Taylor, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Zemel, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Bartlett, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Pereira, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', and Weinberger, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' (eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' ), Advances in Neural  Information Processing Systems, volume 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Curran Associates, Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Long, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Lu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Ma, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', and Dong, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' PDE-net: Learning PDEs from data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' In Dy, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' and Krause, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' (eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' ), Proceedings  of the 35th International Conference on Machine Learning, volume 80, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' 3208–3216.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' PMLR, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Lyons, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' and McLeod, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Signature methods in machine learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' arXiv preprint arXiv:2206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='14674, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Lyons, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Caruana, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', and L´evy, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Differential Equations driven by Rough Paths, volume 1908 of Lecture Notes in  Mathematics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Springer, Berlin, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Lyons, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Ni, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', and Oberhauser, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' A feature set for streams and an application to high-frequency financial tick data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' In  Proceedings of the 2014 International Conference on Big Data Science and Computing, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' ACM, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Marion, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Fermanian, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Biau, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', and Vert, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='-P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Scaling resnets in the large-depth regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  arXiv preprint  arXiv:2206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='06929, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Marx, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' and Eilers, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Generalized linear regression on sampled signals and curves: a P-spline approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Techno-  metrics, 41:1–13, 1999.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Morrill, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Fermanian, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Kidger, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', and Lyons, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' A generalised signature method for multivariate time series feature  extraction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' arXiv preprint arXiv:2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='00873, 2020a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Morrill, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Kidger, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Yang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', and Lyons, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Neural controlled differential equations for online prediction tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' arXiv  preprint arXiv:2106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='11028, 2021a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Morrill, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Salvi, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Kidger, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', and Foster, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Neural rough differential equations for long time series.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' In Meila, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' and  Zhang, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' (eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' ), Proceedings of the 38th International Conference on Machine Learning, volume 139, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' 7829–7838.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  PMLR, 2021b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Morrill, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Kormilitzin, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Nevado-Holgado, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Swaminathan, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Howison, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', and Lyons, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Utilization  of the signature method to identify the early onset of sepsis from multivariate physiological time series in critical care  monitoring.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Critical Care Medicine, 48:e976–e981, 2020b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Morris, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Functional regression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Annual Review of Statistics and Its Application, 2:321–359, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Paireau, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Andronico, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Hoz´e, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Layan, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Crepey, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Roumagnac, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Lavielle, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Bo¨elle, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', and Cauchemez,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' An ensemble model based on early predictors to forecast covid-19 health care demand in france.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Proceedings of the  National Academy of Sciences, 119(18):e2103302119, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Learning the Dynamics of Sparsely Observed Interacting Systems  Papavasiliou, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' and Ladroue, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Parameter estimation for rough differential equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' The Annals of Statistics, 39(4):  2047–2073, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Pedregosa, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Varoquaux, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Gramfort, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Michel, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Thirion, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Grisel, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Blondel, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Prettenhofer, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Weiss, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=',  Dubourg, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Vanderplas, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Passos, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Cournapeau, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Brucher, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Perrot, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', and Duchesnay, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Scikit-learn:  Machine learning in Python.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Journal of Machine Learning Research, 12:2825–2830, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Ramsay, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' and Dalzell, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Some tools for functional data analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Journal of the Royal Statistical Society.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Series B  (Methodological), 53:539–561, 1991.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Ramsay, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' and Silverman, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Functional Data Analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' 2nd Edition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Springer, New York, 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Reizenstein, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' and Graham, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Algorithm 1004: The iisignature library: Efficient calculation of iterated-integral  signatures and log signatures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' ACM Transactions on Mathematical Software, 46(1):1–21, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Rubanova, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Chen, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', and Duvenaud, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Latent ordinary differential equations for irregularly-sampled time  series.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' In Wallach, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Larochelle, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Beygelzimer, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=", d'Alch´e-Buc, F." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Fox, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', and Garnett, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' (eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' ), Advances in  Neural Information Processing Systems, volume 32, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' 5320–5330.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Curran Associates, Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Simeoni, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Magni, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Cammia, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', De Nicolao, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Croci, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Pesenti, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Germani, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Poggesi, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', and Rocchetti, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Predictive pharmacokinetic-pharmacodynamic modeling of tumor growth kinetics in xenograft models after administra-  tion of anticancer agents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Cancer research, 64(3):1094–1101, 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Sutskever, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Vinyals, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', and Le, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Sequence to sequence learning with neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  In Ghahramani, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=',  Welling, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Cortes, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Lawrence, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', and Weinberger, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' (eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' ), Advances in Neural Information Processing Systems,  volume 27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Curran Associates, Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Vershynin, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Introduction to the non-asymptotic analysis of random matrices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' arXiv preprint arXiv:1011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='3027, 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Vershynin, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' High-dimensional probability: An introduction with applications in data science, volume 47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Cambridge  university press, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Wang, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Wu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Taylor, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Lyons, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Liakata, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Nevado-Holgado, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', and Saunders, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Learning to detect  bipolar disorder and borderline personality disorder with language and speech in non-clinical interviews.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Interspeech  2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' 437–441, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Willard, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Jia, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Xu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Steinbach, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', and Kumar, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Integrating physics-based modeling with machine learning: A  survey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' arXiv preprint arXiv:2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='04919, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Yang, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Lyons, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Ni, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Schmid, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', and Jin, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Developing the path signature methodology and its application to  landmark-based human action recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' In Yin, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' and Zariphopoulou, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' (eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' ), Stochastic Analysis, Filtering, and  Stochastic Optimization: A Commemorative Volume to Honor Mark H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Davis’s Contributions, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' 431–464.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Springer,  2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Zubov, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', McCarthy, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Ma, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Calisto, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Pagliarino, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Azeglio, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Bottero, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Luj´an, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Sulzer, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Bharambe, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=',  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' NeuralPDE: Automating physics-informed neural networks (PINNs) with error approximations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' arXiv preprint  arXiv:2107.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='09443, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Zwillinger, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Handbook of differential equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Academic Press, Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', London, 1989.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Learning the Dynamics of Sparsely Observed Interacting Systems  Supplementary Material  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Mathematical details  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' The Riemann-Stieltjes integral  We fitst recall two key properties on the Riemann-Stieljes integral.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' For a general presentation of the Riemann-Stieltjes  integral, we refer to Friz & Victoir (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Proposition A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Let x ∈ C1-var  L  ([0, 1], Rd) and y : [0, 1] → Rd be a continuous path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Then  ����  � t  0  ysdxs  ���� ≤ ∥y∥∞,[0,t] ∥x∥1-var,[0,t]  We refer the reader to Friz & Victoir (2010, Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2) for a proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Proposition A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2 (Integration by parts).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Let x, y ∈ C1-var  L  ([0, 1], Rd).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Then  � t  s  yudxu +  � t  s  xudyu = ytxt − ysxs  See Friz & Victoir (2010, Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='4) for a proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' The truncated tensor algebra  This section introduces notations and definitions on the space in which signatures are defined, namely, the tensor algebra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  While for the exposition of our main results, the truncated signature of a path x ∈ C1-var  L  ([0, 1], Rd) at depth N ≥ 1 can  be assimilated to an element of Rsd(N), it is often useful to place ourselves in the tensor algebra to obtain finer bounds or  technical results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Let x ∈ C1-var  L  ([0, 1], Rd) be a path of bounded variation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' For a word I = (i1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , ik) ∈ {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , d}k of size k, the  signature coefficient SI(x[0,1]) can be seen as an element of the k-th tensor product of Rd with itself, denoted by  �  Rd�⊗k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  For instance, the coefficients of order k = 1 can be written as a vector and the coefficients of order k = 2 as a matrix, and  so on, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=',  X1  [0,1] =  �  ���  � 1  0 dx(1)  s  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  � 1  0 dx(d)  s  �  ���  and  X2  [0,1] =  �  ���  � 1  0 dx(1)  s dx(1)  s  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  � 1  0 dx(1)  s dx(d)  s  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  � 1  0 dx(d)  s dx(1)  s  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  � 1  0 dx(d)  s dx(d)  s  �  ��� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  We now define a norm on (Rd)⊗k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Let a ∈ (Rd)⊗k and (e1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , ed) be the canonical basis of Rd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Then (ei1 ⊗ · · · ⊗  eik)(i1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=',ik)∈{1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=',d}k is a basis of (Rd)⊗k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' We can thus write a as a = (aI)I∈{1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=',d}k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' For every k ≥ 0, the vector space  (Rd)⊗k is naturally endowed with the norm  ∥a∥2  (Rd)⊗k =  �  I∈{1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=',d}k  �  aI�2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Remark that this norm satisfies for any x ∈ (Rd)⊗k and y ∈ (Rd)⊗m,  ∥x ⊗ y∥(Rd)⊗(k+m) = ∥x∥(Rd)⊗k ∥y∥(Rd)⊗m .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  (13)  We refer to Fermanian et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' (2021) for further deails.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' The signature truncated at depth N ≥ 1 collects elements from  R,  �  Rd�⊗2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' ,  �  Rd�⊗N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' It can thus be seen as an element of the truncated tensor algebra  TN(Rd) = R ⊕  �  Rd�⊗2 ⊕ · · · ⊕  �  Rd�⊗N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Learning the Dynamics of Sparsely Observed Interacting Systems  Let a = (a0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , aN) ∈ TN(Rd), where every ak ∈ (Rd)⊗k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' We define the norm  ∥a∥TN(Rd) =  � N  �  k=0  ∥ak∥2  (Rd)⊗k  �1/2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  To clarify, if we consider the truncated signature of x at depth N ≥ 1, which is an element of TN(Rd), then  ��SN(x[0,t])  ��  TN(Rd) =  � N  �  k=0  ���Xk  [0,t]  ���  2  (Rd)⊗k  �1/2  =  � N  �  k=0  �  I∈{1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=',d}k  SI(x[0,t])2�1/2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Note that this norm is exactly equivalent to the Euclidian norm of Rsd(N), which is the space we consider in the exposition  of our main results for the sake of simplicity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  We are now ready to define the tensor product on the truncated tensor algebra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' For two elements a = (a0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , aN) and  b = (b0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , bN) both in TN(Rd), we define  a ⊗ b = (c0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , cj, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , cN),  where cj =  j  �  k=0  ak ⊗ bj−k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  For any k = 0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , N, we let πk : TN(Rd) → (Rd)⊗k be the canonical projection of TN(Rd) onto (Rd)⊗k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' More  precisely, for every a = (a0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , aN) ∈ TN(Rd),  πk(a) = ak  We also define the canonical projection Πk : TN(Rd) → Tk(Rd) defined by  Πk(a) = (a0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , ak) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' The differential product  We first define the differential product, in order to give a precise statement of Assumption 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Definition A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Let F, G : Rp → Rp be two smooth vector fields, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', each of their components is C∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Denote by J(·)  the Jacobian matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' The differential product F ⋆ G : Rp → Rp is the smooth vector field defined for any h ∈ Rp  (F ⋆ G)(h) =  e  �  j=1  ∂G  ∂hj  (h)Fj(h) = J(G)(h)F(h).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  The differential product is not associative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' We therefore use the convention to evaluate it from right to left, that is,  F 1 ⋆ F 2 ⋆ F 3 = F 1 ⋆  �  F 2 ⋆ F 3�  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Let F : Rp → Rp×d be a smooth vector field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' We write F 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , F d the columns of F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Every F i, for i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , d, can  thus be seen as a map from Rp to Rp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Recall that y0 ∈ Rp is the initial condition of the CDE defined in Assumption 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Let  I = (i1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , ik) ∈ {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , d}k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' We now define  ΦI  F(y0) =  �  F i1 ⋆ · · · ⋆ F ik�  (y0) ∈ Rp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  We refer to Fermanian et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' (2021) for greater details on the differential product.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' We now define for all k ≥ 1  Λk(F) =  sup  1≤i1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=',ik≤d  ��ΦI  F(y0)  �� ∈ R,  (14)  and use the convention Λ0(F) = ∥y0∥.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Remark that Assumption 3 implies that  dN+1ΛN+1(F)  (N + 1)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  −→  N→+∞ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Learning the Dynamics of Sparsely Observed Interacting Systems  As an immediate consequence, the truncation bias  �  dN+1ΛN+1(F)  (N + 1)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  �2  introduced in Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2, vanishes as N grows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Analogy with the Taylor extension  The definition of the Taylor expansion of a CDE exposed in the previous subsection is technical.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' However, it can simply  be thought of as a generalization of the the classical Taylor expansion of a C∞ function f : R → R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Recall that in this  case, the Taylor expansion at 0 evaluated at t ∈ R of order N ∈ N writes as a power series  f(t) ≈ f(0) + f ′(0)  1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  t + · · · + f (N)(0)  N!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  tN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  (15)  Every element of this power series is a product of two terms: the derivatives of f encode some information about the  regularity of f at the initial point 0 and do not depend on t, while the polynomial terms tk allow this linearized form to  evolve with time t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Remark that these polynomial terms do not depend on f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Similarly, Equation (3) is also a sum of products of two terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' On the one hand, the evolving nature of the system,  instead of being handled by the polynomial terms tk, are now captured by the signature coefficients SI(x[0,t]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' As the  polynomial terms, they do not depend on F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' On the other hand, the information about the initial value of the system at  time t = 0 and the dynamics of F are summarized by the differential product ΦI  F (y0), which play the same role as the  successive derivatives in Equation (15).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' To capture the multivariate nature of the paths, the Taylor expansion is summed  over multi-indexes, or words, I = (i1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , ik) ∈ {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , d}k of size k for k ∈ N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Properties of subgaussian random vectors  We start with the definition of a subgaussian random variable, see Vershynin (2010) for more details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Definition A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' A real-valued random variable X is said to be σ2-subgaussian if for all t > 0  P(X > t) ≤ exp(−t2/σ2),  or, equivalently, if for all t ∈ R  E(etX) ≤ exp(−ct2σ2),  where c is an universal constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' A random vector Z is subgaussian if, for any vector c of norm 1, ⟨Z, c⟩ is subgaussian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  The norm of a sequence of d subgaussian random variables concentrates around  √  d, as stated by the following lemma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Let X1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , Xn be a sequence of i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' σ2-subgaussian random variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Let X = (X1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , Xd) ∈ Rd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  There exists a universal constant C such that for all t > 0  P(∥X∥2 ≥ t + σ  √  d) ≤ exp(−Ct2/σ2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' We refer to Vershynin (2018, Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='1) for a proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  We can use this lemma to bound the maximum of n sequences of d subgaussian random variables with high probability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Let X1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , Xn be a sequence of i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' σ2-subgaussian random variables, such that for all i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , n,  Xi = (Xi1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , Xid).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Then there exists a universal constant such that for all δ ∈ (0, 1)  P  �  max  i=1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=',n ∥Xi∥ ≤ σ  √  d + σ  �  1  C log(n/δ)  �  ≥ 1 − δ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Learning the Dynamics of Sparsely Observed Interacting Systems  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Using Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='5 and a union bound, we have  P  �  max  i=1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=',n ∥Xi∥ ≥ σ  √  d + σ  �  1  C log(n/δ)  �  = P  �  n  �  i=1  �  ∥Xi∥2 ≥ σ  √  d + σ  �  1  C log(n/δ)  ��  ≤  n  �  i=1  P  �  ∥Xi∥2 ≥ σ  √  d + σ  �  1  C log(n/δ)  �  ≤ δ,  which yields the desired inequality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Notice that the universal constant is identical between both lemmas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' As a consequence of this last lemma, under Assump-  tion 5, the set  Aξ(δ) =  �  max  i=1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=',n,t∈Di  ��ξi  t  �� ≤ vξ  √  d + vξ  �  1  C log(#D/δ)  �  (16)  where #D =  n�  i=1  #Di is of probability at least 1 − δ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  We also need the following lemma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Let X1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , Xn be a sequence of i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' σ2-subgaussian random variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Let Z1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , Zn be random vari-  ables such that for all i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , n, |Zi| ≤ α almost surely.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Then  n�  i=1  XiZi is nσ2α2-subgaussian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' We use the characterization of subgaussian random variables by their characteristic function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' For all t > 0,  E  �  et �n  i=1 XiZi  �  = E  �  n  �  i=1  E  �  etXiZi | Z1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , Zn  ��  ≤ E  �  n  �  i=1  E  �  etXiα��  ≤ E  �  ect2nα2σ2�  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  This finally yields that  E  �  et � XiZi  �  ≤ E  �  ect2nα2σ2�  ,  which concludes the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Proofs  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Preliminary notations  Let (E, ∥·∥E) be a normed vector space and x : [0, 1] → E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' The supremum norm of x is defined for all t ∈ [0, 1] as  ∥x∥∞,[0,t] = sup  s∈[0,t]  ∥xs∥E .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  When referring to the total variation ∥x∥1-var,[0,1] of a path x : [0, 1] → Rd over the whole domain, depending on the  mathematical context, we will sometimes drop the time subscript and simply write ∥x∥1-var.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  When referring to a matrix A = (Aij) ∈ Rn×p, we define classicaly the infinite and Frobenius norms by  ∥A∥∞ =  max  i=1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=',n  j=1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=',p  |Aij|  and  ∥A∥F =  �  �  �  �  �  i=1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=',n  j=1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=',p  |Aij|2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  We now introduce some notations to take advantage of the structure of θ∗  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' The true parameter of the Taylor expansion of  the model CDE, defined in Equation (4), can be written in block notation as  Learning the Dynamics of Sparsely Observed Interacting Systems  θ∗  N =  �  �������������������������������������  θ∗  [0],1  · ·  θ∗  [0],p  θ∗  [1],1  · ·  θ∗  [1],p  θ∗  [2],1  · ·  θ∗  [2],p  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  θ∗  [N],1  · ·  θ∗  [N],p  �  �������������������������������������  ∈ Rsd(N)×p,  where  θ∗  [k],ℓ ∈ Rdk×1, k = 0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , N, ℓ = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  (17)  Every column of θ∗  N corresponds to a dimension of the target, while blocks of lines correspond to signatures layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Thus  for every k = 0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , N and ℓ = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , p, θ∗  [k],ℓ is a column vector of size dk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Similarly, for a general θ ∈ Rsd(N)×p and the SigLasso estimator �θN,M, we will refere to the blocks forming these matrices  as respectively θ[k],ℓ and �θ[k],ℓ, for k = 0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , N and ℓ = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Likewise, the signature feature matrix SD  N ∈ RM×sd(N) can be written in block notation as  SD  N =  �  1  SD  ,[1]  SD  ,[2]  · ·  SD  ,[N]  �  =  �  ��  1  SD  1,[1]  SD  1,[2]  SD  1,[N]  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  · ·  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  1  SD  n,[1]  SD  n,[2]  SD  n,[N]  �  �� ,  where for any k = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , N, SD  ,[k] ∈ RM×dk and, for every individual i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , n, SD  i,[k] ∈ Rmi×dk (recall that mi is  the number of measurements of the target path yi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' More precisely, given her target sampling grid ¯Di = (¯ti  1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , ¯ti  mi), the  individual-specific signature block of depth k is equal to  SD  i,[k] =  �  ���  1  S(1)(Xi  [0,¯ti  1])  · ·  S(d,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=',d)(Xi  [0,¯ti  1])  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  1  S(1)(Xi  [0,¯timi])  · ·  S(d,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=',d)(Xi  [0,¯ti  mi])  �  ��� ,  where the path t → Xi  t is a linear interpolation of the observed time series Xi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' The same notations will be used for the  true signature feature matrix SN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' We use the bracket notation [·] both in θ∗  N and SD  N to emphasise that both the columns of  the feature matrix and the lines of learned parameter correspond to words of the alphabet {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , d}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  The unobserved matrix of true values of the target writes as  Learning the Dynamics of Sparsely Observed Interacting Systems  y =  �  ��  y1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  yn  �  �� =  �  ��  y1  1  · ·  y1  p  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  yn  1  · ·  yn  p  �  �� =  �  ��������������  y1  1,¯t1  1  · ·  y1  p,¯t1  1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  y1  1,¯t1m1  · ·  y1  p,¯t1m1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  yn  1,¯tn  1  · ·  yn  p,¯tn  1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  yn  1,¯tn  mn  · ·  yn  p,¯tn  mn  �  ��������������  ∈ RM×p  (18)  and the measurement matrix Y ∈ RM×p can be written in a similar fashion as  Y =  �  ��  Y1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Yn  �  �� =  �  ��  Y1  1  · ·  Y1  p  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Yn  1  · ·  Yn  p  �  �� =  �  ��������������  Y 1  1,¯t1  1  · ·  Y 1  p,¯t1  1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Y 1  1,¯t1m1  · ·  Y 1  p,¯t1m1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Y n  1,¯tn  1  · ·  Y n  p,¯tn  1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Y n  1,¯tn  mn  · ·  Y n  p,¯tn  mn  �  ��������������  =  �  ��������������  y1  1,¯t1  1 + ε1  1,¯t1  1  · ·  y1  p,¯t1  1 + ε1  p,¯t1  1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  y1  1,¯t1m1 + ε1  1,¯t1m1  · ·  y1  p,¯t1m1 + ε1  p,¯t1m1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  yn  1,¯tn  1 + εn  1,¯tn  1  · ·  yn  p,¯tn  1 + εn  p,¯tn  1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  yn  1,¯tn  mn + εn  1,¯tn  mn  · ·  yn  p,¯tn  mn + εn  p,¯tn  mn  �  ��������������  (19)  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Proof of Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='1  Using the definition of Λk, we get the following proposition which allows to obtain an explicit dependence of the oracle  bound on the regularity of F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Proposition B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Let θ∗  N be defined as in Equation (4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Then  ∥θ∗  N∥2  F ≤  N  �  k=0  dkΛk(F)2,  and, for all k = 0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , N and ℓ = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , p,  ��θ∗  [k],ℓ  ��  1 ≤ dkΛk(F).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' By definition,  ∥θ∗  N∥2  F =  N  �  k=0  �  1≤i1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=',ik≤d  ��F i1 ⋆ · · · ⋆ F ik(y0)  ��2  2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Since for all (i1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , ik) ∈ {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , d}k,  ��F i1 ⋆ · · · ⋆ F ik(y0)  ��2  2 ≤ Λk(F)2,  we get  N  �  k=0  �  1≤i1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=',ik≤d  ��F i1 ⋆ · · · ⋆ F ik(y0)  ��2  2 ≤  N  �  k=0  �  1≤i1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=',ik≤d  Λk(F)2  ≤  N  �  k=0  dkΛk(F)2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Learning the Dynamics of Sparsely Observed Interacting Systems  We now turn to the second inequality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' For k = 0, the inequality holds by definition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' For k = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , N and ℓ = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , p,  by definition of the ℓ1 norm,  ���θ∗  [k],·  ���  1 =  �  1≤i1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=',ik≤d  ��ΦI  F(y0)  ��  1 ,  This yields  ���θ∗  [k],·  ���  1 ≤ dkΛk(F)  and thus  ���θ∗  [k],ℓ  ���  1 ≤ dkΛk(F)  for ℓ = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  The following lemma is needed to leverage classical proof techniques to bound the prediction error of the Lasso estimator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Lemma B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Let x ∈ C1-var  L  ([0, 1], Rd).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Then conditionally on Aξ(δ), for a given signature layer k ≥ 1, the maximum  among all signature coefficients and individuals is bounded from above, that is  ���SD  ,[k]  ���  ∞ ≤ 1  k!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='.  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' It is well known (see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', Fermanian, 2022, Proposition 3) that if Xk is the signature of a path x ∈ C1-var  L  ([0, 1], Rd),  then  ��Xk��  (Rd)⊗k ≤ ∥x∥k  1-var  k!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  As a consequence, for every word I of size k, one gets  ��SI(x))  �� ≤ ∥x∥k  1-var  k!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  The matrix SD  N is constructed by taking signatures of linear interpolations of the Xis normalized by their total variation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' It  therefore contains only signatures of paths of total variation bounded by 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Taking the maximum on I ∈ {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , d}k and  individuals i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , n, we get  ���SD  ,[k]  ���  ∞ ≤ 1  k!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='.  This final inequality being stated, we can now go back to the proof of Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' We prove it in full generality for p ≥ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  In this proof, we make extensive use of the notations introduced in Subsection B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='1 and refer the reader to it if a notation is  unclear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' In all the proof, we place ourselves on the set Aξ(δ) defined by Equation (8), which ensures that the matrix SD  N,  seen as a random quantity, is well defined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Recall that we have two sources of randomness: the feature noises ξi  t on the  Xis and the target noises εi  t on the Yis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' The feature noises appear only in SD  N and make it a random quantity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' For SD  N to  be well-defined, we then need the total variation of the linear interpolation of the feature time series Xi to be finite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' This  holds on the set Aξ(δ) since all noises are then bounded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Recall that we have defined �θN,M as  �θN,M ∈  arg min  θ∈Rsd(N)×p  1  2M  ��Y − SD  Nθ  ��2  F + Ω(θ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Note that  1  2M  ��Y − SD  Nθ  ��2  F + Ω(θ) =  p  �  ℓ=1  1  2M  ��Yℓ − SD  Nθ[·],ℓ  ��2  2 + Ω(θ[·],ℓ)  Learning the Dynamics of Sparsely Observed Interacting Systems  where Yℓ ∈ RM is the ℓ-th column of the target measurement matrix defined in Equation (19).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' The quantity θ[·],ℓ ∈ Rsd(N)  is the ℓ-th column of the parameter matrix defined in Equation (17).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  By definition, for any θ ∈ Rsd(N), we have  ���Yℓ − SD  N �θ[·],ℓ  ���  2  2 ≤  ��Yℓ − SD  Nθ  ��2  2 + Ω(θ) − Ω(�θ[·],ℓ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Moreover, letting εℓ = (ε1  ℓ,¯t1  1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , εn  ℓ,¯tn  mn )⊤ ∈ RM be a vector of i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' noises (see Equation (19)), we have Yℓ = yℓ + εℓ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  The Pythagorean theorem then yields for any θ ∈ Rsd(N),  ��Yℓ − SD  Nθ  ��2  2 =  ��yℓ − SD  Nθ  ��2  2 + ∥εℓ∥2 + 2⟨εℓ, yℓ − SD  Nθ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Putting these two equations together, we obtain  1  2M  ���yℓ − SD  N �θ[·],ℓ  ���  2  2 ≤  1  2M  ��yℓ − SD  Nθ  ��2  2 + 1  M ⟨εℓ, SD  N(�θ[·],ℓ − θ)⟩ + Ω(θ) − Ω(�θ[·],ℓ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  (20)  We now work at each layer of the signature matrix SD  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Towards that end, we rewrite  SD  N  ��θ[·],ℓ − θ  �  =  N  �  k=0  SD  ,[k]  ��θ[k],ℓ − θ[k]  �  ,  and bound  �  εℓ, SD  N(�θ[·],ℓ − θℓ)  �  =  N  �  k=0  �  εℓ, SD  ,[k](�θ[k],ℓ) − θ[k])  �  ≤  N  �  k=0  ∥ε⊤  ℓ SD  ,[k]∥∞∥�θ[k],ℓ − θ[k]∥1  by ℓ1 − ℓ∞ norms duality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' We fix k and study the term ∥ε⊤  ℓ SD  ,[k]∥∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Lemma B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2 ensures that each of the words of the  signature layer of depth k is bounded by 1/k!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='. As a consequence, by Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='7, under Assumption 6, every element of  the vector ε⊤  ℓ SD  ,[k] is vεM/k!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2-subgaussian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' It follows that, for any real number µ > 0,  P  �  ∥ε⊤  ℓ SD  ,[k]∥∞ > µ  �  ≤ 2dk exp  �  − (k!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' )2µ2  vεM  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  We furthermore place ourselves on Aε(¯δ) defined by  Aε(¯δ) =  p�  ℓ=1  N  �  k=0  �  ∥ε⊤  ℓ SD  ,[k]∥∞ ≤ 1  k!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  �  vεM log(2pNdk/¯δ)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  We have just seen that, under Assumption 6 (and still conditionally on Aξ(δ)), one has P(Aε(¯δ)) ≥ 1 − ¯δ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Putting together  all terms in Equation (20) and plugging the definition of Ω given in Equation (9), we obtain that, on the set Aε(¯δ) ∩ Aξ(δ),  for all θ ∈ Rsd(N)×p,  1  2M  ���y − SD  N �θN,M  ���  2  F ≤  1  2M  ��y − SD  Nθ  ��2  F  +  p  �  ℓ=1  N  �  k=0  � 1  M ∥ε⊤  ℓ SD  ,[k]∥∞∥�θ[k],ℓ − θ[k],ℓ∥1 + Ck(¯δ)  k!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  √  M  �  ∥θ[k],ℓ∥1 − ∥�θ[k],ℓ∥1  ��  ≤  1  2M  ��y − SD  Nθ  ��2  F  +  p  �  ℓ=1  N  �  k=0  1  k!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  √  M  �  vε log(2pNdk/¯δ)  �  ∥�θ[k],ℓ − θ[k],ℓ∥1 + ∥θ[k],ℓ∥1 − ∥�θ[k],ℓ∥1  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Choosing θ = θ∗  N, by the triangular inequality,  ∥�θ[k],ℓ − θ∗  [k],ℓ∥1 + ∥θ∗  [k],ℓ∥1 − ∥�θ[k],ℓ∥1 ≤ 2∥θ∗  [k],ℓ∥1,  Learning the Dynamics of Sparsely Observed Interacting Systems  which finally gives us  1  2M  ���y − SD  N �θN,M  ���  2  F ≤  1  2M  ��y − SD  Nθ∗  N  ��2  F +  2  √  M  �  vε log(2pNdN/¯δ)  p  �  ℓ=1  N  �  k=0  ∥θ∗  [k],ℓ∥1  k!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  ≤  1  2M  ��y − SD  Nθ∗  N  ��2  F + 2p  √  M  �  vε log(2pNdN/¯δ)  N  �  k=0  dkΛk(F)  k!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  =  1  2M  ��y − SD  Nθ∗  N  ��2  F + 2pCN(¯δ)  √  M  N  �  k=0  dkΛk(F)  k!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  ,  where the last inequality comes from Proposition B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' To conclude the proof, we just need to compute the probability of  the set Aξ(δ) ∩ Aε(¯δ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' It is an immediate consequence of Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='6 that P(Aξ(δ)) ≥ 1 − δ, and we have seen that  P(Aε(¯δ)|Aξ(δ)) ≥ 1 − ¯δ, which yields that  P(Aξ(δ) ∩ Aε(¯δ)) ≥ (1 − ¯δ)(1 − δ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Proof of Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2  This proof relies on bouding the remainder of the Taylor expansion of the CDE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' For every i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , n and a given point ti ∈ ¯Di, one has, using the upper bound of the approximation error of a  CDE by its Taylor expansion provided by Fermanian et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' (2021, Proposition 4)  ���yi  ti − SN(xi  [0,ti])θ∗  N  ��� ≤ dN+1ΛN+1(F)  (N + 1)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  This immediately gives  1  M ∥y − SNθ∗  N∥2  F = 1  M  n  �  i=1  �  ti∈ ¯  Di  ���yi  ti − SN(xi  [0,ti])θ∗  N  ���  2  ≤ 1  M  M  �  i=1  �dN+1ΛN+1(F)  (N + 1)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  �2  =  �dN+1ΛN+1(F)  (N + 1)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  �2  ,  which concludes the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' A layer-wise bound on the signature  We now prove that signature layers are locally Lipschitz mappings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' We start with the following proposition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Proposition B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Let x ∈ C1-var  L  ([0, 1], Rd).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Then for all t ∈ [0, 1], the path t �→ Xk  [0,t] has 1-variation  ��Xk��  1-var,[0,t] ≤ Lk  k!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' By definition of the total variation,  ��Xk��  1-var,[0,t] = sup  D  m  �  i=1  ���Xk  [0,ti+1] − Xk  [0,ti]  ���  (Rd)⊗k = sup  D  m  �  i=1  ���Xk  [ti,ti+1]  ���  (Rd)⊗k ,  since Xk  [0,t] =  � t  0 dxu1 ⊗ · · · ⊗ dxuk, and where the supremum is taken over finite dissections D = {0 = t1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , tm = 1}  of [0, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Notice that the signature layer of depth k is here written as an element of (Rd)⊗k, which is more convenient for  this proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Then  sup  D  m  �  i=1  ���Xk  [ti,ti+1]  ���  (Rd)⊗k ≤ sup  D  m  �  i=1  ∥x∥k  1-var,[ti,ti+1]  k!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  ≤ 1  k!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' sup  D  � m  �  i=1  ∥x∥1-var,[ti,ti+1]  �k  = 1  k!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' sup  D  ∥x∥k  1-var,[0,1] ≤ Lk  k!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' ,  where the second inequality follows from the multinomial theorem and the last equality comes from the fact that for all  s < u < t, ∥x∥1-var,[s,u] + ∥x∥1-var,[u,t] = ∥x∥1-var,[s,t].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' This ends our proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Learning the Dynamics of Sparsely Observed Interacting Systems  We now state a bound on the difference between the k-th layer of the signatures of two different paths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Theorem B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Let x, z ∈ C1-var([0, 1], Rd).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Then for all k ≥ 2, the difference in supremum norm between the paths  t → Xk  [0,t] and t → Zk  [0,t] is bounded by  ��Xk − Zk��  ∞,[0,t] ≤ 2Lk−1  k−1  �  j=1  1  j!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' ∥x − z∥∞,[0,t] ≤ 2eLk−1 ∥x − z∥∞,[0,t]  and  ���X1  [0,t] − Z1  [0,t]  ��� ≤ 2 ∥x − z∥∞,[0,t] .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Our proof works by induction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Let x, z ∈ C1-var  L  ([0, 1], Rd), and for t ∈ [0, 1] denote by Xk  [0,t] resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Zk  [0,t] the k-th  layer of the signature of x resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' For k = 1 and t ∈ [0, 1], remark that  X1  [0,t] − Z1  [0,t] =  � t  0  d(xu − zu) = xt − zt − (x0 − z0)  such that  ���X1  [0,t] − Z1  [0,t]  ��� ≤ ∥x − z∥∞,[0,t] + ∥x0 − z0∥ ≤ 2 ∥x − z∥∞,[0,t] .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Consider now k ≥ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' We have  Xk  [0,t] − Zk  [0,t] =  � t  0  Xk−1  [0,s] ⊗ dxs −  � t  0  Zk−1  [0,s] ⊗ dzs =  � t  0  Xk−1  [0,s] ⊗ d(xs − zs + zs) −  � t  0  Zk−1  [0,s] ⊗ dzs,  and thus  Xk  [0,t] − Zk  [0,t] =  � t  0  Xk−1  [0,s] ⊗ d(xs − zs) +  � t  0  �  Xk−1  [0,s] − Zk−1  [0,s]  �  ⊗ dzs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  We now bound each of these terms separately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' First,  ����  � t  0  �  Xk−1  [0,s] − Zk−1  [0,s]  �  ⊗ dzs  ����  (Rd)⊗k  ≤  ��Xk−1 − Zk−1��  ∞,[0,t] ∥z∥1-var,[0,t] ≤  ��Xk−1 − Zk−1��  ∞,[0,t] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Moving to the first integral, integration by parts yields  � t  0  Xk−1  [0,s] ⊗ d(xs − zs) = Xk  [0,t] ⊗ (xt − zt) − Xk  [0,0] ⊗ (x0 − z0) −  � t  0  (xs − zs) ⊗ dXk−1  [0,s].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  We stress that Proposition (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2) applies since the integral over the tensor product is taken coordinate-wise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Since Xk−1  [0,0] = 0,  we are left with  � t  0  Xk−1  [0,s] ⊗ d(xs − zs) = Xk  [0,t] ⊗ (xt − zt) −  � t  0  (xs − zs) ⊗ dXk−1  [0,s].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Using Lemma B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='3 and submultiplicativity of the tensor norms, this can thus be bounded by  ����  � t  0  Xk−1  [0,s] ⊗ d(xs − zs)  ����  (Rd)⊗k ≤  ���Xk−1  [0,t]  ���  (Rd)⊗(k−1) ∥x − z∥∞,[0,t] + ∥x − z∥∞,[0,t]  ��Xk−1��  1-var,[0,t]  = 2Lk−1  (k − 1)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' ∥x − z∥∞,[0,t] .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Finally, we are left with  ��Xk − Zk��  ∞,[0,t] ≤ 2Lk−1  (k − 1)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' ∥x − z∥∞,[0,t] +  ��Xk−1 − Zk−1��  ∞,[0,t] L,  which can be recursively bounded by  ��Xk − Zk��  ∞,[0,t] ≤ 2Lk−1 ∥x − z∥∞,[0,t]  k−1  �  j=1  1  j!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' ≤ 2Lk−1e ∥x − z∥∞,[0,t] .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Learning the Dynamics of Sparsely Observed Interacting Systems  Note that this inequality implies that if z is chosen as the linear interpolation of a discretization of x on a grid D, and if the  grid gets finer, all signature layers converge at speed ∥x − z∥∞,[0,t] but the multiplicative constant increases with depth (if  L ≥ 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Figure 4 illustrates this phenomenon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  50  100  150  200  Number of sampling points of X  100  101  102  ||SN(x)  SN(X)||  N=3  N=4  N=5  N=6  50  100  150  200  Number of sampling points of X  101  102  ||SN(x)  SN(X)||  N=3  N=4  N=5  N=6  50  100  150  200  Number of sampling points of X  102  ||SN(x)  SN(X)||  N=3  N=4  N=5  N=6  Figure 4: Difference between the signature of a continuous path x and the signature of its discretized and noisy counterpart  X,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' without noise on the discretization points (left),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' with noise of variance vξ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='082 (middle) and with noise of variance  vξ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' For every number of sampling points, we average the distance between the two signature over 50 randomly  chosen discretizations of the interval [0, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' The discretized path is generated as in the well-specified setting (see Appendix  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Proof of Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='3  First, recall that for a generic path x : [0, 1] → Rd, a modulus of continuity is a continuous function ωx : R≥0 → R≥0  vanishing at 0 such that for all t, s ∈ [0, 1]  ∥xt − xs∥ ≤ ωx(|t − s|).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Also recall that by Heine’s theorem, we can define such a modulus of continuity for every continuous mapping [0, 1] to Rd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  We start by giving a general lemma that bounds the difference between the signature layers of a path and its discretized  version.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Its proof is based on the results of the previous section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Lemma B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Let x ∈ C1-var  L  ([0, 1], Rd) and ωx : R≥0 → R≥0 its modulus of continuity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Let xD : [0, 1] → Rd be the path  obtained by linear interpolation of the discretization of x on a grid D corrupted by additive noise ξ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Let Xk  [0,t] and Xk,D  [0,t]  be their respective k-th layers of signature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Then for all t ∈ [0, 1] and k ≥ 2  ��Xk − Xk,D��  ∞,[0,1] ≤ 2Lk−1  k−1  �  j=1  1  j!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  �  max  0≤s≤|D| ωx(s) + max  t∈D ∥ξt∥  �  ,  and for k = 1  ��X1 − X1,D��  ∞,[0,1] ≤ 2  �  max  0≤s≤|D| ωx(s) + max  t∈D ∥ξt∥  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Theorem B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='4 yields for k ≥ 2  ��Xk − Xk,D��  ∞,[0,1] ≤ 2Lk−1  k−1  �  j=1  1  j!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  ��x − xD��  ∞,[0,t]  Now, remark that  ��x − xD��  ∞,[0,1] ≤ ∥x − ˜x∥∞,[0,1] + max  t∈D ∥ξt∥  (21)  Learning the Dynamics of Sparsely Observed Interacting Systems  from the triangular inequality, where ˜x is the piecewise linear path obtained by linear interpolation of x0, xt1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , xtj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Now, since the paths x and ˜x coincide on 0, t1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , tj, we have  ∥x − ˜x∥∞,[0,1] =  max  i=0,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=',j−1 ∥x − ˜x∥∞,[ti,ti+1] ≤  max  i=0,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=',j−1 ωx  �  |ti+1 − ti|  �  =  max  0≤s≤|D| ωx(s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  This gets us  ��Xk − Xk,D��  ∞,[0,1] ≤ 2Lk−1  k−1  �  j=1  1  j!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  �  max  0≤s≤|D| ωx(s) + max  t∈D ∥ξt∥  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  For the case k = 1, we immediately get  ��X1 − X1,D��  ∞,[0,1] ≤ 2  �  max  0≤s≤|D| ωx(s) + max  t∈D ∥ξt∥  �  using the same technique as above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  This result is illustrated in Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' One can notice that as predicted by our theoretical bounds, the convergence of signature  of high order happens at the same rate than the convergence of signatures of lower order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' However, the multiplicative  constant controlling the tightness of the bound increases with N, leading to a slower convergence when N increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Strong noise hinders the convergence of the signature of the discretized path since in this case, the noise’s variance is  independent of the number of sampling points : adding more sampling points means adding more noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' There thus  are two trade-offs when learning with signatures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' A first trade-off is between sampling frequency and order: with paths  sampled at low resolution, one should prefer lower order signatures, which trade model complexity against precise features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  A second trade-off is between sampling and noise: if the feature time series are very noisy, the precision of the features  increases up to a certain point, past which noise prevails.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  With this result in hand, we can now prove Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' We restrict ourselves to the ω-Lipschitz case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' In this case, ωx(s) = ωs, and Lemma B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='5 becomes  ��Xk − Xk,D��  ∞,[0,1] ≤ 2Lk−1  k−1  �  j=0  1  j!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  �  ω|D| + max  t∈D ∥ξt∥  �  ≤ 2eLk−1�  ω|D| + max  t∈D ∥ξt∥  �  This results holds for a single path on the time interval [0, t].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Now moving to the feature matrices, we have  1  M  ��(SN − SD  N)θ∗  N  ��2  F ≤ 1  M  n  �  i=1  N  �  k=0  ���(Si,[k] − SD  i,[k])θ∗  [k],·  ���  2  F  ≤ 1  M  n  �  i=1  �  t∈ ¯  Di  N  �  k=0  dkΛk(F)2�  2eLk−1�  ω|Di| +  max  t′∈D,t′≤t ∥ξt′∥  ��2  ≤ 4e2�  ω|D| +  max  t′∈D,t′≤t ∥ξt′∥  ��2  L2  N  �  k=0  dkΛk(F)2  k!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2  × k!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2  ≤ 4e2N!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2�  ω|D| +  max  t′∈D,t′≤t ∥ξt′∥  ��2  L2  N  �  k=0  dkΛk(F)2  k!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  On the set Aξ(δ), one has  max  i=1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=',n,t∈Di  ��ξi  t  �� ≤ vξ  √  d + vξ  �  C−1 log(δ−1#D).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  (22)  Learning the Dynamics of Sparsely Observed Interacting Systems  Writing  CD,N(δ) = 4e2L2N!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2�  ω|D| + vξ  √  d + vξ  �  C−1 log(δ−1#D)  �2  One finally gets with probability 1 − δ that  1  M  ��(SN − SD  N)θ∗  N  ��2  F ≤ CD,N(δ)  N  �  k=0  dkΛk(F)2  k!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Proof of the main Theorem  We finally combine all Lemmas to obtain the desired oracle bound.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' First, we have from Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='1 that on Aε(¯δ),  1  2M  ���y − SD  N �θN,M  ���  2  F ≤  1  2M  ��y − SD  Nθ∗  N  ��2  F + 2pCN(¯δ)  √  M  N  �  k=0  dkΛk(F)  k!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  The first term of the right-hand side of this inequality is bounded by  1  2M  ��y − SD  Nθ∗  N  ��2  F ≤ 1  M ∥y − SNθ∗  N∥2  F + 1  M  ��SNθ∗  N − SD  Nθ∗  N  ��2  F .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  By Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2 and Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='3, this can in turn be bounded on Aε(¯δ) ∩ Aξ(δ) by  1  2M  ��y − SD  Nθ∗  N  ��2  F ≤  �  dN+1ΛN+1(F)  (N + 1)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  �2  + CD,N(δ)  N  �  k=0  dkΛk(F)2  k!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2  Combining all the pieces, this finally gives us, on Aε(¯δ) ∩ Aξ(δ),  1  2M  ���y − SD  N �θN,M  ���  2  F ≤  �  dN+1ΛN+1(F)  (N + 1)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  �2  + CD,N(δ)  N  �  k=0  dkΛk(F)2  k!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2  + 2pCN(¯δ)  √  M  N  �  k=0  dkΛk(F)  k!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Asymptotics  We briefly discuss the asymptotic behaviour of the upper bound of the oracle inequality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Sampling coarseness D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  In the noiseless case, CD,N → 0 as |D| → 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' This means that the discretization bias of our  estimator vanishes as the sampling gets finer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' However, in the noisy case - that is, when vξ > 0 - our estimator is durably  biased.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' This is consistent with the literature on learning with fussy features (Loh & Wainwright, 2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Learning the Dynamics of Sparsely Observed Interacting Systems  Truncation depth N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  A natural question is whether the bias of our estimator vanishes as N → ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' If we have perfect  sampling, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' the limit case where D = 0 and vξ = 0, our bound on the prediction error becomes on Aε(¯δ)  1  2M  ���y − SD  N �θN,M  ���  2  F ≤  �  dN+1ΛN+1(F)  (N + 1)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  �2  + 2pCN(¯δ)  √  M  N  �  k=0  dkΛk(F)  k!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  The first term of this bound vanishes as an immediate consequence of Assumption 3, while the second term is a statistical  error term that behaves like  √  log(NdN)  √  M  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' In order to obtain an assymptotical convergence, we thus need that N log(dN) =  o(M).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  In the more realistic setting where |D| > 0, the discretization bias behaves like LN−1N!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='|D|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' It is thus sufficient to assume  that |D| = o(1/N!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=').' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' If vξ > 0, our estimator is durably biased due to the measurement noise, and this bias increases with  N → ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' This is due to a ”propagation of chaos” phenomenon: the difference between the unobserved feature path and  the interpolated feature time series is amplified by taking the successive iterated integrals that define the signature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' This  advocates for using simple, low-order signature models in the presence of noise, as the gain in precision obtained when  taking higher N and reducing the truncation bias will at some point be lost because of the amplified noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Dimension p of the target path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Our oracle bound only depends on p through the statistical error term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' This term is  proportional to p√log p, which is expected in multitask regression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Dimension d of the feature path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Our oracle bound exhibits multiple dependencies in d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' First, the truncation bias grows  polynomially with d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Similarly, the discretization bias also depends polynomially on d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Finally, the statistical error term is  proportional to log d times a polynomial term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Algorithms, experiments, and supplementary results  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Implementation details  Recall that the SigLasso estimator �θN,M is defined as  �θN,M ∈  arg min  θ∈Rsd(N)×p  1  2M  ��Y − SD  Nθ  ��2  F + Ω(θ),  where  Ω(θ) =  N  �  k=0  M  1  2 Ck(¯δ)  k!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  ��θ[k],·  ��  1 ,  and  Ck(¯δ) =  �  vε log(2pNdk/¯δ)  for ¯δ ∈ [0, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Our goal is first to rewrite the penalty Ω(θ) as  Ω(θ) = C  N  �  k=0  λk  ��θ[k],·  ��  1 ,  such that training will only require to scale each layer of θ and to crossvalidate the multiplicative constant C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Since for  k ≥ 1,  Ck(¯δ) =  √  k ×  �  vε(¯δ/k + log(pN)/k + log d) ≤  √  k ×  �  vε(¯δ + log(pN) + log d),  Learning the Dynamics of Sparsely Observed Interacting Systems  we let λk =  √  k  k!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  We now show that the minimization problem with layer-specific penalty can be written as a standard regression problem  with ℓ1 penalization by rescaling the feature matrix, that is, multiplying SD  N by a well-chosen diagonal matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Consider  the ℓ1-penalized problem  min  θ∈Rsd(N)×p  1  2M  ��Y − SD  Nθ  ��2  F + C  N  �  k=0  λk  ��θ[k],·  ��  1 ,  where C > 0 controls the strength of the penalization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Making the change of variable  ˜θ = diag(1, λ1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , λ1  �  ��  �  d repetitions  , λ2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , λ2  �  ��  �  d2 repetitions  , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , λk, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , λk  �  ��  �  dN repetitions  )θ,  which is equivalent to  θ = diag(1, 1/λ1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , 1/λ1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , 1/λk, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , 1/λk)˜θ,  and denoting by W this last weight matrix, we get the equivalent minimization problem  min  ˜θ∈Rsd(N)×p  1  2M  ���Y − SD  NW ˜θ  ���  2  F + C  N  �  k=0  ���˜θ[k],·  ���  1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  We can thus obtain the SigLasso estimator by (i) multiplying the feature matrix SD  N by W and solving the associated  ℓ1-penalized problem (ii) multiplying the obtained solution by W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  The Learn-And-Reconstruct algorithm is the generic algorithm used in our work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' It is applicable for a wide variety of tasks  such as missing values inference, trajectory reconstruction, forecasting and many more.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' It is described in Algorithm 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Algorithm 1 Learn-and-Reconstruct Algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' The algorithm infers for every individual in the test set a reconstructed  time series ˆY i  t .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Learn the dynamics  Input: train dataset of normalized paths (X1, Y1), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , (Xn, Yn) sampled on (D1, ¯D1), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , (Dn, ¯Dn).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Construct the feature matrix SD  N and the target vector Y  for i = 1 to n do  for t in ¯Di do  SD  N ← Append SN(Xi  [0,t])  Y ← Append Y i  t  end for  end for  Compute ˆθN,M by solving (6) with Y, SD  N using coordinate descent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Reconstruct trajectories  Input: test dataset ˜X1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , ˜Xn sampled on ˜D1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , ˜Dn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  for i = 1 to n do  for t in ˜Di do  ˆY i  t = ˆθN,MSN( ˜Xi  [0,t])  end for  end for  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Assessing feature importance  We two metrics used to asses the importance of the different dimensions of the feature path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Given a truncation depth N and a dimension i ∈ {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , d}, we define its pure feature importance (PFI) as the sum of the  norm of the coefficients (or vectors in the case the target is multivariate) of �θN,M that are associated to signatures taken on  Learning the Dynamics of Sparsely Observed Interacting Systems  the words I1 = (i), I2 = (i, i), and so forth until IN = (i, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Mathematically,  PFI(i) = 1  N  � ��θI1��  2 +  ��θI2��  2 + · · · +  ��θIN ��  2  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Since signatures also capture interactions between dimensions of the feature path, we also define the cross feature impor-  tance (CFI) as the sum of norms of the coefficients (or vectors) of �θN,M that are associated to signatures coefficients of  words of length ≤ N in which the letter i appears.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Mathematically,  CFI(i) =  1  sd(N) − sd−1(N)  �  I s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' i ∈ I  ��θI��  2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  For a given truncation depth N, note that there are sd(N) − sd−1(N) =  N  �  k=0  dk −  N  �  k=0  (d − 1)k terms in the last sum, which  justifies our choice of normalization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Details on model implementation and evaluation  SigLasso.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  The SigLasso model is implemented using the CVLasso class in scikit-learn (Pedregosa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', 2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  This implementation optimises the objective function using coordinate descent and features automatic cross-validation of  the penalty strength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' We use iisignature (Reizenstein & Graham, 2020) to compute the signature of the feature time  series.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Every time series is standardized prior to this through division by its own total variation, as suggested by Morrill  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' (2020a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' The depth of the signature is a hyperparameter chosen between 2 and 9 or 6 depending on the experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  An intercept is added.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  GRU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  The GRU is of width 128 and systematically trained with 100 epoches using a learning rate of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Neural CDE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  We use the implementation of Neural CDE provided by torchcde (Kidger et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' We use the  original vector field described in the documentation of this package, with the small tweak that we use a smoother non-  linearity (tanh instead of ReLU).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' We observed that using the rk4 solver instead of dopri5 significantly accelerates the  training time of the Neural CDE without affecting the model’s performances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' The learning rate is hand-tuned to either  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='001 or 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0001 depending on the experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' We train the model for 100 epochs and asses its convergence by using a  standard stopping criteria.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' The MSE is computed in a classical fashion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' To compute the integrate MSE, we compute the L2 distance between  the piecewise constant interpolations of the true yt and the predicted �yt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Details on the well specified model  Generation of the training data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  We generate a two-dimensional feature path by interpolating for every dimension 15  points in [0, 1], each of them being draw randomly for a normal distribution N(0, 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' The interpolation is done with  Hermite cubic splines with backward differences using the package torchcde (Kidger et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Time is added as a  supplementary channel, which is a standard practice when learning with signatures and Neural CDEs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' These paths are then  downsampled by randomly drawing sampling points for the target and the feature time series specific to every individual.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  The target path is the solution of a CDE of the form  dyt = σ  �  Ayt  �  dxt  where σ : Rp → Rp is the hyperbolic tangent, A ∈ Rd×p is a matrix drawn randomly from N(0, Id×p) and xt is the  feature path constructed as above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' The solution of this CDE is computed using torchcde.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Generation of the test data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  We generate the test data in the same way than the training data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' However, this data is not  downsampled as we wish to assess the generalization capacities of our model—i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', is our model capable of approximating  the dynamics and extrapolating to continuous feature paths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Learning the Dynamics of Sparsely Observed Interacting Systems  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Details on Ornstein-Uhlenbeck experiment  We take (xt)t∈[0,1] to be a 1-dimensional Brownian motion with variance σ2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='1, and generate (yt) as a 1-dimensional  Ornstein-Uhlenbeck process driven by (xt), that is, for all t ∈ [0, 1]  dyt = θ(µ − yt)dt + dxt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Simulation of (yt) is done using a standard Euler-Maruyama simulation scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' We let θ = 3 and µ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' The training  data is then downsampled as in the well specified experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Details on the tumor growth experiment  We consider the following tumor growth model taken from (Simeoni et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', 2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Let x ∈ C1−var([0, 1], R).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' The weight  y ∈ C([0, 1], R+) under the concentration of a treatment drug x is governed by the differential system  du1  t =  ��  λ0u1  t  �  1 + (λ0  λ1  yt)ψ��−1/ψ  − k2xtu1  t  �  dt  du2  t =  �  k2xtu1  t − k1u2  t  �  dt  du3  t =  �  k1(u2  t − u3  t)  �  dt  du4  t =  �  k1(u3  t − u4  t)  �  dt  yt = u1  t + u2  t + u3  t + u4  t  with initial condition (u1  0, u2  0, u3  0, u4  0, y0) = (2, 0, 0, 0, 2) and parameters (k1, k2, λ0, λ1, ψ) = (10, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='5, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='9, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='7, 20).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' The  concentration (xt) is chosen to be the squared value of the paths used for the well-specified experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Notice that this  system is non-linear w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Indeed, writing dyt = G(yt, xt)dt, one has, for α ∈ R, G(yt, αxt) ̸= αG(yt, xt).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' The  training data is then downsampled as in the well specified experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Details on the French Covid experiment  We illustrate the performance of our method and competitors on French Covid data from 2021-03-31 to 2021-07-07 avail-  able on Gitlab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Hospital data was obtained from the SI-VIC database, the national inpatient surveillance system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Target path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Following Paireau et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' (2022), we chose the predict the growth rate of incident hospitalisations in each  of the 9 metropolitan regions of France.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' The exponential growth rate was computed from raw data using a 2 days rolling  window and then smoothed using local polynomial regression as in Paireau et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Mathematically, our target time  series is the R-valued growth rate, and we fit a different model for every of the 12 regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' It is displayed for all 12 regions  in Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Feature path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  As in Paireau et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' (2022), we consider a set of 12 time-dependant predictors of different types summa-  rized in Table 2 and plotted in Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Both SIDEP (”Syst`eme d’Information de D´epistage Populationnel”) and VAC-SI  datasets are publicly available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' The mobility data was obtained from Google.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' The mobility-related predictors describe  travel trends for different kind of public spaces such as such as shops and leisure spaces, food stores and pharmacies,  parks, public transport stations, workplaces and residential areas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' The meteorological data was obtained from M´et´eo  France.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  SigLasso (weighted and unweighted), NCDE and GRU algorithms were trained on the period from 2021-03-31  to 2021-06-23 and tested on the period from 2021-06-24 to 2021-07-07.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' We included a history of 10 days at each point  and performed prediction for different horizons ranging from 1 to 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' In others words, at horizon h, features values from  day t − h − 10 to day t − h to were used to compute the prediction at time t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' All feature time series are normalized to have  total variation equal to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Architectural details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  The GRU has width 128 and is trained for 100 epochs with a learning rate of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' The NCDE  is trained for 30 epochs with a learning rate of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' It has 2 hidden layers of width 128, an intermediate Tanh(·) non-  Learning the Dynamics of Sparsely Observed Interacting Systems  2021-03-14  2021-04-13  2021-05-13  2021-06-12  2021-07-12  Date  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='30  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='35  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='prop_pos_symp  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='ARA  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='BFC  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='BRE  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='CVL  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='GES  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='HDF  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='IDF  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='NOR  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='NAQ  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='OCC  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='PDL  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='PAC  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2021-03-14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2021-04-13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2021-05-13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2021-06-12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2021-07-12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='Date  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='40  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='grocery_and_pharmacy  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2021-03-14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2021-04-13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2021-05-13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2021-06-12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2021-07-12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='Date  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='50  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='75  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='100  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='125  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='150  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='parks  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2021-03-14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2021-04-13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2021-05-13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2021-06-12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2021-07-12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='Date  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='40  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='transit_stations  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2021-03-14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2021-04-13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2021-05-13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2021-06-12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2021-07-12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='Date  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='40  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='workplaces  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='ARA  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='BFC  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='BRE  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='CVL  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='GES  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='HDF  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='IDF  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='NOR  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='NAQ  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='OCC  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='PDL  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='PAC  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2021-03-14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2021-04-13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2021-05-13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2021-06-12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2021-07-12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='Date  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='5  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='5  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='5  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='5  residential  2021-03-14  2021-04-13  2021-05-13  2021-06-12  2021-07-12  Date  0  20  40  60  80  IPTCC  2021-03-14  2021-04-13  2021-05-13  2021-06-12  2021-07-12  Date  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='5  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='5  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='5  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='5  25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  temperature  2021-03-14  2021-04-13  2021-05-13  2021-06-12  2021-07-12  Date  55  60  65  70  75  80  85  rel_humidity  ARA  BFC  BRE  CVL  GES  HDF  IDF  NOR  NAQ  OCC  PDL  PAC  2021-03-14  2021-04-13  2021-05-13  2021-06-12  2021-07-12  Date  4  6  8  10  12  14  abs_humidity  2021-03-14  2021-04-13  2021-05-13  2021-06-12  2021-07-12  Date  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='10  P_r  2021-03-14  2021-04-13  2021-05-13  2021-06-12  2021-07-12  Date  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='30  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='35  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='40  couv_complet  Figure 5: The 12 different feature time series used to forecast the hospitalization growth rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Every different color  corresponds to a given region of France.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='Learning the Dynamics of Sparsely Observed Interacting Systems  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='Predictor  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='Type  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='Source  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='Description  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='prop pos symp  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='Epidemiological  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='SIDEP databas  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='proportion of positive tests among symptomatics  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='P r  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='Epidemiological  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='SIDEP database  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='growth rate of positive tests  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='couv-complet  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='Epidemiological  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='VAC-SI database  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='proportion of vaccinated  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='grocery and pharmacy  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='Mobility  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='Google  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='visits to grocery and pharmacy stores  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='parks  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='Mobility  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='Google  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='visits to parks  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='transit stations  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='Mobility  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='Google  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='visits visits to transit stations  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='workplaces  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='Mobility  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='Google  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='visits to workplaces  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='residential  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='Mobility  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='Google  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='visits to residential places  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='IPTCC  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='Meteorological  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='M´et´eo France  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='Index PREDICT of climatic transmissivity  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='temperature  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='Meteorological  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='M´et´eo France  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='temperature  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='rel humidity  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='Meteorological  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='M´et´eo France  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='relative humidity  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='abs humidity  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='Meteorological  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='M´et´eo France  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='absolute humidity  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='Table 2: The set of time-dependant predictors used to predict the hospital admission growth rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' See Figure 5 for a  vizualisation of all different features across regions through time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  2021-03-01  2021-03-15  2021-04-01  2021-04-15  2021-05-01  2021-05-15  2021-06-01  2021-06-15  2021-07-01  Date  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='00  Hospitalization growth rate  ARA  BFC  BRE  CVL  GES  HDF  IDF  NOR  NAQ  OCC  PDL  PAC  Figure 6: Hospitalization growth rate through time during the full period for the 12 different regions of France.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Learning the Dynamics of Sparsely Observed Interacting Systems  2021-04-07  2021-04-19  2021-05-01  2021-05-13  2021-05-25  2021-06-06  2021-06-18  2021-06-30  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='06  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='04  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='02  Growth rate  ARA  2021-04-07  2021-04-19  2021-05-01  2021-05-13  2021-05-25  2021-06-06  2021-06-18  2021-06-30  Days  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='10  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='08  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='06  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='04  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='00  GES  2021-04-07  2021-04-19  2021-05-01  2021-05-13  2021-05-25  2021-06-06  2021-06-18  2021-06-30  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='06  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='04  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='00  NAQ  2021-04-07  2021-04-19  2021-05-01  2021-05-13  2021-05-25  2021-06-06  2021-06-18  2021-06-30  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='10  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='08  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='06  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='04  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='02  Growth rate  BFC  2021-04-07  2021-04-19  2021-05-01  2021-05-13  2021-05-25  2021-06-06  2021-06-18  2021-06-30  Days  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='08  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='06  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='04  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='00  HDF  2021-04-07  2021-04-19  2021-05-01  2021-05-13  2021-05-25  2021-06-06  2021-06-18  2021-06-30  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='06  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='04  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='02  OCC  2021-04-07  2021-04-19  2021-05-01  2021-05-13  2021-05-25  2021-06-06  2021-06-18  2021-06-30  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='15  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='10  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='00  Growth rate  BRE  2021-04-07  2021-04-19  2021-05-01  2021-05-13  2021-05-25  2021-06-06  2021-06-18  2021-06-30  Days  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='08  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='06  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='04  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='00  IDF  2021-04-07  2021-04-19  2021-05-01  2021-05-13  2021-05-25  2021-06-06  2021-06-18  2021-06-30  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='06  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='04  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='00  PDL  2021-04-07  2021-04-19  2021-05-01  2021-05-13  2021-05-25  2021-06-06  2021-06-18  2021-06-30  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='10  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='08  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='06  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='04  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='02  Growth rate  CVL  2021-04-07  2021-04-19  2021-05-01  2021-05-13  2021-05-25  2021-06-06  2021-06-18  2021-06-30  Days  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='06  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='04  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='02  NOR  2021-04-07  2021-04-19  2021-05-01  2021-05-13  2021-05-25  2021-06-06  2021-06-18  2021-06-30  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='06  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='04  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='00  PAC  Figure 7: Interpolation (left of dotted line) and prediction (right of dotted line) of hospitalization growth rate for all 12  french regions using weighted SigLasso.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  linearity and a final linear readout.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' This architecture is identical to the one proposed in (Kidger, 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Penalty strenght of  the SigLasso is crossvalided using the internal implementation LassoCV of scikit-learn (Pedregosa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', 2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  All details, in particular the features used for each individual prediction, can be found in Paireau et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  We refer to the supplementary information file of Paireau et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' (2022) and our code for more details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Figure 12 displays the RMSE (on all regions) of NCDE, SigLasso, GRU, and the Ensemble method for all  prediction horizons h = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Figures 7, 8, 10 and 9 display the obtained interpolation for weighted and unweighted  SigLasso, GRU and NCDE at different horizons (corresponding to different line colors in winter matplotlib palette).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' The  lighter the blue, the smaller the time horizon: the lightest curve corresponds to a time horizon equal to h = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Truth is in  red.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' Additional results  We give in Table 3 some additional results on the experiments described above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Table 3: Training time of SigLasso, GRU and Neural CDE in different simulation settings, averaged over 10 iterations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' In  every setting, n = 50, # ¯Di = 5 for all i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' , n (and therefore M = 250).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Training time (s)  SigLasso  GRU  Neural CDE  Well-specified  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='37 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='23  269 ± 109  1754 ± 587  OU  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='057 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='005  27 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='44  216 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='7  Tumor growth  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='056 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='007  31 ± 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='5  250 ± 14  Learning the Dynamics of Sparsely Observed Interacting Systems  2021-04-07  2021-04-19  2021-05-01  2021-05-13  2021-05-25  2021-06-06  2021-06-18  2021-06-30  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='08  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='06  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='04  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='02  Growth rate  ARA  2021-04-07  2021-04-19  2021-05-01  2021-05-13  2021-05-25  2021-06-06  2021-06-18  2021-06-30  Days  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='10  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='08  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='06  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='04  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='00  GES  2021-04-07  2021-04-19  2021-05-01  2021-05-13  2021-05-25  2021-06-06  2021-06-18  2021-06-30  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='06  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='04  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='00  NAQ  2021-04-07  2021-04-19  2021-05-01  2021-05-13  2021-05-25  2021-06-06  2021-06-18  2021-06-30  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='10  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='08  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='06  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='04  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='02  Growth rate  BFC  2021-04-07  2021-04-19  2021-05-01  2021-05-13  2021-05-25  2021-06-06  2021-06-18  2021-06-30  Days  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='08  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='06  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='04  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='00  HDF  2021-04-07  2021-04-19  2021-05-01  2021-05-13  2021-05-25  2021-06-06  2021-06-18  2021-06-30  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='08  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='06  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='04  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='02  OCC  2021-04-07  2021-04-19  2021-05-01  2021-05-13  2021-05-25  2021-06-06  2021-06-18  2021-06-30  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='15  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='10  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='00  Growth rate  BRE  2021-04-07  2021-04-19  2021-05-01  2021-05-13  2021-05-25  2021-06-06  2021-06-18  2021-06-30  Days  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='08  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='06  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='04  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='00  IDF  2021-04-07  2021-04-19  2021-05-01  2021-05-13  2021-05-25  2021-06-06  2021-06-18  2021-06-30  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='06  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='04  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='00  PDL  2021-04-07  2021-04-19  2021-05-01  2021-05-13  2021-05-25  2021-06-06  2021-06-18  2021-06-30  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='10  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='08  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='06  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='04  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='02  Growth rate  CVL  2021-04-07  2021-04-19  2021-05-01  2021-05-13  2021-05-25  2021-06-06  2021-06-18  2021-06-30  Days  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='06  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='04  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='02  NOR  2021-04-07  2021-04-19  2021-05-01  2021-05-13  2021-05-25  2021-06-06  2021-06-18  2021-06-30  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='06  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='04  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='02  PAC  Figure 8: Interpolation (left of dotted line) and prediction (right of dotted line) of hospitalization growth rate for all 12  french regions using unweighted SigLasso.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  2021-04-07  2021-04-19  2021-05-01  2021-05-13  2021-05-25  2021-06-06  2021-06-18  2021-06-30  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='10  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='10  Growth rate  ARA  2021-04-07  2021-04-19  2021-05-01  2021-05-13  2021-05-25  2021-06-06  2021-06-18  2021-06-30  Days  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='10  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='10  GES  2021-04-07  2021-04-19  2021-05-01  2021-05-13  2021-05-25  2021-06-06  2021-06-18  2021-06-30  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='10  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='10  NAQ  2021-04-07  2021-04-19  2021-05-01  2021-05-13  2021-05-25  2021-06-06  2021-06-18  2021-06-30  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='10  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='10  Growth rate  BFC  2021-04-07  2021-04-19  2021-05-01  2021-05-13  2021-05-25  2021-06-06  2021-06-18  2021-06-30  Days  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='10  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='10  HDF  2021-04-07  2021-04-19  2021-05-01  2021-05-13  2021-05-25  2021-06-06  2021-06-18  2021-06-30  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='10  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='10  OCC  2021-04-07  2021-04-19  2021-05-01  2021-05-13  2021-05-25  2021-06-06  2021-06-18  2021-06-30  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='10  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='10  Growth rate  BRE  2021-04-07  2021-04-19  2021-05-01  2021-05-13  2021-05-25  2021-06-06  2021-06-18  2021-06-30  Days  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='10  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='10  IDF  2021-04-07  2021-04-19  2021-05-01  2021-05-13  2021-05-25  2021-06-06  2021-06-18  2021-06-30  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='10  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='10  PDL  2021-04-07  2021-04-19  2021-05-01  2021-05-13  2021-05-25  2021-06-06  2021-06-18  2021-06-30  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='10  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='10  Growth rate  CVL  2021-04-07  2021-04-19  2021-05-01  2021-05-13  2021-05-25  2021-06-06  2021-06-18  2021-06-30  Days  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='10  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='10  NOR  2021-04-07  2021-04-19  2021-05-01  2021-05-13  2021-05-25  2021-06-06  2021-06-18  2021-06-30  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='10  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='10  PAC  Figure 9: Interpolation (left of dotted line) and prediction (right of dotted line) of hospitalization growth rate for all 12  french regions using NCDE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Learning the Dynamics of Sparsely Observed Interacting Systems  2021-04-07  2021-04-19  2021-05-01  2021-05-13  2021-05-25  2021-06-06  2021-06-18  2021-06-30  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='08  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='06  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='04  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='02  Growth rate  ARA  2021-04-07  2021-04-19  2021-05-01  2021-05-13  2021-05-25  2021-06-06  2021-06-18  2021-06-30  Days  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='10  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='08  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='06  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='04  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='00  GES  2021-04-07  2021-04-19  2021-05-01  2021-05-13  2021-05-25  2021-06-06  2021-06-18  2021-06-30  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='08  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='06  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='04  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='00  NAQ  2021-04-07  2021-04-19  2021-05-01  2021-05-13  2021-05-25  2021-06-06  2021-06-18  2021-06-30  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='10  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='08  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='06  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='04  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='04  Growth rate  BFC  2021-04-07  2021-04-19  2021-05-01  2021-05-13  2021-05-25  2021-06-06  2021-06-18  2021-06-30  Days  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='08  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='06  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='04  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='02  HDF  2021-04-07  2021-04-19  2021-05-01  2021-05-13  2021-05-25  2021-06-06  2021-06-18  2021-06-30  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='08  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='06  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='04  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='02  OCC  2021-04-07  2021-04-19  2021-05-01  2021-05-13  2021-05-25  2021-06-06  2021-06-18  2021-06-30  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='15  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='10  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='00  Growth rate  BRE  2021-04-07  2021-04-19  2021-05-01  2021-05-13  2021-05-25  2021-06-06  2021-06-18  2021-06-30  Days  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='08  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='06  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='04  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='00  IDF  2021-04-07  2021-04-19  2021-05-01  2021-05-13  2021-05-25  2021-06-06  2021-06-18  2021-06-30  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='08  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='06  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='04  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='00  PDL  2021-04-07  2021-04-19  2021-05-01  2021-05-13  2021-05-25  2021-06-06  2021-06-18  2021-06-30  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='10  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='08  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='06  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='04  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='02  Growth rate  CVL  2021-04-07  2021-04-19  2021-05-01  2021-05-13  2021-05-25  2021-06-06  2021-06-18  2021-06-30  Days  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='08  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='06  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='04  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='02  NOR  2021-04-07  2021-04-19  2021-05-01  2021-05-13  2021-05-25  2021-06-06  2021-06-18  2021-06-30  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='08  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='06  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='04  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='00  PAC  Figure 10: Interpolation (left of dotted line) and prediction (right of dotted line) of hospitalization growth rate for all 12  french regions using GRU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  2021−03−26  2021−04−07  2021−04−18  2021−04−30  2021−05−12  2021−05−24  2021−06−05  2021−06−17  2021−06−28  2021−07−10  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='3  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='3  Growth rate  ARA  2021−03−26  2021−04−07  2021−04−18  2021−04−30  2021−05−12  2021−05−24  2021−06−05  2021−06−17  2021−06−28  2021−07−10  Days  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='3  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='3  GES  2021−03−26  2021−04−07  2021−04−18  2021−04−30  2021−05−12  2021−05−24  2021−06−05  2021−06−17  2021−06−28  2021−07−10  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='3  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='3  NAQ  2021−03−26  2021−04−07  2021−04−18  2021−04−30  2021−05−12  2021−05−24  2021−06−05  2021−06−17  2021−06−28  2021−07−10  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='3  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='3  Growth rate  BFC  2021−03−26  2021−04−07  2021−04−18  2021−04−30  2021−05−12  2021−05−24  2021−06−05  2021−06−17  2021−06−28  2021−07−10  Days  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='3  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='3  HDF  2021−03−26  2021−04−07  2021−04−18  2021−04−30  2021−05−12  2021−05−24  2021−06−05  2021−06−17  2021−06−28  2021−07−10  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='3  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='3  OCC  2021−03−26  2021−04−07  2021−04−18  2021−04−30  2021−05−12  2021−05−24  2021−06−05  2021−06−17  2021−06−28  2021−07−10  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='3  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='3  Growth rate  BRE  2021−03−26  2021−04−07  2021−04−18  2021−04−30  2021−05−12  2021−05−24  2021−06−05  2021−06−17  2021−06−28  2021−07−10  Days  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='3  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='3  IDF  2021−03−26  2021−04−07  2021−04−18  2021−04−30  2021−05−12  2021−05−24  2021−06−05  2021−06−17  2021−06−28  2021−07−10  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='3  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='3  PDL  2021−03−26  2021−04−07  2021−04−18  2021−04−30  2021−05−12  2021−05−24  2021−06−05  2021−06−17  2021−06−28  2021−07−10  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='3  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='3  Growth rate  CVL  2021−03−26  2021−04−07  2021−04−18  2021−04−30  2021−05−12  2021−05−24  2021−06−05  2021−06−17  2021−06−28  2021−07−10  Days  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='3  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='3  NOR  2021−03−26  2021−04−07  2021−04−18  2021−04−30  2021−05−12  2021−05−24  2021−06−05  2021−06−17  2021−06−28  2021−07−10  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='3  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='3  PAC  Figure 11: Interpolation (left of dotted line) and prediction (right of dotted line) of hospitalization growth rate for all 12  french regions using ensemble methods (Paireau et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  Learning the Dynamics of Sparsely Observed Interacting Systems  2  4  6  8  10  12  14  Horizon of prediction  100  101  RMSE  SigLasso  SigLasso (weighted)  GRU  NCDE  Ensemble  2  4  6  8  10  12  14  Horizon of prediction  100  101  SigLasso  SigLasso (weighted)  GRU  NCDE  Ensemble  Figure 12: RMSE accross all regions on the training period (left) and the testing period (right) for the ensemble methode  (Paireau et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=', 2022), NCDE, GRU, and SigLasso (weighted and unweighted).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content=' See Figure 13 for a zoom-in on GRU and  SigLasso performances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='  2  4  6  8  10  12  14  Horizon of prediction  5 × 10−1  6 × 10−1  RMSE  SigLasso  SigLasso (weighted)  GRU  2  4  6  8  10  12  14  Horizon of prediction  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='4 × 10−1  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='6 × 10−1  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='8 × 10−1  5 × 10−1  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
+page_content='2 × 10−1  SigLasso  SigLasso (weighted)  GRU  Figure 13: RMSE accross all regions on the training period (left) and the testing period (right) for GRU and SigLasso  (weighted and unweighted).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/N9FJT4oBgHgl3EQf0S3d/content/2301.11647v1.pdf'}
diff --git a/O9AzT4oBgHgl3EQfIfuL/vector_store/index.faiss b/O9AzT4oBgHgl3EQfIfuL/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..e9698ff3771fd96e6460caa30ee509059036f0e5
--- /dev/null
+++ b/O9AzT4oBgHgl3EQfIfuL/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:470925a219c87ac6ded0c2b9522f601bfe1470a1260ef09e99ce1146e3f2161d
+size 4522029
diff --git a/OdE4T4oBgHgl3EQfjw3r/content/tmp_files/2301.05146v1.pdf.txt b/OdE4T4oBgHgl3EQfjw3r/content/tmp_files/2301.05146v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..83bba428bf61df94842a4fc67131d6f6739fda8b
--- /dev/null
+++ b/OdE4T4oBgHgl3EQfjw3r/content/tmp_files/2301.05146v1.pdf.txt
@@ -0,0 +1,1560 @@
+arXiv:2301.05146v1  [quant-ph]  12 Jan 2023
+Heuristic for Diverse Kemeny Rank Aggregation based on
+Quantum Annealing
+Sven Fiergolla1, Kevin Goergen1, Patrick Neises1, and Petra Wolf2
+1University of Trier, Germany, {s4svfier, s4kegoer,s4paneis}@uni-trier.de
+2University of Bergen, Norway, mail@wolfp.net
+Abstract
+The Kemeny Rank Aggregation (KRA) prob-
+lem is a well-studied problem in the field of Social
+Choice with a variety of applications in many differ-
+ent areas like databases and search engines. Intu-
+itively, given a set of votes over a set of candidates,
+the problem asks to find an aggregated ranking of
+candidates that minimizes the overall dissatisfac-
+tion concerning the votes. Recently, a diverse ver-
+sion of KRA was considered which asks for a suf-
+ficiently diverse set of sufficiently good solutions.
+The framework of diversity of solutions is a young
+and thriving topic in the field of artificial intelli-
+gence. The main idea is to provide the user with
+not just one, but with a set of different solutions,
+enabling her to pick a sufficiently good solution that
+satisfies additional subjective criteria that are hard
+or impossible to model.
+In this work, we use a quantum annealer to solve
+the KRA problem and to compute a representa-
+tive set of solutions. Quantum annealing is a meta
+search heuristic that does not only show promising
+runtime behavior on currently existing prototypes
+but also samples the solutions space in an inher-
+ently different way, making use of quantum effects.
+We describe how KRA instances can be solved by
+a quantum annealer and provide an implementa-
+tion as well as experimental evaluations. As exist-
+ing quantum annealers are still restricted in their
+number of qubits, we further implement two differ-
+ent data reduction rules that can split an instance
+into a set of smaller instances. In our evaluation,
+we compare classical heuristics that allow to sample
+multiple solutions such as simulated annealing and
+local search with quantum annealing performed on
+a physical quantum annealer.
+We compare run-
+time, quality of solution, and diversity of solutions,
+with and without applying preceding data reduc-
+tion rules. While our aim is to compute a diverse
+set of solutions, we also include classical heuristics
+that only compute a single solution in our experi-
+ments.
+Keywords: Social Choice, Solution Diversity,
+Quantum Annealing, QUBO, Heuristic Search
+1
+Introduction
+Estimating the potential of quantum comput-
+ers gains more and more importance as their
+technology develops rapidly.
+There are two
+different approaches for utilizing quantum ef-
+fects
+to
+solve
+computational
+problems:
+the
+Quantum Circuit Model
+(an approach followed
+by Google and NASA [Arute et al., 2019], and
+IBM [Steffen et al., 2011]) and the Adiabatic Quan-
+tum
+Model
+(an
+approach
+dominated
+by
+D-
+Wave Systems [King et al., 2022]).
+While both
+models are computationally equivalent
+in the
+sense that they can simulate each other with
+only a polynomial overhead [Farhi et al., 2000,
+Aharonov et al., 2008] their physical realizations
+are quite different.
+The quantum circuit model
+aims at building a universal quantum computer,
+it requires the design of novel quantum algorithms
+to make use of quantum effects.
+As quantum
+algorithms are quite unintuitive, only few quan-
+tum algorithms are known that provide signifi-
+cant benefits over classical algorithms (for instance,
+Grover’s algorithm searching in unstructured data
+with a quadratic speedup [Grover, 1996],
+and
+1
+
+Shor’s algorithm factoring a number in polyno-
+mial time [Shor, 1994]). In contrast, the Adiabatic
+Quantum Model has been realized by D-Wave as a
+solution method called quantum annealing (QA) to
+solve NP-hard optimization problems. The quan-
+tum annealers from D-Wave are designed to solve
+a native problem called the Ising Model 1 on their
+hardware chip. The Ising Model is very closely re-
+lated to the quadratic unconstrained binary opti-
+mization (QUBO) problem which is more acces-
+sible from the perspective of a computer scientist
+and, hence, will be considered in this paper. The
+QUBO problem provides us with a nice interface
+that allows to formulate problems as a classical op-
+timization problem while still utilizing quantum ef-
+fects to speed up the computation. We discuss the
+QUBO problem in detail later.
+Intuitively, in the Adiabatic Quantum Model,
+the system is transformed from an initial low energy
+state, which is easy to prepare, into another low
+energy state such that the final state corresponds
+to minimizing a target function. If this transition
+is performed slowly enough and at very low tem-
+peratures (≤20mK), the system stays in the lowest
+energy state during the transformation and we can
+measure an optimal solution from the final state.
+The Adiabatic Quantum Model was initially pro-
+posed in [Farhi et al., 2001] and soon found its ap-
+plication in neural networks [Kinjo et al., 2003].
+Quantum annealing is a meta search heuristic
+that can be implemented in the native instruc-
+tion set of the Adiabatic Quantum Model.
+The
+most developed realization in form of a quantum
+annealer is the D-Wave Advantage system with
+5,000+ qubits [Willsch et al., 2022]. The quantum
+computer from D-Wave also allows for Quantum
+Machine Learning applications [Hu et al., 2019,
+Adachi and Henderson, 2015].
+The
+company
+rapidly develops new hardware chips for quantum
+annealers, which does not come without some dif-
+ficulties concerning API stability. For more details
+on the technical realization see [Bunyk et al., 2014,
+Harris et al., 2010, Johnson et al., 2011] and for a
+general introduction to the Adiabatic Quantum
+Model see [McGeoch, 2014].
+The
+Adiabatic
+Quantum
+Model
+differs
+1The Ising Model problem is NP-complete [Istrail, 2000,
+Cipra, 2000] and remains NP-complete restricted to the
+class of instances realizable on a D-Wave quantum an-
+nealer [Bunyk et al., 2014].
+from
+classical
+simulations
+of
+thermal
+anneal-
+ing [Kirkpatrick et al., 1983] in the sense that the
+computation starts with a superposition of all
+states with minimal energy, thereby exploiting
+quantum
+parallelism,
+and
+can
+further
+tunnel
+through high energy areas in the solution space
+while classical approaches need to climb over
+those high energy regions.
+Simulations have
+shown that thereby the Adiabatic Quantum Model
+has the potential of outperforming classical sim-
+ulated
+annealing
+[Morita and Nishimori, 2008,
+Ohzeki and Nishimori, 2011,
+Crosson and Harrow, 2016]. Further, experimental
+results show that quantum annealers can find local
+valleys in the solution space that are not found by
+simulated annealers [Koshka and Novotny, 2020].
+This indicates that instances that cannot be solved
+efficiently with classical simulated annealing might
+be efficiently solvable on a quantum annealer.
+Due to its stochastic nature,
+the quantum
+annealing process must be executed and measured
+multiple times to get good solutions.
+But while
+this looks like a weakness of the approach, it
+actually comes with a benefit: While the system
+cools down, one can imagine it as being in a super-
+position of all local minima. Only once measured,
+the system collapse to one minima. By repeating
+the process we can sample the different minima of
+the solution space and do not get stuck in one local
+minima as it is often the case for gradient descent
+approaches. The multiple solutions automatically
+sampled further allow us to get a representation
+of the solution space, an aim that is classically
+modeled by the notion of diversity of solutions,
+a
+recent
+upcoming
+trend
+in
+artificial
+intelli-
+gence [Petit and Trapp, 2019, Baste et al., 2019b,
+Baste et al., 2020,
+Ingmar et al., 2020,
+Fomin et al., 2020].
+While, traditionally, one is interested in getting
+some optimal solution to a computational problem,
+this might not be sufficient in practice when side
+constraints are present, that are hard to model.
+Examples for those subjective criteria are aesthetic,
+economic, political, or environmental criteria. Due
+to its subjective vague nature, it can be impossible
+to model those criteria on the level of the prob-
+lem formulation.
+Hence, it can be preferable for
+the user to choose a slightly less optimal solution
+that suits her subjective criteria better. In order to
+provide the user with the ability to choose the solu-
+2
+
+tion that fits her needs best, it is preferable to pro-
+vide a reasonably sized solution set of sufficiently
+diverse solutions. But formalizing the diversity of
+a solution set is a non-trivial task, see the discus-
+sion in [Baste et al., 2020, Baste et al., 2019a]. In-
+tuitively, diversity serves as a measure of how rep-
+resentative a set of solutions is among the solution
+space. A quantum annealer naturally provides us
+with a set of solutions as it samples the solution
+space. Then, classical post-processing can be ap-
+plied to select a subset of these solutions suitable
+for the criteria at hand.
+Considering diverse alternatives is of relevance
+while
+selecting
+several
+good
+committees
+such
+that each committee member is not overloaded
+with work, as described in [Bredereck et al., 2020].
+Electing committees, or finding a ranking that
+agrees with a set of votes as much as possible,
+are key problems in the field of Social Choice.
+One of the most studied problems in the field is
+the Kemeny Rank Aggregation (KRA) prob-
+lem.
+Here, a set of votes over a set of candi-
+dates is given and the task is to find a rank-
+ing of the candidates that maximizes the satis-
+faction of the voters.
+The problem is of rele-
+vance in a variety of different areas such as simi-
+larity search and classification in high dimensional
+databases [Fagin et al., 2003], constructing genetic
+maps in bioinformatics [Jackson et al., 2008], ag-
+gregating search results and spam detection in
+a search engine [Dwork et al., 2001], etc.
+The
+popularity of KRA is due to the unique prop-
+erty
+of
+the
+Kemeny
+rule
+of
+being
+neutral,
+consistent, and satisfying the Condorcet prop-
+erty [Young and Levenglick, 1978].
+The
+KRA
+problem
+is
+NP-
+complete
+[Bartholdi et al., 1989]
+and
+re-
+mains
+NP-hard
+when
+restricted
+to
+only
+four
+votes
+[Dwork et al., 2001,
+Biedl et al., 2009].
+This hardness motivates the studies of heuris-
+tics
+and
+approximation algorithms for
+KRA,
+see
+[Dwork et al., 2001,
+Ailon et al., 2008,
+van Zuylen and Williamson, 2009],
+as
+well
+as
+parameterized
+algorithms
+[Betzler et al., 2009,
+Simjour, 2009,
+Arrighi et al., 2020,
+Betzler et al., 2014].
+The
+practical
+rele-
+vance
+in
+the
+field
+of
+artificial intelligence
+is
+also
+highlighted
+by
+a
+series
+of
+experimen-
+tal
+studies
+of
+heuristics
+and
+approximations
+of
+the
+KRA
+problem
+[Ali and Meila, 2012,
+Davenport and Kalagnanam, 2004]
+as
+well
+as
+experimental studies of lower bounds for ex-
+act
+solutions
+of
+KRA
+[Conitzer et al., 2006,
+Schalekamp and van Zuylen, 2009]. A parameter-
+ized algorithm for a diverse version of Kemeny
+Rank
+Aggregation
+recently
+appeared
+at
+IJCAI [Arrighi et al., 2021].
+In this work, we utilize the Adiabatic Quan-
+tum Model to get heuristics for the Diverse Ke-
+meny Rank Aggregation problem that provide
+us with a set of samples of the solution space. For
+this, we model KRA as a quadratic unconstrained
+binary optimization problem. Then, we compare
+the quantum based heuristics with classical heuris-
+tics that allow to sample different solutions such
+as simulated annealing and local search, as well as
+classical heuristics that compute deterministically
+only a single solution.
+As quantum computer are still quite restricted
+in the number of available qubits (currently 5,000+
+qubits), large instances are still a challenge to any
+quantum computer. To counter this fact, we imple-
+ment several data reduction rules as a preprocess-
+ing step. Those rules allow us to break an instance
+into smaller instances that can be solved indepen-
+dently. A final solution is then aggregated from the
+solutions of the smaller instances.
+This work is structured as follows. First, we give
+formal definitions for the QUBO and KRA prob-
+lem. Then, we describe the data reduction rules we
+used as well as the QUBO formulation obtained for
+KRA. We continue with the experimental part of
+the paper and introduce the considered solvers. In
+our experiments, we compare the runtime and ob-
+tained solution quality for all the solvers, and diver-
+sity of solutions for solvers that support computing
+multiple solutions. Thereby, we compare three dif-
+ferent preprocessing modes: no preprocessing, ap-
+plying the ≤3/4-majority rule exhaustively, and ap-
+plying the extended Condorcet rule.
+We present
+our observations at the end of this paper. Our im-
+plementation and the used data-sets are available
+as supplementary material.
+2
+Preliminaries
+Let Q be an n × n matrix. We write Qij for the
+entry in row i and column j of Q.
+Let n be a
+non-negative integer. We denote [n] = {1, 2, . . .n}.
+3
+
+Consequently, [0] = ∅.
+2.1
+Quadratic
+Unconstrained
+Bi-
+nary Optimization
+We now give a formal definition of the Quadratic
+Unconstrained
+Binary
+Optimization
+(QUBO) problem.
+Let Q be an n × n ma-
+trix
+of
+weights
+and
+x1, x2, . . . , xn
+be
+binary
+variables. Then, the QUBO problem asks for an
+assignment of the variables xi, for i ∈ [n] that
+minimizes
+�
+i,j
+Qijxixj.
+2.2
+Kemeny Rank Aggregation
+Let C be a finite set of candidates. A vote (or rank-
+ing) π over C is a total order on C. If for two candi-
+dates a, b ∈ C, candidate a is ranked better than b
+in the vote π, then we write a <π b. Therefore, the
+smallest candidate a according to <π is the winner
+of the vote π and can be interpreted as getting posi-
+tion 1. For two votes πi and πj the number of pairs
+of candidates which are ordered differently within
+these votes is called the Kendall Tau distance of
+πi and πj, which is written as KT-distance(πi, πj).
+Formally, this means:
+KT-distance(πi, πj) = |{(c1, c2) ∈ C × C |
+c1 <πi c2 ∧ c1 >πj c2}|
+Given a ranking π over C and a set Π of votes
+over C, the Kemeny score of π w.r.t. Π, is the sum
+of the Kendall Tau distances between π and each
+πi ∈ Π. The goal of KRA is to compute a ranking
+πmin of C, with the smallest possible Kemeny score.
+Such a ranking is called a Kemeny ranking.
+3
+Framework
+In this section, we aim to give a theoretical ex-
+planation of the concepts we are using.
+First,
+we present data reduction rules for KRA, taken
+from [Betzler et al., 2014], that we implemented as
+a preprocessing step.2 Then, we present and our
+QUBO formulation for KRA.
+2In [Betzler et al., 2014] votes are interpreted in the in-
+verse way, meaning that candidate a is ranked better than b
+in a vote if a > b. Hence, in the original work, the following
+rules are defined according to the ≥s-majority.
+3.1
+Data Reduction Rules
+As the number of available qubits on a quantum
+annealer is restricted we use some known data re-
+duction rules as a preprocessing step that cut an
+instance into a collection of smaller instances that
+can be solved independently.
+3.1.1
+≤3/4-Majority Rule
+Let C be a set of candidates and Π be as set of
+votes.
+Further, let a, b ∈ C be candidates.
+If,
+for all votes πi over C, a <πi b, then a < b in
+a Kemeny ranking.
+Intuitively, if a gets a lower
+ranking than b in every single vote, a obviously
+has to be placed lower than b in a Kemeny rank-
+ing. We can generalize this idea in the following
+way. Let s ∈ [0, 1]. If a <πi b in at least s · |Π|
+many votes πi, then we say that the pair (a, b)
+is a clean pair according to the ≤s-majority and
+denote this by a ≤s b. If a candidate a forms a
+clean pair according to the ≤s-majority with ev-
+ery other candidate b ∈ C \ {a}, then we call a a
+clean candidate with respect to the ≤s-majority.
+It was shown in [Betzler et al., 2014, Lemma 1]
+that for clean candidates with respect to the ≤3/4-
+majority (s = 3/4), every Kemeny ranking re-
+spects the clean pairs in which a is involved. Based
+on this observation, a linear partial kernel with
+respect to the parameter da was obtained where
+da = �
+πi,πj∈Π KT-distance(πi, πj)/(|C| · (|C| − 1))
+is the average KT-distance. The kernel is based on
+the following ≤3/4-majority rule:
+For
+a
+KRA
+instance
+(C, Π),
+let
+N
+:=
+{n1, . . . , nt} be the set of clean candidates with re-
+spect to the ≤3/4-majority such that ni ≤3/4 ni+1
+for i ∈ [t − 1]. Then, define
+D0 := {c ∈ C \ N | c ≤3/4 n1},
+Di := {c ∈ C \ N | ni ≤3/4 c ∧ c ≤3/4 ni+1},
+Dt := {c ∈ C \ N | nt ≤3/4 c},
+for i ∈ [t − 1]. Replace the original instance by the
+t + 1 sub-instances induced by Di for 0 ≤ i ≤ t.
+As shown by Betzler et al., this data reduction
+rule is safe and preserves all Kemeny rankings, a
+desirable property for computing a diverse set of
+Kemeny rankings. Another benefit of this rule is
+that the individual sub-instances can be solved in-
+dependently on a quantum annealer needing way
+fewer qubits than the original instance.
+4
+
+3.1.2
+Extended Condorcet Rule
+In the extended Condorcet rule, we move from com-
+paring the relative position of one candidate to all
+other candidates to considering the relative posi-
+tion of a set of candidates C′ to the remaining can-
+didates C \ C′. Thereby, the rule cuts an instance
+according to the strongly connected components of
+its majority graph.
+Definition 1 (Majority graph). Let (C, Π) be
+an instance of KRA. The weak (strict) marjority
+graph of (C, Π) is a directed graph with vertex set
+C and an arc from u to v if and only if u < v in at
+least (in more than) half of the votes.
+As our interest is in computing a diverse set of
+solutions, we use a version of the extended Con-
+dorcet rule which is based on the weak majority
+graph and which preserves all Kemeny rankings. If
+the context is clear, we call this rule the Condorcet
+rule. It works as follows [Betzler et al., 2014]. Let
+(C, Π) be an election and let C1, C2, . . . , Ct ⊆ C
+be the vertex sets of the strongly connected com-
+ponents in the weak majority graph of (C, Π) fol-
+lowing a topological order.
+Replace the original
+instance by the sub-instances induced by Ci with
+|Ci| ≥ 2, i ∈ [t].
+While this rule preserves all Kemeny rank-
+ings, it is possible that the instance obtained af-
+ter applying this rule can still be reduced by
+the ≤3/4-majority rule, as shown in Example 2
+of [Betzler et al., 2014]. If we instead consider the
+strongly connected components of the strict major-
+ity graph, the resulting kernel, with respect to the
+parameter da, cannot be further compressed by the
+≤3/4-majority rule, implying a smaller kernel size,
+but we might lose Kemeny rankings as pairs of can-
+didates with exactly 1/2 of the votes in both direc-
+tions are not connected in the strict majority graph
+and an ordering on them must be fixed during the
+topological ordering. As our objective is to leave
+the computation of multiple solutions to the quan-
+tum annealer, we used the Condorcet rule based on
+the weak majority graph in the following. Alterna-
+tively, we could restrict ourselves to only comput-
+ing multiple solutions on the sub-instances and use
+classical post processing in order to compute all
+topological orderings of the strict majority graph
+and concatenate the solutions of the sub-instances
+accordingly. It is not hard to see that once we have
+the strongly connected components, computing a
+diverse set of topological orderings can be done by
+seeing the problem as an instance of the Comple-
+tion of an Ordering problem with all costs set
+to 1 and using the parameterized algorithm for the
+diverse version proposed in [Arrighi et al., 2021].
+3.2
+QUBO formulation for Kemeny
+Rank Aggregation
+We now discuss our QUBO formulation of KRA:
+Given a ranking over a set of n candidates C,
+we use n2 binary variables, denoted by ci,j with
+1 ≤ i, j ≤ n. Intuitively, if variable ci,j = 1, this
+means candidate i has position j. Binary variables
+might only take the values 0 or 1 which can be
+interpreted as Boolean values.
+We interpret the
+variables ci,j as a two-dimensional grid. In order
+to obtain a valid Kemeny ranking, we have to en-
+sure, that each candidate has exactly one position
+within the final ranking (∀i : �n
+j=1 ci,j = 1, we
+achieve this via so called row-penalties) and that
+each position is taken by exactly one candidate
+(∀j : �n
+i=1 ci,j = 1, this, in turn, is achieved via
+column-penalties).
+A penalty is a huge positive
+weight that is multiplied to a term in the objec-
+tive function which gets a positive value under a
+variable assignment that we want to forbid.
+By
+turning side-constraints into penalty terms, we can
+obtain an unconstrained QUBO instance. There-
+fore, we need to ensure that the cost of a penalty is
+too high to be be paid in any optimal solution. We
+choose P = |C|2 · |Π| as the penalty. This choice
+gets clear later.
+3.2.1
+Row-Penalties
+The row-penalties ensure that each candidate gets
+assigned exactly one position. This is obtained by
+the following term of the final objective function.
+For each row i ∈ [n] we define
+rowi = P
+
+1 − (
+n
+�
+j=1
+ci,j)
+
+
+2
+The minimal value for this equation is 0, which is
+obtained if and only if exactly one of the ci,j in the
+sum is true. If for fixed i, none of the variables ci,j,
+for j ∈ [n] is true, then the term rowi evaluates
+5
+
+to P. If on the other hand k > 1 many variables
+ci,j are true, then rowi evaluates to P(1 − k)2 =
+P(−(k − 1))2 = P(k − 1)2 ≥ P.
+3.2.2
+Column-Penalties
+Similarly, the column-penalties ensure that each
+position j is assigned with exactly one candidate.
+For each j ∈ [n] we set:
+colj = P
+�
+1 − (
+n
+�
+i=1
+ci,j)
+�2
+3.2.3
+Ranking-Penalties
+Lastly, we need to represent the actual votes them-
+selves. This is achieved via penalties for each pair
+of variables ci,j, ci′,j′ with i ̸= i′ and j ̸= j′. The
+goal is to give the quadratic term ci,jci′,j′ a weight
+that reflects how many votes are violated if both,
+candidate i gets position j and candidate i′ gets
+position j′. It was shown in [Arrighi et al., 2020,
+Sec. 5.1] that the Kemeny score of a ranking can be
+computed by summing over the cost of each pair of
+candidates, i.e., the number of votes in which the
+relative position of the pair is violated. This way,
+summing up the penalties over all pairs of candi-
+dates, we obtain the Kemeny score of the ranking
+associated with a variable assignment.
+Let wi,j be the total number of votes, in which
+candidate cj is positioned better than candidate ci.
+More formally3, wi,j = �
+π∈Π[cj <π ci]. If we vi-
+olate this relative position of candidates in an ag-
+gregated ranking, then wi,j is the cost we need to
+pay in order to place candidate ci before candidate
+cj. This leaves us with the following term encoding
+the cost of placing candidate ci before candidate cj.
+For each i, j ∈ [n] we define:
+ranki,j = wi,j ·
+n−1
+�
+k=1
+n
+�
+l>k
+ci,kcj,l
+3.2.4
+The final formulation
+We are ready to formulate the final unconstrained
+objective function depending on all variables ci,j
+3The bracket notation reads as follows: if p is a logical
+proposition, then [p] yields 1 if p is true and else, [p] yields
+0.
+for i, j ∈ [n]:
+f(c1,1 . . . cn,n) =
+n
+�
+i=1
+
+rowi + coli +
+n
+�
+j=1
+ranki,j
+
+
+Coming back to the penalty P used for row-
+and column-penalties:
+Since we choose it to be
+P = |C|2 · |Π|, we now see, that even if every sin-
+gle vote contradicts every single possible relative
+positioning (which is an impossible to reach upper
+bound) breaking the rules of each candidate tak-
+ing exactly one position and each position being
+taken by exactly one candidate, will still come with
+a higher penalty, and thus will never happen in an
+optimal solution.
+4
+Implementation
+The project is written in Python using D-Wave’s
+Dimod API.
+4.1
+Data-sets
+We use two different data-sets in our evaluation.
+The first is the Formula 1 data-set from the ex-
+perimental evaluation of the data reduction rules
+in [Betzler et al., 2014]. The number of candidates
+in this data-set ranges from 6 to 28.
+They also
+considered other real world data-sets such as ski
+rankings and web search results. But those data-
+sets focus on instances with up to 69, resp., 200
+candidates, which are too large to be mapped onto
+the physical hardware of the considered quantum
+annealers. Hence, we exclude them from our eval-
+uation.
+In contrast, we included a second data-set of ran-
+domly generated instances ranging from 3 to 100
+candidates in order to gradually increase the in-
+stance size to find the limitations of the different
+solver. We created the instance by starting with
+a sorted list and then shuffling it with standard
+python methods. As expected, the randomly gen-
+erated instances do not provide much structure for
+the data reduction rules and are used for compar-
+ing the runtime and solution quality of the different
+solvers with different parameters. In contrast, the
+Formula 1 data is used to compare the diversity
+of solutions and the impact of the data reduction
+6
+
+rules. Details on the encoding of the data, docu-
+mentation of our implementation as well as instruc-
+tions on how to run the experiments can be found
+in the supplementary material along with the code
+and the data-sets.
+4.2
+Preprocessing
+We implemented the above described data reduc-
+tion rules that cut instances into subinstances. If
+we aim for a diverse solution set, we concatenate
+the best solutions among the sub-instances in a
+cross-product manner. The available modes are: no
+data reduction, ≤3/4-majority rule, and Condorcet
+rule.
+4.3
+Solving with Different Solvers
+With the problem formulation finished, the BQM
+model can be solved by a variety of different solvers,
+each with different pros and cons. Generally, the
+solvers provided by D-Wave can be split into 3 cate-
+gories: mathematical solving, simulated annealing,
+and real quantum annealing.
+4.3.1
+Steepest Decent
+The first solver, SteepDes, that we consider from
+the repertoire of D-Wave uses a steepest descent
+approach which is the discrete analogue of gradi-
+ent descent, but the best move is computed using
+a local minimization rather than computing a gra-
+dient. For a given input QUBO on n variables, the
+runtime complexity of the underlying C++ imple-
+mentation is O(n2) for the initialization phase and
+O(n) per downhill step.
+At the time of our ex-
+periments, SteepDes did not support to compute
+multiple solutions.
+4.3.2
+Simulated annealing
+Simulated annealing is a probabilistic technique
+for finding local optima of a given objective
+function.
+D-Wave provides with the SimAnl
+solver an
+implementation
+of a
+simulated an-
+nealing algorithm that approximates Boltzmann
+sampling.
+Their
+approach follows the
+work
+of [Kirkpatrick et al., 1983].
+4.3.3
+Quantum annealing
+D-Wave provides two different types of quantum
+annealers: a quantum processing unit (QPU), and a
+hybrid model. In the hybrid model, the Ocean SDK
+takes care of assigning a QUBO instance to qubit
+bias and coupling values for the hardware graph,
+with the drawback of restricted access to parame-
+ters like the number of samples (num_read) or the
+number of output solutions. In contrast, the QPU
+model allows for direct access to the quantum ma-
+chine but requires the user to take care of optimal
+values for parameters as well as finding an embed-
+ding onto the hardware herself. The latter is a non-
+trivial task and without your own implementation,
+just a general heuristic is available that only allows
+to embed significantly smaller instances than pos-
+sible with the hybrid model. The most developed
+QPU family currently available is the Advantage
+model with over 5,000 qubits. In comparison with
+its predecessor, the 2,000Q QPU, it relies on a new
+topology, the Pegasus graph, describing the connec-
+tivity of qubits on the chip. In our experiments we
+use the Advantage model. We refer to the solver
+based on the hybrid model as Hybrid, and to the
+Advantage QPU as QAnl.
+Local
+Search
+We
+implemented
+the
+local
+search
+algorithm
+described
+in
+[Schalekamp and van Zuylen, 2009].
+Local
+search was also considered in the experiments
+in [Ali and Meila, 2012] where it was observed to
+compute significantly better solutions than faster
+algorithms like Borda.
+The algorithms goes
+through the candidates in a random order. When
+considering position i, the candidate at position
+i is moved to the position that gives the largest
+improvement to the current Kemeny score.
+The
+procedure stops if no element has been moved and
+all positions were considered.
+As the algorithms
+uses a random order, we execute the local search
+algorithm multiple times in order to compute
+multiple solutions.
+Borda
+We implemented the Borda algorithm
+from [Ali and Meila, 2012].
+It computes (in our
+notation) for each candidate a the value qci =
+�
+cj∈C wi,j and then returns the permutation of
+candidates that sorts qci
+in descending order.
+As the algorithm computes a single solution de-
+7
+
+terministically it is not able to compute a di-
+verse set of solutions.
+In [Ali and Meila, 2012]
+it
+was
+observed
+that
+in
+the
+case
+of
+no
+or
+strong consensus, the Borda performs best among
+the considered solver.
+Also in the compar-
+ison
+[Schalekamp and van Zuylen, 2009]
+Borda
+performed very well.
+Quick-Sort
+Several
+sorting
+based
+algorithms
+were
+considered
+in
+[Ali and Meila, 2012]
+from
+which the one based on quick sort performed best
+in our experiments. The algorithm sorts the can-
+didates according to the predicate wij < wji that,
+if true, sorts candidate ci left of candidate cj. Also
+QuickSort is only able to compute a single solu-
+tion.
+4.4
+Parameters
+We focus our analysis on the impact of two pa-
+rameters.
+The parameter num_reads determines
+the number of samples performed by the solver.
+Its standard value is 1. Increasing this parameter
+leads to better solutions but causes higher runtime.
+We investigate its impact in Exp. 2. At the time
+of our experiments, num_reads is supported by all
+solvers from D-Wave, except Hybrid. The param-
+eter max_answers determines the number of solu-
+tions output by the solvers. While at the beginning
+of this project max_answers was also supported by
+the Hybrid solver, at the time of our experiment
+it is only supported by QAnl, and SimAnl.
+5
+Experimental Results
+All local solver benchmark tests were performed on
+a system running Linux Pop OS (Ubuntu 22.4 LTS)
+with a 5.17.5 kernel, an AMD Ryzen 5 2600X six
+core processor (12 threads) with a 3.6 GHz base
+clock and a 4.2 GHz boost clock speed, equipped
+with 32GB 3200MHz ram.
+5.1
+Exp. 1:
+Runtime Performance
+(Fig. 1)
+We measure the runtime for each solver on a set
+of randomly generated instances of increasing size
+with 10 instances per size (number of candidates).
+3
+4
+5
+10
+20
+50
+100
+10−4
+10−3
+10−2
+10−1
+100
+101
+102
+103
+Size of Instance [|C|]
+Sample time [s]
+LocSearch
+SteepDes
+Hybrid
+Borda
+QAnl
+QuickSort
+SimAnl
+Figure 1: Sample, respectively, QPU time with in-
+creasing number of candidates, average over 10 ran-
+dom instances.
+Each instance contains as many votes as candi-
+dates. All solvers were initialized with default pa-
+rameters, and only the pure sample time is mea-
+sured. For the Hybrid solver, the QPU time was
+measured.
+We observe that the sampling time of QAnl,
+Hybrid, and LocSearch stays rather constant,
+while the runtime for SimAnl, SteepDes, Borda,
+and QuickSort first outperforms the other solver
+but then increases significantly with larger instance
+sizes.
+5.2
+Exp. 2: Solution Quality (Fig. 2)
+Since a default sample size of 1 is used for QAnl,
+SimAnl, and SteepDes, larger instances are not
+going to be solved optimally. In fact, solution qual-
+ity is greatly decreasing with increasing instance
+size. To improve solution quality, with the param-
+eter num_read we can set the number of samples
+taken.
+In order to measure solution quality, the
+cost of an optimal solution is calculated by an In-
+teger Linear Program and compared with the Ke-
+meny score of the best solution found by the differ-
+ent solvers. We measured average solution quality
+and average runtime for all random instances of size
+20, with increasing num_read. For comparison, also
+the other solvers is visualized, although they do not
+support the parameter. The QAnl solver was ex-
+cluded from this experiment as it could not solve
+the instances of size 20 and only showed trivial be-
+havior on smaller sized instances.
+8
+
+-
+default
+10
+100
+1000
+10000
+1
+1.02
+1.04
+1.06
+1.08
+1.1
+1.12
+1.14
+Number of reads [num read]
+Solution quality as factor of optimal solution
+SimAnl quality
+SteepDes quality
+Hybrid quality
+LocSearch quality
+Borda quality
+QuickSort quality
+10−3
+10−2
+10−1
+100
+101
+Sampletime [s]
+SimAnl time
+SteepDes time
+Hybrid time
+LocSearch time
+Borda time
+QuickSort time
+Figure 2: Solution quality as a factor of the optimal
+solution, average over 10 random instances with 20
+candidates.
+SimAnl and SteepDes show a clear trade-
+off between solution quality and sample time.
+With the default parameters, Hybrid outperforms
+SimAnl and SteepDes in solution quality. With
+increasing num_read, SimAnl and SteepDes do
+outperform Hybrid in terms of solution quality.
+For SimAnl this only happens with a huge increase
+in sample time. With num_read = 100, SteepDes
+outperforms Hybrid in solution quality and sam-
+ple time. Increasing num_read lets SteepDes find
+the optimal solution with a slightly higher sample
+time than Hybrid.
+From those solvers allowing
+to compute multiple solutions, LocSearch shows
+the best solution quality under the standard pa-
+rameters but also has the highest runtime.
+5.3
+Exp. 3:
+Diversity and Prepro-
+cessing (Fig. 3 - 5)
+Next, we measure the solution quality, diversity of
+solutions, and runtime for those solver that can
+compute a set of solution at once. More precisely,
+we compare the annealing based solvers SimAnl,
+Hybrid, QAnl, and LocSearch with and with-
+out preprocessing.
+Recall that Borda, Quick-
+Sort, and SteepDes do not support to output
+multiple solutions on a single run of the solver and
+are hence not included in this experiment. As our
+previously considered randomized data do not con-
+tain enough structure for the data reduction rules,
+we use the Formula 1 data. We observe that on
+the Formula 1 data, the ≤3/4-majority rule never
+0
+10
+20
+30
+40
+50
+0
+10
+20
+30
+40
+50
+Percentage over optimal solution [%]
+Hybrid none
+Hybrid Condorcet
+SimAnl none
+SimAnl Condorcet
+LocSearch none
+QAnl Condorcet
+Figure 3: Depicted is by how much % the Kemeny
+score of the best solution found is above the optimal
+solution.
+applies.
+Hence, we excluded it from the evalua-
+tion presented here. For the SimAnl and D-Wave
+all experiments were performed with num_read =
+10, 000 and up to the best 10 solutions were taken
+into the solution set on which we measure the diver-
+sity as the pairwise minimal KT-distance and the
+average KT-distance. For LocSearch, we run the
+solver 50 times and take the 10 best solutions found
+into account. The depicted runtime is the total run-
+time of all 50 runs. Not all instances were solvable
+on the quantum annealers. When a data point is
+missing, this instance was either not embeddable
+onto the hardware or an invalid solution, break-
+ing a row or column constraint, was returned. The
+instances are sorted by the number of candidates
+in increasing order. As in [Betzler et al., 2014] we
+removed invalid votes containing duplicated candi-
+dates and candidates not appearing in every vote.
+In contrast to SimAnl, LocSearch did not al-
+ways found 10 different solutions. If D-Wave could
+solve the instance at all, it nearly always output 10
+different solutions.
+Observations
+We
+observe
+that
+the
+≤3/4-
+majority rule does not reduce any instance.
+In
+contrast,
+the Condorcet rule cuts 1/3 of the
+instances into two sub-instances and 1/6 of the
+instances into 3 sub-instances. Further, it reduces
+the size of nearly every instance.
+While the
+Hybrid solver was able to solve nearly every
+instance in both preprocessing modes, the QAnl
+could only solve some instances after applying
+the Condorcet rule.
+Applying the Condorcet
+9
+
+0
+10
+20
+30
+40
+50
+0
+50
+100
+150
+200
+250
+KT-distance among diverse solution
+SimAnl none min KT
+SimAnl Condorcet min KT
+SimAnl none avg. KT
+SimAnl Condorcet avg. KT
+LocSearch none avg. KT
+QAnl Condorcet min KT
+QAnl Condorcet avg. KT
+Figure
+4:
+Minimal
+and
+average
+pairwise
+KT-distance over the best 10 solutions found
+with and without Condorcet rule.
+rule increases the solution quality for all solvers
+significantly. With this rule, most of the instances
+were solved optimally by all solvers. Surprisingly
+with respect to solution quality, without prepro-
+cessing, the simulated and non-simulated annealers
+performed similarly.
+Among the considered 10
+best solutions, the Kemeny score of the solutions
+differed only slightly.
+This means that similarly
+good different solutions were found. With respect
+to the diversity,
+applying the Condorcet rule
+reduced the minimal and average KT-distance
+for SimAnl significantly.
+In contrast, for the
+QAnl solver,
+the average KT-distance seems
+to not be affected by the Condorcet rule.
+One
+could observe that the Condorcet rule allows for
+more instances to be solved with the QAnl with
+a better solution quality and a higher diversity,
+but those observations need to be considered
+with caution as we were only able to solve a few
+instances on the plain quantum annealer.
+With
+respect to sample time, the QPU time of Hybrid
+was significantly shorter than the sample time of
+SimAnl.
+While the Condorcet rule reduces the
+total sampling time for SimAnl, it increases the
+total QPU time for Hybrid.
+We explain this
+by the increased charging time for the hardware
+couples which is the biggest part of the QPU time.
+As multiple sub-instances need to be solved, the
+hardware must be charged multiple times.
+We
+explain the higher QPU time of QAnl in contrast
+to Hybrid with the high number of reads for
+QAnl in contrast to the unaccessible standard
+value for Hybrid. When setting num_read= 100,
+0
+10
+20
+30
+40
+50
+10−2
+10−1
+100
+101
+102
+103
+sample / QPU time (sum over kernels) [s]
+SimAnl none
+SimAnl Cond.
+LocSearch none
+Hybrid none
+Hybrid Cond.
+QAnl Cond.
+Figure 5:
+Sample time, respectively, QPU time
+with and without Condorcet rule.
+QAnl showed similar QPU times as Hybrid with
+only a slight decrease in solution quality.
+Even without preprocessing, LocSearch nearly
+always found the optimal solution, but only in
+60% of the instances it found 10 different solutions,
+while SimAnl did so in 90% of the instances. The
+Kemeny score of the 10th best solutions differed
+only slightly between SimAnl and LocSearch. In
+terms of runtime, LocSearch was one magnitude
+faster than SimAnl while Hybrid was the fastest
+on nearly all instances showing a constant runtime.
+If we applied the Condorcet rule as a preprocessing
+step to Hybrid, it found in 50% of the instances
+with more than 15 candidates similar good solu-
+tions as LocSearch.
+6
+Conclusion
+The property of quickly performing a huge num-
+ber of samples of the solution space can become
+one of the main advantages of Quantum Anneal-
+ing. Our experiments indicate that with Quantum
+Annealing, we can compute a set of solutions that
+shows quite good diversity with a very good run-
+time behavior. But the full potential of Quantum
+Annealing can only be examined once the hard-
+ware evolved further and allows to solve larger in-
+stances. Until then, combining Quantum Anneal-
+ing with data reduction rules as a preprocessing
+step can lead to promising near-term applications.
+10
+
+References
+[Adachi and Henderson, 2015] Adachi, S. H. and
+Henderson, M. P. (2015). Application of quan-
+tum annealing to training of deep neural net-
+works. arXiv preprint arXiv:1510.06356.
+[Aharonov et al., 2008] Aharonov, D., van Dam,
+W., Kempe, J., Landau, Z., Lloyd, S., and
+Regev, O. (2008). Adiabatic quantum compu-
+tation is equivalent to standard quantum com-
+putation. SIAM Rev., 50(4):755–787.
+[Ailon et al., 2008] Ailon, N., Charikar, M., and
+Newman, A. (2008).
+Aggregating inconsistent
+information: Ranking and clustering. J. ACM,
+55(5):23:1–23:27.
+[Ali and Meila, 2012] Ali, A. and Meila, M. (2012).
+Experiments with kemeny ranking: What works
+when? Math. Soc. Sci., 64(1):28–40.
+[Arrighi et al., 2020] Arrighi,
+E.,
+Fernau,
+H.,
+de Oliveira Oliveira, M., and Wolf, P. (2020).
+Width notions for ordering-related problems. In
+Saxena, N. and Simon, S., editors, FSTTCS,
+volume 182 of LIPIcs, pages 9:1–9:18. Schloss
+Dagstuhl - Leibniz-Zentrum f¨ur Informatik.
+[Arrighi et al., 2021] Arrighi, E., Fernau, H., Lok-
+shtanov, D., de Oliveira Oliveira, M., and Wolf,
+P. (2021). Diversity in kemeny rank aggregation:
+A parameterized approach. In Zhou, Z., editor,
+IJCAI, pages 10–16. ijcai.org.
+[Arute et al., 2019] Arute, F., Arya, K., Babbush,
+R., Bacon, D., Bardin, J. C., Barends, R.,
+Biswas, R., Boixo, S., Brandao, F. G., Buell,
+D. A., et al. (2019).
+Quantum supremacy us-
+ing a programmable superconducting processor.
+Nature, 574(7779):505–510.
+[Bartholdi et al., 1989] Bartholdi, J., Tovey, C. A.,
+and Trick, M. A. (1989).
+Voting schemes for
+which it can be difficult to tell who won the elec-
+tion. Social Choice and welfare, 6(2):157–165.
+[Baste et al., 2020] Baste, J., Fellows, M. R., Jaf-
+fke, L., Masar´ık, T., de Oliveira Oliveira, M.,
+Philip, G., and Rosamond, F. A. (2020). Diver-
+sity of solutions: An exploration through the lens
+of fixed-parameter tractability theory. In IJCAI,
+pages 1119–1125.
+[Baste et al., 2019a] Baste, J., Jaffke, L., Masaˇr´ık,
+T., Philip, G., and Rote, G. (2019a).
+Fpt al-
+gorithms for diverse collections of hitting sets.
+Algorithms, 12(12):254.
+[Baste et al., 2019b] Baste, J., Jaffke, L., Masaˇr´ık,
+T., Philip, G., and Rote, G. (2019b). FPT al-
+gorithms for diverse collections of hitting sets.
+Algorithms, 12:254.
+[Betzler et al., 2014] Betzler, N., Bredereck, R.,
+and Niedermeier, R. (2014).
+Theoretical and
+empirical evaluation of data reduction for exact
+kemeny rank aggregation. Auton. Agents Multi
+Agent Syst., 28(5):721–748.
+[Betzler et al., 2009] Betzler, N., Fellows, M. R.,
+Guo, J., Niedermeier, R., and Rosamond, F. A.
+(2009). Fixed-parameter algorithms for kemeny
+rankings.
+Theor. Comput. Sci., 410(45):4554–
+4570.
+[Biedl et al., 2009] Biedl, T. C., Brandenburg, F.,
+and Deng,
+X. (2009).
+On the complexity
+of crossings in permutations.
+Discret. Math.,
+309(7):1813–1823.
+[Bredereck et al., 2020] Bredereck, R., Kaczmar-
+czyk, A., and Niedermeier, R. (2020).
+Elect-
+ing successive committees: Complexity and algo-
+rithms. In AAAI, pages 1846–1853. AAAI Press.
+[Bunyk et al., 2014] Bunyk,
+P.
+I.,
+Hoskinson,
+E. M., Johnson, M. W., Tolkacheva, E., Al-
+tomare, F., Berkley, A. J., Harris, R., Hilton,
+J. P., Lanting, T., Przybysz, A. J., et al. (2014).
+Architectural considerations in the design of a
+superconducting quantum annealing processor.
+IEEE Transactions on Applied Superconductiv-
+ity, 24(4):1–10.
+[Cipra, 2000] Cipra, B. A. (2000). The ising model
+is np-complete. SIAM News, 33(6):1–3.
+[Conitzer et al., 2006] Conitzer,
+V.,
+Davenport,
+A. J., and Kalagnanam, J. (2006).
+Improved
+bounds for computing kemeny rankings.
+In
+AAAI, pages 620–626. AAAI Press.
+[Crosson and Harrow, 2016] Crosson, E. and Har-
+row, A. W. (2016). Simulated quantum anneal-
+ing can be exponentially faster than classical
+simulated annealing. In FOCS, pages 714–723.
+IEEE.
+11
+
+[Davenport and Kalagnanam, 2004] Davenport,
+A. J. and Kalagnanam, J. (2004). A computa-
+tional study of the kemeny rule for preference
+aggregation. In McGuinness, D. L. and Fergu-
+son, G., editors, AAAI, pages 697–702. AAAI
+Press / The MIT Press.
+[Dwork et al., 2001] Dwork, C., Kumar, R., Naor,
+M., and Sivakumar, D. (2001). Rank aggregation
+methods for the web. In Shen, V. Y., Saito, N.,
+Lyu, M. R., and Zurko, M. E., editors, WWW,
+pages 613–622. ACM.
+[Fagin et al., 2003] Fagin,
+R.,
+Kumar,
+R.,
+and
+Sivakumar, D. (2003). SIGMOD. pages 301–312.
+ACM.
+[Farhi et al., 2001] Farhi, E., Goldstone, J., Gut-
+mann, S., Lapan, J., Lundgren, A., and Preda,
+D. (2001).
+A quantum adiabatic evolution al-
+gorithm applied to random instances of an np-
+complete problem. Science, 292(5516):472–475.
+[Farhi et al., 2000] Farhi, E., Goldstone, J., Gut-
+mann, S., and Sipser, M. (2000). Quantum com-
+putation by adiabatic evolution. arXiv preprint
+quant-ph/0001106.
+[Fomin et al., 2020] Fomin, F. V., Golovach, P. A.,
+Jaffke, L., Philip, G., and Sagunov, D. (2020).
+Diverse pairs of matchings. In ISAAC. Schloss
+Dagstuhl-Leibniz-Zentrum f¨ur Informatik.
+[Grover, 1996] Grover, L. K. (1996). A fast quan-
+tum mechanical algorithm for database search.
+In Miller, G. L., editor, STOC, pages 212–219.
+ACM.
+[Harris et al., 2010] Harris,
+R.,
+Johansson,
+J.,
+Berkley, A., Johnson, M., Lanting, T., Han, S.,
+Bunyk, P., Ladizinsky, E., Oh, T., Perminov, I.,
+et al. (2010). Experimental demonstration of a
+robust and scalable flux qubit. Physical Review
+B, 81(13):134510.
+[Hu et al., 2019] Hu, F., Wang, B.-N., Wang, N.,
+and Wang, C. (2019). Quantum machine learn-
+ing with d-wave quantum computer. Quantum
+Engineering, 1(2):e12.
+[Ingmar et al., 2020] Ingmar,
+L.,
+de la Banda,
+M. G., Stuckey, P. J., and Tack, G. (2020). Mod-
+elling diversity of solutions.
+In AAAI, pages
+1528–1535. AAAI Press.
+[Istrail, 2000] Istrail, S. (2000). Statistical mechan-
+ics, three-dimensionality and np-completeness: I.
+universality of intracatability for the partition
+function of the ising model across non-planar
+surfaces (extended abstract). In Yao, F. F. and
+Luks, E. M., editors, STOC, pages 87–96. ACM.
+[Jackson et al., 2008] Jackson, B. G.,
+Schnable,
+P. S., and Aluru, S. (2008). Consensus genetic
+maps as median orders from inconsistent sources.
+IEEE ACM Trans. Comput. Biol. Bioinform.,
+5(2):161–171.
+[Johnson et al., 2011] Johnson,
+M.
+W.,
+Amin,
+M. H., Gildert, S., Lanting, T., Hamze, F.,
+Dickson, N., Harris, R., Berkley, A. J., Jo-
+hansson, J., Bunyk, P., et al. (2011).
+Quan-
+tum annealing with manufactured spins. Nature,
+473(7346):194–198.
+[King et al., 2022] King, A. D., Suzuki, S., Ray-
+mond, J., Zucca, A., Lanting, T., Altomare,
+F., Berkley, A. J., Ejtemaee, S., Hoskinson, E.,
+Huang, S., et al. (2022).
+Coherent quantum
+annealing in a programmable 2000-qubit ising
+chain. arXiv preprint arXiv:2202.05847.
+[Kinjo et al., 2003] Kinjo, M., Sato, S., and Naka-
+jima, K. (2003). Quantum adiabatic evolution
+algorithm for a quantum neural network.
+In
+Kaynak, O., Alpaydin, E., Oja, E., and Xu, L.,
+editors, ICANN/ICONIP, volume 2714 of Lec-
+ture Notes in Computer Science, pages 951–958.
+Springer.
+[Kirkpatrick et al., 1983] Kirkpatrick,
+S.,
+Gelatt Jr, C. D., and Vecchi, M. P. (1983).
+Optimization by simulated annealing. Science,
+220(4598):671–680.
+[Koshka and Novotny, 2020] Koshka,
+Y.
+and
+Novotny, M. A. (2020). Comparison of d-wave
+quantum
+annealing
+and
+classical
+simulated
+annealing
+for
+local
+minima
+determination.
+IEEE Journal on Selected Areas in Information
+Theory, 1(2):515–525.
+[McGeoch, 2014] McGeoch, C. C. (2014).
+Adia-
+batic Quantum Computation and Quantum An-
+nealing: Theory and Practice. Synthesis Lectures
+on Quantum Computing. Morgan & Claypool
+Publishers.
+12
+
+[Morita and Nishimori, 2008] Morita,
+S.
+and
+Nishimori, H. (2008). Mathematical foundation
+of quantum annealing. Journal of Mathematical
+Physics, 49(12):125210.
+[Ohzeki and Nishimori, 2011] Ohzeki,
+M.
+and
+Nishimori, H. (2011). Quantum annealing: An
+introduction and new developments.
+Journal
+of Computational and Theoretical Nanoscience,
+8(6):963–971.
+[Petit and Trapp, 2019] Petit, T. and Trapp, A. C.
+(2019).
+Enriching solutions to combinatorial
+problems via solution engineering.
+INFORMS
+Journal on Computing, 31(3):429–444.
+[Schalekamp and van Zuylen, 2009] Schalekamp,
+F. and van Zuylen, A. (2009).
+Rank aggrega-
+tion: Together we’re strong. In Finocchi, I. and
+Hershberger, J., editors, ALENEX, pages 38–51.
+SIAM.
+[Shor, 1994] Shor, P. W. (1994).
+Algorithms for
+quantum computation: Discrete logarithms and
+factoring. In FOCS, pages 124–134. IEEE Com-
+puter Society.
+[Simjour, 2009] Simjour, N. (2009). Improved pa-
+rameterized algorithms for the kemeny aggrega-
+tion problem.
+In Chen, J. and Fomin, F. V.,
+editors, IWPEC, volume 5917 of Lecture Notes
+in Computer Science, pages 312–323. Springer.
+[Steffen et al., 2011] Steffen,
+M.,
+DiVincenzo,
+D. P., Chow, J. M., Theis, T. N., and Ketchen,
+M. B. (2011).
+Quantum computing: An ibm
+perspective.
+IBM Journal of Research and
+Development, 55(5):13–1.
+[van Zuylen and Williamson, 2009] van Zuylen, A.
+and Williamson, D. P. (2009).
+Determinis-
+tic pivoting algorithms for constrained ranking
+and clustering problems.
+Math. Oper. Res.,
+34(3):594–620.
+[Willsch et al., 2022] Willsch,
+D.,
+Willsch,
+M.,
+Gonzalez Calaza, C. D., Jin, F., De Raedt, H.,
+Svensson, M., and Michielsen, K. (2022). Bench-
+marking advantage and d-wave 2000q quantum
+annealers with exact cover problems. Quantum
+Information Processing, 21(4):1–22.
+[Young and Levenglick, 1978] Young,
+H. P. and
+Levenglick, A. (1978). A consistent extension of
+condorcet’s election principle. SIAM Journal on
+applied Mathematics, 35(2):285–300.
+13
+
diff --git a/OdE4T4oBgHgl3EQfjw3r/content/tmp_files/load_file.txt b/OdE4T4oBgHgl3EQfjw3r/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..28fb7cec2d2ec5603d8bc8f3ca84c644d42e595a
--- /dev/null
+++ b/OdE4T4oBgHgl3EQfjw3r/content/tmp_files/load_file.txt
@@ -0,0 +1,882 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf,len=881
+page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='05146v1  [quant-ph]  12 Jan 2023  Heuristic for Diverse Kemeny Rank Aggregation based on  Quantum Annealing  Sven Fiergolla1, Kevin Goergen1, Patrick Neises1, and Petra Wolf2  1University of Trier, Germany, {s4svfier, s4kegoer,s4paneis}@uni-trier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='de  2University of Bergen, Norway, mail@wolfp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='net  Abstract  The Kemeny Rank Aggregation (KRA) prob-  lem is a well-studied problem in the field of Social  Choice with a variety of applications in many differ-  ent areas like databases and search engines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Intu-  itively, given a set of votes over a set of candidates,  the problem asks to find an aggregated ranking of  candidates that minimizes the overall dissatisfac-  tion concerning the votes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Recently, a diverse ver-  sion of KRA was considered which asks for a suf-  ficiently diverse set of sufficiently good solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  The framework of diversity of solutions is a young  and thriving topic in the field of artificial intelli-  gence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' The main idea is to provide the user with  not just one, but with a set of different solutions,  enabling her to pick a sufficiently good solution that  satisfies additional subjective criteria that are hard  or impossible to model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  In this work, we use a quantum annealer to solve  the KRA problem and to compute a representa-  tive set of solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Quantum annealing is a meta  search heuristic that does not only show promising  runtime behavior on currently existing prototypes  but also samples the solutions space in an inher-  ently different way, making use of quantum effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  We describe how KRA instances can be solved by  a quantum annealer and provide an implementa-  tion as well as experimental evaluations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' As exist-  ing quantum annealers are still restricted in their  number of qubits, we further implement two differ-  ent data reduction rules that can split an instance  into a set of smaller instances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' In our evaluation,  we compare classical heuristics that allow to sample  multiple solutions such as simulated annealing and  local search with quantum annealing performed on  a physical quantum annealer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  We compare run-  time, quality of solution, and diversity of solutions,  with and without applying preceding data reduc-  tion rules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' While our aim is to compute a diverse  set of solutions, we also include classical heuristics  that only compute a single solution in our experi-  ments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  Keywords: Social Choice, Solution Diversity,  Quantum Annealing, QUBO, Heuristic Search  1  Introduction  Estimating the potential of quantum comput-  ers gains more and more importance as their  technology develops rapidly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  There are two  different approaches for utilizing quantum ef-  fects  to  solve  computational  problems:  the  Quantum Circuit Model  (an approach followed  by Google and NASA [Arute et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2019], and  IBM [Steffen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2011]) and the Adiabatic Quan-  tum  Model  (an  approach  dominated  by  D-  Wave Systems [King et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2022]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  While both  models are computationally equivalent  in the  sense that they can simulate each other with  only a polynomial overhead [Farhi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2000,  Aharonov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2008] their physical realizations  are quite different.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  The quantum circuit model  aims at building a universal quantum computer,  it requires the design of novel quantum algorithms  to make use of quantum effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  As quantum  algorithms are quite unintuitive, only few quan-  tum algorithms are known that provide signifi-  cant benefits over classical algorithms (for instance,  Grover’s algorithm searching in unstructured data  with a quadratic speedup [Grover, 1996],  and  1  Shor’s algorithm factoring a number in polyno-  mial time [Shor, 1994]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' In contrast, the Adiabatic  Quantum Model has been realized by D-Wave as a  solution method called quantum annealing (QA) to  solve NP-hard optimization problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' The quan-  tum annealers from D-Wave are designed to solve  a native problem called the Ising Model 1 on their  hardware chip.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' The Ising Model is very closely re-  lated to the quadratic unconstrained binary opti-  mization (QUBO) problem which is more acces-  sible from the perspective of a computer scientist  and, hence, will be considered in this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' The  QUBO problem provides us with a nice interface  that allows to formulate problems as a classical op-  timization problem while still utilizing quantum ef-  fects to speed up the computation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' We discuss the  QUBO problem in detail later.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  Intuitively, in the Adiabatic Quantum Model,  the system is transformed from an initial low energy  state, which is easy to prepare, into another low  energy state such that the final state corresponds  to minimizing a target function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' If this transition  is performed slowly enough and at very low tem-  peratures (≤20mK), the system stays in the lowest  energy state during the transformation and we can  measure an optimal solution from the final state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  The Adiabatic Quantum Model was initially pro-  posed in [Farhi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2001] and soon found its ap-  plication in neural networks [Kinjo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2003].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  Quantum annealing is a meta search heuristic  that can be implemented in the native instruc-  tion set of the Adiabatic Quantum Model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  The  most developed realization in form of a quantum  annealer is the D-Wave Advantage system with  5,000+ qubits [Willsch et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2022].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' The quantum  computer from D-Wave also allows for Quantum  Machine Learning applications [Hu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2019,  Adachi and Henderson, 2015].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  The  company  rapidly develops new hardware chips for quantum  annealers, which does not come without some dif-  ficulties concerning API stability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' For more details  on the technical realization see [Bunyk et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2014,  Harris et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2010, Johnson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2011] and for a  general introduction to the Adiabatic Quantum  Model see [McGeoch, 2014].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  The  Adiabatic  Quantum  Model  differs  1The Ising Model problem is NP-complete [Istrail, 2000,  Cipra, 2000] and remains NP-complete restricted to the  class of instances realizable on a D-Wave quantum an-  nealer [Bunyk et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2014].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  from  classical  simulations  of  thermal  anneal-  ing [Kirkpatrick et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 1983] in the sense that the  computation starts with a superposition of all  states with minimal energy, thereby exploiting  quantum  parallelism,  and  can  further  tunnel  through high energy areas in the solution space  while classical approaches need to climb over  those high energy regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  Simulations have  shown that thereby the Adiabatic Quantum Model  has the potential of outperforming classical sim-  ulated  annealing  [Morita and Nishimori, 2008,  Ohzeki and Nishimori, 2011,  Crosson and Harrow, 2016].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Further, experimental  results show that quantum annealers can find local  valleys in the solution space that are not found by  simulated annealers [Koshka and Novotny, 2020].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  This indicates that instances that cannot be solved  efficiently with classical simulated annealing might  be efficiently solvable on a quantum annealer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  Due to its stochastic nature,  the quantum  annealing process must be executed and measured  multiple times to get good solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  But while  this looks like a weakness of the approach, it  actually comes with a benefit: While the system  cools down, one can imagine it as being in a super-  position of all local minima.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Only once measured,  the system collapse to one minima.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' By repeating  the process we can sample the different minima of  the solution space and do not get stuck in one local  minima as it is often the case for gradient descent  approaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' The multiple solutions automatically  sampled further allow us to get a representation  of the solution space, an aim that is classically  modeled by the notion of diversity of solutions,  a  recent  upcoming  trend  in  artificial  intelli-  gence [Petit and Trapp, 2019, Baste et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2019b,  Baste et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2020,  Ingmar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2020,  Fomin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2020].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  While, traditionally, one is interested in getting  some optimal solution to a computational problem,  this might not be sufficient in practice when side  constraints are present, that are hard to model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  Examples for those subjective criteria are aesthetic,  economic, political, or environmental criteria.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Due  to its subjective vague nature, it can be impossible  to model those criteria on the level of the prob-  lem formulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  Hence, it can be preferable for  the user to choose a slightly less optimal solution  that suits her subjective criteria better.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' In order to  provide the user with the ability to choose the solu-  2  tion that fits her needs best, it is preferable to pro-  vide a reasonably sized solution set of sufficiently  diverse solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' But formalizing the diversity of  a solution set is a non-trivial task, see the discus-  sion in [Baste et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2020, Baste et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2019a].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' In-  tuitively, diversity serves as a measure of how rep-  resentative a set of solutions is among the solution  space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' A quantum annealer naturally provides us  with a set of solutions as it samples the solution  space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Then, classical post-processing can be ap-  plied to select a subset of these solutions suitable  for the criteria at hand.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  Considering diverse alternatives is of relevance  while  selecting  several  good  committees  such  that each committee member is not overloaded  with work, as described in [Bredereck et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2020].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  Electing committees, or finding a ranking that  agrees with a set of votes as much as possible,  are key problems in the field of Social Choice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  One of the most studied problems in the field is  the Kemeny Rank Aggregation (KRA) prob-  lem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  Here, a set of votes over a set of candi-  dates is given and the task is to find a rank-  ing of the candidates that maximizes the satis-  faction of the voters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  The problem is of rele-  vance in a variety of different areas such as simi-  larity search and classification in high dimensional  databases [Fagin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2003], constructing genetic  maps in bioinformatics [Jackson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2008], ag-  gregating search results and spam detection in  a search engine [Dwork et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2001], etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  The  popularity of KRA is due to the unique prop-  erty  of  the  Kemeny  rule  of  being  neutral,  consistent, and satisfying the Condorcet prop-  erty [Young and Levenglick, 1978].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  The  KRA  problem  is  NP-  complete  [Bartholdi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 1989]  and  re-  mains  NP-hard  when  restricted  to  only  four  votes  [Dwork et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2001,  Biedl et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2009].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  This hardness motivates the studies of heuris-  tics  and  approximation algorithms for  KRA,  see  [Dwork et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2001,  Ailon et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2008,  van Zuylen and Williamson, 2009],  as  well  as  parameterized  algorithms  [Betzler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2009,  Simjour, 2009,  Arrighi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2020,  Betzler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2014].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  The  practical  rele-  vance  in  the  field  of  artificial intelligence  is  also  highlighted  by  a  series  of  experimen-  tal  studies  of  heuristics  and  approximations  of  the  KRA  problem  [Ali and Meila, 2012,  Davenport and Kalagnanam, 2004]  as  well  as  experimental studies of lower bounds for ex-  act  solutions  of  KRA  [Conitzer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2006,  Schalekamp and van Zuylen, 2009].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' A parameter-  ized algorithm for a diverse version of Kemeny  Rank  Aggregation  recently  appeared  at  IJCAI [Arrighi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2021].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  In this work, we utilize the Adiabatic Quan-  tum Model to get heuristics for the Diverse Ke-  meny Rank Aggregation problem that provide  us with a set of samples of the solution space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' For  this, we model KRA as a quadratic unconstrained  binary optimization problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Then, we compare  the quantum based heuristics with classical heuris-  tics that allow to sample different solutions such  as simulated annealing and local search, as well as  classical heuristics that compute deterministically  only a single solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  As quantum computer are still quite restricted  in the number of available qubits (currently 5,000+  qubits), large instances are still a challenge to any  quantum computer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' To counter this fact, we imple-  ment several data reduction rules as a preprocess-  ing step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Those rules allow us to break an instance  into smaller instances that can be solved indepen-  dently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' A final solution is then aggregated from the  solutions of the smaller instances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  This work is structured as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' First, we give  formal definitions for the QUBO and KRA prob-  lem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Then, we describe the data reduction rules we  used as well as the QUBO formulation obtained for  KRA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' We continue with the experimental part of  the paper and introduce the considered solvers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' In  our experiments, we compare the runtime and ob-  tained solution quality for all the solvers, and diver-  sity of solutions for solvers that support computing  multiple solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Thereby, we compare three dif-  ferent preprocessing modes: no preprocessing, ap-  plying the ≤3/4-majority rule exhaustively, and ap-  plying the extended Condorcet rule.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  We present  our observations at the end of this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Our im-  plementation and the used data-sets are available  as supplementary material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  2  Preliminaries  Let Q be an n × n matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' We write Qij for the  entry in row i and column j of Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  Let n be a  non-negative integer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' We denote [n] = {1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='n}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  3  Consequently, [0] = ∅.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='1  Quadratic  Unconstrained  Bi-  nary Optimization  We now give a formal definition of the Quadratic  Unconstrained  Binary  Optimization  (QUBO) problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  Let Q be an n × n ma-  trix  of  weights  and  x1, x2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' , xn  be  binary  variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Then, the QUBO problem asks for an  assignment of the variables xi, for i ∈ [n] that  minimizes  �  i,j  Qijxixj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='2  Kemeny Rank Aggregation  Let C be a finite set of candidates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' A vote (or rank-  ing) π over C is a total order on C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' If for two candi-  dates a, b ∈ C, candidate a is ranked better than b  in the vote π, then we write a <π b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Therefore, the  smallest candidate a according to <π is the winner  of the vote π and can be interpreted as getting posi-  tion 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' For two votes πi and πj the number of pairs  of candidates which are ordered differently within  these votes is called the Kendall Tau distance of  πi and πj, which is written as KT-distance(πi, πj).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  Formally, this means:  KT-distance(πi, πj) = |{(c1, c2) ∈ C × C |  c1 <πi c2 ∧ c1 >πj c2}|  Given a ranking π over C and a set Π of votes  over C, the Kemeny score of π w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Π, is the sum  of the Kendall Tau distances between π and each  πi ∈ Π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' The goal of KRA is to compute a ranking  πmin of C, with the smallest possible Kemeny score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  Such a ranking is called a Kemeny ranking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  3  Framework  In this section, we aim to give a theoretical ex-  planation of the concepts we are using.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  First,  we present data reduction rules for KRA, taken  from [Betzler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2014], that we implemented as  a preprocessing step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='2 Then, we present and our  QUBO formulation for KRA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  2In [Betzler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2014] votes are interpreted in the in-  verse way, meaning that candidate a is ranked better than b  in a vote if a > b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Hence, in the original work, the following  rules are defined according to the ≥s-majority.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='1  Data Reduction Rules  As the number of available qubits on a quantum  annealer is restricted we use some known data re-  duction rules as a preprocessing step that cut an  instance into a collection of smaller instances that  can be solved independently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='1  ≤3/4-Majority Rule  Let C be a set of candidates and Π be as set of  votes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  Further, let a, b ∈ C be candidates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  If,  for all votes πi over C, a <πi b, then a < b in  a Kemeny ranking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  Intuitively, if a gets a lower  ranking than b in every single vote, a obviously  has to be placed lower than b in a Kemeny rank-  ing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' We can generalize this idea in the following  way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Let s ∈ [0, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' If a <πi b in at least s · |Π|  many votes πi, then we say that the pair (a, b)  is a clean pair according to the ≤s-majority and  denote this by a ≤s b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' If a candidate a forms a  clean pair according to the ≤s-majority with ev-  ery other candidate b ∈ C \\ {a}, then we call a a  clean candidate with respect to the ≤s-majority.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  It was shown in [Betzler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2014, Lemma 1]  that for clean candidates with respect to the ≤3/4-  majority (s = 3/4), every Kemeny ranking re-  spects the clean pairs in which a is involved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Based  on this observation, a linear partial kernel with  respect to the parameter da was obtained where  da = �  πi,πj∈Π KT-distance(πi, πj)/(|C| · (|C| − 1))  is the average KT-distance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' The kernel is based on  the following ≤3/4-majority rule:  For  a  KRA  instance  (C, Π),  let  N  :=  {n1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' , nt} be the set of clean candidates with re-  spect to the ≤3/4-majority such that ni ≤3/4 ni+1  for i ∈ [t − 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Then, define  D0 := {c ∈ C \\ N | c ≤3/4 n1},  Di := {c ∈ C \\ N | ni ≤3/4 c ∧ c ≤3/4 ni+1},  Dt := {c ∈ C \\ N | nt ≤3/4 c},  for i ∈ [t − 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Replace the original instance by the  t + 1 sub-instances induced by Di for 0 ≤ i ≤ t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  As shown by Betzler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', this data reduction  rule is safe and preserves all Kemeny rankings, a  desirable property for computing a diverse set of  Kemeny rankings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Another benefit of this rule is  that the individual sub-instances can be solved in-  dependently on a quantum annealer needing way  fewer qubits than the original instance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  4  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='2  Extended Condorcet Rule  In the extended Condorcet rule, we move from com-  paring the relative position of one candidate to all  other candidates to considering the relative posi-  tion of a set of candidates C′ to the remaining can-  didates C \\ C′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Thereby, the rule cuts an instance  according to the strongly connected components of  its majority graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  Definition 1 (Majority graph).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Let (C, Π) be  an instance of KRA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' The weak (strict) marjority  graph of (C, Π) is a directed graph with vertex set  C and an arc from u to v if and only if u < v in at  least (in more than) half of the votes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  As our interest is in computing a diverse set of  solutions, we use a version of the extended Con-  dorcet rule which is based on the weak majority  graph and which preserves all Kemeny rankings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' If  the context is clear, we call this rule the Condorcet  rule.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' It works as follows [Betzler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2014].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Let  (C, Π) be an election and let C1, C2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' , Ct ⊆ C  be the vertex sets of the strongly connected com-  ponents in the weak majority graph of (C, Π) fol-  lowing a topological order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  Replace the original  instance by the sub-instances induced by Ci with  |Ci| ≥ 2, i ∈ [t].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  While this rule preserves all Kemeny rank-  ings, it is possible that the instance obtained af-  ter applying this rule can still be reduced by  the ≤3/4-majority rule, as shown in Example 2  of [Betzler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2014].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' If we instead consider the  strongly connected components of the strict major-  ity graph, the resulting kernel, with respect to the  parameter da, cannot be further compressed by the  ≤3/4-majority rule, implying a smaller kernel size,  but we might lose Kemeny rankings as pairs of can-  didates with exactly 1/2 of the votes in both direc-  tions are not connected in the strict majority graph  and an ordering on them must be fixed during the  topological ordering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' As our objective is to leave  the computation of multiple solutions to the quan-  tum annealer, we used the Condorcet rule based on  the weak majority graph in the following.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Alterna-  tively, we could restrict ourselves to only comput-  ing multiple solutions on the sub-instances and use  classical post processing in order to compute all  topological orderings of the strict majority graph  and concatenate the solutions of the sub-instances  accordingly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' It is not hard to see that once we have  the strongly connected components, computing a  diverse set of topological orderings can be done by  seeing the problem as an instance of the Comple-  tion of an Ordering problem with all costs set  to 1 and using the parameterized algorithm for the  diverse version proposed in [Arrighi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2021].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='2  QUBO formulation for Kemeny  Rank Aggregation  We now discuss our QUBO formulation of KRA:  Given a ranking over a set of n candidates C,  we use n2 binary variables, denoted by ci,j with  1 ≤ i, j ≤ n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Intuitively, if variable ci,j = 1, this  means candidate i has position j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Binary variables  might only take the values 0 or 1 which can be  interpreted as Boolean values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  We interpret the  variables ci,j as a two-dimensional grid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' In order  to obtain a valid Kemeny ranking, we have to en-  sure, that each candidate has exactly one position  within the final ranking (∀i : �n  j=1 ci,j = 1, we  achieve this via so called row-penalties) and that  each position is taken by exactly one candidate  (∀j : �n  i=1 ci,j = 1, this, in turn, is achieved via  column-penalties).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  A penalty is a huge positive  weight that is multiplied to a term in the objec-  tive function which gets a positive value under a  variable assignment that we want to forbid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  By  turning side-constraints into penalty terms, we can  obtain an unconstrained QUBO instance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' There-  fore, we need to ensure that the cost of a penalty is  too high to be be paid in any optimal solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' We  choose P = |C|2 · |Π| as the penalty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' This choice  gets clear later.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='1  Row-Penalties  The row-penalties ensure that each candidate gets  assigned exactly one position.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' This is obtained by  the following term of the final objective function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  For each row i ∈ [n] we define  rowi = P  \uf8eb  \uf8ed1 − (  n  �  j=1  ci,j)  \uf8f6  \uf8f8  2  The minimal value for this equation is 0, which is  obtained if and only if exactly one of the ci,j in the  sum is true.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' If for fixed i, none of the variables ci,j,  for j ∈ [n] is true, then the term rowi evaluates  5  to P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' If on the other hand k > 1 many variables  ci,j are true, then rowi evaluates to P(1 − k)2 =  P(−(k − 1))2 = P(k − 1)2 ≥ P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='2  Column-Penalties  Similarly, the column-penalties ensure that each  position j is assigned with exactly one candidate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  For each j ∈ [n] we set:  colj = P  �  1 − (  n  �  i=1  ci,j)  �2  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='3  Ranking-Penalties  Lastly, we need to represent the actual votes them-  selves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' This is achieved via penalties for each pair  of variables ci,j, ci′,j′ with i ̸= i′ and j ̸= j′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' The  goal is to give the quadratic term ci,jci′,j′ a weight  that reflects how many votes are violated if both,  candidate i gets position j and candidate i′ gets  position j′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' It was shown in [Arrighi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2020,  Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='1] that the Kemeny score of a ranking can be  computed by summing over the cost of each pair of  candidates, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', the number of votes in which the  relative position of the pair is violated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' This way,  summing up the penalties over all pairs of candi-  dates, we obtain the Kemeny score of the ranking  associated with a variable assignment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  Let wi,j be the total number of votes, in which  candidate cj is positioned better than candidate ci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  More formally3, wi,j = �  π∈Π[cj <π ci].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' If we vi-  olate this relative position of candidates in an ag-  gregated ranking, then wi,j is the cost we need to  pay in order to place candidate ci before candidate  cj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' This leaves us with the following term encoding  the cost of placing candidate ci before candidate cj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  For each i, j ∈ [n] we define:  ranki,j = wi,j ·  n−1  �  k=1  n  �  l>k  ci,kcj,l  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='4  The final formulation  We are ready to formulate the final unconstrained  objective function depending on all variables ci,j  3The bracket notation reads as follows: if p is a logical  proposition, then [p] yields 1 if p is true and else, [p] yields  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  for i, j ∈ [n]:  f(c1,1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' cn,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='n) =  n  �  i=1  \uf8eb  \uf8edrowi + coli +  n  �  j=1  ranki,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='j  \uf8f6  \uf8f8  Coming back to the penalty P used for row-  and column-penalties:  Since we choose it to be  P = |C|2 · |Π|,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' we now see,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' that even if every sin-  gle vote contradicts every single possible relative  positioning (which is an impossible to reach upper  bound) breaking the rules of each candidate tak-  ing exactly one position and each position being  taken by exactly one candidate,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' will still come with  a higher penalty,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' and thus will never happen in an  optimal solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  4  Implementation  The project is written in Python using D-Wave’s  Dimod API.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='1  Data-sets  We use two different data-sets in our evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  The first is the Formula 1 data-set from the ex-  perimental evaluation of the data reduction rules  in [Betzler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2014].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' The number of candidates  in this data-set ranges from 6 to 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  They also  considered other real world data-sets such as ski  rankings and web search results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' But those data-  sets focus on instances with up to 69, resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 200  candidates, which are too large to be mapped onto  the physical hardware of the considered quantum  annealers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Hence, we exclude them from our eval-  uation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  In contrast, we included a second data-set of ran-  domly generated instances ranging from 3 to 100  candidates in order to gradually increase the in-  stance size to find the limitations of the different  solver.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' We created the instance by starting with  a sorted list and then shuffling it with standard  python methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' As expected, the randomly gen-  erated instances do not provide much structure for  the data reduction rules and are used for compar-  ing the runtime and solution quality of the different  solvers with different parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' In contrast, the  Formula 1 data is used to compare the diversity  of solutions and the impact of the data reduction  6  rules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Details on the encoding of the data, docu-  mentation of our implementation as well as instruc-  tions on how to run the experiments can be found  in the supplementary material along with the code  and the data-sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='2  Preprocessing  We implemented the above described data reduc-  tion rules that cut instances into subinstances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' If  we aim for a diverse solution set, we concatenate  the best solutions among the sub-instances in a  cross-product manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' The available modes are: no  data reduction, ≤3/4-majority rule, and Condorcet  rule.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='3  Solving with Different Solvers  With the problem formulation finished, the BQM  model can be solved by a variety of different solvers,  each with different pros and cons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Generally, the  solvers provided by D-Wave can be split into 3 cate-  gories: mathematical solving, simulated annealing,  and real quantum annealing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='1  Steepest Decent  The first solver, SteepDes, that we consider from  the repertoire of D-Wave uses a steepest descent  approach which is the discrete analogue of gradi-  ent descent, but the best move is computed using  a local minimization rather than computing a gra-  dient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' For a given input QUBO on n variables, the  runtime complexity of the underlying C++ imple-  mentation is O(n2) for the initialization phase and  O(n) per downhill step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  At the time of our ex-  periments, SteepDes did not support to compute  multiple solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='2  Simulated annealing  Simulated annealing is a probabilistic technique  for finding local optima of a given objective  function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  D-Wave provides with the SimAnl  solver an  implementation  of a  simulated an-  nealing algorithm that approximates Boltzmann  sampling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  Their  approach follows the  work  of [Kirkpatrick et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 1983].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='3  Quantum annealing  D-Wave provides two different types of quantum  annealers: a quantum processing unit (QPU), and a  hybrid model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' In the hybrid model, the Ocean SDK  takes care of assigning a QUBO instance to qubit  bias and coupling values for the hardware graph,  with the drawback of restricted access to parame-  ters like the number of samples (num_read) or the  number of output solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' In contrast, the QPU  model allows for direct access to the quantum ma-  chine but requires the user to take care of optimal  values for parameters as well as finding an embed-  ding onto the hardware herself.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' The latter is a non-  trivial task and without your own implementation,  just a general heuristic is available that only allows  to embed significantly smaller instances than pos-  sible with the hybrid model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' The most developed  QPU family currently available is the Advantage  model with over 5,000 qubits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' In comparison with  its predecessor, the 2,000Q QPU, it relies on a new  topology, the Pegasus graph, describing the connec-  tivity of qubits on the chip.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' In our experiments we  use the Advantage model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' We refer to the solver  based on the hybrid model as Hybrid, and to the  Advantage QPU as QAnl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  Local  Search  We  implemented  the  local  search  algorithm  described  in  [Schalekamp and van Zuylen, 2009].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  Local  search was also considered in the experiments  in [Ali and Meila, 2012] where it was observed to  compute significantly better solutions than faster  algorithms like Borda.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  The algorithms goes  through the candidates in a random order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' When  considering position i, the candidate at position  i is moved to the position that gives the largest  improvement to the current Kemeny score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  The  procedure stops if no element has been moved and  all positions were considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  As the algorithms  uses a random order, we execute the local search  algorithm multiple times in order to compute  multiple solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  Borda  We implemented the Borda algorithm  from [Ali and Meila, 2012].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  It computes (in our  notation) for each candidate a the value qci =  �  cj∈C wi,j and then returns the permutation of  candidates that sorts qci  in descending order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  As the algorithm computes a single solution de-  7  terministically it is not able to compute a di-  verse set of solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  In [Ali and Meila, 2012]  it  was  observed  that  in  the  case  of  no  or  strong consensus, the Borda performs best among  the considered solver.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  Also in the compar-  ison  [Schalekamp and van Zuylen, 2009]  Borda  performed very well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  Quick-Sort  Several  sorting  based  algorithms  were  considered  in  [Ali and Meila, 2012]  from  which the one based on quick sort performed best  in our experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' The algorithm sorts the can-  didates according to the predicate wij < wji that,  if true, sorts candidate ci left of candidate cj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Also  QuickSort is only able to compute a single solu-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='4  Parameters  We focus our analysis on the impact of two pa-  rameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  The parameter num_reads determines  the number of samples performed by the solver.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  Its standard value is 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Increasing this parameter  leads to better solutions but causes higher runtime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  We investigate its impact in Exp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' At the time  of our experiments, num_reads is supported by all  solvers from D-Wave, except Hybrid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' The param-  eter max_answers determines the number of solu-  tions output by the solvers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' While at the beginning  of this project max_answers was also supported by  the Hybrid solver, at the time of our experiment  it is only supported by QAnl, and SimAnl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  5  Experimental Results  All local solver benchmark tests were performed on  a system running Linux Pop OS (Ubuntu 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='4 LTS)  with a 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='5 kernel, an AMD Ryzen 5 2600X six  core processor (12 threads) with a 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='6 GHz base  clock and a 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='2 GHz boost clock speed, equipped  with 32GB 3200MHz ram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='1  Exp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' 1:  Runtime Performance  (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' 1)  We measure the runtime for each solver on a set  of randomly generated instances of increasing size  with 10 instances per size (number of candidates).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  3  4  5  10  20  50  100  10−4  10−3  10−2  10−1  100  101  102  103  Size of Instance [|C|]  Sample time [s]  LocSearch  SteepDes  Hybrid  Borda  QAnl  QuickSort  SimAnl  Figure 1: Sample, respectively, QPU time with in-  creasing number of candidates, average over 10 ran-  dom instances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  Each instance contains as many votes as candi-  dates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' All solvers were initialized with default pa-  rameters, and only the pure sample time is mea-  sured.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' For the Hybrid solver, the QPU time was  measured.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  We observe that the sampling time of QAnl,  Hybrid, and LocSearch stays rather constant,  while the runtime for SimAnl, SteepDes, Borda,  and QuickSort first outperforms the other solver  but then increases significantly with larger instance  sizes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='2  Exp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' 2: Solution Quality (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' 2)  Since a default sample size of 1 is used for QAnl,  SimAnl, and SteepDes, larger instances are not  going to be solved optimally.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' In fact, solution qual-  ity is greatly decreasing with increasing instance  size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' To improve solution quality, with the param-  eter num_read we can set the number of samples  taken.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  In order to measure solution quality, the  cost of an optimal solution is calculated by an In-  teger Linear Program and compared with the Ke-  meny score of the best solution found by the differ-  ent solvers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' We measured average solution quality  and average runtime for all random instances of size  20, with increasing num_read.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' For comparison, also  the other solvers is visualized, although they do not  support the parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' The QAnl solver was ex-  cluded from this experiment as it could not solve  the instances of size 20 and only showed trivial be-  havior on smaller sized instances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  8 default  10  100  1000  10000  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='02  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='04  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='06  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='08  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='12  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='14  Number of reads [num read]  Solution quality as factor of optimal solution  SimAnl quality  SteepDes quality  Hybrid quality  LocSearch quality  Borda quality  QuickSort quality  10−3  10−2  10−1  100  101  Sampletime [s]  SimAnl time  SteepDes time  Hybrid time  LocSearch time  Borda time  QuickSort time  Figure 2: Solution quality as a factor of the optimal  solution, average over 10 random instances with 20  candidates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  SimAnl and SteepDes show a clear trade-  off between solution quality and sample time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  With the default parameters, Hybrid outperforms  SimAnl and SteepDes in solution quality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' With  increasing num_read, SimAnl and SteepDes do  outperform Hybrid in terms of solution quality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  For SimAnl this only happens with a huge increase  in sample time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' With num_read = 100, SteepDes  outperforms Hybrid in solution quality and sam-  ple time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Increasing num_read lets SteepDes find  the optimal solution with a slightly higher sample  time than Hybrid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  From those solvers allowing  to compute multiple solutions, LocSearch shows  the best solution quality under the standard pa-  rameters but also has the highest runtime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='3  Exp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' 3:  Diversity and Prepro-  cessing (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' 3 - 5)  Next, we measure the solution quality, diversity of  solutions, and runtime for those solver that can  compute a set of solution at once.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' More precisely,  we compare the annealing based solvers SimAnl,  Hybrid, QAnl, and LocSearch with and with-  out preprocessing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  Recall that Borda, Quick-  Sort, and SteepDes do not support to output  multiple solutions on a single run of the solver and  are hence not included in this experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' As our  previously considered randomized data do not con-  tain enough structure for the data reduction rules,  we use the Formula 1 data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' We observe that on  the Formula 1 data, the ≤3/4-majority rule never  0  10  20  30  40  50  0  10  20  30  40  50  Percentage over optimal solution [%]  Hybrid none  Hybrid Condorcet  SimAnl none  SimAnl Condorcet  LocSearch none  QAnl Condorcet  Figure 3: Depicted is by how much % the Kemeny  score of the best solution found is above the optimal  solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  applies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  Hence, we excluded it from the evalua-  tion presented here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' For the SimAnl and D-Wave  all experiments were performed with num_read =  10, 000 and up to the best 10 solutions were taken  into the solution set on which we measure the diver-  sity as the pairwise minimal KT-distance and the  average KT-distance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' For LocSearch, we run the  solver 50 times and take the 10 best solutions found  into account.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' The depicted runtime is the total run-  time of all 50 runs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Not all instances were solvable  on the quantum annealers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' When a data point is  missing, this instance was either not embeddable  onto the hardware or an invalid solution, break-  ing a row or column constraint, was returned.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' The  instances are sorted by the number of candidates  in increasing order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' As in [Betzler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2014] we  removed invalid votes containing duplicated candi-  dates and candidates not appearing in every vote.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  In contrast to SimAnl, LocSearch did not al-  ways found 10 different solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' If D-Wave could  solve the instance at all, it nearly always output 10  different solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  Observations  We  observe  that  the  ≤3/4-  majority rule does not reduce any instance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  In  contrast,  the Condorcet rule cuts 1/3 of the  instances into two sub-instances and 1/6 of the  instances into 3 sub-instances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Further, it reduces  the size of nearly every instance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  While the  Hybrid solver was able to solve nearly every  instance in both preprocessing modes, the QAnl  could only solve some instances after applying  the Condorcet rule.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  Applying the Condorcet  9  0  10  20  30  40  50  0  50  100  150  200  250  KT-distance among diverse solution  SimAnl none min KT  SimAnl Condorcet min KT  SimAnl none avg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' KT  SimAnl Condorcet avg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' KT  LocSearch none avg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' KT  QAnl Condorcet min KT  QAnl Condorcet avg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' KT  Figure  4:  Minimal  and  average  pairwise  KT-distance over the best 10 solutions found  with and without Condorcet rule.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  rule increases the solution quality for all solvers  significantly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' With this rule, most of the instances  were solved optimally by all solvers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Surprisingly  with respect to solution quality, without prepro-  cessing, the simulated and non-simulated annealers  performed similarly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  Among the considered 10  best solutions, the Kemeny score of the solutions  differed only slightly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  This means that similarly  good different solutions were found.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' With respect  to the diversity,  applying the Condorcet rule  reduced the minimal and average KT-distance  for SimAnl significantly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  In contrast, for the  QAnl solver,  the average KT-distance seems  to not be affected by the Condorcet rule.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  One  could observe that the Condorcet rule allows for  more instances to be solved with the QAnl with  a better solution quality and a higher diversity,  but those observations need to be considered  with caution as we were only able to solve a few  instances on the plain quantum annealer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  With  respect to sample time, the QPU time of Hybrid  was significantly shorter than the sample time of  SimAnl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  While the Condorcet rule reduces the  total sampling time for SimAnl, it increases the  total QPU time for Hybrid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  We explain this  by the increased charging time for the hardware  couples which is the biggest part of the QPU time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  As multiple sub-instances need to be solved, the  hardware must be charged multiple times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  We  explain the higher QPU time of QAnl in contrast  to Hybrid with the high number of reads for  QAnl in contrast to the unaccessible standard  value for Hybrid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' When setting num_read= 100,  0  10  20  30  40  50  10−2  10−1  100  101  102  103  sample / QPU time (sum over kernels) [s]  SimAnl none  SimAnl Cond.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  LocSearch none  Hybrid none  Hybrid Cond.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  QAnl Cond.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  Figure 5:  Sample time, respectively, QPU time  with and without Condorcet rule.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  QAnl showed similar QPU times as Hybrid with  only a slight decrease in solution quality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  Even without preprocessing, LocSearch nearly  always found the optimal solution, but only in  60% of the instances it found 10 different solutions,  while SimAnl did so in 90% of the instances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' The  Kemeny score of the 10th best solutions differed  only slightly between SimAnl and LocSearch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' In  terms of runtime, LocSearch was one magnitude  faster than SimAnl while Hybrid was the fastest  on nearly all instances showing a constant runtime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  If we applied the Condorcet rule as a preprocessing  step to Hybrid, it found in 50% of the instances  with more than 15 candidates similar good solu-  tions as LocSearch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  6  Conclusion  The property of quickly performing a huge num-  ber of samples of the solution space can become  one of the main advantages of Quantum Anneal-  ing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Our experiments indicate that with Quantum  Annealing, we can compute a set of solutions that  shows quite good diversity with a very good run-  time behavior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' But the full potential of Quantum  Annealing can only be examined once the hard-  ware evolved further and allows to solve larger in-  stances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Until then, combining Quantum Anneal-  ing with data reduction rules as a preprocessing  step can lead to promising near-term applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  10  References  [Adachi and Henderson, 2015] Adachi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' and  Henderson, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Application of quan-  tum annealing to training of deep neural net-  works.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' arXiv preprint arXiv:1510.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='06356.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  [Aharonov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2008] Aharonov, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', van Dam,  W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Kempe, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Landau, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Lloyd, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', and  Regev, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Adiabatic quantum compu-  tation is equivalent to standard quantum com-  putation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' SIAM Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 50(4):755–787.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  [Ailon et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2008] Ailon, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Charikar, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', and  Newman, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  Aggregating inconsistent  information: Ranking and clustering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' ACM,  55(5):23:1–23:27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  [Ali and Meila, 2012] Ali, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' and Meila, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  Experiments with kemeny ranking: What works  when?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 64(1):28–40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  [Arrighi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2020] Arrighi,  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=',  Fernau,  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=',  de Oliveira Oliveira, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', and Wolf, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  Width notions for ordering-related problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' In  Saxena, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' and Simon, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', editors, FSTTCS,  volume 182 of LIPIcs, pages 9:1–9:18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Schloss  Dagstuhl - Leibniz-Zentrum f¨ur Informatik.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  [Arrighi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2021] Arrighi, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Fernau, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Lok-  shtanov, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', de Oliveira Oliveira, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', and Wolf,  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Diversity in kemeny rank aggregation:  A parameterized approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' In Zhou, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', editor,  IJCAI, pages 10–16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' ijcai.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='org.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  [Arute et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2019] Arute, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Arya, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Babbush,  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Bacon, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Bardin, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Barends, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=',  Biswas, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Boixo, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Brandao, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Buell,  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  Quantum supremacy us-  ing a programmable superconducting processor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  Nature, 574(7779):505–510.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  [Bartholdi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 1989] Bartholdi, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Tovey, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=',  and Trick, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' (1989).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  Voting schemes for  which it can be difficult to tell who won the elec-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Social Choice and welfare, 6(2):157–165.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  [Baste et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2020] Baste, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Fellows, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Jaf-  fke, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Masar´ık, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', de Oliveira Oliveira, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=',  Philip, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', and Rosamond, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Diver-  sity of solutions: An exploration through the lens  of fixed-parameter tractability theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' In IJCAI,  pages 1119–1125.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  [Baste et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2019a] Baste, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Jaffke, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Masaˇr´ık,  T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Philip, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', and Rote, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' (2019a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  Fpt al-  gorithms for diverse collections of hitting sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  Algorithms, 12(12):254.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  [Baste et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2019b] Baste, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Jaffke, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Masaˇr´ık,  T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Philip, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', and Rote, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' (2019b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' FPT al-  gorithms for diverse collections of hitting sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  Algorithms, 12:254.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  [Betzler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2014] Betzler, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Bredereck, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=',  and Niedermeier, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  Theoretical and  empirical evaluation of data reduction for exact  kemeny rank aggregation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Auton.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Agents Multi  Agent Syst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 28(5):721–748.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  [Betzler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2009] Betzler, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Fellows, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=',  Guo, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Niedermeier, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', and Rosamond, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Fixed-parameter algorithms for kemeny  rankings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  Theor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 410(45):4554–  4570.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  [Biedl et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2009] Biedl, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Brandenburg, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=',  and Deng,  X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  On the complexity  of crossings in permutations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  Discret.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=',  309(7):1813–1823.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  [Bredereck et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2020] Bredereck, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Kaczmar-  czyk, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', and Niedermeier, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  Elect-  ing successive committees: Complexity and algo-  rithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' In AAAI, pages 1846–1853.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' AAAI Press.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  [Bunyk et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2014] Bunyk,  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=',  Hoskinson,  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Johnson, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Tolkacheva, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Al-  tomare, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Berkley, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Harris, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Hilton,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Lanting, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Przybysz, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  Architectural considerations in the design of a  superconducting quantum annealing processor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  IEEE Transactions on Applied Superconductiv-  ity, 24(4):1–10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  [Cipra, 2000] Cipra, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' (2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' The ising model  is np-complete.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' SIAM News, 33(6):1–3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  [Conitzer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2006] Conitzer,  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=',  Davenport,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', and Kalagnanam, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  Improved  bounds for computing kemeny rankings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  In  AAAI, pages 620–626.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' AAAI Press.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  [Crosson and Harrow, 2016] Crosson, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' and Har-  row, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Simulated quantum anneal-  ing can be exponentially faster than classical  simulated annealing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' In FOCS, pages 714–723.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  IEEE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  11  [Davenport and Kalagnanam, 2004] Davenport,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' and Kalagnanam, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' A computa-  tional study of the kemeny rule for preference  aggregation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' In McGuinness, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' and Fergu-  son, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', editors, AAAI, pages 697–702.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' AAAI  Press / The MIT Press.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  [Dwork et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2001] Dwork, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Kumar, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Naor,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', and Sivakumar, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' (2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Rank aggregation  methods for the web.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' In Shen, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Saito, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=',  Lyu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', and Zurko, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', editors, WWW,  pages 613–622.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' ACM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  [Fagin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2003] Fagin,  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=',  Kumar,  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=',  and  Sivakumar, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' (2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' SIGMOD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' pages 301–312.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  ACM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  [Farhi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2001] Farhi, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Goldstone, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Gut-  mann, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Lapan, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Lundgren, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', and Preda,  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' (2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  A quantum adiabatic evolution al-  gorithm applied to random instances of an np-  complete problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Science, 292(5516):472–475.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  [Farhi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2000] Farhi, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Goldstone, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Gut-  mann, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', and Sipser, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' (2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Quantum com-  putation by adiabatic evolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' arXiv preprint  quant-ph/0001106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  [Fomin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2020] Fomin, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Golovach, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=',  Jaffke, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Philip, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', and Sagunov, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  Diverse pairs of matchings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' In ISAAC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Schloss  Dagstuhl-Leibniz-Zentrum f¨ur Informatik.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  [Grover, 1996] Grover, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' (1996).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' A fast quan-  tum mechanical algorithm for database search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  In Miller, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', editor, STOC, pages 212–219.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  ACM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  [Harris et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2010] Harris,  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=',  Johansson,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=',  Berkley, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Johnson, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Lanting, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Han, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=',  Bunyk, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Ladizinsky, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Oh, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Perminov, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=',  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Experimental demonstration of a  robust and scalable flux qubit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Physical Review  B, 81(13):134510.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  [Hu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2019] Hu, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Wang, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='-N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Wang, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=',  and Wang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Quantum machine learn-  ing with d-wave quantum computer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Quantum  Engineering, 1(2):e12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  [Ingmar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2020] Ingmar,  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=',  de la Banda,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Stuckey, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', and Tack, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Mod-  elling diversity of solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  In AAAI, pages  1528–1535.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' AAAI Press.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  [Istrail, 2000] Istrail, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' (2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Statistical mechan-  ics, three-dimensionality and np-completeness: I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  universality of intracatability for the partition  function of the ising model across non-planar  surfaces (extended abstract).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' In Yao, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' and  Luks, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', editors, STOC, pages 87–96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' ACM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  [Jackson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2008] Jackson, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=',  Schnable,  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', and Aluru, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Consensus genetic  maps as median orders from inconsistent sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  IEEE ACM Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Biol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Bioinform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=',  5(2):161–171.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  [Johnson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2011] Johnson,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=',  Amin,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Gildert, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Lanting, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Hamze, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=',  Dickson, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Harris, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Berkley, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Jo-  hansson, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Bunyk, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  Quan-  tum annealing with manufactured spins.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Nature,  473(7346):194–198.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  [King et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2022] King, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Suzuki, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Ray-  mond, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Zucca, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Lanting, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Altomare,  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Berkley, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Ejtemaee, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Hoskinson, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=',  Huang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  Coherent quantum  annealing in a programmable 2000-qubit ising  chain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' arXiv preprint arXiv:2202.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='05847.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  [Kinjo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2003] Kinjo, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Sato, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', and Naka-  jima, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' (2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Quantum adiabatic evolution  algorithm for a quantum neural network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  In  Kaynak, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Alpaydin, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Oja, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', and Xu, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=',  editors, ICANN/ICONIP, volume 2714 of Lec-  ture Notes in Computer Science, pages 951–958.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  Springer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  [Kirkpatrick et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 1983] Kirkpatrick,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=',  Gelatt Jr, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', and Vecchi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' (1983).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  Optimization by simulated annealing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Science,  220(4598):671–680.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  [Koshka and Novotny, 2020] Koshka,  Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  and  Novotny, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Comparison of d-wave  quantum  annealing  and  classical  simulated  annealing  for  local  minima  determination.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  IEEE Journal on Selected Areas in Information  Theory, 1(2):515–525.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  [McGeoch, 2014] McGeoch, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  Adia-  batic Quantum Computation and Quantum An-  nealing: Theory and Practice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Synthesis Lectures  on Quantum Computing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Morgan & Claypool  Publishers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  12  [Morita and Nishimori, 2008] Morita,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  and  Nishimori, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Mathematical foundation  of quantum annealing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Journal of Mathematical  Physics, 49(12):125210.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  [Ohzeki and Nishimori, 2011] Ohzeki,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  and  Nishimori, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Quantum annealing: An  introduction and new developments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  Journal  of Computational and Theoretical Nanoscience,  8(6):963–971.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  [Petit and Trapp, 2019] Petit, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' and Trapp, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  Enriching solutions to combinatorial  problems via solution engineering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  INFORMS  Journal on Computing, 31(3):429–444.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  [Schalekamp and van Zuylen, 2009] Schalekamp,  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' and van Zuylen, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  Rank aggrega-  tion: Together we’re strong.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' In Finocchi, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' and  Hershberger, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', editors, ALENEX, pages 38–51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  SIAM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  [Shor, 1994] Shor, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' (1994).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  Algorithms for  quantum computation: Discrete logarithms and  factoring.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' In FOCS, pages 124–134.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' IEEE Com-  puter Society.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  [Simjour, 2009] Simjour, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Improved pa-  rameterized algorithms for the kemeny aggrega-  tion problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  In Chen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' and Fomin, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=',  editors, IWPEC, volume 5917 of Lecture Notes  in Computer Science, pages 312–323.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Springer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  [Steffen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2011] Steffen,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=',  DiVincenzo,  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Chow, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Theis, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', and Ketchen,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  Quantum computing: An ibm  perspective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  IBM Journal of Research and  Development, 55(5):13–1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  [van Zuylen and Williamson, 2009] van Zuylen, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  and Williamson, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  Determinis-  tic pivoting algorithms for constrained ranking  and clustering problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Oper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=',  34(3):594–620.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  [Willsch et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', 2022] Willsch,  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=',  Willsch,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=',  Gonzalez Calaza, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', Jin, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', De Raedt, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=',  Svensson, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=', and Michielsen, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Bench-  marking advantage and d-wave 2000q quantum  annealers with exact cover problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' Quantum  Information Processing, 21(4):1–22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  [Young and Levenglick, 1978] Young,  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' and  Levenglick, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' (1978).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' A consistent extension of  condorcet’s election principle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content=' SIAM Journal on  applied Mathematics, 35(2):285–300.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
+page_content='  13' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OdE4T4oBgHgl3EQfjw3r/content/2301.05146v1.pdf'}
diff --git a/PtE5T4oBgHgl3EQfYw9y/content/tmp_files/2301.05576v1.pdf.txt b/PtE5T4oBgHgl3EQfYw9y/content/tmp_files/2301.05576v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..8a844b8018581aa8562c54f5b65d0849edd4bcb5
--- /dev/null
+++ b/PtE5T4oBgHgl3EQfYw9y/content/tmp_files/2301.05576v1.pdf.txt
@@ -0,0 +1,1856 @@
+1
+Microfluidic Pulse Shaping Methods for
+Molecular Communications
+Maryam Kahvazi Zadeh, Iman Mokari Bolhassan, and Murat Kuscu
+Abstract—Molecular Communication (MC) is a bio-inspired
+communication modality that utilizes chemical signals in the
+form of molecules to exchange information between spatially
+separated entities. Pulse shaping is an important process in all
+communication systems, as it modifies the waveform of trans-
+mitted signals to match the characteristics of the communication
+channel for reliable and high-speed information transfer. In MC
+systems, the unconventional architectures of components, such as
+transmitters and receivers, and the complex, nonlinear, and time-
+varying nature of MC channels make pulse shaping even more
+important. While several pulse shaping methods have been the-
+oretically proposed for MC, their practicality and performance
+are still uncertain. Moreover, the majority of recently proposed
+experimental MC testbeds that rely on microfluidics technology
+lack the incorporation of programmable pulse shaping methods,
+which hinders the accurate evaluation of MC techniques in
+practical settings. To address the challenges associated with pulse
+shaping in microfluidic MC systems, we provide a comprehensive
+overview of practical microfluidic chemical waveform generation
+techniques that have been experimentally validated and whose
+architectures can inform the design of pulse shaping methods
+for microfluidic MC systems and testbeds. These techniques
+include those based on hydrodynamic and acoustofluidic force
+fields, as well as electrochemical reactions. We also discuss the
+fundamental working mechanisms and system architectures of
+these techniques, and compare their performances in terms
+of spatiotemporal resolution, selectivity, system complexity, and
+other performance metrics relevant to MC applications, as well
+as their feasibility for practical MC applications.
+Index Terms—Molecular Communications, pulse shaping, mi-
+crofluidics, testbeds, hydrodynamic gating, acoustofluidics
+I. INTRODUCTION
+T
+He development of unconventional communication sys-
+tems that can process and exchange information via
+molecules and chemical reactions is a rapidly growing re-
+search field, holding the promise of revolutionizing computing
+and communications, and extending our connectivity to mi-
+cro/nanoscale and biological devices and entities. Molecular
+Communications (MC) is a bio-inspired way of communi-
+cation that uses molecules for encoding, transmission, and
+reception of information, and is already ubiquitous among
+living cells [1], [2]. MC is a highly interdisciplinary research
+area at the intersection of information and communication
+The authors are with the Nano/Bio/Physical Information and Communi-
+cations Laboratory (CALICO Lab), Department of Electrical and Electronics
+Engineering, Koc¸ University, Istanbul, Turkey (Corresponding authors’ e-mail:
+{mzadeh22, mkuscu}@ku.edu.tr).
+This work was supported in part by the European Union’s Horizon
+2020 Research and Innovation Programme through the Marie Skłodowska-
+Curie Individual Fellowship under Grant Agreement 101028935, and by The
+Scientific and Technological Research Council of Turkey (TUBITAK) under
+Grant #120E301.
+technologies (ICT), micro/nanotechnology, and biotechnology.
+A variety of paradigm-shifting applications can be achieved
+with the help of MC systems, particularly in the biomedical
+field. The envisioned applications mostly concern the early
+diagnosis and treatment of diseases, such as continuous health
+monitoring, targeted drug delivery in nanomedicine, artificial
+organs, and lab-on-a-chip, in which the use of electromagnetic
+signals is either not desirable due to biocompatibility concerns
+or not feasible due to physical constraints [3], [4], [5], [6], [7].
+Furthermore, MC can be deployed in industrial settings for
+monitoring chemical reactors and nanoscale manufacturing,
+as well as for larger-scale practices, such as monitoring the
+emissions of pollutants and the safe and clean transportation
+of oil [8], [9].
+Unlike conventional communication systems, which typi-
+cally use electromagnetic signals as communication carriers,
+MC uses chemical signals, as conceptually illustrated in Fig. 1.
+Accordingly, a transmitter in an MC system releases molecules
+into a fluidic medium, where the molecules travel through
+diffusion and/or drift, and a portion of them manages to reach
+an MC receiver. Typically, information molecules cause a
+certain reaction at the receiver, through which the receiver
+detects and decodes the transmitted information encoded into
+a distinguishable property of the molecules, such as their
+concentration, type, or release time from the transmitter [10],
+[11], [12].
+While the theoretical aspects of MC have been significantly
+researched, its practical aspects concerning the design and
+prototyping of MC components and systems are yet to be fully
+addressed [2]. This is partly due to the highly interdisciplinary
+technical knowledge and tools required for constructing such
+multi-physics and multi-scale systems [13], [14]. In spite
+of all these issues, a number of experimental studies were
+performed on microfluidic testbeds that can replicate the flow
+conditions of biological environments typically considered for
+MC applications [15], [16]. However, there are important
+challenges, including the lack of high-resolution control of the
+spatiotemporal distribution of molecules inside the microflu-
+idic channels, that hinder the accurate experimental validation
+of the theoretical channel models, as well as the tests and
+the refinement of the developed MC modulation and detection
+techniques [17], [2], [11].
+Pulse shaping is of critical importance in all communication
+systems for enabling accurate and high-rate information trans-
+fer by adjusting the waveform of the signals to be transmitted
+(see Fig. 2) in light of the communication channel’s character-
+istics, e.g., bandwidth, thereby, minimizing the effects of noise
+and intersymbol interference (ISI), and eventually improving
+arXiv:2301.05576v1  [cs.ET]  13 Jan 2023
+
+2
+Electrical Stimuli-responsive
+Hydrogel/Graphene MC Transmitter
+Graphene Biosensor-based
+MC Receiver
+Information 
+Molecules
+Transmitter
+MC Channel
+Receiver
+Transmitted
+Signal
+Received
+Signal
+Fig. 1: A conceptual drawing of an MC system with
+nanomaterial-based transmitter and receiver [2].
+the received signal strength, or equivalently, its signal-to-
+interference-plus-noise ratio (SINR) [18]. As the fluidic MC
+channel manifests peculiar properties, which are quite different
+than its conventional electromagnetic counterparts, such as
+the low-pass characteristics due to the slow diffusion of
+information carriers (i.e., molecules) the importance of pulse
+shaping is more pronounced in MC [4], [19]. Moreover, the
+unique micro/nanoscale architectures of the transmitter and the
+receiver components of the MC system can impose further
+challenges in the transmission and reception of the messages
+encoded into molecules [2], [20], [21]. Furthermore, the dis-
+crete nature of information carriers necessitates rethinking the
+conventional pulse shaping techniques that have been typically
+developed for continuous information carriers, e.g., EM waves.
+The radically different nature of communication channels,
+information carriers, transmitter, and receiver architectures in
+MC also create unique opportunities for pulse shaping, some
+of which have already been explored. For example, different
+diffusion characteristics of molecules of varying sizes were
+exploited to form numerous MC signal waveforms consisting
+of multiple types of molecules with well-defined mixtures [22].
+Additionally, it was shown that the timing and the duration
+of chemical reactions of molecules with certain enzymes can
+be tuned to form well-defined MC pulses inside microfluidic
+channels [13], [23]. Moreover, there were efforts to control the
+physical characteristics of the boundaries of the propagation
+medium, i.e., the communication channel, to form arbitrary
+MC pulse shapes [24], [25]. Although, these approaches
+demonstrated the enhancement of MC performance with pulse
+shaping, the practicality of the employed techniques and their
+actual performances are questionable, as they have not been
+experimentally validated yet.
+Generating well-defined and tunable chemical waveforms
+and concentration gradients in microfluidic systems has also
+attracted considerable attention in various research fields other
+than MC. For example, in biological research, the need for
+dynamically controlling the molecular composition of the
+extracellular matrix (ECM) of cultured biological cells and
+tissues in microfluidic lab-on-a-chip systems motivated the
+development of arbitrary concentration waveform generators
+X(t)
+t
+Y(t)
+t
+Input Signal
+Output Signal
+Pulse Shaping 
+Filter
+Microfluidic
+MC Channel
+MC Transmitter
+Fig. 2: The overall scheme of the pulse shaping in a microflu-
+idic MC system.
+[26]. The proposed techniques utilize different external force
+fields, such as acoustical or hydrodynamic force fields, or
+electrochemical reactions, to program the spatiotemporal dis-
+tribution of molecules inside microfluidic channels with high
+resolution, and generate well-defined concentration waveforms
+that can take arbitrary shapes [27], [28], [29], [30]. De-
+pending on the nature of the external control, the system
+architectures of the waveform generators show a large vari-
+ety in terms of complexity. Their performances in terms of
+selectivity, repeatability, and spatiotemporal resolution of the
+waveforms they generate also differ significantly. Nevertheless,
+the practicality and performances of these techniques have
+been validated through extensive experimental studies, and
+thus, they are promising as externally-controlled pulse shaping
+techniques for use in practical microfluidic MC systems and
+testbeds.
+In this review article, our objective is to thoroughly analyze
+microfluidic chemical waveform generation methods that can
+inform the design of pulse shaping techniques in practical
+microfluidic MC testbeds and systems. We aim to provide a
+comprehensive overview of these techniques, including their
+working mechanisms, system architectures, and additional
+components required for external control. We also conduct
+a comparative analysis of these methods in terms of their
+spatiotemporal resolution and control, selectivity, and system
+complexity, and evaluate their feasibility for a range of prac-
+tical MC applications. We believe that this review will be
+a valuable resource for researchers seeking to innovate in
+the field of MC, as it will help to bridge the gap between
+theory and practice by providing a detailed examination of
+these methods and their suitability for use in microfluidic MC
+testbeds and systems.
+The remainder of this paper is organized as follows: In
+Section II, we explore the significance of pulse shaping in MC
+and review the various methods that have been proposed for
+this purpose in the MC literature. In the following section, we
+delve into microfluidic chemical waveform generation tech-
+niques that enable the production of programmable, dynamic
+chemical signals, examining their underlying mechanisms,
+system architectures, and additional components required for
+external control. Next, in Section 4, we comprehensively
+evaluate the performance of each pulse shaping technique
+in terms of spatiotemporal resolution and control, selectivity,
+repeatability, control over propagation, and system complexity.
+We also discuss their feasibility for integration into practical
+MC applications in Section V. Finally, we conclude the paper
+in Section VI.
+
+3
+II. PULSE SHAPING IN MOLECULAR COMMUNICATIONS
+The characteristics of each component in the MC system,
+e.g., transmitter, channel, and receiver, exhibit additional com-
+munication challenges which highlight the need for pulse
+shaping in MC systems. For instance, at the transmitter, due
+to the limited molecule generation and storage capacity, it
+is necessary to design molecule-efficient pulses in order to
+transmit information molecules effectively. In addition, the
+low-pass characteristic of the MC channel, which typically
+relies on diffusion, leads to significant spatial dispersion of
+the molecular signals as they propagate in the microfluidic
+channel [22]. This may result in substantial ISI that hampers
+the achievable data rates in MC channels [2]. The ISI effect is,
+also, compounded by the fact that practical MC receivers, such
+as nanobiosensors and engineered bacteria, typically employ
+ligand receptors, which interact selectively with the transmitted
+information molecules, i.e., ligands, at finite reaction rates,
+adding to the ISI observed at the receiver. Furthermore, MC
+receivers with ligand receptors typically manifest nonlinear
+responses to the incoming ligand concentrations, and therefore,
+can be severely affected by the saturation of the receptors when
+the received signals in terms of ligand concentrations are not
+optimized. Likewise, in a ligand-receptor-based MC receiver,
+the accuracy of the detection is dependent on the received
+ligand concentration, such that when the receptors are only
+very shortly exposed to the ligand concentration, because of
+the finite reaction rates, there may not be a sufficient number
+of bound receptors for detection [31].
+To overcome the unique challenges of end-to-end MC
+channels, transmission pulses can be optimized according to
+the modulation technique adopted by the transmitter. This
+optimization per se is not sufficient, as we also need practical
+systems that can generate the optimized MC pulse shapes to
+overcome the challenges associated with this system [22], [32],
+[25]. There have been a few proposed pulse shaping methods
+considered for MC in the literature in order to address some
+of these challenges, which are reviewed in the remainder of
+this section.
+A. Pulse Shaping based on Molecular Propagation Charac-
+teristics
+Diversity in the propagation characteristics of different types
+of molecules can be used to shape the transmitted and received
+molecular signals in MC systems. For example, Wicke et
+al. [22] proposed an MC pulse shaping method exploiting
+different diffusion coefficients of molecules that vary in size.
+Accordingly, at the transmitter, they tuned and optimized the
+molecule size mixture to guarantee both a minimum signal
+level and a maximum signal level. A minimum signal level
+was considered for detecting the presence of the signal,
+and a maximum signal level was considered for detecting
+the absence of the signal within a predetermined detection
+window. With this method, suitable molecule sizes can be
+selected optimally for any required detection duration in
+comparison to mixing all molecules together. Moreover, their
+optimization framework can be extended to the cases where
+the channel impulse responses (CIR) of individual types of
+MC
+Receiver
+MC
+Transmitter
+Destroyer
+molecules
+Tunnel-shaped
+MC channel
+Fig. 3: A cylindrical tunnel shape environment for diffusion-
+based MC system [25].
+molecules depend on molecule properties other than their size
+or can be determined only empirically through experiments or
+simulations of complex and reactive environments.
+B. Pulse Shaping Based on Chemical Reactions
+By tuning the rate and the duration of chemical reactions,
+and the concentration of reactants (i.e., input molecules) in a
+controlled microfluidic system, the time-domain concentration
+profile of the reaction products (i.e., output molecules) can be
+patterned for encoding information. In [13], based on a trig-
+gering chemical input, the authors proposed a pulse generator
+for MC which produces predefined molecular concentration
+pulses that are shaped in the transmitter part of the system and
+then transmitted into and propagated through a microfluidic
+channel. The proposed design consists of a microfluidic system
+with standard and reproducible components, whose geometry
+and flow conditions effectively help determine the resulting
+pulse shape. Pulse generation in the proposed method is
+inspired by the motifs observed in cells’ gene regulatory
+networks and compatible with the molecular pulse-modulation
+techniques investigated in the MC literature [33], [34], [35].
+The study also presented a methodology with a modeling and
+analysis framework for diversifying the generated pulse shapes
+with the integration of additional microfluidic components
+inspired by biochemical processes.
+The same group also developed a microfluidic receiver
+in [23] using thresholding and amplification reactions to
+achieve the demodulation of received signals into rectangular
+output signals in the form of concentration of molecules. The
+microfluidic components were characterized as part of an
+analytical study to determine how several design parameters
+such as the concentration of molecules, fluid viscosity,
+diffusion coefficient, and the length of injection time of the
+sample into the system influence the generated pulse and the
+demodulated signal. To optimize the transmitter design, the
+authors proposed a reaction channel length optimization flow
+to control the maximum output pulse concentration at the
+transmitter. They then derived a time gap constraint between
+two consecutive input signals to ensure the continuous
+transmission of non-distorted and identical-shaped pulses.
+
+4
+C. Tunnel-based Pulse Shaping
+To reduce the variance of the receiver-hit time distribution
+of transmitted molecules in diffusion-based MC, which causes
+high propagation delays and ISI, the authors in [25] proposed
+developing a tunnel-based pulse shaping method for MC. This
+method relies on the use of particular types of molecules,
+called destroyer molecules. These molecules clean the MC
+channel from the information molecules remaining from the
+previous transmissions, and thus, control the shape of the
+received signals. In this study, the authors suggested a system
+with an MC channel surrounded by AChE-like destroyer
+molecules to construct a tunnel between the transmitter and the
+receiver, as illustrated in Fig. 3. The use of destroyer molecules
+is inspired by the Acetylcholine (ACh) - Acetylcholinesterase
+(AChE) interaction observed in the Neuromuscular Junctions
+(NMJs) of living organisms. NMJs connect muscle cells to
+nerve cells via an intercellular gap called the synaptic cleft.
+AChE molecules destroy messenger ACh molecules after
+sending a contraction signal to return muscle cells to their
+resting state. It is important to note that the proposed tunnel-
+based pulse shaping method operates in a distinct manner
+compared to other conventional and MC pulse techniques such
+that pulse shaping through chemical reactions in this method is
+realized within the channel through the utilization of destroyer
+molecules.
+In this way, the received signal variance is reduced and the
+communication channel is cleaned for the next signal. Hence,
+the proposed tunnel-based pulse shaping method can control
+the spread and hence the shape of the molecular signals with
+the help of destroyer molecules and the guidance of the tunnel
+geometry, in order to reduce the received signal variance and
+the ISI, thereby significantly increasing the channel capacity.
+III. MICROFLUIDIC PULSE SHAPING METHODS
+Microfluidic chemical waveform generation techniques that
+can produce dynamic chemical signals with programmable
+shapes in microfluidic channels have recently attracted sig-
+nificant interest in many branches of biological research
+concerning the monitoring and manipulation of physiological
+processes, such as immune response, development, embryoge-
+nesis, and cancer metastasis [36]. One prominent application
+of chemical waveform generation in this area is the dynamic
+control of the chemical composition in the ECM of living cells
+cultured in microfluidic platforms, ensuring high spatiotempo-
+ral resolution [37].
+After a brief review of the operating mechanisms and the
+key properties of several microfluidic chemical waveform
+generation techniques in this section, a detailed comparison
+of them is provided in the succeeding sections to compre-
+hensively evaluate their potential for use in microfluidic MC
+testbeds and systems as pulse shaping techniques.
+A. Hydrodynamic Methods
+Chemical concentration waveforms in microfluidic channels
+can be formed through hydrodynamic control, such that the
+modulation of the flow velocity and direction can be exploited
+to tune the injection rate of molecules into the microfluidic
+Microfluidic
+Pressure Controller
+Pressure Control
+Lines
+Buffer
+Waste
+Channel
+outlet
+Information
+molecules
+Gating
+inlet
+Gating
+outlet
+Supply
+inlet
+Valves
+Fig. 4: Schematic representation of microfluidic system setup
+for hydrodynamic gating-based concentration waveform gen-
+eration.
+channel and shape their concentration waveforms propagating
+inside the channel.
+Hydrodynamic gating is one of the most widely used
+hydrodynamic waveform generation techniques, having the
+potential to generate a rich set of dynamic chemical concen-
+tration patterns in microfluidic channels. This method has a
+high degree of precision while being easily implemented and
+operated [38], [39]. An example microfluidic setup for the
+implementation of hydrodynamic gating is conceptually illus-
+trated in Fig. 4, where the cross-shaped microfluidic channel
+can be fabricated via soft-lithography techniques using poly-
+dimethylsiloxane (PDMS) polymer, and the pressure control at
+the micro-channel inlets can be achieved by custom-built or
+commercial pressure control systems, such as programmable
+syringes. Accordingly, in this setup, hydrodynamic gating can
+be achieved by switching on and off the laminar flow that
+comes from the supply inlet and transports the molecules of
+interest through the on-off modulated laminar flow that is
+supplied from the gating inlet. When turned on, the flow from
+the gating inlet generates a hydrodynamic force in the vertical
+direction across the cross-section, that is sufficient enough to
+cut the flow from the supply inlet. Therefore, during the on-
+state of the hydrodynamic gating, the molecules transported
+through the continuous flow from the supply inlet are not able
+to enter the microfluidic channel and are directed towards
+the gating outlet. On the other hand, when gating is turned
+off for a short duration, the vertical hydrodynamic force is
+removed, and thus, the molecules coming from the supply
+inlet are injected into the microfluidic channel. The gating
+duration is therefore critical for tuning the width of the pulses
+propagating inside the channel. The other design parameters
+that play critical roles in determining the shape of generated
+chemical waveforms include the absolute and relative flow
+velocities or pressures applied at the supply and gating inlets,
+and the concentration of molecules transported from the supply
+inlet [28]. As the hydrodynamic gating method involves a
+relatively small number of design parameters that can be fine-
+tuned by the state-of-the-art micro/nanofabrication techniques
+and pressure control devices, it provides a high level of
+reproducibility, which is crucial for reliable and communicable
+experiments. The technique has been experimentally shown to
+generate various chemical pulses and pulse sequences with
+
+5
+a
+b
+c
+t = 10 s
+t = 12.18 s
+t = 15.19 s
+t = 10 s
+t = 12.18 s
+t = 15.19 s
+Concentration (µM)
+Concentration (µM)
+Concentration (µM)
+Y-position (mm)
+Y-position (mm)
+Y-position (mm)
+X-position (mm)
+X-position (mm)
+X-position (mm)
+X-position (mm)
+X-position (mm)
+X-position (mm)
+Fig. 5: An illustration of a concentration pulse sampled at three different time instances: (a) t = 10.00s, (b) t = 12.18s, and (c)
+t = 15.19s, corresponding to different states of the hydrodynamic gating process. (a) and (c) depict the gating state, and (b)
+depicts the injection state. Simulated with COMSOL Multiphysics.
+different frequencies, amplitudes, and shapes [38], [28], [40],
+[41].
+To validate the high spatiotemporal control promised by the
+hydrodynamic gating method, we carried out finite element
+simulations in COMSOL Multiphysics, the results of which
+are provided in Fig. 5. On the left-hand side of the figure
+is shown the 2D concentration profile of molecules sampled
+at specific times; and on the right-hand side, the graphs plot
+the concentration of molecules sampled across the overall
+microfluidic channel from the supply inlet to the channel
+outlet using a concentration probe right at the middle of
+the channel. Accordingly, the concentration profiles observed
+during the three basic states are provided; (a): the first gating
+state, (b): the injection state, and (c): the second gating state.
+During the first gating state (a), all the molecules coming
+from the supply inlet are diverted to the gating outlet by
+the vertical flow applied from the gating inlet such that they
+are not able to pass through the cross-section towards the
+microfluidic channel. During the injection state, however, the
+gating flow is turned off for a short time duration such
+that a small number of molecules can propagate into the
+microfluidic channel without being diverted. When the gating
+flow is turned on again, the system returns to its initial state,
+such that the molecule transport into the microfluidic channel
+stops. As a result, a short concentration pulse of molecules is
+generated, which then continues its propagation towards the
+channel outlet. As the concentration pulse propagates along
+the microfluidic channel, it experiences dispersion due to the
+diffusional transport that accompanies conventional transport.
+The interplay between diffusion and convection determines
+pulse dispersion, which can be an important metric that is
+directly connected to the ISI in MC applications.
+To observe the ISI, we also performed simulations for the
+consecutive generation of short concentration pulses through
+the hydrodynamic gating technique. Fig. 6 shows the 2D and
+1D propagation profiles of the five consecutive concentration
+pulses generated with the same gating durations and even
+pulse generation intervals. The effect of dispersion on the
+width and the peak amplitude of the individual concentration
+pulses can be observed. Although the pulse peaks are easily
+distinguishable for this setup with a particular channel length,
+it can be observed that the interference of consecutive pulses
+increases as they near the end of the microfluidic channel.
+These results highlight the importance of generating short
+concentration pulses to avoid or minimize the ISI.
+Fig. 7 presents the concentration of consecutive pulses over
+time, measured at two different locations in the channel: the
+midpoint and the outlet, for better demonstrating the effect of
+
+mm
+10
+30
+10
+20
+Y-position
+8
+10
+6
+0
+4
+-10
+2
+-20
+0
+-30
+-0.07
+0
+50
+mm
+X-position10
+9
+Concentration (μM)
+8
+7
+6
+5
+4
+3
+2
+1
+0
+20
+40
+60
+80
+X-position (mm)mm
+10.3
+30
+10
+20
+Y-position
+8
+10
+6
+4
+-10
+2
+-20
+0
+-30
+-0.23
+0
+50
+mm
+X-position10
+9
+Concentration (μM)
+8
+7
+6
+5
+4
+3
+2
+1
+0
+20
+40
+60
+80
+X-position (mm)mm
+10.1
+30
+10
+20
+Y-position
+8
+10
+6
+0
+4
+-10
+2
+-20
+0
+-30
+-0.04
+0
+50
+mm
+X-position10
+9
+Concentration (μM)
+8
+7
+6
+5
+4
+3
+2
+1
+0
+20
+40
+60
+80
+X-position (mm)6
+a
+b
+c
+d
+t = 4 s
+t = 4 s
+t = 6.2 s
+t =6.2 s
+t = 14.2 s
+t = 14.2 s
+t = 25.5 s
+t = 25.5 s
+Concentration (µM)
+Concentration (µM)
+Concentration (µM)
+Y-position (mm)
+Y-position (mm)
+Y-position (mm)
+Y-position (mm)
+Concentration (µM)
+X-position (mm)
+X-position (mm)
+X-position (mm)
+X-position (mm)
+X-position (mm)
+X-position (mm)
+X-position (mm)
+X-position (mm)
+Fig. 6: An illustration of consecutive concentration pulses sampled at four different time instances: (a) t = 4.00s, (b) t = 6.20s,
+(c) t = 14.20s and (d) t = 25.50s. By applying a gating flow from the upper inlet at periodic time instances, consecutive
+concentration pulses are generated and propagated within the MC channel. Simulated with COMSOL Multiphysics.
+dispersion on the peak amplitude and width. The concentration
+profile of all of the pulses is shown on the left side of the
+figure, while the concentration profile of only the first pulse
+is shown on the right side of the figure, at both the midpoint
+and outlet of the channel. The examination of the amplitude
+and the width of the first transmitted pulse demonstrates that
+the dispersion effect becomes more prominent at the outlet of
+the channel. It can also be observed that the peak of the last
+propagated pulse is lower than that of the other five pulses.
+The reason for this phenomenon is that the velocity within
+the microchannel decreases significantly after the last gating
+and pulse creation, causing the last generated pulse that is still
+propagating in the channel to move slowly towards the outlet
+and with more dispersion.
+The programmability of hydrodynamic concentration wave-
+form generation methods can be extended through electrical
+control with the utilization of electrical microfluidic valves
+with a low response time, which modulate the injection rate
+of buffer and chemical solutions. By utilizing concepts and
+tools from electrical engineering and fluid mechanics, this
+microfluidic system can deliver time-varying concentrations
+and arbitrary waveforms fast and accurately. In this system,
+concentration waveforms are modulated through pulse width
+modulation (PWM), a standard approach for creating analog
+signals from digital inputs.
+An example microfluidic platform combining hydrodynamic
+gating and electrical control was implemented in [42]. As
+shown in Fig. 8(a), the proposed system is comprised of
+three different functional microfluidic chips connected to each
+other: (i) filter chip, (ii) resistor chip, and (iii) mixer chip.
+Filter chip consists of an elastic membrane-capped cavity
+that functions as a microfluidic capacitor and a serpentine
+
+mm
+10
+60
+10
+(mm)
+40
+8
+20
+-position
+6
+0
+4
+-20
+2
+-40
+0
+-60
+-0.03
+0
+50
+100
+150
+mm
+X-position (mm)10
+9
+Concentration (μM)
+8
+7
+６
+5
+4
+3
+2
+1
+0
+50
+100
+150
+X-position (mm)mm
+10.8
+60
+(mm)
+40
+10
+20
+8
+0
+6
+4
+-20
+2
+-40
+0
+-60
+-0.65
+0
+50
+100
+150
+mm
+X-position (mm)10
+9
+Concentration (μM)
+8
+7
+6
+5
+4
+3
+2
+1
+0
+50
+100
+150
+X-position (mm)mm
+10.6
+60
+(mm)
+40
+10
+20
+8
+6
+0
+4
+-20
+2
+-40
+0
+-60
+-0.59
+0
+50
+100
+150
+mm
+X-position (mm)10
+9
+Concentration (μM)
+8
+7
+6
+5
+4
+3
+2
+1
+o
+0
+50
+100
+150
+X-position (mm)mm
+10.9
+60
+(mm)
+40
+10
+20
+8
+-position
+0
+6
+-20
+4
+-40
+2
+0
+09-
+-1.25×10-3
+0
+50
+100
+150
+mm
+X-position (mm)10
+9
+Concentration (μM)
+8
+7
+6
+5
+4
+3
+2
+1
+OE
+0
+50
+100
+150
+X-position (mm)7
+a
+b
+Pulse Amplitude = 2.7 µM
+Pulse Amplitude = 6.3 µM
+Pulse Width = 1.55 s
+Pulse Width = 0.87s
+Concentration (µM)
+Concentration (µM)
+Concentration (µM)
+Concentration (µM)
+Time (s)
+Time (s)
+Time (s)
+Time (s)
+Fig. 7: An illustration of the concentration profile of consecutive pulses as a function of time, sampled at periodic time instances
+at two different points of the channel: (a) The channel’s midpoint (b) The channel’s outlet. The left side of the figure shows the
+propagation of all of the consecutive pulses as a function of time, while the results on the right side of the figure illustrate only
+the propagation profile of the first transmitted pulse as it passes the midpoint and the outlet of the channel. These simulations
+were carried out using COMSOL Multiphysics.
+channel that functions as a microfluidic resistor. The resistor
+chip contains a serpentine channel whereas the mixer chip
+has a Y-shaped channel. There are three reservoirs in the
+system. One of the reservoirs holds the buffer, which is
+deionized (DI) water, whereas the other two hold fluorescein
+solutions. These two reservoirs are connected to the inlets of
+the filter chip through a selection valve and located at different
+heights to create different hydrostatic pressures. Even though
+the concentrations of these two solutions are the same, the
+instantaneous output flow rates are different when the flow
+selection valve is regulated to switch between them, resulting
+in differing volumes of the solution flowing into the filter chip
+per unit time.
+The filter chip uses a combination of a capacitor and a
+resistor to attenuate the high-frequency components of the
+PWM signal. Through an elastic membrane-capped cavity,
+the capacitor allows low-frequency signals to pass through
+while blocking high-frequency signals, whereas the serpentine
+channel resistor provides resistance to the flow of current
+and determines the rate at which the filter circuit responds
+to changes in the input signal. The filter produces an analog
+output signal that corresponds to the average pulse period of
+the PWM signal, and the specific response characteristics of
+the filter, such as its time constant and cutoff frequency, can be
+adjusted by changing the design parameters of the capacitor
+and resistor. A reservoir containing the buffer is connected to
+the inlet of the resistor chip through a stop valve, enabling
+the solution to be switched off manually. The mixer chip is
+used to achieve the mixing of the solution with the buffer
+to generate the final form of the concentration waveform
+that propagates in the microfluidic channel. By connecting
+a syringe pump to the mixer’s outlet instead of the system
+inlets, liquid can be withdrawn at a constant flow rate. It
+should be noted that this configuration is particularly useful
+in complex microfluidic systems such as this setup where
+maintaining stable and same flow conditions among multiple
+interconnected chips is important. Using this setup, as shown
+in Fig. 8(b), a PWM signal (top plot) is converted into the
+target signal, i.e., a red sinusoidal wave in the bottom plot.
+Additionally, by low-pass filtering of the PWM signal, the
+actual signal (blue ragged sinusoidal wave in the bottom plot)
+is derived, which closely resembles the red sinusoidal signal
+of the target. The employment of the electrically controlled
+PWM technique for the microfluidic device gives the system
+the ability to rapidly and in a programmable manner generate
+sinusoidal, triangle, sawtooth, square, and even more complex
+waveforms with a high level of accuracy, hence, is promising
+for pulse shaping in microfluidic MC systems [42].
+B. Electrochemical Methods
+Chemical concentration waveforms can also be formed
+through electrical control by exploiting electrochemical reac-
+tions, e.g., reduction-oxidation (redox) reactions, of the propa-
+gating molecules on the surfaces of electrodes that are placed
+inside microfluidic channels. Accordingly, in this method,
+by positioning the electrodes in various arrangements, con-
+centration gradients can be generated along the microfluidic
+channel through the interplay between reaction, diffusion, and
+convection processes. The shape of the resulting concentration
+gradients or waveforms can also be controlled by space-
+and time-modulating the electrical potential applied to the
+electrodes, which modulates the rates of the electrochemical
+
+7
+6
+Concentration (μM)
+5
+4
+3
+2
+1
+0
+10
+20
+30
+Time (s)6
+Concentration (μM)
+5
+4
+3
+1
+0
+13
+14
+15
+16
+Time (s)2.5
+Concentration (μM)
+2
+1.5
+1
+0.5
+0
+25
+26
+27
+28
+Time (s)3.5
+(uM)
+3
+Concentration 
+2.5
+2
+1.5
+1
+0.5
+0
+20
+30
+40
+50
+Time (s)8
+a
+b
+Fig. 8: A programmable microfluidic device designed to gen-
+erate chemical waveforms hydrodynamically. (b) The top plot
+is the input PWM signal with Y-axis showing the flow rate and
+the bottom plot is the output signal (ragged sinusoidal) with Y-
+axis showing the concentration. Reproduced with permission
+from [42].
+reactions [43]. The typical implementation of this technique
+involves a microfluidic device composed of four electrodes,
+i.e., two working electrodes (E1, E2), a reference electrode
+(RF), and a counter electrode (CE), all positioned at the
+bottom of the rectangular microfluidic channel in a dual-
+channel-electrode configuration, as shown in Fig. 9 [27]. In
+this example setup, the pseudo-reference electrode is located
+in the upstream part of the channel to keep the base electrical
+potential stable during the operation. The microfluidic channel
+is filled with a solution of electrically neutral molecules,
+which is continuously supplied from the channel inlet with a
+constant flow velocity. When the electrical potential of the first
+working electrode E1 is turned on, the neutral molecules, as
+they are transported over the electrode through convection and
+diffusion, undergo an oxidation reaction which converts them
+into electroactive molecules. Counter electrode, meanwhile,
+serves as a site for the reduction of the oxidized molecules
+that are generated at the working electrode, allowing the
+overall reaction to proceed smoothly and efficiently [44]. The
+generated electroactive molecules propagate downstream along
+Fig. 9: A typical microfluidic device for electrochemical
+generation of chemical waveforms, consisting of a reference
+electrode (RE), two working electrodes (E1, E2), and a counter
+electrode (CE) placed at the bottom of a rectangular microflu-
+idic channel. Reproduced with permission from [27].
+the microfluidic channel with a concentration waveform that
+depends on the duration and the amount of electrical potential
+applied to E1 in addition to the flow velocity in the channel,
+and the diffusion coefficient of the molecules. Hence the elec-
+trical potential applied to E1 can solely modulate the generated
+concentration waveforms when the other system parameters
+are kept constant. The role of the second electrode E2 is to
+monitor the generated waveforms as they propagate through
+the channel, and convert them back to neutral molecules
+through a reduction reaction. Thus, the overall system with
+two working electrodes can be considered as operating in a
+generator-collector mode. It is to be noted that the potential
+difference between E1 and E2 electrodes generates an electric
+field along the microfluidic channel, which contributes to
+the transport of molecules downstream in addition to the
+hydrodynamic forces.
+The electrochemical method has been theoretically and ex-
+perimentally shown to generate a wide range of concentration
+waveforms through the modulation of the first working elec-
+trode potential [27], [36]. According to the simulation results
+shown in Fig. 10, the generated waveforms can take various
+shapes, such as peaks and plugs, depending on the duration of
+the applied electrical potential. The top section of the figure
+demonstrates the 2D concentration distribution of four distinct
+shapes of concentration pulses that can be generated between
+electrodes E1 and E2 (as shown in the bottom section of the
+figure). These results were obtained through finite element
+simulations, sampled at specific time instances. By adjusting
+the duration and amount of electrical potential applied to E1
+and changing the flow velocity in the microfluidic channel,
+it is possible to generate these unique concentration pulse
+shapes. The use of electrochemical reactions in microfluidic
+MC testbeds is promising for pulse shaping. The technique
+provides a high level of programmability through electrical
+access and can be miniaturized easily to be integrated into
+
+Pulse-width modulation input signal
+Amplitude
+0.5
+0
+0
+0.2
+0.4
+0.6
+0.8
+1
+1.2
+1.4
+1.6
+1.8
+2
+Time (s)
+Target (red) and actual (blue) output signal
+Amplitude
+0.5
+0
+0
+0.2
+0.4
+0.6
+0.8
+1
+1.2
+1.4
+1.6
+1.8
+2
+Time (s)Tme (s)
+Concentration
+Concentration
+i&ii
+iii
+b
+Time
+Time
+Concentration
+High-Pressure Analyte
+iv
+Buffer
+Time
+Height
+Low-pressure Analyte
+Flow Rate
+Flow Rate
+Time
+Time
+Stop Valve
+Flow Rate
+iv
+Resistor Chip
+ili
+Selection
+Time
+Valve,
+withdraw
+iv
+Mixer Chip
+Filter ChipA
+5mm
+E1
+E2
+RE
+CE
+contact
+pads
+ndu
+uchannel
+output
+PDMS
+RE
+E1
+E2
+CE
+1 flow
+μchannel
+TL
+g
+WE1
+We29
+Fig. 10: (Top) Chemical concentration signals generated by
+the electrochemical method, sampled at a given time between
+E1 and E2 electrodes in the microfluidic device. (Bottom)
+Corresponding concentration waveforms along the x-axis. Re-
+produced with permission from [27].
+MC testbeds of various scales [27].
+C. Acoustofluidic Methods
+Acoustofluidics, the manipulation of molecules, nanopar-
+ticles, and biological entities through acoustic forces in mi-
+crofluidic structures has been of great interest recently due to
+its noninvasiveness and ease of integration into microfluidic
+systems [45], [46]. The acoustic vibration forces that are
+generated at ultrasonic frequencies in the hundreds of kHz
+to tens of MHz range have wavelengths that are well-suited
+to microfluidic channel scales [47]. This method is primarily
+used in the separation of nanoparticles, cancer cells, bacteria,
+extracellular vesicles, blood components, droplets, and other
+particles, which is a fundamental process in bioanalytical
+research [48]. The acoustofluidic method has the capability to
+generate spatiotemporally modulated concentration waveforms
+in microfluidic channels with the help of a micromixer struc-
+ture exposed to the acoustic field. Micromixer is typically a
+microbubble that is trapped inside the microfluidic channel and
+oscillates at certain frequencies under the effect of an acoustic
+field. The oscillation of microbubble transduces acoustic force
+into mechanical force, which in turn, helps rapid mixing of
+buffer and solution that transports the molecules of interest
+from the inlet to the microfluidic channel [30], [49].
+In [37], Ahmed et al. proposed an acoustofluidic chemical
+waveform generator based on the active mixing of a buffer
+with a chemical solution of interest using acoustically driven
+oscillating bubbles. A schematic diagram of this platform is
+shown in Fig. 11(a), which exploits the bubble oscillation in
+an acoustic field to generate arbitrary chemical waveforms
+inside the microfluidic channel [50]. The proposed device
+consists of a single-layer PDMS-based microfluidic channel
+with two inlets and one outlet. The architecture of the device,
+including the number of inlets and outlets, however, can
+vary depending on its purpose. In this setup, the microfluidic
+channel is equipped with a horseshoe structure (HSS) that traps
+j
+Fig. 11: Acoustofluidic chemical waveform generation: (a)
+Schematic of a typical setup with HSS. Piezoelectric trans-
+ducers, which are placed adjacent to the microfluidic channel
+on a glass slide, produce low-intensity acoustic waves. The
+generated acoustic waves oscillate the bubble trapped in the
+HSS, which is positioned at the interface of the two liquids.
+(b) Acoustic microstreaming and flow recirculation during
+the bubble oscillation. (c-i) Acoustofluidic generation of a
+chemical waveform observed at different time instances. When
+an ink solution and a buffer are used as the inlet solutions,
+the resulting chemical waveforms are monitored through the
+optical density in the region of interest (ROI). (j) The diagram
+of the chemical waveforms produced by acoustic signals in
+the shape of a square wave. Reproduced with permission from
+[37].
+a single bubble via surface tension. A piezoelectric transducer,
+that generates the acoustic field, is placed adjacent to the
+microfluidic channel. The membrane of the trapped bubble
+oscillates under an acoustic force field generated by a piezo-
+electric transducer, which is controlled through an electronic
+function generator. Maximum bubble oscillation occurs at its
+resonance frequency, which depends on the bubble size. A
+pressure gradient is generated in the fluid due to the second-
+order effect of nonlinearity in the Navier-Stokes equation
+at the resonance frequency, driving acoustic microstreams.
+When the trapped bubble is vibrated, the counter-rotating
+vortices resulting from microstreaming disrupt the smooth
+buffer-solution interface that is resulting from the laminar
+flow regime in the microchannel. Through the disruption of
+
+(a)
+flow
+介
+(b)
+(c)
+Y
+(d)
+X
+(a)
+(b)
+(c)
+(d)a
+C
+Bluedye
+Red dye
+0ms
+ROI
+ROL
+6m
+13ms
+Transducer
+HSS
+Bubble
+20ms
+27ms
+33ms
+100um
+96ms
+60umSquarewave,period2and5s
+Normailizedintensity
+1.0
+8r0
+0.6
+0.4
+0.2
+0.0
+4
+6
+8
+10
+12
+14
+16
+18
+20
+Time (s)10
+the interface, the microstreams drastically enhance the mass
+transport along the direction perpendicular to the laminar flow,
+effectively mixing the liquids. This is referred to as the ON
+state of mixing. This mixing process is shown in Fig. 11(c-i).
+When the acoustic force field is turned off for a short duration
+by the piezoelectric transducer, the mixing of inlet solutions
+stops, and the characteristic laminar flow manifests again. This
+is referred to as the OFF state of mixing. Hydrodynamic forces
+dominate the system once the acoustic field is eliminated in the
+OFF state, and this leads to the propagation of the generated
+chemical waveforms along the channel. As a result of the fast
+responses of the electrical and acoustic fields, the system can
+toggle between ON and OFF states swiftly and transforms
+the electrical signals into chemical waveforms which will
+propagate through the channel, as shown in Fig. 11(j) [30],
+[50], [51].
+IV. DISCUSSION ON PULSE SHAPING PERFORMANCE
+This section examines and the performance of the microflu-
+idic chemical waveform generation methods introduced in Sec-
+tion III in terms of their capacity to be utilized in microfluidic
+MC testbeds and systems for pulse shaping. This capacity
+is evaluated based on a couple of key performance criteria,
+including spatiotemporal resolution, complexity, repeatability,
+selectivity, and control over propagation. A summary compar-
+ison of the methods based on these criteria is presented in
+Table I.
+A. Spatiotemporal Resolution
+As in all communication systems, the achievable commu-
+nication rate is a critical performance metric for MC systems.
+Communication rate in MC depends on the concentration pulse
+generation rate on the transmitter side, and the imperfections
+in the channel that could lead to the distortion and the
+dispersion of the generated pulses as they propagate along
+the channel, which in turn might result in, for example, the
+ISI. To be able to test a wide range of communication rates in
+practical MC testbeds with particular channel conditions and
+receiver designs, the transmitter should be capable of gen-
+erating concentration pulses with well-defined and persistent
+waveforms at a high rate. This capability of the transmitter
+can be evaluated in terms of its temporal resolution. The
+spatial resolution, on the other hand, measures the capability
+of the transmitter, i.e., the waveform generation technique,
+to produce well-defined square concentration waveforms. In
+other words, it gives a measure of the bandwidth of the
+generated concentration waveforms. Higher the bandwidth, the
+wider range of concentration waveforms that the method is
+able to generate inside the microfluidic channel. The temporal
+and spatial resolutions are connected to each other in their
+dependence on the design and operating mechanism of the
+waveform generation technique, and thus, evaluated in this
+section together by being referred to as the spatiotemporal
+resolution.
+The spatiotemporal resolution in hydrodynamic and electro-
+chemical methods is at a medium level. In [28], 20 consecu-
+tive concentration pulses generated via hydrodynamic method
+could be injected into the microfluidic channel with a time
+interval of 500 ms between every two consecutive pulses,
+demonstrating that the hydrodynamic method is capable of
+generating chemical waveforms with a temporal resolution
+of approximately 2 Hz. Nevertheless, because of the band
+limitations of a microfluidic channel, distortions are inevitably
+generated as the pulses propagate along the channel, leading
+to the degradation of the spatial resolution of this technique.
+Likewise, the reported temporal resolutions for the electro-
+chemical technique range between 2-4 Hz [27]. Moreover, the
+pulses generated by these methods well approximate a square-
+wave right after their generation (see Fig. 5 and Fig. 10),
+overall indicating a medium level of spatiotemporal resolution.
+In comparison with the other methods mentioned above,
+acoustofluidic methods were reported to exhibit a higher level
+of spatiotemporal resolution. The experimental results from
+[37] reveal that this method provides very high temporal reso-
+lution reaching up to 30 Hz frequency. Also, generated pulses
+approximate square waves much better compared to other
+techniques (see Fig. 11), overall making the acoustofluidic
+methods most promising for the microfluidic MC testbeds
+supporting high data transmission rates.
+B. Control over Propagation
+In microfluidic MC testbeds, not only the generation of
+arbitrary chemical waveforms but also their propagation and
+the evolution of their profile along the microfluidic channels
+can be important to accurately test the performances of MC
+modulation and detection techniques and validate MC channel
+models. The assessment for control over the propagation of
+each method considers to what extent the technique that
+generates the pulses is also able to control their propagation
+inside the channel, independently of the generation process.
+Among the chemical waveform generation methods consid-
+ered in this paper, the electrochemical method provides the
+highest degree of control over the propagation of generated
+waveforms. In the electrochemical method, the redox reactions
+between the molecules and the first working electrode convert
+the electrically neutral molecules into electroactive molecules,
+meaning that they can be influenced by the electric field effect.
+As there are two working electrodes (E1 and E2, see Fig. 9),
+separated by a certain distance in the microfluidic channel, the
+potential difference between them generates an electric field
+along the channel, which acts upon the generated concentration
+signal of the electroactive molecules. Therefore, depending on
+the polarity of the electroactive molecules, and the magnitude
+of the potential difference between electrodes, the propagation
+characteristics of the generated concentration waveforms can
+be modulated independently of their generation process [43].
+In the hydrodynamic method, however, both the generation
+and the propagation of concentration waveforms are controlled
+by hydrodynamic forces. This limits the ability to control
+propagation characteristics independently of the waveform
+generation process inside the channel. Thus, the hydrodynamic
+technique can be considered to have a medium level of control
+over the propagation of generated waveforms in comparison
+to the other two methods [28].
+
+11
+TABLE I: A Comparison of the Microfluidic Pulse Shaping Methods Based on
+Key Performance Criteria
+Methods
+Spatio-temporal
+Resolution
+Control over
+Propagation
+Repeatability
+Selectivity
+System
+Complexity
+Hydrodynamic
+Methods
+Medium
+Medium
+High
+Low
+Low
+Electrochemical
+Methods
+Medium
+High
+Medium
+High
+Medium
+Acoustofluidic
+Methods
+High
+Low
+High
+Low
+High
+On the other hand, the acoustofluidic method has the lowest
+level of control over the propagation of the generated wave-
+forms, as the bubble oscillations due to the acoustic force fields
+create space-limited vortices, localized only around the bubble
+contained in HSS. Therefore, the resulting vibrational force
+fields do not extend into the microfluidic channel, limiting the
+capacity of this method to dynamically tune the propagation
+characteristics of the generated chemical waveforms. This lack
+of control over propagation in this method, however, can be
+improved with the modulation of the hydrodynamic forces
+inside the channel, for example, by tuning the inlet pressures
+[37], [51].
+C. Repeatability
+The repeatability of the chemical waveform generation
+techniques can be evaluated based on the number of suc-
+cessively generated waveforms that have approximately the
+same shape when introduced into the microfluidic channel.
+The repeatability is of crucial importance for practical MC
+testbeds and systems, as MC scenarios typically require the
+transmission of multiple concentration pulses successively, for
+example, to evaluate the impact of ISI, and determine the
+achievable data transmission rates.
+An important factor in generating approximately the same
+waveforms, and therefore having high repeatability in each
+transmission is the stability and durability of the microfluidic
+chip structure, especially in the transmitter part. As is shown
+in Fig. 6 and Fig. 11, consecutively generated pulses by both
+hydrodynamic and acoustofluidic methods have approximately
+the same waveform, indicating the superb repeatability of
+these methods. This is due to the fact that all the parameters
+involved in the design of the transmitter structure and the
+microfluidic chip for both acoustic and hydrodynamic based
+methods can be controlled and engineered to yield utmost
+stability in generating concentration waveforms [28], [37].
+The electrochemical method, on the other hand, can be
+considered to have lower repeatability over long operation
+times, due to the chemical reactions involved in the generation
+of the waveforms. More specifically, the chemical reactions
+on the electrode surface are highly prone to the effects of
+environmental fluctuations, such as those in the temperature.
+Second, chemical reactions are inherently stochastic processes,
+adding to the low-level repeatability of the electrochemical
+method.
+D. Selectivity
+In practical MC applications, there could be many different
+types of molecules co-existing in the MC channel, that can
+result from a biological process at the background or another
+MC network accessing the same channel. The co-existence
+of different types of molecules can lead to substantial inter-
+ference with the communication process. Researchers have
+already developed several theoretical detection and channel
+sensing techniques to reduce or eliminate the effect of such
+background or multi-user interference [31]. To enable the
+performance tests of these methods under interference, and
+the development of more practical techniques to cope with
+it, microfluidic MC testbeds should be able to replicate the
+interference conditions. From the transmitter aspect, the pulse
+shaping technique should be able to selectively control the
+waveform generation process, such that only the molecules
+of interest, among other interfering molecules, are modulated
+in concentration. The electrochemical waveform generation
+method can be considered to support selectivity for such
+MC scenarios, due to the inherent specificity of the chemical
+reactions involved in the waveform generation process [27].
+In the hydrodynamic method, however, the concentration
+of molecules is modulated solely by hydrodynamic forces,
+which does not make a distinction between different types
+of molecules co-existing in the channel. The only factor that
+can enable selectivity in hydrodynamic waveform generation
+is the diffusion coefficient of molecules, which may differ
+depending on the size of the molecules. However, as the effect
+of diffusion on the shape of generated waveforms is limited,
+manifesting itself only in the dispersion of the waveforms as
+they propagate, it cannot enable the required level of selectivity
+in pulse shaping in MC testbeds.
+Similar to the hydrodynamic method, the selectivity of the
+acoustofluidic methods is low. The external acoustic force
+fields applied by the transducer in this method modulate the
+oscillation frequency of the bubbles trapped inside the HSS
+structure, which then only indirectly affect the transport of
+the molecules around the structure through the hydrodynamic
+forces. As there is no direct impact of the acoustic force
+fields on molecular transport, the method cannot selectively
+distinguish between different types of molecules. Hence, the
+only element that can lead to a low level of selectivity in this
+method could be again the diffusion coefficient that depends
+on the type, i.e., the size, of molecules. [29], [37].
+
+12
+E. System Complexity
+The complexity of the microfluidic chemical waveform
+generation techniques is evaluated based on the number and
+the heterogeneity of individual components required for the
+waveform generation, and the fabrication methods by which
+the overall system, including the microfluidic chip and other
+external components, is assembled to generate chemical wave-
+forms. Systems with less complexity, of course, can be favored
+because of the ease and low cost of the fabrication process,
+and more importantly, the increased level of reproducibility.
+Acoustofluidic waveform generation is typically based on
+a complex system architecture involving a multitude of ex-
+ternal components, such as a piezoelectric transducer capable
+of producing low-intensity acoustic waves, and a horseshoe
+structure (HSS), which traps the bubble that is oscillated via
+the acoustic waves inside the microfluidic channel.
+The electrochemical waveform generation method has a
+medium level of complexity compared to the other two meth-
+ods. In terms of fabrication, the system architecture consists
+of a hybrid PDMS-glass chip. Electrodes can be deposited on
+the glass substrate with a specified spacing with a sputtering
+mechanism. The waveform generation process in this method
+is based on the consecutive electric potential pulses applied
+to the electrodes and the subsequent electrochemical reactions
+of the molecules on the first working electrode. Therefore,
+the electrochemical method can be considered to require a
+much simpler fabrication process and have a simpler operating
+mechanism compared to the acoustofluidic method [43], [27].
+Hydrodynamic methods, on the other hand, have a less
+complex system architecture consisting of only a PDMS-
+based microfluidic chip at the fundamental level. Note that
+the microfluidic chip and the external pressure control systems
+that drive the fluid flow inside the channels are common to all
+microfluidic waveform generation techniques investigated in
+this paper. The waveform generation process is also relatively
+simple in hydrodynamic methods, as it only requires the
+hydrodynamic forces which are inherent to the microfluidic
+systems [28], [27]. These make the hydrodynamic method the
+least complex waveform generation method considering that
+the other methods require additional external force fields, such
+as acoustic fields, or electrochemical reactions.
+V. DISCUSSION ON APPLICATIONS AND FEASIBILITY
+Most of the MC applications envisioned in the literature,
+including those concerning intrabody environments, can po-
+tentially be facilitated by high-resolution and programmable
+MC pulse shaping techniques integrated into MC transmitter
+architectures. This is because high-resolution control over
+the waveform of the generated concentration pulses can help
+address the problems resulting from ISI, and nonlinear and
+time-varying channel and transmitter/receiver characteristics,
+as explained in Section 2. Many of these problems require the
+generation of various concentration waveforms, and sometimes
+the ability to adaptively tune their properties in order to
+improve the accuracy of information transfer. Understanding
+the relationship between physical design parameters and gen-
+erated pulse shapes can reveal practical limitations and identify
+areas of further engineering and optimization, as well as
+inform the design of optimal and practical MC modulation and
+detection techniques. This practical understanding is crucial
+for moving beyond the commonly utilized assumption of
+instant, impulsive molecule release with point transmitters,
+which lacks practical relevance [2].
+Microfluidic pulse shaping techniques discussed in this pa-
+per are particularly promising for integration into microfluidic
+MC testbeds. These techniques can allow for a broader range
+of MC scenarios to be practically tested and enable more
+accurate and programmable platforms for optimization and
+validation. The implementation of these practical MC pulse
+shaping techniques in microfluidic MC testbeds can immedi-
+ately make the following contributions to the MC literature:
+• Enabling the accurate testing of existing or new MC
+modulation and detection methods, and facilitating the
+design of realistic MC techniques that are compatible
+with the pulse shapes that can be practically generated.
+• Optimizing transmitted pulse shapes (e.g., the duration
+of a rectangular concentration pulse) from a commu-
+nication perspective for different practical MC channel
+and receiver architectures and configurations, such as
+MC receivers with ligand receptors that may experience
+saturation depending on concentration pulse amplitude
+and duration. Such optimization can be readily validated
+through the integration of the investigated pulse shaping
+techniques into microfluidic MC testbeds.
+• Eventually, optimizing the overall MC system, including
+the physical receiver architecture, under various MC
+scenarios given the pulse shaping technique and the
+corresponding set of concentration waveforms that can
+be generated.
+Furthermore, leveraging the chemical waveform genera-
+tion techniques with MC tools and theories in microfluidic
+chips can significantly contribute to lab-on-chip and organ-
+on-chip technologies. For example, replicating the signaling
+dynamics between cell groups and tissues in microfluidic
+chips is essential for creating organ function in organ-on-
+chip systems. High-resolution and programmable microfluidic
+pulse shaping techniques that allow for the implementation of
+various MC modulation techniques in microfluidic chips can
+enable ICT-based organ-on-chip platforms that can accurately
+control chemical signal patterns between different biological
+components, providing an opportunity to probe and study the
+role of information flow in microphysiological systems. Such
+ICT-based platforms can open new avenues in drug delivery
+and drug design research. Merging ICT with microfluidic
+technologies through MC pulse shaping techniques can also
+have implications in biomedical sensor research. These multi-
+disciplinary platforms can allow for the information-theoretical
+optimization of sensor architectures for sensing time-varying
+concentration waveforms of biomarkers generated through
+microfluidic MC pulse shaping techniques.
+It should be noted, however, that none of the chemical
+waveform generation techniques investigated in this paper have
+been demonstrated in in vivo environments, such as inside
+the human body. This raises the question of whether the
+
+13
+microfluidic MC pulse shaping techniques can be integrated
+into practical MC transmitters for in vivo MC applications.
+The main challenge in implementing these techniques in in
+vivo environments will be system complexity, as discussed in
+Section IV-E, and the spatiotemporal control of pulse shapes
+independently of the surrounding biological force fields. For
+example, the high-level complexity of the acoustofluidic pulse
+shaping techniques, which necessitate fine tuning of the exter-
+nal acoustic transducer and the horseshoe structure for bubble
+oscillation, may hinder their feasibility for such applications.
+On the other hand, while the system complexity of hydrody-
+namic methods is relatively low, the pulse shaping function
+in this method is based on tuning hydrodynamic force fields,
+e.g., fluid flow rate, which may not be feasible to control
+independently of the flow conditions of biological fluids, e.g.,
+blood. Electrochemical methods, although having advantages
+in terms of system complexity and scalability, may lead to
+biocompatibility issues due to the required electrochemical
+reactions. In summary, the investigated microfluidic MC pulse
+shaping methods are currently not feasible for integration
+into in vivo MC applications. However, further advances in
+micro/nanotechnologies may provide new opportunities for
+improving their practicality or offer alternative pulse shaping
+methods that are more compatible with such applications.
+VI. CONCLUSION
+This paper provided a comprehensive overview of practical
+microfluidic chemical waveform generation techniques which
+are promising as pulse shaping methods for microfluidic MC
+systems and testbeds. Pulse shaping is essential for accurate
+and high-rate information transfer in MC systems because
+the inherent low-pass characteristic of the MC channel leads
+to significant dispersion of the molecular signals as they
+propagate. The programmability of the spatiotemporal distri-
+bution of molecules of interest inside microfluidic channels
+is also crucial for extending the capabilities of microfluidic
+MC testbeds. The chemical waveform generation techniques
+highlighted in this paper utilize different external forces, such
+as hydrodynamic and acoustic force fields, or electrochem-
+ical reactions, to program the spatiotemporal distribution of
+molecules inside the microfluidic channels. These methods
+were analyzed in terms of their operating mechanisms and
+the characteristics of the generated concentration signals. To
+accurately assess the suitability and potential utility of these
+techniques for application in microfluidic MC systems and
+testbeds, we identified a set of key performance criteria
+including spatiotemporal resolution, control over propagation,
+system complexity, repeatability, selectivity, and compatibility
+with a wide range of applications. Through this comprehensive
+evaluation, we aim to bridge the gap between theory and
+practice in MC technology. We believe that this review and
+the accompanying evaluation will help researchers incorporate
+programmable, high-resolution pulse shaping techniques into
+their microfluidic MC testbeds for a more accurate assessment
+of the developed MC techniques, such as modulation and
+detection techniques, with well-defined MC signal waveforms
+inside microfluidic channels.
+ACKNOWLEDGMENT
+This work was supported in part by The Scientific and
+Technological Research Council of Turkey (TUBITAK) un-
+der Grant #120E301, and European Union’s Horizon 2020
+Research and Innovation Programme through the Marie
+Skłodowska-Curie Individual Fellowship under Grant Agree-
+ment #101028935.
+REFERENCES
+[1] I. F. Akyildiz, M. Pierobon, and S. Balasubramaniam, “Moving forward
+with molecular communication: From theory to human health applica-
+tions [point of view],” Proceedings of the IEEE, vol. 107, no. 5, pp.
+858–865, 2019.
+[2] M. Kuscu, E. Dinc, B. A. Bilgin, H. Ramezani, and O. B. Akan,
+“Transmitter and receiver architectures for molecular communications:
+A survey on physical design with modulation, coding, and detection
+techniques,” Proceedings of the IEEE, vol. 107, no. 7, pp. 1302–1341,
+2019.
+[3] L. Felicetti, M. Femminella, G. Reali, and P. Li`o, “Applications of
+molecular communications to medicine: A survey,” Nano Communica-
+tion Networks, vol. 7, pp. 27–45, 2016.
+[4] O. B. Akan, H. Ramezani, T. Khan, N. A. Abbasi, and M. Kuscu,
+“Fundamentals of molecular information and communication science,”
+Proceedings of the IEEE, vol. 105, no. 2, pp. 306–318, 2016.
+[5] D. Bi, A. Almpanis, A. Noel, Y. Deng, and R. Schober, “A survey of
+molecular communication in cell biology: Establishing a new hierarchy
+for interdisciplinary applications,” IEEE Communications Surveys &
+Tutorials, vol. 23, no. 3, pp. 1494–1545, 2021.
+[6] M. T. Barros, M. Veleti´c, M. Kanada, M. Pierobon, S. Vainio, I. Balas-
+ingham, and S. Balasubramaniam, “Molecular communications in viral
+infections research: Modeling, experimental data, and future directions,”
+IEEE Transactions on Molecular, Biological and Multi-Scale Commu-
+nications, vol. 7, no. 3, pp. 121–141, 2021.
+[7] M. Kuscu and B. D. Unluturk, “Internet of bio-nano things: A review
+of applications, enabling technologies and key challenges,” ITU Journal
+on Future and Evolving Technologies,, vol. 2, no. 3, 2021.
+[8] I. F. Akyildiz, J. M. Jornet, and M. Pierobon, “Nanonetworks: A new
+frontier in communications,” Communications of the ACM, vol. 54,
+no. 11, pp. 84–89, 2011.
+[9] W. Haselmayr, A. Springer, G. Fischer, C. Alexiou, H. Boche, P. A.
+Hoeher, F. Dressler, and R. Schober, “Integration of molecular com-
+munications into future generation wireless networks,” 1st 6G Wireless
+Summit. IEEE, Levi, Finland, 2019.
+[10] S. Hiyama, Y. Moritani, T. Suda, R. Egashira, A. Enomoto, M. Moore,
+and T. Nakano, “Molecular communication,” Journal-Institute of Elec-
+tronics Information and Communication Engineers, vol. 89, no. 2, p.
+162, 2006.
+[11] N. Farsad, H. B. Yilmaz, A. Eckford, C.-B. Chae, and W. Guo, “A
+comprehensive survey of recent advancements in molecular communi-
+cation,” IEEE Communications Surveys & Tutorials, vol. 18, no. 3, pp.
+1887–1919, 2016.
+[12] M. Kuscu and O. B. Akan, “Detection in molecular communications
+with ligand receptors under molecular interference,” Digital Signal
+Processing, vol. 124, p. 103186, 2022.
+[13] Y. Deng, M. Pierobon, and A. Nallanathan, “A microfluidic feed forward
+loop pulse generator for molecular communication,” in GLOBECOM
+2017-2017 IEEE Global Communications Conference.
+IEEE, 2017,
+pp. 1–7.
+[14] S. Balasubramaniam, S. Ben-Yehuda, S. Pautot, A. Jesorka, Y. Kouch-
+eryavy, et al., “A review of experimental opportunities for molecular
+communication,” Nano Communication Networks, vol. 4, no. 2, pp. 43–
+52, 2013.
+[15] M. Kuscu, H. Ramezani, E. Dinc, S. Akhavan, and O. B. Akan,
+“Fabrication and microfluidic analysis of graphene-based molecular
+communication receiver for internet of nano things (iont),” Scientific
+reports, vol. 11, no. 1, pp. 1–20, 2021.
+[16] A. Amerizadeh, A. Mashhadian, M. Farahnak-Ghazani, H. Arjmandi,
+M. A. Rad, A. Shamloo, M. Vosoughi, and M. Nasiri-Kenari, “Bacterial
+receiver prototype for molecular communication using rhamnose operon
+in a microfluidic environment,” IEEE Transactions on NanoBioscience,
+vol. 20, no. 4, pp. 426–435, 2021.
+
+14
+[17] M. Kuscu, “Nano/bio-receiver architectures and detection methods for
+molecular communications,” Ph.D. dissertation, University of Cam-
+bridge, 2020.
+[18] J. G. Proakis and M. Salehi, Fundamentals of communication systems.
+Pearson Education India, 2007.
+[19] M. Kuscu and O. B. Akan, “Modeling convection-diffusion-reaction
+systems for microfluidic molecular communications with surface-based
+receivers in internet of bio-nano things,” PloS one, vol. 13, no. 2, p.
+e0192202, 2018.
+[20] ——, “On the physical design of molecular communication receiver
+based on nanoscale biosensors,” IEEE Sensors Journal, vol. 16, no. 8,
+pp. 2228–2243, 2016.
+[21] M. Rezaei, H. K. Rudsari, M. Javan, N. Mokari, E. A. Jorswieck, and
+M. Orooji, “Molecular communication transmitter design in limited-
+capacity storage regime,” IEEE Transactions on NanoBioscience, 2022.
+[22] W. Wicke, R. C. Felsheim, L. Brand, V. Jamali, H. M. Loos, A. Buettner,
+and R. Schober, “Pulse shaping for mc via particle size,” arXiv preprint
+arXiv:2201.06425, 2022.
+[23] D. Bi, Y. Deng, M. Pierobon, and A. Nallanathan, “Chemical reactions-
+based microfluidic transmitter and receiver design for molecular com-
+munication,” IEEE Transactions on Communications, vol. 68, no. 9, pp.
+5590–5605, 2020.
+[24] A. O. Bicen and I. F. Akyildiz, “System-theoretic analysis and least-
+squares design of microfluidic channels for flow-induced molecular
+communication,” IEEE Transactions on Signal Processing, vol. 61,
+no. 20, pp. 5000–5013, 2013.
+[25] M. S¸. Kuran, H. B. Yilmaz, and T. Tugcu, “A tunnel-based approach for
+signal shaping in molecular communication,” in 2013 IEEE international
+conference on communications workshops (ICC). IEEE, 2013, pp. 776–
+781.
+[26] P. Chen, S. Li, Y. Guo, X. Zeng, and B.-F. Liu, “A review on microflu-
+idics manipulation of the extracellular chemical microenvironment and
+its emerging application to cell analysis,” Analytica Chimica Acta, vol.
+1125, pp. 94–113, 2020.
+[27] T. Abadie, C. Sella, P. Perrodin, and L. Thouin, “Electrochemical
+generation and detection of transient concentration gradients in microflu-
+idic channels. theoretical and experimental investigations,” Frontiers in
+chemistry, p. 704, 2019.
+[28] P. Chen, X. Feng, J. Sun, Y. Wang, W. Du, and B.-F. Liu, “Hydrodynamic
+gating for sample introduction on a microfluidic chip,” Lab on a Chip,
+vol. 10, no. 11, pp. 1472–1475, 2010.
+[29] P.-H. Huang, C. Y. Chan, P. Li, Y. Wang, N. Nama, H. Bachman, and T. J.
+Huang, “A sharp-edge-based acoustofluidic chemical signal generator,”
+Lab on a Chip, vol. 18, no. 10, pp. 1411–1421, 2018.
+[30] D. Ahmed, C. Y. Chan, S.-C. S. Lin, H. S. Muddana, N. Nama,
+S. J. Benkovic, and T. J. Huang, “Tunable, pulsatile chemical gradient
+generation via acoustically driven oscillating bubbles,” Lab on a Chip,
+vol. 13, no. 3, pp. 328–331, 2013.
+[31] M. Kuscu and O. B. Akan, “Channel sensing in molecular commu-
+nications with single type of ligand receptors,” IEEE Transactions on
+Communications, vol. 67, no. 10, pp. 6868–6884, 2019.
+[32] A.
+Kang
+and
+V.
+Sharma,
+“Pulse
+shape
+filtering
+in
+wireless
+communication-a critical analysis,” IJACSA) International Journal of
+Advanced Computer Science and Applications, vol. 2, no. 3, 2011.
+[33] E. B. Pehlivanoglu, B. D. Unluturk, and O. B. Akan, “Modulation in
+molecular communications: A look on methodologies,” in Modeling,
+Methodologies and Tools for Molecular and Nano-scale Communica-
+tions.
+Springer, 2017, pp. 79–97.
+[34] Y. Huang, M. Wen, L.-L. Yang, C.-B. Chae, and F. Ji, “Spatial mod-
+ulation for molecular communication,” IEEE transactions on nanobio-
+science, vol. 18, no. 3, pp. 381–395, 2019.
+[35] U. Alon, “Network motifs: theory and experimental approaches,” Nature
+Reviews Genetics, vol. 8, no. 6, pp. 450–461, 2007.
+[36] P. Perrodin, C. Sella, and L. Thouin, “Electrochemical generation of
+steady-state linear concentration gradients within microfluidic channels
+perpendicular to the flow field,” Analytical Chemistry, vol. 92, no. 11,
+pp. 7699–7707, 2020.
+[37] D. Ahmed, H. S. Muddana, M. Lu, J. B. French, A. Ozcelik, Y. Fang,
+P. J. Butler, S. J. Benkovic, A. Manz, and T. J. Huang, “Acoustofluidic
+chemical waveform generator and switch,” Analytical chemistry, vol. 86,
+no. 23, pp. 11 803–11 810, 2014.
+[38] Y. Guo, P. Chen, Z. Gao, Y. Li, S. Li, X. Feng, and B.-F. Liu, “A time-
+coded multi-concentration microfluidic chemical waveform generator
+for high-throughput probing suspension single-cell signaling,” Chinese
+Chemical Letters, 2021.
+[39] P. Chen, P. Chen, X. Feng, W. Du, and B.-F. Liu, “Analysis of intercel-
+lular communication by flexible hydrodynamic gating on a microfluidic
+chip,” Analytical and bioanalytical chemistry, vol. 405, no. 1, pp. 307–
+314, 2013.
+[40] P. Chen, Y. Guo, X. Feng, S. Yan, J. Wang, Y. Li, W. Du, and B.-F.
+Liu, “Microfluidic chemical function generator for probing dynamic cell
+signaling,” Analytical Chemistry, vol. 89, no. 17, pp. 9209–9217, 2017.
+[41] C.-D. Xue, Y.-J. Li, J.-T. Na, Y.-X. Wang, H.-J. Yu, B. Liu, T. Cao,
+and K.-R. Qin, “A microfluidic platform enabling real-time control of
+dynamic biochemical stimuli to biological cells,” Journal of Microme-
+chanics and Microengineering, vol. 30, no. 9, p. 095011, 2020.
+[42] J. Garrison, Z. Li, B. Palanisamy, L. Wang, and E. Seker, “An
+electrically-controlled programmable microfluidic concentration wave-
+form generator,” Journal of biological engineering, vol. 12, no. 1, pp.
+1–10, 2018.
+[43] S. O. Krabbenborg and J. Huskens, “Electrochemically generated gra-
+dients,” Angewandte Chemie International Edition, vol. 53, no. 35, pp.
+9152–9167, 2014.
+[44] T. Delahaye, T. Lombardo, C. Sella, and L. Thouin, “Electrochemical
+assessments of droplet contents in microfluidic channels. application to
+the titration of heterogeneous droplets,” Analytica Chimica Acta, vol.
+1155, p. 338344, 2021.
+[45] H. Bruus, “Acoustofluidics 7: The acoustic radiation force on small
+particles,” Lab on a Chip, vol. 12, no. 6, pp. 1014–1021, 2012.
+[46] J. Rufo, F. Cai, J. Friend, M. Wiklund, and T. J. Huang, “Acoustofluidics
+for biomedical applications,” Nature Reviews Methods Primers, vol. 2,
+no. 1, pp. 1–21, 2022.
+[47] J. Friend and L. Y. Yeo, “Microscale acoustofluidics: Microfluidics
+driven via acoustics and ultrasonics,” Reviews of Modern Physics,
+vol. 83, no. 2, p. 647, 2011.
+[48] M. Wu, A. Ozcelik, J. Rufo, Z. Wang, R. Fang, and T. Jun Huang,
+“Acoustofluidic separation of cells and particles,” Microsystems &
+nanoengineering, vol. 5, no. 1, pp. 1–18, 2019.
+[49] G. Destgeer, K. H. Lee, J. H. Jung, A. Alazzam, and H. J. Sung,
+“Continuous separation of particles in a pdms microfluidic channel via
+travelling surface acoustic waves (tsaw),” Lab on a Chip, vol. 13, no. 21,
+pp. 4210–4216, 2013.
+[50] P. Glynne-Jones, R. J. Boltryk, and M. Hill, “Acoustofluidics 9: Mod-
+elling and applications of planar resonant devices for acoustic particle
+manipulation,” Lab on a Chip, vol. 12, no. 8, pp. 1417–1426, 2012.
+[51] G. Destgeer, S. Im, B. Hang Ha, J. Ho Jung, M. Ahmad Ansari,
+and H. Jin Sung, “Adjustable, rapidly switching microfluidic gradient
+generation using focused travelling surface acoustic waves,” Applied
+Physics Letters, vol. 104, no. 2, p. 023506, 2014.
+
diff --git a/PtE5T4oBgHgl3EQfYw9y/content/tmp_files/load_file.txt b/PtE5T4oBgHgl3EQfYw9y/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..7a89361bd604f034b208e5170201dc3217bc9427
--- /dev/null
+++ b/PtE5T4oBgHgl3EQfYw9y/content/tmp_files/load_file.txt
@@ -0,0 +1,935 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf,len=934
+page_content='1  Microfluidic Pulse Shaping Methods for  Molecular Communications  Maryam Kahvazi Zadeh, Iman Mokari Bolhassan, and Murat Kuscu  Abstract—Molecular Communication (MC) is a bio-inspired  communication modality that utilizes chemical signals in the  form of molecules to exchange information between spatially  separated entities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Pulse shaping is an important process in all  communication systems, as it modifies the waveform of trans-  mitted signals to match the characteristics of the communication  channel for reliable and high-speed information transfer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' In MC  systems, the unconventional architectures of components, such as  transmitters and receivers, and the complex, nonlinear, and time-  varying nature of MC channels make pulse shaping even more  important.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' While several pulse shaping methods have been the-  oretically proposed for MC, their practicality and performance  are still uncertain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Moreover, the majority of recently proposed  experimental MC testbeds that rely on microfluidics technology  lack the incorporation of programmable pulse shaping methods,  which hinders the accurate evaluation of MC techniques in  practical settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' To address the challenges associated with pulse  shaping in microfluidic MC systems, we provide a comprehensive  overview of practical microfluidic chemical waveform generation  techniques that have been experimentally validated and whose  architectures can inform the design of pulse shaping methods  for microfluidic MC systems and testbeds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' These techniques  include those based on hydrodynamic and acoustofluidic force  fields, as well as electrochemical reactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' We also discuss the  fundamental working mechanisms and system architectures of  these techniques, and compare their performances in terms  of spatiotemporal resolution, selectivity, system complexity, and  other performance metrics relevant to MC applications, as well  as their feasibility for practical MC applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  Index Terms—Molecular Communications, pulse shaping, mi-  crofluidics, testbeds, hydrodynamic gating, acoustofluidics  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' INTRODUCTION  T  He development of unconventional communication sys-  tems that can process and exchange information via  molecules and chemical reactions is a rapidly growing re-  search field, holding the promise of revolutionizing computing  and communications, and extending our connectivity to mi-  cro/nanoscale and biological devices and entities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Molecular  Communications (MC) is a bio-inspired way of communi-  cation that uses molecules for encoding, transmission, and  reception of information, and is already ubiquitous among  living cells [1], [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' MC is a highly interdisciplinary research  area at the intersection of information and communication  The authors are with the Nano/Bio/Physical Information and Communi-  cations Laboratory (CALICO Lab), Department of Electrical and Electronics  Engineering, Koc¸ University, Istanbul, Turkey (Corresponding authors’ e-mail:  {mzadeh22, mkuscu}@ku.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='tr).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  This work was supported in part by the European Union’s Horizon  2020 Research and Innovation Programme through the Marie Skłodowska-  Curie Individual Fellowship under Grant Agreement 101028935, and by The  Scientific and Technological Research Council of Turkey (TUBITAK) under  Grant #120E301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  technologies (ICT), micro/nanotechnology, and biotechnology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  A variety of paradigm-shifting applications can be achieved  with the help of MC systems, particularly in the biomedical  field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' The envisioned applications mostly concern the early  diagnosis and treatment of diseases, such as continuous health  monitoring, targeted drug delivery in nanomedicine, artificial  organs, and lab-on-a-chip, in which the use of electromagnetic  signals is either not desirable due to biocompatibility concerns  or not feasible due to physical constraints [3], [4], [5], [6], [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  Furthermore, MC can be deployed in industrial settings for  monitoring chemical reactors and nanoscale manufacturing,  as well as for larger-scale practices, such as monitoring the  emissions of pollutants and the safe and clean transportation  of oil [8], [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  Unlike conventional communication systems, which typi-  cally use electromagnetic signals as communication carriers,  MC uses chemical signals, as conceptually illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  Accordingly, a transmitter in an MC system releases molecules  into a fluidic medium, where the molecules travel through  diffusion and/or drift, and a portion of them manages to reach  an MC receiver.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Typically, information molecules cause a  certain reaction at the receiver, through which the receiver  detects and decodes the transmitted information encoded into  a distinguishable property of the molecules, such as their  concentration, type, or release time from the transmitter [10],  [11], [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  While the theoretical aspects of MC have been significantly  researched, its practical aspects concerning the design and  prototyping of MC components and systems are yet to be fully  addressed [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' This is partly due to the highly interdisciplinary  technical knowledge and tools required for constructing such  multi-physics and multi-scale systems [13], [14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' In spite  of all these issues, a number of experimental studies were  performed on microfluidic testbeds that can replicate the flow  conditions of biological environments typically considered for  MC applications [15], [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' However, there are important  challenges, including the lack of high-resolution control of the  spatiotemporal distribution of molecules inside the microflu-  idic channels, that hinder the accurate experimental validation  of the theoretical channel models, as well as the tests and  the refinement of the developed MC modulation and detection  techniques [17], [2], [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  Pulse shaping is of critical importance in all communication  systems for enabling accurate and high-rate information trans-  fer by adjusting the waveform of the signals to be transmitted  (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 2) in light of the communication channel’s character-  istics, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=', bandwidth, thereby, minimizing the effects of noise  and intersymbol interference (ISI), and eventually improving  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='05576v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='ET]  13 Jan 2023  2  Electrical Stimuli-responsive  Hydrogel/Graphene MC Transmitter  Graphene Biosensor-based  MC Receiver  Information  Molecules  Transmitter  MC Channel  Receiver  Transmitted  Signal  Received  Signal  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 1: A conceptual drawing of an MC system with  nanomaterial-based transmitter and receiver [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  the received signal strength, or equivalently, its signal-to-  interference-plus-noise ratio (SINR) [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' As the fluidic MC  channel manifests peculiar properties, which are quite different  than its conventional electromagnetic counterparts, such as  the low-pass characteristics due to the slow diffusion of  information carriers (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=', molecules) the importance of pulse  shaping is more pronounced in MC [4], [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Moreover, the  unique micro/nanoscale architectures of the transmitter and the  receiver components of the MC system can impose further  challenges in the transmission and reception of the messages  encoded into molecules [2], [20], [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Furthermore, the dis-  crete nature of information carriers necessitates rethinking the  conventional pulse shaping techniques that have been typically  developed for continuous information carriers, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=', EM waves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  The radically different nature of communication channels,  information carriers, transmitter, and receiver architectures in  MC also create unique opportunities for pulse shaping, some  of which have already been explored.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' For example, different  diffusion characteristics of molecules of varying sizes were  exploited to form numerous MC signal waveforms consisting  of multiple types of molecules with well-defined mixtures [22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  Additionally, it was shown that the timing and the duration  of chemical reactions of molecules with certain enzymes can  be tuned to form well-defined MC pulses inside microfluidic  channels [13], [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Moreover, there were efforts to control the  physical characteristics of the boundaries of the propagation  medium, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=', the communication channel, to form arbitrary  MC pulse shapes [24], [25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Although, these approaches  demonstrated the enhancement of MC performance with pulse  shaping, the practicality of the employed techniques and their  actual performances are questionable, as they have not been  experimentally validated yet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  Generating well-defined and tunable chemical waveforms  and concentration gradients in microfluidic systems has also  attracted considerable attention in various research fields other  than MC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' For example, in biological research, the need for  dynamically controlling the molecular composition of the  extracellular matrix (ECM) of cultured biological cells and  tissues in microfluidic lab-on-a-chip systems motivated the  development of arbitrary concentration waveform generators  X(t)  t  Y(t)  t  Input Signal  Output Signal  Pulse Shaping  Filter  Microfluidic  MC Channel  MC Transmitter  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 2: The overall scheme of the pulse shaping in a microflu-  idic MC system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  [26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' The proposed techniques utilize different external force  fields, such as acoustical or hydrodynamic force fields, or  electrochemical reactions, to program the spatiotemporal dis-  tribution of molecules inside microfluidic channels with high  resolution, and generate well-defined concentration waveforms  that can take arbitrary shapes [27], [28], [29], [30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' De-  pending on the nature of the external control, the system  architectures of the waveform generators show a large vari-  ety in terms of complexity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Their performances in terms of  selectivity, repeatability, and spatiotemporal resolution of the  waveforms they generate also differ significantly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Nevertheless,  the practicality and performances of these techniques have  been validated through extensive experimental studies, and  thus, they are promising as externally-controlled pulse shaping  techniques for use in practical microfluidic MC systems and  testbeds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  In this review article, our objective is to thoroughly analyze  microfluidic chemical waveform generation methods that can  inform the design of pulse shaping techniques in practical  microfluidic MC testbeds and systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' We aim to provide a  comprehensive overview of these techniques, including their  working mechanisms, system architectures, and additional  components required for external control.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' We also conduct  a comparative analysis of these methods in terms of their  spatiotemporal resolution and control, selectivity, and system  complexity, and evaluate their feasibility for a range of prac-  tical MC applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' We believe that this review will be  a valuable resource for researchers seeking to innovate in  the field of MC, as it will help to bridge the gap between  theory and practice by providing a detailed examination of  these methods and their suitability for use in microfluidic MC  testbeds and systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  The remainder of this paper is organized as follows: In  Section II, we explore the significance of pulse shaping in MC  and review the various methods that have been proposed for  this purpose in the MC literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' In the following section, we  delve into microfluidic chemical waveform generation tech-  niques that enable the production of programmable, dynamic  chemical signals, examining their underlying mechanisms,  system architectures, and additional components required for  external control.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Next, in Section 4, we comprehensively  evaluate the performance of each pulse shaping technique  in terms of spatiotemporal resolution and control, selectivity,  repeatability, control over propagation, and system complexity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  We also discuss their feasibility for integration into practical  MC applications in Section V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Finally, we conclude the paper  in Section VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  3  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' PULSE SHAPING IN MOLECULAR COMMUNICATIONS  The characteristics of each component in the MC system,  e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=', transmitter, channel, and receiver, exhibit additional com-  munication challenges which highlight the need for pulse  shaping in MC systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' For instance, at the transmitter, due  to the limited molecule generation and storage capacity, it  is necessary to design molecule-efficient pulses in order to  transmit information molecules effectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' In addition, the  low-pass characteristic of the MC channel, which typically  relies on diffusion, leads to significant spatial dispersion of  the molecular signals as they propagate in the microfluidic  channel [22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' This may result in substantial ISI that hampers  the achievable data rates in MC channels [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' The ISI effect is,  also, compounded by the fact that practical MC receivers, such  as nanobiosensors and engineered bacteria, typically employ  ligand receptors, which interact selectively with the transmitted  information molecules, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=', ligands, at finite reaction rates,  adding to the ISI observed at the receiver.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Furthermore, MC  receivers with ligand receptors typically manifest nonlinear  responses to the incoming ligand concentrations, and therefore,  can be severely affected by the saturation of the receptors when  the received signals in terms of ligand concentrations are not  optimized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Likewise, in a ligand-receptor-based MC receiver,  the accuracy of the detection is dependent on the received  ligand concentration, such that when the receptors are only  very shortly exposed to the ligand concentration, because of  the finite reaction rates, there may not be a sufficient number  of bound receptors for detection [31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  To overcome the unique challenges of end-to-end MC  channels, transmission pulses can be optimized according to  the modulation technique adopted by the transmitter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' This  optimization per se is not sufficient, as we also need practical  systems that can generate the optimized MC pulse shapes to  overcome the challenges associated with this system [22], [32],  [25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' There have been a few proposed pulse shaping methods  considered for MC in the literature in order to address some  of these challenges, which are reviewed in the remainder of  this section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Pulse Shaping based on Molecular Propagation Charac-  teristics  Diversity in the propagation characteristics of different types  of molecules can be used to shape the transmitted and received  molecular signals in MC systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' For example, Wicke et  al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' [22] proposed an MC pulse shaping method exploiting  different diffusion coefficients of molecules that vary in size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  Accordingly, at the transmitter, they tuned and optimized the  molecule size mixture to guarantee both a minimum signal  level and a maximum signal level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' A minimum signal level  was considered for detecting the presence of the signal,  and a maximum signal level was considered for detecting  the absence of the signal within a predetermined detection  window.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' With this method, suitable molecule sizes can be  selected optimally for any required detection duration in  comparison to mixing all molecules together.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Moreover, their  optimization framework can be extended to the cases where  the channel impulse responses (CIR) of individual types of  MC  Receiver  MC  Transmitter  Destroyer  molecules  Tunnel-shaped  MC channel  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 3: A cylindrical tunnel shape environment for diffusion-  based MC system [25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  molecules depend on molecule properties other than their size  or can be determined only empirically through experiments or  simulations of complex and reactive environments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Pulse Shaping Based on Chemical Reactions  By tuning the rate and the duration of chemical reactions,  and the concentration of reactants (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=', input molecules) in a  controlled microfluidic system, the time-domain concentration  profile of the reaction products (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=', output molecules) can be  patterned for encoding information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' In [13], based on a trig-  gering chemical input, the authors proposed a pulse generator  for MC which produces predefined molecular concentration  pulses that are shaped in the transmitter part of the system and  then transmitted into and propagated through a microfluidic  channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' The proposed design consists of a microfluidic system  with standard and reproducible components, whose geometry  and flow conditions effectively help determine the resulting  pulse shape.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Pulse generation in the proposed method is  inspired by the motifs observed in cells’ gene regulatory  networks and compatible with the molecular pulse-modulation  techniques investigated in the MC literature [33], [34], [35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  The study also presented a methodology with a modeling and  analysis framework for diversifying the generated pulse shapes  with the integration of additional microfluidic components  inspired by biochemical processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  The same group also developed a microfluidic receiver  in [23] using thresholding and amplification reactions to  achieve the demodulation of received signals into rectangular  output signals in the form of concentration of molecules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' The  microfluidic components were characterized as part of an  analytical study to determine how several design parameters  such as the concentration of molecules, fluid viscosity,  diffusion coefficient, and the length of injection time of the  sample into the system influence the generated pulse and the  demodulated signal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' To optimize the transmitter design, the  authors proposed a reaction channel length optimization flow  to control the maximum output pulse concentration at the  transmitter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' They then derived a time gap constraint between  two consecutive input signals to ensure the continuous  transmission of non-distorted and identical-shaped pulses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  4  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Tunnel-based Pulse Shaping  To reduce the variance of the receiver-hit time distribution  of transmitted molecules in diffusion-based MC, which causes  high propagation delays and ISI, the authors in [25] proposed  developing a tunnel-based pulse shaping method for MC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' This  method relies on the use of particular types of molecules,  called destroyer molecules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' These molecules clean the MC  channel from the information molecules remaining from the  previous transmissions, and thus, control the shape of the  received signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' In this study, the authors suggested a system  with an MC channel surrounded by AChE-like destroyer  molecules to construct a tunnel between the transmitter and the  receiver, as illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' The use of destroyer molecules  is inspired by the Acetylcholine (ACh) - Acetylcholinesterase  (AChE) interaction observed in the Neuromuscular Junctions  (NMJs) of living organisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' NMJs connect muscle cells to  nerve cells via an intercellular gap called the synaptic cleft.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  AChE molecules destroy messenger ACh molecules after  sending a contraction signal to return muscle cells to their  resting state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' It is important to note that the proposed tunnel-  based pulse shaping method operates in a distinct manner  compared to other conventional and MC pulse techniques such  that pulse shaping through chemical reactions in this method is  realized within the channel through the utilization of destroyer  molecules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  In this way, the received signal variance is reduced and the  communication channel is cleaned for the next signal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Hence,  the proposed tunnel-based pulse shaping method can control  the spread and hence the shape of the molecular signals with  the help of destroyer molecules and the guidance of the tunnel  geometry, in order to reduce the received signal variance and  the ISI, thereby significantly increasing the channel capacity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' MICROFLUIDIC PULSE SHAPING METHODS  Microfluidic chemical waveform generation techniques that  can produce dynamic chemical signals with programmable  shapes in microfluidic channels have recently attracted sig-  nificant interest in many branches of biological research  concerning the monitoring and manipulation of physiological  processes, such as immune response, development, embryoge-  nesis, and cancer metastasis [36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' One prominent application  of chemical waveform generation in this area is the dynamic  control of the chemical composition in the ECM of living cells  cultured in microfluidic platforms, ensuring high spatiotempo-  ral resolution [37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  After a brief review of the operating mechanisms and the  key properties of several microfluidic chemical waveform  generation techniques in this section, a detailed comparison  of them is provided in the succeeding sections to compre-  hensively evaluate their potential for use in microfluidic MC  testbeds and systems as pulse shaping techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Hydrodynamic Methods  Chemical concentration waveforms in microfluidic channels  can be formed through hydrodynamic control, such that the  modulation of the flow velocity and direction can be exploited  to tune the injection rate of molecules into the microfluidic  Microfluidic  Pressure Controller  Pressure Control  Lines  Buffer  Waste  Channel  outlet  Information  molecules  Gating  inlet  Gating  outlet  Supply  inlet  Valves  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 4: Schematic representation of microfluidic system setup  for hydrodynamic gating-based concentration waveform gen-  eration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  channel and shape their concentration waveforms propagating  inside the channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  Hydrodynamic gating is one of the most widely used  hydrodynamic waveform generation techniques, having the  potential to generate a rich set of dynamic chemical concen-  tration patterns in microfluidic channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' This method has a  high degree of precision while being easily implemented and  operated [38], [39].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' An example microfluidic setup for the  implementation of hydrodynamic gating is conceptually illus-  trated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 4, where the cross-shaped microfluidic channel  can be fabricated via soft-lithography techniques using poly-  dimethylsiloxane (PDMS) polymer, and the pressure control at  the micro-channel inlets can be achieved by custom-built or  commercial pressure control systems, such as programmable  syringes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Accordingly, in this setup, hydrodynamic gating can  be achieved by switching on and off the laminar flow that  comes from the supply inlet and transports the molecules of  interest through the on-off modulated laminar flow that is  supplied from the gating inlet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' When turned on, the flow from  the gating inlet generates a hydrodynamic force in the vertical  direction across the cross-section, that is sufficient enough to  cut the flow from the supply inlet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Therefore, during the on-  state of the hydrodynamic gating, the molecules transported  through the continuous flow from the supply inlet are not able  to enter the microfluidic channel and are directed towards  the gating outlet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' On the other hand, when gating is turned  off for a short duration, the vertical hydrodynamic force is  removed, and thus, the molecules coming from the supply  inlet are injected into the microfluidic channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' The gating  duration is therefore critical for tuning the width of the pulses  propagating inside the channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' The other design parameters  that play critical roles in determining the shape of generated  chemical waveforms include the absolute and relative flow  velocities or pressures applied at the supply and gating inlets,  and the concentration of molecules transported from the supply  inlet [28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' As the hydrodynamic gating method involves a  relatively small number of design parameters that can be fine-  tuned by the state-of-the-art micro/nanofabrication techniques  and pressure control devices, it provides a high level of  reproducibility, which is crucial for reliable and communicable  experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' The technique has been experimentally shown to  generate various chemical pulses and pulse sequences with  5  a  b  c  t = 10 s  t = 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='18 s  t = 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='19 s  t = 10 s  t = 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='18 s  t = 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='19 s  Concentration (µM)  Concentration (µM)  Concentration (µM)  Y-position (mm)  Y-position (mm)  Y-position (mm)  X-position (mm)  X-position (mm)  X-position (mm)  X-position (mm)  X-position (mm)  X-position (mm)  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 5: An illustration of a concentration pulse sampled at three different time instances: (a) t = 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='00s, (b) t = 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='18s, and (c)  t = 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='19s, corresponding to different states of the hydrodynamic gating process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' (a) and (c) depict the gating state, and (b)  depicts the injection state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Simulated with COMSOL Multiphysics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  different frequencies, amplitudes, and shapes [38], [28], [40],  [41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  To validate the high spatiotemporal control promised by the  hydrodynamic gating method, we carried out finite element  simulations in COMSOL Multiphysics, the results of which  are provided in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' On the left-hand side of the figure  is shown the 2D concentration profile of molecules sampled  at specific times;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' and on the right-hand side, the graphs plot  the concentration of molecules sampled across the overall  microfluidic channel from the supply inlet to the channel  outlet using a concentration probe right at the middle of  the channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Accordingly, the concentration profiles observed  during the three basic states are provided;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' (a): the first gating  state, (b): the injection state, and (c): the second gating state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  During the first gating state (a), all the molecules coming  from the supply inlet are diverted to the gating outlet by  the vertical flow applied from the gating inlet such that they  are not able to pass through the cross-section towards the  microfluidic channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' During the injection state, however, the  gating flow is turned off for a short time duration such  that a small number of molecules can propagate into the  microfluidic channel without being diverted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' When the gating  flow is turned on again, the system returns to its initial state,  such that the molecule transport into the microfluidic channel  stops.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' As a result, a short concentration pulse of molecules is  generated, which then continues its propagation towards the  channel outlet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' As the concentration pulse propagates along  the microfluidic channel, it experiences dispersion due to the  diffusional transport that accompanies conventional transport.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  The interplay between diffusion and convection determines  pulse dispersion, which can be an important metric that is  directly connected to the ISI in MC applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  To observe the ISI, we also performed simulations for the  consecutive generation of short concentration pulses through  the hydrodynamic gating technique.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 6 shows the 2D and  1D propagation profiles of the five consecutive concentration  pulses generated with the same gating durations and even  pulse generation intervals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' The effect of dispersion on the  width and the peak amplitude of the individual concentration  pulses can be observed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Although the pulse peaks are easily  distinguishable for this setup with a particular channel length,  it can be observed that the interference of consecutive pulses  increases as they near the end of the microfluidic channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  These results highlight the importance of generating short  concentration pulses to avoid or minimize the ISI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 7 presents the concentration of consecutive pulses over  time, measured at two different locations in the channel: the  midpoint and the outlet, for better demonstrating the effect of  mm  10  30  10  20  Y-position  8  10  6  0  4  10  2  20  0  30  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='07  0  50  mm  X-position10  9  Concentration (μM)  8  7  6  5  4  3  2  1  0  20  40  60  80  X-position (mm)mm  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='3  30  10  20  Y-position  8  10  6  4  10  2  20  0  30  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='23  0  50  mm  X-position10  9  Concentration (μM)  8  7  6  5  4  3  2  1  0  20  40  60  80  X-position (mm)mm  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='1  30  10  20  Y-position  8  10  6  0  4  10  2  20  0  30  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='04  0  50  mm  X-position10  9  Concentration (μM)  8  7  6  5  4  3  2  1  0  20  40  60  80  X-position (mm)6  a  b  c  d  t = 4 s  t = 4 s  t = 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='2 s  t =6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='2 s  t = 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='2 s  t = 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='2 s  t = 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='5 s  t = 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='5 s  Concentration (µM)  Concentration (µM)  Concentration (µM)  Y-position (mm)  Y-position (mm)  Y-position (mm)  Y-position (mm)  Concentration (µM)  X-position (mm)  X-position (mm)  X-position (mm)  X-position (mm)  X-position (mm)  X-position (mm)  X-position (mm)  X-position (mm)  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 6: An illustration of consecutive concentration pulses sampled at four different time instances: (a) t = 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='00s, (b) t = 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='20s,  (c) t = 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='20s and (d) t = 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='50s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' By applying a gating flow from the upper inlet at periodic time instances, consecutive  concentration pulses are generated and propagated within the MC channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Simulated with COMSOL Multiphysics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  dispersion on the peak amplitude and width.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' The concentration  profile of all of the pulses is shown on the left side of the  figure, while the concentration profile of only the first pulse  is shown on the right side of the figure, at both the midpoint  and outlet of the channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' The examination of the amplitude  and the width of the first transmitted pulse demonstrates that  the dispersion effect becomes more prominent at the outlet of  the channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' It can also be observed that the peak of the last  propagated pulse is lower than that of the other five pulses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  The reason for this phenomenon is that the velocity within  the microchannel decreases significantly after the last gating  and pulse creation, causing the last generated pulse that is still  propagating in the channel to move slowly towards the outlet  and with more dispersion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  The programmability of hydrodynamic concentration wave-  form generation methods can be extended through electrical  control with the utilization of electrical microfluidic valves  with a low response time, which modulate the injection rate  of buffer and chemical solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' By utilizing concepts and  tools from electrical engineering and fluid mechanics, this  microfluidic system can deliver time-varying concentrations  and arbitrary waveforms fast and accurately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' In this system,  concentration waveforms are modulated through pulse width  modulation (PWM), a standard approach for creating analog  signals from digital inputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  An example microfluidic platform combining hydrodynamic  gating and electrical control was implemented in [42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' As  shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 8(a), the proposed system is comprised of  three different functional microfluidic chips connected to each  other: (i) filter chip, (ii) resistor chip, and (iii) mixer chip.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  Filter chip consists of an elastic membrane-capped cavity  that functions as a microfluidic capacitor and a serpentine  mm  10  60  10  (mm)  40  8  20  position  6  0  4  20  2  40  0  60  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='03  0  50  100  150  mm  X-position (mm)10  9  Concentration (μM)  8  7  ６  5  4  3  2  1  0  50  100  150  X-position (mm)mm  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='8  60  (mm)  40  10  20  8  0  6  4  20  2  40  0  60  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='65  0  50  100  150  mm  X-position (mm)10  9  Concentration (μM)  8  7  6  5  4  3  2  1  0  50  100  150  X-position (mm)mm  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='6  60  (mm)  40  10  20  8  6  0  4  20  2  40  0  60  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='59  0  50  100  150  mm  X-position (mm)10  9  Concentration (μM)  8  7  6  5  4  3  2  1  o  0  50  100  150  X-position (mm)mm  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='9  60  (mm)  40  10  20  8  position  0  6  20  4  40  2  0  09-  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='25×10-3  0  50  100  150  mm  X-position (mm)10  9  Concentration (μM)  8  7  6  5  4  3  2  1  OE  0  50  100  150  X-position (mm)7  a  b  Pulse Amplitude = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='7 µM  Pulse Amplitude = 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='3 µM  Pulse Width = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='55 s  Pulse Width = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='87s  Concentration (µM)  Concentration (µM)  Concentration (µM)  Concentration (µM)  Time (s)  Time (s)  Time (s)  Time (s)  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 7: An illustration of the concentration profile of consecutive pulses as a function of time, sampled at periodic time instances  at two different points of the channel: (a) The channel’s midpoint (b) The channel’s outlet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' The left side of the figure shows the  propagation of all of the consecutive pulses as a function of time, while the results on the right side of the figure illustrate only  the propagation profile of the first transmitted pulse as it passes the midpoint and the outlet of the channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' These simulations  were carried out using COMSOL Multiphysics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  channel that functions as a microfluidic resistor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' The resistor  chip contains a serpentine channel whereas the mixer chip  has a Y-shaped channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' There are three reservoirs in the  system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' One of the reservoirs holds the buffer, which is  deionized (DI) water, whereas the other two hold fluorescein  solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' These two reservoirs are connected to the inlets of  the filter chip through a selection valve and located at different  heights to create different hydrostatic pressures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Even though  the concentrations of these two solutions are the same, the  instantaneous output flow rates are different when the flow  selection valve is regulated to switch between them, resulting  in differing volumes of the solution flowing into the filter chip  per unit time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  The filter chip uses a combination of a capacitor and a  resistor to attenuate the high-frequency components of the  PWM signal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Through an elastic membrane-capped cavity,  the capacitor allows low-frequency signals to pass through  while blocking high-frequency signals, whereas the serpentine  channel resistor provides resistance to the flow of current  and determines the rate at which the filter circuit responds  to changes in the input signal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' The filter produces an analog  output signal that corresponds to the average pulse period of  the PWM signal, and the specific response characteristics of  the filter, such as its time constant and cutoff frequency, can be  adjusted by changing the design parameters of the capacitor  and resistor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' A reservoir containing the buffer is connected to  the inlet of the resistor chip through a stop valve, enabling  the solution to be switched off manually.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' The mixer chip is  used to achieve the mixing of the solution with the buffer  to generate the final form of the concentration waveform  that propagates in the microfluidic channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' By connecting  a syringe pump to the mixer’s outlet instead of the system  inlets, liquid can be withdrawn at a constant flow rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' It  should be noted that this configuration is particularly useful  in complex microfluidic systems such as this setup where  maintaining stable and same flow conditions among multiple  interconnected chips is important.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Using this setup, as shown  in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 8(b), a PWM signal (top plot) is converted into the  target signal, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=', a red sinusoidal wave in the bottom plot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  Additionally, by low-pass filtering of the PWM signal, the  actual signal (blue ragged sinusoidal wave in the bottom plot)  is derived, which closely resembles the red sinusoidal signal  of the target.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' The employment of the electrically controlled  PWM technique for the microfluidic device gives the system  the ability to rapidly and in a programmable manner generate  sinusoidal, triangle, sawtooth, square, and even more complex  waveforms with a high level of accuracy, hence, is promising  for pulse shaping in microfluidic MC systems [42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Electrochemical Methods  Chemical concentration waveforms can also be formed  through electrical control by exploiting electrochemical reac-  tions, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=', reduction-oxidation (redox) reactions, of the propa-  gating molecules on the surfaces of electrodes that are placed  inside microfluidic channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Accordingly, in this method,  by positioning the electrodes in various arrangements, con-  centration gradients can be generated along the microfluidic  channel through the interplay between reaction, diffusion, and  convection processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' The shape of the resulting concentration  gradients or waveforms can also be controlled by space-  and time-modulating the electrical potential applied to the  electrodes, which modulates the rates of the electrochemical  7  6  Concentration (μM)  5  4  3  2  1  0  10  20  30  Time (s)6  Concentration (μM)  5  4  3  1  0  13  14  15  16  Time (s)2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='5  Concentration (μM)  2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='5  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='5  0  25  26  27  28  Time (s)3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='5  (uM)  3  Concentration  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='5  2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='5  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='5  0  20  30  40  50  Time (s)8  a  b  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 8: A programmable microfluidic device designed to gen-  erate chemical waveforms hydrodynamically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' (b) The top plot  is the input PWM signal with Y-axis showing the flow rate and  the bottom plot is the output signal (ragged sinusoidal) with Y-  axis showing the concentration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Reproduced with permission  from [42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  reactions [43].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' The typical implementation of this technique  involves a microfluidic device composed of four electrodes,  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=', two working electrodes (E1, E2), a reference electrode  (RF), and a counter electrode (CE), all positioned at the  bottom of the rectangular microfluidic channel in a dual-  channel-electrode configuration, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 9 [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' In  this example setup, the pseudo-reference electrode is located  in the upstream part of the channel to keep the base electrical  potential stable during the operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' The microfluidic channel  is filled with a solution of electrically neutral molecules,  which is continuously supplied from the channel inlet with a  constant flow velocity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' When the electrical potential of the first  working electrode E1 is turned on, the neutral molecules, as  they are transported over the electrode through convection and  diffusion, undergo an oxidation reaction which converts them  into electroactive molecules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Counter electrode, meanwhile,  serves as a site for the reduction of the oxidized molecules  that are generated at the working electrode, allowing the  overall reaction to proceed smoothly and efficiently [44].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' The  generated electroactive molecules propagate downstream along  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 9: A typical microfluidic device for electrochemical  generation of chemical waveforms, consisting of a reference  electrode (RE), two working electrodes (E1, E2), and a counter  electrode (CE) placed at the bottom of a rectangular microflu-  idic channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Reproduced with permission from [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  the microfluidic channel with a concentration waveform that  depends on the duration and the amount of electrical potential  applied to E1 in addition to the flow velocity in the channel,  and the diffusion coefficient of the molecules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Hence the elec-  trical potential applied to E1 can solely modulate the generated  concentration waveforms when the other system parameters  are kept constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' The role of the second electrode E2 is to  monitor the generated waveforms as they propagate through  the channel, and convert them back to neutral molecules  through a reduction reaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Thus, the overall system with  two working electrodes can be considered as operating in a  generator-collector mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' It is to be noted that the potential  difference between E1 and E2 electrodes generates an electric  field along the microfluidic channel, which contributes to  the transport of molecules downstream in addition to the  hydrodynamic forces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  The electrochemical method has been theoretically and ex-  perimentally shown to generate a wide range of concentration  waveforms through the modulation of the first working elec-  trode potential [27], [36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' According to the simulation results  shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 10, the generated waveforms can take various  shapes, such as peaks and plugs, depending on the duration of  the applied electrical potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' The top section of the figure  demonstrates the 2D concentration distribution of four distinct  shapes of concentration pulses that can be generated between  electrodes E1 and E2 (as shown in the bottom section of the  figure).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' These results were obtained through finite element  simulations, sampled at specific time instances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' By adjusting  the duration and amount of electrical potential applied to E1  and changing the flow velocity in the microfluidic channel,  it is possible to generate these unique concentration pulse  shapes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' The use of electrochemical reactions in microfluidic  MC testbeds is promising for pulse shaping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' The technique  provides a high level of programmability through electrical  access and can be miniaturized easily to be integrated into  Pulse-width modulation input signal  Amplitude  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='5  0  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='8  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='8  2  Time (s)  Target (red) and actual (blue) output signal  Amplitude  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='5  0  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='8  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='8  2  Time (s)Tme (s)  Concentration  Concentration  i&ii  iii  b  Time  Time  Concentration  High-Pressure Analyte  iv  Buffer  Time  Height  Low-pressure Analyte  Flow Rate  Flow Rate  Time  Time  Stop Valve  Flow Rate  iv  Resistor Chip  ili  Selection  Time  Valve,  withdraw  iv  Mixer Chip  Filter ChipA  5mm  E1  E2  RE  CE  contact  pads  ndu  uchannel  output  PDMS  RE  E1  E2  CE  1 flow  μchannel  TL  g  WE1  We29  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 10: (Top) Chemical concentration signals generated by  the electrochemical method, sampled at a given time between  E1 and E2 electrodes in the microfluidic device.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' (Bottom)  Corresponding concentration waveforms along the x-axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Re-  produced with permission from [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  MC testbeds of various scales [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Acoustofluidic Methods  Acoustofluidics, the manipulation of molecules, nanopar-  ticles, and biological entities through acoustic forces in mi-  crofluidic structures has been of great interest recently due to  its noninvasiveness and ease of integration into microfluidic  systems [45], [46].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' The acoustic vibration forces that are  generated at ultrasonic frequencies in the hundreds of kHz  to tens of MHz range have wavelengths that are well-suited  to microfluidic channel scales [47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' This method is primarily  used in the separation of nanoparticles, cancer cells, bacteria,  extracellular vesicles, blood components, droplets, and other  particles, which is a fundamental process in bioanalytical  research [48].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' The acoustofluidic method has the capability to  generate spatiotemporally modulated concentration waveforms  in microfluidic channels with the help of a micromixer struc-  ture exposed to the acoustic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Micromixer is typically a  microbubble that is trapped inside the microfluidic channel and  oscillates at certain frequencies under the effect of an acoustic  field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' The oscillation of microbubble transduces acoustic force  into mechanical force, which in turn, helps rapid mixing of  buffer and solution that transports the molecules of interest  from the inlet to the microfluidic channel [30], [49].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  In [37], Ahmed et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' proposed an acoustofluidic chemical  waveform generator based on the active mixing of a buffer  with a chemical solution of interest using acoustically driven  oscillating bubbles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' A schematic diagram of this platform is  shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 11(a), which exploits the bubble oscillation in  an acoustic field to generate arbitrary chemical waveforms  inside the microfluidic channel [50].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' The proposed device  consists of a single-layer PDMS-based microfluidic channel  with two inlets and one outlet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' The architecture of the device,  including the number of inlets and outlets, however, can  vary depending on its purpose.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' In this setup, the microfluidic  channel is equipped with a horseshoe structure (HSS) that traps  j  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 11: Acoustofluidic chemical waveform generation: (a)  Schematic of a typical setup with HSS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Piezoelectric trans-  ducers, which are placed adjacent to the microfluidic channel  on a glass slide, produce low-intensity acoustic waves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' The  generated acoustic waves oscillate the bubble trapped in the  HSS, which is positioned at the interface of the two liquids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  (b) Acoustic microstreaming and flow recirculation during  the bubble oscillation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' (c-i) Acoustofluidic generation of a  chemical waveform observed at different time instances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' When  an ink solution and a buffer are used as the inlet solutions,  the resulting chemical waveforms are monitored through the  optical density in the region of interest (ROI).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' (j) The diagram  of the chemical waveforms produced by acoustic signals in  the shape of a square wave.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Reproduced with permission from  [37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  a single bubble via surface tension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' A piezoelectric transducer,  that generates the acoustic field, is placed adjacent to the  microfluidic channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' The membrane of the trapped bubble  oscillates under an acoustic force field generated by a piezo-  electric transducer, which is controlled through an electronic  function generator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Maximum bubble oscillation occurs at its  resonance frequency, which depends on the bubble size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' A  pressure gradient is generated in the fluid due to the second-  order effect of nonlinearity in the Navier-Stokes equation  at the resonance frequency, driving acoustic microstreams.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  When the trapped bubble is vibrated, the counter-rotating  vortices resulting from microstreaming disrupt the smooth  buffer-solution interface that is resulting from the laminar  flow regime in the microchannel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Through the disruption of  (a)  flow  介  (b)  (c)  Y  (d)  X  (a)  (b)  (c)  (d)a  C  Bluedye  Red dye  0ms  ROI  ROL  6m  13ms  Transducer  HSS  Bubble  20ms  27ms  33ms  100um  96ms  60umSquarewave,period2and5s  Normailizedintensity  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='0  8r0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='0  4  6  8  10  12  14  16  18  20  Time (s)10  the interface, the microstreams drastically enhance the mass  transport along the direction perpendicular to the laminar flow,  effectively mixing the liquids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' This is referred to as the ON  state of mixing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' This mixing process is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 11(c-i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  When the acoustic force field is turned off for a short duration  by the piezoelectric transducer, the mixing of inlet solutions  stops, and the characteristic laminar flow manifests again.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' This  is referred to as the OFF state of mixing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Hydrodynamic forces  dominate the system once the acoustic field is eliminated in the  OFF state, and this leads to the propagation of the generated  chemical waveforms along the channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' As a result of the fast  responses of the electrical and acoustic fields, the system can  toggle between ON and OFF states swiftly and transforms  the electrical signals into chemical waveforms which will  propagate through the channel, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 11(j) [30],  [50], [51].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' DISCUSSION ON PULSE SHAPING PERFORMANCE  This section examines and the performance of the microflu-  idic chemical waveform generation methods introduced in Sec-  tion III in terms of their capacity to be utilized in microfluidic  MC testbeds and systems for pulse shaping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' This capacity  is evaluated based on a couple of key performance criteria,  including spatiotemporal resolution, complexity, repeatability,  selectivity, and control over propagation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' A summary compar-  ison of the methods based on these criteria is presented in  Table I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Spatiotemporal Resolution  As in all communication systems, the achievable commu-  nication rate is a critical performance metric for MC systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  Communication rate in MC depends on the concentration pulse  generation rate on the transmitter side, and the imperfections  in the channel that could lead to the distortion and the  dispersion of the generated pulses as they propagate along  the channel, which in turn might result in, for example, the  ISI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' To be able to test a wide range of communication rates in  practical MC testbeds with particular channel conditions and  receiver designs, the transmitter should be capable of gen-  erating concentration pulses with well-defined and persistent  waveforms at a high rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' This capability of the transmitter  can be evaluated in terms of its temporal resolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' The  spatial resolution, on the other hand, measures the capability  of the transmitter, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=', the waveform generation technique,  to produce well-defined square concentration waveforms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' In  other words, it gives a measure of the bandwidth of the  generated concentration waveforms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Higher the bandwidth, the  wider range of concentration waveforms that the method is  able to generate inside the microfluidic channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' The temporal  and spatial resolutions are connected to each other in their  dependence on the design and operating mechanism of the  waveform generation technique, and thus, evaluated in this  section together by being referred to as the spatiotemporal  resolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  The spatiotemporal resolution in hydrodynamic and electro-  chemical methods is at a medium level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' In [28], 20 consecu-  tive concentration pulses generated via hydrodynamic method  could be injected into the microfluidic channel with a time  interval of 500 ms between every two consecutive pulses,  demonstrating that the hydrodynamic method is capable of  generating chemical waveforms with a temporal resolution  of approximately 2 Hz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Nevertheless, because of the band  limitations of a microfluidic channel, distortions are inevitably  generated as the pulses propagate along the channel, leading  to the degradation of the spatial resolution of this technique.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  Likewise, the reported temporal resolutions for the electro-  chemical technique range between 2-4 Hz [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Moreover, the  pulses generated by these methods well approximate a square-  wave right after their generation (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 5 and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 10),  overall indicating a medium level of spatiotemporal resolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  In comparison with the other methods mentioned above,  acoustofluidic methods were reported to exhibit a higher level  of spatiotemporal resolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' The experimental results from  [37] reveal that this method provides very high temporal reso-  lution reaching up to 30 Hz frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Also, generated pulses  approximate square waves much better compared to other  techniques (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 11), overall making the acoustofluidic  methods most promising for the microfluidic MC testbeds  supporting high data transmission rates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Control over Propagation  In microfluidic MC testbeds, not only the generation of  arbitrary chemical waveforms but also their propagation and  the evolution of their profile along the microfluidic channels  can be important to accurately test the performances of MC  modulation and detection techniques and validate MC channel  models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' The assessment for control over the propagation of  each method considers to what extent the technique that  generates the pulses is also able to control their propagation  inside the channel, independently of the generation process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  Among the chemical waveform generation methods consid-  ered in this paper, the electrochemical method provides the  highest degree of control over the propagation of generated  waveforms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' In the electrochemical method, the redox reactions  between the molecules and the first working electrode convert  the electrically neutral molecules into electroactive molecules,  meaning that they can be influenced by the electric field effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  As there are two working electrodes (E1 and E2, see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 9),  separated by a certain distance in the microfluidic channel, the  potential difference between them generates an electric field  along the channel, which acts upon the generated concentration  signal of the electroactive molecules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Therefore, depending on  the polarity of the electroactive molecules, and the magnitude  of the potential difference between electrodes, the propagation  characteristics of the generated concentration waveforms can  be modulated independently of their generation process [43].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  In the hydrodynamic method, however, both the generation  and the propagation of concentration waveforms are controlled  by hydrodynamic forces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' This limits the ability to control  propagation characteristics independently of the waveform  generation process inside the channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Thus, the hydrodynamic  technique can be considered to have a medium level of control  over the propagation of generated waveforms in comparison  to the other two methods [28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  11  TABLE I: A Comparison of the Microfluidic Pulse Shaping Methods Based on  Key Performance Criteria  Methods  Spatio-temporal  Resolution  Control over  Propagation  Repeatability  Selectivity  System  Complexity  Hydrodynamic  Methods  Medium  Medium  High  Low  Low  Electrochemical  Methods  Medium  High  Medium  High  Medium  Acoustofluidic  Methods  High  Low  High  Low  High  On the other hand,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' the acoustofluidic method has the lowest  level of control over the propagation of the generated wave-  forms,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' as the bubble oscillations due to the acoustic force fields  create space-limited vortices,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' localized only around the bubble  contained in HSS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Therefore, the resulting vibrational force  fields do not extend into the microfluidic channel, limiting the  capacity of this method to dynamically tune the propagation  characteristics of the generated chemical waveforms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' This lack  of control over propagation in this method, however, can be  improved with the modulation of the hydrodynamic forces  inside the channel, for example, by tuning the inlet pressures  [37], [51].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Repeatability  The repeatability of the chemical waveform generation  techniques can be evaluated based on the number of suc-  cessively generated waveforms that have approximately the  same shape when introduced into the microfluidic channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  The repeatability is of crucial importance for practical MC  testbeds and systems, as MC scenarios typically require the  transmission of multiple concentration pulses successively, for  example, to evaluate the impact of ISI, and determine the  achievable data transmission rates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  An important factor in generating approximately the same  waveforms, and therefore having high repeatability in each  transmission is the stability and durability of the microfluidic  chip structure, especially in the transmitter part.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' As is shown  in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 6 and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 11, consecutively generated pulses by both  hydrodynamic and acoustofluidic methods have approximately  the same waveform, indicating the superb repeatability of  these methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' This is due to the fact that all the parameters  involved in the design of the transmitter structure and the  microfluidic chip for both acoustic and hydrodynamic based  methods can be controlled and engineered to yield utmost  stability in generating concentration waveforms [28], [37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  The electrochemical method, on the other hand, can be  considered to have lower repeatability over long operation  times, due to the chemical reactions involved in the generation  of the waveforms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' More specifically, the chemical reactions  on the electrode surface are highly prone to the effects of  environmental fluctuations, such as those in the temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  Second, chemical reactions are inherently stochastic processes,  adding to the low-level repeatability of the electrochemical  method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Selectivity  In practical MC applications, there could be many different  types of molecules co-existing in the MC channel, that can  result from a biological process at the background or another  MC network accessing the same channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' The co-existence  of different types of molecules can lead to substantial inter-  ference with the communication process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Researchers have  already developed several theoretical detection and channel  sensing techniques to reduce or eliminate the effect of such  background or multi-user interference [31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' To enable the  performance tests of these methods under interference, and  the development of more practical techniques to cope with  it, microfluidic MC testbeds should be able to replicate the  interference conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' From the transmitter aspect, the pulse  shaping technique should be able to selectively control the  waveform generation process, such that only the molecules  of interest, among other interfering molecules, are modulated  in concentration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' The electrochemical waveform generation  method can be considered to support selectivity for such  MC scenarios, due to the inherent specificity of the chemical  reactions involved in the waveform generation process [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  In the hydrodynamic method, however, the concentration  of molecules is modulated solely by hydrodynamic forces,  which does not make a distinction between different types  of molecules co-existing in the channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' The only factor that  can enable selectivity in hydrodynamic waveform generation  is the diffusion coefficient of molecules, which may differ  depending on the size of the molecules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' However, as the effect  of diffusion on the shape of generated waveforms is limited,  manifesting itself only in the dispersion of the waveforms as  they propagate, it cannot enable the required level of selectivity  in pulse shaping in MC testbeds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  Similar to the hydrodynamic method, the selectivity of the  acoustofluidic methods is low.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' The external acoustic force  fields applied by the transducer in this method modulate the  oscillation frequency of the bubbles trapped inside the HSS  structure, which then only indirectly affect the transport of  the molecules around the structure through the hydrodynamic  forces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' As there is no direct impact of the acoustic force  fields on molecular transport, the method cannot selectively  distinguish between different types of molecules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Hence, the  only element that can lead to a low level of selectivity in this  method could be again the diffusion coefficient that depends  on the type, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=', the size, of molecules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' [29], [37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  12  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' System Complexity  The complexity of the microfluidic chemical waveform  generation techniques is evaluated based on the number and  the heterogeneity of individual components required for the  waveform generation, and the fabrication methods by which  the overall system, including the microfluidic chip and other  external components, is assembled to generate chemical wave-  forms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Systems with less complexity, of course, can be favored  because of the ease and low cost of the fabrication process,  and more importantly, the increased level of reproducibility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  Acoustofluidic waveform generation is typically based on  a complex system architecture involving a multitude of ex-  ternal components, such as a piezoelectric transducer capable  of producing low-intensity acoustic waves, and a horseshoe  structure (HSS), which traps the bubble that is oscillated via  the acoustic waves inside the microfluidic channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  The electrochemical waveform generation method has a  medium level of complexity compared to the other two meth-  ods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' In terms of fabrication, the system architecture consists  of a hybrid PDMS-glass chip.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Electrodes can be deposited on  the glass substrate with a specified spacing with a sputtering  mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' The waveform generation process in this method  is based on the consecutive electric potential pulses applied  to the electrodes and the subsequent electrochemical reactions  of the molecules on the first working electrode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Therefore,  the electrochemical method can be considered to require a  much simpler fabrication process and have a simpler operating  mechanism compared to the acoustofluidic method [43], [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  Hydrodynamic methods, on the other hand, have a less  complex system architecture consisting of only a PDMS-  based microfluidic chip at the fundamental level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Note that  the microfluidic chip and the external pressure control systems  that drive the fluid flow inside the channels are common to all  microfluidic waveform generation techniques investigated in  this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' The waveform generation process is also relatively  simple in hydrodynamic methods, as it only requires the  hydrodynamic forces which are inherent to the microfluidic  systems [28], [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' These make the hydrodynamic method the  least complex waveform generation method considering that  the other methods require additional external force fields, such  as acoustic fields, or electrochemical reactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' DISCUSSION ON APPLICATIONS AND FEASIBILITY  Most of the MC applications envisioned in the literature,  including those concerning intrabody environments, can po-  tentially be facilitated by high-resolution and programmable  MC pulse shaping techniques integrated into MC transmitter  architectures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' This is because high-resolution control over  the waveform of the generated concentration pulses can help  address the problems resulting from ISI, and nonlinear and  time-varying channel and transmitter/receiver characteristics,  as explained in Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Many of these problems require the  generation of various concentration waveforms, and sometimes  the ability to adaptively tune their properties in order to  improve the accuracy of information transfer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Understanding  the relationship between physical design parameters and gen-  erated pulse shapes can reveal practical limitations and identify  areas of further engineering and optimization, as well as  inform the design of optimal and practical MC modulation and  detection techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' This practical understanding is crucial  for moving beyond the commonly utilized assumption of  instant, impulsive molecule release with point transmitters,  which lacks practical relevance [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  Microfluidic pulse shaping techniques discussed in this pa-  per are particularly promising for integration into microfluidic  MC testbeds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' These techniques can allow for a broader range  of MC scenarios to be practically tested and enable more  accurate and programmable platforms for optimization and  validation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' The implementation of these practical MC pulse  shaping techniques in microfluidic MC testbeds can immedi-  ately make the following contributions to the MC literature:  Enabling the accurate testing of existing or new MC  modulation and detection methods, and facilitating the  design of realistic MC techniques that are compatible  with the pulse shapes that can be practically generated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  Optimizing transmitted pulse shapes (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=', the duration  of a rectangular concentration pulse) from a commu-  nication perspective for different practical MC channel  and receiver architectures and configurations, such as  MC receivers with ligand receptors that may experience  saturation depending on concentration pulse amplitude  and duration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Such optimization can be readily validated  through the integration of the investigated pulse shaping  techniques into microfluidic MC testbeds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  Eventually, optimizing the overall MC system, including  the physical receiver architecture, under various MC  scenarios given the pulse shaping technique and the  corresponding set of concentration waveforms that can  be generated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  Furthermore, leveraging the chemical waveform genera-  tion techniques with MC tools and theories in microfluidic  chips can significantly contribute to lab-on-chip and organ-  on-chip technologies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' For example, replicating the signaling  dynamics between cell groups and tissues in microfluidic  chips is essential for creating organ function in organ-on-  chip systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' High-resolution and programmable microfluidic  pulse shaping techniques that allow for the implementation of  various MC modulation techniques in microfluidic chips can  enable ICT-based organ-on-chip platforms that can accurately  control chemical signal patterns between different biological  components, providing an opportunity to probe and study the  role of information flow in microphysiological systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Such  ICT-based platforms can open new avenues in drug delivery  and drug design research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Merging ICT with microfluidic  technologies through MC pulse shaping techniques can also  have implications in biomedical sensor research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' These multi-  disciplinary platforms can allow for the information-theoretical  optimization of sensor architectures for sensing time-varying  concentration waveforms of biomarkers generated through  microfluidic MC pulse shaping techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  It should be noted, however, that none of the chemical  waveform generation techniques investigated in this paper have  been demonstrated in in vivo environments, such as inside  the human body.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' This raises the question of whether the  13  microfluidic MC pulse shaping techniques can be integrated  into practical MC transmitters for in vivo MC applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  The main challenge in implementing these techniques in in  vivo environments will be system complexity, as discussed in  Section IV-E, and the spatiotemporal control of pulse shapes  independently of the surrounding biological force fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' For  example, the high-level complexity of the acoustofluidic pulse  shaping techniques, which necessitate fine tuning of the exter-  nal acoustic transducer and the horseshoe structure for bubble  oscillation, may hinder their feasibility for such applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  On the other hand, while the system complexity of hydrody-  namic methods is relatively low, the pulse shaping function  in this method is based on tuning hydrodynamic force fields,  e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=', fluid flow rate, which may not be feasible to control  independently of the flow conditions of biological fluids, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=',  blood.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Electrochemical methods, although having advantages  in terms of system complexity and scalability, may lead to  biocompatibility issues due to the required electrochemical  reactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' In summary, the investigated microfluidic MC pulse  shaping methods are currently not feasible for integration  into in vivo MC applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' However, further advances in  micro/nanotechnologies may provide new opportunities for  improving their practicality or offer alternative pulse shaping  methods that are more compatible with such applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' CONCLUSION  This paper provided a comprehensive overview of practical  microfluidic chemical waveform generation techniques which  are promising as pulse shaping methods for microfluidic MC  systems and testbeds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Pulse shaping is essential for accurate  and high-rate information transfer in MC systems because  the inherent low-pass characteristic of the MC channel leads  to significant dispersion of the molecular signals as they  propagate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' The programmability of the spatiotemporal distri-  bution of molecules of interest inside microfluidic channels  is also crucial for extending the capabilities of microfluidic  MC testbeds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' The chemical waveform generation techniques  highlighted in this paper utilize different external forces, such  as hydrodynamic and acoustic force fields, or electrochem-  ical reactions, to program the spatiotemporal distribution of  molecules inside the microfluidic channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' These methods  were analyzed in terms of their operating mechanisms and  the characteristics of the generated concentration signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' To  accurately assess the suitability and potential utility of these  techniques for application in microfluidic MC systems and  testbeds, we identified a set of key performance criteria  including spatiotemporal resolution, control over propagation,  system complexity, repeatability, selectivity, and compatibility  with a wide range of applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Through this comprehensive  evaluation, we aim to bridge the gap between theory and  practice in MC technology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' We believe that this review and  the accompanying evaluation will help researchers incorporate  programmable, high-resolution pulse shaping techniques into  their microfluidic MC testbeds for a more accurate assessment  of the developed MC techniques, such as modulation and  detection techniques, with well-defined MC signal waveforms  inside microfluidic channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  ACKNOWLEDGMENT  This work was supported in part by The Scientific and  Technological Research Council of Turkey (TUBITAK) un-  der Grant #120E301, and European Union’s Horizon 2020  Research and Innovation Programme through the Marie  Skłodowska-Curie Individual Fellowship under Grant Agree-  ment #101028935.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  REFERENCES  [1] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Akyildiz, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Pierobon, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Balasubramaniam, “Moving forward  with molecular communication: From theory to human health applica-  tions [point of view],” Proceedings of the IEEE, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 107, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 5, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  858–865, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  [2] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Kuscu, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Dinc, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Bilgin, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Ramezani, and O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Akan,  “Transmitter and receiver architectures for molecular communications:  A survey on physical design with modulation, coding, and detection  techniques,” Proceedings of the IEEE, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 107, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 7, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 1302–1341,  2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  [3] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Felicetti, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Femminella, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Reali, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Li`o, “Applications of  molecular communications to medicine: A survey,” Nano Communica-  tion Networks, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 7, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 27–45, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  [4] O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Akan, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Ramezani, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Khan, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Abbasi, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Kuscu,  “Fundamentals of molecular information and communication science,”  Proceedings of the IEEE, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 105, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 306–318, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  [5] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Bi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Almpanis, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Noel, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Deng, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Schober, “A survey of  molecular communication in cell biology: Establishing a new hierarchy  for interdisciplinary applications,” IEEE Communications Surveys &  Tutorials, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 23, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 1494–1545, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  [6] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Barros, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Veleti´c, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Kanada, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Pierobon, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Vainio, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Balas-  ingham, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Balasubramaniam, “Molecular communications in viral  infections research: Modeling, experimental data, and future directions,”  IEEE Transactions on Molecular, Biological and Multi-Scale Commu-  nications, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 7, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 121–141, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  [7] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Kuscu and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Unluturk, “Internet of bio-nano things: A review  of applications, enabling technologies and key challenges,” ITU Journal  on Future and Evolving Technologies,, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 2, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 3, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  [8] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Akyildiz, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Jornet, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Pierobon, “Nanonetworks: A new  frontier in communications,” Communications of the ACM, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 54,  no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 11, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 84–89, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  [9] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Haselmayr, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Springer, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Fischer, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Alexiou, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Boche, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  Hoeher, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Dressler, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Schober, “Integration of molecular com-  munications into future generation wireless networks,” 1st 6G Wireless  Summit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' IEEE, Levi, Finland, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  [10] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Hiyama, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Moritani, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Suda, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Egashira, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Enomoto, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Moore,  and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Nakano, “Molecular communication,” Journal-Institute of Elec-  tronics Information and Communication Engineers, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 89, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 2, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  162, 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  [11] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Farsad, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Yilmaz, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Eckford, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='-B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Chae, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Guo, “A  comprehensive survey of recent advancements in molecular communi-  cation,” IEEE Communications Surveys & Tutorials, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 18, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  1887–1919, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  [12] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Kuscu and O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Akan, “Detection in molecular communications  with ligand receptors under molecular interference,” Digital Signal  Processing, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 124, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 103186, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  [13] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Deng, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Pierobon, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Nallanathan, “A microfluidic feed forward  loop pulse generator for molecular communication,” in GLOBECOM  2017-2017 IEEE Global Communications Conference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  IEEE, 2017,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 1–7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  [14] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Balasubramaniam, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Ben-Yehuda, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Pautot, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Jesorka, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Kouch-  eryavy, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=', “A review of experimental opportunities for molecular  communication,” Nano Communication Networks, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 4, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 43–  52, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  [15] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Kuscu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Ramezani, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Dinc, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Akhavan, and O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Akan,  “Fabrication and microfluidic analysis of graphene-based molecular  communication receiver for internet of nano things (iont),” Scientific  reports, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 11, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 1–20, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  [16] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Amerizadeh, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Mashhadian, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Farahnak-Ghazani, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Arjmandi,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Rad, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Shamloo, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Vosoughi, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Nasiri-Kenari, “Bacterial  receiver prototype for molecular communication using rhamnose operon  in a microfluidic environment,” IEEE Transactions on NanoBioscience,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 20, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 4, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 426–435, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  14  [17] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Kuscu, “Nano/bio-receiver architectures and detection methods for  molecular communications,” Ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' dissertation, University of Cam-  bridge, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  [18] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Proakis and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Salehi, Fundamentals of communication systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  Pearson Education India, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  [19] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Kuscu and O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Akan, “Modeling convection-diffusion-reaction  systems for microfluidic molecular communications with surface-based  receivers in internet of bio-nano things,” PloS one, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 13, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 2, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  e0192202, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  [20] ——, “On the physical design of molecular communication receiver  based on nanoscale biosensors,” IEEE Sensors Journal, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 16, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 8,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 2228–2243, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  [21] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Rezaei, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Rudsari, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Javan, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Mokari, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Jorswieck, and  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Orooji, “Molecular communication transmitter design in limited-  capacity storage regime,” IEEE Transactions on NanoBioscience, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  [22] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Wicke, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Felsheim, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Brand, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Jamali, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Loos, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Buettner,  and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Schober, “Pulse shaping for mc via particle size,” arXiv preprint  arXiv:2201.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='06425, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  [23] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Bi, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Deng, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Pierobon, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Nallanathan, “Chemical reactions-  based microfluidic transmitter and receiver design for molecular com-  munication,” IEEE Transactions on Communications, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 68, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 9, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  5590–5605, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  [24] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Bicen and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Akyildiz, “System-theoretic analysis and least-  squares design of microfluidic channels for flow-induced molecular  communication,” IEEE Transactions on Signal Processing, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 61,  no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 20, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 5000–5013, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  [25] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' S¸.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Kuran, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Yilmaz, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Tugcu, “A tunnel-based approach for  signal shaping in molecular communication,” in 2013 IEEE international  conference on communications workshops (ICC).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' IEEE, 2013, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 776–  781.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  [26] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Chen, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Li, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Guo, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Zeng, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='-F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Liu, “A review on microflu-  idics manipulation of the extracellular chemical microenvironment and  its emerging application to cell analysis,” Analytica Chimica Acta, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  1125, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 94–113, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  [27] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Abadie, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Sella, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Perrodin, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Thouin, “Electrochemical  generation and detection of transient concentration gradients in microflu-  idic channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' theoretical and experimental investigations,” Frontiers in  chemistry, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 704, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  [28] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Chen, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Feng, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Sun, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Wang, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Du, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='-F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Liu, “Hydrodynamic  gating for sample introduction on a microfluidic chip,” Lab on a Chip,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 10, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 11, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 1472–1475, 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  [29] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Huang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Chan, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Li, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Wang, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Nama, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Bachman, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  Huang, “A sharp-edge-based acoustofluidic chemical signal generator,”  Lab on a Chip, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 18, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 10, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 1411–1421, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  [30] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Ahmed, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Chan, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Lin, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Muddana, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Nama,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Benkovic, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Huang, “Tunable, pulsatile chemical gradient  generation via acoustically driven oscillating bubbles,” Lab on a Chip,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 13, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 328–331, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  [31] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Kuscu and O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Akan, “Channel sensing in molecular commu-  nications with single type of ligand receptors,” IEEE Transactions on  Communications, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 67, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 10, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 6868–6884, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  [32] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  Kang  and  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  Sharma,  “Pulse  shape  filtering  in  wireless  communication-a critical analysis,” IJACSA) International Journal of  Advanced Computer Science and Applications, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 2, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 3, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  [33] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Pehlivanoglu, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Unluturk, and O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Akan, “Modulation in  molecular communications: A look on methodologies,” in Modeling,  Methodologies and Tools for Molecular and Nano-scale Communica-  tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  Springer, 2017, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 79–97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  [34] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Huang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Wen, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Yang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='-B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Chae, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Ji, “Spatial mod-  ulation for molecular communication,” IEEE transactions on nanobio-  science, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 18, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 381–395, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  [35] U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Alon, “Network motifs: theory and experimental approaches,” Nature  Reviews Genetics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 8, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 6, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 450–461, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  [36] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Perrodin, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Sella, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Thouin, “Electrochemical generation of  steady-state linear concentration gradients within microfluidic channels  perpendicular to the flow field,” Analytical Chemistry, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 92, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 11,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 7699–7707, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  [37] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Ahmed, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Muddana, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Lu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' French, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Ozcelik, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Fang,  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Butler, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Benkovic, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Manz, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Huang, “Acoustofluidic  chemical waveform generator and switch,” Analytical chemistry, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 86,  no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 23, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 11 803–11 810, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  [38] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Guo, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Chen, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Gao, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Li, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Li, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Feng, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='-F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Liu, “A time-  coded multi-concentration microfluidic chemical waveform generator  for high-throughput probing suspension single-cell signaling,” Chinese  Chemical Letters, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  [39] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Chen, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Chen, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Feng, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Du, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='-F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Liu, “Analysis of intercel-  lular communication by flexible hydrodynamic gating on a microfluidic  chip,” Analytical and bioanalytical chemistry, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 405, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 307–  314, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  [40] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Chen, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Guo, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Feng, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Yan, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Wang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Li, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Du, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='-F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  Liu, “Microfluidic chemical function generator for probing dynamic cell  signaling,” Analytical Chemistry, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 89, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 17, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 9209–9217, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  [41] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='-D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Xue, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Li, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='-T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Na, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='-X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Wang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Yu, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Liu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Cao,  and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='-R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Qin, “A microfluidic platform enabling real-time control of  dynamic biochemical stimuli to biological cells,” Journal of Microme-  chanics and Microengineering, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 30, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 9, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 095011, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  [42] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Garrison, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Li, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Palanisamy, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Wang, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Seker, “An  electrically-controlled programmable microfluidic concentration wave-  form generator,” Journal of biological engineering, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 12, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  1–10, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  [43] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Krabbenborg and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Huskens, “Electrochemically generated gra-  dients,” Angewandte Chemie International Edition, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 53, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 35, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  9152–9167, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  [44] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Delahaye, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Lombardo, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Sella, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Thouin, “Electrochemical  assessments of droplet contents in microfluidic channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' application to  the titration of heterogeneous droplets,” Analytica Chimica Acta, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  1155, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 338344, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  [45] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Bruus, “Acoustofluidics 7: The acoustic radiation force on small  particles,” Lab on a Chip, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 12, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 6, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 1014–1021, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  [46] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Rufo, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Cai, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Friend, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Wiklund, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Huang, “Acoustofluidics  for biomedical applications,” Nature Reviews Methods Primers, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 2,  no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 1–21, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  [47] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Friend and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Yeo, “Microscale acoustofluidics: Microfluidics  driven via acoustics and ultrasonics,” Reviews of Modern Physics,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 83, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 2, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 647, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  [48] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Wu, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Ozcelik, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Rufo, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Wang, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Fang, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Jun Huang,  “Acoustofluidic separation of cells and particles,” Microsystems &  nanoengineering, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 5, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 1–18, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  [49] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Destgeer, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Lee, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Jung, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Alazzam, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Sung,  “Continuous separation of particles in a pdms microfluidic channel via  travelling surface acoustic waves (tsaw),” Lab on a Chip, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 13, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 21,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 4210–4216, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  [50] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Glynne-Jones, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Boltryk, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Hill, “Acoustofluidics 9: Mod-  elling and applications of planar resonant devices for acoustic particle  manipulation,” Lab on a Chip, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 12, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 8, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 1417–1426, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content='  [51] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Destgeer, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Im, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Hang Ha, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Ho Jung, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Ahmad Ansari,  and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' Jin Sung, “Adjustable, rapidly switching microfluidic gradient  generation using focused travelling surface acoustic waves,” Applied  Physics Letters, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 104, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 2, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
+page_content=' 023506, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PtE5T4oBgHgl3EQfYw9y/content/2301.05576v1.pdf'}
diff --git a/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf b/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..7b05f7297ccf93a3956e0765791541b322158a70
--- /dev/null
+++ b/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:b7f3e610035d8a2b38f215082160520e87e72155398fa454d5d137ae0524b0c1
+size 594315
diff --git a/QdAyT4oBgHgl3EQfU_c5/vector_store/index.pkl b/QdAyT4oBgHgl3EQfU_c5/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..47c2ff5067c4111ce4055270f63cf20c57a10a19
--- /dev/null
+++ b/QdAyT4oBgHgl3EQfU_c5/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:64cf9e208ac65ed671dbbb1eb1a1b105ffe7a7ad16a92bfeda3342442029c4f0
+size 115927
diff --git a/QdE0T4oBgHgl3EQf1QKQ/content/tmp_files/2301.02697v1.pdf.txt b/QdE0T4oBgHgl3EQf1QKQ/content/tmp_files/2301.02697v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..86daa2bb106aa048d74dd878f657211cd0d662bb
--- /dev/null
+++ b/QdE0T4oBgHgl3EQf1QKQ/content/tmp_files/2301.02697v1.pdf.txt
@@ -0,0 +1,320 @@
+arXiv:2301.02697v1  [econ.TH]  6 Jan 2023
+Preferences on Ranked-Choice Ballots
+Brian Duricy∗
+December 19, 2022
+Abstract
+This paper formalizes the lattice structure of the ballot voters cast in a ranked-choice election and
+the preferences that this structure induces. These preferences are shown to be counter to previous
+assumptions about the preferences of voters, which indicate that ranked-choice elections require
+different considerations for voters and candidates alike. While this model assumes that voters vote
+sincerely, the model of ranked-choice elections this paper presents allows for considerations of strategic
+voting in future work.
+JEL Codes: D71, D72
+Keywords: Ranked-choice voting, preferences, lattice theory
+1
+Introduction
+Social choice models and results usually require strict preference relations, or those where every
+alternative is uniquely ranked with respect to the others. This includes the subset of social choice theory
+dedicated to voting, despite real-life elections that use ranked-choice voting1 either mandating non-strict
+preference relations or showing that voters effectively vote as if this is the case. Regarding the former,
+the 2021 Primary Elections for New York City Mayor allowed voters to rank up to five candidates (Board
+of Elections in the City of New York (2021)), while the Democratic Primary had 13 total candidates to
+choose from (not including write-ins). Regarding the latter, Kilgour et al. (2020) list 17 ranked-choice
+elections and, amongst them, the highest average percentage of candidates on a ballot who were ranked
+was slightly above 80%. Experimental results such as Nielson (2017) similarly show that respondents
+generally do not approach ranking all—or even most—of the candidates. Ranked-choice elections serve
+as a compelling counterexample against mandating strict preference relations in all social choice models.
+∗bduricy@alumni.cmu.edu
+1Elections between multiple candidates in which voters are required to vote for one and only one candidate satisfy this
+trivially.
+1
+
+The preferences that do appear in ranked-choice elections are an example of the preferences studied in
+Kreps (1979).
+This paper focuses on the structure of the ballots used in these elections, referred to as ranked-choice
+ballots. A ranked-choice ballot is the result of a voter having a top-truncated order (or, alternatively,
+such as in Fitzsimmons and Lackner (2020), a top order) over the set of candidates. These terms are
+fully defined in Section 2, but the intuition is that not all alternatives must be uniquely ranked. Whereas
+previous work on top-truncated preferences like Ayadi et al. (2022) and Terzopoulou and Endriss (2021)
+have focused on scoring rules associated with these preferences, this paper examines the more foundational
+order-theoretic properties2 that arise from equipping a set with a top-truncated order. As Tomlinson et
+al. (2022) prove that differing ballot lengths can produce different winners in the same instant-runoff
+election, determining which scoring rule to use is an important related line of research.
+Another area of research on top-truncated preferences focuses on computational questions (e.g., Menon
+and Larson (2017)). Top-truncated preferences also necessitate a discussion of results that do not require
+a lattice, as similar work like Chambers and Echenique (2009) is based upon a lattice rather than a
+semilattice. That a top-truncated set is a join semilattice is the paper’s first result, and one that informs
+the rest of the paper’s findings. The results in Section 3 follow a unique and smooth path from lattice
+theory to utility functions, stopping along the way to provide novel applications of results from the
+preference and voting theory literature.
+The pairing of lattice theory with preference relations is common, and this paper contributes to this
+literature by focusing on antitone preference relations. Ranked-choice voting motivates the need for an
+exploration into if—and how—results from this literature apply to a context that is suited for antitone
+preferences. This paper is the first to identify the connection between top-truncated preferences and
+ranked-choice voting, and it connects multiple strands of literature that have previously existed somewhat
+independently of one another. With an understanding of some mathematical properties of ranked-choice
+ballots and the preferences that define them, normative work regarding the value of ranked-choice voting
+vis-a-vis other voting methods will be enhanced.
+2
+The Model and Additional Terminology
+2.1
+The Model
+A ranked-choice election (V, C, ≿) consists of a (possibly infinite) set of voters, V , a finite set of at
+least three candidates, C, and a complete top-truncated order profile for (V, C), ≿, which assigns to each
+2A complete treatment of order, and more specifically lattice, theory can be found in Caspard et al. (2012) and Gr¨atzer
+(2011), respectively.
+2
+
+voter v ∈ V a complete top-truncated order on C3. We define (C, ≿v) as a ranked-choice ballot for voter
+v4. In general, (C, ≿v) is a ballot, with the type of order profile ≿ unspecified. Each voter can rank
+as many candidates (i.e., declare these candidates distinguishable to the others) as they wish, but they
+must rank at least one candidate. Example 1 below provides a sample ranked-choice ballot and its lattice
+representation.
+Example 1 Let C = {a, b, c, d, x, y, z} and let voter v ∈ V ’s preferences over C be x ≻ y ≻ z ≻ a ∼ b ∼
+c ∼ d. This is alternatively represented as v ranking candidate x first, y second, z third, and candidates
+a, b, c, and d unranked and tied for fourth.
+The lattice construction of this ballot is shown below;
+straight lines indicate strict preference between candidates and wavy lines indicate indifference between
+candidates.
+x
+y
+z
+♦♦♦♦♦♦♦♦♦♦♦♦♦♦
+❄
+❄
+❄
+❄
+❄
+❄
+❄
+�������
+a
+���
+b
+���
+c
+���
+d
+It should be clear that these preferences exhibit the same “desire for flexibility” (Kreps (1979), p. 566)
+studied in Kreps’ paper. If a set of candidates is a subset of another, the preferences on the latter are
+strictly preferred to the former if a ranked candidate is a member of the latter and not the former, and
+weakly preferred if the only members of the latter that are not members of the former are (additional)
+unranked candidates.
+The utility function this paper uses assumes that voters do not vote strategically—i.e., a candidate is
+ranked above another candidate if and only if the voter would receive a greater utility from the former
+candidate winning the election than the latter; similarly, if multiple candidates are unranked, then each
+of those candidates winning provides the same utility to the voter. This can be formalized as follows:
+u : C � R such that for all x, y ∈ C,
+3This is a specification of the Osborne (2022) construction, where a collective choice problem (N, X, ≿) is defined with
+N a set of individuals and X a set of alternatives, with the latter two sets functioning analogously to the sets V and C,
+respectively. ≿ in Osborne (2022) is a preference profile, with each ≿ a preference relation, defined to be a complete and
+transitive binary relation.
+4In the Results section of the paper, the specification notation will be omitted, but the results apply to the individual
+ballot of each voter.
+3
+
+u(x) > u(y) ⇔ x ≻ y
+u(x) = u(y) ⇔ x ∼ y
+Additional terminology is needed for a full connection to the results of this paper and are defined in
+the next subsection.
+2.2
+Additional Terminology
+The concepts in this subsection can be divided into two parts: one that focuses on the order- and
+lattice-theoretic concepts needed, and one that focuses on the concepts regarding the utility function used
+in this paper.
+A partial order is a reflexive, transitive, and asymmetric binary relation. A set with a partial order is
+a partially ordered set. A binary relation ≿ is monotone if for all x, y ∈ C, x ≥ y ⇒ x ≿ y and antitone
+if for all x, y ∈ C, x ≥ y ⇒ x ≾ y. If a candidate x is preferred to candidate y by a voter v, we write
+x ≻v y. If candidates x and y are indistinguishable to voter v, then we write x ∼v y. In the results section
+of this paper, it is sometimes easier to refer to candidates as ranked or unranked; the former refers to
+candidates that are not indistinguishable to any other candidate5, whereas the latter refers to candidates
+that are indistinguishable to at least one other candidate. A voter who ranks all candidates except for
+one trivially causes that last candidate to be ranked as well.
+A weak order is a partial order where indistinguishability is transitive. A top-truncated order is a
+weak order where only the minimal elements are indistinguishable to one another, and a set with a top-
+truncated order is a top-truncated set A partial order where every pair of elements are comparable is a
+complete partial order. A partially ordered set where no pair of elements are indistinguishable is a totally
+ordered set.
+A join semilattice is a partially ordered set where the least upper bound of each two elements in the
+set exists6. An element x ∈ C is join-irreducible if there exists a unique element y ∈ C such that x covers
+y7. Conversely, an element x ∈ C is meet-irreducible if there exists a unique element y ∈ C such that x
+is covered by y. An element is an atom if it covers the least element of the set and is a co-atom if it is
+covered by the greatest element of the set.
+Remark 2 Some elementary lattice-theoretic properties of top-truncated sets are noted here without
+proof.
+If a top-truncated set has a join-irreducible element, that element is also an atom.
+A top-
+5Except, of course, itself, by the reflexivity of the binary relation.
+6I.e., for all x, y ∈ C, there exists z such that z = sup{x, y} = x ∨ y.
+7I.e., x ≻ y and there does not exist an element z ∈ C such that x ≻ z ≻ y.
+4
+
+truncated set with a join-irreducible element is a totally ordered set. Every top-truncated set contains
+n − 1 meet-irreducible elements and has 1 ≤ m ≤ n − 1 co-atoms. □
+A binary relation ≿ is modular (or strongly quasisubmodular) if for all x, y ∈ C, x ∼ (x∨y) ⇒ x∨z ∼
+(x ∨ y) ∨ z. A representation of ≿ is a function u : C � R such that for all x, y ∈ C x ≿ y ⇒ u(x) ≥ u(y)
+and x ≻ y ⇒ u(x) > u(y). A representation u : C � R is submodular for a join semilattice if for all
+x, y ∈ C such that there exists a greatest lower bound8, u(x ∧ y) + u(x ∨ y) ≤ u(x) + u(y). As some
+methods of ranked-choice voting are used to elect multiple candidates from a single election—with “elect”
+here either meaning being one of the overall winners of the election or being one of the candidates who
+moves on to a head-to-head runoff—results relating to the representation of the preference relation are
+especially important for this context.
+Kalandrakis (2010) focuses on a similar notion, rationalizability. u : C � R is strictly rationalizable if
+u(x) > u(y) for each pair x, y ∈ C such that x ≿ y and rationalizable if u(x) ≥ u(y) for each pair x, y ∈ C
+such that x ≿ y. Clearly if a ballot has multiple unranked candidates, this leads to u not being strictly
+rationalizable. u : C � R is almost strictly rationalizable if it is rationalizable over all pairs x, y ∈ C and
+strictly rationalizable for each pair x, y ∈ C such that it is not the case that x ≿ y and y ≿ x. As should
+be clear from the definitions already provided, this allows for some results to be applied to the context of
+ranked-choice voting. Finally, u : C � R is strictly concave if u(λx + (1 − λ)y) > λu(x) + (1 − λ)u(y) for
+all x, y with x ̸= y and for all λ ∈ (0, 1), and strictly quasiconcave if ui(λx+(1−λ)y) > min{ui(x), ui(y)}
+for all x, y with x ̸= y and for all λ ∈ (0, 1).
+While strategic voting is a usual feature of research regarding ranked-choice voting, providing a
+utility function that reflects this is beyond the scope of this paper. Contextualizing the results of this
+paper with a utility function for strategic voting is an area of future research. Strategic voting also
+potentially complicates analyses that rely on the preference relation being monotone, such as Chambers
+and Echenique (2008) and Chambers et al. (2020). The structure of a ranked-choice ballot for a voter
+who votes sincerely reflects an antitone preference relation—the candidate (say, x) that would provide
+the voter with the greatest utility is ranked 1, descending until the candidate (or candidates) who would
+provide the voter with the least utility (say, without loss of generality, y) is ranked k; so y > . . . > x ⇒
+u(y) < . . . < u(x). Chateauneuf et al. (2017) provide a result that is dualized below that is similar to
+one found in Chambers and Echenique (2008), but for an antitone preference relation.
+8I.e., for all x, y ∈ C, there exists z such that z = inf{x, y} = x ∧ y.
+5
+
+3
+Results
+Having defined a ranked-choice ballot above, we begin providing results by formally connecting it to
+a well-known mathematical structure.
+Theorem 3 If a ballot is a ranked-choice ballot, then it is a join semilattice.
+Proof: Let (C, ≿) be a ranked-choice ballot. Since it is a top-truncated set, it necessarily is a partially
+ordered set. So all that remains to be shown is that the join exists for each pair of candidates. Let x, y ∈ C.
+If x and y are distinguishable, then, without loss of generality, say x ≻ y; x = x ∨ y immediately follows.
+If x and y are not distinguishable, i.e., x ∼ y, there exists at least one other candidate in the election, say,
+z, since at least one candidate must be ranked. If z is the only other candidate, then z ≻ x ∼ y, which in
+turn means that z ≻ x and z ≻ y. So z = x ∨ y similarly follows. If multiple candidates are ranked, for
+the previous relationships to hold, select z as the candidate ranked last amongst them; z = x ∨ y again
+follows. Therefore, the join exists for each pair of candidates. Hence, (C, ≿) is a join semilattice. □
+With a substantive literature on preferences over semilattices, this result is the first to highlight the
+connection to ranked-choice voting. This, along with a couple of other features inherent in ranked-choice
+ballots, unlocks some important properties of the utility function associated with these ballots. These
+properties support the usage of ranked-choice voting as a way to increase the overall utility from an
+election. The next result is the second of the features needed to satisfy the conditions for the first result
+regarding utility functions.
+Proposition 4 If ≿ is a top-truncated order, then it is modular.
+Proof: Let ≿ be a top-truncated order on C and let x, y ∈ C such that x ∼ (x ∨ y). Then, since x ∨ y
+must be a ranked candidate and x ∼ (x ∨ y), x must be x ∨ y since a ranked candidate can only be
+indistinguishable to itself. So, since x = (x∨y), x∨z ∼ (x∨y)∨z, satisfying the definition of modularity.
+Therefore, top-truncated orders are modular. □
+Ranked-choice ballots are proven to be (finite) join semilattices, with top-truncated orders being mod-
+ular (or strongly quasisubmodular). Additionally, the top-truncated orders in this model are complete,
+and thus a type of complete preorder. Finally, as the preferences in this paper are antitone, they are
+(weakly) decreasing. Therefore, ranked-choice ballots have all of the necessary conditions to satisfy the
+following proposition.
+Proposition 5 (Dual of Corollary 2 from Chateauneuf et al. (2017).) For a complete preorder ≿ on
+a finite join semilattice (C, ≿), the following are equivalent:
+1. ≿ is weakly decreasing and strongly quasisubmodular.
+6
+
+2. ≿ has a weakly decreasing and submodular representation. □
+We can then establish the subsequent corollary.
+Corollary 6 A ranked-choice ballot has a submodular representation. □
+We next show that the preferences over ranked-choice ballots allow for a result from Kalandrakis
+(2010) to hold that further characterizes the utility function associated with these ballots. It helps to
+first define the following concepts: let P ⊆ C×C be the set of pairs of candidates, with (x, y) ∈ P meaning
+that x is (weakly) preferred to y. The potential weakness of preferences is necessary, as indistinguishable
+candidates x, y are in P as the separate pairs (x, y) ∈ P and (y, x) ∈ P. Let Y (P) be the set of candidates
+that are (weakly) preferred to at least one other candidate, and N(P) be the set of candidates that are
+(weakly) not preferred to at least one other candidate. Finally, let E(C) be the set of extreme points, or
+the candidates that are unable to be written as a strict convex combination of candidates in C; E(C(P))
+indicates that these candidates are part of at least one pair in P. The following theorem is needed to
+apply the remainder of the result from Kalandrakis (2010). A necessary fact about the set of extreme
+points regarding ranked-choice ballots is that the highest-ranked candidate in a set and the lowest-ranked
+candidate are the extreme points; if a set has multiple unranked (i.e., lowest-ranked) candidates, each of
+those candidates are in the set of extreme points, unless the set contains only unranked candidates, as
+that set would then have no extreme points.
+Theorem 7 For all nonempty P ′ ⊆ P, either
+1. there exists x ∈ E(C(P ′)) such that x ̸∈ Y (P ′)
+2. there exists a nonempty P ′′ ⊆ P ′ such that N(P ′′) = Y (P ′′) ⊆ E(C(P ′)) and Y (P ′′)∩Y (P ′ \P ′′) =
+∅.
+Proof: The proof proceeds in three parts which correspond to the three possible combinations of candi-
+dates in P ′—all ranked, at least one ranked and at least one unranked, and no ranked candidates. First,
+let P ′ ⊆ P such that all candidates in P ′ are ranked. Then, E(C(P ′)) = {x, y} with x the highest-ranked
+and y the lowest-ranked candidate; Y (P ′) = P ′\{y}; and N(P ′) = P ′ \{x}. Clearly, as y ∈ E(C(P ′)) but
+y ̸∈ Y (P ′), the conditions hold. Next, let P ′ ⊆ P consist of at least one ranked candidate, x, and at least
+one unranked candidate, y. Then, without loss of generality, E(C(P ′)) = {x, y}; Y (P ′) = P ′ \ {y}; and
+N(P ′) = P ′ \ {x}. Again, as y ∈ E(C(P ′)) but y ̸∈ Y (P ′), the conditions hold. Finally, let P ′ ⊆ P such
+that P ′ consists of only unranked candidates. Then, E(C(P ′)) = ∅. Similarly, Y (P ′) = N(P ′) = P ′.
+So for any subset of P ′, say, P ′′ ⊆ P ′, also has Y (P ′′) = N(P ′′). However, since all nonempty P ′′ are
+7
+
+such that N(P ′′) = Y (P ′′) and N(P ′′) = Y (P ′′) ̸⊆ E(C(P ′)) = ∅, this satisfies the contrapositive of the
+second condition. □
+The following result from Kalandrakis (2010) proves that ranked-choice ballots lead to voters having
+concave utility functions. As work on the strategic voting of candidates such as Tajika (2021) assumes
+that voters have convex utility functions, candidates as well as voters have an incentive to act differently
+in a ranked-choice election than in a traditional first-past-the-post election.
+Theorem 8 (Theorem 2 from Kalandrakis (2010).) Let C be the set of candidates and P ⊆ C × C be
+the voting record for a given voter. Then the following conditions are equivalent:
+1. For all nonempty P ′ ⊆ P, either there exists x ∈ E(C(P ′)) such that x ̸∈ Y (P ′) or there exists a
+nonempty P ′′ ⊆ P ′ such that N(P ′′) = Y (P ′′) ⊆ E(C(P ′)) and Y (P ′′) ∩ Y (P ′ \ P ′′) = ∅.
+2. There exists a strictly concave utility function that almost strictly rationalizes P.
+3. There exists a strictly quasiconcave utility function that almost strictly rationalizes P.
+4. There exists a strictly concave utility function that rationalizes P.
+5. There exists a strictly quasiconcave utility function that rationalizes P. □
+4
+Conclusion
+This paper was the first to formalize the preferences of ranked-choice voting and explore what structure
+a ballot having those preferences takes. Top-truncated preferences elicit specific types of representations
+and utility functions; now that these have been identified, a more substantive appraisal of ranked-choice
+voting’s value can be done.
+There are also multiple areas of future research that can build upon the results from this paper. Ayadi
+et al. (2022) mention the need for normative work on top-truncated preferences, which is especially impor-
+tant because these preferences have been shown to be concave (and quasiconcave)—types of preferences
+not always assumed to reflect voters’ actual preferences. Whether these preference types are affected
+if the utility function accounts for strategic voting is a valuable question to explore. Coughlin (1983)
+addresses utility functions for strategic voting, but in the context of candidates’ utility functions rather
+than voters’ utility functions. Ranked-choice voting provides both the opportunity for a voter to express
+their full set of preferences and the opportunity to vote strategically. This paper has explored theoretical
+properties associated with the former; the next step is to see if and where there is an intersection with
+the latter.
+8
+
+References
+Ayadi, M., Amor, N. B., & Lang, J. (2022). Approximating voting rules from truncated ballots. Au-
+tonomous Agents and Multi-Agent Systems, 36, 24.
+Board of Elections in the City of New York. (2021). Ranked choice voting. Retrieved May 25, 2022, from
+https://vote.nyc/page/ranked-choice-voting
+Caspard, N., Monjardet, B., & Leclerc, B. (2012). Finite ordered sets: Concepts, results and uses. Cam-
+bridge University Press.
+Chambers, C. P., & Echenique, F. (2008). Ordinal notions of submodularity. Journal of Mathematical
+Economics, 44, 1243–1245.
+Chambers, C. P., & Echenique, F. (2009). Supermodularity and preferences. Journal of Economic Theory,
+144, 1004–1014.
+Chambers, C. P., Miller, A. D., & Yenmez, M. B. (2020). Closure and preferences. Journal of Mathematical
+Economics, 88, 161–166.
+Chateauneuf, A., Vergopoulos, V., & Zhang, J. (2017). Infinite supermodularity and preferences. Eco-
+nomic Theory, 63, 99–109.
+Coughlin, P. J. (1983). Social utility functions for strategic decisions in probabilistic voting models.
+Mathematical Social Sciences, 4, 275–293.
+Fitzsimmons, Z., & Lackner, M. (2020). Incomplete Preferences in Single-Peaked Electorates. Journal of
+Artificial Intelligence Research, 67, 797–833.
+Gr¨atzer, G. (2011). Lattice theory: Foundation. Birkh¨auser.
+Kalandrakis, T. (2010). Rationalizable voting. Theoretical Economics, 5, 93–125.
+Kilgour, D. M., Gr´egoire, J.-C., & Foley, A. M. (2020). The prevalence and consequences of ballot trun-
+cation in ranked-choice elections. Public Choice, 184, 197–218.
+Kreps, D. M. (1979). A representation theorem for ‘Preference for Flexibility’. Econometrica, 47, 565–577.
+Menon, V., & Larson, K. (2017). Computational aspects of strategic behavior in elections with top-
+truncated ballots. Autonomous Agents and Multi-Agent Systems, 31, 1506–1547.
+Nielson, L. (2017). Ranked Choice Voting and Attitudes toward Democracy in the United States: Results
+from a Survey Experiment. Politics and Policy, 45, 535–570.
+Osborne, M. J. (2022). Models in political economy [https://www.economics.utoronto.ca/osborne/mpe/mpeDraft20220519.pdf(visited
+2022-05-31)].
+Tajika, T. (2021). Polarization and inefficient information aggregation under strategic voting. Social
+Choice and Welfare, 56, 67–100.
+Terzopoulou, Z., & Endriss, U. (2021). The Borda class: An axiomatic study of the Borda rule on top-
+truncated preferences. Journal of Mathematical Economics, 92, 31–40.
+9
+
+Tomlinson, K., Ugander, J., & Kleinberg, J. (2022). Ballot length in instant runoff voting. https://arxiv.org/abs/2207.08958
+10
+
diff --git a/QdE0T4oBgHgl3EQf1QKQ/content/tmp_files/load_file.txt b/QdE0T4oBgHgl3EQf1QKQ/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d32a931ef8b7409eb71a0971140e443334061dd6
--- /dev/null
+++ b/QdE0T4oBgHgl3EQf1QKQ/content/tmp_files/load_file.txt
@@ -0,0 +1,317 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf,len=316
+page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='02697v1  [econ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='TH]  6 Jan 2023  Preferences on Ranked-Choice Ballots  Brian Duricy∗  December 19, 2022  Abstract  This paper formalizes the lattice structure of the ballot voters cast in a ranked-choice election and  the preferences that this structure induces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' These preferences are shown to be counter to previous  assumptions about the preferences of voters, which indicate that ranked-choice elections require  different considerations for voters and candidates alike.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' While this model assumes that voters vote  sincerely, the model of ranked-choice elections this paper presents allows for considerations of strategic  voting in future work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  JEL Codes: D71, D72  Keywords: Ranked-choice voting, preferences, lattice theory  1  Introduction  Social choice models and results usually require strict preference relations, or those where every  alternative is uniquely ranked with respect to the others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' This includes the subset of social choice theory  dedicated to voting, despite real-life elections that use ranked-choice voting1 either mandating non-strict  preference relations or showing that voters effectively vote as if this is the case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Regarding the former,  the 2021 Primary Elections for New York City Mayor allowed voters to rank up to five candidates (Board  of Elections in the City of New York (2021)), while the Democratic Primary had 13 total candidates to  choose from (not including write-ins).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Regarding the latter, Kilgour et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' (2020) list 17 ranked-choice  elections and, amongst them, the highest average percentage of candidates on a ballot who were ranked  was slightly above 80%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Experimental results such as Nielson (2017) similarly show that respondents  generally do not approach ranking all—or even most—of the candidates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Ranked-choice elections serve  as a compelling counterexample against mandating strict preference relations in all social choice models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  ∗bduricy@alumni.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='cmu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='edu  1Elections between multiple candidates in which voters are required to vote for one and only one candidate satisfy this  trivially.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  1  The preferences that do appear in ranked-choice elections are an example of the preferences studied in  Kreps (1979).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  This paper focuses on the structure of the ballots used in these elections, referred to as ranked-choice  ballots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' A ranked-choice ballot is the result of a voter having a top-truncated order (or, alternatively,  such as in Fitzsimmons and Lackner (2020), a top order) over the set of candidates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' These terms are  fully defined in Section 2, but the intuition is that not all alternatives must be uniquely ranked.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Whereas  previous work on top-truncated preferences like Ayadi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' (2022) and Terzopoulou and Endriss (2021)  have focused on scoring rules associated with these preferences, this paper examines the more foundational  order-theoretic properties2 that arise from equipping a set with a top-truncated order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' As Tomlinson et  al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' (2022) prove that differing ballot lengths can produce different winners in the same instant-runoff  election, determining which scoring rule to use is an important related line of research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  Another area of research on top-truncated preferences focuses on computational questions (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=', Menon  and Larson (2017)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Top-truncated preferences also necessitate a discussion of results that do not require  a lattice, as similar work like Chambers and Echenique (2009) is based upon a lattice rather than a  semilattice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' That a top-truncated set is a join semilattice is the paper’s first result, and one that informs  the rest of the paper’s findings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' The results in Section 3 follow a unique and smooth path from lattice  theory to utility functions, stopping along the way to provide novel applications of results from the  preference and voting theory literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  The pairing of lattice theory with preference relations is common, and this paper contributes to this  literature by focusing on antitone preference relations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Ranked-choice voting motivates the need for an  exploration into if—and how—results from this literature apply to a context that is suited for antitone  preferences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' This paper is the first to identify the connection between top-truncated preferences and  ranked-choice voting, and it connects multiple strands of literature that have previously existed somewhat  independently of one another.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' With an understanding of some mathematical properties of ranked-choice  ballots and the preferences that define them, normative work regarding the value of ranked-choice voting  vis-a-vis other voting methods will be enhanced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  2  The Model and Additional Terminology  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='1  The Model  A ranked-choice election (V, C, ≿) consists of a (possibly infinite) set of voters, V , a finite set of at  least three candidates, C, and a complete top-truncated order profile for (V, C), ≿, which assigns to each  2A complete treatment of order, and more specifically lattice, theory can be found in Caspard et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' (2012) and Gr¨atzer  (2011), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  2  voter v ∈ V a complete top-truncated order on C3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' We define (C, ≿v) as a ranked-choice ballot for voter  v4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' In general, (C, ≿v) is a ballot, with the type of order profile ≿ unspecified.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Each voter can rank  as many candidates (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=', declare these candidates distinguishable to the others) as they wish, but they  must rank at least one candidate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Example 1 below provides a sample ranked-choice ballot and its lattice  representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  Example 1 Let C = {a, b, c, d, x, y, z} and let voter v ∈ V ’s preferences over C be x ≻ y ≻ z ≻ a ∼ b ∼  c ∼ d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' This is alternatively represented as v ranking candidate x first, y second, z third, and candidates  a, b, c, and d unranked and tied for fourth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  The lattice construction of this ballot is shown below;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  straight lines indicate strict preference between candidates and wavy lines indicate indifference between  candidates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  x  y  z  ♦♦♦♦♦♦♦♦♦♦♦♦♦♦  ❄  ❄  ❄  ❄  ❄  ❄  ❄  �������  a  ���  b  ���  c  ���  d  It should be clear that these preferences exhibit the same “desire for flexibility” (Kreps (1979), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' 566)  studied in Kreps’ paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' If a set of candidates is a subset of another, the preferences on the latter are  strictly preferred to the former if a ranked candidate is a member of the latter and not the former, and  weakly preferred if the only members of the latter that are not members of the former are (additional)  unranked candidates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  The utility function this paper uses assumes that voters do not vote strategically—i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=', a candidate is  ranked above another candidate if and only if the voter would receive a greater utility from the former  candidate winning the election than the latter;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' similarly, if multiple candidates are unranked, then each  of those candidates winning provides the same utility to the voter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' This can be formalized as follows:  u : C � R such that for all x, y ∈ C,  3This is a specification of the Osborne (2022) construction, where a collective choice problem (N, X, ≿) is defined with  N a set of individuals and X a set of alternatives, with the latter two sets functioning analogously to the sets V and C,  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' ≿ in Osborne (2022) is a preference profile, with each ≿ a preference relation, defined to be a complete and  transitive binary relation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  4In the Results section of the paper, the specification notation will be omitted, but the results apply to the individual  ballot of each voter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  3  u(x) > u(y) ⇔ x ≻ y  u(x) = u(y) ⇔ x ∼ y  Additional terminology is needed for a full connection to the results of this paper and are defined in  the next subsection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='2  Additional Terminology  The concepts in this subsection can be divided into two parts: one that focuses on the order- and  lattice-theoretic concepts needed, and one that focuses on the concepts regarding the utility function used  in this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  A partial order is a reflexive, transitive, and asymmetric binary relation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' A set with a partial order is  a partially ordered set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' A binary relation ≿ is monotone if for all x, y ∈ C, x ≥ y ⇒ x ≿ y and antitone  if for all x, y ∈ C, x ≥ y ⇒ x ≾ y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' If a candidate x is preferred to candidate y by a voter v, we write  x ≻v y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' If candidates x and y are indistinguishable to voter v, then we write x ∼v y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' In the results section  of this paper, it is sometimes easier to refer to candidates as ranked or unranked;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' the former refers to  candidates that are not indistinguishable to any other candidate5, whereas the latter refers to candidates  that are indistinguishable to at least one other candidate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' A voter who ranks all candidates except for  one trivially causes that last candidate to be ranked as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  A weak order is a partial order where indistinguishability is transitive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' A top-truncated order is a  weak order where only the minimal elements are indistinguishable to one another, and a set with a top-  truncated order is a top-truncated set A partial order where every pair of elements are comparable is a  complete partial order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' A partially ordered set where no pair of elements are indistinguishable is a totally  ordered set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  A join semilattice is a partially ordered set where the least upper bound of each two elements in the  set exists6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' An element x ∈ C is join-irreducible if there exists a unique element y ∈ C such that x covers  y7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Conversely, an element x ∈ C is meet-irreducible if there exists a unique element y ∈ C such that x  is covered by y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' An element is an atom if it covers the least element of the set and is a co-atom if it is  covered by the greatest element of the set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  Remark 2 Some elementary lattice-theoretic properties of top-truncated sets are noted here without  proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  If a top-truncated set has a join-irreducible element, that element is also an atom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  A top-  5Except, of course, itself, by the reflexivity of the binary relation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  6I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=', for all x, y ∈ C, there exists z such that z = sup{x, y} = x ∨ y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  7I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=', x ≻ y and there does not exist an element z ∈ C such that x ≻ z ≻ y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  4  truncated set with a join-irreducible element is a totally ordered set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Every top-truncated set contains  n − 1 meet-irreducible elements and has 1 ≤ m ≤ n − 1 co-atoms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' □  A binary relation ≿ is modular (or strongly quasisubmodular) if for all x, y ∈ C, x ∼ (x∨y) ⇒ x∨z ∼  (x ∨ y) ∨ z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' A representation of ≿ is a function u : C � R such that for all x, y ∈ C x ≿ y ⇒ u(x) ≥ u(y)  and x ≻ y ⇒ u(x) > u(y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' A representation u : C � R is submodular for a join semilattice if for all  x, y ∈ C such that there exists a greatest lower bound8, u(x ∧ y) + u(x ∨ y) ≤ u(x) + u(y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' As some  methods of ranked-choice voting are used to elect multiple candidates from a single election—with “elect”  here either meaning being one of the overall winners of the election or being one of the candidates who  moves on to a head-to-head runoff—results relating to the representation of the preference relation are  especially important for this context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  Kalandrakis (2010) focuses on a similar notion, rationalizability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' u : C � R is strictly rationalizable if  u(x) > u(y) for each pair x, y ∈ C such that x ≿ y and rationalizable if u(x) ≥ u(y) for each pair x, y ∈ C  such that x ≿ y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Clearly if a ballot has multiple unranked candidates, this leads to u not being strictly  rationalizable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' u : C � R is almost strictly rationalizable if it is rationalizable over all pairs x, y ∈ C and  strictly rationalizable for each pair x, y ∈ C such that it is not the case that x ≿ y and y ≿ x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' As should  be clear from the definitions already provided, this allows for some results to be applied to the context of  ranked-choice voting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Finally, u : C � R is strictly concave if u(λx + (1 − λ)y) > λu(x) + (1 − λ)u(y) for  all x, y with x ̸= y and for all λ ∈ (0, 1), and strictly quasiconcave if ui(λx+(1−λ)y) > min{ui(x), ui(y)}  for all x, y with x ̸= y and for all λ ∈ (0, 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  While strategic voting is a usual feature of research regarding ranked-choice voting, providing a  utility function that reflects this is beyond the scope of this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Contextualizing the results of this  paper with a utility function for strategic voting is an area of future research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Strategic voting also  potentially complicates analyses that rely on the preference relation being monotone, such as Chambers  and Echenique (2008) and Chambers et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' The structure of a ranked-choice ballot for a voter  who votes sincerely reflects an antitone preference relation—the candidate (say, x) that would provide  the voter with the greatest utility is ranked 1, descending until the candidate (or candidates) who would  provide the voter with the least utility (say, without loss of generality, y) is ranked k;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' so y > .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' > x ⇒  u(y) < .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' < u(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Chateauneuf et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' (2017) provide a result that is dualized below that is similar to  one found in Chambers and Echenique (2008), but for an antitone preference relation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  8I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=', for all x, y ∈ C, there exists z such that z = inf{x, y} = x ∧ y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  5  3  Results  Having defined a ranked-choice ballot above, we begin providing results by formally connecting it to  a well-known mathematical structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  Theorem 3 If a ballot is a ranked-choice ballot, then it is a join semilattice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  Proof: Let (C, ≿) be a ranked-choice ballot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Since it is a top-truncated set, it necessarily is a partially  ordered set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' So all that remains to be shown is that the join exists for each pair of candidates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Let x, y ∈ C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  If x and y are distinguishable, then, without loss of generality, say x ≻ y;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' x = x ∨ y immediately follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  If x and y are not distinguishable, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=', x ∼ y, there exists at least one other candidate in the election, say,  z, since at least one candidate must be ranked.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' If z is the only other candidate, then z ≻ x ∼ y, which in  turn means that z ≻ x and z ≻ y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' So z = x ∨ y similarly follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' If multiple candidates are ranked, for  the previous relationships to hold, select z as the candidate ranked last amongst them;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' z = x ∨ y again  follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Therefore, the join exists for each pair of candidates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Hence, (C, ≿) is a join semilattice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' □  With a substantive literature on preferences over semilattices, this result is the first to highlight the  connection to ranked-choice voting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' This, along with a couple of other features inherent in ranked-choice  ballots, unlocks some important properties of the utility function associated with these ballots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' These  properties support the usage of ranked-choice voting as a way to increase the overall utility from an  election.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' The next result is the second of the features needed to satisfy the conditions for the first result  regarding utility functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  Proposition 4 If ≿ is a top-truncated order, then it is modular.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  Proof: Let ≿ be a top-truncated order on C and let x, y ∈ C such that x ∼ (x ∨ y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Then, since x ∨ y  must be a ranked candidate and x ∼ (x ∨ y), x must be x ∨ y since a ranked candidate can only be  indistinguishable to itself.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' So, since x = (x∨y), x∨z ∼ (x∨y)∨z, satisfying the definition of modularity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  Therefore, top-truncated orders are modular.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' □  Ranked-choice ballots are proven to be (finite) join semilattices, with top-truncated orders being mod-  ular (or strongly quasisubmodular).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Additionally, the top-truncated orders in this model are complete,  and thus a type of complete preorder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Finally, as the preferences in this paper are antitone, they are  (weakly) decreasing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Therefore, ranked-choice ballots have all of the necessary conditions to satisfy the  following proposition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  Proposition 5 (Dual of Corollary 2 from Chateauneuf et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=') For a complete preorder ≿ on  a finite join semilattice (C, ≿), the following are equivalent:  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' ≿ is weakly decreasing and strongly quasisubmodular.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  6  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' ≿ has a weakly decreasing and submodular representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' □  We can then establish the subsequent corollary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  Corollary 6 A ranked-choice ballot has a submodular representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' □  We next show that the preferences over ranked-choice ballots allow for a result from Kalandrakis  (2010) to hold that further characterizes the utility function associated with these ballots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' It helps to  first define the following concepts: let P ⊆ C×C be the set of pairs of candidates, with (x, y) ∈ P meaning  that x is (weakly) preferred to y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' The potential weakness of preferences is necessary, as indistinguishable  candidates x, y are in P as the separate pairs (x, y) ∈ P and (y, x) ∈ P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Let Y (P) be the set of candidates  that are (weakly) preferred to at least one other candidate, and N(P) be the set of candidates that are  (weakly) not preferred to at least one other candidate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Finally, let E(C) be the set of extreme points, or  the candidates that are unable to be written as a strict convex combination of candidates in C;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' E(C(P))  indicates that these candidates are part of at least one pair in P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' The following theorem is needed to  apply the remainder of the result from Kalandrakis (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' A necessary fact about the set of extreme  points regarding ranked-choice ballots is that the highest-ranked candidate in a set and the lowest-ranked  candidate are the extreme points;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' if a set has multiple unranked (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=', lowest-ranked) candidates, each of  those candidates are in the set of extreme points, unless the set contains only unranked candidates, as  that set would then have no extreme points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  Theorem 7 For all nonempty P ′ ⊆ P, either  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' there exists x ∈ E(C(P ′)) such that x ̸∈ Y (P ′)  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' there exists a nonempty P ′′ ⊆ P ′ such that N(P ′′) = Y (P ′′) ⊆ E(C(P ′)) and Y (P ′′)∩Y (P ′ \\P ′′) =  ∅.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  Proof: The proof proceeds in three parts which correspond to the three possible combinations of candi-  dates in P ′—all ranked, at least one ranked and at least one unranked, and no ranked candidates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' First,  let P ′ ⊆ P such that all candidates in P ′ are ranked.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Then, E(C(P ′)) = {x, y} with x the highest-ranked  and y the lowest-ranked candidate;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Y (P ′) = P ′\\{y};' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' and N(P ′) = P ′ \\{x}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Clearly, as y ∈ E(C(P ′)) but  y ̸∈ Y (P ′), the conditions hold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Next, let P ′ ⊆ P consist of at least one ranked candidate, x, and at least  one unranked candidate, y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Then, without loss of generality, E(C(P ′)) = {x, y};' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Y (P ′) = P ′ \\ {y};' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' and  N(P ′) = P ′ \\ {x}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Again, as y ∈ E(C(P ′)) but y ̸∈ Y (P ′), the conditions hold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Finally, let P ′ ⊆ P such  that P ′ consists of only unranked candidates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Then, E(C(P ′)) = ∅.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Similarly, Y (P ′) = N(P ′) = P ′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  So for any subset of P ′, say, P ′′ ⊆ P ′, also has Y (P ′′) = N(P ′′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' However, since all nonempty P ′′ are  7  such that N(P ′′) = Y (P ′′) and N(P ′′) = Y (P ′′) ̸⊆ E(C(P ′)) = ∅, this satisfies the contrapositive of the  second condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' □  The following result from Kalandrakis (2010) proves that ranked-choice ballots lead to voters having  concave utility functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' As work on the strategic voting of candidates such as Tajika (2021) assumes  that voters have convex utility functions, candidates as well as voters have an incentive to act differently  in a ranked-choice election than in a traditional first-past-the-post election.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  Theorem 8 (Theorem 2 from Kalandrakis (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=') Let C be the set of candidates and P ⊆ C × C be  the voting record for a given voter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Then the following conditions are equivalent:  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' For all nonempty P ′ ⊆ P, either there exists x ∈ E(C(P ′)) such that x ̸∈ Y (P ′) or there exists a  nonempty P ′′ ⊆ P ′ such that N(P ′′) = Y (P ′′) ⊆ E(C(P ′)) and Y (P ′′) ∩ Y (P ′ \\ P ′′) = ∅.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' There exists a strictly concave utility function that almost strictly rationalizes P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' There exists a strictly quasiconcave utility function that almost strictly rationalizes P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' There exists a strictly concave utility function that rationalizes P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' There exists a strictly quasiconcave utility function that rationalizes P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' □  4  Conclusion  This paper was the first to formalize the preferences of ranked-choice voting and explore what structure  a ballot having those preferences takes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Top-truncated preferences elicit specific types of representations  and utility functions;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' now that these have been identified, a more substantive appraisal of ranked-choice  voting’s value can be done.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  There are also multiple areas of future research that can build upon the results from this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Ayadi  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' (2022) mention the need for normative work on top-truncated preferences, which is especially impor-  tant because these preferences have been shown to be concave (and quasiconcave)—types of preferences  not always assumed to reflect voters’ actual preferences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Whether these preference types are affected  if the utility function accounts for strategic voting is a valuable question to explore.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Coughlin (1983)  addresses utility functions for strategic voting, but in the context of candidates’ utility functions rather  than voters’ utility functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Ranked-choice voting provides both the opportunity for a voter to express  their full set of preferences and the opportunity to vote strategically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' This paper has explored theoretical  properties associated with the former;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' the next step is to see if and where there is an intersection with  the latter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  8  References  Ayadi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=', Amor, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=', & Lang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Approximating voting rules from truncated ballots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Au-  tonomous Agents and Multi-Agent Systems, 36, 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  Board of Elections in the City of New York.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Ranked choice voting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Retrieved May 25, 2022, from  https://vote.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='nyc/page/ranked-choice-voting  Caspard, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=', Monjardet, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=', & Leclerc, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Finite ordered sets: Concepts, results and uses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Cam-  bridge University Press.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  Chambers, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=', & Echenique, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Ordinal notions of submodularity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Journal of Mathematical  Economics, 44, 1243–1245.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  Chambers, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=', & Echenique, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Supermodularity and preferences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Journal of Economic Theory,  144, 1004–1014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  Chambers, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=', Miller, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=', & Yenmez, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Closure and preferences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Journal of Mathematical  Economics, 88, 161–166.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  Chateauneuf, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=', Vergopoulos, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=', & Zhang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Infinite supermodularity and preferences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Eco-  nomic Theory, 63, 99–109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  Coughlin, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' (1983).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Social utility functions for strategic decisions in probabilistic voting models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  Mathematical Social Sciences, 4, 275–293.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  Fitzsimmons, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=', & Lackner, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Incomplete Preferences in Single-Peaked Electorates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Journal of  Artificial Intelligence Research, 67, 797–833.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  Gr¨atzer, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Lattice theory: Foundation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Birkh¨auser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  Kalandrakis, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Rationalizable voting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Theoretical Economics, 5, 93–125.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  Kilgour, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=', Gr´egoire, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=', & Foley, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' The prevalence and consequences of ballot trun-  cation in ranked-choice elections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Public Choice, 184, 197–218.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  Kreps, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' (1979).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' A representation theorem for ‘Preference for Flexibility’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Econometrica, 47, 565–577.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  Menon, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=', & Larson, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Computational aspects of strategic behavior in elections with top-  truncated ballots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Autonomous Agents and Multi-Agent Systems, 31, 1506–1547.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  Nielson, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Ranked Choice Voting and Attitudes toward Democracy in the United States: Results  from a Survey Experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Politics and Policy, 45, 535–570.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  Osborne, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Models in political economy [https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='economics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='utoronto.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='ca/osborne/mpe/mpeDraft20220519.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='pdf(visited  2022-05-31)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  Tajika, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Polarization and inefficient information aggregation under strategic voting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Social  Choice and Welfare, 56, 67–100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  Terzopoulou, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=', & Endriss, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' The Borda class: An axiomatic study of the Borda rule on top-  truncated preferences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Journal of Mathematical Economics, 92, 31–40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='  9  Tomlinson, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=', Ugander, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=', & Kleinberg, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' Ballot length in instant runoff voting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content=' https://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='org/abs/2207.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
+page_content='08958  10' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdE0T4oBgHgl3EQf1QKQ/content/2301.02697v1.pdf'}
diff --git a/RNAzT4oBgHgl3EQf0P4Y/content/tmp_files/2301.01780v1.pdf.txt b/RNAzT4oBgHgl3EQf0P4Y/content/tmp_files/2301.01780v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a8787111659a695610b15002ff04205c31d90638
--- /dev/null
+++ b/RNAzT4oBgHgl3EQf0P4Y/content/tmp_files/2301.01780v1.pdf.txt
@@ -0,0 +1,1353 @@
+Superradiant axion clouds around
+asteroid-mass primordial black holes
+Nuno P. Branco,a Ricardo Z. Ferreira,b Jo˜ao G. Rosaa
+aUniv Coimbra, Faculdade de Ciˆencias e Tecnologia da Universidade de Coimbra and CFisUC,
+Rua Larga, 3004-516 Coimbra, Portugal
+bInstitut de F´ısica d’Altes Energies (IFAE) and Barcelona Institute of Science and Technol-
+ogy (BIST), Campus UAB, 08193 Bellaterra, Barcelona, Spain
+E-mail: popebranco@hotmail.com, rzambujal@ifae.es, jgrosa@uc.pt
+Abstract. We analyze the dynamics and observational signatures of axion clouds formed
+via the superradiant instability around primordial black holes, focusing on the mass range
+1014−1018 kg where the latter may account for all the dark matter. We take into account the
+leading effects of axion self-interactions, showing that, even though these limit the number
+of axions produced within each cloud, a large number of superradiant axions become free of
+the black hole’s gravitational potential and accumulate in the intergalactic medium or even
+in the host galaxy, depending on their escape velocity. This means that primordial black
+hole dark matter may lead to a sizeable astrophysical population of non-relativistic axions,
+with masses ranging from 0.1 eV to 1 MeV, depending on the primordial black hole mass
+and spin.
+We then show that if such axions couple to photons their contribution to the
+galactic and extragalactic background flux, mainly in the X-ray and gamma-ray band of the
+spectrum, is already beyond current observational limits for a large range of parameters that
+are, therefore, excluded. We finish by showing the prospects of the Athena X-ray telescope
+to further probe this co-existence of primordial black holes and axions.
+arXiv:2301.01780v1  [hep-ph]  4 Jan 2023
+
+Contents
+1
+Introduction
+1
+2
+Conditions for efficient superradiance
+3
+3
+Cloud dynamics with self-interactions
+5
+3.1
+Axions within the superradiant cloud
+5
+3.2
+Axions ionized from the cloud
+9
+3.3
+Total number of axions and PBH spin loss
+11
+3.4
+Numerical analysis
+12
+4
+Electromagnetic signatures of superradiant axions
+12
+4.1
+Extragalactic emission
+13
+4.2
+Galactic emission
+14
+4.3
+Discussion of the constraints
+14
+5
+Conclusion
+16
+1
+Introduction
+Superradiant scattering in classical systems was originally considered by Zel’dovich, who
+showed that scalar waves can be amplified upon scattering off a rotating absorbing cylinder,
+provided that their frequency satisfies the superradiance condition ω < mΩ, where m is the
+azimuthal angular momentum quantum number and Ω is the cylinder’s angular velocity [1].
+Rotational superradiance is, in fact, characteristic of any rotating absorbing medium,
+in particular Kerr black holes [2–6]. Over four decades ago, Press and Teukolsky envisaged
+the idea of a “black hole bomb” [7, 8] or superradiant instability, which would result from
+multiple superradiant scatterings induced by enclosing the black hole with a reflecting mirror.
+Although this may a priori seem like a purely academic exercise, a natural mirror-like effect
+occurs for massive fields, which are confined in quasi-bound states by the black hole’s gravi-
+tational potential [9–19]. If these states satisfy the superradiance condition, their occupation
+numbers grow exponentially fast (presumably from small initial quantum fluctuations), lead-
+ing to a cloud of particles surrounding the black hole. This provides an extremely efficient
+particle production mechanism, which is fueled by the black hole’s rotational energy, there-
+fore depleting the latter’s spin down to the angular velocity that saturates the superradiance
+condition, i.e. for which ω = mΩ.
+Since the black hole’s gravitional potential is Coulomb-like at large distances, the spec-
+trum of quasi-bound states for a (spinless) field of mass µ around a black hole of mass M
+has a Hydrogen-like form:
+ℏωn ≃ µc2
+�
+1 − α2
+2n2
+�
+(1.1)
+in the non-relativistic regime where the dimensionless mass coupling
+α = µGM/ℏc ≃ 0.75
+� M
+M⊙
+��
+µ
+10−10eV
+�
+,
+(1.2)
+– 1 –
+
+with n denoting the principal quantum number and M⊙ the solar mass. To leading order, the
+superradiance condition may be recast in the form α < ˜a/2(1 +
+√
+1 − ˜a2), where 0 ≤ ˜a ≤ 1
+is the black hole’s dimensionless spin parameter, so that even for extremal black holes the
+dimensionless mass coupling satisfies α < 1/2 and the spectrum is essentially Hydrogen-like.
+Astrophysical black holes suffer from superradiant instabilities in the presence of ultra-
+light fields, with µ ≲ 10−10 eV. This has attracted a significant interest in the recent literature
+as a novel “laboratory” to probe the existence of such particles, including in particular the
+QCD axion and other axion-like particles1 [20–35], as well as hidden photons or massive
+gravitons [36–40].
+The universe may, however, be (or have been) filled with a large number of much
+lighter black holes, potentially as light as the Planck mass MP ≃ 2.18 × 10−8 kg. These
+primordial black holes (PBHs), originally proposed by Hawking [41, 42], may have formed
+in the early universe through a plethora of possible different mechanisms (see e.g.
+[43–
+45] for recent reviews), and can account for a fraction of the present dark matter density.
+Sub-solar mass PBHs are prone to superradiant instabilities for heavier fields. These can
+include Standard Model particles such as pions [46] but potentially many other novel particles
+predicted in extensions of the Standard Model, including axions and other dark particles [27,
+47], whose mass does not necessarily lie in the above-mentioned ultra-light range. Moreover,
+superradiant instabilities of sub-solar mass PBHs may occur on cosmological timescales even
+if PBHs are born with low spin parameters as we will explicitly discuss here (see also [47]).
+Although the PBH cosmological abundance is quite constrained for a wide range of
+masses [44, 48], PBHs can, in fact, still account for all the dark matter in the present universe
+if they lie in the asteroid-mass range 1014 ≲ M ≲ 1018 kg [44] where they can trigger
+superradiant instabilities of axions with masses in the eV-MeV range. In this work, we study
+the dynamics of axion superradiant instabilities around PBHs in these mass ranges. We will
+show that a significant cosmological axion population may result from PBH superradiance if
+the PBHs account for all the dark matter and such a population can give rise to detectable
+observational signatures if the axion couples to photons.
+In our dynamical study, we will take into account the leading effects of axion self-
+interactions that, albeit suppressed by tiny coupling constants, are greatly enhanced by the
+exponentially large numbers of axions that constitute the superradiant clouds, as shown in
+[49, 50] (see also [51–55]). We will see that, as first pointed out in [50], self-interactions
+may quench the growth of the particle number within the clouds, but that this is achieved
+at the expense of a large number of axions becoming free of the PBH’s gravitational at-
+traction. These “ionized” axions may be confined within the PBH’s host galaxy, if released
+with sufficiently small velocity (α < 10−2 as we will see below), or otherwise travel through
+the intergalactic medium. Hence, even in scenarios where only a small fraction of the ax-
+ions remains bound to the clouds, PBH superradiance is nevertheless a very efficient axion
+production mechanism.
+A key parameter in our analysis will, of course, be the PBH natal spin. On the one
+hand, when PBHs are born from the gravitational collapse of large overdensities once they
+become sub-horizon in a radiation-dominated epoch, typical spin parameters are expected
+to lie at or even below the percent level, ˜a ≲ 0.01 [56–58]. If, on the other hand, PBH
+formation occurs in an early matter-dominated era, the low ambient pressure favours an
+anisotropic collapse and the consequent generation of near-extremal PBHs [59]. While there
+1In this work we will generically refer to these particles as axions.
+– 2 –
+
+may be several other formation mechanisms yielding intermediate spin parameters, we will
+consider these two limiting regimes to illustrate how the PBH spin affects superradiant axion
+production.
+The last ingredient of our study is the possibility that the produced axions decay in
+photon pairs such that PBH superradiance can then contribute, for example, to the galactic
+or extragalactic background flux, distort the CMB or even overheat some galaxies. We will
+use existing limits on the amount of dark matter that can decay into photons [60–65] to
+constrain the axion-photon coupling in the different mass ranges, and we will also briefly
+discuss how future X-ray telescopes such as Athena [66] will further test the co-existence of
+axions and dark matter PBHs.
+This work is organized as follows. In the next section we discuss the axion mass range
+for which superradiant production is efficient and compute the maximum number of axions
+produced. In Section 3 we analyze in detail the dynamics of the superradiant clouds, taking
+into account the PBH’s mass and spin depletion, the effect of axion self-interactions and
+the axion decay into photons. In particular, we analytically compute the number of axions
+generated within the superradiant clouds and the number of axions that get ionized, and
+confirm our results with numerical simulations. In Section 4, we discuss the electromagnetic
+signatures of PBH-axion superradiance associated with the decay of axions into photons
+and use observational data (mainly of galactic and extragalactic background fluxes) to place
+constraints on the axion-photon coupling constant. Finally, we summarize our results and
+discuss future prospects in Section 5.
+2
+Conditions for efficient superradiance
+We start with a short overview of black hole superradiance, discussing the necessary con-
+ditions for it to occur and determining in which cases the superradiant cloud can grow
+significantly within the lifetime of the universe. This will allow us to identify the range of
+masses, of both the PBHs and the axions, for which superradiance can play an important
+role.
+As mentioned above, whilst the superradiance condition is satisfied, numerous axions
+are copiously produced in quasi-bound states in the vicinity of the black hole at the expense
+of its rotational energy, N ∼ ∆J/m. The time scale for the superradiant modes to grow
+depends strongly on the angular momentum number l of the quasi-bound state and decreases
+with α as α−4l−5. Therefore, the fastest growing state has quantum numbers |nlm⟩ = |211⟩
+and is populated much faster than all others. The number of axions in this level grows as
+N2 = exp(Γ2 t) where Γ2 ≡ Γ211 is the the superradiant rate given, for small ˜a, by [8, 11] 2
+Γnlm = 2r+Cnlm(mΩ − ωnlm)α4l+4µ
+(2.2)
+where the coefficient Cnlm is given by
+Cnlm =
+24l+1(n + l)!
+n2l+4(n − l − 1)!
+l�
+k=1
+�
+k2(1 − ˜a)2 − (˜am − 2˜r+α)2�
+(2.3)
+2For large values of ˜a and α the analytical expression for the superradiant rates in eq. 2.2 is no longer
+accurate. A phenomenological expression for Γ211 that provides a good fit in this regime is given by [46]
+Γimp
+211 = Γ211
+�
+1 +
+3
+128
+˜a9/5
+√1 − ˜a
+�r+µ
+˜a
+�6�
+.
+(2.1)
+We will use this corrected expression in this work whenever ˜a and α are large.
+– 3 –
+
+Figure 1.
+Yellow and orange bands are the regions of PBH mass M and axion mass µ where
+the superradiant condition is satisfied and the cloud grows to its maximal value (in the absence of
+interactions) within the lifetime of the universe for two representative values of the initial black hole
+spin: ˜a = 0.01 (yellow band), and ˜a = 0.99 (orange band). Solid lines are iso-countours of α.
+and the radial coordinate of the inner (Cauchy) and outer (event) horizons are given by
+r± = GM ˜r+ = GM(1 ±
+√
+1 − ˜a2), with the angular velocity of the black hole at the event
+horizon being given by Ω = ˜a/(2r+). For slow-rotation ˜a ≪ 1 and small α the rate above
+simplifies to Γ2 ≃ α8µ(˜a − 4α)/24.
+The number of particles in a given state grows until the superradiance condition is
+saturated, i.e. ω = Ω. In the absence of interactions, this happens for the dominant mode
+(|211⟩) at a time tmax = ln (Nmax
+2
+)/Γ2 when the number of axions in this state is
+Nmax
+2
+= ∆J ≃ (˜ai − ˜af) GM2 ,
+(2.4)
+where ˜ai and ˜af = 4α are, respectively, the initial and final spins of the black hole and we
+have neglected the variation of the black hole mass, Mi ≃ Mf, which is a good approximation
+for α ≪ 1 since ∆M/M = α˜a∆J/J. However, superradiance only plays an important role if
+the cloud fills up in a time scale smaller than the age of the universe, i.e.
+tuni ≳ tmax = ln (Nmax
+2
+)/Γ2 .
+(2.5)
+Figure 1 shows the range of PBH and axion masses where the superradiance condition
+and the lifetime condition, eq. 2.5, are simultaneously satisfied for two benchmark values of
+˜a (˜a = 0.01, ˜a = 0.99) that we will consider throughout this work and that, as described
+earlier, are representative of two PBH formation mechanisms: during radiation domination
+(small spin) and during an early matter domination (near extremal).
+As also previously
+– 4 –
+
+106
+660 = p
+α = 0.2
+a = 0.01
+105
+α = 0.01
+104
+α = 0.001
+103
+μ(eV)
+α = 0.0002
+102
+101
+10°
+10-1
+1014
+1015
+1016
+1017
+1018
+M(kg)discussed, we will restrict our analysis to the mass range M ∼ 1014 − 1018 kg for which the
+PBHs can account for all the dark matter [44]. The figure shows that superradiance can
+efficiently produce axions with masses from 0.1 eV to a few keV for slowly spinning PBHs,
+while in the near-extremal limit this range is widened up to MeV masses.
+3
+Cloud dynamics with self-interactions
+In the absence of interactions the number of particles within the superradiant cloud grows un-
+til it reaches its maximal value N ≃ Nmax
+2
+. However, if the bosonic field has self-interactions,
+as in the case of axions, this growth can be quenched significantly. The goal of this section
+is to study the role of self-interactions in the evolution of the cloud.
+We consider the typical axion Lagrangian3
+La ⊃ 1
+2∂µa ∂µa + µ2f2
+a
+�
+1 − cos
+� a
+fa
+��
++ caγγ
+αEM
+8π
+a
+fa
+Fµν ˜F µν ,
+(3.1)
+where a denotes the axion field, αEM is the electromagnetic fine structure constant, fa is the
+axion decay constant and caγγ a dimensionless coefficient proportional to the electromagnetic
+anomaly. In this work, we fix the coefficient caγγ = 1 so that the coupling fa fixes both the
+strength of the self-interactions and the coupling to photons, although our results can be
+easily generalized for other values of this coefficient. For later convenience we also define
+gaγγ ≡ αEM/(2πfa).
+On the one hand, the cosine potential induces self-interactions amongst the axions. For
+a ≪ fa the leading self-interaction term is quartic and characterized by a dimensionless
+coupling λ = µ2/f2
+a ≃ 10−32(µ/keV)2(1010 GeV/fa)2. Although this is typically very small,
+processes within a superradiant cloud are Bose-enhanced by huge factors due to the expo-
+nentially large number of axions, as we will explore below. On the other hand, through the
+axion-photon coupling axions can decay into two photons at a rate
+Γaγγ = g2
+aγγµ3
+64π
+.
+(3.2)
+Although we will consider parametric regimes where this decay has a negligible influence on
+the dynamics of the clouds, it will be crucial when exploring the observational signatures of
+PBH-axion superradiance.
+We will begin by considering the dynamical effects of self-interactions amongst axions
+in the main superradiant bound states. As we will see, this may lead to a significant number
+of axions escaping the cloud.
+3.1
+Axions within the superradiant cloud
+Self-interactions become progressively more important as a approaches fa. The growth of
+the cloud is halted roughly when the quartic self-interactions start to compete with the
+gravitational binding energy, as analyzed in detail in [50].
+The relevant 2 → 2 scattering processes in this dynamics have been identified in [50]
+and involve the superradiant levels |211⟩ and |322⟩, and axions that either escape to infinity
+3Additional couplings of the axion to other Standard Model fields can be considered but do not affect
+our results because we will be consider axions with masses below the electron mass that can only decay into
+photons.
+– 5 –
+
+211
+211
+322
+BH
+322
+322
+211
+∞
+Figure 2. Leading scattering processes for the dynamics of the superradiant cloud: depletion (left),
+and replenishment (right). We follow the notation of [50] and denote the superradiant states by their
+quantum numbers nlm, the states absorbed by the black hole by BH and those that escape the cloud
+by ∞.
+(∞) or are absorbed by the black hole (BH). They can be summarized as (see also Figure
+2):
+Depletion:
+|211⟩ + |211⟩
+ΓD
+−→ BH + |322⟩
+(3.3)
+Replenishment:
+|322⟩ + |322⟩
+ΓR
+−→ ∞ + |211⟩ ,
+(3.4)
+where the nomenclature refers to the effect of these processes on the dominant |211⟩ state,
+and occur respectively at a rate [50]
+ΓD = 4 × 10−7α7λ2h(˜a)µ
+(3.5)
+ΓR = 10−8α4λ2µ ,
+(3.6)
+where we have defined h(˜a) ≡ 1 +
+√
+1 − ˜a2. The axions that escape to infinity have angular
+momentum m = 3 and energy larger than the axion rest mass, while those absorbed by the
+black hole have m = 0, i.e. are in a non-superradiant bound state. Therefore, the latter
+changes the black hole mass but not its spin. To track how the processes above affect the
+evolution of the cloud we solve the following Boltzmann equations for the number of particles
+in the |211⟩ and |322⟩ states, N2 and N3 respectively,4
+dN2
+dt
+= N2 [Γ2 − Γaγγ + N3 (ΓRN3 − 2ΓDN2)]
+(3.7)
+dN3
+dt
+= N3 [Γ3 − Γaγγ + N2 (ΓDN2 − 2ΓRN3)] ,
+(3.8)
+where Γ3 ≡ Γ322 is the superradiance rate of the |322⟩ state given in eq. 2.2. The first terms
+on the right hand side capture the effect of superradiance; the second terms correspond to
+the decays of the axions in the cloud into photons; the third terms incorporate the effects
+of depletion and replenishment due to axion self-scatterings. Superradiance drains spin and
+mass from the black hole by populating the leading superradiant levels but part of the black
+hole mass is recovered in the depletion process. Therefore, the Boltzmann equations above
+need to be complemented by the corresponding evolution equations for the black hole mass
+M and spin J
+dM
+dt
+= −µ (Γ2N2 + Γ3N3 − ΓDN2
+2 N3)
+(3.9)
+dJ
+dt = −(Γ2N2 + 2Γ3N3) .
+(3.10)
+4We neglect stimulation effects that may enhance the decay into photons under certain conditions [27].
+– 6 –
+
+Table 1. Different regimes for the evolution of the superradiant cloud.
+Spin-down
+No
+Incomplete
+Complete
+Fast
+Regime
+fa ≲ fspin-↓
+a
+fspin-↓
+a
+≲ fa ≲ fno-spin
+a
+fno-spin
+a
+≲ fa ≲ fno-eq
+a
+fa > fno-eq
+a
+Equation
+3.15
+3.15, 3.19
+3.19, 3.20
+3.20
+We now proceed to describe the dynamics in more detail. We will neglect the terms
+in Γ3 and Γaγγ in the analysis as they are sub-leading in the range of parameters that we
+consider. However, we explicitly include them in our numerical analysis of the above system
+of equations. The decay rate into photons will be crucial in Section 4 when studying the
+observational signatures of this scenario. We note that there are other sub-leading scattering
+processes, as well as gravitational wave emission, that we are not including but can be found
+in [50].
+Initially, the |211⟩ level starts to grow exponentially fast through the superradiance
+term, Γ2. As N2 grows, the terms in N2
+2 start to move a considerable number of particles to
+the level |322⟩. An equilibrium is eventually reached when
+dN2
+dt
+= dN3
+dt
+= 0
+(3.11)
+and the two levels reach the equilibrium values
+Neq
+2
+=
+2
+ΓD
+�
+ΓRΓ2
+3
+≃ 50
+√
+3
+√˜a − 4α
+α
+�fa
+µ
+�2
+(3.12)
+Neq
+3
+=
+�
+Γ2
+3ΓR
+≃ 2000
+√
+3 α2√
+˜a − 4α
+�fa
+µ
+�2
+,
+(3.13)
+where in the last equalities we have used eqs. 2.2, 3.5 and 3.6 in the slow-rotation limit.
+There are two main conditions that determine the fate of the cloud: 1) whether the
+black hole loses a significant part of its spin within the life-time of the universe; 2) whether
+the equilibrium value is larger or smaller than the maximum number of particles that can be
+produced via superradiance (eq. 2.4). These conditions are connected with the strength of
+self-interactions, controlled by fa, and lead to different regimes in the evolution of the cloud
+that we describe below and summarize in Table 1.
+No spin-down:
+When the interactions are relatively strong (smaller fa), the cloud
+reaches the equilibrium state more quickly, with a smaller equilibrium number of axions
+Neq
+2 . Therefore, the amount of spin extracted from the black hole during the lifetime of
+the universe is rather small and N2 remains at the equilibrium value. We call this the no
+spin-down regime. The emission of axions to infinity is also less efficient because both N2
+and N3 are relatively small.
+To estimate the range of parameters that lie within this regime we compare the time
+scale tJ for the black hole to lose a significant amount of its spin
+tJ ≃ J
+˙J
+≃ ˜aGM2
+Neq
+2 Γ2
+(3.14)
+with the age of the universe. In terms of fa, no spin-down corresponds to
+fa < fspin-↓
+a
+≡ 4.4 × 109
+˜a1/2
+(˜a − 4α)3/4
+�keV
+µ
+�1/2 �4 × 10−4
+α
+�5/2
+GeV .
+(3.15)
+– 7 –
+
+Incomplete spin-down: If fa > fspin-↓
+a
+the equilibrium numbers are larger than in the
+previous regime and, as consequence, tJ < tuni and the PBH spin starts decreasing signifi-
+cantly, therefore considerably reducing the superradiance growth rate Γ2. Nevertheless, as
+long as this rate is sufficiently large to compensate for the cloud’s depletion due to self-
+interactions (Γ2N2 ≫ ΓDN2
+2 N3, ΓRN2
+3 N2), an equilibrium configuration is approximately
+maintained, with N2 ≃ Neq
+2 (t) as given by eq. 3.12 with a decreasing Γ2(t). In this adiabatic
+regime, we may obtain a solution for N2 by substituting N2 ≃ Neq
+2 (t) in the spin evolution
+eq. 3.10 and solving for ˜a (taking into account that Γ3N3 ≪ Γ2N2 and neglecting the PBH
+mass change). An analytical solution can then be obtained for slowly rotating PBHs away
+from the superradiance threshold, ˜a ≳ 4α for which Γ2 ∝ ˜a, yielding:
+N2(t > tJ) =
+Neq
+2
+1 + 1
+2
+Neq
+2
+Nmax
+2
+Γ2(t − tJ)
+,
+(3.16)
+where Neq
+2 refers to the equilibrium value attained before the PBH begins its spin-down at tJ.
+Note that within the age of the universe the present occupation number of the |211⟩ state is
+only significantly reduced compared to its initial equilibrium value if Neq
+2 /N max
+2
+≳ (Γ2tuni)−1.
+Complete spin-down: For even larger values of fa, and so also of Neq
+2 , the adiabatic
+regime is efficient enough to spin-down the BH so much that superradiance is no longer effec-
+tive in populating the cloud and the dynamics becomes instead dominated by the depletion
+and replenishment processes in eqs. 3.3 and 3.4. Once the PBH spins down sufficiently to
+nearly saturate the superradiance condition at tno-spin, we may neglect the superradiance
+terms in the evolution equations for N2 and N3 in eqs. 3.7 and 3.8. The resulting coupled
+system of equations admits solutions of the form N3/N2 = ΓD/(2ΓR) ≡ d ≈ const., such that
+N2 evolves in time as
+N2(t > tno-spin > tJ) =
+Nno-spin
+�
+1 + 3d ΓDN2
+no-spin(t − tno-spin)
+�1/2
+(3.17)
+where Nno-spin is the value of N2 at the time tno-spin. We may estimate tno-spin by matching
+eqs. 3.16 and 3.17 yielding
+tno-spin ≃ 6.8 × 1012
+�keV
+µ
+� �1011GeV
+fa
+�4 �4 × 10−4
+α
+�2
+years .
+(3.18)
+Complete spin-down will occur whenever tno-spin < tuni, which corresponds to decay constants
+fa > fno-spin
+a
+≡ 4.7 × 1011
+�keV
+µ
+�1/4 �4 × 10−4
+α
+�1/2
+GeV .
+(3.19)
+In Figure 3 we show the numerical evolution of N2 for fa = 1011 GeV where the three
+different dynamical stages discussed so far are clearly illustrated: (1) superradiant growth
+until teq, at which the equilibrium is attained; (2) at tJ the PBH starts spinning down
+and the equilibrium value decreases adiabatically until (3) tno-spin, after which superradiance
+shuts down and the dynamics of the cloud is controlled by the self-interactions. We leave a
+more general discussion of the numerical results to Section 3.4, although we note the clear
+agreement between our analytical description and the numerical solution in this figure.
+– 8 –
+
+Figure 3. Numerical evolution (solid red curve) of the number of particles in the dominant |211⟩
+state for a PBH with M = 1014 kg and ˜a = 0.01 and an axion with µ = 1 keV and fa = 1011 GeV.
+The dashed green and blue lines correspond to the analytical solutions in the incomplete spin-down
+and complete spin-down regimes given in eqs. 3.16 and 3.17. Note that although fa = 1011 GeV
+corresponds to the incomplete spin-down regime, here we can also see the complete spin-down phase
+because we have extended the time domain beyond the age of the universe.
+Fast spin-down: The final regime occurs for even larger fa when Neq is so large that the
+cloud saturates at Nmax
+2
+5, i.e. superradiance shuts down before an equilibrium is reached.
+This happens when Neq
+2 > Nmax
+2
+or equivalently for
+fa > fno-eq
+a
+≡ 1.8 × 1013
+�
+α
+4 × 10−4
+�3/2
+(˜a − 4α)1/4 GeV .
+(3.20)
+With the superradiance source turned off, the dynamics is again controlled by self-interactions
+just like in the complete spin-down regime. Therefore, N2 will still evolve like in eq. 3.17
+but with Nno-spin, tno-spin replaced by Nmax
+2
+and tmax. Noteworthy, this is the only regime
+among those we described where most of the axions are still in the cloud today and only
+a small fraction has escaped. However, as we will show in Section 4, when discussing the
+observational impact of the dynamics, the fast spin-down is not yet accessible with current
+data since the associated axion-photon coupling is too small while the total number of axions
+produced remains roughly unchanged.
+3.2
+Axions ionized from the cloud
+So far we have described the dynamics of the axions within the superradiant cloud and we
+have seen that self-interactions can strongly quench its growth. However, the replenishment
+processes in eq. 3.4 (and Figure 2) are continuously producing axions that escape the cloud.
+At the end of the dynamics most of the axions are, in fact, outside the cloud (except in the
+fast spin-down regime where self-interactions play a negligible role). At the same time, the
+5We neglect here the subsequent growth of the cloud through the sub-leading superradiant levels as these
+rates are small and do not affect the dynamics.
+– 9 –
+
+fa = 10llGeV
+teq
+tno-spin
+1041
+1039
+1037
+M
+1035
+ Numerical
+1033
+Incomplete spin-down
+1031
+Complete spin-down
+10
+105
+109
+1013
+t(years)coupling to photons allows these particles to decay into photon pairs at a rate Γaγγ given in
+eq. 3.2. The number of particles that escape the cloud obeys therefore
+dN∞
+dt
+= ΓRN2
+3 N2 − ΓaγγN∞
+(3.21)
+being fully determined by the solutions for N2 and N3 derived in Section 3.1.
+What we have left to understand is the fate of these ionized axions, in particular, if
+they become bounded to the PBH host galaxy and how many of them decay to photons. Let
+us begin by addressing the first point. Conservation of energy in the replenishment process
+implies that the ionized axions are emitted with non-relativistic energy E∞ = α2µ/72 and a
+velocity
+v∞ ≃ α
+6 = 6.7 × 10−5
+�
+α
+4 × 10−4
+�
+.
+(3.22)
+This value needs to be compared with the escape velocity of the host galaxy. Axions with
+v∞ < vesc will be bound to the host galaxy while the remaining ones will escape to the
+intergalactic space. This distinction will be important in the next section when comparing
+the flux of photons from superradiant axion decay with the observational data. In the next
+section we will use X-ray and gamma-ray data from the Milky Way (MW), Andromeda (M31)
+and Segue 1 (Seg1) galaxies, and bounds on the rate of energy injection in the Leo-T galaxy.
+Their escape velocities are respectively given by vMW
+esc
+= 0.0018, vM31
+esc
+= 0.0016, vSeg1
+esc
+= 0.0002
+[67–69] 6. Hence, we conclude that the ionized axions will typically remain bound to the
+host galaxy for slowly rotating black holes with ˜a ≲ 0.01, since the superradiance condition
+requires in this case α ≲ 10−3.
+Secondly, as the number of free axions grows, it is possible that at some point their
+decay rate into photons, i.e. the first term on the right-hand side of eq. 3.21, balances the
+rate at which they are produced via the replenishment processes. This will happen when
+N∞Γaγγ = ΓRN2
+3 N2 .
+(3.23)
+For the range of parameters that we studied in this work, this balance only occurs in the
+no-spin down regime where N2, N3 reached the (constant) equilibrium values in eqs. 3.12
+and 3.13. Therefore, during this phase N∞ will grow linearly in time at the rate ΓRN2
+3 N2
+until it saturates the condition 3.23 at a time
+tdecay ≃ 3.1 × 1010
+�
+fa
+108GeV
+�2 �keV
+µ
+�3
+years
+(3.24)
+when
+N∞ = Neq
+∞ ≡ 1.9 × 1040 (˜a − 4α)3/2
+h(˜a)
+�
+α
+4 × 10−4
+�7 �
+fa
+108GeV
+�4 �keV
+µ
+�4
+.
+(3.25)
+As we can see from eq. 3.24, only for small values of the axion decay constant fa,
+fa ≲ 6.5 × 107� µ
+keV
+�3/2
+GeV
+(3.26)
+6The escape velocity increases as one approaches the galactic center.
+Here, we conservatively use vesc
+evaluated at a kpc distance from the galactic center (except for Segue 1 where the quoted value is estimated
+from the gravitational potential at the center of the galaxy).
+For Leo-T we take vLeo-T
+esc
+= O(10−4) as a
+benchmark value [70].
+– 10 –
+
+Figure 4. Numerical solutions for µ = 1 keV, M = 1014 kg, ˜a = 0.01 and different fa values. In
+red/brown we plot the number of axions in the dominant/sub-dominant superradiant state (N2/N3)
+and in magenta the number of axions that escape the black hole’s gravitational potential (N∞). In
+blue/green we show the variation of the black hole’s mass (M)/angular momentum (J). In cyan we
+plot the maximum allowed axion number (N max
+2
+). Analytical solutions for N2 and N∞ are plotted in
+dashed black between teq ≤ t ≤ tuni where they overlap with the corresponding numerical solutions.
+is the equilibrium reached within the lifetime of the universe. The effects of the decays are
+shown in the upper left corner of Figure 4 where we can see the linear growth of N∞ until
+the equilibrium value Neq
+∞ is attained.
+3.3
+Total number of axions and PBH spin loss
+The spin of the black hole feeds the cloud with axions. Therefore, in the regimes where the
+decay into photons is less efficient than the superradiant axion production (all values of fa
+except those in eq. 3.26 that we discuss below), the final number of axions can be calculated
+by conservation of angular momentum:
+Ntot = N2 + 2N3 + 3N∞ ≃ ∆J
+(3.27)
+where we have used the fact that the axions that are emitted to infinity have angular momen-
+tum m = 3. Moreover, in the previous subsection we concluded that the number of axions
+outside the cloud is larger than the number within the cloud for a broad fa range (see also
+– 11 –
+
+— N² — N3 — N
+W-
+max
+1041
+fa = 10'GeV
+1031
+1021
+1011
+10
+100
+105
+108
+t(years)JNα
+Analytical
+1041
+fa = 10llGeV
+1031
+1021
+1011
+10
+100
+105
+108
+t(years)1041
+fa = 1012GeV
+1031
+1021
+1011
+10
+100
+105
+108
+t(years)1041
+fa = 1014GeV
+1031
+1021
+1011
+10
+100
+105
+108
+t(years)Figure 4). Therefore, ∆J(tuni) ≃ 3N∞(tuni) except for the fast spin-down regime where most
+axions are still bounded to the PBH within the cloud and ∆J(tuni) ≃ Nmax
+2
+.
+The other exception is for fa larger than 3.26 (i.e. small couplings).
+In this case,
+N∞(tuni) ≃ Neq
+∞ ≫ N2, but the total number of photons produced is even larger Nγ(tuni) =
+2 tuniΓaγγNeq
+∞ ≫ Neq
+∞ and this is where most of the black hole spin is dumped.
+3.4
+Numerical analysis
+In Figure 4 we show numerical solutions of the system of equations comprising the Boltzmann
+equations 3.7 and 3.8 for the number of axions in the two main superradiant states, and the
+dynamical equations for the PBH mass and spin, 3.9 and 3.10. We consider a fixed value
+of α = 4 × 10−4 (corresponding to M = 1014 kg and µ = 1 keV) and spin ˜a = 0.01, and
+four different values of fa that are representative of the different regimes identified in Table
+1. In all cases, the PBH mass remains approximately constant throughout the cosmological
+evolution until the present day and the cloud reaches an equilibrium at around 107 years.
+For low values of fa (fa = 107 GeV upper left corner), the cloud is in the no spin-down
+regime and remains approximately stable until today. However, as we increase fa to fa = 1011
+GeV (upper right corner) the system enters the incomplete spin-down regime where the cloud
+reaches a larger equilibrium number that starts to slowly decrease over time as the PBH loses
+a sizeable amount of its spin (green line in Figure 4).
+In the lower left corner we show the evolution in the complete spin-down regime with
+fa = 1012 GeV. In this case, the equilibrium number is so large that the PBH loses spin
+much faster and superradiance eventually shuts down before the present day. Afterwards,
+the dynamics of the cloud is dominated by axion self-interactions.
+Finally the lower right corner shows the evolution for fa = 1014 GeV, within the fast
+spin-down regime, where the cloud reaches the maximal occupation number, at which super-
+radiance shuts down, before reaching the equilibrium state. In this regime, self-interactions
+are rather weak so N2 remains roughly constant and most of the axions are presently still
+within the cloud rather than escaping the latter.
+We end this section by noting that, even though in some cases the axion’s lifetime is
+smaller than the age of the universe, the fact that the superradiant rate Γ2 > Γaγγ enforces
+that the total number of axions is always growing over time. The effect of the decay into
+photon pairs is only significant in the upper left plot of Figure 4 where it halts the growth
+of N∞.
+4
+Electromagnetic signatures of superradiant axions
+We have studied in the previous sections how a population of spinning PBHs may lead to a
+significant axion abundance. If these axions couple to photons they can provide interesting
+electromagnetic (EM) signatures of this co-existence of PBH and relatively heavy axions.
+In this section we will show that in a large range (see Figure 5) of axion and PBH masses,
+these signatures surpass existing observational data, mainly galactic and extragalactic X-ray
+and gamma-ray fluxes, and that upcoming X-ray telescopes may further strengthen these
+constraints.
+To perform the analysis of these EM signals, we need to keep track of the total number
+of axions produced per PBH, both inside and outside the cloud, and their photon emission.
+A relevant quantity is the fraction of the dark matter in superradiant axions, given by
+r = Ntot(tuni) µ
+M
+(4.1)
+– 12 –
+
+where M/µ is the would be number of axions per PBH if axions were all the dark matter
+and Ntot(tuni) ≃ N2 + N∞ is the number of axions produced per PBH in each case, with N2
+and N∞ given in Section 3 for the different regimes.
+We will separate the discussion in two parts. First, we discuss the extragalactic emission,
+which is common to all cases and that originates from the extragalactic density of PBHs.
+Then, we look at situations where the “ionized” axions are bounded to the host galaxy.
+4.1
+Extragalactic emission
+In the analysis of the extragalactic axions we use two different types of constraints.
+For axion masses between 20.4 eV (twice the energy of the Lyman-α line) and a few keV,
+the leading source of extragalactic constraints on the axion-photon coupling are CMB spectral
+distortions. We use the COBE/FIRAS bounds on the rate of dark matter decays into photons
+derived in [62] but re-scaled by the factor r in eq. 4.1, for each value of the axion mass, to
+take into account the fact that the axions produced by PBH superradiance are only a small
+fraction of the dark matter abundance, which we assume is fully accounted for by the PBHs.
+The aforementioned constraints take into account the effects of photon injection throughout
+the cosmic history. We expect that for quasi-stable particles, with lifetimes greater than
+the age of the universe, the largest CMB spectral distortions are generated at the latest
+times, when the relative energy injection into photons ∆ργ/ργ is maximal due to the relative
+enhancement of dark matter over radiation. Therefore, we expect that these constraints are
+also applicable in our scenario where photons are only produced at low redshifts after the
+superradiant production of axions takes place. However, we caution the reader that a more
+accurate translation of the bounds of [62] may require a more detailed analysis.
+For larger masses we estimate the background flux originated from the extragalactic
+axions and impose that it should be smaller than the observed one. We assume that the
+distribution of both the PBHs and the free axions is approximately isotropic. The emission
+rate per unit volume at a time t is given by [71, 72],
+dnγ
+dt (Eγ(t), t) ≃ nPBH(t)Eγ(t) d2Nγ
+dEγdt(Eγ(t), t)
+(4.2)
+where nPBH(t) = Ω0
+PBHρ0(1 + z)3/M is the PBH number density and ΩPBH ≃ 0.24 the
+present PBH abundance, that we fix to the dark matter abundance, and ρ0 ≃ 8.4 × 10−33
+kg cm−3 the critical density today [73]. The redshift (z) factors account for the dilution due
+to the expansion of the universe. We have also approximated the photon emission rate as
+dNγ/dt ≃ Eγ d2Nγ/(dEγdt) [72] where Eγ is the energy of the emitted photon. Since both
+the axions in the cloud and those that are ionized are non-relativistic, we may approximate
+the emission spectrum per PBH, d2Nγ/(dEγdt), as monochromatic [46]
+dNγ
+dEγdt ≃ 2NtotΓaγγ δ (Eγ(t) − µ/2) .
+(4.3)
+where Ntot is the total number of produced axions in eq. 3.27 at a given time. To obtain the
+photon flux, I ≃ nγ(tuni)/(4π) 7, we integrate eq. 4.2 in time until today and find
+I(E) = 3
+4πΩ0
+PBH ρ0 tuni Γaγγ
+Ntot(te)
+M
+� E
+µ/2
+�3/2
+(4.4)
+7We remark that we are using natural units, otherwise a factor c, the speed of light, should appear in the
+relation between I and nγ.
+– 13 –
+
+where te is the time of emission of the photon that arrived today with energy E and that
+can be obtained through the redshift relation 1 + ze(te) = µ/(2E).
+We have used that
+most photons are emitted during the matter-dominated epoch given the timescales involved
+in the dynamics of the superradiant clouds (and neglected the current era of dark energy
+domination).
+The flux at energies E < µ/2 corresponds to the photons emitted before today. As we
+have mentioned at the end of the previous section, the total number of axions never decreases
+over time; the decays into photons at most halt its growth. Therefore, most of the EM flux
+will be due to the non-relativistic axions that are around “today” and so to compare with
+data we simply evaluate the flux at E = µ/2 for each value of the parameters (µ, M, gaγγ).
+We define the excluded regions of parameters as those where the EM flux is larger than the
+double power law fit to the X-ray and gamma-ray background data used in [61].
+4.2
+Galactic emission
+The axions within the cloud and those that are ionized with sufficiently small velocities
+remain bound to the host galaxy.
+Their decay into photons contributes to the galactic
+background fluxes where observational constraints are typically stronger. We assume that
+their density tracks the dark matter profile in the galaxy but, similarly to the COBE/FIRAS
+bounds derived above, with an amplitude that is suppressed by the fraction r in eq. 4.1
+so that we can rescale existing constraints on the rate of dark matter decays into photons
+from the Andromeda [60], Milky Way [63, 64] and Leo-T [65] galaxies. Finally, we study
+the prospects of detection with future ATHENA X-ray telescope using the forecasted bounds
+on dark matter decays into photons from Msec observations of the Segue 1 dwarf spheroidal
+galaxy [66].
+4.3
+Discussion of the constraints
+The resulting constraints in the gaγγ vs µ plane are shown in Figure 5 for slowly rotating
+(˜a = 0.01, top) and extremal (˜a = 0.99, bottom) PBHs, and for different values of their mass
+(in different colors). The constraints are stronger in the case of near-extremal black holes
+because the spin-down of the black hole leads to a larger axion abundance.
+For each value of the PBH mass the boundary of the constrained region is delimited on
+the right (large α) by the superradiance condition and on the left (small α) by the fact that
+the photon flux decreases for smaller axion masses. On the other hand, by increasing fa at
+µ we move from the no spin-down regime into the incomplete spin-down and eventually into
+the complete spin-down region. In the incomplete spin-down region, a sizeable portion of the
+PBH spin is already extracted hence N∞ is almost maximal. Therefore, increasing fa further
+will only decrease the flux, and that is even more so in the complete spin-down where the
+flux decays as f−2
+a .
+In the near-extremal case, there is a sudden change in the constrained region, around
+µ ≃ 30 keV for M = 1014 kg. This change originates from the fact that for larger masses (large
+α) the emitted axions have escape velocities larger than 10−3 and so only the extragalactic
+bounds can be applied, whereas for smaller masses the Milky Way and Andromeda constraints
+on the fluxes can be used. The same logic explains why the forecasted sensitivity of ATHENA
+stops at a few keV; the analysis of [66], used in this work, relies on an observation of the
+Segue 1 galaxy where the escape velocity is of order 10−4.
+Finally, we compare the constraints obtained in this work with existing constraints
+on the axion-photon coupling that do not rely on an initial thermal or dark matter axion
+– 14 –
+
+Figure 5. Constraints on the axion-photon coupling from PBH superradiance, assuming 100% of
+dark matter in 1014 kg (blue), 1016 kg (red), 1018 kg (green) PBHs. The top plot is for PBHs with
+spin ˜a = 0.01 and the bottom plot for ˜a = 0.99. For comparison, we show in gray/black existing
+constraints on axions from globular clusters, SN1987A(γ), solar axions, and freeze-in production at or
+below BBN temperatures [74–78]. The predicted exclusion potential of the future ATHENA telescope
+is shown with a dashed blue line.
+– 15 –
+
+10-9
+Globular clusters
+10-10
+107
+SN1987A()
+SB
+10-11
+108
+10-12
+109
+BBN + Ne
+(GeV-1)
+10-13
+1010
+(GeV)
+10-14
+1011
+10-15
+1012
+10-16
+1013
+10-17
+1014
+10-18
+M = 1015kg
+1015
+M = 1014kg
+a = 0.01
+10-19
+100
+101
+102
+103
+104
+105
+106
+107
+μ(eV)10-9
+Globular clusters
+10-10
+107
+SN1987A()
+10-11
+SB
+108
+10-12
+109
+BBN + Ne
+(GeV-1)
+10-13
+1010
+(GeV)
+10-14
+1011
+10-15
+1012
+Q
+10-16
+1013
+10-17
+1014
+M = 1018kg
+10-18
+M = 10l6kg
+1015
+M = 1014kg
+660 = P
+10-19
+100
+101
+102
+103
+104
+105
+106
+107
+μ(eV)abundance and that originate from: globular clusters [74], axions accumulating in the solar
+basin [75], supernova 1987A [76], and freeze-in production at or below BBN temperatures
+[77, 78]. We have extracted this data from the repository [79]. Our constaints are stronger
+than the existing constraints for a wide range of parameters, particularly in the case of near-
+extremal PBHs for which superradiant axion production is most efficient. X-ray telescopes
+such as ATHENA will be able to probe this scenario even further.
+5
+Conclusion
+PBHs with asteroid-like masses in the range 1014 − 1018 kg can account for all the dark
+mater but are hard to probe due to their minuscule size. In this work, we showed that the
+co-existence of an axion with a 0.1 − 106 eV mass can dramatically change this picture.
+The mechanism underlying our study is black hole superradiance: the draining of the
+black hole’s spin into a densely packed bosonic cloud of a field with mass below the black
+hole’s inverse radius. We considered two benchmark values for the PBH spin parameter,
+slow-spin ˜a = 0.01 and near-extremal ˜a ≃ 0.99, which correspond to PBHs born in the
+radiation era or an early matter era, respectively; and restricted the axion and PBH masses
+to ranges where superradiant clouds form within the age of the universe (c.f. Figure 1).
+Building upon the work of [50], we then studied the cloud’s evolution in the presence
+of the characteristic axionic self-interactions, the main effect of which is to trigger a non-
+linear mixing between the two dominant superradiant states, |211⟩ and |322⟩, alongside with
+axion reabsorption by the black hole and emission to infinity of axions ionized from the
+superradiant cloud.
+We studied the dynamics of the system by solving numerically and
+analytically a coupled set of Boltzmann equations for the number of particles in the leading
+superradiant levels alongside the evolution equations for the PBH mass and spin.
+We identified four main regimes in the dynamics (c.f. Table 1), that are characterized
+by different ranges of the axion decay constant fa, and provided an accurate analytical
+description in Section 3.1. In all regimes the cloud starts growing exponentially due to the
+superradiant instability, which occurs on cosmological timescales even for slowly spinning
+PBHs. However, when self-interactions are strong fa < fspin-↓
+a
+, the cloud quickly reaches
+an equilibrium state where the occupation numbers of the leading superradiant levels are
+approximately constant. This is sustained by the superradiant instability that continuously
+drains spin from the PBH but at a slower rate. We labelled this regime no spin-down.
+For fspin-↓
+a
+< fa < fno-spin
+a
+, self-interactions become less efficient and the quenched
+equilibrium is reached later, when the cloud is denser. To keep this denser equilibrium, the
+black hole has to lose spin at a much faster rate and so, after some time, it eventually loses a
+significant portion of its initial spin. At this point, the system enters a new adiabatic regime
+where both the spin and the equilibrium numbers decrease slowly. This is the incomplete
+spin-down regime. The complete spin-down regime occurs for even weaker self-interactions,
+fno-spin
+a
+< fa < fno-eq
+a
+, when the adiabatic regime is able to drain so much spin that the
+superradiance condition is no longer satisfied and the black hole can no longer refill the
+cloud. From then on, the fate of the cloud is fully determined by the self-interactions that
+continue dissipating axions to infinity and back into the black hole (through non-superradiant
+bound states). Finally, for fa > fno-eq
+a
+, self-interactions are so weak that the cloud reaches its
+maximal occupation number, by shutting down the (leading) superradiant instability before
+any quenched equilibrium is reached. This fast spin-down regime is equivalent in its dynamics
+to the vanilla case of superradiance of a non-interacting massive bosonic field.
+– 16 –
+
+In the last three regimes mentioned above (incomplete, complete and fast spin-down)
+the PBH loses a significant part of its spin before the present day. This energy is lost into
+axions that either escaped to infinity (incomplete and complete spin-down) or are still mostly
+within the cloud (fast spin-down). Therefore, the final axion abundance can be very large, in
+particular in the case of highly-spinning PBHs, and this begged the question, what happens
+to these axions? Can they give observational signatures of this scenario?
+We addressed this in Section 4 where we assumed that the produced axions decay
+into photons, with a rate directly related to the strength of their self-interactions (i.e. we
+set the electromagnetic anomaly coefficient in eq. 3.1 to one), and explored the resulting
+electromagnetic signals assuming a monochromatic PBH spectrum accounting for all dark
+matter. We identified two main signatures: i) an extragalactic photon flux that results from
+the decay of axions produced by the cosmological PBH population; and ii) galactic fluxes
+from the axions that are ionized from the cloud with a velocity below the host galaxy’s
+escape velocity. We imposed constraints from galactic and extragalactic (X-ray and gamma-
+ray) background data, and existing constraints on the rate of dark matter decay into photons
+from COBE/FIRAS and the Leo-T dwarf galaxy (see Section 4 for more details), all properly
+rescaled to account for the axion abundance, to derive bounds on the axion mass and decay
+constant fa. Finally, we have also shown how future X-ray telescopes such as ATHENA will
+be able to further probe this scenario. These results are summarized in Figure 5 and show
+that the assumption of PBH dark matter excludes the existence of 20−106 eV axions coupled
+to photons for a broad range of fa values, depending on the PBH mass and spin.
+There are a few interesting aspects that would be interesting to further explore in
+the future. A sub-leading effect that we have discarded in our analysis is the emission of
+gravitational waves by the axion clouds.
+Although this has no significant impact on the
+dynamics, it may potentially provide additional observational signals. Given that typically
+only a very small fraction of the PBH mass is transferred to the superradiant clouds, observing
+individual clouds is virtually impossible, but the large PBH abundance may potentially lead
+to an observable stochastic background, which we plan to investigate in the future.
+In our analysis we have followed the results obtained in [50] in what concerns the leading
+effects of axion self-interactions. Since the dimensionless mass coupling α < 1/2 in all cases
+considered, we expect a non-relativistic approach to be at least a reasonable approximation,
+although one may expect considerable corrections for the larger α values attained in the
+near-extremal regime such as the Bosenova regimes observed in [51, 52, 54, 55].
+In addition, this analysis also neglects higher-order interactions (from the axion poten-
+tial). Even though the equilibrium number of axions within the cloud is always sufficiently
+small that the field value a ≲ fa, it would be interesting to take a closer look into the signif-
+icance of higher-dimensional interactions leading to multiple axion scattering processes, as
+well as into how non-linearities affect the cloud’s density profile and growth rate [55].
+Our results should therefore be viewed in the light of the approximations employed and
+motivate a further exploration of these issues. Nevertheless, an important take-home message
+of this work is that self-interactions only change the timescale at which the PBH lose most of
+its spin. Given enough time, the total number of axions produced (whether they remain or
+not bound to the black hole) approaches the maximum number produced in the absence of
+self-interactions, up to O(1) factors. In our analysis, we have found that this occurs within
+the universe’s age in most cases except for very low values of the axion decay constant.
+We hope that our results motivate further studies of PBH superradiance and of its
+relevance for fundamental particle physics and cosmology.
+– 17 –
+
+Acknowledgements
+RZF is supported by the Direcci´o General de Recerca del Departament d’Empresa i Coneix-
+ement (DGR) and by the EC through the program Marie Sk�lodowska-Curie COFUND (GA
+801370)-Beatriu de Pinos. NPB is supported by Centro de F´ısica da Universidade de Coim-
+bra (CFisUC) and by Funda¸c˜ao para a Ciˆencia e a Tecnologia, I.P./MCTES through national
+funds (PIDDAC). This work was supported by the CFisUC project No. UID/FIS/04564/2020
+and by the FCT-CERN grant No. CERN/FIS-PAR/0027/2021.
+References
+[1] Y.B. Zel’dovich, Pis’ ma zh. eksp. teor. fiz. 14, 270 (1971)[jetp lett. 14, 180 (1971)], Zh. Eksp.
+Teor. Fiz 62 (1972) 2076.
+[2] A.A. Starobinsky, Amplification of waves reflected from a rotating ”black hole”., Sov. Phys.
+JETP 37 (1973) 28.
+[3] A.A. Starobinsky and S.M. Churilov, Zh. Eksp. Teor. Fiz 65, 3 (1973) [Sov. Phys. JETP 38, 1
+(1973)] .
+[4] S.A. Teukolsky, Perturbations of a rotating black hole. 1. Fundamental equations for
+gravitational electromagnetic and neutrino field perturbations, Astrophys. J. 185 (1973) 635.
+[5] W.H. Press and S.A. Teukolsky, Perturbations of a Rotating Black Hole. II. Dynamical
+Stability of the Kerr Metric, Astrophys. J. 185 (1973) 649.
+[6] S.A. Teukolsky and W.H. Press, Perturbations of a rotating black hole. III - Interaction of the
+hole with gravitational and electromagnet ic radiation, Astrophys. J. 193 (1974) 443.
+[7] W.H. Press and S.A. Teukolsky, Floating Orbits, Superradiant Scattering and the Black-hole
+Bomb, Nature 238 (1972) 211.
+[8] V. Cardoso, O.J.C. Dias, J.P.S. Lemos and S. Yoshida, The Black hole bomb and superradiant
+instabilities, Phys. Rev. D 70 (2004) 044039 [hep-th/0404096].
+[9] T. Damour, N. Deruelle and R. Ruffini, On Quantum Resonances in Stationary Geometries,
+Lett. Nuovo Cim. 15 (1976) 257.
+[10] T.J.M. Zouros and D.M. Eardley, INSTABILITIES OF MASSIVE SCALAR
+PERTURBATIONS OF A ROTATING BLACK HOLE, Annals Phys. 118 (1979) 139.
+[11] S.L. Detweiler, KLEIN-GORDON EQUATION AND ROTATING BLACK HOLES, Phys.
+Rev. D 22 (1980) 2323.
+[12] H. Furuhashi and Y. Nambu, Instability of massive scalar fields in Kerr-Newman space-time,
+Prog. Theor. Phys. 112 (2004) 983 [gr-qc/0402037].
+[13] V. Cardoso and S. Yoshida, Superradiant instabilities of rotating black branes and strings,
+JHEP 07 (2005) 009 [hep-th/0502206].
+[14] S.R. Dolan, Instability of the massive Klein-Gordon field on the Kerr spacetime, Phys. Rev. D
+76 (2007) 084001 [0705.2880].
+[15] J.G. Rosa, The Extremal black hole bomb, JHEP 06 (2010) 015 [0912.1780].
+[16] S.R. Dolan, Superradiant instabilities of rotating black holes in the time domain, Phys. Rev. D
+87 (2013) 124026 [1212.1477].
+[17] W.E. East and F. Pretorius, Superradiant Instability and Backreaction of Massive Vector
+Fields around Kerr Black Holes, Phys. Rev. Lett. 119 (2017) 041101 [1704.04791].
+[18] W.E. East, Superradiant instability of massive vector fields around spinning black holes in the
+relativistic regime, Phys. Rev. D 96 (2017) 024004 [1705.01544].
+– 18 –
+
+[19] S.R. Dolan, Instability of the Proca field on Kerr spacetime, Phys. Rev. D 98 (2018) 104006
+[1806.01604].
+[20] A. Arvanitaki, S. Dimopoulos, S. Dubovsky, N. Kaloper and J. March-Russell, String Axiverse,
+Phys. Rev. D 81 (2010) 123530 [0905.4720].
+[21] A. Arvanitaki and S. Dubovsky, Exploring the String Axiverse with Precision Black Hole
+Physics, Phys. Rev. D 83 (2011) 044026 [1004.3558].
+[22] J.G. Rosa, Boosted black string bombs, JHEP 02 (2013) 014 [1209.4211].
+[23] H. Witek, V. Cardoso, A. Ishibashi and U. Sperhake, Superradiant instabilities in astrophysical
+systems, Phys. Rev. D 87 (2013) 043513 [1212.0551].
+[24] R. Brito, V. Cardoso and P. Pani, Black holes as particle detectors: evolution of superradiant
+instabilities, Class. Quant. Grav. 32 (2015) 134001 [1411.0686].
+[25] A. Arvanitaki, M. Baryakhtar, S. Dimopoulos, S. Dubovsky and R. Lasenby, Black Hole
+Mergers and the QCD Axion at Advanced LIGO, Phys. Rev. D 95 (2017) 043001 [1604.03958].
+[26] R. Brito, S. Ghosh, E. Barausse, E. Berti, V. Cardoso, I. Dvorkin et al., Stochastic and
+resolvable gravitational waves from ultralight bosons, Phys. Rev. Lett. 119 (2017) 131101
+[1706.05097].
+[27] J.G. Rosa and T.W. Kephart, Stimulated Axion Decay in Superradiant Clouds around
+Primordial Black Holes, Phys. Rev. Lett. 120 (2018) 231102 [1709.06581].
+[28] D. Baumann, H.S. Chia and R.A. Porto, Probing Ultralight Bosons with Binary Black Holes,
+Phys. Rev. D 99 (2019) 044001 [1804.03208].
+[29] T. Ikeda, R. Brito and V. Cardoso, Blasts of Light from Axions, Phys. Rev. Lett. 122 (2019)
+081101 [1811.04950].
+[30] E. Berti, R. Brito, C.F.B. Macedo, G. Raposo and J.L. Rosa, Ultralight boson cloud depletion
+in binary systems, Phys. Rev. D 99 (2019) 104039 [1904.03131].
+[31] D. Baumann, H.S. Chia, J. Stout and L. ter Haar, The Spectra of Gravitational Atoms, JCAP
+12 (2019) 006 [1908.10370].
+[32] V. Cardoso, O.J.C. Dias, G.S. Hartnett, M. Middleton, P. Pani and J.E. Santos, Constraining
+the mass of dark photons and axion-like particles through black-hole superradiance, JCAP 03
+(2018) 043 [1801.01420].
+[33] T.D.P. Edwards, M. Chianese, B.J. Kavanagh, S.M. Nissanke and C. Weniger, Unique
+Multimessenger Signal of QCD Axion Dark Matter, Phys. Rev. Lett. 124 (2020) 161101
+[1905.04686].
+[34] V.M. Mehta, M. Demirtas, C. Long, D.J.E. Marsh, L. Mcallister and M.J. Stott, Superradiance
+Exclusions in the Landscape of Type IIB String Theory, 2011.08693.
+[35] D. Blas and S.J. Witte, Imprints of Axion Superradiance in the CMB, Phys. Rev. D 102
+(2020) 103018 [2009.10074].
+[36] J.G. Rosa and S.R. Dolan, Massive vector fields on the Schwarzschild spacetime: quasi-normal
+modes and bound states, Phys. Rev. D 85 (2012) 044043 [1110.4494].
+[37] P. Pani, V. Cardoso, L. Gualtieri, E. Berti and A. Ishibashi, Perturbations of slowly rotating
+black holes: massive vector fields in the Kerr metric, Phys. Rev. D 86 (2012) 104017
+[1209.0773].
+[38] R. Brito, V. Cardoso and P. Pani, Massive spin-2 fields on black hole spacetimes: Instability of
+the Schwarzschild and Kerr solutions and bounds on the graviton mass, Phys. Rev. D 88 (2013)
+023514 [1304.6725].
+– 19 –
+
+[39] M. Baryakhtar, R. Lasenby and M. Teo, Black Hole Superradiance Signatures of Ultralight
+Vectors, Phys. Rev. D 96 (2017) 035019 [1704.05081].
+[40] A. Caputo, S.J. Witte, D. Blas and P. Pani, Electromagnetic signatures of dark photon
+superradiance, Phys. Rev. D 104 (2021) 043006 [2102.11280].
+[41] S. Hawking, Gravitationally collapsed objects of very low mass, Mon. Not. Roy. Astron. Soc.
+152 (1971) 75.
+[42] B.J. Carr and S.W. Hawking, Black holes in the early Universe, Mon. Not. Roy. Astron. Soc.
+168 (1974) 399.
+[43] C.T. Byrnes and P.S. Cole, Lecture notes on inflation and primordial black holes, 12, 2021
+[2112.05716].
+[44] A.M. Green and B.J. Kavanagh, Primordial black holes as a dark matter candidate, Journal of
+Physics G: Nuclear and Particle Physics 48 (2021) 043001.
+[45] B. Carr, F. Kuhnel and M. Sandstad, Primordial Black Holes as Dark Matter, Phys. Rev. D 94
+(2016) 083504 [1607.06077].
+[46] P.B. Ferraz, T.W. Kephart and J.a.G. Rosa, Superradiant pion clouds around primordial black
+holes, JCAP 07 (2022) 026 [2004.11303].
+[47] J. March-Russell and J.a.G. Rosa, Micro-Bose/Proca dark matter stars from black hole
+superradiance, 2205.15277.
+[48] B. Carr, K. Kohri, Y. Sendouda and J. Yokoyama, Constraints on primordial black holes, Rept.
+Prog. Phys. 84 (2021) 116902 [2002.12778].
+[49] A. Gruzinov, Black Hole Spindown by Light Bosons, 1604.06422.
+[50] M. Baryakhtar, M. Galanis, R. Lasenby and O. Simon, Black hole superradiance of
+self-interacting scalar fields, Phys. Rev. D 103 (2021) 095019 [2011.11646].
+[51] H. Yoshino and H. Kodama, Bosenova collapse of axion cloud around a rotating black hole,
+Prog. Theor. Phys. 128 (2012) 153 [1203.5070].
+[52] H. Yoshino and H. Kodama, The bosenova and axiverse, Class. Quant. Grav. 32 (2015) 214001
+[1505.00714].
+[53] H. Omiya, T. Takahashi and T. Tanaka, Renormalization group analysis of superradiant growth
+of self-interacting axion cloud, PTEP 2021 (2021) 043E02 [2012.03473].
+[54] H. Omiya, T. Takahashi, T. Tanaka and H. Yoshino, Impact of multiple modes on the evolution
+of self-interacting axion condensate around rotating black holes, 2211.01949.
+[55] H. Omiya, T. Takahashi and T. Tanaka, Adiabatic evolution of the self-interacting axion field
+around rotating black holes, PTEP 2022 (2022) 043E03 [2201.04382].
+[56] T. Chiba and S. Yokoyama, Spin Distribution of Primordial Black Holes, PTEP 2017 (2017)
+083E01 [1704.06573].
+[57] V. De Luca, V. Desjacques, G. Franciolini, A. Malhotra and A. Riotto, The initial spin
+probability distribution of primordial black holes, JCAP 05 (2019) 018 [1903.01179].
+[58] M. Mirbabayi, A. Gruzinov and J. Nore˜na, Spin of primordial black holes, Journal of
+Cosmology and Astroparticle Physics 2020 (2020) 017.
+[59] T. Harada, C.-M. Yoo, K. Kohri and K.-I. Nakao, Spins of primordial black holes formed in the
+matter-dominated phase of the universe, Physical Review D 96 (2017) .
+[60] K.C.Y. Ng, B.M. Roach, K. Perez, J.F. Beacom, S. Horiuchi, R. Krivonos et al., New
+Constraints on Sterile Neutrino Dark Matter from NuSTAR M31 Observations, Phys. Rev. D
+99 (2019) 083005 [1901.01262].
+– 20 –
+
+[61] G. Ballesteros, J. Coronado-Bl´azquez and D. Gaggero, X-ray and gamma-ray limits on the
+primordial black hole abundance from Hawking radiation, Phys. Lett. B 808 (2020) 135624
+[1906.10113].
+[62] B. Bolliet, J. Chluba and R. Battye, Spectral distortion constraints on photon injection from
+low-mass decaying particles, Mon. Not. Roy. Astron. Soc. 507 (2021) 3148 [2012.07292].
+[63] R. Laha, J.B. Mu˜noz and T.R. Slatyer, INTEGRAL constraints on primordial black holes and
+particle dark matter, Phys. Rev. D 101 (2020) 123514 [2004.00627].
+[64] J.W. Foster, M. Kongsore, C. Dessert, Y. Park, N.L. Rodd, K. Cranmer et al., Deep Search for
+Decaying Dark Matter with XMM-Newton Blank-Sky Observations, Phys. Rev. Lett. 127 (2021)
+051101 [2102.02207].
+[65] D. Wadekar and Z. Wang, Strong constraints on decay and annihilation of dark matter from
+heating of gas-rich dwarf galaxies, Phys. Rev. D 106 (2022) 075007 [2111.08025].
+[66] A. Neronov and D. Malyshev, Toward a full test of the νMSM sterile neutrino dark matter
+model with Athena, Phys. Rev. D 93 (2016) 063518 [1509.02758].
+[67] A.J. Deason, A. Fattahi, V. Belokurov, N.W. Evans, R.J.J. Grand, F. Marinacci et al., The
+local high-velocity tail and the Galactic escape speed, 1901.02016.
+[68] P.R. Kafle, S. Sharma, G.F. Lewis, A.S.G. Robotham and S.P. Driver, The Need for Speed:
+Escape velocity and dynamical mass measurements of the Andromeda galaxy, Mon. Not. Roy.
+Astron. Soc. 475 (2018) 4043 [1801.03949].
+[69] A.N. Baushev, S. Federici and M. Pohl, Spectral analysis of the gamma-ray background near the
+dwarf Milky Way satellite Segue 1: Improved limits on the cross section of neutralino dark
+matter annihilation, Phys. Rev. D 86 (2012) 063521 [1205.3620].
+[70] Y. Faerman, A. Sternberg and C.F. McKee, Ultra-Compact High Velocity Clouds as Minihalos
+and Dwarf Galaxies, Astrophys. J. 777 (2013) 119 [1309.0815].
+[71] E. Masso and R. Toldra, New constraints on a light spinless particle coupled to photons, Phys.
+Rev. D 55 (1997) 7967 [hep-ph/9702275].
+[72] B.J. Carr, K. Kohri, Y. Sendouda and J. Yokoyama, New cosmological constraints on
+primordial black holes, Phys. Rev. D 81 (2010) 104019 [0912.5297].
+[73] Planck collaboration, Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys.
+641 (2020) A6 [1807.06209].
+[74] A. Ayala, I. Dom´ınguez, M. Giannotti, A. Mirizzi and O. Straniero, Revisiting the bound on
+axion-photon coupling from Globular Clusters, Phys. Rev. Lett. 113 (2014) 191302 [1406.6053].
+[75] W. DeRocco, S. Wegsman, B. Grefenstette, J. Huang and K. Van Tilburg, First Indirect
+Detection Constraints on Axions in the Solar Basin, Phys. Rev. Lett. 129 (2022) 101101
+[2205.05700].
+[76] J. Jaeckel, P.C. Malta and J. Redondo, Decay photons from the axionlike particles burst of type
+II supernovae, Phys. Rev. D 98 (2018) 055032 [1702.02964].
+[77] P.F. Depta, M. Hufnagel and K. Schmidt-Hoberg, Robust cosmological constraints on axion-like
+particles, JCAP 05 (2020) 009 [2002.08370].
+[78] K. Langhoff, N.J. Outmezguine and N.L. Rodd, Irreducible Axion Background, Phys. Rev. Lett.
+129 (2022) 241101 [2209.06216].
+[79] C. O’Hare, “cajohare/axionlimits: Axionlimits.”
+https://cajohare.github.io/AxionLimits/, July, 2020. 10.5281/zenodo.3932430.
+– 21 –
+
diff --git a/RNAzT4oBgHgl3EQf0P4Y/content/tmp_files/load_file.txt b/RNAzT4oBgHgl3EQf0P4Y/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..2f2ddf9843c1086457c0253d926b4a4025035c9d
--- /dev/null
+++ b/RNAzT4oBgHgl3EQf0P4Y/content/tmp_files/load_file.txt
@@ -0,0 +1,1103 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf,len=1102
+page_content='Superradiant axion clouds around  asteroid-mass primordial black holes  Nuno P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Branco,a Ricardo Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Ferreira,b Jo˜ao G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Rosaa  aUniv Coimbra, Faculdade de Ciˆencias e Tecnologia da Universidade de Coimbra and CFisUC,  Rua Larga, 3004-516 Coimbra, Portugal  bInstitut de F´ısica d’Altes Energies (IFAE) and Barcelona Institute of Science and Technol-  ogy (BIST), Campus UAB, 08193 Bellaterra, Barcelona, Spain  E-mail: popebranco@hotmail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='com, rzambujal@ifae.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='es, jgrosa@uc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='pt  Abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' We analyze the dynamics and observational signatures of axion clouds formed  via the superradiant instability around primordial black holes, focusing on the mass range  1014−1018 kg where the latter may account for all the dark matter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' We take into account the  leading effects of axion self-interactions, showing that, even though these limit the number  of axions produced within each cloud, a large number of superradiant axions become free of  the black hole’s gravitational potential and accumulate in the intergalactic medium or even  in the host galaxy, depending on their escape velocity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' This means that primordial black  hole dark matter may lead to a sizeable astrophysical population of non-relativistic axions,  with masses ranging from 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='1 eV to 1 MeV, depending on the primordial black hole mass  and spin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  We then show that if such axions couple to photons their contribution to the  galactic and extragalactic background flux, mainly in the X-ray and gamma-ray band of the  spectrum, is already beyond current observational limits for a large range of parameters that  are, therefore, excluded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' We finish by showing the prospects of the Athena X-ray telescope  to further probe this co-existence of primordial black holes and axions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='01780v1  [hep-ph]  4 Jan 2023  Contents  1  Introduction  1  2  Conditions for efficient superradiance  3  3  Cloud dynamics with self-interactions  5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='1  Axions within the superradiant cloud  5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='2  Axions ionized from the cloud  9  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='3  Total number of axions and PBH spin loss  11  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='4  Numerical analysis  12  4  Electromagnetic signatures of superradiant axions  12  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='1  Extragalactic emission  13  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='2  Galactic emission  14  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='3  Discussion of the constraints  14  5  Conclusion  16  1  Introduction  Superradiant scattering in classical systems was originally considered by Zel’dovich, who  showed that scalar waves can be amplified upon scattering off a rotating absorbing cylinder,  provided that their frequency satisfies the superradiance condition ω < mΩ, where m is the  azimuthal angular momentum quantum number and Ω is the cylinder’s angular velocity [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  Rotational superradiance is, in fact, characteristic of any rotating absorbing medium,  in particular Kerr black holes [2–6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Over four decades ago, Press and Teukolsky envisaged  the idea of a “black hole bomb” [7, 8] or superradiant instability, which would result from  multiple superradiant scatterings induced by enclosing the black hole with a reflecting mirror.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  Although this may a priori seem like a purely academic exercise, a natural mirror-like effect  occurs for massive fields, which are confined in quasi-bound states by the black hole’s gravi-  tational potential [9–19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' If these states satisfy the superradiance condition, their occupation  numbers grow exponentially fast (presumably from small initial quantum fluctuations), lead-  ing to a cloud of particles surrounding the black hole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' This provides an extremely efficient  particle production mechanism, which is fueled by the black hole’s rotational energy, there-  fore depleting the latter’s spin down to the angular velocity that saturates the superradiance  condition, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' for which ω = mΩ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  Since the black hole’s gravitional potential is Coulomb-like at large distances, the spec-  trum of quasi-bound states for a (spinless) field of mass µ around a black hole of mass M  has a Hydrogen-like form:  ℏωn ≃ µc2  �  1 − α2  2n2  �  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='1)  in the non-relativistic regime where the dimensionless mass coupling  α = µGM/ℏc ≃ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='75  � M  M⊙  ��  µ  10−10eV  �  ,  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='2)  – 1 –  with n denoting the principal quantum number and M⊙ the solar mass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' To leading order, the  superradiance condition may be recast in the form α < ˜a/2(1 +  √  1 − ˜a2), where 0 ≤ ˜a ≤ 1  is the black hole’s dimensionless spin parameter, so that even for extremal black holes the  dimensionless mass coupling satisfies α < 1/2 and the spectrum is essentially Hydrogen-like.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  Astrophysical black holes suffer from superradiant instabilities in the presence of ultra-  light fields, with µ ≲ 10−10 eV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' This has attracted a significant interest in the recent literature  as a novel “laboratory” to probe the existence of such particles, including in particular the  QCD axion and other axion-like particles1 [20–35], as well as hidden photons or massive  gravitons [36–40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  The universe may, however, be (or have been) filled with a large number of much  lighter black holes, potentially as light as the Planck mass MP ≃ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='18 × 10−8 kg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' These  primordial black holes (PBHs), originally proposed by Hawking [41, 42], may have formed  in the early universe through a plethora of possible different mechanisms (see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [43–  45] for recent reviews), and can account for a fraction of the present dark matter density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  Sub-solar mass PBHs are prone to superradiant instabilities for heavier fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' These can  include Standard Model particles such as pions [46] but potentially many other novel particles  predicted in extensions of the Standard Model, including axions and other dark particles [27,  47], whose mass does not necessarily lie in the above-mentioned ultra-light range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Moreover,  superradiant instabilities of sub-solar mass PBHs may occur on cosmological timescales even  if PBHs are born with low spin parameters as we will explicitly discuss here (see also [47]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  Although the PBH cosmological abundance is quite constrained for a wide range of  masses [44, 48], PBHs can, in fact, still account for all the dark matter in the present universe  if they lie in the asteroid-mass range 1014 ≲ M ≲ 1018 kg [44] where they can trigger  superradiant instabilities of axions with masses in the eV-MeV range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' In this work, we study  the dynamics of axion superradiant instabilities around PBHs in these mass ranges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' We will  show that a significant cosmological axion population may result from PBH superradiance if  the PBHs account for all the dark matter and such a population can give rise to detectable  observational signatures if the axion couples to photons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  In our dynamical study, we will take into account the leading effects of axion self-  interactions that, albeit suppressed by tiny coupling constants, are greatly enhanced by the  exponentially large numbers of axions that constitute the superradiant clouds, as shown in  [49, 50] (see also [51–55]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' We will see that, as first pointed out in [50], self-interactions  may quench the growth of the particle number within the clouds, but that this is achieved  at the expense of a large number of axions becoming free of the PBH’s gravitational at-  traction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' These “ionized” axions may be confined within the PBH’s host galaxy, if released  with sufficiently small velocity (α < 10−2 as we will see below), or otherwise travel through  the intergalactic medium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Hence, even in scenarios where only a small fraction of the ax-  ions remains bound to the clouds, PBH superradiance is nevertheless a very efficient axion  production mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  A key parameter in our analysis will, of course, be the PBH natal spin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' On the one  hand, when PBHs are born from the gravitational collapse of large overdensities once they  become sub-horizon in a radiation-dominated epoch, typical spin parameters are expected  to lie at or even below the percent level, ˜a ≲ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='01 [56–58].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' If, on the other hand, PBH  formation occurs in an early matter-dominated era, the low ambient pressure favours an  anisotropic collapse and the consequent generation of near-extremal PBHs [59].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' While there  1In this work we will generically refer to these particles as axions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  – 2 –  may be several other formation mechanisms yielding intermediate spin parameters, we will  consider these two limiting regimes to illustrate how the PBH spin affects superradiant axion  production.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  The last ingredient of our study is the possibility that the produced axions decay in  photon pairs such that PBH superradiance can then contribute, for example, to the galactic  or extragalactic background flux, distort the CMB or even overheat some galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' We will  use existing limits on the amount of dark matter that can decay into photons [60–65] to  constrain the axion-photon coupling in the different mass ranges, and we will also briefly  discuss how future X-ray telescopes such as Athena [66] will further test the co-existence of  axions and dark matter PBHs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  This work is organized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' In the next section we discuss the axion mass range  for which superradiant production is efficient and compute the maximum number of axions  produced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' In Section 3 we analyze in detail the dynamics of the superradiant clouds, taking  into account the PBH’s mass and spin depletion, the effect of axion self-interactions and  the axion decay into photons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' In particular, we analytically compute the number of axions  generated within the superradiant clouds and the number of axions that get ionized, and  confirm our results with numerical simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' In Section 4, we discuss the electromagnetic  signatures of PBH-axion superradiance associated with the decay of axions into photons  and use observational data (mainly of galactic and extragalactic background fluxes) to place  constraints on the axion-photon coupling constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Finally, we summarize our results and  discuss future prospects in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  2  Conditions for efficient superradiance  We start with a short overview of black hole superradiance, discussing the necessary con-  ditions for it to occur and determining in which cases the superradiant cloud can grow  significantly within the lifetime of the universe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' This will allow us to identify the range of  masses, of both the PBHs and the axions, for which superradiance can play an important  role.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  As mentioned above, whilst the superradiance condition is satisfied, numerous axions  are copiously produced in quasi-bound states in the vicinity of the black hole at the expense  of its rotational energy, N ∼ ∆J/m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' The time scale for the superradiant modes to grow  depends strongly on the angular momentum number l of the quasi-bound state and decreases  with α as α−4l−5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Therefore, the fastest growing state has quantum numbers |nlm⟩ = |211⟩  and is populated much faster than all others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' The number of axions in this level grows as  N2 = exp(Γ2 t) where Γ2 ≡ Γ211 is the the superradiant rate given, for small ˜a, by [8, 11] 2  Γnlm = 2r+Cnlm(mΩ − ωnlm)α4l+4µ  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='2)  where the coefficient Cnlm is given by  Cnlm =  24l+1(n + l)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  n2l+4(n − l − 1)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  l�  k=1  �  k2(1 − ˜a)2 − (˜am − 2˜r+α)2�  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='3)  2For large values of ˜a and α the analytical expression for the superradiant rates in eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='2 is no longer  accurate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' A phenomenological expression for Γ211 that provides a good fit in this regime is given by [46]  Γimp  211 = Γ211  �  1 +  3  128  ˜a9/5  √1 − ˜a  �r+µ  ˜a  �6�  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='1)  We will use this corrected expression in this work whenever ˜a and α are large.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  – 3 –  Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  Yellow and orange bands are the regions of PBH mass M and axion mass µ where  the superradiant condition is satisfied and the cloud grows to its maximal value (in the absence of  interactions) within the lifetime of the universe for two representative values of the initial black hole  spin: ˜a = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='01 (yellow band), and ˜a = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='99 (orange band).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Solid lines are iso-countours of α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  and the radial coordinate of the inner (Cauchy) and outer (event) horizons are given by  r± = GM ˜r+ = GM(1 ±  √  1 − ˜a2), with the angular velocity of the black hole at the event  horizon being given by Ω = ˜a/(2r+).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' For slow-rotation ˜a ≪ 1 and small α the rate above  simplifies to Γ2 ≃ α8µ(˜a − 4α)/24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  The number of particles in a given state grows until the superradiance condition is  saturated, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' ω = Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' In the absence of interactions, this happens for the dominant mode  (|211⟩) at a time tmax = ln (Nmax  2  )/Γ2 when the number of axions in this state is  Nmax  2  = ∆J ≃ (˜ai − ˜af) GM2 ,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='4)  where ˜ai and ˜af = 4α are, respectively, the initial and final spins of the black hole and we  have neglected the variation of the black hole mass, Mi ≃ Mf, which is a good approximation  for α ≪ 1 since ∆M/M = α˜a∆J/J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' However, superradiance only plays an important role if  the cloud fills up in a time scale smaller than the age of the universe, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  tuni ≳ tmax = ln (Nmax  2  )/Γ2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='5)  Figure 1 shows the range of PBH and axion masses where the superradiance condition  and the lifetime condition, eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='5, are simultaneously satisfied for two benchmark values of  ˜a (˜a = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='01, ˜a = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='99) that we will consider throughout this work and that, as described  earlier, are representative of two PBH formation mechanisms: during radiation domination  (small spin) and during an early matter domination (near extremal).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  As also previously  – 4 –  106  660 = p  α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='2  a = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='01  105  α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='01  104  α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='001  103  μ(eV)  α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='0002  102  101  10°  10-1  1014  1015  1016  1017  1018  M(kg)discussed, we will restrict our analysis to the mass range M ∼ 1014 − 1018 kg for which the  PBHs can account for all the dark matter [44].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' The figure shows that superradiance can  efficiently produce axions with masses from 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='1 eV to a few keV for slowly spinning PBHs,  while in the near-extremal limit this range is widened up to MeV masses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  3  Cloud dynamics with self-interactions  In the absence of interactions the number of particles within the superradiant cloud grows un-  til it reaches its maximal value N ≃ Nmax  2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' However, if the bosonic field has self-interactions,  as in the case of axions, this growth can be quenched significantly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' The goal of this section  is to study the role of self-interactions in the evolution of the cloud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  We consider the typical axion Lagrangian3  La ⊃ 1  2∂µa ∂µa + µ2f2  a  �  1 − cos  � a  fa  ��  + caγγ  αEM  8π  a  fa  Fµν ˜F µν ,  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='1)  where a denotes the axion field, αEM is the electromagnetic fine structure constant, fa is the  axion decay constant and caγγ a dimensionless coefficient proportional to the electromagnetic  anomaly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' In this work, we fix the coefficient caγγ = 1 so that the coupling fa fixes both the  strength of the self-interactions and the coupling to photons, although our results can be  easily generalized for other values of this coefficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' For later convenience we also define  gaγγ ≡ αEM/(2πfa).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  On the one hand, the cosine potential induces self-interactions amongst the axions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' For  a ≪ fa the leading self-interaction term is quartic and characterized by a dimensionless  coupling λ = µ2/f2  a ≃ 10−32(µ/keV)2(1010 GeV/fa)2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Although this is typically very small,  processes within a superradiant cloud are Bose-enhanced by huge factors due to the expo-  nentially large number of axions, as we will explore below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' On the other hand, through the  axion-photon coupling axions can decay into two photons at a rate  Γaγγ = g2  aγγµ3  64π  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='2)  Although we will consider parametric regimes where this decay has a negligible influence on  the dynamics of the clouds, it will be crucial when exploring the observational signatures of  PBH-axion superradiance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  We will begin by considering the dynamical effects of self-interactions amongst axions  in the main superradiant bound states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' As we will see, this may lead to a significant number  of axions escaping the cloud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='1  Axions within the superradiant cloud  Self-interactions become progressively more important as a approaches fa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' The growth of  the cloud is halted roughly when the quartic self-interactions start to compete with the  gravitational binding energy, as analyzed in detail in [50].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  The relevant 2 → 2 scattering processes in this dynamics have been identified in [50]  and involve the superradiant levels |211⟩ and |322⟩, and axions that either escape to infinity  3Additional couplings of the axion to other Standard Model fields can be considered but do not affect  our results because we will be consider axions with masses below the electron mass that can only decay into  photons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  – 5 –  211  211  322  BH  322  322  211  ∞  Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Leading scattering processes for the dynamics of the superradiant cloud: depletion (left),  and replenishment (right).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' We follow the notation of [50] and denote the superradiant states by their  quantum numbers nlm, the states absorbed by the black hole by BH and those that escape the cloud  by ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  (∞) or are absorbed by the black hole (BH).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' They can be summarized as (see also Figure  2):  Depletion:  |211⟩ + |211⟩  ΓD  −→ BH + |322⟩  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='3)  Replenishment:  |322⟩ + |322⟩  ΓR  −→ ∞ + |211⟩ ,  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='4)  where the nomenclature refers to the effect of these processes on the dominant |211⟩ state,  and occur respectively at a rate [50]  ΓD = 4 × 10−7α7λ2h(˜a)µ  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='5)  ΓR = 10−8α4λ2µ ,  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='6)  where we have defined h(˜a) ≡ 1 +  √  1 − ˜a2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' The axions that escape to infinity have angular  momentum m = 3 and energy larger than the axion rest mass, while those absorbed by the  black hole have m = 0, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' are in a non-superradiant bound state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Therefore, the latter  changes the black hole mass but not its spin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' To track how the processes above affect the  evolution of the cloud we solve the following Boltzmann equations for the number of particles  in the |211⟩ and |322⟩ states, N2 and N3 respectively,4  dN2  dt  = N2 [Γ2 − Γaγγ + N3 (ΓRN3 − 2ΓDN2)]  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='7)  dN3  dt  = N3 [Γ3 − Γaγγ + N2 (ΓDN2 − 2ΓRN3)] ,  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='8)  where Γ3 ≡ Γ322 is the superradiance rate of the |322⟩ state given in eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' The first terms  on the right hand side capture the effect of superradiance;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' the second terms correspond to  the decays of the axions in the cloud into photons;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' the third terms incorporate the effects  of depletion and replenishment due to axion self-scatterings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Superradiance drains spin and  mass from the black hole by populating the leading superradiant levels but part of the black  hole mass is recovered in the depletion process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Therefore, the Boltzmann equations above  need to be complemented by the corresponding evolution equations for the black hole mass  M and spin J  dM  dt  = −µ (Γ2N2 + Γ3N3 − ΓDN2  2 N3)  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='9)  dJ  dt = −(Γ2N2 + 2Γ3N3) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='10)  4We neglect stimulation effects that may enhance the decay into photons under certain conditions [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  – 6 –  Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Different regimes for the evolution of the superradiant cloud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  Spin-down  No  Incomplete  Complete  Fast  Regime  fa ≲ fspin-↓  a  fspin-↓  a  ≲ fa ≲ fno-spin  a  fno-spin  a  ≲ fa ≲ fno-eq  a  fa > fno-eq  a  Equation  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='15  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='15, 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='19  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='19, 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='20  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='20  We now proceed to describe the dynamics in more detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' We will neglect the terms  in Γ3 and Γaγγ in the analysis as they are sub-leading in the range of parameters that we  consider.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' However, we explicitly include them in our numerical analysis of the above system  of equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' The decay rate into photons will be crucial in Section 4 when studying the  observational signatures of this scenario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' We note that there are other sub-leading scattering  processes, as well as gravitational wave emission, that we are not including but can be found  in [50].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  Initially, the |211⟩ level starts to grow exponentially fast through the superradiance  term, Γ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' As N2 grows, the terms in N2  2 start to move a considerable number of particles to  the level |322⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' An equilibrium is eventually reached when  dN2  dt  = dN3  dt  = 0  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='11)  and the two levels reach the equilibrium values  Neq  2  =  2  ΓD  �  ΓRΓ2  3  ≃ 50  √  3  √˜a − 4α  α  �fa  µ  �2  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='12)  Neq  3  =  �  Γ2  3ΓR  ≃ 2000  √  3 α2√  ˜a − 4α  �fa  µ  �2  ,  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='13)  where in the last equalities we have used eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='2, 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='5 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='6 in the slow-rotation limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  There are two main conditions that determine the fate of the cloud: 1) whether the  black hole loses a significant part of its spin within the life-time of the universe;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' 2) whether  the equilibrium value is larger or smaller than the maximum number of particles that can be  produced via superradiance (eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' These conditions are connected with the strength of  self-interactions, controlled by fa, and lead to different regimes in the evolution of the cloud  that we describe below and summarize in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  No spin-down:  When the interactions are relatively strong (smaller fa), the cloud  reaches the equilibrium state more quickly, with a smaller equilibrium number of axions  Neq  2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Therefore, the amount of spin extracted from the black hole during the lifetime of  the universe is rather small and N2 remains at the equilibrium value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' We call this the no  spin-down regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' The emission of axions to infinity is also less efficient because both N2  and N3 are relatively small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  To estimate the range of parameters that lie within this regime we compare the time  scale tJ for the black hole to lose a significant amount of its spin  tJ ≃ J  ˙J  ≃ ˜aGM2  Neq  2 Γ2  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='14)  with the age of the universe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' In terms of fa, no spin-down corresponds to  fa < fspin-↓  a  ≡ 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='4 × 109  ˜a1/2  (˜a − 4α)3/4  �keV  µ  �1/2 �4 × 10−4  α  �5/2  GeV .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='15)  – 7 –  Incomplete spin-down: If fa > fspin-↓  a  the equilibrium numbers are larger than in the  previous regime and, as consequence, tJ < tuni and the PBH spin starts decreasing signifi-  cantly, therefore considerably reducing the superradiance growth rate Γ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Nevertheless, as  long as this rate is sufficiently large to compensate for the cloud’s depletion due to self-  interactions (Γ2N2 ≫ ΓDN2  2 N3, ΓRN2  3 N2), an equilibrium configuration is approximately  maintained, with N2 ≃ Neq  2 (t) as given by eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='12 with a decreasing Γ2(t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' In this adiabatic  regime, we may obtain a solution for N2 by substituting N2 ≃ Neq  2 (t) in the spin evolution  eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='10 and solving for ˜a (taking into account that Γ3N3 ≪ Γ2N2 and neglecting the PBH  mass change).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' An analytical solution can then be obtained for slowly rotating PBHs away  from the superradiance threshold, ˜a ≳ 4α for which Γ2 ∝ ˜a, yielding:  N2(t > tJ) =  Neq  2  1 + 1  2  Neq  2  Nmax  2  Γ2(t − tJ)  ,  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='16)  where Neq  2 refers to the equilibrium value attained before the PBH begins its spin-down at tJ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  Note that within the age of the universe the present occupation number of the |211⟩ state is  only significantly reduced compared to its initial equilibrium value if Neq  2 /N max  2  ≳ (Γ2tuni)−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  Complete spin-down: For even larger values of fa, and so also of Neq  2 , the adiabatic  regime is efficient enough to spin-down the BH so much that superradiance is no longer effec-  tive in populating the cloud and the dynamics becomes instead dominated by the depletion  and replenishment processes in eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='3 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Once the PBH spins down sufficiently to  nearly saturate the superradiance condition at tno-spin, we may neglect the superradiance  terms in the evolution equations for N2 and N3 in eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='7 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' The resulting coupled  system of equations admits solutions of the form N3/N2 = ΓD/(2ΓR) ≡ d ≈ const.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=', such that  N2 evolves in time as  N2(t > tno-spin > tJ) =  Nno-spin  �  1 + 3d ΓDN2  no-spin(t − tno-spin)  �1/2  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='17)  where Nno-spin is the value of N2 at the time tno-spin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' We may estimate tno-spin by matching  eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='16 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='17 yielding  tno-spin ≃ 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='8 × 1012  �keV  µ  � �1011GeV  fa  �4 �4 × 10−4  α  �2  years .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='18)  Complete spin-down will occur whenever tno-spin < tuni, which corresponds to decay constants  fa > fno-spin  a  ≡ 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='7 × 1011  �keV  µ  �1/4 �4 × 10−4  α  �1/2  GeV .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='19)  In Figure 3 we show the numerical evolution of N2 for fa = 1011 GeV where the three  different dynamical stages discussed so far are clearly illustrated: (1) superradiant growth  until teq, at which the equilibrium is attained;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' (2) at tJ the PBH starts spinning down  and the equilibrium value decreases adiabatically until (3) tno-spin, after which superradiance  shuts down and the dynamics of the cloud is controlled by the self-interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' We leave a  more general discussion of the numerical results to Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='4, although we note the clear  agreement between our analytical description and the numerical solution in this figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  – 8 –  Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Numerical evolution (solid red curve) of the number of particles in the dominant |211⟩  state for a PBH with M = 1014 kg and ˜a = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='01 and an axion with µ = 1 keV and fa = 1011 GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  The dashed green and blue lines correspond to the analytical solutions in the incomplete spin-down  and complete spin-down regimes given in eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='16 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Note that although fa = 1011 GeV  corresponds to the incomplete spin-down regime, here we can also see the complete spin-down phase  because we have extended the time domain beyond the age of the universe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  Fast spin-down: The final regime occurs for even larger fa when Neq is so large that the  cloud saturates at Nmax  2  5, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' superradiance shuts down before an equilibrium is reached.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  This happens when Neq  2 > Nmax  2  or equivalently for  fa > fno-eq  a  ≡ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='8 × 1013  �  α  4 × 10−4  �3/2  (˜a − 4α)1/4 GeV .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='20)  With the superradiance source turned off, the dynamics is again controlled by self-interactions  just like in the complete spin-down regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Therefore, N2 will still evolve like in eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='17  but with Nno-spin, tno-spin replaced by Nmax  2  and tmax.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Noteworthy, this is the only regime  among those we described where most of the axions are still in the cloud today and only  a small fraction has escaped.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' However, as we will show in Section 4, when discussing the  observational impact of the dynamics, the fast spin-down is not yet accessible with current  data since the associated axion-photon coupling is too small while the total number of axions  produced remains roughly unchanged.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='2  Axions ionized from the cloud  So far we have described the dynamics of the axions within the superradiant cloud and we  have seen that self-interactions can strongly quench its growth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' However, the replenishment  processes in eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='4 (and Figure 2) are continuously producing axions that escape the cloud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  At the end of the dynamics most of the axions are, in fact, outside the cloud (except in the  fast spin-down regime where self-interactions play a negligible role).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' At the same time, the  5We neglect here the subsequent growth of the cloud through the sub-leading superradiant levels as these  rates are small and do not affect the dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  – 9 –  fa = 10llGeV  teq  tno-spin  1041  1039  1037  M  1035  Numerical  1033  Incomplete spin-down  1031  Complete spin-down  10  105  109  1013  t(years)coupling to photons allows these particles to decay into photon pairs at a rate Γaγγ given in  eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' The number of particles that escape the cloud obeys therefore  dN∞  dt  = ΓRN2  3 N2 − ΓaγγN∞  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='21)  being fully determined by the solutions for N2 and N3 derived in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  What we have left to understand is the fate of these ionized axions, in particular, if  they become bounded to the PBH host galaxy and how many of them decay to photons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Let  us begin by addressing the first point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Conservation of energy in the replenishment process  implies that the ionized axions are emitted with non-relativistic energy E∞ = α2µ/72 and a  velocity  v∞ ≃ α  6 = 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='7 × 10−5  �  α  4 × 10−4  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='22)  This value needs to be compared with the escape velocity of the host galaxy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Axions with  v∞ < vesc will be bound to the host galaxy while the remaining ones will escape to the  intergalactic space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' This distinction will be important in the next section when comparing  the flux of photons from superradiant axion decay with the observational data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' In the next  section we will use X-ray and gamma-ray data from the Milky Way (MW), Andromeda (M31)  and Segue 1 (Seg1) galaxies, and bounds on the rate of energy injection in the Leo-T galaxy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  Their escape velocities are respectively given by vMW  esc  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='0018, vM31  esc  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='0016, vSeg1  esc  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='0002  [67–69] 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Hence, we conclude that the ionized axions will typically remain bound to the  host galaxy for slowly rotating black holes with ˜a ≲ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='01, since the superradiance condition  requires in this case α ≲ 10−3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  Secondly, as the number of free axions grows, it is possible that at some point their  decay rate into photons, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' the first term on the right-hand side of eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='21, balances the  rate at which they are produced via the replenishment processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' This will happen when  N∞Γaγγ = ΓRN2  3 N2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='23)  For the range of parameters that we studied in this work, this balance only occurs in the  no-spin down regime where N2, N3 reached the (constant) equilibrium values in eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='12  and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Therefore, during this phase N∞ will grow linearly in time at the rate ΓRN2  3 N2  until it saturates the condition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='23 at a time  tdecay ≃ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='1 × 1010  �  fa  108GeV  �2 �keV  µ  �3  years  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='24)  when  N∞ = Neq  ∞ ≡ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='9 × 1040 (˜a − 4α)3/2  h(˜a)  �  α  4 × 10−4  �7 �  fa  108GeV  �4 �keV  µ  �4  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='25)  As we can see from eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='24, only for small values of the axion decay constant fa,  fa ≲ 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='5 × 107� µ  keV  �3/2  GeV  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='26)  6The escape velocity increases as one approaches the galactic center.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  Here, we conservatively use vesc  evaluated at a kpc distance from the galactic center (except for Segue 1 where the quoted value is estimated  from the gravitational potential at the center of the galaxy).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  For Leo-T we take vLeo-T  esc  = O(10−4) as a  benchmark value [70].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  – 10 –  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Numerical solutions for µ = 1 keV, M = 1014 kg, ˜a = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='01 and different fa values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' In  red/brown we plot the number of axions in the dominant/sub-dominant superradiant state (N2/N3)  and in magenta the number of axions that escape the black hole’s gravitational potential (N∞).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' In  blue/green we show the variation of the black hole’s mass (M)/angular momentum (J).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' In cyan we  plot the maximum allowed axion number (N max  2  ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Analytical solutions for N2 and N∞ are plotted in  dashed black between teq ≤ t ≤ tuni where they overlap with the corresponding numerical solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  is the equilibrium reached within the lifetime of the universe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' The effects of the decays are  shown in the upper left corner of Figure 4 where we can see the linear growth of N∞ until  the equilibrium value Neq  ∞ is attained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='3  Total number of axions and PBH spin loss  The spin of the black hole feeds the cloud with axions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Therefore, in the regimes where the  decay into photons is less efficient than the superradiant axion production (all values of fa  except those in eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='26 that we discuss below), the final number of axions can be calculated  by conservation of angular momentum:  Ntot = N2 + 2N3 + 3N∞ ≃ ∆J  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='27)  where we have used the fact that the axions that are emitted to infinity have angular momen-  tum m = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=" Moreover, in the previous subsection we concluded that the number of axions  outside the cloud is larger than the number within the cloud for a broad fa range (see also  – 11 –  — N² — N3 — N  W-  max  1041  fa = 10'GeV  1031  1021  1011  10  100  105  108  t(years)JNα  Analytical  1041  fa = 10llGeV  1031  1021  1011  10  100  105  108  t(years)1041  fa = 1012GeV  1031  1021  1011  10  100  105  108  t(years)1041  fa = 1014GeV  1031  1021  1011  10  100  105  108  t(years)Figure 4)." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Therefore, ∆J(tuni) ≃ 3N∞(tuni) except for the fast spin-down regime where most  axions are still bounded to the PBH within the cloud and ∆J(tuni) ≃ Nmax  2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  The other exception is for fa larger than 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='26 (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' small couplings).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  In this case,  N∞(tuni) ≃ Neq  ∞ ≫ N2, but the total number of photons produced is even larger Nγ(tuni) =  2 tuniΓaγγNeq  ∞ ≫ Neq  ∞ and this is where most of the black hole spin is dumped.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='4  Numerical analysis  In Figure 4 we show numerical solutions of the system of equations comprising the Boltzmann  equations 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='7 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='8 for the number of axions in the two main superradiant states, and the  dynamical equations for the PBH mass and spin, 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='9 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' We consider a fixed value  of α = 4 × 10−4 (corresponding to M = 1014 kg and µ = 1 keV) and spin ˜a = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='01, and  four different values of fa that are representative of the different regimes identified in Table  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' In all cases, the PBH mass remains approximately constant throughout the cosmological  evolution until the present day and the cloud reaches an equilibrium at around 107 years.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  For low values of fa (fa = 107 GeV upper left corner), the cloud is in the no spin-down  regime and remains approximately stable until today.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' However, as we increase fa to fa = 1011  GeV (upper right corner) the system enters the incomplete spin-down regime where the cloud  reaches a larger equilibrium number that starts to slowly decrease over time as the PBH loses  a sizeable amount of its spin (green line in Figure 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  In the lower left corner we show the evolution in the complete spin-down regime with  fa = 1012 GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' In this case, the equilibrium number is so large that the PBH loses spin  much faster and superradiance eventually shuts down before the present day.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Afterwards,  the dynamics of the cloud is dominated by axion self-interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  Finally the lower right corner shows the evolution for fa = 1014 GeV, within the fast  spin-down regime, where the cloud reaches the maximal occupation number, at which super-  radiance shuts down, before reaching the equilibrium state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' In this regime, self-interactions  are rather weak so N2 remains roughly constant and most of the axions are presently still  within the cloud rather than escaping the latter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  We end this section by noting that, even though in some cases the axion’s lifetime is  smaller than the age of the universe, the fact that the superradiant rate Γ2 > Γaγγ enforces  that the total number of axions is always growing over time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' The effect of the decay into  photon pairs is only significant in the upper left plot of Figure 4 where it halts the growth  of N∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  4  Electromagnetic signatures of superradiant axions  We have studied in the previous sections how a population of spinning PBHs may lead to a  significant axion abundance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' If these axions couple to photons they can provide interesting  electromagnetic (EM) signatures of this co-existence of PBH and relatively heavy axions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  In this section we will show that in a large range (see Figure 5) of axion and PBH masses,  these signatures surpass existing observational data, mainly galactic and extragalactic X-ray  and gamma-ray fluxes, and that upcoming X-ray telescopes may further strengthen these  constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  To perform the analysis of these EM signals, we need to keep track of the total number  of axions produced per PBH, both inside and outside the cloud, and their photon emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  A relevant quantity is the fraction of the dark matter in superradiant axions, given by  r = Ntot(tuni) µ  M  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='1)  – 12 –  where M/µ is the would be number of axions per PBH if axions were all the dark matter  and Ntot(tuni) ≃ N2 + N∞ is the number of axions produced per PBH in each case, with N2  and N∞ given in Section 3 for the different regimes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  We will separate the discussion in two parts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' First, we discuss the extragalactic emission,  which is common to all cases and that originates from the extragalactic density of PBHs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  Then, we look at situations where the “ionized” axions are bounded to the host galaxy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='1  Extragalactic emission  In the analysis of the extragalactic axions we use two different types of constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  For axion masses between 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='4 eV (twice the energy of the Lyman-α line) and a few keV,  the leading source of extragalactic constraints on the axion-photon coupling are CMB spectral  distortions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' We use the COBE/FIRAS bounds on the rate of dark matter decays into photons  derived in [62] but re-scaled by the factor r in eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='1, for each value of the axion mass, to  take into account the fact that the axions produced by PBH superradiance are only a small  fraction of the dark matter abundance, which we assume is fully accounted for by the PBHs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  The aforementioned constraints take into account the effects of photon injection throughout  the cosmic history.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' We expect that for quasi-stable particles, with lifetimes greater than  the age of the universe, the largest CMB spectral distortions are generated at the latest  times, when the relative energy injection into photons ∆ργ/ργ is maximal due to the relative  enhancement of dark matter over radiation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Therefore, we expect that these constraints are  also applicable in our scenario where photons are only produced at low redshifts after the  superradiant production of axions takes place.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' However, we caution the reader that a more  accurate translation of the bounds of [62] may require a more detailed analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  For larger masses we estimate the background flux originated from the extragalactic  axions and impose that it should be smaller than the observed one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' We assume that the  distribution of both the PBHs and the free axions is approximately isotropic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' The emission  rate per unit volume at a time t is given by [71, 72],  dnγ  dt (Eγ(t), t) ≃ nPBH(t)Eγ(t) d2Nγ  dEγdt(Eγ(t), t)  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='2)  where nPBH(t) = Ω0  PBHρ0(1 + z)3/M is the PBH number density and ΩPBH ≃ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='24 the  present PBH abundance, that we fix to the dark matter abundance, and ρ0 ≃ 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='4 × 10−33  kg cm−3 the critical density today [73].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' The redshift (z) factors account for the dilution due  to the expansion of the universe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' We have also approximated the photon emission rate as  dNγ/dt ≃ Eγ d2Nγ/(dEγdt) [72] where Eγ is the energy of the emitted photon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Since both  the axions in the cloud and those that are ionized are non-relativistic, we may approximate  the emission spectrum per PBH, d2Nγ/(dEγdt), as monochromatic [46]  dNγ  dEγdt ≃ 2NtotΓaγγ δ (Eγ(t) − µ/2) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='3)  where Ntot is the total number of produced axions in eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='27 at a given time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' To obtain the  photon flux, I ≃ nγ(tuni)/(4π) 7, we integrate eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='2 in time until today and find  I(E) = 3  4πΩ0  PBH ρ0 tuni Γaγγ  Ntot(te)  M  � E  µ/2  �3/2  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='4)  7We remark that we are using natural units, otherwise a factor c, the speed of light, should appear in the  relation between I and nγ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  – 13 –  where te is the time of emission of the photon that arrived today with energy E and that  can be obtained through the redshift relation 1 + ze(te) = µ/(2E).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  We have used that  most photons are emitted during the matter-dominated epoch given the timescales involved  in the dynamics of the superradiant clouds (and neglected the current era of dark energy  domination).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  The flux at energies E < µ/2 corresponds to the photons emitted before today.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' As we  have mentioned at the end of the previous section, the total number of axions never decreases  over time;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' the decays into photons at most halt its growth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Therefore, most of the EM flux  will be due to the non-relativistic axions that are around “today” and so to compare with  data we simply evaluate the flux at E = µ/2 for each value of the parameters (µ, M, gaγγ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  We define the excluded regions of parameters as those where the EM flux is larger than the  double power law fit to the X-ray and gamma-ray background data used in [61].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='2  Galactic emission  The axions within the cloud and those that are ionized with sufficiently small velocities  remain bound to the host galaxy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  Their decay into photons contributes to the galactic  background fluxes where observational constraints are typically stronger.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' We assume that  their density tracks the dark matter profile in the galaxy but, similarly to the COBE/FIRAS  bounds derived above, with an amplitude that is suppressed by the fraction r in eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='1  so that we can rescale existing constraints on the rate of dark matter decays into photons  from the Andromeda [60], Milky Way [63, 64] and Leo-T [65] galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Finally, we study  the prospects of detection with future ATHENA X-ray telescope using the forecasted bounds  on dark matter decays into photons from Msec observations of the Segue 1 dwarf spheroidal  galaxy [66].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='3  Discussion of the constraints  The resulting constraints in the gaγγ vs µ plane are shown in Figure 5 for slowly rotating  (˜a = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='01, top) and extremal (˜a = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='99, bottom) PBHs, and for different values of their mass  (in different colors).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' The constraints are stronger in the case of near-extremal black holes  because the spin-down of the black hole leads to a larger axion abundance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  For each value of the PBH mass the boundary of the constrained region is delimited on  the right (large α) by the superradiance condition and on the left (small α) by the fact that  the photon flux decreases for smaller axion masses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' On the other hand, by increasing fa at  µ we move from the no spin-down regime into the incomplete spin-down and eventually into  the complete spin-down region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' In the incomplete spin-down region, a sizeable portion of the  PBH spin is already extracted hence N∞ is almost maximal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Therefore, increasing fa further  will only decrease the flux, and that is even more so in the complete spin-down where the  flux decays as f−2  a .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  In the near-extremal case, there is a sudden change in the constrained region, around  µ ≃ 30 keV for M = 1014 kg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' This change originates from the fact that for larger masses (large  α) the emitted axions have escape velocities larger than 10−3 and so only the extragalactic  bounds can be applied, whereas for smaller masses the Milky Way and Andromeda constraints  on the fluxes can be used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' The same logic explains why the forecasted sensitivity of ATHENA  stops at a few keV;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' the analysis of [66], used in this work, relies on an observation of the  Segue 1 galaxy where the escape velocity is of order 10−4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  Finally, we compare the constraints obtained in this work with existing constraints  on the axion-photon coupling that do not rely on an initial thermal or dark matter axion  – 14 –  Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Constraints on the axion-photon coupling from PBH superradiance, assuming 100% of  dark matter in 1014 kg (blue), 1016 kg (red), 1018 kg (green) PBHs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' The top plot is for PBHs with  spin ˜a = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='01 and the bottom plot for ˜a = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' For comparison, we show in gray/black existing  constraints on axions from globular clusters, SN1987A(γ), solar axions, and freeze-in production at or  below BBN temperatures [74–78].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' The predicted exclusion potential of the future ATHENA telescope  is shown with a dashed blue line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  – 15 –  10-9  Globular clusters  10-10  107  SN1987A()  SB  10-11  108  10-12  109  BBN + Ne  (GeV-1)  10-13  1010  (GeV)  10-14  1011  10-15  1012  10-16  1013  10-17  1014  10-18  M = 1015kg  1015  M = 1014kg  a = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='01  10-19  100  101  102  103  104  105  106  107  μ(eV)10-9  Globular clusters  10-10  107  SN1987A()  10-11  SB  108  10-12  109  BBN + Ne  (GeV-1)  10-13  1010  (GeV)  10-14  1011  10-15  1012  Q  10-16  1013  10-17  1014  M = 1018kg  10-18  M = 10l6kg  1015  M = 1014kg  660 = P  10-19  100  101  102  103  104  105  106  107  μ(eV)abundance and that originate from: globular clusters [74],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' axions accumulating in the solar  basin [75],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' supernova 1987A [76],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' and freeze-in production at or below BBN temperatures  [77,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' 78].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' We have extracted this data from the repository [79].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Our constaints are stronger  than the existing constraints for a wide range of parameters, particularly in the case of near-  extremal PBHs for which superradiant axion production is most efficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' X-ray telescopes  such as ATHENA will be able to probe this scenario even further.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  5  Conclusion  PBHs with asteroid-like masses in the range 1014 − 1018 kg can account for all the dark  mater but are hard to probe due to their minuscule size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' In this work, we showed that the  co-existence of an axion with a 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='1 − 106 eV mass can dramatically change this picture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  The mechanism underlying our study is black hole superradiance: the draining of the  black hole’s spin into a densely packed bosonic cloud of a field with mass below the black  hole’s inverse radius.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' We considered two benchmark values for the PBH spin parameter,  slow-spin ˜a = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='01 and near-extremal ˜a ≃ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='99, which correspond to PBHs born in the  radiation era or an early matter era, respectively;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' and restricted the axion and PBH masses  to ranges where superradiant clouds form within the age of the universe (c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Figure 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  Building upon the work of [50], we then studied the cloud’s evolution in the presence  of the characteristic axionic self-interactions, the main effect of which is to trigger a non-  linear mixing between the two dominant superradiant states, |211⟩ and |322⟩, alongside with  axion reabsorption by the black hole and emission to infinity of axions ionized from the  superradiant cloud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  We studied the dynamics of the system by solving numerically and  analytically a coupled set of Boltzmann equations for the number of particles in the leading  superradiant levels alongside the evolution equations for the PBH mass and spin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  We identified four main regimes in the dynamics (c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Table 1), that are characterized  by different ranges of the axion decay constant fa, and provided an accurate analytical  description in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' In all regimes the cloud starts growing exponentially due to the  superradiant instability, which occurs on cosmological timescales even for slowly spinning  PBHs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' However, when self-interactions are strong fa < fspin-↓  a  , the cloud quickly reaches  an equilibrium state where the occupation numbers of the leading superradiant levels are  approximately constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' This is sustained by the superradiant instability that continuously  drains spin from the PBH but at a slower rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' We labelled this regime no spin-down.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  For fspin-↓  a  < fa < fno-spin  a  , self-interactions become less efficient and the quenched  equilibrium is reached later, when the cloud is denser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' To keep this denser equilibrium, the  black hole has to lose spin at a much faster rate and so, after some time, it eventually loses a  significant portion of its initial spin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' At this point, the system enters a new adiabatic regime  where both the spin and the equilibrium numbers decrease slowly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' This is the incomplete  spin-down regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' The complete spin-down regime occurs for even weaker self-interactions,  fno-spin  a  < fa < fno-eq  a  , when the adiabatic regime is able to drain so much spin that the  superradiance condition is no longer satisfied and the black hole can no longer refill the  cloud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' From then on, the fate of the cloud is fully determined by the self-interactions that  continue dissipating axions to infinity and back into the black hole (through non-superradiant  bound states).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Finally, for fa > fno-eq  a  , self-interactions are so weak that the cloud reaches its  maximal occupation number, by shutting down the (leading) superradiant instability before  any quenched equilibrium is reached.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' This fast spin-down regime is equivalent in its dynamics  to the vanilla case of superradiance of a non-interacting massive bosonic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  – 16 –  In the last three regimes mentioned above (incomplete, complete and fast spin-down)  the PBH loses a significant part of its spin before the present day.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' This energy is lost into  axions that either escaped to infinity (incomplete and complete spin-down) or are still mostly  within the cloud (fast spin-down).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Therefore, the final axion abundance can be very large, in  particular in the case of highly-spinning PBHs, and this begged the question, what happens  to these axions?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Can they give observational signatures of this scenario?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  We addressed this in Section 4 where we assumed that the produced axions decay  into photons, with a rate directly related to the strength of their self-interactions (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' we  set the electromagnetic anomaly coefficient in eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='1 to one), and explored the resulting  electromagnetic signals assuming a monochromatic PBH spectrum accounting for all dark  matter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' We identified two main signatures: i) an extragalactic photon flux that results from  the decay of axions produced by the cosmological PBH population;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' and ii) galactic fluxes  from the axions that are ionized from the cloud with a velocity below the host galaxy’s  escape velocity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' We imposed constraints from galactic and extragalactic (X-ray and gamma-  ray) background data, and existing constraints on the rate of dark matter decay into photons  from COBE/FIRAS and the Leo-T dwarf galaxy (see Section 4 for more details), all properly  rescaled to account for the axion abundance, to derive bounds on the axion mass and decay  constant fa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Finally, we have also shown how future X-ray telescopes such as ATHENA will  be able to further probe this scenario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' These results are summarized in Figure 5 and show  that the assumption of PBH dark matter excludes the existence of 20−106 eV axions coupled  to photons for a broad range of fa values, depending on the PBH mass and spin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  There are a few interesting aspects that would be interesting to further explore in  the future.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' A sub-leading effect that we have discarded in our analysis is the emission of  gravitational waves by the axion clouds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  Although this has no significant impact on the  dynamics, it may potentially provide additional observational signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Given that typically  only a very small fraction of the PBH mass is transferred to the superradiant clouds, observing  individual clouds is virtually impossible, but the large PBH abundance may potentially lead  to an observable stochastic background, which we plan to investigate in the future.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  In our analysis we have followed the results obtained in [50] in what concerns the leading  effects of axion self-interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Since the dimensionless mass coupling α < 1/2 in all cases  considered, we expect a non-relativistic approach to be at least a reasonable approximation,  although one may expect considerable corrections for the larger α values attained in the  near-extremal regime such as the Bosenova regimes observed in [51, 52, 54, 55].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  In addition, this analysis also neglects higher-order interactions (from the axion poten-  tial).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Even though the equilibrium number of axions within the cloud is always sufficiently  small that the field value a ≲ fa, it would be interesting to take a closer look into the signif-  icance of higher-dimensional interactions leading to multiple axion scattering processes, as  well as into how non-linearities affect the cloud’s density profile and growth rate [55].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  Our results should therefore be viewed in the light of the approximations employed and  motivate a further exploration of these issues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Nevertheless, an important take-home message  of this work is that self-interactions only change the timescale at which the PBH lose most of  its spin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Given enough time, the total number of axions produced (whether they remain or  not bound to the black hole) approaches the maximum number produced in the absence of  self-interactions, up to O(1) factors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' In our analysis, we have found that this occurs within  the universe’s age in most cases except for very low values of the axion decay constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  We hope that our results motivate further studies of PBH superradiance and of its  relevance for fundamental particle physics and cosmology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  – 17 –  Acknowledgements  RZF is supported by the Direcci´o General de Recerca del Departament d’Empresa i Coneix-  ement (DGR) and by the EC through the program Marie Sk�lodowska-Curie COFUND (GA  801370)-Beatriu de Pinos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' NPB is supported by Centro de F´ısica da Universidade de Coim-  bra (CFisUC) and by Funda¸c˜ao para a Ciˆencia e a Tecnologia, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='/MCTES through national  funds (PIDDAC).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' This work was supported by the CFisUC project No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' UID/FIS/04564/2020  and by the FCT-CERN grant No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' CERN/FIS-PAR/0027/2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  References  [1] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Zel’dovich, Pis’ ma zh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' eksp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' teor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' fiz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' 14, 270 (1971)[jetp lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' 14, 180 (1971)], Zh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Eksp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  Teor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Fiz 62 (1972) 2076.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [2] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Starobinsky, Amplification of waves reflected from a rotating ”black hole”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=', Sov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  JETP 37 (1973) 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [3] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Starobinsky and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Churilov, Zh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Eksp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Teor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Fiz 65, 3 (1973) [Sov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' JETP 38, 1  (1973)] .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [4] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Teukolsky, Perturbations of a rotating black hole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Fundamental equations for  gravitational electromagnetic and neutrino field perturbations, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' 185 (1973) 635.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [5] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Press and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Teukolsky, Perturbations of a Rotating Black Hole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Dynamical  Stability of the Kerr Metric, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' 185 (1973) 649.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [6] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Teukolsky and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Press, Perturbations of a rotating black hole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' III - Interaction of the  hole with gravitational and electromagnet ic radiation, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' 193 (1974) 443.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [7] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Press and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Teukolsky, Floating Orbits, Superradiant Scattering and the Black-hole  Bomb, Nature 238 (1972) 211.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [8] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Cardoso, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Dias, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Lemos and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Yoshida, The Black hole bomb and superradiant  instabilities, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' D 70 (2004) 044039 [hep-th/0404096].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [9] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Damour, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Deruelle and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Ruffini, On Quantum Resonances in Stationary Geometries,  Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Nuovo Cim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' 15 (1976) 257.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [10] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Zouros and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Eardley, INSTABILITIES OF MASSIVE SCALAR  PERTURBATIONS OF A ROTATING BLACK HOLE, Annals Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' 118 (1979) 139.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [11] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Detweiler, KLEIN-GORDON EQUATION AND ROTATING BLACK HOLES, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' D 22 (1980) 2323.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [12] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Furuhashi and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Nambu, Instability of massive scalar fields in Kerr-Newman space-time,  Prog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Theor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' 112 (2004) 983 [gr-qc/0402037].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [13] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Cardoso and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Yoshida, Superradiant instabilities of rotating black branes and strings,  JHEP 07 (2005) 009 [hep-th/0502206].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [14] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Dolan, Instability of the massive Klein-Gordon field on the Kerr spacetime, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' D  76 (2007) 084001 [0705.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='2880].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [15] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Rosa, The Extremal black hole bomb, JHEP 06 (2010) 015 [0912.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='1780].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [16] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Dolan, Superradiant instabilities of rotating black holes in the time domain, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' D  87 (2013) 124026 [1212.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='1477].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [17] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' East and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Pretorius, Superradiant Instability and Backreaction of Massive Vector  Fields around Kerr Black Holes, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' 119 (2017) 041101 [1704.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='04791].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [18] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' East, Superradiant instability of massive vector fields around spinning black holes in the  relativistic regime, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' D 96 (2017) 024004 [1705.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='01544].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  – 18 –  [19] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Dolan, Instability of the Proca field on Kerr spacetime, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' D 98 (2018) 104006  [1806.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='01604].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [20] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Arvanitaki, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Dimopoulos, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Dubovsky, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Kaloper and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' March-Russell, String Axiverse,  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' D 81 (2010) 123530 [0905.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='4720].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [21] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Arvanitaki and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Dubovsky, Exploring the String Axiverse with Precision Black Hole  Physics, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' D 83 (2011) 044026 [1004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='3558].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [22] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Rosa, Boosted black string bombs, JHEP 02 (2013) 014 [1209.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='4211].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [23] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Witek, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Cardoso, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Ishibashi and U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Sperhake, Superradiant instabilities in astrophysical  systems, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' D 87 (2013) 043513 [1212.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='0551].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [24] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Brito, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Cardoso and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Pani, Black holes as particle detectors: evolution of superradiant  instabilities, Class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Quant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Grav.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' 32 (2015) 134001 [1411.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='0686].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [25] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Arvanitaki, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Baryakhtar, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Dimopoulos, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Dubovsky and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Lasenby, Black Hole  Mergers and the QCD Axion at Advanced LIGO, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' D 95 (2017) 043001 [1604.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='03958].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [26] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Brito, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Ghosh, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Barausse, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Berti, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Cardoso, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Dvorkin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=', Stochastic and  resolvable gravitational waves from ultralight bosons, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' 119 (2017) 131101  [1706.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='05097].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [27] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Rosa and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Kephart, Stimulated Axion Decay in Superradiant Clouds around  Primordial Black Holes, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' 120 (2018) 231102 [1709.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='06581].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [28] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Baumann, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Chia and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Porto, Probing Ultralight Bosons with Binary Black Holes,  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' D 99 (2019) 044001 [1804.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='03208].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [29] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Ikeda, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Brito and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Cardoso, Blasts of Light from Axions, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' 122 (2019)  081101 [1811.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='04950].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [30] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Berti, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Brito, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Macedo, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Raposo and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Rosa, Ultralight boson cloud depletion  in binary systems, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' D 99 (2019) 104039 [1904.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='03131].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [31] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Baumann, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Chia, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Stout and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' ter Haar, The Spectra of Gravitational Atoms, JCAP  12 (2019) 006 [1908.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='10370].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [32] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Cardoso, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Dias, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Hartnett, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Middleton, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Pani and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Santos, Constraining  the mass of dark photons and axion-like particles through black-hole superradiance, JCAP 03  (2018) 043 [1801.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='01420].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [33] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Edwards, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Chianese, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Kavanagh, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Nissanke and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Weniger, Unique  Multimessenger Signal of QCD Axion Dark Matter, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' 124 (2020) 161101  [1905.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='04686].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [34] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Mehta, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Demirtas, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Long, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Marsh, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Mcallister and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Stott, Superradiance  Exclusions in the Landscape of Type IIB String Theory, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='08693.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [35] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Blas and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Witte, Imprints of Axion Superradiance in the CMB, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' D 102  (2020) 103018 [2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='10074].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [36] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Rosa and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Dolan, Massive vector fields on the Schwarzschild spacetime: quasi-normal  modes and bound states, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' D 85 (2012) 044043 [1110.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='4494].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [37] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Pani, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Cardoso, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Gualtieri, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Berti and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Ishibashi, Perturbations of slowly rotating  black holes: massive vector fields in the Kerr metric, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' D 86 (2012) 104017  [1209.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='0773].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [38] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Brito, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Cardoso and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Pani, Massive spin-2 fields on black hole spacetimes: Instability of  the Schwarzschild and Kerr solutions and bounds on the graviton mass, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' D 88 (2013)  023514 [1304.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='6725].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  – 19 –  [39] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Baryakhtar, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Lasenby and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Teo, Black Hole Superradiance Signatures of Ultralight  Vectors, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' D 96 (2017) 035019 [1704.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='05081].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [40] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Caputo, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Witte, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Blas and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Pani, Electromagnetic signatures of dark photon  superradiance, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' D 104 (2021) 043006 [2102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='11280].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [41] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Hawking, Gravitationally collapsed objects of very low mass, Mon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Roy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  152 (1971) 75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [42] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Carr and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Hawking, Black holes in the early Universe, Mon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Roy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  168 (1974) 399.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [43] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Byrnes and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Cole, Lecture notes on inflation and primordial black holes, 12, 2021  [2112.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='05716].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [44] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Green and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Kavanagh, Primordial black holes as a dark matter candidate, Journal of  Physics G: Nuclear and Particle Physics 48 (2021) 043001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [45] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Carr, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Kuhnel and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Sandstad, Primordial Black Holes as Dark Matter, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' D 94  (2016) 083504 [1607.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='06077].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [46] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Ferraz, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Kephart and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Rosa, Superradiant pion clouds around primordial black  holes, JCAP 07 (2022) 026 [2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='11303].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [47] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' March-Russell and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Rosa, Micro-Bose/Proca dark matter stars from black hole  superradiance, 2205.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='15277.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [48] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Carr, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Kohri, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Sendouda and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Yokoyama, Constraints on primordial black holes, Rept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  Prog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' 84 (2021) 116902 [2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='12778].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [49] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Gruzinov, Black Hole Spindown by Light Bosons, 1604.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='06422.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [50] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Baryakhtar, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Galanis, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Lasenby and O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Simon, Black hole superradiance of  self-interacting scalar fields, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' D 103 (2021) 095019 [2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='11646].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [51] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Yoshino and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Kodama, Bosenova collapse of axion cloud around a rotating black hole,  Prog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Theor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' 128 (2012) 153 [1203.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='5070].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [52] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Yoshino and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Kodama, The bosenova and axiverse, Class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Quant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Grav.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' 32 (2015) 214001  [1505.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='00714].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [53] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Omiya, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Takahashi and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Tanaka, Renormalization group analysis of superradiant growth  of self-interacting axion cloud, PTEP 2021 (2021) 043E02 [2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='03473].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [54] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Omiya, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Takahashi, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Tanaka and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Yoshino, Impact of multiple modes on the evolution  of self-interacting axion condensate around rotating black holes, 2211.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='01949.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [55] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Omiya, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Takahashi and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Tanaka, Adiabatic evolution of the self-interacting axion field  around rotating black holes, PTEP 2022 (2022) 043E03 [2201.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='04382].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [56] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Chiba and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Yokoyama, Spin Distribution of Primordial Black Holes, PTEP 2017 (2017)  083E01 [1704.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='06573].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [57] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' De Luca, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Desjacques, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Franciolini, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Malhotra and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Riotto, The initial spin  probability distribution of primordial black holes, JCAP 05 (2019) 018 [1903.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='01179].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [58] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Mirbabayi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Gruzinov and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Nore˜na, Spin of primordial black holes, Journal of  Cosmology and Astroparticle Physics 2020 (2020) 017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [59] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Harada, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='-M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Yoo, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Kohri and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='-I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Nakao, Spins of primordial black holes formed in the  matter-dominated phase of the universe, Physical Review D 96 (2017) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [60] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Ng, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Roach, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Perez, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Beacom, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Horiuchi, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Krivonos et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=', New  Constraints on Sterile Neutrino Dark Matter from NuSTAR M31 Observations, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' D  99 (2019) 083005 [1901.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='01262].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  – 20 –  [61] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Ballesteros, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Coronado-Bl´azquez and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Gaggero, X-ray and gamma-ray limits on the  primordial black hole abundance from Hawking radiation, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' B 808 (2020) 135624  [1906.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='10113].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [62] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Bolliet, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Chluba and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Battye, Spectral distortion constraints on photon injection from  low-mass decaying particles, Mon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Roy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' 507 (2021) 3148 [2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='07292].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [63] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Laha, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Mu˜noz and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Slatyer, INTEGRAL constraints on primordial black holes and  particle dark matter, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' D 101 (2020) 123514 [2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='00627].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [64] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Foster, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Kongsore, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Dessert, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Park, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Rodd, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Cranmer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=', Deep Search for  Decaying Dark Matter with XMM-Newton Blank-Sky Observations, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' 127 (2021)  051101 [2102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='02207].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [65] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Wadekar and Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Wang, Strong constraints on decay and annihilation of dark matter from  heating of gas-rich dwarf galaxies, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' D 106 (2022) 075007 [2111.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='08025].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [66] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Neronov and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Malyshev, Toward a full test of the νMSM sterile neutrino dark matter  model with Athena, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' D 93 (2016) 063518 [1509.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='02758].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [67] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Deason, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Fattahi, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Belokurov, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Evans, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Grand, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Marinacci et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=', The  local high-velocity tail and the Galactic escape speed, 1901.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='02016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [68] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Kafle, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Sharma, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Lewis, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Robotham and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Driver, The Need for Speed:  Escape velocity and dynamical mass measurements of the Andromeda galaxy, Mon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Roy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' 475 (2018) 4043 [1801.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='03949].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [69] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Baushev, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Federici and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Pohl, Spectral analysis of the gamma-ray background near the  dwarf Milky Way satellite Segue 1: Improved limits on the cross section of neutralino dark  matter annihilation, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' D 86 (2012) 063521 [1205.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='3620].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [70] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Faerman, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Sternberg and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' McKee, Ultra-Compact High Velocity Clouds as Minihalos  and Dwarf Galaxies, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' 777 (2013) 119 [1309.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='0815].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [71] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Masso and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Toldra, New constraints on a light spinless particle coupled to photons, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' D 55 (1997) 7967 [hep-ph/9702275].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [72] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Carr, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Kohri, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Sendouda and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Yokoyama, New cosmological constraints on  primordial black holes, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' D 81 (2010) 104019 [0912.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='5297].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [73] Planck collaboration, Planck 2018 results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Cosmological parameters, Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  641 (2020) A6 [1807.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='06209].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [74] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Ayala, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Dom´ınguez, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Giannotti, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Mirizzi and O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Straniero, Revisiting the bound on  axion-photon coupling from Globular Clusters, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' 113 (2014) 191302 [1406.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='6053].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [75] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' DeRocco, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Wegsman, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Grefenstette, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Huang and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Van Tilburg, First Indirect  Detection Constraints on Axions in the Solar Basin, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' 129 (2022) 101101  [2205.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='05700].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [76] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Jaeckel, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Malta and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Redondo, Decay photons from the axionlike particles burst of type  II supernovae, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' D 98 (2018) 055032 [1702.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='02964].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [77] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Depta, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Hufnagel and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Schmidt-Hoberg, Robust cosmological constraints on axion-like  particles, JCAP 05 (2020) 009 [2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='08370].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [78] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Langhoff, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Outmezguine and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Rodd, Irreducible Axion Background, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  129 (2022) 241101 [2209.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='06216].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  [79] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' O’Hare, “cajohare/axionlimits: Axionlimits.”  https://cajohare.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='io/AxionLimits/, July, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='5281/zenodo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='3932430.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
+page_content='  – 21 –' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RNAzT4oBgHgl3EQf0P4Y/content/2301.01780v1.pdf'}
diff --git a/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf b/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..44df9e1b2b181215339f4db635710b60620a8d17
--- /dev/null
+++ b/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:c297ab212f930678d5e0f0c27e912f16628548add9d36c96d7ac00f9ae2e2e3f
+size 797927
diff --git a/RtFJT4oBgHgl3EQfKyxj/vector_store/index.faiss b/RtFJT4oBgHgl3EQfKyxj/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..f5fd7fef30393ec6d6447a978335c88631a348a3
--- /dev/null
+++ b/RtFJT4oBgHgl3EQfKyxj/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:332e427cff7ae0d2b2d48bbf22d959ccdac8fdf110eb6ffc3931c0ef33f14f97
+size 4194349
diff --git a/RtFJT4oBgHgl3EQfKyxj/vector_store/index.pkl b/RtFJT4oBgHgl3EQfKyxj/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..dbb2a8b1ec25654ba8204dc565c61c2b795c9d84
--- /dev/null
+++ b/RtFJT4oBgHgl3EQfKyxj/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:1556354f7a6c69ecbcd4f42c801a2e907a8034ee95e07036038c518874aea6bb
+size 127109
diff --git a/SNE2T4oBgHgl3EQfCAY8/content/2301.03608v1.pdf b/SNE2T4oBgHgl3EQfCAY8/content/2301.03608v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..93b0f73582c5b7f08923ddc388c0978aa0f09670
--- /dev/null
+++ b/SNE2T4oBgHgl3EQfCAY8/content/2301.03608v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:01a4ce2398abf78e750a4c8b58809e3ca037fbe85605cb51ad653cff3a7c4fe5
+size 1410161
diff --git a/SNE2T4oBgHgl3EQfCAY8/vector_store/index.faiss b/SNE2T4oBgHgl3EQfCAY8/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..221fadb0ca40703b6ed5afa5e46cb0de575bd728
--- /dev/null
+++ b/SNE2T4oBgHgl3EQfCAY8/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:c0473c0fa07a5d4488daa37af5a488a7379f7cc2e6ed4dc1db815cbc218dacbf
+size 8388653
diff --git a/StA0T4oBgHgl3EQfD_-h/vector_store/index.faiss b/StA0T4oBgHgl3EQfD_-h/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..2ac45107ef4cec04b343e64e89b9fa46f38e3c55
--- /dev/null
+++ b/StA0T4oBgHgl3EQfD_-h/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:7b5fbc2558769d4a2f384072124d7f0f0f71926be2c90838d0b6a76defbef23a
+size 4128813
diff --git a/StA0T4oBgHgl3EQfD_-h/vector_store/index.pkl b/StA0T4oBgHgl3EQfD_-h/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..4fa5502d6f8ef8c6a8138aa4413944a14f04eb05
--- /dev/null
+++ b/StA0T4oBgHgl3EQfD_-h/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:0a2825c2187c8988b9554794dff7798f95f83197a0b0362dc553812e7677e74b
+size 153582
diff --git a/TdE2T4oBgHgl3EQfCgYE/content/tmp_files/2301.03613v1.pdf.txt b/TdE2T4oBgHgl3EQfCgYE/content/tmp_files/2301.03613v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..3521171ad7927e12835c1d1e1ea13343588714c9
--- /dev/null
+++ b/TdE2T4oBgHgl3EQfCgYE/content/tmp_files/2301.03613v1.pdf.txt
@@ -0,0 +1,14909 @@
+Draft version January 11, 2023
+Typeset using LATEX twocolumn style in AASTeX631
+Hard X-Ray to Radio Multiwavelength SED Analysis of Local U/LIRGs in GOALS Sample with
+Self-consistent AGN Model Including Polar-dust Component
+Satoshi Yamada
+,1, 2 Yoshihiro Ueda
+,2 Mart´ın Herrera-Endoqui
+,3 Yoshiki Toba
+,4, 2, 5, 6, 7
+Takamitsu Miyaji
+,3 Shoji Ogawa
+,2 Ryosuke Uematsu
+,2 Atsushi Tanimoto
+,8 Masatoshi Imanishi
+,4, 9 and
+Claudio Ricci
+10, 11
+1RIKEN Cluster for Pioneering Research, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
+2Department of Astronomy, Kyoto University, Kitashirakawa-Oiwake-cho, Sakyo-ku, Kyoto 606-8502, Japan
+3Instituto de Astronom´ıa sede Ensenada, Universidad Nacional Aut´onoma de M´exico, Km 107, Carret. Tij.-Ens., Ensenada, 22060, BC,
+M´exico
+4National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan
+5Department of Physics, Nara Women’s University, Kitauoyanishi-machi, Nara, Nara 630-8506, Japan
+6Academia Sinica Institute of Astronomy and Astrophysics, 11F of Astronomy-Mathematics Building, AS/NTU, No.1, Section 4,
+Roosevelt Road, Taipei 10617, Taiwan
+7Research Center for Space and Cosmic Evolution, Ehime University, 2-5 Bunkyo-cho, Matsuyama, Ehime 790-8577, Japan
+8Graduate School of Science and Engineering, Kagoshima University, Kagoshima 890-0065, Japan
+9Department of Astronomical Science, Graduate University for Advanced Studies (SOKENDAI), 2-21-1 Osawa, Mitaka, Tokyo 181-8588,
+Japan
+10N´ucleo de Astronom´ıa de la Facultad de Ingenier´ıa, Universidad Diego Portales, Av. Ej´ercito Libertador 441, Santiago, Chile
+11Kavli Institute for Astronomy and Astrophysics, Peking University, Beijing 100871, People’s Republic of China
+(Received October 14, 2022; Revised December 6, 2022; Accepted January 6, 2023)
+ABSTRACT
+We conduct a hard X-ray to radio multiwavelength spectral energy distribution (SED) decomposition
+for 57 local luminous and ultraluminous infrared galaxies (U/LIRGs) observed with Nuclear Spectro-
+scopic Telescope Array and/or Swift/Burst Alert Telescope in GOALS (Armus et al. 2009) sample. We
+modify the latest SED-fitting code X-CIGALE by implementing the infrared (IR) CLUMPY model,
+allowing the multiwavelength study with the X-ray torus model (XCLUMPY) self-consistently. Adopt-
+ing the torus parameters obtained by the X-ray fitting (Yamada et al. 2021), we estimate the properties
+of host galaxies, active galactic nucleus (AGN) tori, and polar dust. The star formation rates (SFRs)
+become larger with merger stage and most of them are above the main sequence. The SFRs are cor-
+related with radio luminosity, indicating starburst emission is dominant in the radio band. Although
+polar-dust extinction is much smaller than torus extinction, the UV-to-IR (mainly IR) polar dust lu-
+minosities are ∼2 times larger than the torus ones. The polar-dust temperature decreases while the
+physical size, estimated by the temperature and dust sublimation radius, increases with AGN lumi-
+nosity from a few tens of parsec (early mergers) to kiloparsec scales (late mergers), where the polar
+dust is likely the expanding (i.e., evolving) dusty outflows. The comparison between SFRs and intrin-
+sic AGN luminosities suggests that the starbursts occur first and AGNs arise later, and overall their
+growth rates follow the simultaneous coevolution relation that can establish the local galaxy–SMBH
+mass relation. We confirm the coexistence of intense starbursts, AGNs, and large-scale outflows in late
+mergers, supporting a standard AGN feedback scenario.
+Corresponding author: Satoshi Yamada
+satoshi.yamada@riken.jp
+arXiv:2301.03613v1  [astro-ph.GA]  9 Jan 2023
+
+ID2
+Yamada et al.
+Keywords: Infrared galaxies (790); Active galactic nuclei (16); X-ray active galactic nuclei (2035);
+Optical observation (1169); Infrared photometry (792); Radio continuum emission (1340)
+1. INTRODUCTION
+Galaxies and supermassive black holes (SMBHs) at
+their centers show a tight correlation between the masses
+of bulges (Mbulge) and SMBHs (MBH), indicating that
+they have coevolved by regulating each other’s growth
+(see e.g., Marconi & Hunt 2003; Kormendy & Ho 2013).
+Due to a huge scale gap between galaxies (∼1 kpc) and
+SMBHs (≪1 pc), the mechanism of their physical con-
+nection has been controversial (e.g., Hopkins et al. 2008;
+Madau & Dickinson 2014). For understanding the mech-
+anism of coevolution, the merging galaxies have received
+attention since the merger can extract the angular mo-
+mentum of the gas and trigger obscuration and rapid ac-
+cretion onto SMBHs (e.g., Koss et al. 2010, 2012, 2018;
+Kocevski et al. 2015; Lansbury et al. 2017; Ricci et al.
+2017a, 2021; Yamada et al. 2018, 2021).
+According to the major merger scenario, galaxies in
+the most active phase of mergers become luminous in-
+frared galaxies (LIRGs; L8−1000µm ≥ 1011L⊙) and ul-
+traluminous infrared galaxies (ULIRGs; L8−1000µm ≥
+1012L⊙), combined as U/LIRGs (Sanders & Mirabel
+1996). Their large bolometric luminosities are derived
+from the starbursts and/or active galactic nuclei (AGNs)
+surrounded by gas and dust, most of which are radiated
+in the infrared (IR) band.
+After quenching the star-
+forming activities, U/LIRGs are thought to transit to
+unobscured quasars or elliptical galaxies (e.g., Hopkins
+et al. 2008).
+The AGNs in U/LIRGs are well studied in the X-
+ray to radio multiwavelength bands (e.g., U 2022 for
+a review).
+When AGNs are heavily obscured, they
+radiate dimmed UV-to-near-IR emission compared to
+the AGN luminosity identified in the mid-IR and X-
+ray bands (see e.g., Hickox & Alexander 2018).
+The
+mid-IR studies reveal that the AGNs in U/LIRGs are
+deeply buried by a large amount of gas and dust, where
+even the direction of the lowest dust column-density
+can be opaque to the ionizing UV photons (e.g., Iman-
+ishi et al. 2006, 2008; Lee et al. 2012; Yamada et al.
+2019). Hard X-ray observations, which are less affected
+by the contamination of starburst emission, can identify
+the AGNs with large hydrogen column densities (NH).
+For local U/LIRGs observed with Nuclear Spectroscopic
+Telescope Array (NuSTAR; Harrison et al. 2013), Ricci
+et al. (2017a, 2021) analyze the broadband X-ray spec-
+tra and find the large fraction of Compton-thick (CT;
+NH > 1024 cm−2) AGNs in late mergers.
+By con-
+ducting the X-ray spectroscopy with the X-ray clumpy
+torus model (XCLUMPY; Tanimoto et al. 2019), Ya-
+mada et al. (2021) present the individual torus covering
+fractions, supporting the buried AGN structure in the
+late mergers.
+Yamada et al. (2021) report that the AGNs in the fi-
+nal phase of mergers show high Eddington ratios (λEdd)
+and the signatures of multiphase outflows at subparsec
+to kiloparsec scales: that is, ultrafast outflows (UFOs),
+ionized outflows, and molecular outflows.
+The UFOs
+are extremely fast (∼0.1–0.3c) and highly ionized winds
+at ∼0.01 pc (e.g., Tombesi et al. 2015; Mizumoto et al.
+2019; Smith et al. 2019). The ionized outflows are the
+fast (∼1000 km s−1) winds with a size of kiloparsecs de-
+tected by optical and near-IR spectroscopy (e.g., Rich
+et al. 2015; Cortijo-Ferrero et al. 2017; Kakkad et al.
+2018; Boettcher et al. 2020; Fluetsch et al. 2021). Molec-
+ular outflows are cold gas winds on ∼400 pc with a veloc-
+ity of ∼500 km s−1 discovered at far-IR and submillime-
+ter wavelengths (e.g., Spoon et al. 2013; Veilleux et al.
+2013; Cicone et al. 2014; Gonz´alez-Alfonso et al. 2017;
+Laha et al. 2018). However, the properties of outflows in
+many U/LIRGs are still unclear because these methods
+using the blue-shifted emission/absorption lines have
+difficulty detecting weak outflows. Therefore, the new
+methods to systematically reveal the outflow properties
+are necessary to present the schematic picture of the
+merger-driven coevolution.
+The observations of outflowing dust (e.g., H¨onig 2019;
+Venanzi et al. 2020) may be an ideal means for the sys-
+tematic studies on the outflows in U/LIRGs.
+Recent
+mid-IR observations with high spatial resolutions detect
+the extended dust emission along the polar direction,
+called polar dust (e.g., Asmus et al. 2016; Stalevski et al.
+2017). An issue at this point is that, due to the poor
+understanding of the polar dust structure, it is not even
+clear whether the polar dust is (1) the galactic ISM or
+dust in a narrow line region (NLR) only being illumi-
+nated by the AGN or (2) the “outflowing” dusty winds
+launched from the inner edge of the torus. Asmus (2019)
+finds a positive correlation between their physical sizes
+and the Eddington ratios, supporting that the polar dust
+structure may be related to the AGN activities. The
+analytical model of polar dust emission has been imple-
+mented into the latest multiwavelength spectral energy
+distribution (SED) models (e.g., X-CIGALE; Boquien
+et al. 2019; Yang et al. 2020a). These models help us to
+estimate the properties of polar dust (e.g., Toba et al.
+
+3
+2021a; Buat et al. 2021), even though the degeneracy of
+torus and polar dust emission will provide uncertainties.
+The combination of X-ray and IR observations will
+become the best way to constrain the properties of po-
+lar dust. The broadband X-ray study with XCLUMPY
+for several tens of Swift/Burst Alert Telescope (BAT)-
+selected AGNs by Ogawa et al. (2021) successfully con-
+strains the torus covering fractions (CT).
+These esti-
+mates are well consistent with the typical λEdd–CT re-
+lation (Ricci et al. 2017a), while are much smaller than
+those estimated with the IR CLUMPY model (Nenkova
+et al. 2008a,b). They indicate that the difference can
+be explained by the presence of the polar dust, which
+should have small effects on the obscuration in the X-
+ray band but re-radiate the large IR luminosities. Thus,
+the updated CLUMPY model consisting of the clumpy
+torus and polar dust components will provide rich infor-
+mation on polar dust by applying the torus parameters
+obtained by the X-ray fitting with XCLUMPY (Yamada
+et al. 2021).
+In this study, we generate the updated CLUMPY
+model that can reproduce the IR emission from the
+clumpy torus and polar dust, and perform the multi-
+wavelength (hard X-ray to radio) SED decomposition
+for the sample of 57 local U/LIRGs in Yamada et al.
+(2021). We first investigate the features of multiwave-
+length radiation, which are helpful to understand the
+environments from the nucleus to galactic scales. This
+will be incidentally useful for future works to explore
+buried AGNs in U/LIRGs in the distant universe. Tak-
+ing into account these results, we examine the polar dust
+structures and their relation to the AGN activities, and
+finally discuss the coevolution process of the galaxies,
+SMBHs, and outflows in the merger phase.
+This paper is organized as follows.
+In Section 2
+and Section 3, we show the sample and their photo-
+metric data of multiwavelength observations, respec-
+tively.
+Section 4 describes the implementation of the
+updated CLUMPY model we create and the best-fit
+parameters of the multiwavelength SED decomposition.
+Section 5 illustrates the features of multiwavelength
+emission to understand the characteristics of the host
+galaxies and AGNs in U/LIRGs. In Section 6, we dis-
+cuss the structure of the polar dust in U/LIRGs based
+on the results of the multiwavelength SED analysis.
+Section 7 provides the discussion on the coevolution
+process of galaxies, SMBHs, and outflows in U/LIRGs.
+The main results are summarized in Section 8. In this
+paper, we adopt the cosmology of a flat universe with
+H0 = 70 km s−1 Mpc−1, ΩM = 0.3, and ΩΛ = 0.7.
+Throughout this paper, the uncertainties are at the 1σ
+level unless otherwise stated, and the initial mass func-
+tion (IMF) of Chabrier (2003) is assumed.1
+2. SAMPLE
+The sample selection of 57 local U/LIRGs observed
+with the hard X-ray observations is described as fol-
+lows. We focus on the Great Observatories All-sky LIRG
+Survey (GOALS; Armus et al. 2009), which consists
+of 180 LIRGs and 22 ULIRGs in the local universe at
+redshifts z < 0.088. They are contained in the IRAS
+Revised Bright Galaxy Sample (RBGS; Sanders et al.
+2003), a complete sample of 629 extragalactic objects
+having 60 µm fluxes above 5.24 Jy at Galactic latitudes
+|b| > 5◦.
+These U/LIRGs have been observed in the
+multiwavelength bands, by the IR telescopes of Spitzer
+(e.g., Imanishi et al. 2007; D´ıaz-Santos et al. 2010; Pet-
+ric et al. 2011; Inami et al. 2013; Stierwalt et al. 2013),
+AKARI (e.g., Imanishi et al. 2008; Lee et al. 2012; In-
+ami et al. 2018), Herschel (e.g., D´ıaz-Santos et al. 2013,
+2014; Chu et al. 2017; Lu et al. 2017), and X-ray tele-
+scopes of Chandra (e.g., Iwasawa et al. 2011; Torres-
+Alb`a et al. 2018), and NuSTAR (Teng et al. 2015; Ricci
+et al. 2017a, 2021; Privon et al. 2020; Yamada et al.
+2021). Here, we select the same targets as in Yamada
+et al. (2021), the 57 local U/LIRGs containing 84 in-
+dividual galaxies observed with the hard X-ray tele-
+scopes NuSTAR and/or Swift/BAT. According to the
+detailed X-ray spectral analysis combining the available
+soft X-ray observations, our targets are comprised of 40
+AGNs (two unobscured AGNs, 21 obscured AGNs, 16
+CT AGNs, one jet-dominated AGN), and 44 starburst-
+dominant or hard X-ray–undetected sources.
+Here, the source coordinates, redshift, merger stages,
+and the projected separation between the two nuclei are
+taken from Table 1 of Yamada et al. (2021).
+Based
+on high-spatial-resolution images (e.g., Stierwalt et al.
+2013), the merger stages are classified into five stages:
+stage A (galaxy pairs before a first encounter), stage B
+(post-first encounter with symmetric galaxy disks but
+showing signature of tidal tails), stage C (showing some
+signatures of mergers, such as tidal tails, amorphous
+disks), stage D (two nuclei within a common envelope),
+and stage N (no signatures of mergers or massive neigh-
+bors). In the same manner as Yamada et al. (2021), we
+hereafter call stage A–B galaxies as early mergers, stage
+C–D as late mergers, and stage N as nonmergers.
+1 When the values of the star formation rates (SFR) and stellar
+masses (M∗) are referred from previous works, we correct these
+values assuming Salpeter (1955) by decreasing 0.15 and 0.24 dex,
+or values assuming Kroupa (2001) by subtracting 0.02 and 0.03
+dex, respectively (e.g., Santini et al. 2014; Speagle et al. 2014).
+
+4
+Yamada et al.
+Table 1. Basic Information of our Sample
+ID
+IRAS Name
+Object Name
+z
+M
+D12
+D12
+AGN
+Type
+log(LIR)
+IRS
+(arcsec)
+(kpc)
+(L⊙)
+(1)
+(2)
+(3)
+(4)
+(5)
+(6)
+(7)
+(8)
+(9)
+(10)
+(11)
+ID01
+F00085−1223
+NGC 34
+0.0196
+D
+S
+S
+Y
+Obs
+11.49
+Y
+ID02
+F00163−1039a
+MCG−02-01-052/MCG−02-01-051
+0.0272
+B
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+ID03
+F00163−1039 N
+MCG−02-01-052
+0.0273
+B
+56.1
+30.7
+n
+n
+[11.48]
+n
+ID04
+F00163−1039 S
+MCG−02-01-051
+0.0271
+B
+56.1
+30.7
+n
+n
+11.48
+Y
+ID05
+F00344−3349
+ESO 350−38
+0.0206
+C
+5.2
+2.2
+Y?
+n
+11.28
+Y
+ID06
+F00402−2349a
+NGC 232/NGC 235
+0.0224
+B
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+ID07
+F00402−2349 W
+NGC 232
+0.0226
+B
+120.8
+54.7
+n
+n
+[11.44]:
+Y
+ID08
+F00402−2349 E
+NGC 235
+0.0222
+B
+120.8
+54.7
+Y
+Obs
+[11.44]:
+Y
+ID09
+F00506+7248
+MCG+12-02-001
+0.0157
+C
+0.9
+0.3
+Y
+CT
+11.50
+Y
+ID10
+F01053−1746b
+IC 1623A/IC 1623B
+0.0202
+C
+15.7
+6.4
+n
+n/n
+11.71
+n/Y
+ID11
+F02071−1023a
+NGC 833/NGC 835
+0.0132
+A
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+ID12
+F02071−1023 W2
+NGC 833
+0.0129
+A
+56.4
+15.3
+Y
+Obs
+[11.05]:
+Y
+ID13
+F02071−1023 W
+NGC 835
+0.0136
+A
+56.4
+15.3
+Y
+Obs
+[11.05]:
+Y
+ID14
+F02071−1023 E
+NGC 838
+0.0128
+A
+148.8
+39.1
+n
+n
+[11.05]:
+Y
+ID15
+F02071−1023 S
+NGC 839
+0.0129
+A
+148.8
+39.1
+n
+n
+[11.05]:
+Y
+ID16
+F02401−0013
+NGC 1068
+0.0038†
+N
+n
+n
+Y
+CT
+11.40
+Y
+ID17
+F03117+4151a
+UGC 2608/UGC 2612
+0.0276
+N
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+ID18
+F03117+4151 N
+UGC 2608
+0.0233
+N
+n
+n
+Y
+CT
+11.41
+Y
+ID19
+F03117+4151 S
+UGC 2612
+0.0318
+N
+n
+n
+n
+n
+[11.41]
+Y
+ID20
+F03164+4119
+NGC 1275
+0.0176
+N
+n
+n
+Y
+Jet
+11.26
+Y
+ID21
+F03316−3618
+NGC 1365
+0.0055†
+N
+n
+n
+Y
+Obs
+11.00
+Y
+ID22
+F04454−4838
+ESO 203−1
+0.0529
+B
+7.5
+7.7
+n
+n
+11.86
+Y
+ID23
+F05054+1718a
+CGCG 468-002W/CGCG 468-002E
+0.0171
+B
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+ID24
+F05054+1718 W
+CGCG 468-002W
+0.0175
+B
+29.5
+10.3
+Y
+Obs
+[11.22]:
+Y
+ID25
+F05054+1718 E
+CGCG 468-002E
+0.0168
+B
+29.5
+10.3
+n
+n
+[11.22]:
+Y
+ID26
+F05189−2524
+IRAS F05189−2524
+0.0426
+D
+S
+S
+Y
+Obs
+12.16
+Y
+ID27
+F06076−2139b
+IRAS F06076−2139/
+0.0374
+C
+8.3
+6.2
+Y
+Obs/n
+11.65
+Y/n
+2MASS 06094601−2140312
+ID28
+F08354+2555
+NGC 2623
+0.0185
+D
+S
+S
+Y
+Obs
+11.60
+Y
+ID29
+F08520−6850b
+ESO 060−IG016 West/East
+0.0451
+B
+15.4
+13.6
+Y
+n/Obs
+11.82
+n/Y
+ID30
+F08572+3915
+IRAS F08572+3915
+0.0580
+D
+4.4
+5.6
+Y
+Obs
+12.16
+Y
+ID31
+F09320+6134
+UGC 5101
+0.0394
+D
+S
+S
+Y
+Obs
+12.01
+Y
+ID32
+F09333+4841a
+MCG+08-18-012/MCG+08-18-013
+0.0255
+A
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+ID33
+F09333+4841 W
+MCG+08-18-012
+0.0252
+A
+65.3
+33.6
+n
+n
+[11.34]
+n
+ID34
+F09333+4841 E
+MCG+08-18-013
+0.0259
+A
+65.3
+33.6
+n
+n
+11.34
+Y
+ID35
+F10015−0614a
+MCG−01-26-013/NGC 3110
+0.0165
+A
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+ID36
+F10015−0614 S
+MCG−01-26-013
+0.0161
+A
+108.8
+36.5
+n
+n
+[11.37]
+n
+ID37
+F10015−0614 N
+NGC 3110
+0.0169
+A
+108.8
+36.5
+n
+n
+11.37
+Y
+ID38
+F10038−3338
+ESO 374−IG032
+0.0340
+D
+S
+S
+Y?
+n
+11.78
+Y
+ID39
+F10257−4339
+NGC 3256
+0.0094
+D
+5.1
+1.0
+n
+n
+11.64
+Y
+ID40
+F10565+2448
+IRAS F10565+2448
+0.0431
+D
+7.4
+6.7
+n
+n
+12.08
+Y
+Table 1 continued
+
+5
+Table 1 (continued)
+ID
+IRAS Name
+Object Name
+z
+M
+D12
+D12
+AGN
+Type
+log(LIR)
+IRS
+(arcsec)
+(kpc)
+(L⊙)
+(1)
+(2)
+(3)
+(4)
+(5)
+(6)
+(7)
+(8)
+(9)
+(10)
+(11)
+ID41
+F11257+5850b
+NGC 3690 West/East
+0.0103
+C
+22.0
+4.6
+Y
+CT/n
+11.93
+Y/Y
+ID42
+F12043−3140b
+ESO 440−58/MCG−05-29-017
+0.0230
+B
+11.8
+5.5
+n
+n/n
+11.43
+Y/Y
+ID43
+F12112+0305
+IRAS F12112+0305
+0.0733
+D
+3.0
+4.1
+n
+n
+12.36
+Y
+ID44
+F12243−0036a
+NGC 4418/MCG+00-32-013
+0.00735
+A
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+ID45
+F12243−0036 NW
+NGC 4418
+0.0073†
+A
+179.9
+29.4
+Y?
+n
+11.19
+Y
+ID46
+F12243−0036 SE
+MCG+00-32-013
+0.0074†
+A
+179.9
+29.4
+n
+n
+[11.19]
+n
+ID47
+F12540+5708
+Mrk 231
+0.0422
+D
+S
+S
+Y
+Obs
+12.57
+Y
+ID48
+F12590+2934b
+NGC 4922S/NGC 4922N
+0.0238
+C
+22.1
+10.6
+Y
+n/Obs
+11.38
+n/Y
+ID49
+F13126+2453
+IC 860
+0.0112
+N
+n
+n
+n
+n
+11.14
+Y
+ID50
+13120−5453
+IRAS 13120−5453
+0.0308
+D
+S
+S
+Y
+CT
+12.32
+Y
+ID51
+F13188+0036
+NGC 5104
+0.0186
+N
+n
+n
+n
+n
+11.27
+Y
+ID52
+F13197−1627
+MCG−03-34-064
+0.0165
+N
+n
+n
+Y
+Obs
+11.28
+Y
+ID53
+F13229−2934
+NGC 5135
+0.0137
+N
+n
+n
+Y
+CT
+11.30
+Y
+ID54
+F13362+4831b
+Mrk 266B/Mrk 266A
+0.0278
+B
+10.1
+5.6
+Y
+CT/Obs
+11.56
+Y/Y
+ID55
+F13428+5608
+Mrk 273
+0.0378
+D
+0.9
+0.7
+Y
+Obs
+12.21
+Y
+ID56
+F14348−1447
+IRAS F14348−1447
+0.0827
+D
+3.4
+5.2
+Y
+CT
+12.39
+Y
+ID57
+F14378−3651
+IRAS F14378−3651
+0.0681
+D
+S
+S
+n
+Y
+12.23
+Y
+ID58
+F14544−4255b
+IC 4518A/IC 4518B
+0.0159
+B
+35.5
+11.5
+Y
+Obs/n
+11.23
+Y/n
+ID59
+F15250+3608
+IRAS F15250+3608
+0.0552
+D
+0.7
+0.8
+n
+n
+12.08
+Y
+ID60
+F15327+2340b
+Arp 220W/Arp 220E
+0.0181
+D
+1.0
+0.4
+Y
+CT/n
+12.28
+Y(u)
+ID61
+F16504+0228b
+NGC 6240S/NGC 6240N
+0.0245
+D
+1.7
+0.8
+Y
+CT
+11.93
+Y(u)
+ID62
+F16504+0228a
+NGC 6285/NGC 6286
+0.0186
+B
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+ID63
+F16577+5900 N
+NGC 6285
+0.0190
+B
+91.0
+34.5
+n
+n
+[11.37]
+Y
+ID64
+F16577+5900 S
+NGC 6286
+0.0183
+B
+91.0
+34.5
+Y
+CT
+11.37
+Y
+ID65
+F17138−1017
+IRAS F17138−1017
+0.0173
+D
+S
+S
+Y
+Obs
+11.49
+Y
+ID66
+F18293−3413
+IRAS F18293−3413
+0.0182
+N
+S
+S
+n
+n
+11.88
+Y
+ID67
+F19297−0406
+IRAS F19297−0406
+0.0857
+D
+S
+S
+n
+n
+12.45
+Y
+ID68
+F20221−2458b
+NGC 6907/NGC 6908
+0.0104
+B
+43.9
+9.4
+n
+n/n
+11.11
+Y/n
+ID69
+20264+2533a
+NGC 6921/MCG+04-48-002
+0.0142
+A
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+ID70
+20264+2533 W
+NGC 6921
+0.0145
+A
+91.4
+26.5
+Y
+CT
+[11.11]
+n
+ID71
+20264+2533 E
+MCG+04-48-002
+0.0139
+A
+91.4
+26.5
+Y
+Obs
+11.11
+Y
+ID72
+F20550+1655b
+II Zw 096/IRAS F20550+1655 SE
+0.0353
+C
+11.6
+8.1
+n
+n/n
+11.94
+Y/Y
+ID73
+F20551−4250
+ESO 286−19
+0.0430
+D
+S
+S
+n
+n
+12.06
+Y
+ID74
+F21453−3511
+NGC 7130
+0.0162
+N
+n
+n
+Y
+CT
+11.42
+Y
+ID75
+F23007+0836a
+NGC 7469/IC 5283
+0.0162
+A
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+ID76
+F23007+0836 S
+NGC 7469
+0.0163
+A
+79.7
+26.2
+Y
+Unobs
+11.65
+Y
+ID77
+F23007+0836 N
+IC 5283
+0.0160
+A
+79.7
+26.2
+n
+n
+[11.65]
+n
+ID78
+F23128−5919
+ESO 148−2
+0.0446
+C
+4.5
+3.9
+Y
+CT
+12.06
+Y
+ID79
+F23157+0618
+NGC 7591
+0.0165
+N
+n
+n
+n
+n
+11.12
+Y
+ID80
+F23254+0830a
+NGC 7674/MCG+01-59-081
+0.0292
+A
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+Table 1 continued
+
+6
+Yamada et al.
+Table 1 (continued)
+ID
+IRAS Name
+Object Name
+z
+M
+D12
+D12
+AGN
+Type
+log(LIR)
+IRS
+(arcsec)
+(kpc)
+(L⊙)
+(1)
+(2)
+(3)
+(4)
+(5)
+(6)
+(7)
+(8)
+(9)
+(10)
+(11)
+ID81
+F23254+0830 W
+NGC 7674
+0.0289
+A
+33.3
+19.5
+Y
+Obs
+11.56
+Y
+ID82
+F23254+0830 E
+MCG+01-59-081
+0.0295
+A
+33.3
+19.5
+n
+n
+[11.56]
+n
+ID83
+23262+0314a
+NGC 7679/NGC 7682
+0.0171
+A
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+ID84
+23262+0314 W
+NGC 7679
+0.0171
+A
+269.8
+93.8
+Y
+Unobs
+11.11
+Y
+ID85
+23262+0314 E
+NGC 7682
+0.0171
+A
+269.8
+93.8
+Y
+Obs
+[11.11]
+n
+Note—Columns: (1) Target ID; (2) IRAS name. “a” marks 13 total systems of resolved pairs to our targets. “b” marks 12 U/LIRGs (24
+individual galaxies) that are too close to be separated by the Hershel PACS 70 µm images or UV-to-near-IR images; (3) object name; (4)
+redshift from NASA/IPAC Extragalactic Database (NED); (5) merger stage based on the high-spatial-resolution images (e.g., Stierwalt
+et al. 2013); (6–7) projected separation between the two nuclei in arcseconds and kiloparsecs. S and n mean that a single nucleus is
+observed in merging and nonmerging U/LIRGs, respectively; (8) Y and n mark the presence of a hard X-ray–detected AGN or not,
+respectively. Y? marks AGN candidates among the hard X-ray–undetected sources identified by the multiwavelength SED analysis (see
+Section 4.2.4); (9) X-ray classification (Unobs = unobscured AGN, Obs = obscured AGN, CT = CT AGN, Jet = jet-dominant AGN,
+and n = hard X-ray–undetected sources); (10) logarithmic total IR luminosity in units of L⊙ (Armus et al. 2009). Values in brackets
+should be upper limits due to contamination from nearby much brighter (or equally bright with the suffix “:”) IR sources; (11) Y and
+n mark detection and nondetection with Spitzer/IRS in the 10–20 µm (SH) or 19–38 µm (LH) band, respectively (Alonso-Herrero et al.
+2012; Mazzarella et al. 2012; Inami et al. 2013). The (u) means that the two nuclei are not divided. All information in Column (2–11)
+are referred from Yamada et al. (2021).
+† Throughout the paper, redshift-independent measurements of the luminosity distance are utilized for the multiwavelength results (e.g.,
+luminosities) of the closest objects at z < 0.01, NGC 1068 (14.4 Mpc; Tully 1988; Bauer et al. 2015), NGC 1365 (17.3 Mpc; Venturi et al.
+2018), and NGC 4418/MCG+00-32-013 (34 Mpc; e.g., Ohyama et al. 2019).
+(This table is available in its entirety in machine-readable form.)
+Some of the pair galaxies are too close to be separated
+by the other wavelength bands. Particularly, the spa-
+tial distributions of far-IR emissions within the GOALS
+sources are poorly determined because of the limitations
+in the angular resolution of pre-Herschel data (IRAS,
+ISO, and AKARI). Chu et al. (2017) provided the total
+system fluxes and component fluxes (where possible) in
+all Herschel bands for the GOALS sample. The beam
+profiles have a mean FWHM value of 5.′′6 for the Pho-
+todetector Array Camera and Spectrometer (PACS; Pil-
+bratt et al. 2010) 70 µm band, the shortest wavelength
+band of Herschel data. After the cross-matching with
+multiwavelength catalogs (Section 3), we treat each in-
+teracting pair as a total system for 11 U/LIRGs (22
+individual galaxies) that are too close (with a projected
+separation of ≲20′′) to be resolved by the Hershel PACS
+images, whose flux densities of individual galaxies are
+summed in all wavelength bands. Since we do not ob-
+tain any fluxes for IC 4518B but for a total system in
+the UV-to-near-IR bands, the other wavelength pho-
+tometries are also combined as total fluxes of IC 4518A
+and IC 4518B (35.′′5). Here, the 12 pairs are unresolved
+among 84 galaxies, and thus our sample has 72 individ-
+ual sources in 57 local U/LIRGs.
+Finally, to investigate the difference between the re-
+sults of multiwavelength SED analysis by using the com-
+bined photometry of a total system and separated pho-
+tometries of the individual galaxies, we duplicately add
+the 13 total systems of resolved pairs (with a projected
+separation of ≳30′′) to our targets (see Section 4.4).
+Therefore, our sample host 85 sources consisting of 72
+individual sources and 13 systems of resolved pairs.
+3. MULTIWAVELENGTH OBSERVATIONS
+For the 57 U/LIRGs (containing 84 individual sources
+in Yamada et al. 2021), we compiled the multiwave-
+length data from hard X-ray to radio bands. As noted in
+Section 2, the system fluxes of the close interacting pairs
+are calculated by adding the component fluxes. We note
+that neither the upper limits nor low-significant (<5σ)
+values were utilized unless otherwise stated.
+While
+considering the spatial resolutions of individual instru-
+ments, we took care to utilize the multiwavelength pho-
+tometries whose apertures sufficiently cover the fluxes
+derived from the extended emission of each target. In
+the following sections, we describe the multiwavelength
+data for each telescope. The characteristics of the mul-
+tiwavelength surveys are summarized in Table 2.
+
+7
+Table 2. Characteristics of the Multiwavelength Catalogs Utilized in This Work
+Class
+Instrument
+Band
+Wavelength
+∆R (FWHM)
+Area Coverage
+Ref.
+(1)
+(2)
+(3)
+(4)
+(5)
+(6)
+(7)
+Hard X-ray
+Swift/BAT
+14–195 keV
+0.0064–0.0886 nm
+1170′′
+All sky
+1,2,3
+NuSTAR
+3–79 keV
+0.016–0.413 nm
+18′′
+Targeted obs.
+3,4
+Suzaku/HXD-PIN
+10–70 keV
+0.018–0.124 nm
+· · ·
+Targeted obs.
+3,5
+Soft X-ray
+XMM-Newton
+0.1–15 keV
+0.083–12.40 nm
+∼6′′
+Targeted obs.
+3,6
+Chandra
+0.2–10 keV
+0.12–6.20 nm
+≲0.′′5
+Targeted obs.
+3,7
+Suzaku/XIS
+0.2–12 keV
+0.10–6.20 nm
+96′′–120′′
+Targeted obs.
+3,5
+Swift/XRT
+0.3–10 keV
+0.12–4.13 nm
+8.′′8
+Targeted obs.
+1,3
+UV
+GALEX
+FUV
+152.8 (134.4–178.6) nm
+4.′′2
+24,790 deg2
+8,9
+GALEX
+NUV
+231.0 (177.1–283.1) nm
+5.′′2
+24,790 deg2
+8,9
+Optical
+Pan-STARRS
+g
+481.1 (394.3–559.3) nm
+1.′′47
+δ ≥ −30◦ (3π)
+10,11
+Pan-STARRS
+r
+615.6 (538.6–703.6) nm
+1.′′31
+δ ≥ −30◦ (3π)
+10,11
+Pan-STARRS
+i
+750.4 (677.8–830.4) nm
+1.′′19
+δ ≥ −30◦ (3π)
+10,11
+Pan-STARRS
+z
+866.9 (802.8–934.6) nm
+1.′′14
+δ ≥ −30◦ (3π)
+10,11
+Pan-STARRS
+y
+961.3 (910.1–1083.9) nm
+1.′′09
+δ ≥ −30◦ (3π)
+10,11
+SkyMapper
+u
+350.0 (306.7–386.7) nm
+3.′′1
+δ ≲ 0◦ (2π)
+10,12,13
+SkyMapper
+v
+387.9 (355.0–421.7) nm
+2.′′9
+δ ≲ 0◦ (2π)
+10,12,13
+SkyMapper
+g
+501.6 (410.3–657.0) nm
+2.′′6
+δ ≲ 0◦ (2π)
+10,12,13
+SkyMapper
+r
+607.7 (492.5–723.2) nm
+2.′′4
+δ ≲ 0◦ (2π)
+10,12,13
+SkyMapper
+i
+773.3 (692.9–864.7) nm
+2.′′3
+δ ≲ 0◦ (2π)
+10,12,13
+SkyMapper
+z
+912.0 (815.9–1067.9) nm
+2.′′3
+δ ≲ 0◦ (2π)
+10,12,13
+SDSS
+u
+355.1 nm
+1.′′53
+14,555 deg2
+14,15
+SDSS
+g
+468.6 nm
+1.′′44
+14,555 deg2
+14,15
+SDSS
+r
+616.5 nm
+1.′′32
+14,555 deg2
+14,15
+SDSS
+i
+748.1 nm
+1.′′26
+14,555 deg2
+14,15
+SDSS
+z
+893.1 nm
+1.′′29
+14,555 deg2
+14,15
+Near-IR
+2MASS
+J
+1.235 (1.081–1.407) µm
+∼2.′′5
+All sky
+10,16,17
+2MASS
+H
+1.662 (1.479–1.823) µm
+∼2.′′5
+All sky
+10,16,17
+2MASS
+Ks
+2.159 (1.954–2.355) µm
+∼2.′′5
+All sky
+10,16,17
+Mid-IR
+WISE
+W1
+3.353 (2.754–3.872) µm
+6.′′1
+All sky
+10,18
+WISE
+W2
+4.603 (3.963–5.341) µm
+6.′′4
+All sky
+10,18
+WISE
+W3
+11.56 (7.443–17.261) µm
+6.′′5
+All sky
+10,18
+WISE
+W4
+22.09 (19.52–27.91) µm
+12.′′0
+All sky
+10,18
+AKARI
+S9W
+8.228 (5.846–12.188) µm
+5.′′5
+All sky
+10,19,20
+AKARI
+L18W
+17.61 (13.61–28.67) µm
+5.′′7
+All sky
+10,19,20
+Far-IR
+Herschel
+PACS blue
+70 µm (60–85) µm
+5.′′6
+Targeted obs.†
+21,22
+Herschel
+PACS green
+100 µm (85–130) µm
+6.′′8
+Targeted obs.†
+21,22
+Herschel
+PACS red
+160 µm (130–210) µm
+11.′′3
+Targeted obs.†
+21,22
+Herschel
+PSW
+250 µm
+18.′′1
+Targeted obs.†
+21,23
+Herschel
+PMW
+350 µm
+25.′′2
+Targeted obs.†
+21,23
+Herschel
+PLW
+500 µm
+36.′′6
+Targeted obs.†
+21,23
+Radio
+VLA (VLASS)
+3.0 GHz
+99.9 mm
+2.5′′
+δ ≥ −40◦ (3.3π)
+24
+VLA (NVSS)
+1.4 GHz
+214.1 mm
+45′′
+δ ≥ −40◦ (3.3π)
+25
+VLA (FIRST)
+1.4 GHz
+214.1 mm
+5′′
+10,575 deg2
+26
+VLA (WENSS)
+325.125 MHz
+922.1 mm
+54′′
+δ ≥ +30◦ (π)
+27
+VLA (VLSSr)
+73.8 MHz
+4.06 m
+75′′
+δ ≥ −40◦ (3.3π)
+28
+MOST (SUMSS)
+843 MHz
+355.6 mm
+45′′
+δ ≤ −30◦ (π)
+29,30
+MWA (GLEAM)
+170–231 MHz
+1.50 (1.30–1.76) m
+120′′
+δ ≤ +30◦ (3π)
+31,32
+MWA (GLEAM)
+147–154 MHz
+1.99 (1.95–2.04) m
+120′′
+δ ≤ +30◦ (3π)
+31,32
+MWA (GLEAM)
+72–80 MHz
+3.94 (3.75–4.16) m
+120′′
+δ ≤ +30◦ (3π)
+31,32
+GMRT (TGSS)
+147.5 (140–156) MHz
+2.03 (1.92–2.14) m
+25′′
+δ ≥ −53◦ (3.6π)
+33
+Note—Comments: (1) wavelength class; (2–3) instrument and its wavelength band; (4) wavelength range for the X-ray bands, effective
+wavelength for the UV-to-far-IR bands, and the typical wavelength for the radio bands. Bandwidth is denoted in parentheses; (5)
+angular resolution; (6) area coverage of each survey; (7) References of column (3)–(6).
+References: (1) Gehrels et al. (2004); (2) Oh et al. (2018); (3) Yamada et al. (2021) and the references therein; (4) Harrison et al.
+(2013); (5) Mitsuda et al. (2007); (6) Jansen et al. (2001); (7) Garmire et al. (2003); (8) Bianchi et al. (2017); (9) Morrissey et al.
+(2007); (10) Spanish Virtual Observatory (SVO) Filter Profile Servise (http://svo2.cab.inta-csic.es/theory/fps/; (11) Chambers et al.
+(2016); (12) Wolf et al. (2018); (13) Onken et al. (2019); (14) Albareti et al. (2017); (15) Ahumada et al. (2020) and the information
+(scope and image quality) on the DR16 website (https://www.sdss.org/dr16/); (16) Cohen et al. (2003); (17) Skrutskie et al. (2006);
+(18) Wright et al. (2010); (19) Murakami et al. (2007); (20) Ishihara et al. (2010); (21) Chu et al. (2017); (22) Poglitsch et al.
+(2010); (23) Griffin et al. (2010); (24) Gordon et al. (2021); (25) Condon et al. (1998); (26) Helfand et al. (2015); (27) Rengelink
+et al. (1997); (28) Lane et al. (2014); (29) Mauch et al. (2003); (30) Mauch et al. (2008); (31) Hurley-Walker et al. (2017); (32)
+Hurley-Walker et al. (2019); (33) Intema et al. (2017).
+† All of U/LIRGs in GOALS sample are mapped by the Herschel with both the PACS and SPIRE (see Chu et al. 2017).
+
+8
+Yamada et al.
+3.1. X-ray Spectra
+Among 57 U/LIRGs, Yamada et al. (2021) carried out
+the broadband X-ray spectral analysis for 49 U/LIRG
+systems by using all of the available NuSTAR, Chan-
+dra (Garmire et al. 2003), XMM-Newton (Jansen et al.
+2001), and Suzaku (Mitsuda et al. 2007) data observed
+by 2020 April.
+They also performed the analysis of
+Swift/X-Ray Telescope (XRT; Burrows et al. 2005) data
+when no other soft X-ray data were obtained, and uti-
+lized the Swift/BAT spectra in the 105-month catalog
+(Oh et al. 2018) if detected.
+Considering that X-ray
+spectral works support the clumpy nature of AGN tori
+(see e.g., Liu & Li 2014; Furui et al. 2016; Tanimoto et al.
+2018, 2019; Buchner et al. 2019), these best-fitting mod-
+els were provided with a Monte Carlo-based model from
+a clumpy torus (XCLUMPY; Tanimoto et al. 2019),
+which enables us to constrain the torus covering frac-
+tions for individual AGNs (e.g., Ogawa et al. 2019, 2021;
+Tanimoto et al. 2020, 2022; Yamada et al. 2020, 2021;
+Uematsu et al. 2021; Inaba et al. 2022). The broadband
+X-ray spectral analysis for three other sources UGC
+2608, NGC 5135, and NGC 7469 was also conducted
+with XCLUMPY (Yamada et al. 2020; Ogawa et al.
+2021). Therefore, we compiled these X-ray results of 52
+U/LIRG systems with XCLUMPY to compare the re-
+sults from the multiwavelength SED decomposition with
+an updated CLUMPY model (Section 4.1).
+For the other five U/LIRGs, Yamada et al. (2021)
+only analyzed the NuSTAR data because their spec-
+tra show complex features. Instead of the XCLUMPY
+model,
+we
+analyzed
+their
+NuSTAR
+spectra
+(∼3–
+70 keV) by adopting the best-fitting models in pre-
+vious works for three nonmerging LIRGs NGC 1068
+(M2d in Bauer et al. 2015), NGC 1275 (Model2 in Rani
+et al. 2018), NGC 1365 (final model for Observation
+4 in Rivers et al. 2015), and two dual-AGN systems
+Mrk 266B/Mrk 266A (SW-R model in Iwasawa et al.
+2020)2 and NGC 6240S/NGC 6240N (sum of two AGN
+models with MYtorus in Puccetti et al. 2016), respec-
+tively.
+The best-fitting spectral models were applied in the
+multiwavelength SEDs.
+By following the same man-
+ner as Yamada et al. (2021), we calculated the 5σ up-
+per limits in the 8–24 keV band from the NuSTAR
+2 The torus reflection component reproduced by the SW-R model
+(Ikeda et al. 2009) is defined only in the 1–100 keV band. As-
+suming the power-law model with the same slope as in the 80–
+100 keV band, we approximately expanded the X-ray model to
+the 100–200 keV spectra in Figures E1 and E7.
+counts for the hard X-ray–undetected sources, by us-
+ing the HEASARC tool WebPIMMS v4.11a assuming
+a power law of Γ = 1.8 (e.g., Ueda et al. 2014; Ricci
+et al. 2017b) with Galactic absorption, whose hydro-
+gen column density was fixed at the value of Willingale
+et al. (2013). The 2–7 keV upper limits were provided
+from the XMM-Newton/MOS (MOS1 and MOS2) for
+IC 5283 and MCG+01-59-081, since their NuSTAR 8–
+24 keV fluxes were smaller than those of the interacting
+companion that causes the high contamination.
+3.2. UV Photometry
+The far-UV (FUV; λeff ∼ 152.8 nm) and near-UV
+(NUV; λeff ∼ 231.0 nm) photometries were compiled
+from the latest version of the Galaxy Evolution Ex-
+plore (GALEX; Martin et al. 2005; Bianchi et al. 2011)
+satellite catalog (GR6plus7 data release; Bianchi et al.
+2017).3 The GALEX observation area covers almost all
+of the sky (≳ 90%). Cross-matching the optical posi-
+tions of the individual nuclei and the UV peak positions,
+we extracted the GALEX photometries (FUV mag and
+NUV mag). To ensure reliable data, we finally selected
+the data with Fexf = 0 and Nexf = 0, where the Fexf
+and Nexf represent the extended flags for FUV and NUV
+bands, respectively.
+3.3. Optical Photometry
+The
+optical
+photometries
+were
+taken
+from
+the
+large catalogs with three ground-base telescopes, Pan-
+STARRS1 (PS1) DR2 (e.g., Chambers et al. 2016;
+Flewelling et al. 2020; Magnier et al. 2020a,b,c; Waters
+et al. 2020), SkyMapper Southern Survey DR1 and DR2
+(Wolf et al. 2018; Onken et al. 2019), and SDSS DR16
+(Ahumada et al. 2020). The current coverage areas are
+∼3/4 sky (north of δ = −30◦) for Pan-STARRS, ∼1/2
+sky (south of δ = 0◦) for SkyMapper, and ∼1/3 sky (a
+large part of the northern area) for SDSS. We preferen-
+tially used the Pan-STARRS mean object magnitudes
+in g, r, i, z, and y bands. Since most of our targets are
+extended sources, we calculated the flux densities from
+their Kron magnitudes (Kron 1980), which were cor-
+rected for the missing fluxes (about 10%)4 by multiply-
+ing 100/90 (or −0.115 mag). When the Pan-STARRS
+data were not available, we applied the SkyMapper data
+in u, v, g, r, i, and z bands. Since the Petrosian magni-
+tudes for extended sources were given in the SkyMapper
+catalog, we adopted them and corrected for the missing
+3 The GALEX observations utilized in this paper can be accessed
+via 10.17909/t9-pyxy-kg53.
+4 https://outerspace.stsci.edu/display/PANSTARRS/PS1+
+Kron+photometry+of+extended+sources
+
+9
+fluxes by −0.130 mag (Graham et al. 2005) assuming
+the typical Sersic index to be 3 (e.g., Haan et al. 2011).
+We finally chose the SDSS photometry (cmodelMag) in
+u, g, r, i, and z bands for the other sources, and for
+NGC 4418/MCG+00-32-013 and Mrk 266B/Mrk 266A
+because the Pan-STARRS photometries of these two
+systems were >0.4 mag fainter than those of SDSS val-
+ues.
+We extracted the optical photometry from these cat-
+alogs in each of three bins, u–v, g–z, and y bands. The
+averaged differences of the optical magnitudes, ∆Mag
+(SkyMapper − Pan-STARRS) = 0.07, 0.11, −0.12,
+−0.16, and ∆Mag (SDSS − Pan-STARRS) = 0.14, 0.11,
+0.02, −0.19 for g, r, i, and z bands, respectively. Here,
+we systematically added the 10% uncertainties (∼0.115
+mag) for the whole optical flux densities as a systematic
+error derived from the different measurements. We ex-
+cluded five pieces of the optical photometry for NGC 232
+(SkyMapper v-band), ESO 374−IG032 (SkyMapper v-
+band), IRAS F12112+0305 (Pan-STARRS y-band), and
+NGC 6907/NGC 6908 (SkyMapper u–v bands) because
+their flux densities were much smaller than those in
+other optical bands by a factor of 3–10.
+3.4. Near-IR Photometry
+In the near-IR bands, we utilized the data of the Two
+Micron All Sky Survey (2MASS; Skrutskie et al. 2006).5
+The effective wavelengths of 2MASS filters are 1.235 µm,
+1.662 µm, and 2.159 µm for J, H, and Ks bands, re-
+spectively (Turner 2011). The data of our targets were
+taken from the extended catalog. Since the values were
+not presented only for IRAS F17138–1017, we took its
+values from the point source catalog.
+Finally, we ex-
+tracted the data with cc flg = “000” to avoid the effects
+of artifacts.
+3.5. Mid-IR Photometry
+The mid-IR data were compiled from the Wide-field
+IR Survey Explorer (WISE; Wright et al. 2010) and
+AKARI (Murakami et al. 2007).6 We employed the pho-
+tometry in W1 (3.4 µm), W2 (4.6 µm), W3 (12 µm),
+and W4 (22 µm) bands from the ALLWISE catalog
+(Cutri et al. 2021), or ALLSKY catalog (Cutri & et al.
+2012) if not obtained. We primarily utilized the “gmag”
+(elliptical aperture magnitude), or secondarily “mpro”
+(instrumental profile-fit photometry magnitude), with
+w1-4sat=0 and w1-4cc map=0. The AKARI fluxes in
+5 The Digital Object Identifier (DOI) of the 2MASS catalog is
+10.26131/IRSA2.
+6 The DOIs of the WISE and AKARI catalogs are 10.26131/IRSA1
+and 10.26131/IRSA181, respectively.
+S9W (9 µm) and L18W (18 µm) bands were obtained
+from AKARI/IRC mid-IR all-sky Survey (Ishihara et al.
+2010), where we selected the data with q S09=0 &
+X09=0 for S9W, and q S18=0 & X18=0 for L18W, re-
+spectively.
+3.6. Far-IR Photometry
+We applied the far-IR fluxes presented by Chu et al.
+(2017), using the Herschel Space Observatory (Pilbratt
+et al. 2010) Photodetector Array Camera and Spec-
+trometer (PACS; Poglitsch et al. 2010) and the Spec-
+tral and Photometric Imaging Receiver (SPIRE; Griffin
+et al. 2010). For all the PACS bands (70 µm, 100 µm,
+160 µm) and SPIRE bands (250 µm, 350 µm, 500 µm),
+they computed the total system fluxes and component
+fluxes of individual galaxies (where possible) for the en-
+tire GOALS sample. The aperture radius was set by the
+band with the largest beam size for each instrument:
+usually the 160 µm band for PACS, and the 500 µm
+band for SPIRE.
+3.7. Radio Photometry
+Radio surveys with large sky coverages have been per-
+formed over a wide frequency range (see e.g., Shimwell
+et al. 2019; Stein et al. 2021). In our study, we utilized
+eight kinds of wide-area radio catalogs, which have been
+conducted with four main telescopes: Karl G. Jansky
+Very Large Array (VLA), Molonglo Observatory Syn-
+thesis Telescope (MOST; Mills 1981; Robertson 1991),
+Murchison Widefield Array (MWA; Lonsdale et al.
+2009; Tingay et al. 2013), and Giant Metrewave Radio
+Telescope (GMRT; Swarup 1991).
+The catalogs are
+described below:
+The catalogs of the VLA observations:
+(1) The Very Large Array Sky Survey (VLASS; Gor-
+don et al. 2021), observing the entire sky north of
+δ = −40◦ (82% sky region) at 3 GHz.
+(2) The NRAO VLA Sky Survey (NVSS; Condon
+et al. 1998) covering the sky north of δ = −40◦
+at 1.4 GHz.
+(3) The Faint Images of the Radio Sky at Twenty-
+centimeters (FIRST; Helfand et al. 2015), observ-
+ing in 10,575 deg2 of sky coverage (8,444 deg2
+in the north Galactic cap and 2,131 deg2 in the
+southern cap) at 1.4 GHz.
+(4) The Westerbork Northern Sky Survey (WENSS;
+Rengelink et al. 1997), a low-frequency radio sur-
+vey that will cover the whole sky north of δ = +30◦
+at 325.125 MHz.
+
+10
+Yamada et al.
+(5) The
+VLA
+Low-frequency
+Sky
+Survey
+Redux
+(VLSSr; Cohen et al. 2007; Lane et al. 2014), cov-
+ering the sky north of δ = −40◦ at 73.8 MHz.
+The catalogs of the other radio observations:
+(6) The Sydney University Molonglo Sky Survey
+(SUMSS) catalog, Version 2.1r (updated in 2012;
+Mauch et al. 2003, 2008) with MOST, covering
+the sky south of δ = −30◦ at 843 MHz. The data
+of IRAS F13120–5453 are not listed in the original
+catalog but are obtained from Allison et al. (2014).
+(7) The GaLactic and Extragalactic All-sky MWA
+(GLEAM; Hurley-Walker et al. 2017) survey, cov-
+ering 24,831 deg2 over sky south of δ = +30◦
+and Galactic latitudes outside 10◦ of the Galactic
+plane, excluding some areas such as the Magellanic
+Clouds, across 72–231 MHz. Hurley-Walker et al.
+(2019) also presented the GLEAM catalog of the
+Galactic plane (2,860 deg2); in which only the sys-
+tem of MCG+04-48-002 and NGC 6921 was con-
+tained, but their fluxes were not utilized because
+both galaxies are not divided by the MWA. To
+get similar data from VLA catalogs for northern-
+sky targets, we picked out the fluxes in the 170–
+231 MHz, 147–154 MHz, and 72–80 MHz bands.
+(8) The TIFR GMRT Sky Survey (TGSS; Intema
+et al. 2017), observing 36,900 deg2 of the sky
+north of δ = −53◦ (∼90% sky), at 147.5 MHz
+(with a bandwidth of 140–156 MHz).
+We basically utilized the integrated fluxes referred
+from these radio catalogs.
+Although only the peaked
+fluxes were presented in the VLSSr catalog, they should
+be the same as integrated fluxes for unresolved point
+sources because of the large beam size (75′′; see Ta-
+ble 2). To avoid flux underestimates due to the resolved-
+out extended emission, we basically employed the radio
+catalogs excluding the two catalogs observed with the
+high-spatial-resolution instruments: VLASS (2.′′5) and
+FIRST (5′′).7 For the faint sources that any data are
+not obtained, we adopted the 5σ upper limits from the
+TGSS catalog (<24.5 mJy at 150 MHz). Additionally,
+we used the fluxes of these faint sources from the VLASS
+(3.0 GHz) and FIRST (1.4 GHz) catalogs if detected
+at the ≳5σ level8, or the 5σ upper limits (<0.44 and
+<1.00 mJy, respectively).
+7 Since the uncertainties of FIRST flux densities were not provided,
+we assume them as 10% uncertainties.
+8 We utilized the VLASS fluxes for the low-significance radio
+sources, NGC 833 (3.3σ) and MCG+01-59-081 (4.4σ).
+3.8. Correction for Galactic Extinction
+The magnitudes in the FUV, NUV, u–y, J, H, Ks, W1
+and W2 bands were corrected for the Galactic extinction
+by following Schlegel et al. (1998), hereafter SFD. We
+adopted the correction factors, Rλ (= Aλ/E(B−V )SFD,
+where Aλ is the extinction at the λ band in units of
+magnitude, calculated by Aλ = 1.086τλ) from Bianchi
+et al. (2017) for GALEX, Schlafly & Finkbeiner (2011)
+for Pan-STARRS, Wolf et al. (2018) for SkyMapper, and
+Yuan et al. (2013) for the other telescopes:
+• GALEX:
+[RFUV, RNUV] = [8.06, 7.95]
+• Pan-STARRS:
+[Rg, Rr, Ri, Rz, Ry]
+= [3.172, 2.271, 1.682, 1.322, 1.087]
+• SkyMapper:
+[Ru, Rv, Rg, Rr, Ri, Rz]
+= [4.294, 4.026, 2.986, 2.288, 1.588, 1.206]
+• SDSS:
+[Ru, Rg, Rr, Ri, Rz]
+= [4.39, 3.30, 2.31, 1.71, 1.29]
+• 2MASS:
+[RJ, RH, RKs] = [0.72, 0.46, 0.306]
+• WISE:
+[RW1, RW2] = [0.18, 0.16]
+The magnitudes of E(B − V ) reddening and the flux
+densities of the UV-to-radio photometries corrected for
+the Galactic extinction in our sample are summarized
+in Table E1 (λ < 1 µm), Table E2 (λ = 1–200 µm), and
+Table E3 (λ > 200 µm).
+4. MULTIWAVELENGTH SED MODEL AND
+BEST-FIT PARAMETERS
+To best constrain the properties of polar dust, we
+update the latest multiwavelength SED-fitting code X-
+CIGALE (Yang et al. 2020a) by implementing the IR
+CLUMPY model (Section 4.1), whose geometry is the
+same as in XCLUMPY. The UV-to-IR SEDs are ana-
+lyzed with the modified code for all targets (Section 4.2).
+For the radio data, we perform the fitting of radio pho-
+tometry after the UV-to-IR SED decomposition (Sec-
+tion 4.3). We finally combine the results of X-ray spec-
+tral analysis (Yamada et al. 2021), UV-to-IR SED de-
+composition, and radio fitting. The validity of the best-
+fit parameters are evaluated in Section 4.4.
+
+11
+10
+7
+10
+5
+10
+3
+10
+1
+101
+103
+105
+107
+F  (mJy)
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+10
+4
+10
+2
+100
+102
+104
+106
+Observed  ( m)
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID01_NGC_34
+ (z=0.0196, reduced ²=2.1)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID01_NGC_34
+ (z=0.0196, reduced ²=2.1)
+Figure 1. An example of the hard-X-ray-to-radio SED and best-fitting models for a stage-D merger NGC 34 (ID01). Upper
+panel: observed wavelength vs.
+flux density.
+Lower panel: rest-frame frequency vs.
+luminosity.
+The bottom panels show
+the residuals in the UV-to-radio bands.
+The individual curves show the SED models of radio non-thermal emission (pink
+dashed), attenuated stellar emission (blue dash-dotted), nebular emission (gray), dust emission (red), AGN torus (green),
+escaped AGN disk (cyan), polar dust (orange), absorption-corrected AGN X-ray emission (blue dotted), the X-ray emission
+from AGN scatters and X-ray binaries (light green), and X-ray thermal emission (light purple). Purple and red circles represent
+the observed and model flux densities, respectively. Red crosses in the X-ray band denote the NuSTAR spectra analyzed by
+Yamada et al. (2021). The results for all targets are given in Figures E1–E10.
+
+12
+Yamada et al.
+The tables of best-fitting parameters and supple-
+mental measurements of each target are listed in Ap-
+pendix A. The results of a mock analysis (i.e., the test for
+the reliability of the estimates, given the uncertainty of
+the photometry) are shown in Appendix B. The compar-
+ison of our results with the previous works is discussed
+in Appendix C, and the comparison of the results with a
+different AGN model (SKIRTOR; Stalevski et al. 2016)
+is in Appendix D. The hard X-ray to radio multiwave-
+length SEDs and their best-fitting models are presented
+in Figure 1 and Figures E1–E10 (see Appendix E).
+4.1. New Implementation of CLUMPY for X-CIGALE
+4.1.1. AGN Model in Multiwavelength SED
+The combination of X-ray and IR data enables us to
+constrain the distribution of the gas and dust in the
+AGNs (e.g., Hickox & Alexander 2018). For making the
+analysis consistent with the XCLUMPY X-ray spectra,
+Miyaji et al. (2019) have modified the CIGALE package,
+a fitting code to model the UV-to-radio SEDs of galax-
+ies (Burgarella et al. 2005; Noll et al. 2009; Boquien
+et al. 2019), to include an implementation of CLUMPY
+(Nenkova et al. 2008a,b). They conduct the X-ray spec-
+tral analysis with XCLUMPY and the UV-to-IR SED
+decomposition with CLUMPY as a module, and suc-
+cessfully estimate the torus parameters of an AKARI-
+selected CT AGN, such as X-ray absorbing column,
+torus optical depth, torus angular width, and inclina-
+tion angle. Recent works (Tanimoto et al. 2020; Ogawa
+et al. 2021) show that these clumpy torus models mostly
+present the larger covering fraction in the IR band than
+those in X-rays, consistent with the presence of the polar
+dust (see e.g., Asmus et al. 2016; Asmus 2019; L´opez-
+Gonzaga et al. 2016; L´opez-Gonzaga & Jaffe 2016; H¨onig
+& Kishimoto 2017; H¨onig 2019; Lyu & Rieke 2018; Buat
+et al. 2021; Toba et al. 2021a; Andonie et al. 2022).
+Yang et al. (2020a) develop a new X-ray module for
+CIGALE, allowing it to fit SEDs, named X-CIGALE
+(but their X-ray model does not consider the absorption
+from the target, our Galaxy, and/or the intergalactic
+medium).9 Torus models are mainly classified by their
+dust distribution such as smooth, clumpy, and two-phase
+(clumpy and smooth) models. The current version of X-
+CIGALE (CIGALE v2020.0) includes two AGN mod-
+els of a classical smooth torus model by Fritz et al.
+(2006) and a modern two-phase model (SKIRTOR) by
+Stalevski et al. (2012, 2016). They also implement the
+9 Yang et al. (2022) improve the X-CIGALE code mainly related
+to AGN intrinsic X-ray anisotropy, X-ray binary emission, AGN
+accretion-disk SED shape, and AGN radio emission (new version
+as CIGALE v2022.1).
+model of polar-dust extinction (e.g., Lyu & Rieke 2018;
+H¨onig 2019). For maintaining energy conservation in the
+scheme of X-CIGALE, the polar dust model considers
+the radiative energy absorbed by their dust. The model
+of polar dust assumes the isotropic dust re-radiation and
+the “gray body” model (e.g., Casey 2012).
+Since a clumpy distribution of the dust is neces-
+sary to prevent the destruction of grains (e.g., Krolik
+& Begelman 1988), many works adopt the SKIRTOR
+model in X-CIGALE (e.g., Yang et al. 2020a, 2022;
+Buat et al. 2021).
+However, conducting the SED fit
+by a self-consistent AGN model with X-CIGALE and
+XCLUMPY is difficult because the torus component of
+SKIRTOR has different geometry and parameter def-
+initions from those of XCLUMPY. Thus we use the
+CLUMPY module by combining the SKIRTOR’s polar
+dust component.
+4.1.2. Differences between CLUMPY and SKIRTOR
+The CLUMPY model assumes an isotropic emission
+of the central source commonly adopted in the litera-
+ture (e.g., Schartmann et al. 2005; H¨onig et al. 2006).
+Strong correlations between X-ray and nuclear 12 µm
+fluxes (i.e., least biased by extra-nuclear emission) are
+reported for both Seyfert 1 and 2 galaxies (e.g., Gandhi
+et al. 2009; Asmus et al. 2015). When taking the X-ray
+emission as an isotropic tracer for the AGN luminosity,
+the low scatter of the mid-IR/X-ray luminosity correla-
+tion suggests that the mid-IR emission is also close to
+isotropic. The reason is that the hollow cone is visible
+to the observer at any inclination in the inflowing disk
+and outflowing polar dust (H¨onig & Kishimoto 2017;
+H¨onig 2019).
+The intrinsic SED of the central AGN
+disk emission in CLUMPY follows the piecewise power-
+law distribution in Rowan-Robinson (1995), where the
+CLUMPY model adopts λRJ = 1 µm (wavelength mark-
+ing the onset of the Rayleigh-Jeans tail).
+CLUMPY
+model results in a Gaussian angular distribution.
+A
+density gradient along the polar angle is proportional
+to exp(−θ2/σ2), where θ is the elevation angle and σ is
+torus angular width (typically ∼20◦; e.g., Ogawa et al.
+2021; Yamada et al. 2021). Whereas, SKIRTOR consid-
+ers the anisotropy of the central source (Netzer 1987)
+and employs larger λRJ = 5 µm than that in CLUMPY.
+SKIRTOR assumes a sharp-edged angular distribution
+of high-density clumps embedded in a smooth compo-
+nent with low density.
+A density gradient along the
+polar angle is proportional to exp(−x|cos(90◦ − θ)|) in
+SKIRTOR, where x is a torus density angular parameter
+typically fixed to 1.0 (e.g., Yang et al. 2020a).
+Stalevski et al. (2016) demonstrate that the difference
+in the input SED shape of the central engine (e.g., λRJ)
+
+13
+Disk
+Torus  (τV ~ 400–1200)
+(Escaped disk)
+(Polar dust)
+Polar dust 
+(τV ~ 0–3)
+(Torus)
+σ
+i
+Equ
+X-ray Spectroscopy
+Figure 2. A schematic picture of the AGN structure assumed in the updated CLUMPY model. Central black circle and blue
+bar represent the SMBH and accretion disk, respectively. Brown circles show the clumps of torus, whose structure is constrained
+by the X-ray spectroscopy with XCLUMPY. Light-brown annular sector illustrates the polar dust. Green arrays mark the torus
+reflection emission. Blue thick (solid and dotted) arrays are the AGN disk emission, while a blue thin array is the escaped disk
+emission via the clump gaps. These emissions are attenuated by the polar dust, marked as dashed lines. Orange arrow shows the
+dust re-radiation from the polar dust. The symbols “σ” and “i” mean the torus angular width and inclination angle, respectively.
+has little effect on the resulting dust emission: what
+matter is the total amount of emission from the central
+engine.10 By comparing the results obtained with the
+clumpy torus model of isotropic disk radiation, Stalevski
+et al. (2012) report that the anisotropic assumption only
+reduces dust fluxes by a factor of at most 2, keeping
+roughly the similar shape of IR SEDs.
+On the other
+hand, the smooth component in SKIRTOR can produce
+a more attenuated silicate feature and have a stronger
+near-IR emission than without the smoothly distributed
+element (Stalevski et al. 2012, 2016; see also Efstathiou
+et al. 2022). Moreover, the dependence of the dust dis-
+tribution on θ in SKIRTOR tends to be less and may
+cause a stronger near-IR emission than in CLUMPY
+(Gaussian angular distribution). Although we find such
+a trend by examining how much of the differences in
+the results derived from the fits with CLUMPY and
+SKIRTOR (see Appendix D), both models consequently
+present similar intrinsic AGN luminosities for almost
+all of the U/LIRGs in our sample (Figure D1). Hence,
+our multiwavelength SED analysis is less affected by the
+model assumption between CLUMPY and SKIRTOR.
+4.1.3. Implementation of CLUMPY Model
+Figure 2 shows a schematic picture of our updated
+CLUMPY model containing the polar dust component.
+The model assumes the situation of an AGN structure
+10 https://sites.google.com/site/skirtorus/sed-library
+consisting of (1) an accretion disk at ≪1 pc scale, (2)
+a clumpy torus at ≲10 pc scale, and (3) polar dust at
+≳10 pc scale (see Section 4.2.3). In the torus model of
+CLUMPY, the radial distribution of clumps is a power
+law with an index of q (i.e., r−q), and the angular distri-
+bution is a Gaussian distribution. The number of clumps
+along a line-of-sight path (N LOS
+clump) is described by:
+N LOS
+clump(θ) = N Equ
+clump exp(−θ2/σ2),
+(1)
+where N Equ
+clump is the number of clumps along the equa-
+torial plane.
+The updated CLUMPY considers dust
+absorption, re-emission, and scattering (Nenkova et al.
+2008a,b), except for the scattering effect in the smooth
+polar-dust region.
+Since the total mass of polar dust
+is much smaller than that contained in the torus, the
+X-ray spectrum is almost unaffected by the polar dust
+component at energies above a few keV (e.g. Liu et al.
+2019). Thus, the clump distribution derived from the X-
+ray spectroscopy with XCLUMPY (e.g., Yamada et al.
+2021) traces the structure of the clumpy torus without
+the polar dust. A part of the disk emission is escaped via
+the clump gap, keeping the shape of its intrinsic AGN
+SED. Considering the optical depth of a single clump of
+the torus with τV = 40–120 in this work (corresponds to
+τλ > 1 in the UV-to-optical bands, the escape probabil-
+ity, Pesc, is calculated by Pesc ≃ exp(−N LOS
+clump) (see also
+Equation A4 in Nenkova et al. 2008a and Section 2.2 in
+Nenkova et al. 2008b).
+The distribution of the polar dust is determined by the
+region with θ ≥ σ (or the region with the angle between
+
+14
+Yamada et al.
+the polar axis and edge of the torus in SKIRTOR). By
+limiting the range of the polar dust temperature between
+100–250 K, the polar dust model in this work reflects the
+extended dust at ≳10 pc (see Section 4.2.3 and 6.5). We
+allow the line-of-sight optical depth (τV) of polar dust
+as a typical range in previous studies, τV ≲ 3 (e.g., Buat
+et al. 2021; Toba et al. 2021a; see Section 4.2.3 and 6.2).
+The value is much smaller than the equatorial optical
+depth of the torus (τ Equ
+V
+∼ 400–1200), where the number
+of clumps is 10 (Section 4.2.2). Here, the distributions of
+polar dust and the galaxy’s interstellar medium (ISM)
+are not distinguished. Finally, to keep energy conserva-
+tion, the dust extinction and re-radiation of polar dust
+in the UV-to-IR bands are included in the same manner
+as the original X-CIGALE code.
+4.2. UV-to-IR SED Fitting with CLUMPY
+By using the X-CIGALE code with the CLUMPY im-
+plementation, we conduct the UV-to-IR SED decom-
+position, whose best-fit parameters are adopted for the
+radio fitting (Section 4.3).
+The details of the UV-to-
+IR SED model are described for the host galaxy (stel-
+lar emission, nebular emission, and dust emission; Sec-
+tion 4.2.1), torus (torus and escaped disk emission;
+Section 4.2.2), and polar dust emission (Section 4.2.3
+and 4.2.4). The models and parameters we adopted are
+summarized in Table 3.
+4.2.1. Host Galaxy Model
+We utilize a delayed star formation history (SFH)
+model to allow for an instantaneous burst of the star-
+burst activities (e.g., Ciesla et al. 2015; Nersesian et al.
+2019).
+The parameter ranges of the SFH model are
+mainly referred from the works with CIGALE code for
+local Herschel-selected galaxies (Buat et al. 2018) and
+U/LIRGs (Paspaliaris et al. 2021).
+The stellar emis-
+sion is modeled as a 5 Gyr simple stellar population
+(BC03; Bruzual & Charlot 2003). Here, the Chabrier
+(2003) IMF, solar metallicity, and the standard nebu-
+lar emission model (see Inoue 2011) are adopted. We
+consider the attenuation law for the stellar continuum
+of Calzetti et al. (2000), where the nebular emission is
+reddened with a Milky Way extinction curve (Cardelli
+et al. 1989).
+The reddening of the nebular emission,
+E(B − V )line is a free parameter, while the ratio of the
+reddening of the emission lines and whole stellar contin-
+uum, E(B−V )star/E(B−V )line, was found to be 0.44 for
+local starbursts (Calzetti 2001). Since the contribution
+of the UV bump for local galaxies is small (∼1/3 of that
+of the MW bump) and can be ignored as it affects the
+near-UV magnitude by only 0.1 mag (Salim et al. 2018),
+we fix the amplitude at zero. Recent works report that
+the extinction curves show a great diversity in power-law
+slope (e.g., Salim et al. 2018; Salim & Narayanan 2020),
+whose range of the slopes is covered from −0.8 to 0.0.
+We fit the cold dust emission from the host galaxy with
+the physical dust model from Draine et al. (2014), the
+updated model of the previous one (Draine & Li 2007).
+The parameter ranges of qpah (qpah; 0.47–2.50), umin
+(1–50) and alpha (2.0 or 2.5) are referred from recent
+works (e.g., Buat et al. 2018, 2021). The dust fraction in
+photo-dissociation regions (PDRs) is fixed to 0.02 (e.g.,
+Draine & Li 2007; Dale et al. 2012; Magdis et al. 2012;
+Buat et al. 2018).
+4.2.2. Torus Model (CLUMPY and SKIRTOR)
+For the torus component, we adopt the CLUMPY
+model implemented in the X-CIGALE code (Model I).
+The number of clumps along the equator of N Equ
+clump = 10,
+the ratio of the outer to inner radii of Y = 20, and the
+radial clumpy distribution index of q = 0.5 are assumed
+to make the analysis consistent with XCLUMPY (Tani-
+moto et al. 2019). The torus optical depth in the V band
+is a free parameter (τV; 40, 80, or 120), while the torus
+angular width (σ; 15◦ to 70◦ in steps of 5◦) and inclina-
+tion angle (i; 30◦, 60◦, or 80◦) are fixed as be the closest
+values to the parameters of the best-fitting model in the
+X-ray works (Yamada et al. 2020, 2021; Ogawa et al.
+2021).11 For the systems whose individual galaxies have
+different inclinations (NGC 6921/MCG+04-48-002 and
+NGC 7679/NGC 7682), we select σ = 20◦ and i = 60◦
+as typical values in the X-ray results.
+The UV-to-IR
+SEDs of starburst-dominant or hard X-ray–undetected
+sources are modeled without AGN component (fAGN =
+0), while allowing the AGN fraction in the IR band to
+free between 0.05–0.8 for AGNs.
+We also perform the SED decomposition with the
+SKIRTOR model (Model II; see Appendix D). A torus
+density radial parameter (q) and torus density angular
+parameter (x) are fixed to be 1.0 (e.g., Stalevski et al.
+2016; Yang et al. 2020a).12 The equatorial optical depth
+at 9.7 µm (τ9.7) is a free parameter (5, 9, or 11). The
+angular distribution of clumps has a sharp edge corre-
+sponding to the angle between the equatorial plane and
+edge of the torus (∆). Here, the unobscured and ob-
+11 Since the reduced χ2 is larger than 10 for IRAS F08572+3915,
+its inclination of 80◦ is chosen that present the smallest χ2. For
+NGC 1068, NGC 1275, NGC 1365, Mrk 266B/Mrk 266A, and
+NGC 6240S/NGC 6240N, we assume σ to be a typical value of
+20◦ (e.g., Yamada et al. 2021; Ogawa et al. 2021), and select the
+inclination angle showing the smallest χ2 from 30◦, 60◦, and 80◦.
+12 We confirm that the results and discussion are unchanged even
+if q = 0.5 to keep consistency with CLUMPY model.
+
+15
+Table 3. Summary of Models and Input Parameters in the UV-to-IR SED Fitting
+Model
+Module
+Parameter
+Value
+SFH model
+shfdelayedbq
+tau main (Myr)
+1000, 3000, 5000
+age main (Myr)
+4500, 7000, 9500, 12000
+age bq (Myr)
+10, 20, 100
+r sfr
+1, 3.16, 10, 31.6, 100, 1000
+Stellar emission
+bc03
+imf
+1 (Chabrier)
+metallicity
+0.02
+Nebular emission
+nebular
+logU
+−3.0
+f esc
+0.0
+f dust
+0.0
+lines width (km s−1)
+300
+Attenuation law
+dustatt modified starburst
+E BV lines
+0.1, 0.25, 0.5, 0.75, 1.0, 1.5, 2.0
+E BV factor
+0.44
+uv bump wavelength (nm)
+217.5
+uv bump width (nm)
+35.0
+uv bump amplitude
+0.0
+powerlaw slope
+−0.8, −0.4, 0.0
+Ext law emission lines
+1 (Milky Way)
+Rv
+3.1
+Dust emission
+dl2014
+qpah (= qpah)
+0.47, 1.12, 2.50
+umin
+1, 5, 10, 25, 50
+alpha
+2.0, 2.5
+gamma
+0.02
+AGN (torus/disk)
+CLUMPY (Model I)
+Y ratio (= Y )
+20
+tau V (= τV)
+40, 80, 120
+N 0 (= N Equ
+clump)
+10
+q (= q)
+0.5
+sigma (= σ; degree)
+15 to 70 (per bin 5; fixed)
+inclination (= i; degree)
+30, 60, 80 (fixed)
+fracAGN (= fAGN)
+0.0 (for starburst-dominant sources), or
+0.05, 0.1, 0.2, 0.3, 0.4,
+0.5, 0.6, 0.7, 0.8 (for AGNs)
+SKIRTOR (Model II; Appendix D)
+R (= Y )
+20
+t (= τ9.7)
+5, 9, 11
+oa (= ∆; degree)
+30, 40, 60 (fixed)
+i (= i; degree)
+30, 60, 80 (fixed)
+fracAGN (= fAGN)
+0.0 (for starburst-dominant sources), or
+0.05, 0.1, 0.2, 0.3, 0.4,
+0.5, 0.6, 0.7, 0.8 (for AGNs)
+AGN (polar)
+CLUMPY/SKIRTOR
+law
+0 (SMC)
+EBV (= E(B − V ); mag)
+0.0 (fixed), or 0.05, 0.3, 0.8
+temperature (= Tpolar; K)
+100, 150, 200, 250
+emissivity (= β)
+1.6
+
+16
+Yamada et al.
+scured AGNs are determined by the inclination angle
+above i < 90◦ − ∆ or not, respectively. To keep fully
+consistency between the SKIRTOR-based AGN classifi-
+cation and X-ray classification in our sample (Table 1),
+we convert the torus angular width (σ) of [10◦–15◦, 15◦–
+25◦, 25◦–70◦] to the ∆ of [30◦, 40◦, 60◦], respectively.
+4.2.3. Polar Dust Model
+In the polar dust model, we adopt the Small Magel-
+lanic Cloud (SMC; Prevot et al. 1984) extinction curve,
+which is preferred from AGN observations (e.g., Hop-
+kins et al. 2004; Salvato et al. 2009; Bongiorno et al.
+2012; Buat et al. 2021). The reddening E(B −V ) is free
+(0.05, 0.3, and 0.8; e.g., Buat et al. 2021; Paspaliaris
+et al. 2021; Toba et al. 2021a; Yang et al. 2022), or set-
+ting E(B − V ) = 0 if no significant AGN contribution
+(fAGN = 0). The emissivity (β) is fixed at 1.6 as a typical
+value (e.g., Draine & Lee 1984; Casey 2012; Yang et al.
+2020a). The previous IR works indicate the tempera-
+ture of polar dust (Tpolar) is ∼100–200 K (e.g., Lopez-
+Rodriguez et al. 2018; Lyu & Rieke 2018; H¨onig 2019),
+while the temperature of the torus is ≳300 K (e.g., Tris-
+tram et al. 2009; Tristram & Schartmann 2011). Recent
+high-spatial-resolution mid-IR observation of the nearby
+Seyfert 2 galaxy, the Circinus galaxy, with Very Large
+Telescope Interferometer also supports the similar tem-
+peratures (∼370 K within the subparsec-scale central
+region and ∼200 K in outer polar dust regions; Isbell
+et al. 2022). These temperatures are much larger than
+those expected for a galaxy’s ISM heated only by star
+formation (∼20–60 K; e.g., Casey 2012; Clements et al.
+2018; da Cunha et al. 2021). Although the higher tem-
+perature dust above 300 K should radiate the near-IR
+emission from a ring-like dust structure on the subparsec
+central region (e.g., Krolik 2007; Schartmann et al. 2014;
+Baba et al. 2018; H¨onig 2019; Lyu & Rieke 2021; G´amez
+Rosas et al. 2022; Matsumoto et al. 2022), the material
+of the inner edge of a torus and accompanying polar dust
+would be difficult to distinguish by both near-IR and X-
+ray observations. Therefore, we select the range of the
+polar dust temperature within 100–250 K, and clarify
+that (1) the estimates of the physical properties of ex-
+tended (≳10 pc; see also Section 6.5) polar dust that
+are not taken into account for the hot (>300 K) dust
+component on the subparsec region and (2) the central
+hot dust emission are predominantly considered as the
+torus emission in this study.
+4.2.4. Significance Test for Torus and Polar-dust Emission
+We examine the Bayesian information criterion (BIC;
+Schwarz 1978) for two kinds of fits with and without the
+AGN (torus and polar dust) component. Using the χ2
+statistics, the BIC is provided by the equation as BIC =
+χ2+k×ln(N), where k is the number of free parameters
+and N is the number of photometric data (Ciesla et al.
+2018; Buat et al. 2019). Among the sources yielding a
+poor fit with reduced χ2 above 6, the three galaxies,
+ESO 350−38, ESO 374−IG032, and NGC 4418, show
+the ∆BIC = BICwoAGN − BICwAGN > 6 (significantly
+improvement with a posterior probability above 95%;
+Raftery 1995). Thus, we re-classify these three galax-
+ies as AGN candidates and select the inclination angle
+providing the smallest χ2.
+Furthermore, we conduct the significance test for the
+polar dust component in the UV-to-IR SED analy-
+sis.
+The left panel of Figure 3 presents the fraction
+of sources showing BIC > 6 for a polar dust compo-
+nent with two kinds of torus models.
+We find that
+the analysis with SKIRTOR provides larger fractions
+of the AGNs showing significant polar dust contribu-
+tion than with CLUMPY. This stronger significance
+of mid-IR polar dust emission can be explained by
+the flatter SED slope of the torus component in the
+SKIRTOR model due to the strong near-IR emission
+from smooth low-density dust (Section 4.1.2 and Ap-
+pendix D). Although the sample is quite limited to the
+nine AGNs, the signatures of polar-dust radiation are
+reported by high-resolution mid-IR images and inter-
+ferometry (NGC 1068, NGC 1365, NGC 3690 West,
+Mrk 231, MCG−03-34-064, NGC 5135, IC 4518W,
+NGC 7469, and NGC 7674; L´opez-Gonzaga et al. 2014,
+2016; L´opez-Gonzaga & Jaffe 2016; Asmus et al. 2016;
+Asmus 2019; Lopez-Rodriguez et al. 2017, 2018; Mattila
+et al. 2018; G´amez Rosas et al. 2022).13
+Six of these
+AGNs hosting polar dust emissions do not show any
+significant BIC values with these torus models (right
+panel of Figure 3). This is mainly because the available
+photometries of them in the near-IR (2MASS) and/or
+mid-IR (WISE and AKARI) bands are insufficient to
+give a diagnosis, which may be derived by the artifacts
+related to their IR emission from extended or compre-
+hensive morphology. So, we adopt the polar dust model
+for the AGNs with one or more signs from mid-IR im-
+ages, interferometry, and BIC tests by SED analysis
+with CLUMPY and SKIRTOR. For the seven AGNs
+without any signs of polar dust contribution, most of
+whose IR photometries are available, we treat them as
+AGNs without polar dust emission by applying E(B−V )
+= 0, i.e., returning to the original torus model. Impres-
+13 The presence of polar dust in Mrk 231 is implied by near-to-mid-
+IR polarimetry (Lopez-Rodriguez et al. 2017), and in NGC 3690
+West by detecting the time variability of nucleus IR SED due
+to the tidal disruption event radiating the polar dust emission
+(Mattila et al. 2018).
+
+17
+A
+B
+C
+D
+N
+Merger Stage
+0
+20
+40
+60
+80
+100
+Fraction of AGNs with polar dust [%]
+Image, Interferometry
+SED with CLUMPY
+SED with SKIRTOR
+Mixture of them
+Image+Interferometry(9)
+[only 9 sources in sub-sample]
+CLUMPY(15)
+SKIRTOR(26)
+w/o Polar(7)
+A(1)
+A(1), B(1), 
+C(1), D(1), N(2)
+C(1), D(1)
+N(2)
+A(2), B(2), 
+C(2), D(5), N(1)
+A(1), B(1), 
+C(2), D(6), N(1)
+A(4), B(2), N(1)
+Figure 3.
+Left panel: Histogram of the fraction of the sources that shows some signatures of the presence of polar dust
+emission for the AGNs with merger stage.
+Each signature derived from the high-resolution image (e.g., Asmus 2019) and
+interferometry (e.g., L´opez-Gonzaga et al. 2016; L´opez-Gonzaga & Jaffe 2016) in the mid-IR band (blue), the UV-to-IR SED
+decomposition with CLUMPY (black) and with SKIRTOR (red) are color-coded. Green histogram illustrates the fraction for
+the AGNs with one or more signs of polar dust emission (green). Right panel: Venn diagram of the sources with/without the
+signs of polar dust emission. The numbers of the sources for individual categories and merger stages are illustrated in parentheses.
+sively, we find that these AGNs are in early mergers and
+nonmergers, while all of the AGNs in late mergers show
+the signatures of polar dust emission, as discussed in
+Section 6.5.2. Finally, we list the best fitting parame-
+ters in the tables of Appendix A (e.g., Table A1–A5).
+4.3. Radio Fitting
+By fixing the best-fitting parameters obtained by the
+UV-to-IR SED analysis, we finally conduct the radio
+SED decomposition. The radio model is composed of
+the continuum from the nebular emission (free-free, free-
+bound, and two-photon continua)14, which also radi-
+ates UV-to-IR emission (Section 4.2.1), and indepen-
+dent synchrotron emission from AGN and/or starburst
+(Boquien et al. 2019). We parameterized a correlation
+coefficient between total-IR luminosity and monochro-
+matic radio luminosity of the synchrotron emission at
+1.4 GHz (qIR = logLIR/L1.4GHz), and the power-law
+slope of synchrotron emission (αradio) derived from the
+low-frequency radio emission in the 0.1–4 m or 0.07–
+3.0 GHz bands.
+We choose the parameter ranges of
+qIR between −1.50 and +3.50 with a step of 0.01 (e.g.,
+Yun et al. 2001; U et al. 2012; Vardoulaki et al. 2015),
+and αradio between 0.00 and 1.50 with a step of 0.01
+(e.g., Murphy 2013; Toba et al. 2019b). If only a sin-
+14 The model of the nebular component covers the UV to radio
+1 m emission. To expand the available wavelength, we assume
+the slope between the fluxes in the 0.8 and 1 m bands to the 1–
+10 m radio emission for the nebular component, where it is less
+dominant than the synchrotron component.
+gle radio photometry or upper limit values are available,
+we fix αradio to be 0.5, a median value in the <5 GHz
+bands among local U/LIRGs (Murphy 2013), consistent
+with the averaged value of the estimates in our study
+(αradio =0.48±0.16). The best-fitting parameters and
+radio luminosities are listed in Table A3, and the com-
+bined hard X-ray to radio multiwavelength SEDs and
+their best-fitting models are shown in Figures 1 and Ap-
+pendix E.
+4.4. Best-fit Parameters and Their Validity
+We have performed the multiwavelength SED analysis
+for the local U/LIRGs, covering the hard X-ray to radio
+wavelength bands. The best-fit parameters of individ-
+ual sources are summarized in Tables A1–A5, and the
+averaged values of these results are shown in Table 4.
+The histogram of the reduced χ2 of the UV-to-IR SED
+decomposition for the 72 individual targets in our sam-
+ple is displayed in Figure 4. The SED decomposition of
+some targets shows a relatively large χ2 above 5, which
+is mainly caused by the noisy photometric data in the
+UV or optical band (Figures E1–E10 in Appendix E).
+Conducting a mock analysis, we confirm that the best-
+fit parameters derived from our multiwavelength SED
+decomposition are less affected by photometric uncer-
+tainties (see Appendix B). However, the SED fitting of
+IRAS F08572+3915 shows a large reduced χ2 over 10
+because the model presents weaker near-IR fluxes than
+the photometric data.
+Its SED is moderately repro-
+duced with SKIRTOR (with reduced χ2 of 6.7).
+Al-
+though its AGN luminosity may be underestimated (at
+
+18
+Yamada et al.
+0
+2
+4
+6
+8
+10
+12
+Reduced 
+2
+0
+5
+10
+15
+20
+25
+Number of sources
+Total Number = 72
+Figure 4. Histogram of the reduced χ2 derived from the
+UV-to-IR SED decomposition for the 72 individual targets
+in our sample.
+worse ∼0.4 dex), the AGN luminosities for the other
+sources derived with CLUMPY are well consistent with
+the values with SKIRTOR (Appendix D). Thus, we uti-
+lize the results from the multiwavelength analysis with
+CLUMPY for all targets to discuss their characteristics
+of the host galaxy and AGN.
+Next, we investigate the significance of the AGN fea-
+ture in the multiwavelength SED decomposition. Fig-
+ure 5 shows the histogram of the ∆BIC on the different
+fits with and without the AGN component for the 72
+individual targets in our sample (see also Section 4.2.4).
+Remarkably, most of the sources are distributed around
+the threshold of ∆BIC = 6, regardless of whether the
+sources are the AGNs (hard X-ray–detected AGNs and
+three newly identified AGN candidates by the diag-
+nostics of ∆BIC > 6) or the other sources (starburst-
+dominant or hard X-ray–undetected sources). This in-
+dicates that the AGNs in U/LIRGs are difficult to detect
+only with the SED decomposition. Therefore, the strong
+constraints on the AGN structure derived from the X-
+ray spectral analysis will effectively solve the complex
+SEDs in the IR band.
+We evaluate the effects on the results if unresolved
+photometries are utilized.
+For the stellar mass (M∗)
+and SFR, the comparison of our results and previous
+works of SED analysis by using the photometry of total
+systems are presented in Appendix E. Figure 6 presents
+the differences in the results derived from the combined
+photometry of a total system and the separated pho-
+tometries of individual galaxies for the 13 resolved pairs.
+The stellar masses and SFRs are not affected by using
+0
+100
+200
+300
+BIC (torus + polar dust)
+0
+5
+10
+Number of sources
+BIC >  6
+(Significant AGN comp.)
+AGN (41)
+non-AGN (31)
+Figure 5. Histogram of ∆BIC (= BICwoAGN−BICwAGN)
+for the 72 individual targets in our sample. The black solid
+line shows the threshold of ∆BIC = 6 as the significant
+differences (posterior probability above 95%) in two fits
+with and without adding the AGN (torus and polar dust)
+component.
+The red histogram shows the number of the
+hard X-ray–detected AGNs and three newly identified
+AGN candidates.
+The blue histogram is the number of
+the other sources, i.e., starburst-dominant sources or hard
+X-ray–undetected sources.
+the summed fluxes of individual galaxies. On the other
+hand, for the 10 pairs hosting AGNs, the UV-to-IR
+torus (Ltorus) and polar dust luminosities (Lpolar), and
+intrinsic (bolometric) AGN disk luminosities (LAGN,int)
+derived from the combined photometries become larger
+than those from separated ones. According to the SED
+models in Figures E1–E10, the slope of the IR SEDs
+of the starburst component is similar to the one of the
+AGN (see also Section 5.4). This makes it difficult to ac-
+curately extract the AGN contribution from the IR SED
+when the photometries of a starburst-dominant source
+and a galaxy hosting an AGN are mixed. The overes-
+timation of AGN luminosities for unresolved sources is
+found to be ∼0.2 dex, which is a small effect on the
+following discussion.
+5. RESULTS: MULTIWAVELENGTH EMISSION
+FROM U/LIRGS
+Before the discussion on the properties of polar dust in
+U/LIRGs (Section 6), we first study the characteristics
+of the multiwavelength radiation, which are helpful to
+understand the detailed environments from the nucleus
+to galactic scales.
+We also aim to investigate unique
+features for future works to explore buried AGNs in
+
+19
+M* t
+SFR t
+Ltorus
+Lpolar
+LAGN, int
+0.2
+0.1
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+X  [dex]
+. .
+||
+X = logX (Total) 
+ log[X (Target1) + X (Target2)]
+Figure 6. The differences in M∗, SFR, Ltorus, Lpolar, and
+LAGN,int derived from the UV-to-IR SED analysis by using
+the combined photometry of a total system and separated
+photometries of the individual galaxies for 13 resolved pairs.
+Diamonds and these uncertainties denote the averaged
+values and 1σ dispersions, respectively.
+U/LIRGs at higher redshift. For these purposes, we here
+examine the SFR–M∗ relation as an indicator of the host
+galaxy’s properties (Section 5.1). Next, we evaluate the
+activities of AGNs and starbursts by focusing on the ra-
+dio emission (Section 5.2), WISE IR color (Section 5.3),
+and averaged multiwavelength SEDs (Section 5.4). Fi-
+nally, we discuss the properties of AGNs in U/LIRGs by
+comparing the X-ray and other wavelength luminosities
+corrected for the torus absorption (Section 5.5).
+The
+main findings are summarized in Section 5.6.
+5.1. Characteristics of Host Galaxies
+We investigate the properties of host galaxies in
+U/LIRGs by using the measurements of stellar masses
+(M∗) and SFRs.
+A strong correlation between these
+quantities for the majority of star-forming galaxies has
+been well reported (e.g., Brinchmann et al. 2004; Noeske
+et al. 2007; Elbaz et al. 2007; Speagle et al. 2014; Sain-
+tonge et al. 2016; Tomczak et al. 2016; Pearson et al.
+2018), called the main sequence (MS). Generally, galax-
+ies above the MS are qualified as “starburst”, while
+galaxies below the relation are passive galaxies in terms
+of their star-formation activity. Thus, the comparison
+of these physical quantities enables us to understand the
+galaxy’s evolution in the populations.
+Figure 7 shows the averaged values of M∗ and SFR
+compared with merger stages. The M∗ is almost simi-
+lar for all merger stages, while the SFR increases with
+merger stage. The left panel of Figure 8 presents the
+SFR–M∗ relation obtained by the multiwavelength SED
+analysis for our U/LIRGs color-coded by the merger
+stages. We overplot the values of Palmer–Green (PG)
+quasars at z < 0.1 as gray diamonds. For these quasars,
+the SFRs are estimated by the UV-to-IR SED decompo-
+sition (Lyu et al. 2017) and stellar masses are referred
+from Xie et al. (2021) based on the high-resolution opti-
+cal and near-IR images (Zhang et al. 2016) or the M∗–
+MBH relation of Greene et al. (2020).15 For comparison,
+we also plot some MS relations for SDSS star-forming
+galaxies at 0.015 ≤ z ≤ 0.1 (Elbaz et al. 2007), a large
+homogeneous collection of star-forming galaxies out to
+z ∼ 6 (the relation at z ≈ 0 is adopted; Speagle et al.
+2014), and SDSS DR7 galaxies with 0.01 < z < 0.05
+and M∗ > 108M⊙ on the basis of SFRs derived from
+UV and mid-IR (12 or 22 µm) luminosities (Saintonge
+et al. 2016).
+The previous IR SED analysis of local U/LIRGs using
+the photometry of unresolved total systems by Shang-
+guan et al. (2019) decouples the contributions of AGN
+and starburst emission and suggests the whole U/LIRGs
+are above the MS. On the other hand, using the sepa-
+rated photometry of individual sources as possible in
+the SED fitting, we find that some component sources
+in early mergers sit on or lie below the MS. The early
+mergers and PG quasars have wide ranges of SFRs above
+and below the MS, while the late mergers have the high-
+est SFRs above the MS. Except for some early merg-
+ers, the distributions of the stellar masses are compa-
+rable in both U/LIRGs and PG quasars. As a result,
+the average specific SFR, sSFR (= SFR/M∗), is much
+larger in late mergers (log(sSFR/yr−1) = −8.51±0.58)
+than those in early mergers (−9.58±0.98), nonmergers
+(−9.50±0.51), and PG quasars (−10.16±0.64). Inter-
+estingly, this is well consistent with the recent high-
+resolution simulations of gas-rich major mergers (Blecha
+et al. 2018), which predicts the starbursts with the high-
+est sSFR (−8.4 in a logarithmic scale) in the final phase
+of mergers. Although the progenitor of quasars are not
+necessarily triggered by mergers (e.g., Xie et al. 2021),
+these results support that the starburst activities in
+U/LIRGs are triggered in early mergers, and suppressed
+after late mergers with high sSFR (e.g., Di Matteo et al.
+2005; Hopkins et al. 2008; Ellison et al. 2013; Barrera-
+Ballesteros et al. 2015; Shangguan et al. 2019; U et al.
+2019; Yamada et al. 2021).
+15 The values of MBH are referred from Veilleux et al. (2009a)
+by averaging the results from different measurements, including
+spheroid luminosity, spheroid velocity dispersion, reverberation
+mapping, and virial relation (see Zhang et al. 2016).
+
+20
+Yamada et al.
+Table 4. Averaged Values of Best-fit Parameters and Accompanying Results.
+No.
+Parameter
+Merger Stage
+A
+B
+C
+D
+A–B
+C–D
+N
+Free parameters (UV-to-IR SED analysis; Section 4.2)
+1
+log(tau main) (Myr)
+3.38 ± 0.23
+3.42 ± 0.22
+3.50 ± 0.12
+3.53 ± 0.09
+3.40 ± 0.23
+3.52 ± 0.10
+3.38 ± 0.19
+2
+log(age main) (Myr)
+3.89 ± 0.12
+3.85 ± 0.10
+3.91 ± 0.07
+3.89 ± 0.06
+3.87 ± 0.11
+3.89 ± 0.07
+3.87 ± 0.08
+3
+log(age bq) (Myr)
+1.65 ± 0.22
+1.68 ± 0.21
+1.55 ± 0.32
+1.39 ± 0.31
+1.67 ± 0.22
+1.44 ± 0.32
+1.61 ± 0.16
+4
+log(r sfr)
+1.12 ± 0.79
+1.39 ± 0.88
+1.57 ± 0.77
+2.19 ± 0.64
+1.24 ± 0.84
+2.01 ± 0.74
+1.26 ± 0.85
+5
+E BV lines
+0.72 ± 0.51
+0.99 ± 0.43
+0.83 ± 0.38
+1.37 ± 0.29
+0.84 ± 0.50
+1.22 ± 0.41
+0.98 ± 0.56
+6
+powerlaw slope
+−0.47 ± 0.24
+−0.41 ± 0.31
+−0.39 ± 0.27
+−0.35 ± 0.29
+−0.45 ± 0.27
+−0.36 ± 0.29
+−0.40 ± 0.29
+7
+qpah
+1.19 ± 0.58
+1.16 ± 0.68
+0.85 ± 0.38
+0.80 ± 0.54
+1.17 ± 0.62
+0.82 ± 0.50
+1.23 ± 0.59
+8
+umin
+10.18 ± 11.07
+15.49 ± 15.10
+25.15 ± 14.95
+29.93 ± 15.15
+12.50 ± 13.25
+28.57 ± 15.25
+7.91 ± 6.52
+9
+alpha
+2.19 ± 0.20
+2.20 ± 0.23
+2.18 ± 0.22
+2.31 ± 0.22
+2.19 ± 0.22
+2.27 ± 0.23
+2.17 ± 0.20
+10
+τV
+81.51 ± 8.95
+85.26 ± 6.15
+74.31 ± 22.58
+73.37 ± 23.63
+83.01 ± 8.16
+73.67 ± 23.31
+67.56 ± 15.52
+11
+fAGN
+0.16 ± 0.13
+0.11 ± 0.04
+0.26 ± 0.18
+0.18 ± 0.19
+0.14 ± 0.11
+0.20 ± 0.19
+0.36 ± 0.26
+12
+E(B − V ) (mag)
+0.40 ± 0.26
+0.25 ± 0.17
+0.39 ± 0.19
+0.33 ± 0.27
+0.33 ± 0.23
+0.35 ± 0.25
+0.59 ± 0.21
+13
+Tpolar (K)
+164.03 ± 37.97
+173.29 ± 8.66
+134.10 ± 27.44
+132.57 ± 33.06
+168.15 ± 29.25
+133.06 ± 31.40
+172.83 ± 59.96
+Fixed Parameters (UV-to-IR SED analysis; Section 4.2)
+14
+σ (degree)
+24.4 ± 14.6
+19.2 ± 1.9
+24.2 ± 9.3
+19.2 ± 2.7
+22.3 ± 11.7
+20.8 ± 6.1
+19.3 ± 3.2
+15
+i (degree)
+54.4 ± 18.9
+63.3 ± 7.5
+61.7 ± 16.7
+60.0 ± 15.2
+58.0 ± 16.0
+60.5 ± 15.7
+62.9 ± 21.9
+Free Parameters (radio fitting; Section 4.3)
+16
+α†
+radio
+0.54 ± 0.16
+0.52 ± 0.07
+0.52 ± 0.14
+0.38 ± 0.15
+0.54 ± 0.13
+0.43 ± 0.16
+0.52 ± 0.16
+17
+q†
+ir
+2.39 ± 0.41
+2.26 ± 0.29
+2.50 ± 0.19
+2.57 ± 0.27
+2.34 ± 0.37
+2.55 ± 0.25
+2.10 ± 0.94
+Accompanying results
+18
+log(M∗) (M⊙)
+10.23 ± 0.91
+10.42 ± 0.39
+10.43 ± 0.35
+10.35 ± 0.52
+10.31 ± 0.74
+10.37 ± 0.48
+10.54 ± 0.45
+19
+log(SFR) (M⊙ yr−1)
+0.49 ± 0.82
+1.06 ± 0.55
+1.53 ± 0.38
+1.98 ± 0.32
+0.74 ± 0.77
+1.86 ± 0.40
+1.04 ± 0.34
+20
+log(sSFR) (yr−1)
+−9.74 ± 1.08
+−9.36 ± 0.80
+−8.90 ± 0.49
+−8.36 ± 0.54
+−9.58 ± 0.98
+−8.51 ± 0.58
+−9.50 ± 0.51
+21
+log(L1.4GHz)† (erg s−1)
+38.19 ± 0.88
+38.75 ± 0.52
+39.09 ± 0.30
+39.47 ± 0.44
+38.44 ± 0.80
+39.36 ± 0.44
+38.97 ± 0.90
+22
+q†
+excess
+0.12 ± 0.08
+0.11 ± 0.11
+0.08 ± 0.02
+0.08 ± 0.03
+0.11 ± 0.10
+0.08 ± 0.03
+0.08 ± 0.02
+23
+log(L6,AGN) (erg s−1)
+42.39 ± 0.95
+42.77 ± 0.60
+43.30 ± 0.48
+43.52 ± 0.50
+42.54 ± 0.85
+43.45 ± 0.50
+43.18 ± 0.54
+24
+log(L12,t) (erg s−1)
+43.03 ± 0.83
+43.31 ± 0.49
+43.93 ± 0.50
+44.09 ± 0.52
+43.14 ± 0.73
+44.04 ± 0.52
+43.74 ± 0.51
+25
+log(L12,p) (erg s−1)
+43.24 ± 0.29
+43.07 ± 0.75
+43.10 ± 0.24
+43.46 ± 0.75
+43.16 ± 0.55
+43.35 ± 0.65
+43.34 ± 0.84
+26
+log(L12,AGN) (erg s−1)
+43.21 ± 0.85
+43.52 ± 0.53
+44.04 ± 0.40
+44.23 ± 0.53
+43.34 ± 0.75
+44.17 ± 0.50
+43.98 ± 0.56
+27
+log(Ltorus) (erg s−1)
+43.18 ± 0.80
+43.43 ± 0.44
+43.98 ± 0.45
+44.14 ± 0.50
+43.28 ± 0.69
+44.09 ± 0.49
+43.80 ± 0.51
+28
+log(Lpolar) (erg s−1)
+43.62 ± 0.54
+43.40 ± 0.18
+44.07 ± 0.39
+44.29 ± 0.59
+43.53 ± 0.43
+44.22 ± 0.55
+43.99 ± 0.46
+29
+log(LAGN,int) (erg s−1)
+43.49 ± 0.71
+43.80 ± 0.36
+44.35 ± 0.45
+44.53 ± 0.57
+43.61 ± 0.62
+44.47 ± 0.54
+44.31 ± 0.53
+30
+log(MBH) (M⊙)
+7.80 ± 0.41
+7.83 ± 0.24
+7.34 ± 0.28
+7.83 ± 0.46
+7.81 ± 0.35
+7.67 ± 0.47
+7.79 ± 0.25
+31
+log(λEdd)
+−2.43 ± 1.01
+−2.17 ± 0.47
+−1.15 ± 0.45
+−1.29 ± 0.67
+−2.33 ± 0.85
+−1.24 ± 0.61
+−1.63 ± 0.75
+32
+log(Rpolar) (pc)
+1.77 ± 0.59
+1.56 ± 0.05
+2.24 ± 0.45
+2.35 ± 0.40
+1.68 ± 0.45
+2.32 ± 0.42
+1.90 ± 0.55
+Note—Comments: The table summarizes the averaged values of each parameter for individual merger stages. (1–13) Free parameters as listed in Table 3
+(see Section 4.2); (14–15) Two fixed parameters of torus angular width and inclination angle as listed in Table 3 (Section 4.2); (16–17) free parameters
+of the radio fitting (Section 4.3); (18–20) stellar mass (M∗), SFR, and specific SFR (sSFR = SFR/M∗) as listed in Table A2; (21–22) rest-frame radio
+1.4 GHz luminosity and radio-excess parameter (qexcess) as listed in Table A3 (see Section 5.2); (23–26) rest-frame 6 µm luminosity of AGN (torus and
+polar dust) component, rest-frame 12 µm luminosities of the torus, polar dust, and total AGN component (see Table A4); (27–32) UV-to-IR (mainly
+IR) luminosities (torus, polar dust, and AGN components), SMBH mass, Eddington ratio, and physical sizes of the polar dust structure (Section 6.5) as
+listed in Table A5.
+† The values of the sources whose αradio is fixed at 0.5 are excluded.
+The right panel of Figure 8 denotes the SFR–M∗ re-
+lation for U/LIRGs with or without AGNs. Red stars
+mark the hard X-ray–detected AGNs and three AGNs
+that are re-classified by the significance test with BIC
+values (Section 4.2.4), while dark gray circles mark the
+starburst-dominant or hard X-ray–undetected sources.
+The U/LIRGs but several early mergers below the MS
+show similar distributions regardless of the presence or
+absence of AGNs.
+About 50% of the AGNs in late
+mergers are CT AGNs and, among the hard X-ray–
+undetected sources, there are few CT AGN candidates
+based on their 3σ upper limits in the 8–24 keV band
+(Yamada et al. 2021). These results support that the
+obscuration of the AGNs is not related to the difference
+in the SFR–M∗ distribution with and without AGNs.
+A similar result in the IR band for local U/LIRGs of
+GOALS sample is reported by Shangguan et al. (2019),
+who evaluate the presence of AGNs when the IR SED
+fit is significantly improved by adding the torus compo-
+nent. Their AGN classification is based on the signa-
+
+21
+N
+A
+B
+C
+D
+9.0
+9.5
+10.0
+10.5
+11.0
+11.5
+logM *   [M ]
+N
+A
+B
+C
+D
+0.5
+0.0
+0.5
+1.0
+1.5
+2.0
+2.5
+logSFR  [M  yr
+1]
+Figure 7.
+Left panel: averaged values of logarithmic M∗ compared with merger stages.
+Right panel: averaged values of
+logarithmic SFR compared with merger stages.
+7
+8
+9
+10
+11
+12
+logM *
+2
+1
+0
+1
+2
+3
+logSFR
+Speagle+14
+Saintonge+16
+Elbaz+07 (z<0.1 SDSS)
+PG QSO (z<0.1)
+Stage-A(Early)
+Stage-B(Early)
+Stage-C(Late)
+Stage-D(Late)
+Stage-N
+7
+8
+9
+10
+11
+12
+logM *
+2
+1
+0
+1
+2
+3
+logSFR
+Speagle+14
+Saintonge+16
+Elbaz+07 (z<0.1 SDSS)
+AGN (U/LIRG)
+SB or HX nondet. (U/LIRG)
+PG QSO (z<0.1)
+Figure 8. Left panel: logarithmic stellar mass in M⊙ vs. logarithmic SFR in M⊙ yr−1. The blue circles, green triangles,
+orange diamonds, red stars, and purple triangles represent the sources in stages A, B (early mergers), C, D (late mergers), and
+N (nonmergers) U/LIRGs, respectively. The gray diamonds illustrate the PG QSOs at z < 0.1, whose SFRs are estimated by
+the UV-to-IR SED decomposition (Lyu et al. 2017). The black dotted curve and cyan area denote the MS and 1σ uncertain
+reported by Speagle et al. (2014), while the dashed solid curve and shading represent those reported by Saintonge et al. (2016).
+The green dotted line is the MS among z < 0.1 SDSS galaxies Elbaz et al. (2007). Right panel: the same but the sources are
+classified by AGNs in U/LIRGs (red star), starburst-dominant or hard X-ray–nondetected sources in U/LIRGs (gray circle),
+and PG QSOs (gray diamond).
+ture of strong mid-IR emission from the AGNs. Thus,
+no matter which classifications of hard X-ray or mid-IR
+observations we select, the SFR–M∗ relation implies the
+small influence of the AGN activities on the starburst
+activities in the phase of U/LIRGs.
+5.2. Origin of Radio Emission from U/LIRGs
+Radio observation is a potential approach to reveal a
+mixture of starburst and AGN activities in U/LIRGs.
+About 10% of AGNs radiate strong synchrotron emis-
+sion primarily from the powerful relativistic jets in the
+radio band, observable as radio-loud AGNs (e.g., Begel-
+man et al. 1984). The other AGNs are classified as radio-
+quiet AGNs, whose radio emissions are derived from
+a wide range of possible mechanisms: star formation,
+AGN-driven wind, free-free emission from photoionized
+gas, low power jets, and the innermost accretion disc
+coronal activities (e.g., Panessa et al. 2019; Kawamuro
+et al. 2022). Thanks to the long wavelengths, radio ob-
+servations can overcome the effects of dust obscuration
+in U/LIRGs and investigate their central engines, par-
+ticularly starbursts and/or AGNs (e.g., Condon et al.
+
+22
+Yamada et al.
+1991; Lonsdale et al. 2003; Murphy 2013; Vardoulaki
+et al. 2015).
+5.2.1. Radio Slope
+For star-forming galaxies, the radio emission typically
+appears as a power law spectrum (Sν ∝ ν−α) from ther-
+mal and non-thermal emission associated with the for-
+mation of massive stars. The thermal emission is pro-
+duced by the young massive O/B stars dominating the
+ionization in HII regions, and the non-thermal emission
+is produced by supernova remnants of the more mas-
+sive stars than ≳8 M⊙, accelerating cosmic-ray electrons
+(e.g., Helou et al. 1985; Condon 1992). Under such con-
+ditions, the thermal bremsstrahlung free-free emission
+from the HII regions has a flat slope (α ∼ 0.1), while
+the non-thermal free-free emission shows a steep slope
+(α ∼ 0.8; e.g., Niklas et al. 1997). The contribution of
+non-thermal emission is much larger at frequencies be-
+low 10 GHz than the thermal emission, as confirmed by
+the best-fit models of synchrotron (pink) and nebular
+free-free (gray) emission in the radio band (see Figure 1
+and Figures E1–E10).
+However, since the AGNs also
+radiate the synchrotron emission with a similar slope
+to the starburst emission (α ∼ 0.8; e.g., Krolik 1999;
+Niklas et al. 1997; but see the study of radio-slope map
+by Vardoulaki et al. 2015 and Linden et al. 2019), this
+makes difficult to separate the starburst and AGN ra-
+dio emission. For U/LIRGs, the nuclear radio emission
+should have flat spectra due to optically-thick free-free
+absorption (Condon et al. 1991; Clemens et al. 2008;
+Leroy et al. 2011; Murphy et al. 2013; Murphy 2013),
+and thus the radio slope could not be a tracer of AGNs
+but an indicator of the surrounding environment of the
+nuclear starbursts and AGNs.
+The top panels of Figure 9 display the radio slope
+within the 0.07–3.0 GHz band, αradio, (Section 4.3) as
+a function of the SFR and the fraction of the AGN lu-
+minosity in the IR band. The previous radio study of
+U/LIRGs performed by Murphy (2013) reports that the
+median value of the radio slope at ≲5 GHz for U/LIRGs
+is 0.5, and the slopes decrease with merger stage. The
+values in our work are well consistent with their me-
+dian value and decreasing trend. The flat slope in late
+mergers with high SFRs (αradio ∼ 0.0–0.5) can be ex-
+plained by the optically-thick free-free absorption due
+to the rich environment of the nuclear region.16 In the
+right panel, the hard X-ray–detected AGNs and three
+16 The AGNs with high-Eddington ratios also show the flat radio
+slope (Laor et al. 2019; Yang et al. 2020b), whose contribution
+of the radio emission may be smaller than those of starbursts as
+discussed on the correlation coefficient (qIR).
+newly-identified AGN candidates are characterized as
+the positive values of the fraction of AGN luminosity.
+As mentioned above, the AGN fraction (i.e., the domi-
+nance of AGN activity) is not correlated with the radio
+slope for U/LIRGs.
+5.2.2. Radio–IR Correlation Coefficient
+Alternatively,
+the correlation coefficient,
+qIR
+(=
+logLIR/L1.4GHz; see Section 4.3), can be a comple-
+mentary parameter to unveil the presence of AGNs in
+U/LIRGs.
+For star-forming galaxies, a tight correla-
+tion between radio and IR luminosities is reported (e.g.,
+Kennicutt 1998; Bonzini et al. 2015), whose luminos-
+ity ratio is expressed by qIR. For the AGN-dominant
+sources, the value should be small due to the powerful
+synchrotron emission from the AGN (e.g., Yun et al.
+2001; U et al. 2012).
+We investigate the distribution
+of qIR as a function of the SFR and the fraction of the
+AGN luminosity (bottom panels of Figure 9). Except for
+three outliers below the criteria specified as radio-excess
+(qIR < 1.64, marked by gray dotted line; Yun et al.
+2001), these U/LIRGs are distributed around the typi-
+cal value of star-forming galaxies, ∼2.64 (black dashed
+line; Bell 2003), without regard for merger stage and
+SFR. Remarkably, the sources having larger fractions of
+AGN luminosity tend to show smaller qIR, indicating the
+strong radio emission due to the synchrotron radiation
+from the AGNs. Not only the sources with qIR < 1.64
+(Yun et al. 2001), but those with qIR < 2 have AGNs
+for the U/LIRGs in our sample.
+5.2.3. Radio Excess Parameter
+In the left panel of Figure 10, we also compare
+the SFR and radio 1.4 GHz luminosities (L1.4GHz) for
+U/LIRGs. The black dashed line is the empirical corre-
+lation from the radio–far-IR luminosity relation and the
+conversion factor between SFR and far-IR luminosity
+for star-forming galaxies in Kennicutt (1998), assuming
+Chabrier IMF (see also Bonzini et al. 2015):
+log(L1.4GHz/erg s−1) = log(SFR) + 37.60.
+(2)
+Our targets roughly follow the empirical relation.
+Delvecchio et al. (2017) introduce a new diagnostics for
+AGNs by using the radio excess parameter, qexcess =
+log(L1.4GHz/SFR). They suggest that the sources hav-
+ing qexcess > 38.130×(1+z)0.013 in (erg s−1)/(M⊙ yr−1)
+are likely attributable to AGN activities. As shown in
+the right panel, the radio-excess sources in our samples
+have fAGN > 0 (i.e., hosting AGNs) in the IR band.
+As a whole, the radio-excess sources in U/LIRGs host
+AGNs detected in the IR and X-ray bands. Whereas,
+the other major population of radio-quiet sources in
+
+23
+0.5
+0.0
+0.5
+1.0
+1.5
+2.0
+2.5
+3.0
+logSFR
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+radio
+Murphy+13
+Stage-A(Early)
+Stage-B(Early)
+Stage-C(Late)
+Stage-D(Late)
+Stage-N
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+fAGN (= LIR, AGN/LIR)
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+radio
+Murphy+13
+Stage-A(Early)
+Stage-B(Early)
+Stage-C(Late)
+Stage-D(Late)
+Stage-N
+2
+1
+0
+1
+2
+3
+logSFR
+1
+0
+1
+2
+3
+4
+qir = log(LIR/L1.4GHz)
+radio-excess (Yun+01)
+Bell (2003)
+ = 0.5 (fixed)
+Stage-A(Early)
+Stage-B(Early)
+Stage-C(Late)
+Stage-D(Late)
+Stage-N
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+fAGN (= LIR, AGN/LIR)
+1
+0
+1
+2
+3
+4
+qir = log(LIR/L1.4GHz)
+radio-excess (Yun+01)
+Bell (2003)
+ = 0.5 (fixed)
+Stage-A(Early)
+Stage-B(Early)
+Stage-C(Late)
+Stage-D(Late)
+Stage-N
+Figure 9. Top panels: logarithmic SFR vs. αradio (left) and fraction of AGN luminosity in the IR band vs. αradio (right),
+excluding the sources whose αradio is fixed at 0.5. The sources with fAGN = 0.0 mean the U/LIRGs which do not have AGNs.
+The dashed line is the median of low-frequency (<5 GHz) αradio among U/LIRGs reported by Murphy (2013). Bottom panels:
+logarithmic SFR vs. qIR (left) and fraction of AGN luminosity in the IR band vs. qIR (right). The dashed line is the averaged
+values reported in Bell (2003), and the dotted gray line illustrates the threshold for radio-excess (qIR < 1.64) as a tracer of an
+AGN (Yun et al. 2001; U et al. 2012). Large symbols are the same in Figure 8, while small crosses denote the sources where
+αradio = 0.5 is assumed in the radio fitting.
+2
+1
+0
+1
+2
+3
+logSFR
+35
+36
+37
+38
+39
+40
+41
+42
+logL1.4GHz  [erg s
+1]
+Kennicutt+98
+ = 0.5 (fixed)
+Stage-A(Early)
+Stage-B(Early)
+Stage-C(Late)
+Stage-D(Late)
+Stage-N
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+fAGN (= LIR, AGN/LIR)
+36
+37
+38
+39
+40
+41
+qexcess = log(L1.4GHz/SFR)
+Delvecchio+17
+ = 0.5 (fixed)
+Stage-A(Early)
+Stage-B(Early)
+Stage-C(Late)
+Stage-D(Late)
+Stage-N
+Figure 10. Left panel: logarithmic SFR vs. logarithmic radio luminosity at 1.4 GHz. The black dashed line is obtained by
+the empirical radio-far-IR relation in star-forming galaxies in Kennicutt (1998), assuming Chabrier IMF (see Bonzini et al.
+2015). Right panel: fraction of AGN luminosity in the IR band (fAGN) vs. radio excess parameter (qexcess). The sources with
+fAGN = 0.0 mean the U/LIRGs which do not have AGNs. The black solid curve shows the threshold of radio-excess sources at
+z ≈ 0.0 (Delvecchio et al. 2017). The symbols are the same in Figure 9.
+
+24
+Yamada et al.
+U/LIRGs are indistinguishable from AGNs or not. The
+same results are reported for AKARI-selected star-
+forming galaxies with and without AGNs (Mori´c et al.
+2010), indicating that the AGNs in U/LIRGs are typical
+radio-quiet AGNs in star-forming galaxies (i.e., the large
+contribution of the radio emission from the intense star-
+bursts). Therefore, although sources with high qexcess
+values likely contain AGNs, the radio emission reflects
+the intensity of the starburst activities (e.g., SFR) for
+the majority of U/LIRGs.
+5.3. WISE Color: New Wedge of Buried AGNs
+Near-IR to mid-IR observations have been thought
+of as a promising tool to detect the AGN emission in
+U/LIRGs (e.g., Veilleux et al. 2009b; Petric et al. 2011;
+Imanishi & Saito 2014; Imanishi et al. 2020; D´ıaz-Santos
+et al. 2017). A large part of the emission from central
+AGNs in U/LIRGs is absorbed by the surrounding ma-
+terials such as the torus with a large covering fraction
+(e.g., Imanishi et al. 2006, 2008; Ricci et al. 2017a; Ya-
+mada et al. 2019) and re-radiated chiefly in the mid-IR
+wavelength.
+The ∼3–30 µm SEDs of the reprocessed
+dust emission heated by the AGN is characterized as a
+steep power-law slope (e.g., Laurent et al. 2000; Stern
+et al. 2005; Assef et al. 2010). Indeed, the IR color se-
+lection with WISE has been exploited to search for the
+optically obscured AGNs (e.g., Jarrett et al. 2011; Stern
+et al. 2012; Mateos et al. 2012, 2013; Assef et al. 2013,
+2018; Secrest et al. 2015; Toba et al. 2015; Ellison et al.
+2017; Satyapal et al. 2017; Weston et al. 2017; Goulding
+et al. 2018a; Pfeifle et al. 2022).
+5.3.1. W1–W2 Color
+Figure 11 presents the WISE W1–W2 (or [3.4]–[4.6]
+in Vega magnitude) color as a function of SFR (left)
+and AGN fraction in the IR band (right).17
+Here,
+the WISE magnitudes are corrected for Galactic ex-
+tinction (Section 3.8). Stern et al. (2012) introduce a
+simple mid-IR color criterion of [3.4] − [4.6] > 0.8 by
+using the WISE-selected sources in the Cosmic Evo-
+lution Survey (COSMOS; Scoville et al. 2007).
+Sim-
+ilarly, Satyapal et al. (2014) report that a more in-
+clusive [3.4] − [4.6] > 0.5 cut identifies AGNs in low-z
+(z < 0.2) mergers selected from the SDSS survey (El-
+lison et al. 2013). For our U/LIRGs, we find that all
+late mergers have logSFR ≳ 1.5 and [3.4] − [4.6] ≳ 0.5,
+while most early mergers and nonmergers have smaller
+17 The WISE photometry of Mrk 231, a stage D merger hosting the
+AGN with high λEdd, is not utilized in the SED analysis due to
+the flag of w1-3sat ≈ 0.06 (W1, W2, W3 = 7.80±0.01, 6.58±0.01,
+3.54±0.01, respectively), but is only provided in Figures 11–12
+since it will be a small effect on the WISE colors.
+SFRs and [3.4] − [4.6] ≲ 0.5, making it easy to select
+the IR-luminous late mergers.
+However, the compar-
+ison between WISE color and AGN fraction suggests
+that the hard X-ray–detected and newly-identified AGN
+candidates (i.e., fAGN > 0) are not distinguished from
+the other starburst-dominant or hard X-ray–undetected
+sources by the [3.4]–[4.6] color. These results indicate
+that for U/LIRGs, the [3.4]–[4.6] criteria could not nec-
+essarily discriminate between the intense starbursts and
+the AGNs discovered with the hard X-ray observations
+(e.g., Ricci et al. 2016, 2017a; Yamada et al. 2021).
+5.3.2. WISE Color–color Diagram
+Figure 12 shows the WISE color–color diagram ([3.4]–
+[4.6] versus [4.6]–[12]) for our sample. The AGN wedges
+that have been well utilized for the low-z galaxies are
+overplotted (Jarrett et al. 2011; Mateos et al. 2012;
+Blecha et al. 2018).
+Almost all late mergers are lo-
+cated within the AGN wedge that is based on the hy-
+drodynamics and radiative transfer simulation of gas-
+rich mergers (dashed line; see Equation (1) in Blecha
+et al. 2018). In late mergers, it is notable that the val-
+ues of [4.6]–[12] magnitudes decrease with the values of
+[3.4]–[4.6] magnitudes for the AGNs, while they increase
+for the other sources.
+Particularly, the AGNs with
+[4.6]–[12] ≲ 3 in stage D mergers (IRAS F05189−2524,
+IRAS F08572+3915, UGC 5101, ESO 374−IG032, and
+Mrk 231) show the excess in the ∼3–10 µm wave-
+length relative to the best-fit SED models with updated
+CLUMPY model (Figures E1–E10), corresponding to
+the dust emission at the temperature of ∼300–1000 K
+(e.g., Lyu & Rieke 2021). The contribution of the near-
+IR emission from the old stellar population (e.g., Pol-
+letta et al. 2007) is extracted by the multiwavelength
+SED analysis, the origin of the ∼3–10 µm excess can be
+explainable by the additional nuclear hot dust heated by
+the AGNs, such as inner part of the dusty disk and/or
+hot polar dust within the inner parsecs (e.g., H¨onig et al.
+2013; Garc´ıa-Bernete et al. 2017, 2022; Lyu et al. 2017;
+Lyu & Rieke 2021; Mattila et al. 2018; Mizukoshi et al.
+2022). The near-IR excess in a sample of type 1 AGN is
+well reported (Netzer et al. 2007; Mor et al. 2009; Mor
+& Netzer 2012) and this hot dust component can also
+be part of the known outflows in Mrk 231 (e.g., Feruglio
+et al. 2015; Morganti et al. 2016; Veilleux et al. 2016).
+The strong near-IR emission from the dusty disk, hot
+polar dust, or both is a unique feature of buried AGNs
+in late mergers.
+Although the complete selection of hard X-ray–
+detected AGNs by the WISE color seems to be difficult,
+some buried AGNs in local U/LIRGs are characterized
+by the near-IR excess appearing in the improved AGN
+
+25
+2
+1
+0
+1
+2
+3
+logSFR
+0.0
+0.5
+1.0
+1.5
+2.0
+2.5
+3.0
+[3.4] 
+ [4.6] in Vega mag
+Satyapal+14
+Stage-A(Early)
+Stage-B(Early)
+Stage-C(Late)
+Stage-D(Late)
+Stage-N
+SB or HX nondet.
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+fAGN (= LIR, AGN/LIR)
+0.0
+0.5
+1.0
+1.5
+2.0
+2.5
+3.0
+[3.4] 
+ [4.6] in Vega mag
+Satyapal+14
+Stage-A(Early)
+Stage-B(Early)
+Stage-C(Late)
+Stage-D(Late)
+Stage-N
+SB or HX nondet.
+Figure 11. WISE W1–W2 color as a function of SFR (left) and the fraction of AGN luminosity in the IR band (right). Dashed
+line illustrates the W1 − W2 > 0.5 threshold (Satyapal et al. 2014).
+2.0
+2.5
+3.0
+3.5
+4.0
+4.5
+5.0
+5.5
+[4.6] 
+ [12] in Vega mag
+0.0
+0.5
+1.0
+1.5
+2.0
+2.5
+3.0
+[3.4] 
+ [4.6] in Vega mag
+UGC5101
+F05189
+F08572
+ESO374
+Mrk231
+This Work
+Jarrett+11
+Mateos+12
+Blecha+18
+Stage-A(Early)
+Stage-B(Early)
+Stage-C(Late)
+Stage-D(Late)
+Stage-N
+SB or HX nondet.
+Figure 12. WISE color–color diagram. The AGN selection wedges are illustrated as the areas within the dotted gray (Jarrett
+et al. 2011), dash-dotted gray (Mateos et al. 2012), and black dashed (Blecha et al. 2018) boxes, and the pink shaded area is
+presented in This work, respectively. Large symbols are the same in Figure 8, while small circles illustrate the sources where
+fAGN = 0.0 (starburst-dominant or hard X-ray–nondetected sources).
+color selection (pink shade);
+2.2 < [4.6] − [12] < 4.2, and
+[3.4] − [4.6] > 0.1 × ([4.6] − [12]) + 0.38,
+(3)
+which are the combination of the previous AGN wedge
+for QSOs, Seyfert galaxies, and obscured AGNs (dot-
+ted line; see Equation (1) in Jarrett et al. 2011) and
+the higher [3.4]–[4.6] region. Among our local U/LIRGs
+within the new wedge, the selection purity of the AGNs
+in stage C–D mergers is 72+11
+−12% (9/12). Here the frac-
+tion and uncertainty are the 50th and 16th–84th quan-
+tiles of a binomial distribution, respectively, calculated
+with the beta function (Cameron 2011). By contrast,
+the completeness of selecting AGNs with the new wedge
+is low (40% ± 10%; 9/23). Considering that only the
+most luminous AGNs (e.g., IRAS F05189−2524, IRAS
+F08572+3915, and Mrk 231) tend to be selected, the low
+completeness suggests the difficulty of the identification
+of low-luminous AGNs in late mergers. We also need
+to keep in mind that this criterion should be adopted
+for local U/LIRGs since it includes the typical criteria
+for QSOs and normal AGNs (Jarrett et al. 2011). Thus,
+
+26
+Yamada et al.
+10
+4
+10
+2
+100
+102
+104
+106
+Rest-frame wavelength [ m]
+10
+9
+10
+7
+10
+5
+10
+3
+10
+1
+101
+103
+105
+F  (normalized at Ks band)
+Stage-A (Early: 8)
+Stage-B (Early: 6)
+Stage-C (Late:  5)
+Stage-D (Late:12)
+Stage-N (7)
+Averaged SEDs for Hard X-ray Detected AGNs
+10
+4
+10
+2
+100
+102
+104
+106
+Rest-frame wavelength [ m]
+10
+9
+10
+7
+10
+5
+10
+3
+10
+1
+101
+103
+105
+F  (normalized at Ks band)
+Stage-A (Early: 5)
+Stage-B (Early: 6)
+Stage-C (Late: 2)
+Stage-D (Late: 7)
+Stage-N (2)
+Averaged SEDs for Hard X-ray Nondetected Sources
+Figure 13. Top panel: rest-frame wavelength vs. flux density normalized at Ks band for the hard X-ray–detected AGNs.
+Bottom panel: the same but for the soft X-ray–detected galaxies among starburst-dominant or hard X-ray–nondetected sources.
+The solid curves represent the averaged SEDs for the sources in stage A (blue), stage B (green), stage C (orange), stage D (red)
+and stage N (purple) U/LIRGs. Values in parentheses are the number of sources. The light-colored curves show the SEDs for
+individual sources.
+this new WISE color–color diagram for local U/LIRGs
+provides valuable information on the presence of the lu-
+minous AGNs hosting the dusty disk, hot polar dust, or
+both within the inner parsecs.
+5.4. Averaged SEDs in U/LIRGs
+To further understand the characteristics of the hard
+X-ray to radio emission in local U/LIRGs, in Figure 13
+we illustrate the SEDs for all sources whose X-ray spec-
+tra above ≳1 keV are analyzed by Yamada et al. (2021).
+The Ks (2.159 µm) band (near the peak of the stel-
+lar emission) is selected for the normalization since it is
+less affected by dust extinction and contamination from
+AGN-heated hot dust (e.g., Kim et al. 2002; Marconi
+& Hunt 2003; Skrutskie et al. 2006; Vika et al. 2012).18
+The left panel shows the best-fit models of 36 single
+and two unresolved dual hard X-ray–detected AGNs
+(Mrk 266B/Mrk 266A and NGC 6240S/NGC 6240N),
+but excluding three newly identified AGN candidates.
+Here, the complex X-ray absorption lines in NGC 1365
+are ignored as it is a dramatically variable feature,
+mainly caused by highly ionized species of Fe in a high-
+velocity outflow (Rivers et al. 2015). On the other hand,
+the right panel shows those of two starburst-dominant
+18 The results are almost unchanged even if the normalization is
+chosen in the H band, which is also a reliable tracer of the stellar
+luminosity (e.g., Marconi & Hunt 2003; Hainline et al. 2011).
+
+27
+10
+4
+10
+2
+100
+102
+104
+106
+Rest-frame wavelength [ m]
+10
+9
+10
+7
+10
+5
+10
+3
+10
+1
+101
+103
+105
+F  (normalized at Ks band)
+Early Merger (NonX:  6)
+Early Merger (AGN: 14)
+Early Merger (SB:  11)
+Late Merger (AGN: 17)
+Late Merger (SB:  9)
+Averaged SEDs for Local U/LIRGs
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+10
+5
+10
+4
+10
+3
+10
+2
+10
+1
+100
+101
+102
+103
+L  (normalized at Ks band)
+Early Merger (NonX:  6)
+Early Merger (AGN: 14)
+Early Merger (SB:  11)
+Late Merger (AGN: 17)
+Late Merger (SB:  9)
+Averaged SEDs for Local U/LIRGs
+Figure 14. Top panel: rest-frame wavelength vs. flux density normalized at Ks band. Bottom panel: rest-frame frequency
+vs. luminosity normalized at Ks band. The dotted green curve shows the averaged SEDs for the sources whose X-ray spectra
+above ≳1 keV are not obtained in stage A–B (early) mergers.
+The solid curves represent the averaged SEDs for the hard
+X-ray–detected AGNs in stage A–B (early mergers; blue) and stage C–D (late mergers; red). The dashed curves are the same
+ones for the soft X-ray–detected galaxies among starburst-dominant or hard X-ray–nondetected sources. Values in parentheses
+are the number of sources. These SED templates are available in Table 5.
+sources detected in the hard X-ray band (IC 1623A
+and NGC 3256) and 20 hard X-ray–undetected sources.
+Since the ≲3 keV spectra are complex due to the Galac-
+tic extinction and the optically thin thermal emission in
+the host galaxy, we plot the best-fit models of the X-ray
+spectra in the 3–200 keV band for AGNs and 3–20 keV
+for the other sources.
+These SEDs exhibit several common features in the
+UV-to-radio bands regardless of the presence or absence
+of AGNs. First, they have a dip in the UV-to-optical
+wavelength, even though the SEDs are corrected for
+Galactic extinction.
+The UV emission from the stel-
+lar populations and/or AGN disk is absorbed by the
+gas and dust of the host galaxy, torus, and polar dust.
+Second, the IR-to-radio fluxes relative to the Ks band
+increase with merger stage due to the re-radiation from
+the dust of AGNs and primarily intense starbursts (Sec-
+tion 5.1 and Section 5.2). Third, the increase of the IR
+emission causes the steep slope in the near-to-mid-IR
+band to appear as the features in WISE [3.4]–[4.6] color
+(Section 5.3).
+Figure 14 presents the averaged SEDs for AGNs and
+the other sources in both early and late mergers, whose
+X-ray spectra above ≳1 keV are analyzed. We also plot
+the averaged UV-to-radio SEDs for the sources whose X-
+ray spectra above ≳1 keV are not obtained, all of which
+
+28
+Yamada et al.
+100
+101
+102
+Rest-frame wavelength [ m]
+100
+101
+102
+103
+104
+F  (normalized at Ks band)
+Early Merger (Non-X: 6)
+Early Merger (AGN: 14)
+Early Merger (SB:  11)
+Late Merger (AGN: 17)
+Late Merger (SB:  9)
+F08572 (WISE)
+F08572 (others)
+Averaged SEDs for Local U/LIRGs
+Figure 15. Enlarged picture of the IR (1–600 µm) wave-
+length of the left panel in Figure 14 (rest-frame wavelength
+vs. flux density normalized at Ks band). Stars and squares
+mark the photometry of WISE and other IR instruments
+(2MASS, AKARI, and Herschel) for the AGN in IRAS
+F08572+3915.
+are in early mergers. These averaged SED templates in
+Figure 14 are available in Table 5. By comparing the
+AGNs (solid curves) and the others (dashed and dot-
+ted curves), we find that the averaged SEDs of the lat-
+ter population show stronger far-IR fluxes than those of
+the former. This support that the starburst-dominant
+sources have cooler dust than AGNs. Whereas, the UV-
+to-radio SEDs of AGNs and non-AGN sources holisti-
+cally resemble each other, regardless of the merger stage.
+The difference in the far-IR fluxes is smaller than the
+scattering among the individual sources as shown in Fig-
+ure 13. This resemblance makes it difficult to identify
+the AGNs in U/LIRGs.
+In Figure 15, we compare the averaged SEDs and the
+photometry of the buried AGNs in IRAS F08572+3915,
+which is one of the most luminous AGNs in our sam-
+ple and is well selected by the WISE color–color di-
+agram (Section 5.3).
+We find that the source shows
+the flux peak at shorter IR wavelengths than in nor-
+mal U/LIRGs.
+This suggests the presence of a large
+amount of hot dust, which can be a unique feature of
+the luminous AGNs deeply hidden by gas and dust. Re-
+gardless of the presence of the IR-excess features, the
+X-ray spectra of AGNs and others are completely dif-
+ferent (Figure 14). The AGNs have much larger X-ray
+fluxes than those in the starburst-dominant or hard X-
+ray–undetected sources. According to the X-ray spec-
+tral analysis in Yamada et al. (2021), the observed X-
+rays of AGNs become dimmed with merger stage due to
+Table 5. Averaged SED Templates in Our Targets
+Column Name
+Format
+Unit
+Description
+Class
+LONG
+Classification
+Wavelength
+DOUBLE
+µm
+Wavelength
+Frequency
+DOUBLE
+Hz
+Frequency
+Normed FNU
+DOUBLE
+Flux density at each wavelength
+Normed LNU
+DOUBLE
+Luminosity at each wavelength
+(This table is available in its entirety in machine-readable form.)
+the increase of the hydrogen column density, while for
+the starburst-dominant sources, the soft X-rays domi-
+nated by the X-ray binary emission in the host galaxy
+(e.g., Mineo et al. 2012) become brighter in late merg-
+ers with high SFRs than in early mergers. Overall, the
+AGNs show a significant X-ray excess relative to the
+other wavelength emission, as represented by the com-
+parison between observed X-ray luminosity and SFR in
+Section 6.3 of Yamada et al. (2021). Therefore, despite
+the effects of the X-ray weakness (Section 5.5), the ex-
+cess of X-ray fluxes relative to the UV-to-radio SEDs
+should be an incomparable characteristic enabling us to
+reveal the true energy sources (intense starbursts and/or
+buried AGNs) in U/LIRGs.
+5.5. X-ray Weak AGNs in IR-luminous Galaxies
+We finally investigate the multiwavelength AGN lumi-
+nosities corrected for the absorption of the host galaxy,
+torus, and polar dust. Yamada et al. (2021) estimate the
+de-absorbed 2–10 keV AGN luminosities and find that
+the ratio of the bolometric AGN luminosity to the X-ray
+luminosity is quite large for the AGNs in late mergers.
+This X-ray weakness has been thought of as a particular
+property of the AGNs in local U/LIRGs (e.g., Teng et al.
+2014, 2015), and its origin (e.g., the optically thick failed
+winds launched from an inner region of the disk) is dis-
+cussed in Yamada et al. (2021). For understanding the
+AGN activities in U/LIRGs through cosmic history, it is
+at least necessary to probe whether the X-ray weakness
+is a common feature for both low-z and high-z U/LIRGs.
+5.5.1. 6 µm Luminosity vs. 2–10 keV Luminosity
+Figure 16 illustrates the relation between monochro-
+matic luminosity of the AGN emission at rest-frame
+6 µm derived from the multiwavelength SED decomposi-
+tion (L6,AGN) and unabsorbed (i.e., de-absorbed) X-ray
+luminosity in the rest-frame 2–10 keV band (LX,unabs).
+Many studies report that the mid-IR and X-ray lumi-
+nosities of the AGN component are strongly correlated
+over a wide luminosity ranges (e.g., Lutz et al. 2004;
+
+29
+40
+41
+42
+43
+44
+45
+46
+47
+48
+logL6, AGN [erg s
+1]
+40
+41
+42
+43
+44
+45
+46
+47
+logLX, unabs [erg s
+1]
+Stern (2015)
+Mateos et al. (2015)
+Toba et al. (2022)
+This Work
+ELIRG(z~2)
+WISSH(z~2
+4)
+GOODS Herschel(z~1
+3)
+Extremely Red Quasar(z~2
+3)
+BL DOG(z~1)
+IR-bright/Hot DOG(z~1-3)
+Stage-A(Early)
+Stage-B(Early)
+Stage-C(Late)
+Stage-D(Late)
+Stage-N
+Figure 16. Rest-frame 6 µm luminosity contributed from AGNs vs. unabsorbed (absorption-corrected) rest-frame 2–10 keV
+luminosity for AGNs in various IR-luminous galaxies. The cyan triangle indicates an ELIRG at z ∼ 2 (Toba et al. 2021b).
+The yellow circles represent WISSH quasars at z ∼ 2–4 (Martocchia et al. 2017; Zappacosta et al. 2020). The pink circles
+indicate mid-IR luminous quasars at z ∼ 1–3 in the GOODS–Herschel fields (Del Moro et al. 2016) while pink diamonds show
+extremely red quasars at z ∼ 2–3 (Goulding et al. 2018b). The pink and red squares mark broad-line DOGs at z ∼ 1 (Zou
+et al. 2020) and IR-bright/hot DOGs at z ∼ 1–3 (Ricci et al. 2017c; Vito et al. 2018; Zappacosta et al. 2018; Toba et al. 2020a),
+respectively. Their colors (cyan, yellow, pink. and red) are largely categorized by the typical NH of the populations (see the
+text). The other symbols are the same in Figure 8. The green dashed and blue dotted lines illustrate the linear relation using a
+sample drawn from the eROSITA Final Equatorial Depth Survey (Toba et al. 2022a) and the Bright Ultra-hard XMM-Newton
+Survey (Mateos et al. 2015), respectively. The black solid curve denotes the 2D polynomial relations from Stern (2015). Red
+dash-dotted line and the pink shaded area are the best-fitting relation and its 1σ dispersion among stage C–D mergers and the
+high-z IR-luminous sources, respectively.
+Ramos Almeida et al. 2007; Gandhi et al. 2009; Ichikawa
+et al. 2012, 2017; Asmus et al. 2015; Mateos et al. 2015;
+Stern 2015; Garc´ıa-Bernete et al. 2016; Chen et al. 2017;
+Toba et al. 2019a, 2022a).
+Here, we plot the values
+for local U/LIRGs color-coded by merger stages, and
+overplot those for IR-luminous galaxies corresponding
+to high-z U/LIRGs: an extremely luminous IR galaxy
+(ELIRG) at z ∼ 2 (Toba et al. 2021b); WISE/SDSS
+selected hyper-luminous (WISSH) quasars at z ∼ 2–4
+(Martocchia et al. 2017; Zappacosta et al. 2020); mid-IR
+luminous quasars at z ∼ 1–3 from the GOODS-Herschel
+fields (Del Moro et al. 2016); extremely red quasars at
+z ∼ 2–3 (Goulding et al. 2018b); dust-obscured galax-
+ies (DOGs) with broad optical/UV emission lines (BL
+DOGs) at z ∼ 1 (Zou et al. 2020); and IR-bright DOGs
+at z ∼ 1 (Toba et al. 2020a) and hot DOGs at z ∼ 1–3
+(Ricci et al. 2017c; Vito et al. 2018; Zappacosta et al.
+2018).19 The values of L6,AGN and LX,unabs for high-z
+IR-luminous galaxies are presented in their references
+mostly by the IR SED decomposition and X-ray spec-
+tral analysis, respectively. The AGNs are unobscured
+19 The L6,AGN of extremely red quasars in Goulding et al. (2018b)
+and hot DOGs in Ricci et al. (2017c) are provided by assuming
+that the 6 µm emission is AGN-dominant (see e.g., Del Moro
+et al. 2016 for extremely red quasars; e.g., Stern et al. 2014;
+Assef et al. 2016, 2020; Tsai et al. 2018; Zappacosta et al. 2018
+for hot DOGs).
+
+30
+Yamada et al.
+(≲1022 cm−2) for an ELIRG (cyan), weakly obscured
+(∼1021–1023 cm−2) for WISSH quasars (yellow), moder-
+ately obscured (∼1022–1024 cm−2) for mid-IR luminous
+quasars in the GOODS-Herschel fields, extremely red
+quasars, and BL DOGs (pink), and heavily obscured
+(≳1023 cm−2) for IR-bright/hot DOGs (red).
+More-
+over, we compare these values with the typical relation
+obtained from the SDSS-selected low-z Seyfert galaxies
+(Stern 2015), the Bright Ultra-hard XMM-Newton Sur-
+vey (BUXS; Mateos et al. 2015), and the eROSITA Final
+Equatorial Depth Survey (eFEDS; Toba et al. 2022a).
+We find that several late mergers of local U/LIRGs lie
+below the typical L6,AGN–LX,unabs relation, supporting
+the X-ray weakness. For late mergers (stage C and D)
+and high-z IR-luminous galaxies, we conduct a Bayesian
+maximum likelihood method of Kelly (2007) between the
+two parameters. The resulting linear function is
+log(LX,unabs) = 0.80 log(L6,AGN) + 7.69,
+(4)
+and the 1σ dispersion is ±0.50 dex (red dashed line
+and pink shaded area).
+The correlation coefficient is
+r = 0.92 ± 0.02, confirming a tight correlation for low-
+z and high-z IR-luminous sources. These AGNs in the
+IR-luminous sources at z ∼ 0–4 are obscured sources
+and show smaller de-absorbed X-ray luminosities rel-
+ative to the mid-IR luminosities than the typical rela-
+tions. In particular, most AGNs in IR-bright/hot DOGs
+are heavily obscured (≳1023 cm−2) and explicitly X-ray
+weak among them (e.g., Ricci et al. 2017c; Toba et al.
+2020a), sharing similarity with the X-ray weak AGNs in
+late mergers for local U/LIRGs (Yamada et al. 2021).
+5.5.2. Optical to X-ray Spectral Index
+Additionally, we display the comparison between Ed-
+dington ratio (λEdd) and the optical to X-ray spec-
+tral index (αOX;
+Tananbaum et al. 1979) in Fig-
+ure 17.
+The definition of αOX is provided by using
+the monochromatic luminosity at rest-frame 2500 ˚A of
+the intrinsic AGN disk emission (L2500,disk) and the de-
+absorbed monochromatic luminosity at rest-frame 2 keV
+(L2keV,unabs) as below:
+αOX = log(L2keV,unabs/L2500,disk)
+log(ν2keV/ν2500)
+.
+(5)
+The L2500,disk is obtained by multiwavelength SED anal-
+ysis in this work, and L2keV,unabs is calculated from the
+best-fit models of the broadband X-ray spectra (Sec-
+tion 3.1).
+The αOX probes the balance between the
+accretion disk and hot corona activities, radiating op-
+tical and X-ray emission respectively. Several works re-
+port a moderate correlation between the Eddington ra-
+tio and αOX (e.g., Lusso et al. 2010; Chiaraluce et al.
+4
+3
+2
+1
+0
+1
+log
+Edd
+2.4
+2.2
+2.0
+1.8
+1.6
+1.4
+1.2
+1.0
+0.8
+OX
+Upper limit of z=7.2 ULIRG (GNz7q) 
+Mrk 231
+F08572
+Lusso+10
+Stage-A(Early)
+Stage-B(Early)
+Stage-C(Late)
+Stage-D(Late)
+Stage-N
+WISSH(z~2
+4)
+Figure 17. Logarithmic Eddington ratio vs. αOX computed
+using extinction-corrected 2500 ˚A and unabsorbed 2 keV
+luminosities.
+The black solid curve represents the best-fit
+relation among local and high-z AGNs, respectively (Lusso
+et al. 2010). The gray shaded area shows its 1σ uncertainty.
+The upper limit of a ULIRG at z = 7.2 (GNz7q; Fujimoto
+et al. 2022) is shown as a red dashed line since its SMBH
+mass and Eddington ratios are not constrained.
+Yellow
+circles mark the WISSH quasars in z ∼ 2–4 (Zappacosta
+et al. 2020). The other symbols are the same in Figure 8.
+2018) for X-ray selected AGNs and a typical relation of
+Lusso et al. (2010) is illustrated by a black solid line in
+Figure 17. We overplot the values of WISSH quasars
+(yellow circles; Martocchia et al. 2017; Zappacosta et al.
+2020), and the upper limit of αOX (< −2.23) provided
+with deep Chandra observation for a z = 7.2 red quasar
+GHz7q, classified as U/LIRG (red dashed line; Fujimoto
+et al. 2022).
+Although the Eddington ratios contain uncertainties
+of about ±0.5 dex originating from the MBH measure-
+ments (Yamada et al. 2021), some AGNs in stage D
+mergers show much smaller αOX than the typical re-
+lation.
+The distribution of αOX for X-ray selected
+and optical-selected AGNs (Just et al. 2007; Lusso
+et al. 2010; Dong et al. 2012; Martocchia et al. 2017;
+Chiaraluce et al. 2018) mostly covers from −1.0 to
+−2.0. Whereas, we find that the local stage-D merg-
+ers with the largest AGN luminosities (Mrk 231 and
+IRAS F08572+3915), many WISSH quasars, and GHz7q
+lie αOX ≲ −2.
+The caveat is that the X-ray lumi-
+nosity of GHz7q is only corrected for Galactic absorp-
+tion, but the Chandra observation of GHz7q confirms
+the lack of rest-frame hard X-rays, and the signifi-
+cant UV emission suggests the AGN is not heavily ob-
+scured.
+Its bolometric AGN luminosity estimated by
+the optical-to-millimeter SED analysis is (1.7 ± 0.1) ×
+
+31
+1046 erg s−1, which is ∼7 times larger than that of IRAS
+F08572+3915 (LAGN,int ∼ 2.5 × 1045 erg s−1). Unless
+the AGN of GHz7q has an extreme Eddington ratio
+above λEdd ∼ 10, the upper limit of αOX suggests the
+possibility that the AGN is also X-ray weak.
+5.5.3. X-ray Weakness as a Common Feature
+In
+summary,
+considering
+the
+small
+values
+of
+LX,unabs/L6,AGN ratio and αOX, the de-absorbed multi-
+wavelength SEDs support that the X-ray weakness may
+be a common feature among the AGNs in IR-luminous
+galaxies over cosmic history (z ∼ 0–7).
+Intriguingly,
+the strong AGN-driven outflows have been discovered
+from the z ≲ 1 U/LIRGs (e.g., Chen et al. 2020) and
+the high-z IR-luminous galaxies such as WISSH quasars
+(Bischetti et al. 2017; Travascio et al. 2020; Vietri et al.
+2022), extremely red quasars (Zakamska et al. 2016;
+Hamann et al. 2017; Goulding et al. 2018b), and IR-
+bright and hot DOGs (e.g., Ricci et al. 2017c; Toba
+et al. 2017a,b; Wu et al. 2018; Finnerty et al. 2020).
+As discussed in Section 6.1.6 of Yamada et al. (2021)
+for local late-stage U/LIRGs, the physical mechanism
+of the extreme X-ray weakness (e.g., the X-ray attenu-
+ation due to overionized optically-thick failed winds at
+∼102–103 rg) can enhance the UV-driven winds, which
+may effectively trigger the massive outflows in low-z and
+high-z U/LIRGs.
+5.6. Summary of Multiwavelength Features
+Here, we summarize the multiwavelength features of
+local U/LIRGs. The component galaxies in early merg-
+ers have a wide range of SFRs above and below the MS,
+while galaxies in late mergers have the highest SFRs
+above the MS. Similar SFR–M∗ distributions of AGNs
+and non-AGN sources imply the small influence of the
+AGN activities on the star formation in the phase of
+U/LIRGs (Section 5.1). The flat slope of radio emission
+in late mergers may be caused by the optically-thick
+free-free absorption due to the rich environment of the
+nuclear region.
+The SFRs are correlated with radio
+luminosity, indicating the major origin of the radio
+emission is from the starburst emission except for the
+radio-excess AGNs (Section 5.2). In the WISE color–
+color diagram, we propose a new wedge of the buried
+AGNs in late mergers.
+The strong near-IR emission
+of the hard X-ray–detected AGNs in late mergers sug-
+gests that they host the dusty disk and/or hot polar
+dust within the inner parsecs (Section 5.3). The aver-
+aged SEDs suggest that the excess of the X-rays is an
+incomparable characteristic enabling us to reveal the
+true energy sources (intense starbursts and/or buried
+AGNs) in U/LIRGs (Section 5.4).
+The absorption-
+corrected AGN SEDs show the extreme X-ray weakness
+relative to the other wavelengths. This may be a com-
+mon feature among the AGNs in IR-luminous galaxies
+over the cosmic history (z ∼ 0–7), whose mechanism
+will be related to their massive outflows (Section 5.5).
+In short, our results support that (1) the intense star-
+burst and buried AGNs occur in late mergers and (2)
+these buried AGNs may have dusty disks and/or hot
+polar dust, whose X-ray weakness may be related to the
+massive outflows.
+6. DISCUSSION I: EVOLUTION OF POLAR DUST
+IN U/LIRGS
+In this Section, we investigate the structure of polar
+dust in U/LIRGs based on the results of the multiwave-
+length SED analysis. The detailed results of the polar
+dust are discussed on the obscuration and luminosity
+(Section 6.1), gas-to-dust ratio (Section 6.2), the contri-
+bution to the IR AGN luminosity (Section 6.3), polar
+dust temperature (Section 6.4), and the unified view of
+the polar dust structure in U/LIRGs (Section 6.5).
+6.1. Obscuration and Luminosity
+The top left panel of Figure 18 presents the histograms
+of the line-of-sight extinction in the V band by the torus
+(A(LOS)
+V ,torus), while the bottom left panel shows for po-
+lar dust extinction (A(LOS)
+V ,polar). The dust extinction of
+the polar dust is calculated with RV = 3.1 (Cardelli
+et al. 1989) and given when 90◦ − i > σ (Section 4.1.3).
+We note that the values are much smaller than those
+of torus due to the initial condition of E(B − V ) = 0–
+0.8 mag (Section 4.2.2 and 4.2.3; see e.g., Buat et al.
+2021). We compare the histograms of different groups
+of unobscured, obscured, and CT AGNs. As expected
+from the dominance of the torus in the dust extinction,
+the A(LOS)
+V ,torus becomes larger with the line-of-sight AGN
+obscuration in the X-ray band. Whereas, A(LOS)
+V ,polar does
+not show any positive correlation with the X-ray ob-
+scuration. Considering that the hydrogen column den-
+sities mainly reflect the absorption by the broad line
+region and/or torus for obscured AGNs (e.g., Tanimoto
+et al. 2020; Ogawa et al. 2021; Andonie et al. 2022)20,
+the decorrelation between A(LOS)
+V ,polar and AGN types will
+be derived by the difference in the scales of the torus
+(∼1 pc) and the extended polar dust emission (∼10–
+1000 pc; see Section 6.5) whose typical temperatures
+are allowed between 100–250 K (Section 4.2.3).
+20 Particularly for U/LIRGs, the AGNs show the dramatic vari-
+ability in NH, supporting the presence of compact-scale (a few
+parsecs) obscurer (Laha et al. 2020; Yamada et al. 2021).
+
+32
+Yamada et al.
+10
+1
+100
+101
+102
+103
+A(LOS)
+V
+ [mag]
+0
+3
+6
+Number of sources
+< 10
+1
+Torus: Unobscured
+Torus: C-thin
+Torus: CT
+41
+42
+43
+44
+45
+46
+logLtorus [erg s
+1]
+0
+4
+8
+Number of sources
+10
+1
+100
+101
+102
+103
+A(LOS)
+V
+ [mag]
+0
+3
+6
+Number of sources
+< 10
+1
+Polar: Unobscured
+Polar: C-thin
+Polar: CT
+42
+43
+44
+45
+46
+logLpolar [erg s
+1]
+0
+4
+8
+Number of sources
+Non
+Figure 18. Top left panel: histogram of the line-of-sight extinction in the V band by the torus A(LOS)
+V ,torus (top). These are divided
+by the X-ray AGN classification (unobscured, Compton-thin, and CT AGNs; Yamada et al. 2021). Bottom left panel: the
+same for the polar dust extinction, A(LOS)
+V ,polar (bottom). The seven sources showing 90◦ − i > σ (i.e., A(LOS)
+V ,polar = 0) are excluded.
+Top right panel: histogram of the torus (top) luminosity in the UV-to-IR band.
+Bottom right panel: the same for polar
+dust luminosity. The number of AGNs whose best-fit SED models do not include a polar dust component is shown on the left side.
+In the top right panel, we illustrate the distributions
+of the integrated UV-to-IR (mainly IR) torus (Ltorus),
+and in the bottom right panel for polar dust luminosities
+(Lpolar). They cover the ranges of logLtorus/(erg s−1) ∼
+42–45 and logLpolar/(erg s−1) ∼ 43–45.5, respectively.
+Although seven sources show no signatures of the polar
+dust emission (Section 4.2.4), the distribution of the po-
+lar dust luminosities is larger than that of the torus ones.
+This is in agreement with the high-spatial-resolution
+mid-IR imaging by Asmus (2019), who reports that a
+large part of the mid-IR luminosities is derived from the
+extended emission.
+6.2. Gas-to-dust Ratio
+The comparison between X-ray absorption and dust
+extinction has been investigated to evaluate the gas-to-
+dust ratio. The X-rays trace all material of gas and dust
+(NH), and the optical-to-IR emission primarily traces
+the dust component (AV ).
+Maiolino et al. (2001) re-
+port that the NH/AV ratios are larger than the Galac-
+tic value (NH/AV = 1.87 × 1021 cm−2 mag−1; Draine
+2003), while for unobscured AGNs those are smaller (see
+also Burtscher et al. 2016). Recent works with the torus
+models of CLUMPY and XCLUMPY, but not including
+the polar dust component, (Miyaji et al. 2019; Tanimoto
+et al. 2020; Ogawa et al. 2021) support that the NH/AV
+values are higher than or similar to the Galactic value
+for obscured AGNs, but smaller for unobscured AGNs.
+Ogawa et al. (2021) suggest that the trend could be ex-
+plained if the torus angular widths are overestimated in
+the IR band due to the contamination from the polar
+dust emission.
+
+33
+1020
+1021
+1022
+1023
+1024
+1025
+N(LOS)
+H
+ [cm
+2]
+100
+101
+102
+103
+A(LOS)
+V, torus + A(LOS)
+V, polar  [mag]
+Galactic value
+AV(Polar) >  AV(Torus)
+Stage-A(Early)
+Stage-B(Early)
+Stage-C(Late)
+Stage-D(Late)
+Stage-N
+Figure 19. Line-of-sight hydrogen column density N (LOS)
+H
+derived from X-ray spectra vs.
+A(LOS)
+V ,torus, and polar dust,
+A(LOS)
+V ,polar (if 90◦ − i > σ, A(LOS)
+V ,polar = 0).
+Solid line shows
+the Galactic gas-to-dust ratio (NH/AV = 1.87 × 1021 cm−2
+mag−1; Draine 2003). Large orange circles mark the AGNs
+showing A(LOS)
+V ,polar > A(LOS)
+V ,torus.
+The other symbols are the
+same in Figure 8.
+Our
+SED
+decomposition
+provides
+the
+values
+of
+A(LOS)
+V ,torus and A(LOS)
+V ,polar. In Figure 19, we compare the X-
+ray obscuration and dust extinction. The three AGNs
+with A(LOS)
+V ,torus < A(LOS)
+V ,polar have a wide range of gas-to-
+dust ratios. As mentioned in Section 6.1, both parame-
+ters may trace the different regions of a compact torus
+in X-rays and extended polar dust in the optical-to-IR
+bands, respectively. Except for them, the AGNs with
+NH > 1022 cm−2 in our U/LIRGs show A(LOS)
+V ,torus >
+A(LOS)
+V ,polar, meaning the small contribution of the polar
+dust component to the dust extinction. We find that
+the obscured AGNs have similar or higher NH/AV ra-
+tios than the Galactic one, indicating that the materials
+on the compact (a few parsecs) scales in the U/LIRGs
+show a large gas-to-dust ratio.
+Similarly, it is reported that the gas-to-dust mass ra-
+tio (Mgas/Mdust) is ∼200–300 for local ULIRGs (e.g.,
+Seaquist et al. 2004), which is larger than the Galactic
+value. These results may be explainable mainly by two
+scenarios. The first scenario is that the AV decreases
+by the destruction of the small dust grains by super-
+nova shocks and/or expelled by strong AGN winds (e.g.,
+Draine & Salpeter 1979; Jones et al. 1994; Savage &
+Sembach 1996; Maiolino et al. 2001; Gaskell et al. 2004;
+Liang et al. 2004; Rupke et al. 2008; Mannucci et al.
+2010; Roseboom et al. 2012; Asano et al. 2013; R´emy-
+Ruyer et al. 2014). The second is that the NH increases
+by dust-free gas clouds covering the line-of-sight in BLR
+of the AGN (e.g., Granato et al. 1997; Burtscher et al.
+2016; Ichikawa et al. 2019; Ogawa et al. 2021; Mizukoshi
+et al. 2022). More investigations are needed to reveal
+the origin of the large gas-to-dust ratios in U/LIRGs.
+6.3. Contribution to the IR AGN Luminosity
+The torus and polar dust luminosities in the UV-to-IR
+bands are primarily determined by the total AGN lumi-
+nosity times their apparent covering fractions (and/or
+large volumes). Considering the averaged torus angu-
+lar width is σ ∼ 20◦ (Ogawa et al. 2021; Yamada et al.
+2021), the apparent covering fractions of polar dust can
+be expected as Ω/4π = 1 − sin(20◦) ∼ 0.66. The polar
+dust luminosities are ∼2 times larger than those of the
+torus component (left panel of Figure 20; see also Sec-
+tion 6.1). If polar dust is likely the dust component of
+the AGN-driven outflows, their activities should be cor-
+related with the Eddington ratios. Although it is natural
+under the situation that the polar dust luminosities are
+proportional to the AGN luminosities, we confirm the
+positive correlation between the polar dust luminosities
+and Eddington ratios in our sample.
+In the X-rays, it is thought that the torus covering
+fractions of Compton-thin matters becomes smaller with
+larger Eddington ratios due to the radiation pressure
+from the AGN (Ricci et al. 2017d, 2022). By analyzing
+the broadband X-ray spectra with XCLUMPY, Yamada
+et al. (2021) find that the individual torus covering frac-
+tion for AGNs in U/LIRGs follow the typical relation,
+except for two buried AGNs with λEdd ∼ 1 in stage-D
+mergers. On the other hand, the torus angular width
+(or covering fraction) in the IR band with CLUMPY
+(Ichikawa et al. 2015; Garc´ıa-Bernete et al. 2019) are
+larger than those of X-ray results with XCLUMPY, sup-
+porting the significant polar dust emission (Ogawa et al.
+2021).
+Several works with other AGN models calculate the
+torus covering fractions in the IR band by using the con-
+version factor from the Ltorus/LAGN,int (e.g., Stalevski
+et al. 2016; Ichikawa et al. 2019). However, consider-
+ing that the polar dust is thought to be a hollow-cone
+structure (e.g., H¨onig 2019; Isbell et al. 2022), it is diffi-
+cult to calculate the true covering fractions of the polar
+dust assuming the uniform conical distribution (Yang
+et al. 2020a). In Figure 21, we investigate the UV-to-IR
+luminosities relative to the intrinsic AGN disk luminos-
+ity (LAGN,int) for the torus and polar dust components,
+as a function of the Eddington ratio. As noted above,
+the Ltorus/LAGN,int ratios are smaller than those of po-
+lar dust, and both simple luminosity ratios are not well
+correlated with Eddington ratios.
+
+34
+Yamada et al.
+43.0
+43.5
+44.0
+44.5
+45.0
+45.5
+logLtorus [erg s
+1]
+43.0
+43.5
+44.0
+44.5
+45.0
+45.5
+logLpolar [erg s
+1]
+Stage-A(Early)
+Stage-B(Early)
+Stage-C(Late)
+Stage-D(Late)
+Stage-N
+2.5
+2.0
+1.5
+1.0
+0.5
+0.0
+log
+Edd
+43.0
+43.5
+44.0
+44.5
+45.0
+45.5
+logLpolar [erg s
+1]
+Stage-A(Early)
+Stage-B(Early)
+Stage-C(Late)
+Stage-D(Late)
+Stage-N
+Figure 20. Left panel: logarithmic torus luminosity vs. logarithmic polar-dust luminosity in the UV-to-IR bands. Right
+panel: logarithmic Eddington ratio vs. logarithmic polar-dust luminosity. The symbols are the same in Figure 8.
+4
+3
+2
+1
+0
+log
+Edd
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Ltorus / LAGN, int
+  0.47
+Stage-A(Early)
+Stage-B(Early)
+Stage-C(Late)
+Stage-D(Late)
+Stage-N
+4
+3
+2
+1
+0
+log
+Edd
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Lpolar / LAGN, int
+  0.57
+Stage-A(Early)
+Stage-B(Early)
+Stage-C(Late)
+Stage-D(Late)
+Stage-N
+Figure 21. Left panel: logarithmic Eddington ratio vs. ratio of the torus and intrinsic AGN luminosities. Two AGNs whose
+luminosity ratio above 1 are plotted as Ltorus/LAGN,int = 1. Right panel: logarithmic Eddington ratio vs. ratio of polar dust
+and intrinsic AGN luminosities. The symbols are the same in Figure 8.
+We find that the AGNs with Lpolar/LAGN,int > 0.5
+have the Eddington ratios of logλEdd ≳ −3.0. In the
+X-ray band, Fabian et al. (2008) proposed the NH–
+λEdd diagram to evaluate the presence of outflow, where
+dusty clouds are pushed away by radiation pressure
+against the gravitational force.
+In our sample, the
+AGNs with higher Eddington ratios than the criteria
+show multi-scale outflows, such as UFO, ionized out-
+flow, and molecular outflows (Yamada et al. 2021). Re-
+cently, Venanzi et al. (2020) compute similar diagnostics
+for the IR-dominant outflows (i.e., polar dust). When
+the AGN radiative acceleration and gravity are equal
+(aAGN = ag), the dusty outflows are pushed away for the
+AGNs with logλEdd ≳ −2.5 assuming NH ≈ 1022 cm−2
+or logλEdd ≳ −3.0 assuming NH ≈ 1021.5 cm−2 (see also
+Alonso-Herrero et al. 2021). Thus, the decline of the po-
+lar dust luminosity for low-Eddington AGNs is consis-
+tent with the theoretical prediction of the IR-dominant
+dusty winds caused by the radiation pressure.
+6.4. Polar Dust Temperature
+In this study, we newly constrain the polar dust tem-
+perature (Tpolar) for the AGNs in U/LIRGs, thanks to
+the combination of X-ray spectroscopy and multiwave-
+length SED analysis.
+Figure 22 provides the relation
+between the polar dust luminosity and its temperature.
+For these AGNs with signs of the polar dust emission,
+we find that the averaged values of polar dust luminos-
+ity increase from early mergers (log(Lpolar/erg s−1) =
+43.53 ± 0.43) to late mergers (44.22 ± 0.55; see Table 4).
+On the other hand, the polar dust temperature appears
+to decrease with merger stage. Here, it is notable that
+the Tpolar mostly lie in the range of ∼100–200 K, which
+are in good agreement with the researches of the IR in-
+terferometric observations and IR SED analysis as listed
+in Section 4.2.3. Even though the SED fitting with the
+range of Tpolar within 100–300 K is examined, we con-
+firm that the results are almost unchanged.
+
+35
+42.5
+43.0
+43.5
+44.0
+44.5
+45.0
+45.5
+46.0
+logLpolar [erg s
+1]
+100
+150
+200
+250
+Tpolar [K]
+Stage-A(Early)
+Stage-B(Early)
+Stage-C(Late)
+Stage-D(Late)
+Stage-N
+Figure 22. Logarithmic polar-dust luminosity vs. polar-
+dust temperature. The symbols are the same in Figure 8.
+N
+A
+B
+C
+D
+Merger Stage
+Tpolar  [K]
+100
+150
+200
+Figure 23. Differences in the polar-dust temperature with
+merger stage, described in the logarithmic scale. Diamonds
+and uncertainties represent the averaged value and 1σ
+dispersions, respectively.
+To confirm the trend of the polar dust temperature,
+we also compare the averaged values with merger stages
+as illustrated in Figure 23. Notably, the temperatures of
+late mergers (∼130 K) decline from the values of early
+mergers or nonmergers (∼170 K). Although the allowed
+range is above 100 K, these averaged values are much
+larger than the dust temperature of the ISM in local
+U/LIRGs and high-z submillimeter galaxies (∼20–60 K;
+e.g., Casey 2012; Clements et al. 2018; da Cunha et al.
+2021). All AGNs in late mergers show significant signs
+of the presence of polar dust emission (Section 4.2.4).
+Taking into account the high AGN luminosities (pro-
+portional to polar dust luminosity; Section 6.3) in late
+mergers, the decline of the dust temperature within the
+inner parsecs seems to be unlikely. The preferable reason
+is that the polar dust emission is radiated farther away
+from the center (see also e.g., Lyu & Rieke 2018; Buat
+et al. 2021), implying the development of the physical
+size of the polar dust structure.
+6.5. Polar Dust Structure
+6.5.1. Physical Size of the Polar Dust
+Finally, we estimate the physical size of the polar dust
+for local U/LIRGs by using the polar dust temperature.
+For a simple analytic model, the luminosity absorbed
+by dust grains at a distance (r) from the central radia-
+tion source, Labs, is calculated by the following equation
+(see also e.g., Barvainis 1987; H¨onig & Kishimoto 2011;
+Venanzi et al. 2020):
+Labs = 16πr2Qabs;P(T)σSBT 4,
+(6)
+where Qabs;P(T) is the Planck mean absorption effi-
+ciency and σSB is Stefan–Boltzmann constant. The po-
+lar dust model in our multiwavelength SED analysis as-
+sumes the dust emissivity of β = 1.6 (e.g., Draine & Lee
+1984; Casey 2012; Yang et al. 2020a), and the Qabs;P(T)
+is proportional to T 1.6. The typical scales of polar dust
+(Rpolar) can be estimated by solving the equation:
+Rpolar = rsub × (Tpolar/1500 K)−2.8.
+(7)
+The rsub is the sublimation radius at the temperature
+of Tsub = 1500 K and can be calculated by rsub = 0.4 ×
+(LAGN,int/1045 erg s−1)1/2 pc in the CLUMPY model
+(Nenkova et al. 2008a,b). Table A5 lists the estimates
+of Rpolar for the U/LIRGs in our sample.
+In the top panel of Figure 24, we present the relation
+between the intrinsic (bolometric) AGN disk luminosity
+and Rpolar.
+The linear regression analysis in log–log
+space is performed for the targets by using the Bayesian
+maximum-likelihood method (Kelly 2007).
+The best-
+fitting relation (red dashed line) is
+log(Rpolar) = 0.78 log(LAGN,int/erg s−1) − 32.40.
+(8)
+Its 1σ dispersion is ±0.35 dex and the correlation coef-
+ficient is 0.80, implying a tight relation.
+It is notably that the radius of the polar dust emission
+measured by the high-spatial-resolution imaging in the
+mid-IR 12 µm band (Asmus 2019) for U/LIRGs (gray
+diamond) and normal galaxies (gray square) are well
+consistent with the best-fitting relation. For NGC 1068,
+the compact radius of the mid-IR emission (∼54 pc)
+relative to the AGN luminosity is in good agreement
+with our estimate (Rpolar ∼ 45 pc). The distribution of
+the Rpolar obtained from our methods and by the mid-IR
+images (Asmus 2019) shows a steeper slope (∼0.8) than
+the relationship with the constant temperature (0.5).
+This supports that the typical polar dust temperatures
+
+36
+Yamada et al.
+42.5
+43.0
+43.5
+44.0
+44.5
+45.0
+45.5
+46.0
+logLAGN, int  [erg s
+1]
+1.0
+1.5
+2.0
+2.5
+3.0
+3.5
+logRpolar  [pc]
+NGC 1068
+F08572
+Mrk 231
+Rpolar, SED = rsub × (Tpolar/1500 K)
+2.8
+Tpolar=100K
+Tpolar=150K
+Tpolar=200K
+This Work
+MIR (U/LIRG; Image)
+MIR (normal; Image)
+Ion (U/LIRG; Image)
+Mol (U/LIRG; Image)
+Stage-A(Early; SED)
+Stage-B(Early; SED)
+Stage-C(Late; SED)
+Stage-D(Late; SED)
+Stage-N (SED)
+~10 pc
+~100 pc
+~10 pc
+~1 kpc
+~1500 K 
+(sublimation radius)
+~100 K (LAGN=1045.5)
+~150 K (LAGN=1044)
+~200 K (LAGN=1043)
+Evolution
+Polar dust
+NLR
+t U/LIRG 

+~ 30-100 Myr
+Early Merger
+Late Merger
+Figure 24. Top panel: logarithmic intrinsic AGN luminosity vs. logarithmic physical size of the dominant IR emission from
+the polar dust, estimated from the sublimation radius and polar dust temperature. The dashed red line and pink shade show
+the best-fitting linear relation and its 1σ dispersion among the AGNs, respectively. The green circles illustrate the physical
+size of ionized outflows measured with optical IFU observations, and light blue circles mark the size of molecular outflows
+measured with submillimeter observations in the subsample of our U/LIRGs (Fluetsch et al. 2019, 2021). The gray diamonds
+and small circles denote the sizes of extended mid-IR emission for U/LIRGs and non-U/LIRG sources respectively (Asmus
+2019).
+For the size of molecular outflows and extended mid-IR region, the bolometric AGN luminosities of U/LIRGs are
+adopted to the estimates in this study, while those of non-U/LIRGs are calculated as the X-ray luminosity (Asmus 2019) times
+20 (e.g., Vasudevan & Fabian 2007). The other symbols are the same in Figure 8. Bottom panel: schematic picture of the AGN
+structure (polar dust, NLR, torus, failed winds, accretion disk, and SMBH) in U/LIRGs.
+
+37
+decrease with AGN luminosity or physical size of the
+polar dust (Rpolar).
+It should be emphasized that Equation (6) can be gen-
+erally applied to an optically thin, continuous dust en-
+vironment. Whereas, the extinction of the polar dust
+in the V band is not (A(LOS)
+V ,polar ∼ 1–3; see Section 6.1).
+A plausible explanation of this discrepancy is that the
+polar dust consists of optically thin layers of other-
+wise optically thick dust clouds, where the tempera-
+ture and emission profile is dominated by direct heat-
+ing from the central source (H¨onig & Kishimoto 2010,
+2011).21 This is consistent with the radiative hydrody-
+namic (RHD) simulations expecting that the polar dust
+structure would be smoothly distributed with most sub-
+structure being filamentary and/or clumpy (Wada et al.
+2009; Wada 2012; Schartmann et al. 2011; Dorodnitsyn
+et al. 2012; Chan & Krolik 2016, 2017; Dorodnitsyn &
+Kallman 2017; Williamson et al. 2019).
+If the polar dust structure is a bipolar hollow cone
+with the opening angle of θ1–θ2, its volume (Vpolar) is
+calculated by:
+Vpolar = 2 × (4/3)πr3 × 2π[1 − (cos(θ2))]/4π
+− 2 × (4/3)πr3 × 2π[1 − (cos(θ1))]/4π
+= (4/3)πr3[cos(θ1) − cos(θ2)].
+(9)
+The conical structure of the polar dust model in our
+study can be described as a simple case of θ1 = 0◦ and
+θ2 = 90◦ − σ. Lyu & Rieke (2018) introduce a power-
+law dust density profile, ρ(r) ∝ r−α, and the value of
+α is 0 < α ≲ 2 based on the previous observational
+studies (Behar 2009; Faucher-Gigu`ere & Quataert 2012;
+Feruglio et al. 2015; Revalski et al. 2018). The total mass
+of the extended (≳10 pc) polar dust within the radius
+of r, Mpolar(r), follows the mass profile of dMpolar/dr ∝
+(dVpolar/dr)ρ(r) ∝ r2−α. Assuming that the polar dust
+emission depends on their mass, a large part of the polar
+dust emission is derived from the large-scale structure
+at r ∼ Rpolar. However, the polar dust sizes for three
+AGNs in NGC 1068, IRAS F08572+3915, and Mrk 231
+are much smaller than the best-fitting relation. Interest-
+ingly, Feruglio et al. (2015) investigate the spatial dis-
+tribution of the intense molecular CO(2−1) outflows in
+Mrk 231 with Atacama Large Millimeter/submillimeter
+21 The polar dust temperature assuming the gray body model is
+different from the inverse peak-wavelength temperature (Tpeak)
+measured by Wein’s displacement law (i.e., λpeak = 2.898 ×
+103 µm K/Tpeak, which only applies to perfect black bodies;
+Casey 2012). Though the assumption of the emitter (e.g., gray
+body or smooth distribution with clumps) may cause a system-
+atic uncertainty of the polar dust temperature, the results of the
+decrease in Tpolar with merger stage will be almost unchanged.
+Array (ALMA) and report that its mass profile (or the
+outflow filling factor) follows α ≈ 2. This suggests that
+the polar dust emission in Mrk 231 is derived from the
+whole structure. Although the spatial distribution for
+NGC 1068 and IRAS F08572+3915 is unclear, the den-
+sity profile may cause the seemingly hot and compact
+emission from the polar dust.
+Except for these three
+AGNs, the Rpolar is thought to be the spatial scale of
+the polar dust detected in the mid-IR images (Asmus
+2019). Thus, the best-fitting relation between AGN lu-
+minosity and Rpolar suggests that the IR-luminous po-
+lar dust structure expands from a few tens parsec (early
+mergers) to kiloparsec scales (late mergers).
+6.5.2. Scenario of the Outflowing Polar Dust
+To distinguish whether the polar dust is (1) the galac-
+tic ISM or dust near the edge of NLR being illuminated
+by the AGN or (2) the outflowing dusty winds launched
+from the inner edge of the torus, we investigate the
+spatial sizes of the ionized and molecular outflows for
+our U/LIRGs (Table A5). Fluetsch et al. (2021) ana-
+lyze the optical integral field unit (IFU) data of 26 lo-
+cal U/LIRGs with Very Large Telescope (VLT)/Multi
+Unit Spectroscopic Explorer (MUSE). From the liter-
+ature, they also include 31 galaxies with spatially re-
+solved multiphase outflow information (e.g., Rupke &
+Veilleux 2013; Rupke et al. 2017). For eight U/LIRGs
+in our sample (small-green circles), they estimate the
+radius of the ionized outflow based on the extent of the
+broad Hα component.
+Fluetsch et al. (2019) investi-
+gate the molecular outflows primarily by using CO data
+from the ALMA archive in a sample of 45 local galax-
+ies. The radius of the molecular outflows is measured
+for nine U/LIRGs in our targets (light-blue circles). We
+find that the sizes of ionized and molecular outflows are
+similar to or larger than those of the polar dust size,
+supporting that the materials outside the polar dust are
+outflowing.
+Many works predict that the polar dusty outflows are
+launched from the surface of the inner torus (e.g., H¨onig
+& Kishimoto 2010; H¨onig et al. 2012, 2013; Gallagher
+et al. 2015; Ishibashi et al. 2018). The semi-analytical
+disk and wind models suggest that the dusty winds can
+be launched by the AGN radiation pressure and the
+heated dust itself (Venanzi et al. 2020). Similarly, RHD
+simulations also support that dusty winds are naturally
+driven (e.g., Schartmann et al. 2014; Wada et al. 2016,
+2018; Williamson et al. 2019, 2020). Some observational
+attempts to test this hypothesis have been performed by
+analyzing the IR SEDs (e.g., Lyu & Rieke 2018) and by
+comparing the polar dust luminosities with the strength
+
+38
+Yamada et al.
+of the multiphase outflows (e.g., Alonso-Herrero et al.
+2021).
+Since the polar dust emission does not show the emis-
+sion/absorption lines, it is difficult to estimate its ve-
+locity. For the starburst galaxy M 82, Yoshida et al.
+(2011) carry out the spectropolarimetry of the optical
+emission lines. The outflowing dust grains are predicted
+to polarize the continuum and emission lines emanating
+from the nuclear starburst region, acting as “moving
+mirrors” for nuclear light. By comparing the velocities
+between the normal and polarized emission lines, they
+find that the velocity of the polar dust (vpolar) decreases
+from ∼200 km s−1 at a few hundred parsecs to ∼20–
+30 km s−1 at 1–1.2 kpc. For the U/LIRGs hosting nu-
+clear starbursts and AGNs, the minimum velocity of the
+polar dust should be ≳ 30 km s−1 at 1 kpc. The typ-
+ical lifetime of the U/LIRGs containing submillimeter
+galaxies at z ∼ 1–2 (tU/LIRG) are ∼30–100 Myr (Hop-
+kins et al. 2006, 2008; Meier et al. 2010; Hickox et al.
+2012; Inayoshi et al. 2018) or at most 300 Myr (Swin-
+bank et al. 2006; Meng et al. 2010; Privon et al. 2013).
+The migration length of the outflowing dusts can be
+roughly estimated by the velocity (vpolar ≳ 30 km s−1)
+times the U/LIRG lifetime (tU/LIRG ≳ 30 Myr), i.e.,
+≳1 kpc. The smaller fraction of the AGNs with signs of
+polar dust emission for early mergers than that for late
+mergers also supports the evolution of the polar dust
+(Section 4.2.4). Although the possible contribution of
+the polar dust emission from the non-outflowing dust in
+the NLR should not be rejected, the polar dust seems
+to be dusty winds as expected by recent simulations.
+Thus, the polar dust size (Rpolar) increases from a few
+tens of parsec (early mergers) to kiloparsec scales (late
+mergers), indicating that the polar dust is likely the ex-
+panding (i.e., evolving) dusty outflows.
+6.5.3. Unified View of the Polar Dust Structure in
+U/LIRGs
+In the bottom panel of Figure 24,
+we present
+the schematic picture of the polar dust structure in
+U/LIRGs. The polar dust sizes, estimated from the po-
+lar dust temperature and dust sublimation radius, in-
+crease with AGN luminosity (or merger stage). The po-
+lar dust temperature decrease with the polar dust size
+from ∼200 K (a few tens of parsec) to ∼100 K (kilopar-
+sec scale). Considering the typical dust density profile of
+0 < α ≲ 2, their sizes corresponds to the outer structure
+of the extended polar dust (Section 6.5.1). The polar
+dust sizes are smaller than those of ionized and molecu-
+lar outflows, and their expansion with merger stage can
+be explained by the polar dust velocity and U/LIRG
+lifetime (Section 6.5.2).
+At the parsec-scale regions, RHD simulations show
+that
+the
+innermost
+torus
+structure
+is
+formed
+by
+radiation-driven fountain-like outflows (e.g., Wada et al.
+2018). A multiphase dynamic nature of torus (pink el-
+lipses) and circumnuclear region (CND; yellow ocher) in
+the r ≲ tens of parsecs torus region is confirmed by re-
+cent ALMA observations (e.g., Izumi et al. 2016, 2018).
+H¨onig (2019) mentions that the polar dust is expected
+to be launched by the inner edge of the torus due to the
+AGN radiation (coming from the AGN disk or vicin-
+ity of the SMBH). As noted in Section 6.5.1, the po-
+lar dust structure would be smoothly distributed with
+most substructure being filamentary and/or clumpy, as
+expected by RHD simulations (Wada 2012; Schartmann
+et al. 2011; Williamson et al. 2019), although we sim-
+ply describe it by a smooth distribution. According to
+these results, the schematic picture illustrates the AGN
+structures, containing the polar dust, NLR, torus, failed
+winds around the torus, accretion disk, and SMBH in
+the early-to-late merging U/LIRGs.
+6.5.4. Polar Dust vs. Molecular Outflow
+This study indicates that the multiwavelength SED
+analysis is one of the key means to evaluate the ac-
+tivities of the dust components of large-scale outflows.
+In Figure 25, we compare the polar dust luminosities
+with the molecular outflow velocity (Vout,mol; left panel)
+and mass transfer rates ( ˙Mout,mol; right panel). Yamada
+et al. (2021) lists the values of Vout,mol and
+˙Mout,mol for
+local U/LIRGs by referring the previous works based on
+the broad CO emission lines and OH absorption lines
+(e.g., Gonz´alez-Alfonso et al. 2017; Laha et al. 2018 and
+references therein). We find that the polar dust lumi-
+nosity and Vout,mol show no significant relation. This
+may be due to the dispersion of the slope of the dust
+density profiles (α), or the dispersion of the size of the
+molecular outflows relative to the polar dust size (Fig-
+ure 24). Whereas, the polar dust luminosity and mass
+transfer rates of the molecular outflows show a positive
+correlation. This may be a reasonable result by taking
+into account that the polar dust luminosities depend
+on their mass (particularly containing the large-scale
+mass at r ∼ Rpolar; Section 6.5.1).
+We calculate the
+best-fitting relation by using the Bayesian maximum-
+likelihood method as below:
+log(Lpolar) = 0.77 log( ˙Mout,mol) + 42.79,
+(10)
+where the 1σ dispersion is ±0.67 dex and the correla-
+tion coefficient is 0.71. Since the sample is quite limited,
+further studies using large samples are necessary to es-
+tablish the general relation between polar dust (i.e.,
+dusty winds) and molecular outflows.
+
+39
+0
+200
+400
+600
+800
+1000
+Vout, mol (AGN; Yamada+21)
+43.0
+43.5
+44.0
+44.5
+45.0
+45.5
+46.0
+logLpolar
+Stage-D(Late)
+Stage-N
+0.5
+1.0
+1.5
+2.0
+2.5
+3.0
+3.5
+logMdotout, mol (AGN; Yamada+21)
+43.0
+43.5
+44.0
+44.5
+45.0
+45.5
+46.0
+logLpolar
+This Work
+Stage-D(Late)
+Stage-N
+Figure 25.
+Polar-dust luminosity as a function of molecular outflow velocity (left) and logarithmic mass transfer rate of
+molecular outflow (right) referred from Yamada et al. (2021). The red dashed line and pink shaded area mark the best-fitting
+relation and its 1σ dispersion. The symbols are the same in Figure 8.
+7. DISCUSSION II: COEVOLUTION PROCESS OF
+GALAXY, SMBH, AND OUTFLOW
+7.1. Activities of Starburst and AGN
+To understand the origin of the coevolution of galaxies
+and SMBHs, their growth rates are well studied. Numer-
+ical simulations of galaxy mergers predict that the SFR,
+AGN luminosities, and obscuration of the central AGN
+increase with merger stage (e.g., Di Matteo et al. 2005;
+Hopkins et al. 2006, 2008; Narayanan et al. 2010; Angl´es-
+Alc´azar et al. 2017; Blecha et al. 2018; Kawaguchi et al.
+2020; Yutani et al. 2022). The observational studies us-
+ing multiwavelength data support their increases with
+merger stage (e.g., Imanishi et al. 2010; Lee et al. 2012;
+Ellison et al. 2013; Satyapal et al. 2014; Ricci et al.
+2017a, 2021; Koss et al. 2018; Pfeifle et al. 2019; Shang-
+guan et al. 2019; Yamada et al. 2019, 2021).
+By combining the broadband X-ray spectroscopy and
+multiwavelength SED decomposition, this study esti-
+mates the SFRs and AGN luminosities for a large sample
+of 72 resolved sources in U/LIRGs, which are treated
+separately divided into 41 hard X-ray–detected AGNs
+(containing 36 single AGNs, 2 unresolved dual AGN
+systems, and 3 newly identified AGNs) and 31 other
+sources (starburst-dominant or hard X-ray–undetected
+sources). In Figure 26, we investigate the distribution
+of SFR (left) and intrinsic (bolometric) AGN luminos-
+ity (right) as a function of projected separation between
+two galaxies.
+For the starburst-dominant or hard X-
+ray–undetected sources, we refer to the AGN luminosi-
+ties estimated from the [O IV] 25.89 µm luminosity
+(L[O IV]; small crosses) in Yamada et al. (2021). They
+confirm that these values are consistent with the 3σ up-
+per limits of the predicted 2–10 keV AGN luminosity
+from the X-ray counts by assuming NH ≤ 1025 cm−2
+and LX,unabs–L[O IV] relation (Liu et al. 2014). We note
+that the dispersion of the low values of SFRs and AGN
+luminosities for the early mergers with the ∼10–40 kpc
+are caused by the faint companion galaxies that are not
+IR-luminous galaxies.
+Focusing on the largest values
+of individual merger stages, our results support that the
+SFRs and AGN luminosities increase with projected sep-
+aration and merger stage, consistent with the results in
+Section 5.6.
+In Figure 27, we compare the SFRs and bolometric
+AGN luminosities in our sample. By the same method
+in Yamada et al. (2021), we draw the galaxy–SMBH
+“simultaneous evolution” relation (see also e.g., Ueda
+et al. 2018), where the growing systems keeping the
+SFR–LAGN,int relation are expected to establish the lo-
+cal Mbulge–MBH relation. Here, the relation assumes the
+fraction of stellar mass that are taken back to the ISM
+(return fraction) as R = 0.41 (Chabrier 2003), the ratio
+of stellar masses to SMBH masses in the local universe
+as A ∼ 200 (Kormendy & Ho 2013), and a radiative
+efficiency as η = 0.05 (Ueda et al. 2014). The detailed
+explanations are presented in Yamada et al. (2021). The
+relation is described as
+log(LAGN,int) = log(SFR/M⊙ yr−1) + 42.94.
+(11)
+The hard X-ray–detected and newly identified AGNs
+in U/LIRGs follows the simultaneous coevolution re-
+lation, consistent with the results by Yamada et al.
+(2021).
+For the AGNs in our sample excluding non-
+mergers and outliers with logSFR < 0, we calculate the
+best-fitting relation based on the Bayesian maximum-
+likelihood method:
+log(LAGN,int) = 0.89 log(SFR) + 42.71.
+(12)
+The 1σ uncertainty is ±0.66 dex and the correlation co-
+efficient is 0.54. As mentioned in Appendix C (see Fig-
+ure C3), the AGN luminosities in Yamada et al. (2021)
+
+40
+Yamada et al.
+0
+20
+40
+60
+80
+100
+Separation [kpc]
+2
+1
+0
+1
+2
+3
+logSFR
+Stage-A(Early)
+Stage-B(Early)
+Stage-C(Late)
+Stage-D(Late)
+Stage-N
+0
+20
+40
+60
+80
+100
+Separation [kpc]
+41
+42
+43
+44
+45
+46
+logLAGN, int [erg s
+1]
+Stage-A(Early)
+Stage-B(Early)
+Stage-C(Late)
+Stage-D(Late)
+Stage-N
+SB or HX nondet.
+Figure 26.
+SFR and intrinsic AGN luminosity as a function of projected separation between two galaxies in units of
+kiloparsecs. Single nuclei in merging (stage D) and nonmerging (stage N) sources are plotted on the left (negative value) and
+right sides, respectively. Large symbols are the same in Figure 8, while small crosses illustrate the starburst-dominant or hard
+X-ray–nondetected sources.
+2
+1
+0
+1
+2
+3
+logSFR
+41
+42
+43
+44
+45
+46
+logLAGN, int  [erg s
+1]
+Trakhtenbrot+10
+(Sy2,QSO)
+This Work
+local Mbulge-MBH
+Stage-A(Early)
+Stage-B(Early)
+Stage-C(Late)
+Stage-D(Late)
+Stage-N
+PG QSO (z<0.1)
+SB or HX nondet.
+Figure 27. Logarithmic SFR vs. intrinsic AGN luminosity. Black dotted line denotes the typical relation among low-z Seyfert
+2s, QUEST QSOs, and high-z QSOs (Trakhtenbrot & Netzer 2010).
+The red dashed line and pink shaded area mark the
+best-fitting relation and its 1σ dispersion for the AGNs in U/LIRGs, excluding the nonmergers and AGNs with logSFR < 0.
+The black solid line is the galaxy–SMBH “simultaneous evolution” line for A = 200 (see also Ueda et al. 2018). The large
+symbols are the same in Figure 8. The small crosses mark the starburst-dominant or hard X-ray–nondetected sources, whose
+LAGN,int values are derived from the [O IV] luminosities (Yamada et al. 2021).
+
+41
+are larger than the values in this work, and then their
+typical relation is ∼0.4 dex brighter in the AGN lumi-
+nosity.
+Their AGN luminosities are derived from the
+averages of four different measurements; the [O IV] lu-
+minosity (e.g., Gruppioni et al. 2016), bolometric AGN
+fraction (e.g., D´ıaz-Santos et al. 2017), and IR SED de-
+composition and Spitzer/IRS spectral fitting (Alonso-
+Herrero et al. 2012; Shangguan et al. 2019). Its system-
+atic scatter related to the application of the averaged
+values is reported as about ±0.27 dex. Our best-fitting
+relation with the 1σ uncertainty is overlapped on not
+only the relation of Yamada et al. (2021) but the si-
+multaneous coevolution relation (black solid line). This
+supports that the AGNs in U/LIRGs are exactly in the
+coevolution phase of galaxies and SMBHs.
+Yamada et al. (2021) report that the AGNs in stage D
+mergers show the multiphase massive outflows at sub-
+parsec to kiloparsec scales, that is, UFOs (e.g., Feruglio
+et al. 2015; Tombesi et al. 2015; Mizumoto et al. 2019;
+Smith et al. 2019), ionized outflows (e.g., Fischer et al.
+2013; Rich et al. 2015; Kakkad et al. 2018; Fluetsch et al.
+2021; Toba et al. 2022b), and molecular outflows with
+velocities above 500 km s−1 (e.g., Gonz´alez-Alfonso et al.
+2017; Laha et al. 2018; Fluetsch et al. 2019). As dis-
+cussed in Section 6.3 and 6.5, the polar dust luminosi-
+ties are ∼ 2/3×LAGN,int, and the physical sizes increase
+with AGN luminosities from a few tens of parsec to kilo-
+parsec scales. In short, the polar dust luminosities and
+sizes are the largest in the stage D mergers with high
+AGN luminosities. Moreover, we plot the quantities of
+PG quasars at z ≲ 0.1 (Lyu et al. 2017) and empirical re-
+lation for local AGNs and quasars (Trakhtenbrot & Net-
+zer 2010). They lie in the AGN-dominant region above
+the coevolution relation, which should have strong gas
+outflows (e.g., Woo et al. 2020). The coexistence of in-
+tense starbursts, luminous AGNs, and massive outflows
+(UFOs, ionized outflows, molecular outflows, and dusty
+winds) particularly in the phase of U/LIRGs support a
+standard AGN feedback scenario that the AGN-driven
+outflows suppress star-forming activities and ULIRGs
+eventually transit to the unobscured quasars (e.g., Di
+Matteo et al. 2005; Hopkins et al. 2008; Alexander &
+Hickox 2012; Ananna et al. 2022; see also Yamada et al.
+2021).
+7.2. Mass Growth of Galaxy and SMBH
+According to the obtained SFRs and AGN luminosi-
+ties, we evaluate the total growth masses of galaxies and
+SMBHs. The increase in the stellar mass (∆M∗) can
+be calculated by the SFR times the growth timescale
+(tgrowth). The mass accretion rates ( ˙MBH) are estimated
+by using a radiative efficiency (η = 0.05; Ueda et al.
+2014) and the light speed (c) as
+˙MBH = LAGN,int × (1 − η)/(ηc2).
+(13)
+The increase in the SMBH mass (∆MBH) corresponds
+to the
+˙MBH times tgrowth. Here, the multiwavelength
+SED analysis presents the SFRs and AGN luminosities
+for the U/LIRGs in the various merger stages. Since the
+history of these quantities during the U/LIRG lifetime
+(tU/LIRG ∼ 30–100 Myr; Section 6.5.2) is unclear, we
+compute the increased masses assuming tgrowth is 30 Myr
+as a time scale of early mergers or late mergers. For the
+three resolved dual AGN systems in stage A mergers
+(NGC 833/NGC 835, NGC 6921/MCG+04-48-002, and
+NGC 7679/NGC 7682), we also calculate the total mass
+of the two galaxies and SMBHs after the galaxy collision,
+containing the increased masses from their starburst and
+AGN activities for 30 Myr.
+Figure 28 describes the relation between the stellar
+masses and SMBH masses for the hard X-ray–detected
+AGNs in our sample. We plot the local Mbulge–MBH re-
+lation (Kormendy & Ho 2013), scaled relation assuming
+Chabrier IMF, and a typical M∗–MBH relation for classi-
+cal bulges and ellipticals (Reines & Volonteri 2015). The
+stellar masses are obtained by our SED fitting, while the
+SMBH masses are referred from Yamada et al. (2021).
+The distributions of these masses in our U/LIRGs at
+z < 0.1 are well consistent with the study of z < 0.3
+U/LIRGs by Farrah et al. (2022). The caveat is that
+the SMBH masses we refer are derived from the av-
+eraged values of the four kinds of different measure-
+ments: stellar mass to SMBH mass relation (e.g., Reines
+& Volonteri 2015), M–σ∗ relation (e.g., G¨ultekin et al.
+2009), photometric bulge luminosity (e.g., Veilleux et al.
+2009a; Winter et al. 2009; Haan et al. 2011), and vari-
+ous other methods such as the flux density of old stellar
+emission at 2 µm (Caramete & Biermann 2010), veloc-
+ity dispersion of [O III] emission (Alonso-Herrero et al.
+2012), water masers (Lodato & Bertin 2003; Kl¨ockner
+& Baan 2004; Izumi et al. 2016), and so on. Although
+the systematic differences appear to depend on neither
+the intrinsic AGN luminosity nor Eddington ratio (Ya-
+mada et al. 2021), systematic uncertainties of the aver-
+aged SMBH masses are not negligible (at most ±0.5 dex;
+gray error bars). Thus, the figure does not necessarily
+indicate that the SMBH masses are a bit small relative
+to the local relations.
+We overplot the expected masses due to the star-
+bursts and AGN activities for 30 Myr (arrows) and
+the additional collision of two galaxies (empty stars).
+For the two stage-D mergers with low stellar masses
+of log(M∗/M⊙) ∼ 9.0–9.5 (IRAS F08572+3915 and
+IRAS F17138−1017), their galaxies and SMBHs are
+
+42
+Yamada et al.
+9.0
+9.5
+10.0
+10.5
+11.0
+11.5
+logM *
+6.5
+7.0
+7.5
+8.0
+8.5
+9.0
+logMBH
+SB+AGN(30 Myr)
+Collision
+Kormendy13 (Mbulge-MBH)
+Kormendy13 (scaled)
+Reines+15 (M*-MBH)
+Stage-A (Early; AGN)
+Stage-B (Early; AGN)
+Stage-C (Late; AGN)
+Stage-D (Late; AGN)
+Figure 28. Logarithmic stellar mass vs. logarithmic SMBH mass referred from Yamada et al. (2021) for the AGNs in stage
+C (orange diamond) and stage D (red star) U/LIRGs. Solid arrows represent the expected masses of the galaxy and SMBH if
+they evolve with the constant growth rates (SFR and
+˙MBH) for 30 Myr. For three dual-AGN systems in stage A mergers, the
+merged masses of the two sources including the mass increase for 30 Myr are marked as empty blue stars with dotted lines.
+The black solid line denotes the local bulge mass (Mbulge) and SMBH mass (MBH) relation for classical bulges and elliptical
+galaxies (Kormendy & Ho 2013). The dashed line shows the scaled relation that has bulge masses scaled down by 0.33 dex
+to consider the difference in the adopted mass-to-light ratios, and blue dotted line presents the typical M∗–MBH relation for
+classical bulges and ellipticals (Reines & Volonteri 2015).
+rapidly growing thanks to the starburst and AGN ac-
+tivities. We find that, however, the increased masses for
+the other U/LIRGs are small by these activities even
+though some of the stage-D U/LIRGs have the high-
+est SFRs (∼100–300 M⊙ yr−1) and AGN luminosities
+(logLAGN,int ∼ 45.0–45.5). Notably, the galaxy collision
+causes rapid growth for these high-mass systems.
+Soltan’s argument (Soltan 1982), one of the well-
+known discussions on the cosmic growth of SMBHs, sug-
+gests that the SMBHs are thought to have grown primar-
+ily by the gas accretion, not SMBH–SMBH coalescence.
+This requirement is imposed to explain the SMBH mass
+density at redshift z and the accreting gas mass density
+from z = ∞ to 0 (Yu & Tremaine 2002; Shankar et al.
+2004). Because the SMBH–SMBH coalescence conserves
+the SMBH mass density, the argument does not reject
+the presence of ubiquitous merger events (e.g., Enoki
+et al. 2004; Jahnke & Macci`o 2011). In this context, the
+growth events keeping the balanced SFR–LAGN,int rela-
+tion triggered by galaxy mergers (see Figure 27; see also
+e.g., Di Matteo et al. 2005) should be helpful to con-
+struct the local Mbulge–MBH relation. Whereas we need
+to keep in mind that, focusing on individual galaxies,
+the galaxy collision generates such high-mass galaxies
+with log(M∗/M⊙ ≳ 10). Therefore, our results indicate
+that galaxy merger is a vital process to establish the
+local Mbulge–MBH relation and build up the high-mass
+galaxies such as local elliptical galaxies.
+7.3. Perspective of the Galaxy–SMBH Coevolution in
+Mergers
+Finally, we summarize the perspective of the merger-
+driven coevolution of galaxies and SMBHs as described
+in the schematic picture of Figure 29. The SFRs and
+intrinsic (bolometric) AGN luminosities increase with
+merger stage, where the galaxy growth occurs first and
+rapid mass accretion delivered from the host galaxy to
+the SMBH is triggered later (Section 7.1). The merger
+process in the SFR–LAGN,int diagram should be a key
+mechanism to drive the balanced growth of galaxies and
+SMBHs in the cosmic history (e.g., Madau & Dickinson
+2014; Ueda et al. 2014; Aird et al. 2015) and then to es-
+
+43
+Stage A        ~        Stage D   Quasar   Elliptical
+(Time)
+Galaxy Evolution (Starburst)
+SMBH Evolution (AGN)
+Inflow
+NGC 833/NGC 835 (SDSS)
+NGC 3690 (SDSS)
+Mrk 231 (SDSS)
+M 87 (Pan-STARRS)
+H1821+643 (Pan-STARRS)
+Outflows
+Merger-driven Growth
+→  Cosmological 
+Coevolution
+Collision    → Hierarchical Mass Growth
+Figure 29.
+Schematic picture of merger-driven coevolution of galaxies and SMBHs.
+Middle panels are compiled from
+Pan-STARRS DR2 and SDSS DR16 images (Section 3.3), whose sources are merging U/LIRGs (NGC 833/NGC 835, NGC
+3690, Mrk 231) and post-merger candidates (a quasar H1821+643, e.g., Jadhav et al. 2021; and an elliptical galaxy M87, e.g.,
+Longobardi et al. 2015).
+tablish the local Mbulge–MBH relation (e.g., Kormendy
+& Ho 2013). Moreover, galaxy collision is another im-
+portant process to induce hierarchical mass growth and
+build up the high mass system such as local elliptical
+galaxies (Section 7.2).
+Yamada et al. (2021) find that the AGNs in stage
+D mergers show the multiphase outflows at subparsec
+to kiloparsec scales, e.g., UFOs, ionized outflows, and
+molecular outflows.
+They also unveil that the AGNs
+with high Eddington ratios as λEdd ∼ 1 have moderate
+NH (∼1023 cm−2), where dusty clouds at parsec scales
+are pushed away by radiation pressure against the grav-
+itational force as predicted with the NH–λEdd diagram
+(e.g., Fabian et al. 2008, 2009; Ricci et al. 2017d, 2022).
+The recent high-spatial-resolution ALMA and Chandra
+observations support the feedback effects on the torus
+by evaporating a portion of the gas (Kawamuro et al.
+2021), while the AGNs in U/LIRGs are deeply buried by
+massive inflows and/or outflows (Yamada et al. 2021).
+The X-ray weakness in U/LIRGs should make it easy to
+launch the massive outflows efficiently (Section 5.5). By
+combining the X-ray spectroscopy and multiwavelength
+SED fitting, we constrain the physical parameters of po-
+lar dust structure (e.g., IR luminosity, temperature, and
+spatial scales) that is thought to be launched by the
+AGN radiation pressure and the heated dust itself (Sec-
+tion 6.5; see also Venanzi et al. 2020; Alonso-Herrero
+et al. 2021). The polar dust emission may be negligible
+for some low-Eddington AGNs (λEdd ≲ 10−3) in early
+mergers (Section 4.2.4 and 6.3). For the AGNs show-
+ing significant polar dust emission, the physical size of
+polar dust increases with merger stage from a few tens
+of parsec to kiloparsec scales.
+These results indicate
+that the massive outflows connecting to galaxy scales
+
+44
+Yamada et al.
+are nurtured by the rapid accretion SMBHs and rich
+environments in U/LIRGs.
+The coexistence of intense starburst, AGNs, and large-
+scale massive outflows in local U/LIRGs support a stan-
+dard AGN feedback scenario (see also Chen et al. 2020).
+According to the scenario, the U/LIRGs will transit to
+the unobscured AGNs (Section 7.1). It is still unclear
+whether the star-forming activities are quenched due
+to the high specific SFRs (see e.g., Section 5.1) or the
+AGN feedback by the massive outflows. Considering the
+balanced starburst and AGN activities in the merger
+sequence, the massive outflows would present some kind
+of physical connection between galaxies and SMBHs. To
+completely understand the role of massive outflows in
+late mergers, it is needed to more researches of the mass
+transport mechanism and the effects on star formation
+in the host galaxy. In the near future, the high-spatial-
+resolution IR images will be presented by the Mid-
+InfraRed Instrument (MIRI; Rieke et al. 2015; Wright
+et al. 2015) onboard the James Webb Space Telescope
+(5–28 µm), and The Mid-Infrared Multi-field Imager
+for gaZing at the UnKnown Universe (MIMIZUKU;
+Kamizuka et al. 2020) on The University of Tokyo At-
+acama Observatory (TAO; Yoshii et al. 2010) 6.5m
+ground-based telescope (2–38 µm). Combining the mul-
+tiwavelength images with such as these telescopes and
+ALMA will allow us to study the distribution of the
+warm and cold outflowing matters, and better constrain
+the relationship between the outflows and star-forming
+activities.
+8. CONCLUSION
+The purpose of this work is (1) to understand the fea-
+tures of multiwavelength emissions in U/LIRGs, (2) to
+reveal the structure of the outflowing polar dust, and
+(3) to investigate the activities of host galaxies, SMBHs,
+and outflows for testing whether the merger process is a
+vital factor to establish the local Mbulge–MBH relation.
+To achieve these goals, we have performed a hard X-ray
+to radio multiwavelength SED decomposition for the 57
+local U/LIRGs (containing 84 individual galaxies) ob-
+served with NuSTAR and/or Swift/BAT (Yamada et al.
+2021).
+We compile the broadband X-ray spectra and
+multiwavelength wide-survey catalogs in the UV to ra-
+dio bands. After the cross-matching with them, we fi-
+nally obtain the multiwavelength photometries of the
+sample consisting of 72 resolved sources and 13 dupli-
+cated systems of resolved pairs, which are spatially di-
+vided in the Herschel PACS 70 µm bands. We modify
+the latest SED-fitting code X-CIGALE by implementing
+the infrared (IR) CLUMPY model, allowing the multi-
+wavelength study with the consistent X-ray torus model
+(XCLUMPY). Adopting the torus parameters obtained
+by the X-ray fitting (Yamada et al. 2021), we constrain
+the properties of host galaxies, AGN tori, and polar
+dust. Here, we described the main results as follows.
+1. The sample has 36 single and two unresolved dual
+AGNs detected in the hard X-ray band (Yamada
+et al. 2021). For all targets, we perform the BIC
+test for two kinds of UV-to-IR SED fitting with
+and without AGN (torus and polar dust) compo-
+nents. Although it is difficult to reliably identify
+AGNs solely by the SED fitting, we newly iden-
+tify three AGN candidates by the diagnostics of
+∆BIC > 6. We also examine the significance of the
+polar dust component for these AGNs. The AGNs
+in late mergers support the presence of polar dust
+emission, while some AGNs in early mergers or
+nonmergers show no signatures (Section 4.2.4).
+2. The component galaxies in early mergers have a
+wide range of SFRs above and below the main se-
+quence (MS), while galaxies in late mergers have
+the highest SFRs above the MS. Similar SFR–
+M∗ distributions of AGNs and the others imply
+that the small influence of the AGN activities on
+the star formation in the phase of U/LIRGs (Sec-
+tion 5.1).
+3. The flat slope of radio emission in late mergers
+may be caused by the optically-thick free-free ab-
+sorption due to the rich environment of the nuclear
+region. Most AGNs in U/LIRGs are radio-quiet.
+The SFRs are correlated with radio luminosity, in-
+dicating that starburst emission is dominant (Sec-
+tion 5.2).
+4. In the WISE color–color diagram, we propose a
+new wedge of the buried AGNs in late mergers,
+which show the ∼3–10 µm excess.
+This can be
+explainable by the inner part of the dusty disk
+and/or hot polar dust within the inner parsecs
+(Section 5.3).
+5. The averaged SEDs suggest that the strength of
+the X-rays is the best means to reveal the true
+energy sources (intense starbursts and/or buried
+AGNs) in U/LIRGs (Section 5.4). The absorption-
+corrected AGN SEDs show X-ray weakness rel-
+ative to the other wavelengths.
+This may be a
+common feature among the AGNs in IR-luminous
+galaxies over the cosmic history (z ∼ 0–7), whose
+mechanism will be related to their massive out-
+flows (Section 5.5).
+
+45
+6. Although polar-dust extinction is much smaller
+than torus extinction, the UV-to-IR (mainly IR)
+polar dust luminosities are ∼2 times larger than
+the torus ones because of the seemingly large cov-
+ering fractions (and/or large volumes) of polar
+dust.
+The AGNs with the signs of polar dust
+emission (Section 4.2.4) have logλEdd ≳ −3.0 (Sec-
+tion 6.3).
+7. The polar-dust temperature decreases with merger
+stages. We estimate the physical size of the po-
+lar dust by the temperature and dust sublimation
+radius, consistent with the high-spatial-resolution
+mid-IR images (Asmus 2019). Their sizes increase
+with AGN luminosity from a few tens of parsec
+(early mergers) to kiloparsec scales (late mergers),
+indicating that the polar dust is likely the expand-
+ing (i.e., evolving) dusty outflows (Section 6.5).
+8. The SFRs and intrinsic (bolometric) AGN lumi-
+nosities increase with merger stage. The compar-
+ison between these quantities suggests that the
+starbursts occur first and AGNs arise later, and
+overall their growth rates follow the simultaneous
+coevolution relation that can establish the local
+Mbulge–MBH mass relation (Section 7.1).
+9. Considering the Soltan argument, the balanced
+SFR–LAGN,int relation helps the construction of
+local Mbulge–MBH relation. Whereas, galaxy col-
+lision is also a key process to build up high-
+mass galaxies such as local elliptical galaxies (Sec-
+tion 7.2).
+10. Yamada et al. (2021) and this work suggest that
+the AGNs in late mergers show the multiphase
+outflows at subparsec to kiloparsec scales, that
+is, UFOs, ionized outflows, molecular outflows,
+and expanding dusty winds. The coexistence of
+intense starburst, AGNs, and large-scale massive
+outflows support a standard AGN feedback sce-
+nario (Section 7.3).
+We thank the anonymous referee for constructive com-
+ments and suggestions that helped improve the qual-
+ity of the paper. S.Y. acknowledges Dr. Taiki Kawa-
+muro and Dr.
+Kohei Ichikawa for their helpful dis-
+cussion.
+This work is financially supported by JSPS
+KAKENHI grant numbers 19J22216 and 22K20391
+(S.Y.);
+17K05384 and 20H01946 (Y.U.);
+18J01050,
+19K14759, and 22H01266 (Y.T.);
+21J13894 (S.O.);
+22J22795 (R.U.); and 21K03632 (M.I.). S.Y. is grate-
+ful for support from RIKEN Special Postdoctoral Re-
+searcher Program. M.H.E. and T.M. acknowledge sup-
+port by UNAM-DGAPA PAPIIT IN111319 and CONA-
+CyT Investigaci´on Cient´ıfica B´asica 252531.
+H.M.E.
+also thanks support from a postdoctoral fellowship from
+UNAM-DGAPA. C.R. acknowledges support from the
+Fondecyt Iniciacion grant 11190831 and ANID BASAL
+project FB210003.
+This research has made use of data and/or soft-
+ware provided by the High Energy Astrophysics Sci-
+ence Archive Research Center (HEASARC), which
+is a service of the Astrophysics Science Division at
+NASA/GSFC. This work makes use of data obtained
+from the NuSTAR Data Analysis Software (NuSTAR-
+DAS) jointly developed by the ASI Science Data Center
+(ASDC, Italy) and the California Institute of Technol-
+ogy (USA). This publication makes use of data obtained
+with Chandra, supported by the Chandra X-ray Obser-
+vatory Center at the Smithsonian Astrophysical Obser-
+vatory, and with XMM-Newton, an ESA science mission
+with instruments and contributions directly funded by
+ESA Member States and NASA. This study makes use of
+data obtained from the Suzaku satellite, a collaborative
+mission between the space agencies of Japan (JAXA)
+and the USA (NASA). The scientific results reported in
+this article are based on observations made by UK Swift
+Science Data Centre at the University of Leicester.
+This research makes use of the SIMBAD database, op-
+erated at CDS, Strasbourg, France (Wenger et al. 2000),
+and the Aladin sky atlas, developed at CDS, Strasbourg
+Observatory, France (Bonnarel et al. 2000; Boch & Fer-
+nique 2014).
+Also, this research makes use of data
+from the NASA/IPAC Extragalactic Database (NED)
+and NASA/IPAC Infrared Science Archive (IRSA), op-
+erated by JPL/California Institute of Technology under
+contract with the National Aeronautics and Space Ad-
+ministration (see also IPAC DOIs: Skrutskie et al. 2003;
+Wright et al. 2019; AKARI Team 2020).
+This research is based on observations with GALEX,
+operated for NASA by the California Institute of
+Technology under NASA contract NAS5-98034.
+The
+GALEX data presented in this paper were obtained from
+the Mikulski Archive for Space Telescopes (MAST) at
+the Space Telescope Science Institute (see also MAST
+DOI: Bianchi 2020).
+The Pan-STARRS1 Surveys (PS1) and the PS1 public
+science archive have been made possible through contri-
+butions by the Institute for Astronomy, the University
+of Hawaii, the Pan-STARRS Project Office, the Max-
+Planck Society and its participating institutes, the Max
+Planck Institute for Astronomy, Heidelberg and the Max
+Planck Institute for Extraterrestrial Physics, Garching,
+The Johns Hopkins University, Durham University, the
+
+46
+Yamada et al.
+University of Edinburgh, the Queen’s University Belfast,
+the Harvard-Smithsonian Center for Astrophysics, the
+Las Cumbres Observatory Global Telescope Network
+Incorporated, the National Central University of Tai-
+wan, the Space Telescope Science Institute, the National
+Aeronautics and Space Administration under Grant No.
+NNX08AR22G issued through the Planetary Science Di-
+vision of the NASA Science Mission Directorate, the
+National Science Foundation Grant No. AST-1238877,
+the University of Maryland, Eotvos Lorand University
+(ELTE), the Los Alamos National Laboratory, and the
+Gordon and Betty Moore Foundation.
+The national facility capability for SkyMapper has
+been funded through ARC LIEF grant LE130100104
+from the Australian Research Council, awarded to the
+University of Sydney, the Australian National Univer-
+sity, Swinburne University of Technology, the Univer-
+sity of Queensland, the University of Western Australia,
+the University of Melbourne, Curtin University of Tech-
+nology, Monash University and the Australian Astro-
+nomical Observatory. SkyMapper is owned and oper-
+ated by The Australian National University’s Research
+School of Astronomy and Astrophysics. The survey data
+were processed and provided by the SkyMapper Team
+at ANU. The SkyMapper node of the All-Sky Virtual
+Observatory (ASVO) is hosted at the National Compu-
+tational Infrastructure (NCI). Development and support
+of the SkyMapper node of the ASVO have been funded
+in part by Astronomy Australia Limited (AAL) and the
+Australian Government through the Commonwealth’s
+Education Investment Fund (EIF) and National Col-
+laborative Research Infrastructure Strategy (NCRIS),
+particularly the National eResearch Collaboration Tools
+and Resources (NeCTAR) and the Australian National
+Data Service Projects (ANDS).
+Funding for the SDSS IV has been provided by
+the Alfred P. Sloan Foundation, the U.S. Depart-
+ment of Energy Office of Science, and the Participat-
+ing Institutions.
+SDSS acknowledges support and re-
+sources from the Center for High-Performance Comput-
+ing at the University of Utah. The SDSS web site is
+www.sdss.org. SDSS is managed by the Astrophysical
+Research Consortium for the Participating Institutions
+of the SDSS Collaboration including the Brazilian Par-
+ticipation Group, the Carnegie Institution for Science,
+Carnegie Mellon University, Center for Astrophysics —
+Harvard & Smithsonian (CfA), the Chilean Participa-
+tion Group, the French Participation Group, Instituto
+de Astrof´ısica de Canarias, The Johns Hopkins Univer-
+sity, Kavli Institute for the Physics and Mathematics
+of the Universe (IPMU) / University of Tokyo, the Ko-
+rean Participation Group, Lawrence Berkeley National
+Laboratory, Leibniz Institut f¨ur Astrophysik Potsdam
+(AIP), Max-Planck-Institut f¨ur Astronomie (MPIA Hei-
+delberg), Max-Planck-Institut f¨ur Astrophysik (MPA
+Garching), Max-Planck-Institut f¨ur Extraterrestrische
+Physik (MPE), National Astronomical Observatories of
+China, New Mexico State University, New York Uni-
+versity, University of Notre Dame, Observat´orio Na-
+cional / MCTI, The Ohio State University, Pennsylva-
+nia State University, Shanghai Astronomical Observa-
+tory, United Kingdom Participation Group, Universidad
+Nacional Aut´onoma de M´exico, University of Arizona,
+University of Colorado Boulder, University of Oxford,
+University of Portsmouth, University of Utah, Univer-
+sity of Virginia, University of Washington, University of
+Wisconsin, Vanderbilt University, and Yale University.
+This publication makes use of data products from the
+2MASS, which is a joint project of the University of
+Massachusetts and the Infrared Processing and Anal-
+ysis Center/California Institute of Technology, funded
+by the National Aeronautics and Space Administration
+and the National Science Foundation. This publication
+makes use of data products from the WISE, which is
+a joint project of the University of California, Los An-
+geles, and the Jet Propulsion Laboratory/California In-
+stitute of Technology, funded by the National Aeronau-
+tics and Space Administration. This research is based
+on observations with AKARI, a JAXA project with the
+participation of ESA. Herschel is an ESA space obser-
+vatory with science instruments provided by European-
+led Principal Investigator consortia and with important
+participation from NASA.
+This work makes use of the data from the VLA, op-
+erated by the National Radio Astronomy Observatory
+(NRAO). The NRAO is a facility of the National Sci-
+ence Foundation operated under a cooperative agree-
+ment by Associated Universities, Inc. This study makes
+use of data obtained from the MOST, operated with
+the support of the Australian Research Council and the
+Science Foundation for Physics within the University of
+Sydney. This scientific work makes use of the Murchison
+Radio-astronomy Observatory, operated by CSIRO. We
+acknowledge the Wajarri Yamatji people as the tradi-
+tional owners of the Observatory site. Support for the
+operation of the MWA is provided by the Australian
+Government (NCRIS), under a contract to Curtin Uni-
+versity administered by Astronomy Australia Limited.
+We acknowledge the Pawsey Supercomputing Centre
+which is supported by the Western Australian and Aus-
+tralian Governments. We thank the staff of the GMRT
+that made these observations possible. GMRT is run by
+the National Centre for Radio Astrophysics of the Tata
+Institute of Fundamental Research.
+
+47
+Facilities: NuSTAR, Swift, XMM-Newton, Chan-
+dra,
+Suzaku,
+GALEX,
+Pan-STARRS,
+SkyMapper,
+SDSS, 2MASS, WISE, AKARI, Herschel, VLA, MOST,
+MWA, GMRT.
+Software: XCLUMPY (Tanimoto et al. 2019), HEA-
+soft (v6.25), XSPEC(v12.10.1; Arnaud 1996), NuSTAR-
+DAS(v1.8.0), CIAO(v4.11), SAS (v17.0.0; Gabriel et al.
+2004), TOPCAT (Taylor 2006), X-CIGALE (Boquien
+et al. 2019; Yang et al. 2020a).
+APPENDIX
+A. BEST-FITTING RESULTS
+Here, we present the best-fit parameters derived from
+the UV-to-IR SED decomposition, WISE W1–W4 mag-
+nitude, (Table A1 and A2) and the results of the ra-
+dio fitting (Table A3).
+In Table A4 we list the loga-
+rithmic AGN luminosities in the X-ray, optical, and IR
+bands. The obscuration and UV-to-IR luminosities for
+the torus and polar dust component, Eddington ratios,
+and the spatial scales of the multiphase outflows (Sec-
+tion 6.5) are summarized in Table A5. The multiwave-
+length SEDs and the best-fit SED models are presented
+in Appendix E.
+Table A1. Best-fitting Parameters of the UV-to-IR SED Decomposition
+ID
+Name
+fAGN
+τV
+σ
+i
+E(B − V )polar
+Tpolar
+χ2
+red
+(◦)
+(◦)
+(mag)
+(K)
+(1)
+(2)
+(3)
+(4)
+(5)
+(6)
+(7)
+(8)
+(9)
+ID01
+NGC 34
+0.06±0.03
+95±28
+20
+60
+0.07±0.12
+170±54
+2.1
+ID02
+MCG−02-01-052/MCG−02-01-051
+0.00(f)
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+1.5
+ID03
+MCG−02-01-052
+0.00(f)
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+4.5
+ID04
+MCG−02-01-051
+0.00(f)
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+0.6
+ID05
+ESO 350−38
+0.60±0.03
+41±7
+20
+80
+0.11±0.17
+100±1
+2.5
+ID06
+NGC 232/NGC 235
+0.05±0.01
+93±28
+20
+60
+· · ·
+· · ·
+1.7
+ID07
+NGC 232
+0.00(f)
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+2.0
+ID08
+NGC 235
+0.10±0.01
+87±29
+20
+60
+· · ·
+· · ·
+2.4
+ID09
+MCG+12-02-001
+0.06±0.02
+96±28
+20
+60
+0.55±0.29
+174±44
+1.8
+ID10
+IC 1623A/IC 1623B
+0.00(f)
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+3.3
+ID11
+NGC 833/NGC 835
+0.10±0.01
+87±31
+15
+60
+0.55±0.29
+201±52
+1.7
+ID12
+NGC 833
+0.08±0.03
+82±32
+15
+60
+· · ·
+· · ·
+3.7
+ID13
+NGC 835
+0.10±0.02
+91±30
+15
+60
+0.16±0.26
+190±48
+1.8
+ID14
+NGC 838
+0.00(f)
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+1.3
+ID15
+NGC 839
+0.00(f)
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+3.6
+ID16
+NGC 1068
+0.49±0.07
+79±33
+20
+80
+0.39±0.31
+250±5
+5.3
+ID17
+UGC 2608/UGC 2612
+0.26±0.05
+63±30
+15
+80
+· · ·
+· · ·
+0.8
+ID18
+UGC 2608
+0.20±0.07
+64±32
+15
+80
+· · ·
+· · ·
+1.0
+ID19
+UGC 2612
+0.00(f)
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+4.1
+ID20
+NGC 1275
+0.80±0.01
+41±8
+20
+30
+0.80±0.01
+100±1
+5.6
+ID21
+NGC 1365
+0.10±0.01
+83±32
+20
+30
+0.80±0.02
+235±25
+1.6
+ID22
+ESO 203−1
+0.00(f)
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+1.4
+ID23
+CGCG 468-002W/CGCG 468-002E
+0.17±0.04
+81±32
+15
+60
+0.05±0.02
+126±35
+2.1
+ID24
+CGCG 468-002W
+0.20±0.05
+85±32
+15
+60
+0.06±0.07
+162±36
+4.0
+ID25
+CGCG 468-002E
+0.00(f)
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+2.1
+ID26
+IRAS F05189−2524
+0.70±0.03
+40±3
+15
+60
+0.80±0.04
+100±1
+3.8
+ID27
+IRAS F06076−2139/
+0.07±0.02
+94±28
+20
+60
+0.55±0.29
+137±27
+0.8
+2MASS 06094601−2140312
+Table A1 continued
+
+48
+Yamada et al.
+Table A1 (continued)
+ID
+Name
+fAGN
+τV
+σ
+i
+E(B − V )polar
+Tpolar
+χ2
+red
+(◦)
+(◦)
+(mag)
+(K)
+(1)
+(2)
+(3)
+(4)
+(5)
+(6)
+(7)
+(8)
+(9)
+ID28
+NGC 2623
+0.05±0.01
+104±21
+20
+60
+0.05±0.02
+100±5
+3.5
+ID29
+ESO 060−IG016 West/East
+0.10±0.01
+80±31
+20
+60
+· · ·
+· · ·
+1.0
+ID30
+IRAS F08572+3915
+0.47±0.05
+49±24
+20
+80
+0.05±0.02
+180±41
+11.8
+ID31
+UGC 5101
+0.11±0.04
+45±16
+15
+60
+0.30±0.05
+101±8
+3.7
+ID32
+MCG+08-18-012/MCG+08-18-013
+0.00(f)
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+3.0
+ID33
+MCG+08-18-012
+0.00(f)
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+4.5
+ID34
+MCG+08-18-013
+0.00(f)
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+1.4
+ID35
+MCG−01-26-013/NGC 3110
+0.00(f)
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+1.5
+ID36
+MCG−01-26-013
+0.00(f)
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+2.3
+ID37
+NGC 3110
+0.00(f)
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+3.9
+ID38
+ESO 374−IG032
+0.10±0.02
+54±25
+20
+30
+0.05±0.06
+172±45
+5.9
+ID39
+NGC 3256
+0.00(f)
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+1.7
+ID40
+IRAS F10565+2448
+0.00(f)
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+5.2
+ID41
+NGC 3690 West/East
+0.29±0.11
+88±31
+45
+30
+0.58±0.31
+158±57
+2.6
+ID42
+ESO 440−58/MCG−05-29-017
+0.00(f)
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+1.7
+ID43
+IRAS F12112+0305
+0.00(f)
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+5.7
+ID44
+NGC 4418/MCG+00-32-013
+0.29±0.03
+117±10
+20
+80
+0.65±0.23
+150±1
+3.2
+ID45
+NGC 4418
+0.10±0.01
+82±28
+20
+80
+0.63±0.24
+200±1
+3.4
+ID46
+MCG+00-32-013
+0.00(f)
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+4.9
+ID47
+Mrk 231
+0.28±0.06
+79±33
+25
+60
+0.42±0.29
+186±55
+0.3
+ID48
+NGC 4922S/NGC 4922N
+0.34±0.08
+81±32
+20
+60
+0.38±0.19
+135±42
+0.8
+ID49
+IC 860
+0.00(f)
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+3.1
+ID50
+IRAS 13120−5453
+0.05±0.01
+49±22
+20
+80
+0.23±0.28
+100±5
+2.0
+ID51
+NGC 5104
+0.00(f)
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+2.8
+ID52
+MCG−03-34-064
+0.61±0.10
+48±20
+20
+60
+0.79±0.06
+206±19
+1.8
+ID53
+NGC 5135
+0.06±0.02
+79±33
+15
+80
+0.38±0.31
+138±58
+1.0
+ID54
+Mrk 266B/Mrk 266A
+0.09±0.02
+98±26
+20
+60
+0.10±0.18
+182±45
+1.6
+ID55
+Mrk 273
+0.08±0.02
+73±33
+15
+60
+0.78±0.09
+101±6
+2.4
+ID56
+IRAS F14348−1447
+0.09±0.04
+71±33
+20
+80
+0.40±0.31
+102±11
+2.6
+ID57
+IRAS F14378−3651
+0.00(f)
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+2.4
+ID58
+IC 4518A/IC 4518B
+0.13±0.08
+79±33
+20
+60
+0.39±0.31
+181±58
+0.3
+ID59
+IRAS F15250+3608
+0.00(f)
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+2.8
+ID60
+Arp 220W/Arp 220E
+0.05±0.01
+110±18
+20
+60
+0.72±0.18
+141±20
+6.2
+ID61
+NGC 6240S/NGC 6240N
+0.10±0.01
+104±23
+20
+30
+0.05±0.06
+136±32
+1.4
+ID62
+NGC 6285/NGC 6286
+0.05±0.01
+82±33
+20
+80
+0.38±0.31
+172±74
+4.5
+ID63
+NGC 6285
+0.00(f)
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+2.3
+ID64
+NGC 6286
+0.05±0.01
+82±33
+20
+80
+0.44±0.31
+168±75
+5.5
+ID65
+IRAS F17138−1017
+0.14±0.07
+81±33
+20
+60
+0.37±0.30
+135±54
+5.1
+ID66
+IRAS F18293−3413
+0.00(f)
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+0.9
+ID67
+IRAS F19297−0406
+0.00(f)
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+2.1
+ID68
+NGC 6907/NGC 6908
+0.00(f)
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+2.5
+ID69
+NGC 6921/MCG+04-48-002
+0.10±0.01
+86±31
+20
+60
+· · ·
+· · ·
+0.4
+ID70
+NGC 6921
+0.05±0.01
+82±33
+20
+80
+· · ·
+· · ·
+0.8
+ID71
+MCG+04-48-002
+0.11±0.03
+91±29
+20
+60
+· · ·
+· · ·
+0.7
+Table A1 continued
+
+49
+Table A1 (continued)
+ID
+Name
+fAGN
+τV
+σ
+i
+E(B − V )polar
+Tpolar
+χ2
+red
+(◦)
+(◦)
+(mag)
+(K)
+(1)
+(2)
+(3)
+(4)
+(5)
+(6)
+(7)
+(8)
+(9)
+ID72
+II Zw 096/IRAS F20550+1655 SE
+0.00(f)
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+3.7
+ID73
+ESO 286−19
+0.00(f)
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+2.3
+ID74
+NGC 7130
+0.24±0.10
+79±32
+25
+80
+0.38±0.31
+109±32
+1.6
+ID75
+NGC 7469/IC 5283
+0.34±0.09
+77±33
+15
+30
+0.34±0.36
+102±11
+0.4
+ID76
+NGC 7469
+0.38±0.08
+75±33
+15
+30
+0.72±0.20
+102±10
+0.6
+ID77
+IC 5283
+0.00(f)
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+1.2
+ID78
+ESO 148−2
+0.22±0.07
+45±18
+20
+80
+0.16±0.24
+100±3
+2.6
+ID79
+NGC 7591
+0.00(f)
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+2.3
+ID80
+NGC 7674/MCG+01-59-081
+0.41±0.04
+71±32
+40
+30
+0.06±0.07
+137±48
+0.7
+ID81
+NGC 7674
+0.43±0.05
+60±29
+40
+30
+0.06±0.08
+138±43
+0.6
+ID82
+MCG+01-59-081
+0.00(f)
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+0.3
+ID83
+NGC 7679/NGC 7682
+0.07±0.03
+90±30
+20
+60
+0.49±0.31
+181±57
+1.7
+ID84
+NGC 7679
+0.05±0.01
+88±31
+15
+30
+0.44±0.32
+190±63
+1.1
+ID85
+NGC 7682
+0.15±0.08
+82±32
+60
+60
+· · ·
+· · ·
+1.7
+Note—Comments: (1–2) ID and object name; (3) fraction of AGN luminosity in the IR band. The symbol “(f)” means
+that the value is fixed; (4) optical depth of each clump at V band; (5–6) torus angular width and inclination; (7) E(B −V )
+of the polar dust; (8) temperature of the polar dust; (9) reduced χ2 for the UV-to-IR SED decomposition.
+(This table is available in its entirety in machine-readable form.)
+
+50
+Yamada et al.
+Table A2. Properties of Host Galaxies and WISE Color
+ID
+Name
+logM∗
+logSFR
+logsSFR
+W1
+W2
+W3
+W4
+(M⊙)
+(M⊙ yr−1)
+(yr)
+(mag)
+(mag)
+(mag)
+(mag)
+(1)
+(2)
+(3)
+(4)
+(5)
+(6)
+(7)
+(8)
+(9)
+ID01
+NGC 34
+10.31±0.13
+1.51±0.07
+−8.80±0.14
+9.82±0.01
+9.35±0.01
+5.25±0.01
+2.05±0.01
+ID02
+MCG−02-01-052/MCG−02-01-051
+10.37±0.13
+1.47±0.06
+−8.90±0.14
+· · ·
+· · ·
+· · ·
+· · ·
+ID03
+MCG−02-01-052
+9.85±0.05
+0.57±0.02
+−9.29±0.05
+12.25±0.02
+12.17±0.02
+· · ·
+· · ·
+ID04
+MCG−02-01-051
+10.22±0.15
+1.42±0.06
+−8.80±0.17
+10.80±0.01
+10.35±0.01
+5.89±0.01
+2.95±0.01
+ID05
+ESO 350−38
+9.74±0.16
+0.95±0.07
+−8.79±0.17
+10.79±0.01
+9.50±0.01
+5.49±0.01
+2.10±0.01
+ID06
+NGC 232/NGC 235
+11.07±0.06
+1.35±0.04
+−9.72±0.07
+· · ·
+· · ·
+· · ·
+· · ·
+ID07
+NGC 232
+10.73±0.13
+1.35±0.08
+−9.38±0.15
+9.66±0.01
+9.32±0.01
+5.40±0.01
+2.71±0.01
+ID08
+NGC 235
+10.93±0.03
+0.55±0.03
+−10.38±0.04
+10.03±0.01
+9.47±0.01
+6.44±0.01
+3.71±0.01
+ID09
+MCG+12-02-001
+10.34±0.11
+1.41±0.06
+−8.93±0.12
+· · ·
+8.92±0.01
+4.49±0.01
+1.45±0.01
+ID10
+IC 1623A/IC 1623B
+10.64±0.11
+1.82±0.03
+−8.82±0.11
+9.22±0.01
+8.21±0.01
+4.52±0.01
+1.54±0.01
+ID11
+NGC 833/NGC 835
+11.16±0.07
+0.37±0.24
+−10.80±0.25
+· · ·
+· · ·
+· · ·
+· · ·
+ID12
+NGC 833
+10.76±0.02
+−1.78±0.34
+−12.54±0.34
+9.50±0.01
+9.49±0.01
+· · ·
+5.71±0.04
+ID13
+NGC 835
+10.95±0.05
+0.59±0.07
+−10.36±0.08
+8.91±0.01
+8.77±0.01
+5.33±0.01
+3.32±0.01
+ID14
+NGC 838
+10.36±0.09
+1.11±0.06
+−9.26±0.11
+9.32±0.01
+9.00±0.01
+4.70±0.01
+2.14±0.01
+ID15
+NGC 839
+10.19±0.04
+0.91±0.03
+−9.27±0.05
+9.60±0.01
+9.09±0.01
+4.91±0.01
+1.81±0.01
+ID16
+NGC 1068
+10.07±0.15
+1.25±0.08
+−8.82±0.17
+· · ·
+· · ·
+· · ·
+· · ·
+ID17
+UGC 2608/UGC 2612
+11.05±0.10
+1.36±0.07
+−9.68±0.12
+· · ·
+· · ·
+· · ·
+· · ·
+ID18
+UGC 2608
+10.75±0.11
+1.24±0.11
+−9.51±0.15
+· · ·
+8.70±0.01
+5.09±0.01
+2.33±0.01
+ID19
+UGC 2612
+10.64±0.13
+0.53±0.06
+−10.11±0.14
+· · ·
+10.39±0.01
+7.55±0.01
+5.88±0.04
+ID20
+NGC 1275
+9.70±0.20
+0.91±0.05
+−8.79±0.20
+8.03±0.01
+7.52±0.01
+4.04±0.01
+1.07±0.01
+ID21
+NGC 1365
+10.94±0.08
+0.93±0.09
+−10.01±0.13
+6.30±0.01
+5.95±0.01
+2.32±0.01
+· · ·
+ID22
+ESO 203−1
+9.78±0.22
+1.78±0.06
+−8.00±0.23
+· · ·
+12.15±0.01
+7.92±0.01
+4.36±0.01
+ID23
+CGCG 468-002W/CGCG 468-002E
+10.95±0.10
+0.87±0.20
+−10.07±0.22
+· · ·
+· · ·
+· · ·
+· · ·
+ID24
+CGCG 468-002W
+10.89±0.04
+−0.44±0.48
+−11.34±0.48
+9.93±0.01
+9.47±0.01
+6.44±0.01
+· · ·
+ID25
+CGCG 468-002E
+10.11±0.07
+1.21±0.04
+−8.90±0.08
+· · ·
+· · ·
+6.67±0.01
+3.08±0.01
+ID26
+IRAS F05189−2524
+10.72±0.11
+1.56±0.12
+−9.16±0.16
+8.77±0.01
+7.65±0.01
+4.79±0.01
+1.77±0.01
+ID27
+IRAS F06076−2139/
+10.41±0.19
+1.65±0.11
+−8.76±0.21
+11.31±0.01
+10.78±0.01
+6.84±0.01
+3.81±0.01
+2MASS 06094601−2140312
+ID28
+NGC 2623
+9.86±0.31
+1.53±0.05
+−8.33±0.32
+10.39±0.01
+9.76±0.01
+5.84±0.01
+2.60±0.01
+ID29
+ESO 060−IG016 West/East
+9.85±0.32
+1.68±0.04
+−8.17±0.32
+· · ·
+· · ·
+· · ·
+3.69±0.01
+ID30
+IRAS F08572+3915
+9.18±0.25
+1.89±0.02
+−7.28±0.25
+10.25±0.02
+7.94±0.02
+4.90±0.02
+2.04±0.02
+ID31
+UGC 5101
+10.85±0.14
+2.00±0.09
+−8.86±0.16
+10.10±0.01
+8.46±0.01
+6.07±0.01
+3.20±0.01
+ID32
+MCG+08-18-012/MCG+08-18-013
+10.28±0.10
+1.30±0.06
+−8.98±0.11
+· · ·
+· · ·
+· · ·
+· · ·
+ID33
+MCG+08-18-012
+9.04±0.08
+0.10±0.02
+−8.93±0.08
+13.78±0.03
+13.67±0.03
+10.13±0.07
+· · ·
+ID34
+MCG+08-18-013
+10.30±0.12
+1.30±0.09
+−9.00±0.15
+10.84±0.01
+10.44±0.01
+6.36±0.01
+· · ·
+ID35
+MCG−01-26-013/NGC 3110
+10.68±0.12
+1.26±0.09
+−9.42±0.15
+· · ·
+· · ·
+· · ·
+· · ·
+ID36
+MCG−01-26-013
+10.06±0.10
+0.24±0.04
+−9.82±0.11
+11.42±0.01
+11.24±0.01
+7.64±0.01
+5.15±0.03
+ID37
+NGC 3110
+10.73±0.09
+1.18±0.04
+−9.56±0.09
+9.19±0.01
+8.90±0.01
+4.76±0.01
+2.57±0.01
+ID38
+ESO 374−IG032
+10.43±0.20
+1.72±0.05
+−8.71±0.21
+10.60±0.01
+8.16±0.01
+5.92±0.01
+3.19±0.01
+ID39
+NGC 3256
+10.67±0.12
+1.81±0.06
+−8.86±0.13
+7.58±0.01
+7.05±0.01
+· · ·
+−0.44±0.01
+ID40
+IRAS F10565+2448
+10.71±0.13
+1.95±0.09
+−8.76±0.16
+11.06±0.01
+· · ·
+6.24±0.01
+3.17±0.01
+ID41
+NGC 3690 West/East
+10.82±0.14
+1.69±0.10
+−9.13±0.18
+· · ·
+· · ·
+· · ·
+· · ·
+ID42
+ESO 440−58/MCG−05-29-017
+10.55±0.06
+1.30±0.04
+−9.24±0.08
+· · ·
+· · ·
+· · ·
+· · ·
+ID43
+IRAS F12112+0305
+9.95±0.39
+2.35±0.03
+−7.60±0.39
+12.36±0.01
+11.63±0.01
+7.57±0.01
+4.28±0.01
+ID44
+NGC 4418/MCG+00-32-013
+9.28±0.13
+0.82±0.08
+−8.47±0.15
+· · ·
+· · ·
+· · ·
+· · ·
+ID45
+NGC 4418
+8.97±0.23
+0.96±0.05
+−8.01±0.24
+10.15±0.01
+9.32±0.01
+4.01±0.01
+0.40±0.01
+ID46
+MCG+00-32-013
+7.32±0.19
+−0.80±0.03
+−8.11±0.19
+14.11±0.03
+13.89±0.04
+10.34±0.08
+7.77±0.16
+ID47
+Mrk 231
+10.73±0.42
+2.43±0.08
+−8.30±0.42
+7.80±0.01
+6.58±0.01
+3.54±0.01
+0.57±0.01
+ID48
+NGC 4922S/NGC 4922N
+10.92±0.05
+0.91±0.06
+−10.00±0.08
+· · ·
+· · ·
+· · ·
+· · ·
+Table A2 continued
+
+51
+Table A2 (continued)
+ID
+Name
+logM∗
+logSFR
+logsSFR
+W1
+W2
+W3
+W4
+(M⊙)
+(M⊙ yr−1)
+(yr)
+(mag)
+(mag)
+(mag)
+(mag)
+(1)
+(2)
+(3)
+(4)
+(5)
+(6)
+(7)
+(8)
+(9)
+ID49
+IC 860
+9.68±0.08
+0.85±0.02
+−8.82±0.09
+10.62±0.01
+10.51±0.01
+7.17±0.01
+2.93±0.01
+ID50
+IRAS 13120−5453
+11.15±0.12
+2.34±0.07
+−8.81±0.14
+9.58±0.01
+8.83±0.01
+5.08±0.01
+1.91±0.01
+ID51
+NGC 5104
+10.68±0.06
+0.97±0.06
+−9.71±0.09
+9.62±0.01
+9.38±0.01
+5.74±0.01
+3.18±0.01
+ID52
+MCG−03-34-064
+10.71±0.10
+0.47±0.10
+−10.24±0.14
+9.20±0.01
+7.92±0.01
+4.17±0.01
+1.53±0.01
+ID53
+NGC 5135
+10.93±0.17
+1.19±0.10
+−9.74±0.20
+8.61±0.01
+8.10±0.01
+4.44±0.01
+1.62±0.01
+ID54
+Mrk 266B/Mrk 266A
+10.76±0.14
+1.35±0.06
+−9.41±0.15
+9.88±0.01
+9.48±0.01
+5.57±0.01
+2.56±0.01
+ID55
+Mrk 273
+10.52±0.22
+2.24±0.05
+−8.28±0.22
+10.50±0.01
+9.37±0.01
+5.85±0.01
+2.16±0.01
+ID56
+IRAS F14348−1447
+10.73±0.24
+2.32±0.06
+−8.40±0.24
+12.12±0.01
+11.29±0.01
+7.52±0.01
+3.95±0.01
+ID57
+IRAS F14378−3651
+10.29±0.21
+2.33±0.03
+−7.96±0.21
+12.24±0.02
+11.37±0.02
+7.11±0.02
+3.42±0.02
+ID58
+IC 4518A/IC 4518B
+10.78±0.16
+1.24±0.22
+−9.55±0.27
+· · ·
+· · ·
+· · ·
+· · ·
+ID59
+IRAS F15250+3608
+10.01±0.12
+2.12±0.02
+−7.89±0.13
+12.34±0.02
+10.84±0.02
+5.99±0.01
+2.40±0.01
+ID60
+Arp 220W/Arp 220E
+9.82±0.30
+2.12±0.04
+−7.69±0.31
+9.71±0.01
+9.14±0.01
+4.70±0.01
+0.76±0.01
+ID61
+NGC 6240S/NGC 6240N
+11.02±0.11
+1.60±0.05
+−9.42±0.12
+8.85±0.01
+8.34±0.01
+4.59±0.01
+1.35±0.01
+ID62
+NGC 6285/NGC 6286
+10.61±0.07
+1.35±0.03
+−9.26±0.08
+· · ·
+· · ·
+· · ·
+· · ·
+ID63
+NGC 6285
+10.25±0.19
+0.61±0.05
+−9.63±0.20
+10.89±0.01
+10.66±0.01
+· · ·
+4.62±0.01
+ID64
+NGC 6286
+10.42±0.09
+1.09±0.04
+−9.34±0.10
+9.90±0.02
+9.40±0.02
+5.37±0.01
+3.51±0.02
+ID65
+IRAS F17138−1017
+9.40±0.29
+1.48±0.08
+−7.92±0.30
+9.63±0.02
+9.11±0.02
+4.66±0.01
+1.84±0.01
+ID66
+IRAS F18293−3413
+10.72±0.12
+1.78±0.06
+−8.94±0.13
+8.88±0.01
+8.37±0.01
+4.12±0.01
+1.42±0.01
+ID67
+IRAS F19297−0406
+10.60±0.22
+2.39±0.16
+−8.21±0.27
+11.94±0.02
+11.19±0.02
+6.85±0.02
+3.46±0.02
+ID68
+NGC 6907/NGC 6908
+10.73±0.14
+1.08±0.03
+−9.66±0.15
+· · ·
+· · ·
+· · ·
+· · ·
+ID69
+NGC 6921/MCG+04-48-002
+11.15±0.09
+0.94±0.13
+−10.22±0.16
+· · ·
+· · ·
+· · ·
+· · ·
+ID70
+NGC 6921
+11.20±0.04
+−0.33±0.25
+−11.54±0.25
+8.67±0.01
+8.62±0.01
+· · ·
+5.01±0.02
+ID71
+MCG+04-48-002
+10.42±0.17
+0.88±0.09
+−9.55±0.19
+9.30±0.01
+8.80±0.01
+5.08±0.01
+2.90±0.01
+ID72
+II Zw 096/IRAS F20550+1655 SE
+10.35±0.08
+1.90±0.02
+−8.45±0.08
+11.37±0.02
+10.38±0.02
+5.35±0.01
+· · ·
+ID73
+ESO 286−19
+9.94±0.09
+1.97±0.02
+−7.97±0.09
+11.30±0.01
+9.96±0.01
+5.78±0.01
+· · ·
+ID74
+NGC 7130
+11.06±0.11
+1.30±0.07
+−9.76±0.13
+8.98±0.01
+8.55±0.01
+4.59±0.01
+1.74±0.01
+ID75
+NGC 7469/IC 5283
+10.83±0.17
+1.49±0.08
+−9.34±0.19
+· · ·
+· · ·
+· · ·
+· · ·
+ID76
+NGC 7469
+10.69±0.18
+1.51±0.08
+−9.18±0.20
+8.29±0.01
+· · ·
+3.83±0.01
+0.77±0.01
+ID77
+IC 5283
+10.46±0.08
+0.50±0.16
+−9.97±0.18
+10.30±0.01
+10.10±0.01
+· · ·
+· · ·
+ID78
+ESO 148−2
+10.21±0.40
+1.93±0.05
+−8.28±0.41
+11.02±0.01
+10.01±0.01
+5.92±0.01
+2.63±0.01
+ID79
+NGC 7591
+10.62±0.11
+1.04±0.04
+−9.58±0.11
+9.54±0.01
+9.33±0.01
+5.54±0.01
+2.91±0.01
+ID80
+NGC 7674/MCG+01-59-081
+11.21±0.06
+1.25±0.10
+−9.96±0.11
+· · ·
+· · ·
+· · ·
+· · ·
+ID81
+NGC 7674
+11.10±0.08
+1.22±0.09
+−9.88±0.12
+· · ·
+8.05±0.01
+4.66±0.01
+2.04±0.01
+ID82
+MCG+01-59-081
+10.61±0.09
+0.33±0.07
+−10.28±0.11
+· · ·
+· · ·
+· · ·
+· · ·
+ID83
+NGC 7679/NGC 7682
+10.77±0.03
+1.06±0.02
+−9.72±0.04
+· · ·
+· · ·
+· · ·
+· · ·
+ID84
+NGC 7679
+10.33±0.07
+1.05±0.02
+−9.28±0.07
+9.63±0.01
+9.30±0.01
+5.09±0.01
+2.75±0.01
+ID85
+NGC 7682
+10.62±0.04
+−0.20±0.23
+−10.83±0.23
+10.20±0.01
+10.21±0.01
+7.86±0.02
+5.21±0.03
+Note—Comments: (1–2) ID and object name; (3) logarithmic stellar mass; (4) logarithmic SFR; (5) logarithmic specific SFR (sSFR); (6)–(9) W1,
+W2, W3, and W4 magnitudes (Vega) from ALLWISE catalog (Section 3.5 and 5.3).
+The W1 and W2 magnitudes are corrected for Galactic
+extinction (Section 3.8).
+(This table is available in its entirety in machine-readable form.)
+
+52
+Yamada et al.
+Table A3. Results of the Radio Fitting
+ID
+Name
+αradio
+qir
+logL1.4GHz
+qexcess
+χ2
+red
+(erg s−1)
+(1)
+(2)
+(3)
+(4)
+(5)
+(6)
+(7)
+ID01
+NGC 34
+0.41±0.07
+2.77±0.06
+38.91±0.04
+21.25±0.08
+2.1
+ID02
+MCG−02-01-052/MCG−02-01-051
+0.44±0.09
+2.54±0.05
+39.03±0.05
+21.42±0.08
+1.4
+ID03
+MCG−02-01-052
+0.5(f)
+2.76±0.08
+37.99±0.07
+21.28±0.07
+4.2
+ID04
+MCG−02-01-051
+0.49±0.09
+2.50±0.05
+38.99±0.05
+21.42±0.08
+0.5
+ID05
+ESO 350−38
+0.56±0.07
+2.36±0.04
+38.54±0.04
+21.44±0.08
+2.1
+ID06
+NGC 232/NGC 235
+0.68±0.06
+2.43±0.05
+39.20±0.04
+21.70±0.06
+1.8
+ID07
+NGC 232
+0.52±0.09
+2.58±0.05
+38.98±0.04
+21.49±0.09
+1.8
+ID08
+NGC 235
+0.57±0.08
+1.93±0.05
+38.81±0.04
+22.11±0.05
+2.2
+ID09
+MCG+12-02-001
+0.52±0.06
+2.57±0.05
+38.96±0.04
+21.41±0.07
+1.7
+ID10
+IC 1623A/IC 1623B
+0.67±0.05
+2.25±0.05
+39.52±0.04
+21.56±0.05
+2.7
+ID11
+NGC 833/NGC 835
+0.61±0.07
+2.49±0.05
+38.41±0.05
+21.90±0.25
+1.6
+ID12
+NGC 833
+0.5(f)
+2.59±0.06
+37.02±0.06
+22.66±0.34
+3.1
+ID13
+NGC 835
+0.60±0.09
+2.46±0.05
+38.43±0.05
+21.70±0.08
+1.6
+ID14
+NGC 838
+0.63±0.06
+2.57±0.05
+38.65±0.04
+21.39±0.08
+1.2
+ID15
+NGC 839
+0.51±0.10
+2.98±0.06
+38.24±0.05
+21.18±0.05
+3.3
+ID16
+NGC 1068
+0.56±0.04
+2.09±0.05
+39.23±0.04
+21.83±0.09
+3.6
+ID17
+UGC 2608/UGC 2612
+0.79±0.07
+2.25±0.05
+39.37±0.04
+21.86±0.08
+0.8
+ID18
+UGC 2608
+0.78±0.07
+2.15±0.05
+39.22±0.04
+21.83±0.11
+1.0
+ID19
+UGC 2612
+0.5(f)
+3.47±0.03
+37.40±0.02
+20.72±0.07
+4.0
+ID20
+NGC 1275
+0.47±0.02
+−0.57±0.03
+41.29±0.03
+24.24±0.05
+3.6
+ID21
+NGC 1365
+0.65±0.05
+2.85±0.04
+38.30±0.03
+21.23±0.10
+2.3
+ID22
+ESO 203−1
+0.5(f)
+2.94±0.07
+39.01±0.06
+21.08±0.08
+1.3
+ID23
+CGCG 468-002W/CGCG 468-002E
+0.5(f)
+2.76±0.06
+38.47±0.05
+21.45±0.20
+2.0
+ID24
+CGCG 468-002W
+0.5(f)
+2.79±0.06
+37.84±0.05
+22.14±0.48
+3.4
+ID25
+CGCG 468-002E
+0.5(f)
+3.39±0.06
+38.07±0.03
+20.71±0.05
+2.3
+ID26
+IRAS F05189−2524
+0.5(f)
+2.49±0.05
+39.22±0.05
+21.51±0.13
+3.7
+ID27
+IRAS F06076−2139/
+0.36±0.09
+2.67±0.05
+38.97±0.05
+21.18±0.12
+0.7
+2MASS 06094601−2140312
+ID28
+NGC 2623
+0.26±0.08
+2.66±0.05
+39.00±0.04
+21.32±0.07
+3.1
+ID29
+ESO 060−IG016 West/East
+0.5(f)
+2.62±0.05
+39.19±0.05
+21.36±0.06
+1.0
+ID30
+IRAS F08572+3915
+0.5(f)
+3.40±0.07
+38.69±0.04
+20.65±0.04
+11.3
+ID31
+UGC 5101
+0.22±0.06
+2.14±0.05
+39.92±0.04
+21.78±0.09
+3.3
+ID32
+MCG+08-18-012/MCG+08-18-013
+0.41±0.08
+2.56±0.05
+38.85±0.04
+21.41±0.07
+2.7
+ID33
+MCG+08-18-012
+0.5(f)
+3.20±0.19
+36.91±0.11
+20.66±0.11
+3.9
+ID34
+MCG+08-18-013
+0.40±0.08
+2.55±0.05
+38.87±0.04
+21.42±0.10
+1.3
+ID35
+MCG−01-26-013/NGC 3110
+0.64±0.05
+2.31±0.05
+39.06±0.04
+21.66±0.10
+1.4
+ID36
+MCG−01-26-013
+0.5(f)
+2.45±0.06
+37.82±0.05
+21.43±0.07
+2.2
+ID37
+NGC 3110
+0.64±0.06
+2.32±0.05
+39.06±0.04
+21.74±0.06
+3.4
+ID38
+ESO 374−IG032
+0.51±0.08
+2.87±0.05
+38.92±0.04
+21.06±0.06
+5.3
+ID39
+NGC 3256
+0.52±0.06
+2.52±0.06
+39.36±0.05
+21.41±0.08
+1.3
+ID40
+IRAS F10565+2448
+0.28±0.08
+2.50±0.05
+39.51±0.04
+21.42±0.10
+4.8
+ID41
+NGC 3690 West/East
+0.50±0.05
+2.34±0.05
+39.37±0.04
+21.53±0.11
+2.2
+ID42
+ESO 440−58/MCG−05-29-017
+0.58±0.06
+2.53±0.04
+38.95±0.03
+21.49±0.05
+1.5
+ID43
+IRAS F12112+0305
+0.20±0.10
+2.84±0.06
+39.59±0.04
+21.10±0.05
+5.2
+ID44
+NGC 4418/MCG+00-32-013
+0.5(f)
+3.21±0.07
+37.89±0.05
+20.93±0.10
+3.1
+ID45
+NGC 4418
+0.5(f)
+3.42±0.05
+37.91±0.03
+20.80±0.06
+3.2
+ID46
+MCG+00-32-013
+0.5(f)
+3.31±0.13
+35.98±0.07
+20.63±0.07
+4.2
+ID47
+Mrk 231
+0.37±0.05
+2.27±0.05
+40.25±0.04
+21.67±0.09
+0.3
+ID48
+NGC 4922S/NGC 4922N
+0.33±0.07
+2.37±0.05
+38.84±0.04
+21.78±0.07
+0.9
+Table A3 continued
+
+53
+Table A3 (continued)
+ID
+Name
+αradio
+qir
+logL1.4GHz
+qexcess
+χ2
+red
+(erg s−1)
+(1)
+(2)
+(3)
+(4)
+(5)
+(6)
+(7)
+ID49
+IC 860
+0.19±0.10
+2.98±0.06
+38.08±0.04
+21.08±0.05
+2.8
+ID50
+IRAS 13120−5453
+0.5(f)
+2.41±0.05
+39.98±0.04
+21.49±0.08
+1.9
+ID51
+NGC 5104
+0.60±0.07
+2.60±0.05
+38.63±0.04
+21.52±0.07
+2.6
+ID52
+MCG−03-34-064
+0.35±0.04
+1.44±0.05
+39.16±0.04
+22.55±0.11
+2.5
+ID53
+NGC 5135
+0.60±0.05
+2.31±0.05
+39.08±0.04
+21.75±0.10
+0.9
+ID54
+Mrk 266B/Mrk 266A
+0.60±0.06
+2.01±0.04
+39.50±0.04
+22.01±0.07
+1.5
+ID55
+Mrk 273
+0.41±0.06
+2.46±0.05
+39.83±0.04
+21.44±0.06
+2.2
+ID56
+IRAS F14348−1447
+0.42±0.08
+2.43±0.05
+39.91±0.04
+21.44±0.08
+2.3
+ID57
+IRAS F14378−3651
+0.47±0.08
+2.60±0.05
+39.75±0.04
+21.28±0.04
+2.1
+ID58
+IC 4518A/IC 4518B
+0.40±0.08
+1.90±0.06
+39.21±0.06
+21.83±0.23
+0.7
+ID59
+IRAS F15250+3608
+0.33±0.16
+3.05±0.07
+39.15±0.05
+20.88±0.05
+2.6
+ID60
+Arp 220W/Arp 220E
+0.09±0.06
+2.59±0.05
+39.51±0.04
+21.24±0.06
+5.3
+ID61
+NGC 6240S/NGC 6240N
+0.69±0.04
+1.93±0.04
+39.93±0.04
+22.18±0.06
+1.5
+ID62
+NGC 6285/NGC 6286
+0.44±0.05
+2.23±0.04
+39.29±0.04
+21.79±0.05
+4.2
+ID63
+NGC 6285
+0.5(f)
+2.60±0.06
+38.09±0.05
+21.33±0.07
+2.1
+ID64
+NGC 6286
+0.46±0.05
+2.09±0.04
+39.25±0.04
+22.01±0.06
+5.0
+ID65
+IRAS F17138−1017
+0.55±0.08
+2.75±0.06
+38.80±0.04
+21.17±0.09
+4.6
+ID66
+IRAS F18293−3413
+0.65±0.05
+2.56±0.04
+39.37±0.03
+21.44±0.07
+0.8
+ID67
+IRAS F19297−0406
+0.47±0.09
+2.49±0.05
+39.85±0.04
+21.31±0.16
+1.9
+ID68
+NGC 6907/NGC 6908
+0.57±0.06
+2.55±0.05
+38.69±0.04
+21.47±0.06
+2.8
+ID69
+NGC 6921/MCG+04-48-002
+0.59±0.08
+2.32±0.05
+38.84±0.04
+21.76±0.14
+0.4
+ID70
+NGC 6921
+0.61±0.09
+2.13±0.05
+38.25±0.05
+22.44±0.25
+0.7
+ID71
+MCG+04-48-002
+0.58±0.09
+2.36±0.05
+38.70±0.05
+21.68±0.10
+0.6
+ID72
+II Zw 096/IRAS F20550+1655 SE
+0.77±0.07
+2.65±0.06
+39.23±0.05
+21.18±0.05
+3.1
+ID73
+ESO 286−19
+0.24±0.10
+2.82±0.07
+39.32±0.06
+21.20±0.06
+2.2
+ID74
+NGC 7130
+0.38±0.05
+2.09±0.04
+39.19±0.03
+21.74±0.08
+1.3
+ID75
+NGC 7469/IC 5283
+0.53±0.08
+2.37±0.05
+39.19±0.04
+21.56±0.09
+0.4
+ID76
+NGC 7469
+0.50±0.08
+2.42±0.05
+39.17±0.04
+21.51±0.09
+0.5
+ID77
+IC 5283
+0.86±0.09
+2.72±0.06
+38.02±0.05
+21.38±0.17
+1.1
+ID78
+ESO 148−2
+0.47±0.16
+2.81±0.08
+39.30±0.06
+21.22±0.08
+2.4
+ID79
+NGC 7591
+0.46±0.09
+2.57±0.05
+38.64±0.05
+21.46±0.06
+2.1
+ID80
+NGC 7674/MCG+01-59-081
+0.43±0.06
+1.73±0.05
+39.75±0.05
+22.36±0.11
+0.8
+ID81
+NGC 7674
+0.5(f)
+1.84±0.07
+39.60±0.06
+22.23±0.11
+0.6
+ID82
+MCG+01-59-081
+0.5(f)
+3.21±0.08
+37.39±0.06
+20.92±0.09
+0.6
+ID83
+NGC 7679/NGC 7682
+0.32±0.08
+2.21±0.05
+39.02±0.04
+21.82±0.05
+1.5
+ID84
+NGC 7679
+0.44±0.09
+2.51±0.05
+38.70±0.04
+21.51±0.05
+1.0
+ID85
+NGC 7682
+0.21±0.07
+1.29±0.05
+38.72±0.04
+22.78±0.23
+1.5
+Note—Comments: (1–2) ID and object name; (3) radio spectral index of the power-law synchrotron emission.
+The symbol “(f)” means that the value is fixed; (4) the far-IR/radio correlation coefficient; (5) rest-frame radio
+1.4 GHz luminosity; (6) radio-excess parameter qexcess = log(L1.4GHz/SFR); (7) reduced χ2 for the combination
+of the radio fitting and UV-to-IR SED decomposition.
+(This table is available in its entirety in machine-readable form.)
+
+54
+Yamada et al.
+Table A4. Summary of the logarithmic AGN luminosities
+ID
+Name
+L6,AGN
+L12,t
+L12,p
+L12,AGN
+L12,nuc
+LX,unabs
+L2keV,unabs
+L2500,disk
+αOX
+(1)
+(2)
+(3)
+(4)
+(5)
+(6)
+(7)
+(8)
+(9)
+(10)
+(11)
+ID01
+NGC 34
+43.14
+43.46
+43.70
+43.89
+43.10
+41.90+0.10
+−0.10
+41.63
+43.07
+−1.55
+ID05
+ESO 350−38
+43.23
+43.87
+42.93
+43.92
+· · ·
+· · ·
+· · ·
+43.84
+· · ·
+ID06
+NGC 232/NGC 235
+43.01
+43.59
+· · ·
+43.59
+· · ·
+43.28+0.18
+−0.16
+42.98
+43.24
+−1.10
+ID08
+NGC 235
+42.68
+43.25
+· · ·
+43.25
+43.29
+43.28+0.18
+−0.16
+42.97
+42.84
+−0.95
+ID09
+MCG+12-02-001
+42.54
+43.15
+43.09
+43.42
+· · ·
+41.75+0.33
+−0.08
+41.48
+42.88
+−1.54
+ID11
+NGC 833/NGC 835
+42.49
+42.77
+43.32
+43.43
+· · ·
+42.33+0.28
+−0.24
+42.04
+42.54
+−1.19
+ID12
+NGC 833
+41.37
+41.95
+· · ·
+41.95
+· · ·
+41.99+0.25
+−0.24
+41.78
+41.51
+−0.89
+ID13
+NGC 835
+42.31
+42.89
+42.75
+43.13
+· · ·
+42.06+0.13
+−0.03
+41.67
+42.59
+−1.35
+ID16
+NGC 1068
+43.54
+43.93
+44.52
+44.62
+43.80
+43.34+0.07
+−0.08
+· · ·
+43.96
+· · ·
+ID17
+UGC 2608/UGC 2612
+43.84
+44.48
+· · ·
+44.48
+· · ·
+43.59+0.19
+−0.25
+43.48
+44.55
+−1.41
+ID18
+UGC 2608
+43.49
+44.12
+· · ·
+44.12
+· · ·
+43.59+0.19
+−0.25
+43.33
+44.26
+−1.36
+ID20
+NGC 1275†
+43.88
+44.43
+43.10
+44.45
+44.21
+· · ·
+43.19
+43.84
+−1.25
+ID21
+NGC 1365
+42.79
+43.23
+43.44
+43.65
+42.51
+41.90+0.01
+−0.01
+41.71
+42.65
+−1.36
+ID23
+CGCG 468-002W/CGCG 468-002E
+42.98
+43.55
+42.39
+43.58
+· · ·
+42.84+0.04
+−0.03
+42.49
+43.14
+−1.25
+ID24
+CGCG 468-002W
+42.44
+42.97
+42.83
+43.21
+· · ·
+42.84+0.04
+−0.03
+42.51
+42.64
+−1.05
+ID26
+IRAS F05189−2524
+44.38
+44.92
+43.89
+44.95
+44.87
+43.42+0.01
+−0.02
+43.30
+44.60
+−1.50
+ID27
+IRAS F06076−2139/
+42.94
+43.55
+43.50
+43.82
+· · ·
+42.18+0.15
+−0.14
+41.92
+43.14
+−1.47
+2MASS 06094601−2140312
+ID28
+NGC 2623
+42.77
+43.37
+42.11
+43.39
+43.61
+40.90+0.11
+−0.11
+40.64
+43.00
+−1.91
+ID29
+ESO 060−IG016 West/East
+43.60
+44.14
+· · ·
+44.14
+· · ·
+41.94+0.07
+−0.08
+41.69
+43.73
+−1.78
+ID30
+IRAS F08572+3915
+44.04
+44.70
+44.79
+45.05
+45.13
+41.77+0.06
+−0.07
+41.52
+44.61
+−2.19
+ID31
+UGC 5101
+43.51
+44.05
+42.97
+44.08
+44.35
+43.15+0.25
+−0.15
+42.77
+43.72
+−1.36
+ID38
+ESO 374−IG032
+43.39
+43.93
+43.43
+44.05
+· · ·
+· · ·
+· · ·
+43.28
+· · ·
+ID41
+NGC 3690 West/East
+44.04
+44.70
+42.89
+44.70
+· · ·
+42.66+0.34
+−0.32
+42.55
+43.80
+−1.48
+ID44
+NGC 4418/MCG+00-32-013
+42.33
+43.11
+43.55
+43.68
+· · ·
+· · ·
+· · ·
+43.32
+· · ·
+ID45
+NGC 4418
+42.24
+42.75
+43.49
+43.56
+43.70
+· · ·
+· · ·
+42.89
+· · ·
+ID47
+Mrk 231
+44.60
+45.20
+44.92
+45.38
+· · ·
+42.65+0.02
+−0.02
+42.28
+44.71
+−1.93
+ID48
+NGC 4922S/NGC 4922N
+43.39
+44.02
+42.86
+44.05
+· · ·
+42.00+0.20
+−0.18
+41.74
+43.52
+−1.68
+ID50
+IRAS 13120−5453
+43.29
+43.94
+43.00
+43.99
+· · ·
+42.17+0.59
+−0.11
+41.91
+43.88
+−1.76
+ID52
+MCG−03-34-064
+43.49
+43.95
+44.18
+44.38
+44.00
+43.27+0.06
+−0.07
+43.08
+43.53
+−1.17
+ID53
+NGC 5135
+42.18
+42.82
+42.04
+42.89
+43.23
+43.30+0.42
+−0.26
+43.01
+42.90
+−0.96
+ID54
+Mrk 266B/Mrk 266A
+43.07
+43.56
+43.69
+43.93
+· · ·
+· · ·
+42.71
+43.17
+−1.18
+ID55
+Mrk 273
+43.41
+43.94
+42.91
+43.98
+· · ·
+43.07+0.21
+−0.21
+42.78
+43.73
+−1.36
+ID56
+IRAS F14348−1447
+43.33
+44.05
+43.27
+44.12
+· · ·
+42.70+0.93
+−0.40
+42.46
+44.07
+−1.62
+ID58
+IC 4518A/IC 4518B
+43.14
+43.39
+43.81
+43.95
+43.54
+42.83+0.06
+−0.08
+42.55
+42.93
+−1.14
+ID60
+Arp 220W/Arp 220E
+43.10
+43.70
+43.64
+43.97
+· · ·
+41.59+0.02
+−0.02
+41.33
+43.38
+−1.79
+ID61
+NGC 6240S/NGC 6240N
+43.45
+44.01
+43.52
+44.14
+· · ·
+· · ·
+43.57
+43.42
+−0.94
+ID62
+NGC 6285/NGC 6286
+42.10
+42.94
+42.20
+43.01
+· · ·
+42.01+1.21
+−0.23
+41.64
+42.98
+−1.51
+ID64
+NGC 6286
+41.71
+42.54
+41.96
+42.64
+· · ·
+42.01+1.21
+−0.23
+41.63
+42.80
+−1.45
+ID65
+IRAS F17138−1017
+43.32
+43.92
+42.80
+43.95
+· · ·
+41.68+0.09
+−0.06
+41.41
+43.27
+−1.71
+ID69
+NGC 6921/MCG+04-48-002
+42.96
+43.52
+· · ·
+43.52
+· · ·
+42.96+0.40
+−0.46
+42.64
+43.12
+−1.19
+ID70
+NGC 6921
+41.48
+42.47
+· · ·
+42.47
+· · ·
+42.80+0.37
+−0.44
+42.49
+42.48
+−1.00
+ID71
+MCG+04-48-002
+42.80
+43.37
+· · ·
+43.37
+· · ·
+42.44+0.15
+−0.15
+42.12
+43.02
+−1.34
+ID74
+NGC 7130
+42.91
+43.71
+42.75
+43.75
+43.18
+42.87+0.31
+−0.25
+42.55
+43.58
+−1.39
+ID75
+NGC 7469/IC 5283
+43.76
+44.35
+43.20
+44.38
+· · ·
+43.26+0.03
+−0.02
+43.06
+43.85
+−1.30
+ID76
+NGC 7469
+43.63
+44.21
+43.07
+44.24
+43.83
+43.26+0.03
+−0.02
+43.07
+43.84
+−1.29
+ID78
+ESO 148−2
+43.65
+44.29
+43.35
+44.34
+· · ·
+42.38+0.24
+−0.28
+42.13
+44.25
+−1.81
+ID80
+NGC 7674/MCG+01-59-081
+44.04
+44.58
+42.55
+44.59
+· · ·
+42.59+0.33
+−0.23
+42.29
+43.73
+−1.55
+ID81
+NGC 7674
+44.03
+44.54
+43.53
+44.58
+44.26
+42.59+0.33
+−0.23
+42.28
+43.71
+−1.55
+Table A4 continued
+
+55
+Table A4 (continued)
+ID
+Name
+L6,AGN
+L12,t
+L12,p
+L12,AGN
+L12,nuc
+LX,unabs
+L2keV,unabs
+L2500,disk
+αOX
+(1)
+(2)
+(3)
+(4)
+(5)
+(6)
+(7)
+(8)
+(9)
+(10)
+(11)
+ID83
+NGC 7679/NGC 7682
+42.67
+43.16
+43.47
+43.65
+· · ·
+42.49+0.08
+−0.07
+42.21
+42.70
+−1.19
+ID84
+NGC 7679
+42.58
+42.96
+43.34
+43.49
+42.74
+42.34+0.06
+−0.04
+42.06
+42.47
+−1.16
+ID85
+NGC 7682
+41.05
+42.13
+· · ·
+42.13
+· · ·
+41.94+0.06
+−0.06
+41.68
+41.94
+−1.00
+Note—Comments: (1–2) ID and object name; (3) logarithmic rest-frame 6 µm luminosity of AGN (torus and polar dust) component (L6,AGN);
+(4)–(6) logarithmic rest-frame 12 µm luminosities of torus component (L12,t), polar component (L12,p), and both components (L12,AGN); (7)
+logarithmic nuclear 12 µm luminosity (L12,nuc) referred from Asmus et al. (2014, 2015); (8)–(9) logarithmic unabsorbed (absorption-corrected)
+AGN luminosities in the rest-frame 2–10 keV (LX,unabs) and 2 keV bands (L2keV,unabs); (10) logarithmic extinction-corrected intrinsic AGN disk
+luminosity in the rest-frame 2500 ˚
+A band (L2500,disk); (11) X-ray to optical spectral index computed by αOX ≡ log(L′′
+2keV/L′′
+2500)/log(ν2keV/ν2500),
+where L′′
+2keV = L2keV,unabs/ν2keV and L′′
+2500 = L2500,disk/ν2500.
+† Large fractions of the mid-IR and X-ray luminosities in NGC 1275 could be explained by the jet emission (e.g., Hitomi Collaboration et al. 2018;
+Rani et al. 2018).
+(This table is available in its entirety in machine-readable form.)
+
+56
+Yamada et al.
+Table A5. Summary of the Extinction, AGN Luminosities, and Polar Dust Sizes
+ID
+Name
+N (LOS)
+H
+A(LOS)
+V ,torus
+A(LOS)
+V ,polar
+logLtorus
+logLpolar
+logLAGN,int
+logMBH
+logλEdd
+logRpolar
+logR(mir/io/mo)
+(1022 cm−2)
+(mag)
+(mag)
+(erg s−1)
+(erg s−1)
+(erg s−1)
+(M⊙)
+(pc)
+(pc)
+(1)
+(2)
+(3)
+(4)
+(5)
+(6)
+(7)
+(8)
+(9)
+(10)
+(11)
+(12)
+ID01
+NGC 34
+50.3+10.3
+−9.9
+108.3±32.0
+0.2±0.4
+43.54±0.16
+43.53±0.16
+43.84±0.16
+7.82
+−2.08±0.16
+1.67±0.40
+· · · /· · · /· · ·
+ID05
+ESO 350−38
+· · ·
+346.6±58.5
+0
+43.96±0.04
+44.30±0.04
+44.62±0.04
+· · ·
+· · ·
+2.71±0.02
+· · · /· · · /· · ·
+ID06
+NGC 232/NGC 235
+51.4+8.3
+−6.1
+106.7±32.3
+· · ·
+43.75±0.02
+· · ·
+44.01±0.02
+8.20
+−2.29±0.02
+· · ·
+· · · /· · · /· · ·
+ID08
+NGC 235
+51.4+8.3
+−6.1
+99.4±33.7
+· · ·
+43.35±0.03
+· · ·
+43.61±0.03
+8.20
+−2.69±0.03
+· · ·
+· · · /· · · /· · ·
+ID09
+MCG+12-02-001
+707.5+268.4
+−277.1
+110.3±31.5
+1.7±0.9
+43.33±0.14
+43.48±0.16
+43.66±0.15
+7.04
+−1.48±0.15
+1.55±0.32
+· · · /· · · /· · ·
+ID11
+NGC 833/NGC 835
+· · ·
+17.4±6.2
+1.7±0.9
+42.91±0.07
+43.17±0.04
+43.31±0.06
+· · ·
+· · ·
+1.21±0.31
+· · · /· · · /· · ·
+ID12
+NGC 833
+26.1+1.2
+−1.1
+16.2±6.4
+· · ·
+41.95±0.17
+· · ·
+42.28±0.17
+8.61
+−4.43±0.17
+· · ·
+· · · /· · · /· · ·
+ID13
+NGC 835
+29.8+0.8
+−1.5
+18.2±5.9
+0.5±0.8
+42.99±0.08
+43.12±0.07
+43.37±0.08
+7.85
+−2.58±0.08
+1.30±0.31
+· · · /· · · /· · ·
+ID16
+NGC 1068
+∼1000
+664.8±278.0
+0
+44.04±0.07
+44.49±0.05
+44.74±0.07
+7.35
+−0.71±0.07
+1.65±0.04
+1.73/· · · /2.00
+ID17
+UGC 2608/UGC 2612
+540+700
+−310
+436.8±209.2
+· · ·
+44.52±0.09
+· · ·
+45.33±0.09
+7.64
+−0.42±0.09
+· · ·
+· · · /· · · /· · ·
+ID18
+UGC 2608
+540+700
+−310
+447.1±220.0
+· · ·
+44.22±0.16
+· · ·
+45.04±0.17
+7.64
+−0.71±0.17
+· · ·
+· · · /· · · /· · ·
+ID20
+NGC 1275†
+· · ·
+0.1±0.1
+2.5±0.1
+44.46±0.02
+44.48±0.02
+44.62±0.02
+· · ·
+· · ·
+2.70±0.01
+· · · /· · · /· · ·
+ID21
+NGC 1365
+∼10
+0.1±0.1
+2.5±0.1
+43.28±0.02
+43.30±0.02
+43.43±0.02
+8.13
+−2.80±0.02
+1.07±0.13
+1.74/· · · /· · ·
+ID23
+CGCG 468-002W/CGCG 468-002E
+1.5+0.1
+−0.1
+16.2±6.4
+0.2±0.1
+43.55±0.12
+43.64±0.12
+43.91±0.12
+7.67
+−1.86±0.12
+2.07±0.34
+· · · /· · · /· · ·
+ID24
+CGCG 468-002W
+1.5+0.1
+−0.1
+16.9±6.3
+0.2±0.2
+43.05±0.10
+43.15±0.13
+43.41±0.10
+7.67
+−2.36±0.10
+1.52±0.28
+· · · /· · · /· · ·
+ID26
+IRAS F05189−2524
+7.5+0.1
+−0.1
+8.0±0.5
+2.5±0.1
+44.96±0.02
+45.27±0.02
+45.38±0.02
+7.94
+−0.66±0.02
+3.08±0.01
+· · · /3.48/2.28
+ID27
+IRAS F06076−2139/
+42.2+24.0
+−12.0
+107.7±31.7
+1.7±0.9
+43.59±0.08
+43.73±0.10
+43.92±0.08
+7.30
+−1.48±0.08
+1.97±0.24
+· · · /· · · /· · ·
+2MASS 06094601−2140312
+ID28
+NGC 2623
+6.0+4.5
+−2.1
+119.3±23.9
+0.2±0.1
+43.47±0.02
+43.45±0.02
+43.77±0.02
+7.62
+−1.95±0.02
+2.28±0.06
+· · · /· · · /· · ·
+ID29
+ESO 060−IG016 West/East
+8.4+4.0
+−2.9
+91.9±35.7
+· · ·
+44.25±0.02
+· · ·
+44.51±0.02
+7.79
+−1.38±0.02
+· · ·
+· · · /· · · /· · ·
+ID30
+IRAS F08572+3915
+84.6+129.3
+−28.3
+417.9±199.3
+0
+44.72±0.07
+45.05±0.06
+45.39±0.06
+7.48
+−0.19±0.06
+2.38±0.28
+· · · /3.30/2.91
+ID31
+UGC 5101
+96.3+4.3
+−1.6
+8.9±3.2
+0.9±0.2
+44.11±0.08
+44.35±0.08
+44.50±0.08
+8.17
+−1.77±0.08
+2.64±0.10
+· · · /· · · /· · ·
+ID38
+ESO 374−IG032
+· · ·
+0.1±0.1
+0.2±0.2
+43.95±0.03
+43.75±0.07
+44.05±0.04
+· · ·
+· · ·
+1.77±0.32
+· · · /· · · /· · ·
+ID41
+NGC 3690 West/East
+302.6+60.6
+−49.7
+161.0±56.9
+1.8±1.0
+44.69±0.16
+44.07±0.19
+44.57±0.17
+7.09
+−0.62±0.17
+2.12±0.45
+· · · /· · · /· · ·
+ID44
+NGC 4418/MCG+00-32-013
+· · ·
+991.4±86.0
+0
+43.38±0.03
+43.90±0.03
+44.10±0.03
+· · ·
+· · ·
+1.95±0.01
+· · · /· · · /· · ·
+ID45
+NGC 4418
+· · ·
+695.0±238.8
+0
+42.97±0.02
+43.47±0.02
+43.67±0.02
+· · ·
+· · ·
+1.39±0.01
+· · · /· · · /2.76
+ID47
+Mrk 231
+8.5+0.2
+−0.2
+202.3±83.7
+1.3±0.9
+45.21±0.11
+45.23±0.11
+45.49±0.10
+7.92
+−0.53±0.10
+2.39±0.36
+· · · /3.48/2.78
+ID48
+NGC 4922S/NGC 4922N
+75.9+285.1
+−21.6
+93.1±37.0
+1.2±0.6
+43.98±0.12
+44.11±0.12
+44.30±0.12
+7.79
+−1.59±0.12
+2.18±0.38
+· · · /· · · /· · ·
+ID50
+IRAS 13120−5453
+164.8+21.6
+−20.5
+413.0±183.4
+0
+43.99±0.06
+44.37±0.06
+44.66±0.06
+8.43
+−1.87±0.06
+2.72±0.07
+· · · /2.48/2.25
+ID52
+MCG−03-34-064
+98.4+2.8
+−2.4
+55.3±23.1
+2.5±0.2
+43.97±0.04
+44.14±0.04
+44.30±0.04
+7.95
+−1.75±0.04
+1.67±0.11
+2.33/· · · /· · ·
+ID53
+NGC 5135
+670+1660
+−280
+548.1±228.5
+0
+42.86±0.21
+43.48±0.20
+43.68±0.21
+7.77
+−2.19±0.21
+1.85±0.52
+2.11/2.63/· · ·
+ID54
+Mrk 266B/Mrk 266A
+700/6.8
+111.9±30.2
+0.3±0.5
+43.65±0.10
+43.64±0.09
+43.95±0.10
+· · ·
+· · ·
+1.64±0.31
+· · · /· · · /· · ·
+ID55
+Mrk 273
+49.6+5.5
+−2.8
+14.4±6.5
+2.4±0.3
+44.09±0.13
+44.40±0.13
+44.51±0.13
+8.35
+−1.94±0.13
+2.64±0.10
+· · · /3.60/2.74
+ID56
+IRAS F14348−1447
+128.3+95.0
+−55.4
+602.6±277.5
+0
+44.15±0.15
+44.61±0.18
+44.84±0.17
+7.84
+−1.10±0.17
+2.79±0.15
+· · · /· · · /2.55
+ID58
+IC 4518A/IC 4518B
+17.1+0.5
+−0.9
+90.9±37.4
+1.2±1.0
+43.39±0.27
+43.48±0.27
+43.70±0.26
+7.53
+−1.93±0.26
+1.53±0.41
+2.29/· · · /· · ·
+Table A5 continued
+
+57
+Table A5 (continued)
+ID
+Name
+N (LOS)
+H
+A(LOS)
+V ,torus
+A(LOS)
+V ,polar
+logLtorus
+logLpolar
+logLAGN,int
+logMBH
+logλEdd
+logRpolar
+logR(mir/io/mo)
+(1022 cm−2)
+(mag)
+(mag)
+(erg s−1)
+(erg s−1)
+(erg s−1)
+(M⊙)
+(pc)
+(pc)
+(1)
+(2)
+(3)
+(4)
+(5)
+(6)
+(7)
+(8)
+(9)
+(10)
+(11)
+(12)
+ID60
+Arp 220W/Arp 220E
+1000.0+n
+−22.1
+126.3±20.0
+2.2±0.6
+43.81±0.05
+43.99±0.03
+44.15±0.04
+· · ·
+· · ·
+2.06±0.17
+· · · /· · · /· · ·
+ID61
+NGC 6240S/NGC 6240N
+147/155
+0.1±0.1
+0.2±0.2
+44.11±0.02
+43.89±0.02
+44.20±0.02
+· · ·
+· · ·
+2.12±0.28
+· · · /· · · /2.81
+ID62
+NGC 6285/NGC 6286
+140.2+26.7
+−34.6
+690.5±276.1
+0
+43.06±0.05
+43.50±0.02
+43.75±0.05
+7.98
+−2.33±0.05
+1.61±0.53
+· · · /· · · /· · ·
+ID64
+NGC 6286
+140.2+26.7
+−34.6
+694.8±277.4
+0
+42.88±0.05
+43.35±0.02
+43.58±0.05
+7.98
+−2.50±0.05
+1.55±0.54
+· · · /· · · /· · ·
+ID65
+IRAS F17138−1017
+1000.0+n
+−643.5
+93.2±38.0
+1.1±0.9
+43.72±0.20
+43.84±0.24
+44.05±0.21
+6.76
+−0.81±0.21
+2.06±0.50
+· · · /· · · /· · ·
+ID69
+NGC 6921/MCG+04-48-002
+· · ·
+98.9±35.0
+· · ·
+43.63±0.02
+· · ·
+43.89±0.02
+· · ·
+· · ·
+· · ·
+· · · /· · · /· · ·
+ID70
+NGC 6921
+173.1+27.8
+−31.9
+693.8±275.7
+· · ·
+42.55±0.03
+· · ·
+43.25±0.04
+8.11
+−2.96±0.04
+· · ·
+· · · /· · · /· · ·
+ID71
+MCG+04-48-002
+72.7+14.8
+−8.0
+104.5±32.8
+· · ·
+43.53±0.11
+· · ·
+43.80±0.11
+7.64
+−1.94±0.11
+· · ·
+· · · /· · · /· · ·
+ID74
+NGC 7130
+413.3+13.1
+−7.4
+734.0±292.7
+0
+43.78±0.18
+44.05±0.18
+44.35±0.18
+7.89
+−1.64±0.18
+2.47±0.37
+· · · /3.08/· · ·
+ID75
+NGC 7469/IC 5283
+<0.01
+0.0±0.1
+1.1±1.1
+44.36±0.11
+44.44±0.14
+44.63±0.11
+7.30
+−0.77±0.11
+2.68±0.14
+· · · /· · · /· · ·
+ID76
+NGC 7469
+<0.01
+0.0±0.1
+2.2±0.6
+44.32±0.12
+44.51±0.11
+44.62±0.11
+7.30
+−0.79±0.11
+2.68±0.13
+2.12/· · · /· · ·
+ID78
+ESO 148−2
+158.5+45.0
+−47.6
+383.4±151.1
+0
+44.36±0.10
+44.72±0.11
+45.03±0.10
+7.49
+−0.57±0.10
+2.91±0.06
+· · · /3.41/· · ·
+ID80
+NGC 7674/MCG+01-59-081
+29.6+2.5
+−1.9
+81.1±36.2
+0.2±0.2
+44.66±0.05
+43.95±0.05
+44.51±0.05
+7.99
+−1.58±0.05
+2.26±0.42
+· · · /· · · /· · ·
+ID81
+NGC 7674
+29.6+2.5
+−1.9
+69.1±33.1
+0.2±0.2
+44.64±0.06
+43.93±0.07
+44.49±0.06
+7.99
+−1.60±0.06
+2.25±0.38
+2.59/· · · /· · ·
+ID83
+NGC 7679/NGC 7682
+· · ·
+103.3±34.2
+1.5±1.0
+43.15±0.16
+43.28±0.18
+43.48±0.16
+· · ·
+· · ·
+1.42±0.39
+· · · /· · · /· · ·
+ID84
+NGC 7679
+<0.01
+0.0±0.1
+1.4±1.0
+42.98±0.15
+43.09±0.12
+43.24±0.13
+7.42
+−2.28±0.13
+1.23±0.41
+· · · /· · · /· · ·
+ID85
+NGC 7682
+38.2+6.5
+−7.0
+691.4±268.8
+· · ·
+42.67±0.22
+· · ·
+42.72±0.21
+7.48
+−2.86±0.21
+· · ·
+· · · /· · · /· · ·
+Note—Comments: (1–2) ID and object name; (3) line-of-sight hydrogen column density derived from X-ray spectral analysis (Section 3.1; Yamada
+et al. 2021); (4)–(5) line-of-sight extinction in the V
+band due to torus, A(LOS)
+V ,torus, and polar dust, A(LOS)
+V ,torus; (6)–(8) logarithmic UV-to-IR
+luminosities of torus component (Ltorus), polar dust component (Lpolar), and intrinsic AGN disk component (LAGN,int); (9) SMBH mass estimated
+from the averaged value of four independent measurements in Yamada et al. (2021); (10) logarithmic Eddington ratio (LAGN,int/LEdd). The
+Eddington luminosity is defined as LEdd = 1.26 × 1038MBH/M⊙; (11) physical size of polar dust, estimated by the polar dust temperature and
+dust sublimation radius (Section 6.5.1); (12) physical sizes of the polar dust emission detected in the mid-IR band (Rmir; Asmus 2019), radius of
+ionized outflows (Rio; Fluetsch et al. 2021), and radius of molecular outflows (Rmo; Fluetsch et al. 2019).
+† Large fractions of the X-ray and mid-IR luminosities in NGC 1275 could be explained by the jet emission (e.g., Hitomi Collaboration et al. 2018;
+Rani et al. 2018).
+(This table is available in its entirety in machine-readable form.)
+
+58
+Yamada et al.
+B. MOCK ANALYSIS
+We evaluate the constrainability of a model parame-
+ter by the “mock analysis” of X-CIGALE. This is im-
+plemented in the previous version of CIGALE (see e.g.,
+Buat et al. 2012, 2014; Ciesla et al. 2015; Lo Faro et al.
+2017; Boquien et al. 2019; Toba et al. 2020b; Yang et al.
+2020a). X-CIGALE uses the photometric data for each
+object based on the best-fit parameters. It allows the
+fluxes to vary within the uncertainties of the observa-
+tions by adding a value taken from a Gaussian distribu-
+tion with the same standard deviation as indicated by
+the photometric data.
+Figure B1 shows the results of the mock analysis
+with the best-fit values compared to the mock values
+for the main parameters in this study.
+We find that
+the mean differences (the best-fit values − mock val-
+ues) are small; ∆logM∗ = −0.01 ± 0.11, ∆logSFR =
+−0.01 ± 0.07, ∆fAGN = 0.00 ± 0.03, ∆logLAGN,int =
+0.01 ± 0.08, ∆logLpolar = −0.01 ± 0.08, and ∆Tpolar =
+0.21 ± 18.19. The deviation of the differences in Tpolar
+is relatively large but consistent with the range of 1σ
+uncertainty of each object. Therefore, we conclude that
+these quantities are not sensitive to photometric un-
+certainties thanks to the multiwavelength SED analysis
+with the self-consistent AGN model.
+C. COMPARISON WITH PREVIOUS SED STUDIES
+Here, we examine the difference in the results of this
+study and previous SED works. For the local U/LIRGs
+in GOALS sample, Shangguan et al. (2019) performed
+the IR (1–500 µm) SED fitting and Paspaliaris et al.
+(2021) carried out the UV-to-submillimeter SED analy-
+sis. Our estimates of the SFRs are well consistent with
+their works (Figure C1). Whereas, we find that their
+stellar mass is smaller than those of our results (Fig-
+ure C2). For the results of Shangguan et al. (2019), this
+may be explained by that the lack of optical photomet-
+ric data that causes the overestimation of the fraction
+of the old-stellar population. In this case, the estimates
+of the luminosity from each star become small, and thus
+the total stellar mass will be overestimated. Although it
+is unclear why are the estimates of stellar mass by Pas-
+paliaris et al. (2021) also larger, this may be affected by
+the difference in the contribution of the IR polar dust
+emission in our analysis that applies the torus parame-
+ters obtained from the X-ray fitting.
+In the left panel of Figure C3, we compare the AGN
+luminosities in this study and those in Yamada et al.
+(2021). Their AGN luminosities are estimated by the av-
+eraged values of four different methods (e.g., the [O IV]
+luminosity, bolometric AGN fraction, and IR SED anal-
+ysis). Its typical scatter is reported as ∼0.27 dex when
+we adopt the averaged value.
+Particularly, the esti-
+mates using the [O IV] luminosities may be larger than
+those from other methods, which may be due to the
+contamination from the intense starburst emission in
+U/LIRGs (but see also Yamada et al. 2019). Even if
+the intrinsic AGN luminosities given by Yamada et al.
+(2021) are adopted, the main discussion on the SFR–
+LAGN,int relation is unchanged (see Section 7.1). The
+right panel of Figure C3 presents the comparison be-
+tween the 12 µm luminosity of the AGN component
+(this study) and the nuclear 12 µm luminosities esti-
+mated with the high-spatial-resolution mid-IR images
+(Asmus 2019).
+Although there are a few differences,
+the multiwavelength SED analysis extracts the AGN
+emission that is consistent with the imaging studies.
+D. COMPARISON WITH THE RESULTS OF
+SKIRTOR MODEL
+In this study, we also performed the SED decom-
+position by using the AGN model as the SKIRTOR
+model (Stalevski et al. 2016) instead of the CLUMPY
+model. The σ values are converted from torus angular
+width (σ) of [10◦–15◦, 15◦–25◦, 25◦–70◦] to angle be-
+tween the equatorial plane and edge of the torus (∆)
+of [30◦, 40◦, 60◦], respectively. The smooth component
+in the SKIRTOR model shields the AGN disk emission
+at subparsec scales and re-radiates the strong near-IR
+emission relative to the clumpy torus model (Stalevski
+et al. 2012, 2016). In fact, the UV-to-IR SEDs of IRAS
+F08572+3915 that is not reproduced with CLUMPY
+(χ2
+red = 11.8) due to the near-IR bump (as illustrated in
+the WISE color–color diagram in Section 5.3), while it
+is well fitted with SKIRTOR model (χ2
+red = 6.7). The
+intrinsic AGN luminosities of IRAS F08572+3915 es-
+timated with CLUMPY (logLAGN,int = 45.39 ± 0.06)
+is smaller than that from SKIRTOR (45.82 ± 0.02).
+NGC 833, a stage A merger, is another outlier that
+shows the gap between the estimates with CLUMPY
+(logLAGN,int = 42.28 ± 0.17) and SKIRTOR (42.91 ±
+0.20; left panel of Figure D1), but the reason for the
+difference should be the poor photometry in the 5–
+70 µm band (see Figure E1).
+Except for the IRAS
+F08572+3915 and NGC 833, all sources show similar
+AGN luminosities with these models.
+Identically, the
+polar dust luminosities constrained with the SKIRTOR
+model are well consistent with the values with CLUMPY
+(right panel of Figure D1).
+Additionally, we investigate the polar dust temper-
+ature derived from the fits with SKIRTOR (left panel
+of Figure D2).
+Due to the strong near-IR emission,
+
+59
+8
+9
+10
+11
+12
+logM *  (Mock)
+8
+9
+10
+11
+12
+logM *  (This work)
+F13120
+Stage-A(Early)
+Stage-B(Early)
+Stage-C(Late)
+Stage-D(Late)
+Stage-N
+2
+1
+0
+1
+2
+3
+logSFR (Mock)
+2
+1
+0
+1
+2
+3
+logSFR (This work)
+Stage-A(Early)
+Stage-B(Early)
+Stage-C(Late)
+Stage-D(Late)
+Stage-N
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+fAGN (= LIR, AGN/LIR) (Mock)
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+fAGN (= LIR, AGN/LIR) (This Work)
+Stage-A(Early)
+Stage-B(Early)
+Stage-C(Late)
+Stage-D(Late)
+Stage-N
+42.5
+43.0
+43.5
+44.0
+44.5
+45.0
+45.5
+46.0
+logLAGN, int (Mock)
+42.5
+43.0
+43.5
+44.0
+44.5
+45.0
+45.5
+46.0
+logLAGN, int (This work)
+Stage-A(Early)
+Stage-B(Early)
+Stage-C(Late)
+Stage-D(Late)
+Stage-N
+43.0
+43.5
+44.0
+44.5
+45.0
+45.5
+46.0
+logLpolar (Mock)
+43.0
+43.5
+44.0
+44.5
+45.0
+45.5
+46.0
+logLpolar (This work)
+Stage-A(Early)
+Stage-B(Early)
+Stage-C(Late)
+Stage-D(Late)
+Stage-N
+100
+150
+200
+250
+Tpolar [K] (Mock)
+100
+150
+200
+250
+Tpolar [K] (This work)
+Stage-A(Early)
+Stage-B(Early)
+Stage-C(Late)
+Stage-D(Late)
+Stage-N
+Figure B1.
+Comparison of the best-fit parameters and those derived from the mock analysis for the M∗ (top left), SFR (top
+right), AGN fraction (middle left), intrinsic AGN luminosity (middle right), polar dust luminosity (bottom left), and polar
+dust temperature (bottom right). The symbols are the same in Figure 8.
+
+60
+Yamada et al.
+0.5
+1.0
+1.5
+2.0
+2.5
+3.0
+logSFR (Shangguan+19)
+0.5
+1.0
+1.5
+2.0
+2.5
+3.0
+logSFR (This work)
+Stage-A(Early)
+Stage-B(Early)
+Stage-C(Late)
+Stage-D(Late)
+Stage-N
+0.5
+1.0
+1.5
+2.0
+2.5
+3.0
+logSFR (Paspaliaris+21) 
+ 0.15
+0.5
+1.0
+1.5
+2.0
+2.5
+3.0
+logSFR (This work)
+Stage-A(Early)
+Stage-B(Early)
+Stage-C(Late)
+Stage-D(Late)
+Stage-N
+Figure C1. Left panel: comparison of SFRs estimated in Shangguan et al. (2019) and this work. Right panel: comparison
+of SFRs estimated in Paspaliaris et al. (2021) and this work. The former values are converted from Salpeter (1955) IMF to
+Chabrier (2003) IMF with 0.15 dex. The symbols are the same in Figure 8.
+9.5
+10.0
+10.5
+11.0
+11.5
+12.0
+logM *  (Shangguan+19)
+9.5
+10.0
+10.5
+11.0
+11.5
+12.0
+logM *  (This work)
+Stage-A(Early)
+Stage-B(Early)
+Stage-C(Late)
+Stage-D(Late)
+Stage-N
+9.5
+10.0
+10.5
+11.0
+11.5
+12.0
+logM *  (Paspaliaris+21) 
+ 0.24
+9.5
+10.0
+10.5
+11.0
+11.5
+12.0
+logM *  (This work)
+Stage-A(Early)
+Stage-B(Early)
+Stage-C(Late)
+Stage-D(Late)
+Stage-N
+Figure C2. Left panel: comparison of M∗ estimated in Shangguan et al. (2019) and this work. Right panel: comparison of
+M∗ estimated in Paspaliaris et al. (2021) and this work. The former values are converted from Salpeter (1955) IMF to Chabrier
+(2003) IMF with 0.24 dex. The symbols are the same in Figure 8.
+43.0
+43.5
+44.0
+44.5
+45.0
+45.5
+46.0
+46.5
+logLAGN, int (Yamada+21)
+43.0
+43.5
+44.0
+44.5
+45.0
+45.5
+46.0
+46.5
+logLAGN, int (This work)
+Stage-A(Early)
+Stage-B(Early)
+Stage-C(Late)
+Stage-D(Late)
+Stage-N
+42.5
+43.0
+43.5
+44.0
+44.5
+45.0
+45.5
+logL12, nuc (Asmus+15)
+42.5
+43.0
+43.5
+44.0
+44.5
+45.0
+45.5
+logL12, AGN (Torus + Polar)
+Stage-A(Early)
+Stage-B(Early)
+Stage-C(Late)
+Stage-D(Late)
+Stage-N
+Figure C3. Left panel: comparison of LAGN,int estimated in Yamada et al. (2021) and this work. Right panel: comparison
+with the AGN (torus and polar-dust components) 12 µm luminosity from UV-to-IR SED analysis (L12µm,AGN) and the nuclear
+12 µm luminosity (L12µm,nuc; Asmus et al. 2015).
+
+61
+42.5
+43.0
+43.5
+44.0
+44.5
+45.0
+45.5
+46.0
+logLAGN, int (SKIRTOR)
+42.5
+43.0
+43.5
+44.0
+44.5
+45.0
+45.5
+46.0
+logLAGN, int (CLUMPY)
+Stage-A(Early)
+Stage-B(Early)
+Stage-C(Late)
+Stage-D(Late)
+Stage-N
+43.0
+43.5
+44.0
+44.5
+45.0
+45.5
+logLpolar (SKIRTOR)
+43.0
+43.5
+44.0
+44.5
+45.0
+45.5
+logLpolar (CLUMPY)
+Stage-A(Early)
+Stage-B(Early)
+Stage-C(Late)
+Stage-D(Late)
+Stage-N
+Figure D1.
+Left panel:
+comparison of intrinsic (bolometric) AGN luminosities derived with the CLUMPY model and
+SKIRTOR model. Right panel: comparison of polar-dust luminosities derived with CLUMPY model and SKIRTOR model.
+The symbols are the same in Figure 8.
+100
+150
+200
+250
+300
+Tpolar (SKIRTOR)
+100
+150
+200
+250
+300
+Tpolar (CLUMPY)
+Stage-A(Early)
+Stage-B(Early)
+Stage-C(Late)
+Stage-D(Late)
+Stage-N
+42.5
+43.0
+43.5
+44.0
+44.5
+45.0
+45.5
+46.0
+logLpolar (SKIRTOR)
+100
+150
+200
+250
+Tpolar [K] (SKIRTOR)
+Stage-A(Early)
+Stage-B(Early)
+Stage-C(Late)
+Stage-D(Late)
+Stage-N
+Figure D2. Left panel: comparison of polar dust temperatures derived with the CLUMPY model and SKIRTOR model.
+Right panel: logarithmic polar-dust luminosity vs. polar-dust temperature when SKIRTOR model is adopted. The symbols
+are the same in Figure 8.
+the SEDs of the torus with SKIRTOR are flatter than
+with CLUMPY. In this case, a large part of the mid-IR
+emission will be modeled by the polar dust emission.
+This causes a larger fraction of the AGNs to show the
+signs of polar dust emission with SKIRTOR than with
+CLUMPY (Section 4.2.4).
+Hence, the polar temper-
+ature from the SKIRTOR model is larger than those
+from the CLUMPY model. In the right panel of Fig-
+ure D2, we find that the results with SKIRTOR, that
+is, the trends of the large polar dust luminosities and
+low temperatures in late mergers, are consistent with
+the results with CLUMPY. We note that the estimates
+of the polar dust features by fixing the torus param-
+eters with SKIRTOR are not self-consistent since the
+geometry of the XCLUMPY and SKIRTOR is different.
+Thus, it is preferred to adopt the results with CLUMPY
+particularly when we discuss the polar dust structure.
+E. MULTIWAVELENGTH SED DECOMPOSITION
+For convenience on the multiwavelength studies in our
+sample, we present the hard-X-ray-to-radio SEDs and
+the best fitting models at the observed frame in units of
+flux density in Figures E1. We also illustrate the SEDs
+and the best fitting models at the rest frame in units
+of luminosity in Figures E2–E10. The photometry data
+are summarized in Table E1–E3.
+
+62
+Yamada et al.
+10
+7
+10
+5
+10
+3
+10
+1
+101
+103
+105
+107
+F  (mJy)
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+10
+4
+10
+2
+100
+102
+104
+106
+Observed  ( m)
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID01_NGC_34
+ (z=0.0196, reduced ²=2.1)
+10
+7
+10
+5
+10
+3
+10
+1
+101
+103
+105
+107
+F  (mJy)
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+10
+4
+10
+2
+100
+102
+104
+106
+Observed  ( m)
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID02_MCG-02-01-052_and_MCG-02-01-051
+ (z=0.0272, reduced ²=1.4)
+10
+7
+10
+5
+10
+3
+10
+1
+101
+103
+105
+107
+F  (mJy)
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+10
+4
+10
+2
+100
+102
+104
+106
+Observed  ( m)
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID03_MCG-02-01-052
+ (z=0.0273, reduced ²=4.2)
+10
+7
+10
+5
+10
+3
+10
+1
+101
+103
+105
+107
+F  (mJy)
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+10
+4
+10
+2
+100
+102
+104
+106
+Observed  ( m)
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID04_MCG-02-01-051
+ (z=0.0271, reduced ²=0.51)
+Figure E1. The hard-X-ray-to-radio SEDs and the best fitting models in units of flux density for our sample. The bottom
+panels show the residuals in the UV-to-radio bands. The individual curves are the same as in Figure 1. Purple and red circles
+represent the observed and model flux densities, respectively. Red crosses in the X-ray band denote the NuSTAR spectra (or,
+Swift/BAT for NGC 235 and XMM-Newton/MOS for IC 5283 and MCG+01-59-081). The red arrow and green triangles mark
+the 5σ upper limit.
+(The complete figure set of 85 images is available.)
+
+63
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID01_NGC_34
+ (z=0.0196, reduced ²=2.1)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID02_MCG-02-01-052_and_MCG-02-01-051
+ (z=0.0272, reduced ²=1.4)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID03_MCG-02-01-052
+ (z=0.0273, reduced ²=4.2)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID04_MCG-02-01-051
+ (z=0.0271, reduced ²=0.51)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID05_ESO_350-38
+ (z=0.0206, reduced ²=2.1)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID06_NGC_232_and_NGC_235
+ (z=0.0224, reduced ²=1.8)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID07_NGC_232
+ (z=0.0226, reduced ²=1.8)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID08_NGC_235
+ (z=0.0222, reduced ²=2.2)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID09_MCG+12-02-001
+ (z=0.0157, reduced ²=1.7)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID10_IC_1623A_and_IC_1623B
+ (z=0.0202, reduced ²=2.7)
+Figure E2. The hard-X-ray-to-radio SEDs and the best fitting models in units of luminosity for the sample of ID=1–10. The
+bottom panels show the residuals in the UV-to-radio bands. The individual curves are the same as in Figure 1. Purple and red
+circles represent the observed and model flux densities, respectively. Red crosses in the X-ray band denote the NuSTAR spectra
+(or, Swift/BAT for NGC 235 and XMM-Newton/MOS for IC 5283 and MCG+01-59-081). The red arrow and green triangles
+mark the 5σ upper limit.
+
+64
+Yamada et al.
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID11_NGC_833_and_NGC_835
+ (z=0.0132, reduced ²=1.6)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+Observed upper limits
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID12_NGC_833
+ (z=0.0129, reduced ²=3.1)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID13_NGC_835
+ (z=0.0136, reduced ²=1.6)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID14_NGC_838
+ (z=0.0128, reduced ²=1.2)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID15_NGC_839
+ (z=0.0129, reduced ²=3.3)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID16_NGC_1068
+ (z=0.0038, reduced ²=3.6)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID17_UGC_2608_and_UGC_2612
+ (z=0.0276, reduced ²=0.82)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID18_UGC_2608
+ (z=0.0233, reduced ²=0.98)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+Observed upper limits
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID19_UGC_2612
+ (z=0.0318, reduced ²=4.0)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID20_NGC_1275
+ (z=0.0176, reduced ²=3.6)
+Figure E3. The same as in Figure E2 but for the sample of ID=11–20.
+
+65
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID21_NGC_1365
+ (z=0.0055, reduced ²=2.3)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID22_ESO_203-1
+ (z=0.0529, reduced ²=1.3)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID23_CGCG_468-002W_and_CGCG_468-002E
+ (z=0.0171, reduced ²=2.0)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+Observed upper limits
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID24_CGCG_468-002W
+ (z=0.0175, reduced ²=3.4)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+Observed upper limits
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID25_CGCG_468-002E
+ (z=0.0168, reduced ²=2.3)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID26_IRAS_F05189-2524
+ (z=0.0426, reduced ²=3.7)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID27_IRAS_F06076-2139_and_2MASS_06094601-2140312
+ (z=0.0374, reduced ²=0.69)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID28_NGC_2623
+ (z=0.0185, reduced ²=3.1)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID29_ESO_060-IG016_West_and_ESO_060-IG016_East
+ (z=0.0451, reduced ²=0.97)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID30_IRAS_F08572+3915
+ (z=0.058, reduced ²=1.1e+01)
+Figure E4. The same as in Figure E2 but for the sample of ID=21–30.
+
+66
+Yamada et al.
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID31_UGC_5101
+ (z=0.0394, reduced ²=3.3)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID32_MCG+08-18-012_and_MCG+08-18-013
+ (z=0.0255, reduced ²=2.7)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+Observed upper limits
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID33_MCG+08-18-012
+ (z=0.0252, reduced ²=3.9)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID34_MCG+08-18-013
+ (z=0.0259, reduced ²=1.3)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID35_MCG-01-26-013_and_NGC_3110
+ (z=0.0165, reduced ²=1.4)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID36_MCG-01-26-013
+ (z=0.0161, reduced ²=2.2)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID37_NGC_3110
+ (z=0.0169, reduced ²=3.4)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID38_ESO_374-IG032
+ (z=0.034, reduced ²=5.3)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID39_NGC_3256
+ (z=0.0094, reduced ²=1.3)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID40_IRAS_F10565+2448
+ (z=0.0431, reduced ²=4.8)
+Figure E5. The same as in Figure E2 but for the sample of ID=31–40.
+
+67
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID41_NGC_3690_West_and_NGC_3690_East
+ (z=0.0103, reduced ²=2.2)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID42_ESO_440-58_and_MCG-05-29-017
+ (z=0.023, reduced ²=1.5)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID43_IRAS_F12112+0305
+ (z=0.0733, reduced ²=5.2)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID44_NGC_4418_and_MCG+00-32-013
+ (z=0.00735, reduced ²=3.1)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID45_NGC_4418
+ (z=0.0073, reduced ²=3.2)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+Observed upper limits
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID46_MCG+00-32-013
+ (z=0.0074, reduced ²=4.2)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID47_Mrk_231
+ (z=0.0422, reduced ²=0.31)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID48_NGC_4922S_and_NGC_4922N
+ (z=0.0238, reduced ²=0.9)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID49_IC_860
+ (z=0.0112, reduced ²=2.8)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID50_IRAS_13120-5453
+ (z=0.0308, reduced ²=1.9)
+Figure E6. The same as in Figure E2 but for the sample of ID=41–50.
+
+68
+Yamada et al.
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID51_NGC_5104
+ (z=0.0186, reduced ²=2.6)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID52_MCG-03-34-064
+ (z=0.0165, reduced ²=2.5)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID53_NGC_5135
+ (z=0.0137, reduced ²=0.92)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID54_Mrk_266B_and_Mrk_266A
+ (z=0.0278, reduced ²=1.5)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID55_Mrk_273
+ (z=0.0378, reduced ²=2.2)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID56_IRAS_F14348-1447
+ (z=0.0827, reduced ²=2.3)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID57_IRAS_F14378-3651
+ (z=0.0681, reduced ²=2.1)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID58_IC_4518A_and_IC_4518B
+ (z=0.0159, reduced ²=0.74)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID59_IRAS_F15250+3608
+ (z=0.0552, reduced ²=2.6)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID60_Arp_220W_and_Arp_220E
+ (z=0.0181, reduced ²=5.3)
+Figure E7. The same as in Figure E2 but for the sample of ID=51–60.
+
+69
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID61_NGC_6240S_and_NGC_6240N
+ (z=0.0245, reduced ²=1.5)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID62_NGC_6285_and_NGC_6286
+ (z=0.0186, reduced ²=4.2)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID63_NGC_6285
+ (z=0.019, reduced ²=2.1)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID64_NGC_6286
+ (z=0.0183, reduced ²=5.0)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID65_IRAS_F17138-1017
+ (z=0.0173, reduced ²=4.6)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID66_IRAS_F18293-3413
+ (z=0.0182, reduced ²=0.83)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID67_IRAS_F19297-0406
+ (z=0.0857, reduced ²=1.9)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID68_NGC_6907_and_NGC_6908
+ (z=0.0104, reduced ²=2.8)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID69_NGC_6921_and_MCG+04-48-002
+ (z=0.0142, reduced ²=0.4)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID70_NGC_6921
+ (z=0.0145, reduced ²=0.7)
+Figure E8. The same as in Figure E2 but for the sample of ID=61–70.
+
+70
+Yamada et al.
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID71_MCG+04-48-002
+ (z=0.0139, reduced ²=0.63)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID72_II_Zw_096_and_IRAS_F20550+1655_SE
+ (z=0.0352, reduced ²=3.1)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID73_ESO_286-19
+ (z=0.043, reduced ²=2.2)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID74_NGC_7130
+ (z=0.0162, reduced ²=1.3)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID75_NGC_7469_and_IC_5283
+ (z=0.0162, reduced ²=0.38)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID76_NGC_7469
+ (z=0.0163, reduced ²=0.53)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID77_IC_5283
+ (z=0.016, reduced ²=1.1)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID78_ESO_148-2
+ (z=0.0446, reduced ²=2.4)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID79_NGC_7591
+ (z=0.0165, reduced ²=2.1)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID80_NGC_7674_and_MCG+01-59-081
+ (z=0.0292, reduced ²=0.77)
+Figure E9. The same as in Figure E2 but for the sample of ID=71–80.
+
+71
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID81_NGC_7674
+ (z=0.0289, reduced ²=0.56)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+Observed upper limits
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID82_MCG+01-59-081
+ (z=0.0295, reduced ²=0.63)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID83_NGC_7679_and_NGC_7682
+ (z=0.0171, reduced ²=1.5)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID84_NGC_7679
+ (z=0.0171, reduced ²=0.99)
+1037
+1039
+1041
+1043
+1045
+1047
+L  [erg/s]
+Radio nonthermal
+Stellar attenuated
+Nebular emission
+Dust emission
+AGN torus
+AGN disk
+AGN polar
+Abs-corrected AGN
+XRB + AGN scattered
+X-ray thermal
+Model spectrum
+Model fluxes
+Observed fluxes
+X-ray fluxes
+109
+1011
+1013
+1015
+1017
+1019
+Rest-frame frequency [Hz]
+1
+0
+1
+Relative
+residual
+(Obs-Mod)/Obs
+Best model for ID85_NGC_7682
+ (z=0.0171, reduced ²=1.5)
+Figure E10. The same as in Figure E2 but for the sample of ID=81–85.
+
+72
+Yamada et al.
+Table E1. Photometries of our targets in mJy (λ <1 µm)
+ID
+Name
+E(B − V )
+FUV
+NUV
+u
+v
+F uv
+g
+r
+i
+z
+F griz
+y
+152.8 nm
+231.0 nm
+481.1 nm
+615.6 nm
+750.4 nm
+866.9 nm
+P
+961.3 nm
+350.0 nm
+387.9 nm
+SM
+501.6 nm
+607.7 nm
+773.3 nm
+912.0 nm
+SM
+354.3 nm
+SD
+477.0 nm
+623.1 nm
+762.5 nm
+913.4 nm
+SD
+(1)
+(2)
+(3)
+(4)
+(5)
+(6)
+(7)
+(8)
+(9)
+(10)
+(11)
+(12)
+(13)
+(14)
+ID01
+NGC 34
+0.0268
+0.598
+1.463
+3.26
+6.72
+SM
+18.22
+23.15
+32.05
+36.59
+SM
+41.72
+0.017
+0.016
+0.77
+1.89
+1.86
+2.33
+3.27
+3.70
+4.18
+ID02
+MCG-02-01-052/
+0.0361
+· · ·
+· · ·
+2.72
+· · ·
+SD
+· · ·
+15.05
+17.16
+19.26
+P
+24.05
+MCG-02-01-051
+· · ·
+· · ·
+0.27
+· · ·
+· · ·
+1.54
+1.74
+1.93
+2.43
+ID03
+MCG-02-01-052
+0.0361
+· · ·
+· · ·
+0.84
+· · ·
+SD
+5.44
+7.15
+8.41
+8.37
+P
+8.95
+· · ·
+· · ·
+0.09
+· · ·
+0.55
+0.78
+0.85
+0.85
+0.92
+Note— Columns: (1) target ID; (2) target name; (3) Galactic extinction estimated by Schlegel et al. (1998); (4–5) FUV and NUV flux densities from
+the GALEX database (GR6plus7; Bianchi et al. 2017); (6–8) u-band and v-band flux densities, and the facility of these values, respectively. The
+adopted data of Pan-STARRS DR2 (P; e.g., Chambers et al. 2016), SkyMapper DR1 and DR2 (SK; e.g., Wolf et al. 2018), and SDSS DR16 (SD;
+Ahumada et al. 2020) are listed in Column (8); (9–13) g-band, r-band, i-band, z-band flux densities and the facility of these values, respectively;
+(14) y-band flux density from Pan-STARRS. The Pan-STARRS photometries of g–y bands are converted from the original Kron magnitudes by
+multiplying 100/90 (for 10% missing fluxes or 0.115 mag). The SkyMapper photometries of u–z bands are converted from the original Petrosian
+magnitudes by multiplying 1.127 (e.g., 0.13 mag in case of typical Sersic index of 3; Graham et al. 2005; Haan et al. 2011). The flux densities are
+in units of mJy, and corrected for the Galactic extinction of Column (3), by applying the band passes as noted in the text. Their 1σ uncertainties
+are provided in the row just below. The uncertainties of u–y bands are corrected by adding 10% of their flux densities to consider the dispersions
+among different kinds of measurements in their facilities.
+(This table is available in its entirety in machine-readable form.)
+
+73
+Table E2. Photometries of our targets in mJy (λ =1–200 µm)
+ID
+Name
+J
+H
+Ks
+W1
+W2
+S9W
+W3
+L18W
+W4
+PACS blue
+PACS green
+PACS red
+1.235 µm
+1.662 µm
+2.159 µm
+3.353 µm
+4.603 µm
+8.228 µm
+11.56 µm
+17.61 µm
+22.09 µm
+70 µm
+100 µm
+160 µm
+(1)
+(2)
+(3)
+(4)
+(5)
+(6)
+(7)
+(8)
+(9)
+(10)
+(11)
+(12)
+(13)
+(14)
+ID01
+NGC 34
+· · ·
+· · ·
+· · ·
+35.67
+30.43
+269
+245.26
+· · ·
+1240.58
+18210
+17680
+10650
+· · ·
+· · ·
+· · ·
+0.20
+0.17
+26
+1.36
+· · ·
+6.86
+840
+810
+480
+ID02
+MCG-02-01-052/
+30.59
+33.25
+31.82
+18.32
+14.43
+178
+· · ·
+517
+· · ·
+8038
+9876
+7496
+MCG-02-01-051
+0.78
+1.20
+1.34
+0.11
+0.09
+11
+· · ·
+33
+· · ·
+403
+495
+375
+ID03
+MCG-02-01-052
+13.53
+11.78
+12.44
+3.82
+2.27
+· · ·
+· · ·
+· · ·
+· · ·
+1206
+2081
+1960
+0.65
+0.96
+1.05
+0.08
+0.05
+· · ·
+· · ·
+· · ·
+· · ·
+62
+105
+99
+Note—Columns: (1) target ID; (2) target name; (3–5) J-band, H-band, and Ks-band flux densities from the 2MASS extended catalog, except for
+IRAS F17138–1017 from point-source catalog (e.g., Skrutskie et al. 2006); (6–7), (9), and (11) W1, W2, W3, and W4 flux densities from ALLWISE
+catalog (updated version on February 16, 2021; Cutri et al. 2021) respectively; (8) and (10) S9W and L18W flux densities from AKARI/IRC
+mid-IR all-sky survey (Ishihara et al. 2010); (12–14) flux densities in PACS blue, green, and red bands from Herschel/PACS data (Chu et al.
+2017); The flux densities are in units of mJy. The Galactic extinction in J, H, Ks, W1, and W2 bands are corrected by applying the band passes
+as noted in the text. Their 1σ uncertainties are provided in the row just below.
+(This table is available in its entirety in machine-readable form.)
+
+74
+Yamada et al.
+Table E3. Photometries of our targets in mJy (λ >200 µm)
+ID
+Name
+PSW
+PMW
+PLW
+NVSS
+SUMSS
+WENSS
+GLEAM1
+GLEAM2
+TGSS
+GLEAM3
+VLSSr
+VLASS
+FIRST
+250 µm
+350 µm
+500 µm
+214.1 mm
+355.6 mm
+922.1 mm
+1.50 m
+1.99 m
+2.03 m
+3.94 m
+4.06 m
+99.9 mm
+214.1 mm
+1.4 GHz
+843 MHz
+325.125 MHz
+200.5 MHz
+150.5 MHz
+147.5 MHz
+76 MHz
+73.8 MHz
+3 GHz
+1.4 GHz
+(1)
+(2)
+(3)
+(4)
+(5)
+(6)
+(7)
+(8)
+(9)
+(10)
+(11)
+(12)
+(13)
+(14)
+(15)
+ID01
+NGC 34
+3573
+1239
+339
+66.9
+· · ·
+· · ·
+162.1
+212.3
+125.5
+· · ·
+· · ·
+[41.3]
+· · ·
+214
+75
+21
+2.5
+· · ·
+· · ·
+10.6
+26.5
+14.3
+· · ·
+· · ·
+[1.5]
+· · ·
+ID02
+MCG-02-01-052/
+2862
+1209
+419
+46.7
+· · ·
+· · ·
+· · ·
+· · ·
+123.2
+· · ·
+· · ·
+[12.7]
+[33.6]
+MCG-02-01-051
+189
+81
+33
+1.8
+· · ·
+· · ·
+· · ·
+· · ·
+13.6
+· · ·
+· · ·
+[0.4]
+[3.4]
+ID03
+MCG-02-01-052
+· · ·
+· · ·
+· · ·
+4.3
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+[<0.44]
+[<1.0]
+· · ·
+· · ·
+· · ·
+0.5
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+· · ·
+Note— Columns: (1) target ID; (2) target name; (3–5) flux densities in PSW, PMW, and PLW bands from Herschel/SPIRE data (Chu et al. 2017);
+(6) 1.4 GHz flux densities from NVSS catalog (Condon et al. 1998); (7) 843 MHz flux densities from SUMSS catalog (Mauch et al. 2003); (8)
+325.125 MHz flux densities from WENSS catalog (Rengelink et al. 1997); (9–10) and (12) 200.5 MHz (170–231 MHz), 150.5 MHz (147–154 MHz),
+and 76 MHz (72–80 MHz) flux densities from GLEAM catalog (Hurley-Walker et al. 2017). The values of <5σ of GLEAM catalog are removed;
+(11) 147.5 MHz flux densities from TGSS catalog (Intema et al. 2017); (13) 73.8 MHz flux densities from VLSSr (Lane et al. 2014); (14) 3 GHz
+flux densities with the high angular resolution (2.′′5) from VLASS catalog (Gordon et al. 2021); (15) 1.4 GHz flux densities with the high angular
+resolution (5′′) from FIRST catalog (Becker et al. 1995; Helfand et al. 2015). Since the uncertainties of FIRST flux densities were not provided, we
+assume them as 10% uncertainties. The values in the square brackets for the VLASS and FIRST data represent the flux densities and uncertainties
+that are not utilized in the radio fits (see Section 3.7 in details); The flux densities are in units of mJy. Their 1σ uncertainties are provided in the
+row just below.
+(This table is available in its entirety in machine-readable form.)
+
+75
+REFERENCES
+Ahumada, R., Prieto, C. A., Almeida, A., et al. 2020,
+ApJS, 249, 3, doi: 10.3847/1538-4365/ab929e
+Aird, J., Coil, A. L., Georgakakis, A., et al. 2015, MNRAS,
+451, 1892, doi: 10.1093/mnras/stv1062
+AKARI Team. 2020, AKARI/IRC Point Source Catalogue,
+IPAC, doi: 10.26131/IRSA181
+Albareti, F. D., Allende Prieto, C., Almeida, A., et al. 2017,
+ApJS, 233, 25, doi: 10.3847/1538-4365/aa8992
+Alexander, D. M., & Hickox, R. C. 2012, NewAR, 56, 93,
+doi: 10.1016/j.newar.2011.11.003
+Allison, J. R., Sadler, E. M., & Meekin, A. M. 2014,
+MNRAS, 440, 696, doi: 10.1093/mnras/stu289
+Alonso-Herrero, A., Pereira-Santaella, M., Rieke, G. H., &
+Rigopoulou, D. 2012, ApJ, 744, 2,
+doi: 10.1088/0004-637X/744/1/2
+Alonso-Herrero, A., Garc´ıa-Burillo, S., H¨onig, S. F., et al.
+2021, A&A, 652, A99, doi: 10.1051/0004-6361/202141219
+Ananna, T. T., Urry, C. M., Ricci, C., et al. 2022, ApJL,
+939, L13, doi: 10.3847/2041-8213/ac9979
+Andonie, C., Ricci, C., Paltani, S., et al. 2022, MNRAS,
+511, 5768, doi: 10.1093/mnras/stac403
+Angl´es-Alc´azar, D., Faucher-Gigu`ere, C.-A., Quataert, E.,
+et al. 2017, MNRAS, 472, L109,
+doi: 10.1093/mnrasl/slx161
+Armus, L., Mazzarella, J. M., Evans, A. S., et al. 2009,
+PASP, 121, 559, doi: 10.1086/600092
+Arnaud, K. A. 1996, Astronomical Society of the Pacific
+Conference Series, Vol. 101, XSPEC: The First Ten
+Years, ed. G. H. Jacoby & J. Barnes, 17
+Asano, R. S., Takeuchi, T. T., Hirashita, H., & Nozawa, T.
+2013, MNRAS, 432, 637, doi: 10.1093/mnras/stt506
+Asmus, D. 2019, MNRAS, 489, 2177,
+doi: 10.1093/mnras/stz2289
+Asmus, D., Gandhi, P., H¨onig, S. F., Smette, A., & Duschl,
+W. J. 2015, MNRAS, 454, 766,
+doi: 10.1093/mnras/stv1950
+Asmus, D., H¨onig, S. F., & Gandhi, P. 2016, ApJ, 822, 109,
+doi: 10.3847/0004-637X/822/2/109
+Asmus, D., H¨onig, S. F., Gandhi, P., Smette, A., & Duschl,
+W. J. 2014, MNRAS, 439, 1648,
+doi: 10.1093/mnras/stu041
+Assef, R. J., Stern, D., Noirot, G., et al. 2018, ApJS, 234,
+23, doi: 10.3847/1538-4365/aaa00a
+Assef, R. J., Kochanek, C. S., Brodwin, M., et al. 2010,
+ApJ, 713, 970, doi: 10.1088/0004-637X/713/2/970
+Assef, R. J., Stern, D., Kochanek, C. S., et al. 2013, ApJ,
+772, 26, doi: 10.1088/0004-637X/772/1/26
+Assef, R. J., Walton, D. J., Brightman, M., et al. 2016,
+ApJ, 819, 111, doi: 10.3847/0004-637X/819/2/111
+Assef, R. J., Brightman, M., Walton, D. J., et al. 2020,
+ApJ, 897, 112, doi: 10.3847/1538-4357/ab9814
+Baba, S., Nakagawa, T., Isobe, N., & Shirahata, M. 2018,
+ApJ, 852, 83, doi: 10.3847/1538-4357/aa9f25
+Barrera-Ballesteros, J. K., S´anchez, S. F., Garc´ıa-Lorenzo,
+B., et al. 2015, A&A, 579, A45,
+doi: 10.1051/0004-6361/201425397
+Barvainis, R. 1987, ApJ, 320, 537, doi: 10.1086/165571
+Bauer, F. E., Ar´evalo, P., Walton, D. J., et al. 2015, ApJ,
+812, 116, doi: 10.1088/0004-637X/812/2/116
+Becker, R. H., White, R. L., & Helfand, D. J. 1995, ApJ,
+450, 559, doi: 10.1086/176166
+Begelman, M. C., Blandford, R. D., & Rees, M. J. 1984,
+Reviews of Modern Physics, 56, 255,
+doi: 10.1103/RevModPhys.56.255
+Behar, E. 2009, ApJ, 703, 1346,
+doi: 10.1088/0004-637X/703/2/1346
+Bell, E. F. 2003, ApJ, 586, 794, doi: 10.1086/367829
+Bianchi, L. 2020, GALEX UV Unique Source Catalogs
+(”GUVcat”) and Cross-Matches With Gaia and SDSS
+(”GUVmatch”), STScI/MAST,
+doi: 10.17909/T9-PYXY-KG53
+Bianchi, L., Herald, J., Efremova, B., et al. 2011, Ap&SS,
+335, 161, doi: 10.1007/s10509-010-0581-x
+Bianchi, L., Shiao, B., & Thilker, D. 2017, ApJS, 230, 24,
+doi: 10.3847/1538-4365/aa7053
+Bischetti, M., Piconcelli, E., Vietri, G., et al. 2017, A&A,
+598, A122, doi: 10.1051/0004-6361/201629301
+Blecha, L., Snyder, G. F., Satyapal, S., & Ellison, S. L.
+2018, MNRAS, 478, 3056, doi: 10.1093/mnras/sty1274
+Boch, T., & Fernique, P. 2014, in Astronomical Society of
+the Pacific Conference Series, Vol. 485, Astronomical
+Data Analysis Software and Systems XXIII, ed.
+N. Manset & P. Forshay, 277
+Boettcher, E., Gallagher, John S., I., Ohyama, Y., et al.
+2020, A&A, 637, A17, doi: 10.1051/0004-6361/201834880
+Bongiorno, A., Merloni, A., Brusa, M., et al. 2012, MNRAS,
+427, 3103, doi: 10.1111/j.1365-2966.2012.22089.x
+Bonnarel, F., Fernique, P., Bienaym´e, O., et al. 2000,
+A&AS, 143, 33, doi: 10.1051/aas:2000331
+Bonzini, M., Mainieri, V., Padovani, P., et al. 2015,
+MNRAS, 453, 1079, doi: 10.1093/mnras/stv1675
+Boquien, M., Burgarella, D., Roehlly, Y., et al. 2019, A&A,
+622, A103, doi: 10.1051/0004-6361/201834156
+Brinchmann, J., Charlot, S., White, S. D. M., et al. 2004,
+MNRAS, 351, 1151,
+doi: 10.1111/j.1365-2966.2004.07881.x
+Bruzual, G., & Charlot, S. 2003, MNRAS, 344, 1000,
+doi: 10.1046/j.1365-8711.2003.06897.x
+
+76
+Yamada et al.
+Buat, V., Boquien, M., Ma�lek, K., et al. 2018, A&A, 619,
+A135, doi: 10.1051/0004-6361/201833841
+Buat, V., Ciesla, L., Boquien, M., Ma�lek, K., & Burgarella,
+D. 2019, A&A, 632, A79,
+doi: 10.1051/0004-6361/201936643
+Buat, V., Noll, S., Burgarella, D., et al. 2012, A&A, 545,
+A141, doi: 10.1051/0004-6361/201219405
+Buat, V., Heinis, S., Boquien, M., et al. 2014, A&A, 561,
+A39, doi: 10.1051/0004-6361/201322081
+Buat, V., Mountrichas, G., Yang, G., et al. 2021, A&A,
+654, A93, doi: 10.1051/0004-6361/202141797
+Buchner, J., Brightman, M., Nandra, K., Nikutta, R., &
+Bauer, F. E. 2019, A&A, 629, A16,
+doi: 10.1051/0004-6361/201834771
+Burgarella, D., Buat, V., Small, T., et al. 2005, ApJL, 619,
+L63, doi: 10.1086/423894
+Burrows, D. N., Hill, J. E., Nousek, J. A., et al. 2005,
+SSRv, 120, 165, doi: 10.1007/s11214-005-5097-2
+Burtscher, L., Davies, R. I., Graci´a-Carpio, J., et al. 2016,
+A&A, 586, A28, doi: 10.1051/0004-6361/201527575
+Calzetti, D. 2001, PASP, 113, 1449, doi: 10.1086/324269
+Calzetti, D., Armus, L., Bohlin, R. C., et al. 2000, ApJ,
+533, 682, doi: 10.1086/308692
+Cameron, E. 2011, PASA, 28, 128, doi: 10.1071/AS10046
+Caramete, L. I., & Biermann, P. L. 2010, A&A, 521, A55,
+doi: 10.1051/0004-6361/200913146
+Cardelli, J. A., Clayton, G. C., & Mathis, J. S. 1989, ApJ,
+345, 245, doi: 10.1086/167900
+Casey, C. M. 2012, MNRAS, 425, 3094,
+doi: 10.1111/j.1365-2966.2012.21455.x
+Chabrier, G. 2003, PASP, 115, 763, doi: 10.1086/376392
+Chambers, K. C., Magnier, E. A., Metcalfe, N., et al. 2016,
+arXiv e-prints, arXiv:1612.05560.
+https://arxiv.org/abs/1612.05560
+Chan, C.-H., & Krolik, J. H. 2016, ApJ, 825, 67,
+doi: 10.3847/0004-637X/825/1/67
+—. 2017, ApJ, 843, 58, doi: 10.3847/1538-4357/aa76e4
+Chen, C.-T. J., Hickox, R. C., Goulding, A. D., et al. 2017,
+ApJ, 837, 145, doi: 10.3847/1538-4357/837/2/145
+Chen, X., Akiyama, M., Ichikawa, K., et al. 2020, ApJ, 900,
+51, doi: 10.3847/1538-4357/aba599
+Chiaraluce, E., Vagnetti, F., Tombesi, F., & Paolillo, M.
+2018, A&A, 619, A95, doi: 10.1051/0004-6361/201833631
+Chu, J. K., Sanders, D. B., Larson, K. L., et al. 2017,
+ApJS, 229, 25, doi: 10.3847/1538-4365/aa5d15
+Cicone, C., Maiolino, R., Sturm, E., et al. 2014, A&A, 562,
+A21, doi: 10.1051/0004-6361/201322464
+Ciesla, L., Elbaz, D., Schreiber, C., Daddi, E., & Wang, T.
+2018, A&A, 615, A61, doi: 10.1051/0004-6361/201832715
+Ciesla, L., Charmandaris, V., Georgakakis, A., et al. 2015,
+A&A, 576, A10, doi: 10.1051/0004-6361/201425252
+Clemens, M. S., Vega, O., Bressan, A., et al. 2008, A&A,
+477, 95, doi: 10.1051/0004-6361:20077224
+Clements, D. L., Pearson, C., Farrah, D., et al. 2018,
+MNRAS, 475, 2097, doi: 10.1093/mnras/stx3227
+Cohen, A. S., Lane, W. M., Cotton, W. D., et al. 2007, AJ,
+134, 1245, doi: 10.1086/520719
+Cohen, M., Wheaton, W. A., & Megeath, S. T. 2003, AJ,
+126, 1090, doi: 10.1086/376474
+Condon, J. J. 1992, ARA&A, 30, 575,
+doi: 10.1146/annurev.aa.30.090192.003043
+Condon, J. J., Cotton, W. D., Greisen, E. W., et al. 1998,
+AJ, 115, 1693, doi: 10.1086/300337
+Condon, J. J., Huang, Z. P., Yin, Q. F., & Thuan, T. X.
+1991, ApJ, 378, 65, doi: 10.1086/170407
+Cortijo-Ferrero, C., Gonz´alez Delgado, R. M., P´erez, E.,
+et al. 2017, A&A, 606, A95,
+doi: 10.1051/0004-6361/201730669
+Cutri, R. M., & et al. 2012, VizieR Online Data Catalog,
+II/311
+Cutri, R. M., Wright, E. L., Conrow, T., et al. 2021, VizieR
+Online Data Catalog, II/328
+da Cunha, E., Hodge, J. A., Casey, C. M., et al. 2021, ApJ,
+919, 30, doi: 10.3847/1538-4357/ac0ae0
+Dale, D. A., Aniano, G., Engelbracht, C. W., et al. 2012,
+ApJ, 745, 95, doi: 10.1088/0004-637X/745/1/95
+Del Moro, A., Alexander, D. M., Bauer, F. E., et al. 2016,
+MNRAS, 456, 2105, doi: 10.1093/mnras/stv2748
+Delvecchio, I., Smolˇci´c, V., Zamorani, G., et al. 2017, A&A,
+602, A3, doi: 10.1051/0004-6361/201629367
+Di Matteo, T., Springel, V., & Hernquist, L. 2005, Nature,
+433, 604, doi: 10.1038/nature03335
+D´ıaz-Santos, T., Charmandaris, V., Armus, L., et al. 2010,
+ApJ, 723, 993, doi: 10.1088/0004-637X/723/2/993
+D´ıaz-Santos, T., Armus, L., Charmandaris, V., et al. 2013,
+ApJ, 774, 68, doi: 10.1088/0004-637X/774/1/68
+—. 2014, ApJL, 788, L17,
+doi: 10.1088/2041-8205/788/1/L17
+—. 2017, ApJ, 846, 32, doi: 10.3847/1538-4357/aa81d7
+Dong, R., Greene, J. E., & Ho, L. C. 2012, ApJ, 761, 73,
+doi: 10.1088/0004-637X/761/1/73
+Dorodnitsyn, A., & Kallman, T. 2017, ApJ, 842, 43,
+doi: 10.3847/1538-4357/aa7264
+Dorodnitsyn, A., Kallman, T., & Bisnovatyi-Kogan, G. S.
+2012, ApJ, 747, 8, doi: 10.1088/0004-637X/747/1/8
+Draine, B. T. 2003, ARA&A, 41, 241,
+doi: 10.1146/annurev.astro.41.011802.094840
+Draine, B. T., & Lee, H. M. 1984, ApJ, 285, 89,
+doi: 10.1086/162480
+
+77
+Draine, B. T., & Li, A. 2007, ApJ, 657, 810,
+doi: 10.1086/511055
+Draine, B. T., & Salpeter, E. E. 1979, ApJ, 231, 438,
+doi: 10.1086/157206
+Draine, B. T., Aniano, G., Krause, O., et al. 2014, ApJ,
+780, 172, doi: 10.1088/0004-637X/780/2/172
+Efstathiou, A., Farrah, D., Afonso, J., et al. 2022, MNRAS,
+512, 5183, doi: 10.1093/mnras/stab3642
+Elbaz, D., Daddi, E., Le Borgne, D., et al. 2007, A&A, 468,
+33, doi: 10.1051/0004-6361:20077525
+Ellison, S. L., Mendel, J. T., Patton, D. R., & Scudder,
+J. M. 2013, MNRAS, 435, 3627,
+doi: 10.1093/mnras/stt1562
+Ellison, S. L., Secrest, N. J., Mendel, J. T., Satyapal, S., &
+Simard, L. 2017, MNRAS, 470, L49,
+doi: 10.1093/mnrasl/slx076
+Enoki, M., Inoue, K. T., Nagashima, M., & Sugiyama, N.
+2004, ApJ, 615, 19, doi: 10.1086/424475
+Fabian, A. C., Vasudevan, R. V., & Gandhi, P. 2008,
+MNRAS, 385, L43, doi: 10.1111/j.1745-3933.2008.00430.x
+Fabian, A. C., Vasudevan, R. V., Mushotzky, R. F.,
+Winter, L. M., & Reynolds, C. S. 2009, MNRAS, 394,
+L89, doi: 10.1111/j.1745-3933.2009.00617.x
+Farrah, D., Efstathiou, A., Afonso, J., et al. 2022, MNRAS,
+513, 4770, doi: 10.1093/mnras/stac980
+Faucher-Gigu`ere, C.-A., & Quataert, E. 2012, MNRAS,
+425, 605, doi: 10.1111/j.1365-2966.2012.21512.x
+Feruglio, C., Fiore, F., Carniani, S., et al. 2015, A&A, 583,
+A99, doi: 10.1051/0004-6361/201526020
+Finnerty, L., Larson, K., Soifer, B. T., et al. 2020, ApJ,
+905, 16, doi: 10.3847/1538-4357/abc3bf
+Fischer, T. C., Crenshaw, D. M., Kraemer, S. B., &
+Schmitt, H. R. 2013, ApJS, 209, 1,
+doi: 10.1088/0067-0049/209/1/1
+Flewelling, H. A., Magnier, E. A., Chambers, K. C., et al.
+2020, ApJS, 251, 7, doi: 10.3847/1538-4365/abb82d
+Fluetsch, A., Maiolino, R., Carniani, S., et al. 2019,
+MNRAS, 483, 4586, doi: 10.1093/mnras/sty3449
+—. 2021, MNRAS, 505, 5753, doi: 10.1093/mnras/stab1666
+Fritz, J., Franceschini, A., & Hatziminaoglou, E. 2006,
+MNRAS, 366, 767, doi: 10.1111/j.1365-2966.2006.09866.x
+Fujimoto, S., Brammer, G. B., Watson, D., et al. 2022,
+Nature, 604, 261, doi: 10.1038/s41586-022-04454-1
+Furui, S., Fukazawa, Y., Odaka, H., et al. 2016, ApJ, 818,
+164, doi: 10.3847/0004-637X/818/2/164
+Gabriel, C., Denby, M., Fyfe, D. J., et al. 2004,
+Astronomical Society of the Pacific Conference Series,
+Vol. 314, The XMM-Newton SAS - Distributed
+Development and Maintenance of a Large Science
+Analysis System: A Critical Analysis, ed. F. Ochsenbein,
+M. G. Allen, & D. Egret, 759
+Gallagher, S. C., Everett, J. E., Abado, M. M., & Keating,
+S. K. 2015, MNRAS, 451, 2991,
+doi: 10.1093/mnras/stv1126
+G´amez Rosas, V., Isbell, J. W., Jaffe, W., et al. 2022,
+Nature, 602, 403, doi: 10.1038/s41586-021-04311-7
+Gandhi, P., Horst, H., Smette, A., et al. 2009, A&A, 502,
+457, doi: 10.1051/0004-6361/200811368
+Garc´ıa-Bernete, I., Ramos Almeida, C., Landt, H., et al.
+2017, MNRAS, 469, 110, doi: 10.1093/mnras/stx795
+Garc´ıa-Bernete, I., Ramos Almeida, C., Acosta-Pulido,
+J. A., et al. 2016, MNRAS, 463, 3531,
+doi: 10.1093/mnras/stw2125
+Garc´ıa-Bernete, I., Ramos Almeida, C., Alonso-Herrero, A.,
+et al. 2019, MNRAS, 486, 4917,
+doi: 10.1093/mnras/stz1003
+Garc´ıa-Bernete, I., Gonz´alez-Mart´ın, O., Ramos Almeida,
+C., et al. 2022, A&A, 667, A140,
+doi: 10.1051/0004-6361/202244230
+Garmire, G. P., Bautz, M. W., Ford, P. G., Nousek, J. A.,
+& Ricker, Jr., G. R. 2003, in Proc. SPIE, Vol. 4851,
+X-Ray and Gamma-Ray Telescopes and Instruments for
+Astronomy., ed. J. E. Truemper & H. D. Tananbaum,
+28–44, doi: 10.1117/12.461599
+Gaskell, C. M., Goosmann, R. W., Antonucci, R. R. J., &
+Whysong, D. H. 2004, ApJ, 616, 147, doi: 10.1086/423885
+Gehrels, N., Chincarini, G., Giommi, P., et al. 2004, ApJ,
+611, 1005, doi: 10.1086/422091
+Gonz´alez-Alfonso, E., Fischer, J., Spoon, H. W. W., et al.
+2017, ApJ, 836, 11, doi: 10.3847/1538-4357/836/1/11
+Gordon, Y. A., Boyce, M. M., O’Dea, C. P., et al. 2021,
+ApJS, 255, 30, doi: 10.3847/1538-4365/ac05c0
+Goulding, A. D., Greene, J. E., Bezanson, R., et al. 2018a,
+PASJ, 70, S37, doi: 10.1093/pasj/psx135
+Goulding, A. D., Zakamska, N. L., Alexandroff, R. M.,
+et al. 2018b, ApJ, 856, 4, doi: 10.3847/1538-4357/aab040
+Graham, A. W., Driver, S. P., Petrosian, V., et al. 2005,
+AJ, 130, 1535, doi: 10.1086/444475
+Granato, G. L., Danese, L., & Franceschini, A. 1997, ApJ,
+486, 147, doi: 10.1086/304502
+Greene, J. E., Strader, J., & Ho, L. C. 2020, ARA&A, 58,
+257, doi: 10.1146/annurev-astro-032620-021835
+Griffin, M. J., Abergel, A., Abreu, A., et al. 2010, A&A,
+518, L3, doi: 10.1051/0004-6361/201014519
+
+78
+Yamada et al.
+Gruppioni, C., Berta, S., Spinoglio, L., et al. 2016,
+MNRAS, 458, 4297, doi: 10.1093/mnras/stw577
+G¨ultekin, K., Richstone, D. O., Gebhardt, K., et al. 2009,
+ApJ, 698, 198, doi: 10.1088/0004-637X/698/1/198
+Haan, S., Surace, J. A., Armus, L., et al. 2011, AJ, 141,
+100, doi: 10.1088/0004-6256/141/3/100
+Hainline, L. J., Blain, A. W., Smail, I., et al. 2011, ApJ,
+740, 96, doi: 10.1088/0004-637X/740/2/96
+Hamann, F., Zakamska, N. L., Ross, N., et al. 2017,
+MNRAS, 464, 3431, doi: 10.1093/mnras/stw2387
+Harrison, F. A., Craig, W. W., Christensen, F. E., et al.
+2013, ApJ, 770, 103, doi: 10.1088/0004-637X/770/2/103
+Helfand, D. J., White, R. L., & Becker, R. H. 2015, ApJ,
+801, 26, doi: 10.1088/0004-637X/801/1/26
+Helou, G., Soifer, B. T., & Rowan-Robinson, M. 1985,
+ApJL, 298, L7, doi: 10.1086/184556
+Hickox, R. C., & Alexander, D. M. 2018, ARA&A, 56, 625,
+doi: 10.1146/annurev-astro-081817-051803
+Hickox, R. C., Wardlow, J. L., Smail, I., et al. 2012,
+MNRAS, 421, 284, doi: 10.1111/j.1365-2966.2011.20303.x
+Hitomi Collaboration, Aharonian, F., Akamatsu, H., et al.
+2018, PASJ, 70, 13, doi: 10.1093/pasj/psx147
+H¨onig, S. F. 2019, ApJ, 884, 171,
+doi: 10.3847/1538-4357/ab4591
+H¨onig, S. F., Beckert, T., Ohnaka, K., & Weigelt, G. 2006,
+A&A, 452, 459, doi: 10.1051/0004-6361:20054622
+H¨onig, S. F., & Kishimoto, M. 2010, A&A, 523, A27,
+doi: 10.1051/0004-6361/200912676
+—. 2011, A&A, 534, A121,
+doi: 10.1051/0004-6361/201117750
+—. 2017, ApJL, 838, L20, doi: 10.3847/2041-8213/aa6838
+H¨onig, S. F., Kishimoto, M., Antonucci, R., et al. 2012,
+ApJ, 755, 149, doi: 10.1088/0004-637X/755/2/149
+H¨onig, S. F., Kishimoto, M., Tristram, K. R. W., et al.
+2013, ApJ, 771, 87, doi: 10.1088/0004-637X/771/2/87
+Hopkins, P. F., Hernquist, L., Cox, T. J., & Kereˇs, D. 2008,
+ApJS, 175, 356, doi: 10.1086/524362
+Hopkins, P. F., Somerville, R. S., Hernquist, L., et al. 2006,
+ApJ, 652, 864, doi: 10.1086/508503
+Hopkins, P. F., Strauss, M. A., Hall, P. B., et al. 2004, AJ,
+128, 1112, doi: 10.1086/423291
+Hurley-Walker, N., Callingham, J. R., Hancock, P. J., et al.
+2017, MNRAS, 464, 1146, doi: 10.1093/mnras/stw2337
+Hurley-Walker, N., Hancock, P. J., Franzen, T. M. O., et al.
+2019, PASA, 36, e047, doi: 10.1017/pasa.2019.37
+Ichikawa, K., Ricci, C., Ueda, Y., et al. 2017, ApJ, 835, 74,
+doi: 10.3847/1538-4357/835/1/74
+Ichikawa, K., Ueda, Y., Terashima, Y., et al. 2012, ApJ,
+754, 45, doi: 10.1088/0004-637X/754/1/45
+Ichikawa, K., Packham, C., Ramos Almeida, C., et al. 2015,
+ApJ, 803, 57, doi: 10.1088/0004-637X/803/2/57
+Ichikawa, K., Ricci, C., Ueda, Y., et al. 2019, ApJ, 870, 31,
+doi: 10.3847/1538-4357/aaef8f
+Ikeda, S., Awaki, H., & Terashima, Y. 2009, ApJ, 692, 608,
+doi: 10.1088/0004-637X/692/1/608
+Imanishi, M., Dudley, C. C., Maiolino, R., et al. 2007,
+ApJS, 171, 72, doi: 10.1086/513715
+Imanishi, M., Dudley, C. C., & Maloney, P. R. 2006, ApJ,
+637, 114, doi: 10.1086/498391
+Imanishi, M., Kawamuro, T., Kikuta, S., Nakano, S., &
+Saito, Y. 2020, ApJ, 891, 140,
+doi: 10.3847/1538-4357/ab733e
+Imanishi, M., Nakagawa, T., Ohyama, Y., et al. 2008,
+PASJ, 60, S489, doi: 10.1093/pasj/60.sp2.S489
+Imanishi, M., Nakagawa, T., Shirahata, M., Ohyama, Y., &
+Onaka, T. 2010, ApJ, 721, 1233,
+doi: 10.1088/0004-637X/721/2/1233
+Imanishi, M., & Saito, Y. 2014, ApJ, 780, 106,
+doi: 10.1088/0004-637X/780/1/106
+Inaba, K., Ueda, Y., Yamada, S., et al. 2022, ApJ, 939, 88,
+doi: 10.3847/1538-4357/ac97ec
+Inami, H., Armus, L., Charmandaris, V., et al. 2013, ApJ,
+777, 156, doi: 10.1088/0004-637X/777/2/156
+Inami, H., Armus, L., Matsuhara, H., et al. 2018, A&A,
+617, A130, doi: 10.1051/0004-6361/201833053
+Inayoshi, K., Ichikawa, K., & Haiman, Z. 2018, ApJL, 863,
+L36, doi: 10.3847/2041-8213/aad8ad
+Inoue, A. K. 2011, MNRAS, 415, 2920,
+doi: 10.1111/j.1365-2966.2011.18906.x
+Intema, H. T., Jagannathan, P., Mooley, K. P., & Frail,
+D. A. 2017, A&A, 598, A78,
+doi: 10.1051/0004-6361/201628536
+Isbell, J. W., Meisenheimer, K., Pott, J. U., et al. 2022,
+A&A, 663, A35, doi: 10.1051/0004-6361/202243271
+Ishibashi, W., Fabian, A. C., Ricci, C., & Celotti, A. 2018,
+MNRAS, 479, 3335, doi: 10.1093/mnras/sty1620
+Ishihara, D., Onaka, T., Kataza, H., et al. 2010, A&A, 514,
+A1, doi: 10.1051/0004-6361/200913811
+Iwasawa, K., Sanders, D. B., Teng, S. H., et al. 2011, A&A,
+529, A106, doi: 10.1051/0004-6361/201015264
+Iwasawa, K., Ricci, C., Privon, G. C., et al. 2020, A&A,
+640, A95, doi: 10.1051/0004-6361/202038513
+Izumi, T., Kawakatu, N., & Kohno, K. 2016, ApJ, 827, 81,
+doi: 10.3847/0004-637X/827/1/81
+Izumi, T., Wada, K., Fukushige, R., Hamamura, S., &
+Kohno, K. 2018, ApJ, 867, 48,
+doi: 10.3847/1538-4357/aae20b
+
+79
+Jadhav, Y., Robinson, A., Almeyda, T., Curran, R., &
+Marconi, A. 2021, MNRAS, 507, 484,
+doi: 10.1093/mnras/stab2176
+Jahnke, K., & Macci`o, A. V. 2011, ApJ, 734, 92,
+doi: 10.1088/0004-637X/734/2/92
+Jansen, F., Lumb, D., Altieri, B., et al. 2001, A&A, 365,
+L1, doi: 10.1051/0004-6361:20000036
+Jarrett, T. H., Cohen, M., Masci, F., et al. 2011, ApJ, 735,
+112, doi: 10.1088/0004-637X/735/2/112
+Jones, A. P., Tielens, A. G. G. M., Hollenbach, D. J., &
+McKee, C. F. 1994, ApJ, 433, 797, doi: 10.1086/174689
+Just, D. W., Brandt, W. N., Shemmer, O., et al. 2007, ApJ,
+665, 1004, doi: 10.1086/519990
+Kakkad, D., Groves, B., Dopita, M., et al. 2018, A&A, 618,
+A6, doi: 10.1051/0004-6361/201832790
+Kamizuka, T., Miyata, T., Sako, S., et al. 2020, in Society
+of Photo-Optical Instrumentation Engineers (SPIE)
+Conference Series, Vol. 11447, Society of Photo-Optical
+Instrumentation Engineers (SPIE) Conference Series,
+114475X, doi: 10.1117/12.2560789
+Kawaguchi, T., Yutani, N., & Wada, K. 2020, ApJ, 890,
+125, doi: 10.3847/1538-4357/ab655a
+Kawamuro, T., Ricci, C., Izumi, T., et al. 2021, ApJS, 257,
+64, doi: 10.3847/1538-4365/ac2891
+Kawamuro, T., Ricci, C., Imanishi, M., et al. 2022, ApJ,
+938, 87, doi: 10.3847/1538-4357/ac8794
+Kelly, B. C. 2007, ApJ, 665, 1489, doi: 10.1086/519947
+Kennicutt, Robert C., J. 1998, ARA&A, 36, 189,
+doi: 10.1146/annurev.astro.36.1.189
+Kim, D. C., Veilleux, S., & Sanders, D. B. 2002, ApJS, 143,
+277, doi: 10.1086/343843
+Kl¨ockner, H. R., & Baan, W. A. 2004, A&A, 419, 887,
+doi: 10.1051/0004-6361:20040998
+Kocevski, D. D., Brightman, M., Nandra, K., et al. 2015,
+ApJ, 814, 104, doi: 10.1088/0004-637X/814/2/104
+Kormendy, J., & Ho, L. C. 2013, ARA&A, 51, 511,
+doi: 10.1146/annurev-astro-082708-101811
+Koss, M., Mushotzky, R., Treister, E., et al. 2012, ApJL,
+746, L22, doi: 10.1088/2041-8205/746/2/L22
+Koss, M., Mushotzky, R., Veilleux, S., & Winter, L. 2010,
+ApJL, 716, L125, doi: 10.1088/2041-8205/716/2/L125
+Koss, M. J., Blecha, L., Bernhard, P., et al. 2018, Nature,
+563, 214, doi: 10.1038/s41586-018-0652-7
+Krolik, J. H. 1999, ApJL, 515, L73, doi: 10.1086/311979
+—. 2007, ApJ, 661, 52, doi: 10.1086/515432
+Krolik, J. H., & Begelman, M. C. 1988, ApJ, 329, 702,
+doi: 10.1086/166414
+Kron, R. G. 1980, ApJS, 43, 305, doi: 10.1086/190669
+Kroupa, P. 2001, MNRAS, 322, 231,
+doi: 10.1046/j.1365-8711.2001.04022.x
+Laha, S., Guainazzi, M., Piconcelli, E., et al. 2018, ApJ,
+868, 10, doi: 10.3847/1538-4357/aae390
+Laha, S., Markowitz, A. G., Krumpe, M., et al. 2020, ApJ,
+897, 66, doi: 10.3847/1538-4357/ab92ab
+Lane, W. M., Cotton, W. D., van Velzen, S., et al. 2014,
+MNRAS, 440, 327, doi: 10.1093/mnras/stu256
+Lansbury, G. B., Alexander, D. M., Aird, J., et al. 2017,
+ApJ, 846, 20, doi: 10.3847/1538-4357/aa8176
+Laor, A., Baldi, R. D., & Behar, E. 2019, MNRAS, 482,
+5513, doi: 10.1093/mnras/sty3098
+Laurent, O., Mirabel, I. F., Charmandaris, V., et al. 2000,
+A&A, 359, 887. https://arxiv.org/abs/astro-ph/0005376
+Lee, J. C., Hwang, H. S., Lee, M. G., Kim, M., & Lee, J. H.
+2012, ApJ, 756, 95, doi: 10.1088/0004-637X/756/1/95
+Leroy, A. K., Evans, A. S., Momjian, E., et al. 2011, ApJL,
+739, L25, doi: 10.1088/2041-8205/739/1/L25
+Liang, Y. C., Hammer, F., Flores, H., et al. 2004, A&A,
+423, 867, doi: 10.1051/0004-6361:20035740
+Linden, S. T., Song, Y., Evans, A. S., et al. 2019, ApJ, 881,
+70, doi: 10.3847/1538-4357/ab2872
+Liu, J., H¨onig, S. F., Ricci, C., & Paltani, S. 2019,
+MNRAS, 490, 4344, doi: 10.1093/mnras/stz2908
+Liu, T., Wang, J.-X., Yang, H., Zhu, F.-F., & Zhou, Y.-Y.
+2014, ApJ, 783, 106, doi: 10.1088/0004-637X/783/2/106
+Liu, Y., & Li, X. 2014, ApJ, 787, 52,
+doi: 10.1088/0004-637X/787/1/52
+Lo Faro, B., Buat, V., Roehlly, Y., et al. 2017, MNRAS,
+472, 1372, doi: 10.1093/mnras/stx1901
+Lodato, G., & Bertin, G. 2003, A&A, 398, 517,
+doi: 10.1051/0004-6361:20021672
+Longobardi, A., Arnaboldi, M., Gerhard, O., & Mihos, J. C.
+2015, A&A, 579, L3, doi: 10.1051/0004-6361/201526282
+Lonsdale, C. J., Lonsdale, C. J., Smith, H. E., & Diamond,
+P. J. 2003, ApJ, 592, 804, doi: 10.1086/375778
+Lonsdale, C. J., Cappallo, R. J., Morales, M. F., et al. 2009,
+IEEE Proceedings, 97, 1497,
+doi: 10.1109/JPROC.2009.2017564
+L´opez-Gonzaga, N., Burtscher, L., Tristram, K. R. W.,
+Meisenheimer, K., & Schartmann, M. 2016, A&A, 591,
+A47, doi: 10.1051/0004-6361/201527590
+L´opez-Gonzaga, N., & Jaffe, W. 2016, A&A, 591, A128,
+doi: 10.1051/0004-6361/201527149
+L´opez-Gonzaga, N., Jaffe, W., Burtscher, L., Tristram,
+K. R. W., & Meisenheimer, K. 2014, A&A, 565, A71,
+doi: 10.1051/0004-6361/201323002
+Lopez-Rodriguez, E., Packham, C., Jones, T. J., et al. 2017,
+MNRAS, 464, 1762, doi: 10.1093/mnras/stw2491
+Lopez-Rodriguez, E., Fuller, L., Alonso-Herrero, A., et al.
+2018, ApJ, 859, 99, doi: 10.3847/1538-4357/aabd7b
+
+80
+Yamada et al.
+Lu, N., Zhao, Y., D´ıaz-Santos, T., et al. 2017, ApJS, 230, 1,
+doi: 10.3847/1538-4365/aa6476
+Lusso, E., Comastri, A., Vignali, C., et al. 2010, A&A, 512,
+A34, doi: 10.1051/0004-6361/200913298
+Lutz, D., Maiolino, R., Spoon, H. W. W., & Moorwood,
+A. F. M. 2004, A&A, 418, 465,
+doi: 10.1051/0004-6361:20035838
+Lyu, J., & Rieke, G. H. 2018, ApJ, 866, 92,
+doi: 10.3847/1538-4357/aae075
+—. 2021, ApJ, 912, 126, doi: 10.3847/1538-4357/abee14
+Lyu, J., Rieke, G. H., & Shi, Y. 2017, ApJ, 835, 257,
+doi: 10.3847/1538-4357/835/2/257
+Madau, P., & Dickinson, M. 2014, ARA&A, 52, 415,
+doi: 10.1146/annurev-astro-081811-125615
+Magdis, G. E., Daddi, E., B´ethermin, M., et al. 2012, ApJ,
+760, 6, doi: 10.1088/0004-637X/760/1/6
+Magnier, E. A., Chambers, K. C., Flewelling, H. A., et al.
+2020a, ApJS, 251, 3, doi: 10.3847/1538-4365/abb829
+Magnier, E. A., Sweeney, W. E., Chambers, K. C., et al.
+2020b, ApJS, 251, 5, doi: 10.3847/1538-4365/abb82c
+Magnier, E. A., Schlafly, E. F., Finkbeiner, D. P., et al.
+2020c, ApJS, 251, 6, doi: 10.3847/1538-4365/abb82a
+Maiolino, R., Marconi, A., & Oliva, E. 2001, A&A, 365, 37,
+doi: 10.1051/0004-6361:20000012
+Mannucci, F., Cresci, G., Maiolino, R., Marconi, A., &
+Gnerucci, A. 2010, MNRAS, 408, 2115,
+doi: 10.1111/j.1365-2966.2010.17291.x
+Marconi, A., & Hunt, L. K. 2003, ApJL, 589, L21,
+doi: 10.1086/375804
+Martin, D. C., Fanson, J., Schiminovich, D., et al. 2005,
+ApJL, 619, L1, doi: 10.1086/426387
+Martocchia, S., Piconcelli, E., Zappacosta, L., et al. 2017,
+A&A, 608, A51, doi: 10.1051/0004-6361/201731314
+Mateos, S., Alonso-Herrero, A., Carrera, F. J., et al. 2013,
+MNRAS, 434, 941, doi: 10.1093/mnras/stt953
+—. 2012, MNRAS, 426, 3271,
+doi: 10.1111/j.1365-2966.2012.21843.x
+Mateos, S., Carrera, F. J., Alonso-Herrero, A., et al. 2015,
+MNRAS, 449, 1422, doi: 10.1093/mnras/stv299
+Matsumoto, K., Nakagawa, T., Wada, K., et al. 2022, ApJ,
+934, 25, doi: 10.3847/1538-4357/ac755f
+Mattila, S., P´erez-Torres, M., Efstathiou, A., et al. 2018,
+Science, 361, 482, doi: 10.1126/science.aao4669
+Mauch, T., Murphy, T., Buttery, H. J., et al. 2003,
+MNRAS, 342, 1117,
+doi: 10.1046/j.1365-8711.2003.06605.x
+—. 2008, VizieR Online Data Catalog, VIII/81A
+Mazzarella, J. M., Iwasawa, K., Vavilkin, T., et al. 2012,
+AJ, 144, 125, doi: 10.1088/0004-6256/144/5/125
+Meier, D. S., Turner, J. L., Beck, S. C., et al. 2010, AJ, 140,
+1294, doi: 10.1088/0004-6256/140/5/1294
+Meng, X.-M., Wu, H., Gu, Q.-S., Wang, J., & Cao, C. 2010,
+ApJ, 718, 928, doi: 10.1088/0004-637X/718/2/928
+Mills, B. Y. 1981, PASA, 4, 156,
+doi: 10.1017/S1323358000016222
+Mineo, S., Gilfanov, M., & Sunyaev, R. 2012, MNRAS, 419,
+2095, doi: 10.1111/j.1365-2966.2011.19862.x
+Mitsuda, K., Bautz, M., Inoue, H., et al. 2007, PASJ, 59,
+S1, doi: 10.1093/pasj/59.sp1.S1
+Miyaji, T., Herrera-Endoqui, M., Krumpe, M., et al. 2019,
+ApJL, 884, L10, doi: 10.3847/2041-8213/ab46bc
+Mizukoshi, S., Minezaki, T., Tsunetsugu, S., et al. 2022,
+MNRAS, 516, 2876, doi: 10.1093/mnras/stac2307
+Mizumoto, M., Izumi, T., & Kohno, K. 2019, ApJ, 871,
+156, doi: 10.3847/1538-4357/aaf814
+Mor, R., & Netzer, H. 2012, MNRAS, 420, 526,
+doi: 10.1111/j.1365-2966.2011.20060.x
+Mor, R., Netzer, H., & Elitzur, M. 2009, ApJ, 705, 298,
+doi: 10.1088/0004-637X/705/1/298
+Morganti, R., Veilleux, S., Oosterloo, T., Teng, S. H., &
+Rupke, D. 2016, A&A, 593, A30,
+doi: 10.1051/0004-6361/201628978
+Mori´c, I., Smolˇci´c, V., Kimball, A., et al. 2010, ApJ, 724,
+779, doi: 10.1088/0004-637X/724/1/779
+Morrissey, P., Conrow, T., Barlow, T. A., et al. 2007,
+ApJS, 173, 682, doi: 10.1086/520512
+Murakami, H., Baba, H., Barthel, P., et al. 2007, PASJ, 59,
+S369, doi: 10.1093/pasj/59.sp2.S369
+Murphy, E. J. 2013, ApJ, 777, 58,
+doi: 10.1088/0004-637X/777/1/58
+Murphy, E. J., Stierwalt, S., Armus, L., Condon, J. J., &
+Evans, A. S. 2013, ApJ, 768, 2,
+doi: 10.1088/0004-637X/768/1/2
+Narayanan, D., Dey, A., Hayward, C. C., et al. 2010,
+MNRAS, 407, 1701,
+doi: 10.1111/j.1365-2966.2010.16997.x
+Nenkova, M., Sirocky, M. M., Ivezi´c, ˇZ., & Elitzur, M.
+2008a, ApJ, 685, 147, doi: 10.1086/590482
+Nenkova, M., Sirocky, M. M., Nikutta, R., Ivezi´c, ˇZ., &
+Elitzur, M. 2008b, ApJ, 685, 160, doi: 10.1086/590483
+Nersesian, A., Xilouris, E. M., Bianchi, S., et al. 2019,
+A&A, 624, A80, doi: 10.1051/0004-6361/201935118
+Netzer, H. 1987, MNRAS, 225, 55,
+doi: 10.1093/mnras/225.1.55
+Netzer, H., Lutz, D., Schweitzer, M., et al. 2007, ApJ, 666,
+806, doi: 10.1086/520716
+Niklas, S., Klein, U., & Wielebinski, R. 1997, A&A, 322, 19
+Noeske, K. G., Weiner, B. J., Faber, S. M., et al. 2007,
+ApJL, 660, L43, doi: 10.1086/517926
+
+81
+Noll, S., Burgarella, D., Giovannoli, E., et al. 2009, A&A,
+507, 1793, doi: 10.1051/0004-6361/200912497
+Ogawa, S., Ueda, Y., Tanimoto, A., & Yamada, S. 2021,
+ApJ, 906, 84, doi: 10.3847/1538-4357/abccce
+Ogawa, S., Ueda, Y., Yamada, S., Tanimoto, A., &
+Kawaguchi, T. 2019, ApJ, 875, 115,
+doi: 10.3847/1538-4357/ab0e08
+Oh, K., Koss, M., Markwardt, C. B., et al. 2018, ApJS,
+235, 4, doi: 10.3847/1538-4365/aaa7fd
+Ohyama, Y., Sakamoto, K., Aalto, S., & Gallagher, John S.,
+I. 2019, ApJ, 871, 191, doi: 10.3847/1538-4357/aaf9a5
+Onken, C. A., Wolf, C., Bessell, M. S., et al. 2019, PASA,
+36, e033, doi: 10.1017/pasa.2019.27
+Panessa, F., Baldi, R. D., Laor, A., et al. 2019, Nature
+Astronomy, 3, 387, doi: 10.1038/s41550-019-0765-4
+Paspaliaris, E. D., Xilouris, E. M., Nersesian, A., et al.
+2021, A&A, 649, A137,
+doi: 10.1051/0004-6361/202038605
+Pearson, W. J., Wang, L., Hurley, P. D., et al. 2018, A&A,
+615, A146, doi: 10.1051/0004-6361/201832821
+Petric, A. O., Armus, L., Howell, J., et al. 2011, ApJ, 730,
+28, doi: 10.1088/0004-637X/730/1/28
+Pfeifle, R. W., Satyapal, S., Secrest, N. J., et al. 2019, ApJ,
+875, 117, doi: 10.3847/1538-4357/ab07bc
+Pfeifle, R. W., Ricci, C., Boorman, P. G., et al. 2022, ApJS,
+261, 3, doi: 10.3847/1538-4365/ac5b65
+Pilbratt, G. L., Riedinger, J. R., Passvogel, T., et al. 2010,
+A&A, 518, L1, doi: 10.1051/0004-6361/201014759
+Poglitsch, A., Waelkens, C., Geis, N., et al. 2010, A&A,
+518, L2, doi: 10.1051/0004-6361/201014535
+Polletta, M., Tajer, M., Maraschi, L., et al. 2007, ApJ, 663,
+81, doi: 10.1086/518113
+Prevot, M. L., Lequeux, J., Maurice, E., Prevot, L., &
+Rocca-Volmerange, B. 1984, A&A, 132, 389
+Privon, G. C., Barnes, J. E., Evans, A. S., et al. 2013, ApJ,
+771, 120, doi: 10.1088/0004-637X/771/2/120
+Privon, G. C., Ricci, C., Aalto, S., et al. 2020, ApJ, 893,
+149, doi: 10.3847/1538-4357/ab8015
+Puccetti, S., Comastri, A., Bauer, F. E., et al. 2016, A&A,
+585, A157, doi: 10.1051/0004-6361/201527189
+Raftery, A. E. 1995, Sociological Methodology, 25, 111.
+http://www.jstor.org/stable/271063
+Ramos Almeida, C., P´erez Garc´ıa, A. M., Acosta-Pulido,
+J. A., & Rodr´ıguez Espinosa, J. M. 2007, AJ, 134, 2006,
+doi: 10.1086/522625
+Rani, B., Madejski, G. M., Mushotzky, R. F., Reynolds, C.,
+& Hodgson, J. A. 2018, ApJL, 866, L13,
+doi: 10.3847/2041-8213/aae48f
+Reines, A. E., & Volonteri, M. 2015, ApJ, 813, 82,
+doi: 10.1088/0004-637X/813/2/82
+R´emy-Ruyer, A., Madden, S. C., Galliano, F., et al. 2014,
+A&A, 563, A31, doi: 10.1051/0004-6361/201322803
+Rengelink, R. B., Tang, Y., de Bruyn, A. G., et al. 1997,
+A&AS, 124, 259, doi: 10.1051/aas:1997358
+Revalski, M., Crenshaw, D. M., Kraemer, S. B., et al. 2018,
+ApJ, 856, 46, doi: 10.3847/1538-4357/aab107
+Ricci, C., Bauer, F. E., Treister, E., et al. 2016, ApJ, 819,
+4, doi: 10.3847/0004-637X/819/1/4
+—. 2017a, MNRAS, 468, 1273, doi: 10.1093/mnras/stx173
+Ricci, C., Trakhtenbrot, B., Koss, M. J., et al. 2017b, ApJS,
+233, 17, doi: 10.3847/1538-4365/aa96ad
+Ricci, C., Assef, R. J., Stern, D., et al. 2017c, ApJ, 835,
+105, doi: 10.3847/1538-4357/835/1/105
+Ricci, C., Trakhtenbrot, B., Koss, M. J., et al. 2017d,
+Nature, 549, 488, doi: 10.1038/nature23906
+Ricci, C., Privon, G. C., Pfeifle, R. W., et al. 2021,
+MNRAS, 506, 5935, doi: 10.1093/mnras/stab2052
+Ricci, C., Ananna, T. T., Temple, M. J., et al. 2022, ApJ,
+938, 67, doi: 10.3847/1538-4357/ac8e67
+Rich, J. A., Kewley, L. J., & Dopita, M. A. 2015, ApJS,
+221, 28, doi: 10.1088/0067-0049/221/2/28
+Rieke, G. H., Wright, G. S., B¨oker, T., et al. 2015, PASP,
+127, 584, doi: 10.1086/682252
+Rivers, E., Risaliti, G., Walton, D. J., et al. 2015, ApJ, 804,
+107, doi: 10.1088/0004-637X/804/2/107
+Robertson, J. G. 1991, Australian Journal of Physics, 44,
+729, doi: 10.1071/PH910729
+Roseboom, I. G., Bunker, A., Sumiyoshi, M., et al. 2012,
+MNRAS, 426, 1782,
+doi: 10.1111/j.1365-2966.2012.21777.x
+Rowan-Robinson, M. 1995, MNRAS, 272, 737,
+doi: 10.1093/mnras/272.4.737
+Rupke, D. S. N., G¨ultekin, K., & Veilleux, S. 2017, ApJ,
+850, 40, doi: 10.3847/1538-4357/aa94d1
+Rupke, D. S. N., & Veilleux, S. 2013, ApJ, 768, 75,
+doi: 10.1088/0004-637X/768/1/75
+Rupke, D. S. N., Veilleux, S., & Baker, A. J. 2008, ApJ,
+674, 172, doi: 10.1086/522363
+Saintonge, A., Catinella, B., Cortese, L., et al. 2016,
+MNRAS, 462, 1749, doi: 10.1093/mnras/stw1715
+Salim, S., Boquien, M., & Lee, J. C. 2018, ApJ, 859, 11,
+doi: 10.3847/1538-4357/aabf3c
+Salim, S., & Narayanan, D. 2020, ARA&A, 58, 529,
+doi: 10.1146/annurev-astro-032620-021933
+Salpeter, E. E. 1955, ApJ, 121, 161, doi: 10.1086/145971
+Salvato, M., Hasinger, G., Ilbert, O., et al. 2009, ApJ, 690,
+1250, doi: 10.1088/0004-637X/690/2/1250
+Sanders, D. B., Mazzarella, J. M., Kim, D. C., Surace,
+J. A., & Soifer, B. T. 2003, AJ, 126, 1607,
+doi: 10.1086/376841
+
+82
+Yamada et al.
+Sanders, D. B., & Mirabel, I. F. 1996, ARA&A, 34, 749,
+doi: 10.1146/annurev.astro.34.1.749
+Santini, P., Maiolino, R., Magnelli, B., et al. 2014, A&A,
+562, A30, doi: 10.1051/0004-6361/201322835
+Satyapal, S., Ellison, S. L., McAlpine, W., et al. 2014,
+MNRAS, 441, 1297, doi: 10.1093/mnras/stu650
+Satyapal, S., Secrest, N. J., Ricci, C., et al. 2017, ApJ, 848,
+126, doi: 10.3847/1538-4357/aa88ca
+Savage, B. D., & Sembach, K. R. 1996, ARA&A, 34, 279,
+doi: 10.1146/annurev.astro.34.1.279
+Schartmann, M., Krause, M., & Burkert, A. 2011, MNRAS,
+415, 741, doi: 10.1111/j.1365-2966.2011.18751.x
+Schartmann, M., Meisenheimer, K., Camenzind, M., Wolf,
+S., & Henning, T. 2005, A&A, 437, 861,
+doi: 10.1051/0004-6361:20042363
+Schartmann, M., Wada, K., Prieto, M. A., Burkert, A., &
+Tristram, K. R. W. 2014, MNRAS, 445, 3878,
+doi: 10.1093/mnras/stu2020
+Schlafly, E. F., & Finkbeiner, D. P. 2011, ApJ, 737, 103,
+doi: 10.1088/0004-637X/737/2/103
+Schlegel, D. J., Finkbeiner, D. P., & Davis, M. 1998, ApJ,
+500, 525, doi: 10.1086/305772
+Schwarz, G. 1978, Annals of Statistics, 6, 461
+Scoville, N., Abraham, R. G., Aussel, H., et al. 2007, ApJS,
+172, 38, doi: 10.1086/516580
+Seaquist, E., Yao, L., Dunne, L., & Cameron, H. 2004,
+MNRAS, 349, 1428,
+doi: 10.1111/j.1365-2966.2004.07612.x
+Secrest, N. J., Dudik, R. P., Dorland, B. N., et al. 2015,
+ApJS, 221, 12, doi: 10.1088/0067-0049/221/1/12
+Shangguan, J., Ho, L. C., Li, R., et al. 2019, ApJ, 870, 104,
+doi: 10.3847/1538-4357/aaf21a
+Shankar, F., Salucci, P., Granato, G. L., De Zotti, G., &
+Danese, L. 2004, MNRAS, 354, 1020,
+doi: 10.1111/j.1365-2966.2004.08261.x
+Shimwell, T. W., Tasse, C., Hardcastle, M. J., et al. 2019,
+A&A, 622, A1, doi: 10.1051/0004-6361/201833559
+Skrutskie, M. F., Cutri, R. M., Stiening, R., et al. 2003,
+2MASS All-Sky Point Source Catalog, IPAC,
+doi: 10.26131/IRSA2
+—. 2006, AJ, 131, 1163, doi: 10.1086/498708
+Smith, R. N., Tombesi, F., Veilleux, S., Lohfink, A. M., &
+Luminari, A. 2019, ApJ, 887, 69,
+doi: 10.3847/1538-4357/ab4ef8
+Soltan, A. 1982, MNRAS, 200, 115,
+doi: 10.1093/mnras/200.1.115
+Speagle, J. S., Steinhardt, C. L., Capak, P. L., &
+Silverman, J. D. 2014, ApJS, 214, 15,
+doi: 10.1088/0067-0049/214/2/15
+Spoon, H. W. W., Farrah, D., Lebouteiller, V., et al. 2013,
+ApJ, 775, 127, doi: 10.1088/0004-637X/775/2/127
+Stalevski, M., Asmus, D., & Tristram, K. R. W. 2017,
+MNRAS, 472, 3854, doi: 10.1093/mnras/stx2227
+Stalevski, M., Fritz, J., Baes, M., Nakos, T., & Popovi´c,
+L. ˇC. 2012, MNRAS, 420, 2756,
+doi: 10.1111/j.1365-2966.2011.19775.x
+Stalevski, M., Ricci, C., Ueda, Y., et al. 2016, MNRAS,
+458, 2288, doi: 10.1093/mnras/stw444
+Stein, Y., Vollmer, B., Boch, T., et al. 2021, A&A, 655,
+A17, doi: 10.1051/0004-6361/202039659
+Stern, D. 2015, ApJ, 807, 129,
+doi: 10.1088/0004-637X/807/2/129
+Stern, D., Eisenhardt, P., Gorjian, V., et al. 2005, ApJ, 631,
+163, doi: 10.1086/432523
+Stern, D., Assef, R. J., Benford, D. J., et al. 2012, ApJ,
+753, 30, doi: 10.1088/0004-637X/753/1/30
+Stern, D., Lansbury, G. B., Assef, R. J., et al. 2014, ApJ,
+794, 102, doi: 10.1088/0004-637X/794/2/102
+Stierwalt, S., Armus, L., Surace, J. A., et al. 2013, ApJS,
+206, 1, doi: 10.1088/0067-0049/206/1/1
+Swarup, G. 1991, in Astronomical Society of the Pacific
+Conference Series, Vol. 19, IAU Colloq. 131: Radio
+Interferometry. Theory, Techniques, and Applications, ed.
+T. J. Cornwell & R. A. Perley, 376–380
+Swinbank, A. M., Chapman, S. C., Smail, I., et al. 2006,
+MNRAS, 371, 465, doi: 10.1111/j.1365-2966.2006.10673.x
+Tananbaum, H., Avni, Y., Branduardi, G., et al. 1979,
+ApJL, 234, L9, doi: 10.1086/183100
+Tanimoto, A., Ueda, Y., Kawamuro, T., et al. 2018, ApJ,
+853, 146, doi: 10.3847/1538-4357/aaa47c
+Tanimoto, A., Ueda, Y., Odaka, H., et al. 2019, ApJ, 877,
+95, doi: 10.3847/1538-4357/ab1b20
+—. 2020, ApJ, 897, 2, doi: 10.3847/1538-4357/ab96bc
+Tanimoto, A., Ueda, Y., Odaka, H., Yamada, S., & Ricci,
+C. 2022, ApJS, 260, 30, doi: 10.3847/1538-4365/ac5f59
+Taylor, M. B. 2006, in Astronomical Society of the Pacific
+Conference Series, Vol. 351, Astronomical Data Analysis
+Software and Systems XV, ed. C. Gabriel, C. Arviset,
+D. Ponz, & S. Enrique, 666
+Teng, S. H., Brandt, W. N., Harrison, F. A., et al. 2014,
+ApJ, 785, 19, doi: 10.1088/0004-637X/785/1/19
+Teng, S. H., Rigby, J. R., Stern, D., et al. 2015, ApJ, 814,
+56, doi: 10.1088/0004-637X/814/1/56
+Tingay, S. J., Goeke, R., Bowman, J. D., et al. 2013,
+PASA, 30, e007, doi: 10.1017/pasa.2012.007
+Toba, Y., Bae, H.-J., Nagao, T., et al. 2017a, ApJ, 850,
+140, doi: 10.3847/1538-4357/aa918a
+Toba, Y., Komugi, S., Nagao, T., et al. 2017b, ApJ, 851,
+98, doi: 10.3847/1538-4357/aa9d17
+
+83
+Toba, Y., Ueda, Y., Matsuoka, K., et al. 2019a, MNRAS,
+484, 196, doi: 10.1093/mnras/sty3523
+Toba, Y., Nagao, T., Strauss, M. A., et al. 2015, PASJ, 67,
+86, doi: 10.1093/pasj/psv057
+Toba, Y., Yamashita, T., Nagao, T., et al. 2019b, ApJS,
+243, 15, doi: 10.3847/1538-4365/ab238d
+Toba, Y., Yamada, S., Ueda, Y., et al. 2020a, ApJ, 888, 8,
+doi: 10.3847/1538-4357/ab5718
+Toba, Y., Goto, T., Oi, N., et al. 2020b, ApJ, 899, 35,
+doi: 10.3847/1538-4357/ab9cb7
+Toba, Y., Ueda, Y., Gandhi, P., et al. 2021a, ApJ, 912, 91,
+doi: 10.3847/1538-4357/abe94a
+Toba, Y., Brusa, M., Liu, T., et al. 2021b, A&A, 649, L11,
+doi: 10.1051/0004-6361/202140317
+Toba, Y., Liu, T., Urrutia, T., et al. 2022a, A&A, 661, A15,
+doi: 10.1051/0004-6361/202141547
+Toba, Y., Yamada, S., Matsubayashi, K., et al. 2022b,
+PASJ, 74, 1356, doi: 10.1093/pasj/psac073
+Tombesi, F., Mel´endez, M., Veilleux, S., et al. 2015, Nature,
+519, 436, doi: 10.1038/nature14261
+Tomczak, A. R., Quadri, R. F., Tran, K.-V. H., et al. 2016,
+ApJ, 817, 118, doi: 10.3847/0004-637X/817/2/118
+Torres-Alb`a, N., Iwasawa, K., D´ıaz-Santos, T., et al. 2018,
+A&A, 620, A140, doi: 10.1051/0004-6361/201834105
+Trakhtenbrot, B., & Netzer, H. 2010, MNRAS, 406, L35,
+doi: 10.1111/j.1745-3933.2010.00876.x
+Travascio, A., Zappacosta, L., Cantalupo, S., et al. 2020,
+A&A, 635, A157, doi: 10.1051/0004-6361/201936197
+Tristram, K. R. W., & Schartmann, M. 2011, A&A, 531,
+A99, doi: 10.1051/0004-6361/201116867
+Tristram, K. R. W., Raban, D., Meisenheimer, K., et al.
+2009, A&A, 502, 67, doi: 10.1051/0004-6361/200811607
+Tsai, C.-W., Eisenhardt, P. R. M., Jun, H. D., et al. 2018,
+ApJ, 868, 15, doi: 10.3847/1538-4357/aae698
+Tully, R. B. 1988, Nearby Galaxies Catalog. Cambridge
+Univ. Press, Cambridge
+Turner, D. G. 2011, RMxAA, 47, 127.
+https://arxiv.org/abs/1102.0347
+U, V. 2022, Universe, 8, 392, doi: 10.3390/universe8080392
+U, V., Sanders, D. B., Mazzarella, J. M., et al. 2012, ApJS,
+203, 9, doi: 10.1088/0067-0049/203/1/9
+U, V., Medling, A. M., Inami, H., et al. 2019, ApJ, 871,
+166, doi: 10.3847/1538-4357/aaf1c2
+Ueda, Y., Akiyama, M., Hasinger, G., Miyaji, T., &
+Watson, M. G. 2014, ApJ, 786, 104,
+doi: 10.1088/0004-637X/786/2/104
+Ueda, Y., Hatsukade, B., Kohno, K., et al. 2018, ApJ, 853,
+24, doi: 10.3847/1538-4357/aa9f10
+Uematsu, R., Ueda, Y., Tanimoto, A., et al. 2021, ApJ,
+913, 17, doi: 10.3847/1538-4357/abf0a2
+Vardoulaki, E., Charmandaris, V., Murphy, E. J., et al.
+2015, A&A, 574, A4, doi: 10.1051/0004-6361/201424125
+Vasudevan, R. V., & Fabian, A. C. 2007, MNRAS, 381,
+1235, doi: 10.1111/j.1365-2966.2007.12328.x
+Veilleux, S., Mel´endez, M., Tripp, T. M., Hamann, F., &
+Rupke, D. S. N. 2016, ApJ, 825, 42,
+doi: 10.3847/0004-637X/825/1/42
+Veilleux, S., Kim, D. C., Rupke, D. S. N., et al. 2009a, ApJ,
+701, 587, doi: 10.1088/0004-637X/701/1/587
+Veilleux, S., Rupke, D. S. N., Kim, D. C., et al. 2009b,
+ApJS, 182, 628, doi: 10.1088/0067-0049/182/2/628
+Veilleux, S., Mel´endez, M., Sturm, E., et al. 2013, ApJ, 776,
+27, doi: 10.1088/0004-637X/776/1/27
+Venanzi, M., H¨onig, S., & Williamson, D. 2020, ApJ, 900,
+174, doi: 10.3847/1538-4357/aba89f
+Venturi, G., Nardini, E., Marconi, A., et al. 2018, A&A,
+619, A74, doi: 10.1051/0004-6361/201833668
+Vietri, G., Misawa, T., Piconcelli, E., et al. 2022, A&A,
+668, A87, doi: 10.1051/0004-6361/202243285
+Vika, M., Driver, S. P., Cameron, E., Kelvin, L., &
+Robotham, A. 2012, MNRAS, 419, 2264,
+doi: 10.1111/j.1365-2966.2011.19881.x
+Vito, F., Brandt, W. N., Stern, D., et al. 2018, MNRAS,
+474, 4528, doi: 10.1093/mnras/stx3120
+Wada, K. 2012, ApJ, 758, 66,
+doi: 10.1088/0004-637X/758/1/66
+Wada, K., Fukushige, R., Izumi, T., & Tomisaka, K. 2018,
+ApJ, 852, 88, doi: 10.3847/1538-4357/aa9e53
+Wada, K., Papadopoulos, P. P., & Spaans, M. 2009, ApJ,
+702, 63, doi: 10.1088/0004-637X/702/1/63
+Wada, K., Schartmann, M., & Meijerink, R. 2016, ApJL,
+828, L19, doi: 10.3847/2041-8205/828/2/L19
+Waters, C. Z., Magnier, E. A., Price, P. A., et al. 2020,
+ApJS, 251, 4, doi: 10.3847/1538-4365/abb82b
+Wenger, M., Ochsenbein, F., Egret, D., et al. 2000, A&AS,
+143, 9, doi: 10.1051/aas:2000332
+Weston, M. E., McIntosh, D. H., Brodwin, M., et al. 2017,
+MNRAS, 464, 3882, doi: 10.1093/mnras/stw2620
+Williamson, D., H¨onig, S., & Venanzi, M. 2019, ApJ, 876,
+137, doi: 10.3847/1538-4357/ab17d5
+—. 2020, ApJ, 897, 26, doi: 10.3847/1538-4357/ab989e
+Willingale, R., Starling, R. L. C., Beardmore, A. P., Tanvir,
+N. R., & O’Brien, P. T. 2013, MNRAS, 431, 394,
+doi: 10.1093/mnras/stt175
+Winter, L. M., Mushotzky, R. F., Reynolds, C. S., &
+Tueller, J. 2009, ApJ, 690, 1322,
+doi: 10.1088/0004-637X/690/2/1322
+Wolf, C., Onken, C. A., Luvaul, L. C., et al. 2018, PASA,
+35, e010, doi: 10.1017/pasa.2018.5
+
+84
+Yamada et al.
+Woo, J.-H., Son, D., & Rakshit, S. 2020, ApJ, 901, 66,
+doi: 10.3847/1538-4357/abad97
+Wright, E. L., Eisenhardt, P. R. M., Mainzer, A. K., et al.
+2010, AJ, 140, 1868, doi: 10.1088/0004-6256/140/6/1868
+—. 2019, AllWISE Source Catalog, IPAC,
+doi: 10.26131/IRSA1
+Wright, G. S., Wright, D., Goodson, G. B., et al. 2015,
+PASP, 127, 595, doi: 10.1086/682253
+Wu, J., Jun, H. D., Assef, R. J., et al. 2018, ApJ, 852, 96,
+doi: 10.3847/1538-4357/aa9ff3
+Xie, Y., Ho, L. C., Zhuang, M.-Y., & Shangguan, J. 2021,
+ApJ, 910, 124, doi: 10.3847/1538-4357/abe404
+Yamada, S., Ueda, Y., Oda, S., et al. 2018, ApJ, 858, 106,
+doi: 10.3847/1538-4357/aabacb
+Yamada, S., Ueda, Y., Tanimoto, A., et al. 2021, ApJS,
+257, 61, doi: 10.3847/1538-4365/ac17f5
+—. 2019, ApJ, 876, 96, doi: 10.3847/1538-4357/ab14f0
+—. 2020, ApJ, 897, 107, doi: 10.3847/1538-4357/ab94b1
+Yang, G., Boquien, M., Buat, V., et al. 2020a, MNRAS,
+491, 740, doi: 10.1093/mnras/stz3001
+Yang, G., Boquien, M., Brandt, W. N., et al. 2022, ApJ,
+927, 192, doi: 10.3847/1538-4357/ac4971
+Yang, X., Yao, S., Yang, J., et al. 2020b, ApJ, 904, 200,
+doi: 10.3847/1538-4357/abb775
+Yoshida, M., Kawabata, K. S., & Ohyama, Y. 2011, PASJ,
+63, 493, doi: 10.1093/pasj/63.sp2.S493
+Yoshii, Y., Aoki, T., Doi, M., et al. 2010, in Society of
+Photo-Optical Instrumentation Engineers (SPIE)
+Conference Series, Vol. 7733, Ground-based and Airborne
+Telescopes III, ed. L. M. Stepp, R. Gilmozzi, & H. J.
+Hall, 773308, doi: 10.1117/12.856680
+Yu, Q., & Tremaine, S. 2002, MNRAS, 335, 965,
+doi: 10.1046/j.1365-8711.2002.05532.x
+Yuan, H. B., Liu, X. W., & Xiang, M. S. 2013, MNRAS,
+430, 2188, doi: 10.1093/mnras/stt039
+Yun, M. S., Reddy, N. A., & Condon, J. J. 2001, ApJ, 554,
+803, doi: 10.1086/323145
+Yutani, N., Toba, Y., Baba, S., & Wada, K. 2022, ApJ, 936,
+118, doi: 10.3847/1538-4357/ac87a2
+Zakamska, N. L., Hamann, F., Pˆaris, I., et al. 2016,
+MNRAS, 459, 3144, doi: 10.1093/mnras/stw718
+Zappacosta, L., Piconcelli, E., Duras, F., et al. 2018, A&A,
+618, A28, doi: 10.1051/0004-6361/201732557
+Zappacosta, L., Piconcelli, E., Giustini, M., et al. 2020,
+A&A, 635, L5, doi: 10.1051/0004-6361/201937292
+Zhang, Z., Shi, Y., Rieke, G. H., et al. 2016, ApJL, 819,
+L27, doi: 10.3847/2041-8205/819/2/L27
+Zou, F., Brandt, W. N., Vito, F., et al. 2020, MNRAS, 499,
+1823, doi: 10.1093/mnras/staa2930
+
diff --git a/TdE2T4oBgHgl3EQfCgYE/content/tmp_files/load_file.txt b/TdE2T4oBgHgl3EQfCgYE/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..59d482712f63c74d03a9fc18947b745a820e375e
--- /dev/null
+++ b/TdE2T4oBgHgl3EQfCgYE/content/tmp_files/load_file.txt
@@ -0,0 +1,11165 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf,len=11164
+page_content='Draft version January 11,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2023  Typeset using LATEX twocolumn style in AASTeX631  Hard X-Ray to Radio Multiwavelength SED Analysis of Local U/LIRGs in GOALS Sample with  Self-consistent AGN Model Including Polar-dust Component  Satoshi Yamada  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2 Yoshihiro Ueda  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2 Mart´ın Herrera-Endoqui  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3 Yoshiki Toba  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 5,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 6,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 7  Takamitsu Miyaji  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3 Shoji Ogawa  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2 Ryosuke Uematsu  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2 Atsushi Tanimoto  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8 Masatoshi Imanishi  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 9 and  Claudio Ricci  10,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 11  1RIKEN Cluster for Pioneering Research,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2-1 Hirosawa,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Wako,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Saitama 351-0198,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Japan  2Department of Astronomy,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Kyoto University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Kitashirakawa-Oiwake-cho,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Sakyo-ku,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Kyoto 606-8502,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Japan  3Instituto de Astronom´ıa sede Ensenada,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Universidad Nacional Aut´onoma de M´exico,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Km 107,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Carret.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Tij.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='-Ens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Ensenada, 22060, BC,  M´exico  4National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan  5Department of Physics, Nara Women’s University, Kitauoyanishi-machi, Nara, Nara 630-8506, Japan  6Academia Sinica Institute of Astronomy and Astrophysics, 11F of Astronomy-Mathematics Building, AS/NTU, No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1, Section 4,  Roosevelt Road, Taipei 10617, Taiwan  7Research Center for Space and Cosmic Evolution, Ehime University, 2-5 Bunkyo-cho, Matsuyama, Ehime 790-8577, Japan  8Graduate School of Science and Engineering, Kagoshima University, Kagoshima 890-0065, Japan  9Department of Astronomical Science, Graduate University for Advanced Studies (SOKENDAI), 2-21-1 Osawa, Mitaka, Tokyo 181-8588,  Japan  10N´ucleo de Astronom´ıa de la Facultad de Ingenier´ıa, Universidad Diego Portales, Av.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Ej´ercito Libertador 441, Santiago, Chile  11Kavli Institute for Astronomy and Astrophysics, Peking University, Beijing 100871, People’s Republic of China  (Received October 14, 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Revised December 6, 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Accepted January 6, 2023)  ABSTRACT  We conduct a hard X-ray to radio multiwavelength spectral energy distribution (SED) decomposition  for 57 local luminous and ultraluminous infrared galaxies (U/LIRGs) observed with Nuclear Spectro-  scopic Telescope Array and/or Swift/Burst Alert Telescope in GOALS (Armus et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2009) sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' We  modify the latest SED-fitting code X-CIGALE by implementing the infrared (IR) CLUMPY model,  allowing the multiwavelength study with the X-ray torus model (XCLUMPY) self-consistently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Adopt-  ing the torus parameters obtained by the X-ray fitting (Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021), we estimate the properties  of host galaxies, active galactic nucleus (AGN) tori, and polar dust.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The star formation rates (SFRs)  become larger with merger stage and most of them are above the main sequence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The SFRs are cor-  related with radio luminosity, indicating starburst emission is dominant in the radio band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Although  polar-dust extinction is much smaller than torus extinction, the UV-to-IR (mainly IR) polar dust lu-  minosities are ∼2 times larger than the torus ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The polar-dust temperature decreases while the  physical size, estimated by the temperature and dust sublimation radius, increases with AGN lumi-  nosity from a few tens of parsec (early mergers) to kiloparsec scales (late mergers), where the polar  dust is likely the expanding (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', evolving) dusty outflows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The comparison between SFRs and intrin-  sic AGN luminosities suggests that the starbursts occur first and AGNs arise later, and overall their  growth rates follow the simultaneous coevolution relation that can establish the local galaxy–SMBH  mass relation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' We confirm the coexistence of intense starbursts, AGNs, and large-scale outflows in late  mergers, supporting a standard AGN feedback scenario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Corresponding author: Satoshi Yamada  satoshi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='yamada@riken.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='jp  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='03613v1  [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='GA]  9 Jan 2023  ID2  Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Keywords: Infrared galaxies (790);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Active galactic nuclei (16);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' X-ray active galactic nuclei (2035);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Optical observation (1169);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Infrared photometry (792);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Radio continuum emission (1340)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' INTRODUCTION  Galaxies and supermassive black holes (SMBHs) at  their centers show a tight correlation between the masses  of bulges (Mbulge) and SMBHs (MBH), indicating that  they have coevolved by regulating each other’s growth  (see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Marconi & Hunt 2003;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Kormendy & Ho 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Due to a huge scale gap between galaxies (∼1 kpc) and  SMBHs (≪1 pc), the mechanism of their physical con-  nection has been controversial (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Hopkins et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2008;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Madau & Dickinson 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' For understanding the mech-  anism of coevolution, the merging galaxies have received  attention since the merger can extract the angular mo-  mentum of the gas and trigger obscuration and rapid ac-  cretion onto SMBHs (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Koss et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2010, 2012, 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Kocevski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Lansbury et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Ricci et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2017a, 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018, 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  According to the major merger scenario, galaxies in  the most active phase of mergers become luminous in-  frared galaxies (LIRGs;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' L8−1000µm ≥ 1011L⊙) and ul-  traluminous infrared galaxies (ULIRGs;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' L8−1000µm ≥  1012L⊙), combined as U/LIRGs (Sanders & Mirabel  1996).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Their large bolometric luminosities are derived  from the starbursts and/or active galactic nuclei (AGNs)  surrounded by gas and dust, most of which are radiated  in the infrared (IR) band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  After quenching the star-  forming activities, U/LIRGs are thought to transit to  unobscured quasars or elliptical galaxies (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Hopkins  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The AGNs in U/LIRGs are well studied in the X-  ray to radio multiwavelength bands (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', U 2022 for  a review).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  When AGNs are heavily obscured, they  radiate dimmed UV-to-near-IR emission compared to  the AGN luminosity identified in the mid-IR and X-  ray bands (see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Hickox & Alexander 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The  mid-IR studies reveal that the AGNs in U/LIRGs are  deeply buried by a large amount of gas and dust, where  even the direction of the lowest dust column-density  can be opaque to the ionizing UV photons (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Iman-  ishi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2006, 2008;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Lee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Hard X-ray observations, which are less affected  by the contamination of starburst emission, can identify  the AGNs with large hydrogen column densities (NH).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  For local U/LIRGs observed with Nuclear Spectroscopic  Telescope Array (NuSTAR;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Harrison et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2013), Ricci  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2017a, 2021) analyze the broadband X-ray spec-  tra and find the large fraction of Compton-thick (CT;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  NH > 1024 cm−2) AGNs in late mergers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  By con-  ducting the X-ray spectroscopy with the X-ray clumpy  torus model (XCLUMPY;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Tanimoto et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019), Ya-  mada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2021) present the individual torus covering  fractions, supporting the buried AGN structure in the  late mergers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2021) report that the AGNs in the fi-  nal phase of mergers show high Eddington ratios (λEdd)  and the signatures of multiphase outflows at subparsec  to kiloparsec scales: that is, ultrafast outflows (UFOs),  ionized outflows, and molecular outflows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The UFOs  are extremely fast (∼0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1–0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3c) and highly ionized winds  at ∼0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01 pc (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Tombesi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Mizumoto et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Smith et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The ionized outflows are the  fast (∼1000 km s−1) winds with a size of kiloparsecs de-  tected by optical and near-IR spectroscopy (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Rich  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Cortijo-Ferrero et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Kakkad et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Boettcher et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Fluetsch et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Molec-  ular outflows are cold gas winds on ∼400 pc with a veloc-  ity of ∼500 km s−1 discovered at far-IR and submillime-  ter wavelengths (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Spoon et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Veilleux et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Cicone et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Gonz´alez-Alfonso et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Laha et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' However, the properties of outflows in  many U/LIRGs are still unclear because these methods  using the blue-shifted emission/absorption lines have  difficulty detecting weak outflows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Therefore, the new  methods to systematically reveal the outflow properties  are necessary to present the schematic picture of the  merger-driven coevolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The observations of outflowing dust (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', H¨onig 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Venanzi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020) may be an ideal means for the sys-  tematic studies on the outflows in U/LIRGs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Recent  mid-IR observations with high spatial resolutions detect  the extended dust emission along the polar direction,  called polar dust (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Asmus et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Stalevski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' An issue at this point is that, due to the poor  understanding of the polar dust structure, it is not even  clear whether the polar dust is (1) the galactic ISM or  dust in a narrow line region (NLR) only being illumi-  nated by the AGN or (2) the “outflowing” dusty winds  launched from the inner edge of the torus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Asmus (2019)  finds a positive correlation between their physical sizes  and the Eddington ratios, supporting that the polar dust  structure may be related to the AGN activities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The  analytical model of polar dust emission has been imple-  mented into the latest multiwavelength spectral energy  distribution (SED) models (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', X-CIGALE;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Boquien  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Yang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' These models help us to  estimate the properties of polar dust (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Toba et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  3  2021a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Buat et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021), even though the degeneracy of  torus and polar dust emission will provide uncertainties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The combination of X-ray and IR observations will  become the best way to constrain the properties of po-  lar dust.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The broadband X-ray study with XCLUMPY  for several tens of Swift/Burst Alert Telescope (BAT)-  selected AGNs by Ogawa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2021) successfully con-  strains the torus covering fractions (CT).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  These esti-  mates are well consistent with the typical λEdd–CT re-  lation (Ricci et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017a), while are much smaller than  those estimated with the IR CLUMPY model (Nenkova  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2008a,b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' They indicate that the difference can  be explained by the presence of the polar dust, which  should have small effects on the obscuration in the X-  ray band but re-radiate the large IR luminosities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Thus,  the updated CLUMPY model consisting of the clumpy  torus and polar dust components will provide rich infor-  mation on polar dust by applying the torus parameters  obtained by the X-ray fitting with XCLUMPY (Yamada  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  In this study, we generate the updated CLUMPY  model that can reproduce the IR emission from the  clumpy torus and polar dust, and perform the multi-  wavelength (hard X-ray to radio) SED decomposition  for the sample of 57 local U/LIRGs in Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' We first investigate the features of multiwave-  length radiation, which are helpful to understand the  environments from the nucleus to galactic scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' This  will be incidentally useful for future works to explore  buried AGNs in U/LIRGs in the distant universe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Tak-  ing into account these results, we examine the polar dust  structures and their relation to the AGN activities, and  finally discuss the coevolution process of the galaxies,  SMBHs, and outflows in the merger phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  This paper is organized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  In Section 2  and Section 3, we show the sample and their photo-  metric data of multiwavelength observations, respec-  tively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Section 4 describes the implementation of the  updated CLUMPY model we create and the best-fit  parameters of the multiwavelength SED decomposition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Section 5 illustrates the features of multiwavelength  emission to understand the characteristics of the host  galaxies and AGNs in U/LIRGs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' In Section 6, we dis-  cuss the structure of the polar dust in U/LIRGs based  on the results of the multiwavelength SED analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Section 7 provides the discussion on the coevolution  process of galaxies, SMBHs, and outflows in U/LIRGs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The main results are summarized in Section 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' In this  paper, we adopt the cosmology of a flat universe with  H0 = 70 km s−1 Mpc−1, ΩM = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3, and ΩΛ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Throughout this paper, the uncertainties are at the 1σ  level unless otherwise stated, and the initial mass func-  tion (IMF) of Chabrier (2003) is assumed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' SAMPLE  The sample selection of 57 local U/LIRGs observed  with the hard X-ray observations is described as fol-  lows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' We focus on the Great Observatories All-sky LIRG  Survey (GOALS;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Armus et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2009), which consists  of 180 LIRGs and 22 ULIRGs in the local universe at  redshifts z < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='088.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' They are contained in the IRAS  Revised Bright Galaxy Sample (RBGS;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Sanders et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2003), a complete sample of 629 extragalactic objects  having 60 µm fluxes above 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='24 Jy at Galactic latitudes  |b| > 5◦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  These U/LIRGs have been observed in the  multiwavelength bands, by the IR telescopes of Spitzer  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Imanishi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2007;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' D´ıaz-Santos et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Pet-  ric et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Inami et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Stierwalt et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2013),  AKARI (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Imanishi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2008;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Lee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' In-  ami et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018), Herschel (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', D´ıaz-Santos et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2013,  2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Chu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Lu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017), and X-ray tele-  scopes of Chandra (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Iwasawa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Torres-  Alb`a et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018), and NuSTAR (Teng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Ricci  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017a, 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Privon et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Here, we select the same targets as in Yamada  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2021), the 57 local U/LIRGs containing 84 in-  dividual galaxies observed with the hard X-ray tele-  scopes NuSTAR and/or Swift/BAT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' According to the  detailed X-ray spectral analysis combining the available  soft X-ray observations, our targets are comprised of 40  AGNs (two unobscured AGNs, 21 obscured AGNs, 16  CT AGNs, one jet-dominated AGN), and 44 starburst-  dominant or hard X-ray–undetected sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Here, the source coordinates, redshift, merger stages,  and the projected separation between the two nuclei are  taken from Table 1 of Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Based  on high-spatial-resolution images (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Stierwalt et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2013), the merger stages are classified into five stages:  stage A (galaxy pairs before a first encounter), stage B  (post-first encounter with symmetric galaxy disks but  showing signature of tidal tails), stage C (showing some  signatures of mergers, such as tidal tails, amorphous  disks), stage D (two nuclei within a common envelope),  and stage N (no signatures of mergers or massive neigh-  bors).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' In the same manner as Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2021), we  hereafter call stage A–B galaxies as early mergers, stage  C–D as late mergers, and stage N as nonmergers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  1 When the values of the star formation rates (SFR) and stellar  masses (M∗) are referred from previous works, we correct these  values assuming Salpeter (1955) by decreasing 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='15 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='24 dex,  or values assuming Kroupa (2001) by subtracting 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='03  dex, respectively (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Santini et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Speagle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  4  Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Basic Information of our Sample  ID  IRAS Name  Object Name  z  M  D12  D12  AGN  Type  log(LIR)  IRS  (arcsec)  (kpc)  (L⊙)  (1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10)  (11)  ID01  F00085−1223  NGC 34  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0196  D  S  S  Y  Obs  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='49  Y  ID02  F00163−1039a  MCG−02-01-052/MCG−02-01-051  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0272  B  · ·  · ·  · ·  · ·  · ·  · ·  ID03  F00163−1039 N  MCG−02-01-052  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0273  B  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7  n  n  [11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='48]  n  ID04  F00163−1039 S  MCG−02-01-051  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0271  B  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7  n  n  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='48  Y  ID05  F00344−3349  ESO 350−38  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0206  C  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2  Y?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  n  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='28  Y  ID06  F00402−2349a  NGC 232/NGC 235  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0224  B  · ·  · ·  · ·  · ·  · ·  · ·  ID07  F00402−2349 W  NGC 232  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0226  B  120.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8  54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7  n  n  [11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='44]:  Y  ID08  F00402−2349 E  NGC 235  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0222  B  120.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8  54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7  Y  Obs  [11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='44]:  Y  ID09  F00506+7248  MCG+12-02-001  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0157  C  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='9  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3  Y  CT  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='50  Y  ID10  F01053−1746b  IC 1623A/IC 1623B  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0202  C  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4  n  n/n  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='71  n/Y  ID11  F02071−1023a  NGC 833/NGC 835  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0132  A  · ·  · ·  · ·  · ·  · ·  · ·  ID12  F02071−1023 W2  NGC 833  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0129  A  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3  Y  Obs  [11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05]:  Y  ID13  F02071−1023 W  NGC 835  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0136  A  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3  Y  Obs  [11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05]:  Y  ID14  F02071−1023 E  NGC 838  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0128  A  148.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  n  n  [11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05]:  Y  ID15  F02071−1023 S  NGC 839  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0129  A  148.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  n  n  [11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05]:  Y  ID16  F02401−0013  NGC 1068  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0038†  N  n  n  Y  CT  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='40  Y  ID17  F03117+4151a  UGC 2608/UGC 2612  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0276  N  · ·  · ·  · ·  · ·  · ·  · ·  ID18  F03117+4151 N  UGC 2608  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0233  N  n  n  Y  CT  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='41  Y  ID19  F03117+4151 S  UGC 2612  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0318  N  n  n  n  n  [11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='41]  Y  ID20  F03164+4119  NGC 1275  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0176  N  n  n  Y  Jet  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='26  Y  ID21  F03316−3618  NGC 1365  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0055†  N  n  n  Y  Obs  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='00  Y  ID22  F04454−4838  ESO 203−1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0529  B  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7  n  n  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='86  Y  ID23  F05054+1718a  CGCG 468-002W/CGCG 468-002E  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0171  B  · ·  · ·  · ·  · ·  · ·  · ·  ID24  F05054+1718 W  CGCG 468-002W  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0175  B  29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3  Y  Obs  [11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='22]:  Y  ID25  F05054+1718 E  CGCG 468-002E  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0168  B  29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3  n  n  [11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='22]:  Y  ID26  F05189−2524  IRAS F05189−2524  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0426  D  S  S  Y  Obs  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='16  Y  ID27  F06076−2139b  IRAS F06076−2139/  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0374  C  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2  Y  Obs/n  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='65  Y/n  2MASS 06094601−2140312  ID28  F08354+2555  NGC 2623  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0185  D  S  S  Y  Obs  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='60  Y  ID29  F08520−6850b  ESO 060−IG016 West/East  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0451  B  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6  Y  n/Obs  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='82  n/Y  ID30  F08572+3915  IRAS F08572+3915  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0580  D  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6  Y  Obs  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='16  Y  ID31  F09320+6134  UGC 5101  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0394  D  S  S  Y  Obs  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  Y  ID32  F09333+4841a  MCG+08-18-012/MCG+08-18-013  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0255  A  · ·  · ·  · ·  · ·  · ·  · ·  ID33  F09333+4841 W  MCG+08-18-012  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0252  A  65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3  33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6  n  n  [11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='34]  n  ID34  F09333+4841 E  MCG+08-18-013  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0259  A  65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3  33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6  n  n  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='34  Y  ID35  F10015−0614a  MCG−01-26-013/NGC 3110  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0165  A  · ·  · ·  · ·  · ·  · ·  · ·  ID36  F10015−0614 S  MCG−01-26-013  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0161  A  108.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8  36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  n  n  [11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='37]  n  ID37  F10015−0614 N  NGC 3110  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0169  A  108.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8  36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  n  n  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='37  Y  ID38  F10038−3338  ESO 374−IG032  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0340  D  S  S  Y?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  n  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='78  Y  ID39  F10257−4339  NGC 3256  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0094  D  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  n  n  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='64  Y  ID40  F10565+2448  IRAS F10565+2448  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0431  D  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7  n  n  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  Y  Table 1 continued  5  Table 1 (continued)  ID  IRAS Name  Object Name  z  M  D12  D12  AGN  Type  log(LIR)  IRS  (arcsec)  (kpc)  (L⊙)  (1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10)  (11)  ID41  F11257+5850b  NGC 3690 West/East  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0103  C  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6  Y  CT/n  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='93  Y/Y  ID42  F12043−3140b  ESO 440−58/MCG−05-29-017  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0230  B  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  n  n/n  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='43  Y/Y  ID43  F12112+0305  IRAS F12112+0305  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0733  D  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  n  n  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='36  Y  ID44  F12243−0036a  NGC 4418/MCG+00-32-013  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='00735  A  · ·  · ·  · ·  · ·  · ·  · ·  ID45  F12243−0036 NW  NGC 4418  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0073†  A  179.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='9  29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4  Y?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  n  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='19  Y  ID46  F12243−0036 SE  MCG+00-32-013  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0074†  A  179.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='9  29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4  n  n  [11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='19]  n  ID47  F12540+5708  Mrk 231  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0422  D  S  S  Y  Obs  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='57  Y  ID48  F12590+2934b  NGC 4922S/NGC 4922N  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0238  C  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6  Y  n/Obs  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='38  n/Y  ID49  F13126+2453  IC 860  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0112  N  n  n  n  n  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='14  Y  ID50  13120−5453  IRAS 13120−5453  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0308  D  S  S  Y  CT  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='32  Y  ID51  F13188+0036  NGC 5104  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0186  N  n  n  n  n  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='27  Y  ID52  F13197−1627  MCG−03-34-064  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0165  N  n  n  Y  Obs  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='28  Y  ID53  F13229−2934  NGC 5135  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0137  N  n  n  Y  CT  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='30  Y  ID54  F13362+4831b  Mrk 266B/Mrk 266A  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0278  B  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6  Y  CT/Obs  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='56  Y/Y  ID55  F13428+5608  Mrk 273  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0378  D  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='9  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7  Y  Obs  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='21  Y  ID56  F14348−1447  IRAS F14348−1447  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0827  D  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2  Y  CT  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='39  Y  ID57  F14378−3651  IRAS F14378−3651  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0681  D  S  S  n  Y  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='23  Y  ID58  F14544−4255b  IC 4518A/IC 4518B  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0159  B  35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  Y  Obs/n  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='23  Y/n  ID59  F15250+3608  IRAS F15250+3608  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0552  D  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8  n  n  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  Y  ID60  F15327+2340b  Arp 220W/Arp 220E  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0181  D  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4  Y  CT/n  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='28  Y(u)  ID61  F16504+0228b  NGC 6240S/NGC 6240N  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0245  D  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8  Y  CT  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='93  Y(u)  ID62  F16504+0228a  NGC 6285/NGC 6286  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0186  B  · ·  · ·  · ·  · ·  · ·  · ·  ID63  F16577+5900 N  NGC 6285  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0190  B  91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  n  n  [11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='37]  Y  ID64  F16577+5900 S  NGC 6286  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0183  B  91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  Y  CT  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='37  Y  ID65  F17138−1017  IRAS F17138−1017  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0173  D  S  S  Y  Obs  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='49  Y  ID66  F18293−3413  IRAS F18293−3413  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0182  N  S  S  n  n  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='88  Y  ID67  F19297−0406  IRAS F19297−0406  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0857  D  S  S  n  n  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='45  Y  ID68  F20221−2458b  NGC 6907/NGC 6908  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0104  B  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='9  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4  n  n/n  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11  Y/n  ID69  20264+2533a  NGC 6921/MCG+04-48-002  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0142  A  · ·  · ·  · ·  · ·  · ·  · ·  ID70  20264+2533 W  NGC 6921  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0145  A  91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4  26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  Y  CT  [11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11]  n  ID71  20264+2533 E  MCG+04-48-002  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0139  A  91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4  26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  Y  Obs  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11  Y  ID72  F20550+1655b  II Zw 096/IRAS F20550+1655 SE  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0353  C  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  n  n/n  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='94  Y/Y  ID73  F20551−4250  ESO 286−19  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0430  D  S  S  n  n  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  Y  ID74  F21453−3511  NGC 7130  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0162  N  n  n  Y  CT  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='42  Y  ID75  F23007+0836a  NGC 7469/IC 5283  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0162  A  · ·  · ·  · ·  · ·  · ·  · ·  ID76  F23007+0836 S  NGC 7469  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0163  A  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7  26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2  Y  Unobs  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='65  Y  ID77  F23007+0836 N  IC 5283  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0160  A  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7  26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2  n  n  [11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='65]  n  ID78  F23128−5919  ESO 148−2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0446  C  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='9  Y  CT  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  Y  ID79  F23157+0618  NGC 7591  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0165  N  n  n  n  n  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='12  Y  ID80  F23254+0830a  NGC 7674/MCG+01-59-081  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0292  A  · ·  · ·  · ·  · ·  · ·  · ·  Table 1 continued  6  Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Table 1 (continued)  ID  IRAS Name  Object Name  z  M  D12  D12  AGN  Type  log(LIR)  IRS  (arcsec)  (kpc)  (L⊙)  (1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10)  (11)  ID81  F23254+0830 W  NGC 7674  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0289  A  33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  Y  Obs  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='56  Y  ID82  F23254+0830 E  MCG+01-59-081  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0295  A  33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  n  n  [11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='56]  n  ID83  23262+0314a  NGC 7679/NGC 7682  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0171  A  · ·  · ·  · ·  · ·  · ·  · ·  ID84  23262+0314 W  NGC 7679  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0171  A  269.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8  93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8  Y  Unobs  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11  Y  ID85  23262+0314 E  NGC 7682  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0171  A  269.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8  93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8  Y  Obs  [11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11]  n  Note—Columns: (1) Target ID;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2) IRAS name.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' “a” marks 13 total systems of resolved pairs to our targets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' “b” marks 12 U/LIRGs (24  individual galaxies) that are too close to be separated by the Hershel PACS 70 µm images or UV-to-near-IR images;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (3) object name;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (4)  redshift from NASA/IPAC Extragalactic Database (NED);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (5) merger stage based on the high-spatial-resolution images (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Stierwalt  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2013);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (6–7) projected separation between the two nuclei in arcseconds and kiloparsecs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' S and n mean that a single nucleus is  observed in merging and nonmerging U/LIRGs, respectively;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (8) Y and n mark the presence of a hard X-ray–detected AGN or not,  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Y?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' marks AGN candidates among the hard X-ray–undetected sources identified by the multiwavelength SED analysis (see  Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (9) X-ray classification (Unobs = unobscured AGN, Obs = obscured AGN, CT = CT AGN, Jet = jet-dominant AGN,  and n = hard X-ray–undetected sources);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (10) logarithmic total IR luminosity in units of L⊙ (Armus et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Values in brackets  should be upper limits due to contamination from nearby much brighter (or equally bright with the suffix “:”) IR sources;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (11) Y and  n mark detection and nondetection with Spitzer/IRS in the 10–20 µm (SH) or 19–38 µm (LH) band, respectively (Alonso-Herrero et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Mazzarella et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Inami et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The (u) means that the two nuclei are not divided.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' All information in Column (2–11)  are referred from Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  † Throughout the paper, redshift-independent measurements of the luminosity distance are utilized for the multiwavelength results (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=',  luminosities) of the closest objects at z < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01, NGC 1068 (14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4 Mpc;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Tully 1988;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Bauer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2015), NGC 1365 (17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3 Mpc;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Venturi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2018), and NGC 4418/MCG+00-32-013 (34 Mpc;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Ohyama et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  (This table is available in its entirety in machine-readable form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=')  Some of the pair galaxies are too close to be separated  by the other wavelength bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Particularly, the spa-  tial distributions of far-IR emissions within the GOALS  sources are poorly determined because of the limitations  in the angular resolution of pre-Herschel data (IRAS,  ISO, and AKARI).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Chu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2017) provided the total  system fluxes and component fluxes (where possible) in  all Herschel bands for the GOALS sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The beam  profiles have a mean FWHM value of 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='′′6 for the Pho-  todetector Array Camera and Spectrometer (PACS;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Pil-  bratt et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2010) 70 µm band, the shortest wavelength  band of Herschel data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' After the cross-matching with  multiwavelength catalogs (Section 3), we treat each in-  teracting pair as a total system for 11 U/LIRGs (22  individual galaxies) that are too close (with a projected  separation of ≲20′′) to be resolved by the Hershel PACS  images, whose flux densities of individual galaxies are  summed in all wavelength bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Since we do not ob-  tain any fluxes for IC 4518B but for a total system in  the UV-to-near-IR bands, the other wavelength pho-  tometries are also combined as total fluxes of IC 4518A  and IC 4518B (35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='′′5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Here, the 12 pairs are unresolved  among 84 galaxies, and thus our sample has 72 individ-  ual sources in 57 local U/LIRGs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Finally, to investigate the difference between the re-  sults of multiwavelength SED analysis by using the com-  bined photometry of a total system and separated pho-  tometries of the individual galaxies, we duplicately add  the 13 total systems of resolved pairs (with a projected  separation of ≳30′′) to our targets (see Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Therefore, our sample host 85 sources consisting of 72  individual sources and 13 systems of resolved pairs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' MULTIWAVELENGTH OBSERVATIONS  For the 57 U/LIRGs (containing 84 individual sources  in Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021), we compiled the multiwave-  length data from hard X-ray to radio bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' As noted in  Section 2, the system fluxes of the close interacting pairs  are calculated by adding the component fluxes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' We note  that neither the upper limits nor low-significant (<5σ)  values were utilized unless otherwise stated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  While  considering the spatial resolutions of individual instru-  ments, we took care to utilize the multiwavelength pho-  tometries whose apertures sufficiently cover the fluxes  derived from the extended emission of each target.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' In  the following sections, we describe the multiwavelength  data for each telescope.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The characteristics of the mul-  tiwavelength surveys are summarized in Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  7  Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Characteristics of the Multiwavelength Catalogs Utilized in This Work  Class  Instrument  Band  Wavelength  ∆R (FWHM)  Area Coverage  Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  (1)  (2)  (3)  (4)  (5)  (6)  (7)  Hard X-ray  Swift/BAT  14–195 keV  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0064–0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0886 nm  1170′′  All sky  1,2,3  NuSTAR  3–79 keV  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='016–0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='413 nm  18′′  Targeted obs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  3,4  Suzaku/HXD-PIN  10–70 keV  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='018–0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='124 nm  · ·  Targeted obs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  3,5  Soft X-ray  XMM-Newton  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1–15 keV  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='083–12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='40 nm  ∼6′′  Targeted obs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  3,6  Chandra  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2–10 keV  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='12–6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='20 nm  ≲0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='′′5  Targeted obs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  3,7  Suzaku/XIS  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2–12 keV  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10–6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='20 nm  96′′–120′′  Targeted obs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  3,5  Swift/XRT  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3–10 keV  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='12–4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='13 nm  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='′′8  Targeted obs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  1,3  UV  GALEX  FUV  152.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8 (134.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4–178.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6) nm  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='′′2  24,790 deg2  8,9  GALEX  NUV  231.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0 (177.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1–283.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1) nm  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='′′2  24,790 deg2  8,9  Optical  Pan-STARRS  g  481.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1 (394.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3–559.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3) nm  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='′′47  δ ≥ −30◦ (3π)  10,11  Pan-STARRS  r  615.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6 (538.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6–703.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6) nm  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='′′31  δ ≥ −30◦ (3π)  10,11  Pan-STARRS  i  750.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4 (677.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8–830.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4) nm  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='′′19  δ ≥ −30◦ (3π)  10,11  Pan-STARRS  z  866.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='9 (802.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8–934.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6) nm  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='′′14  δ ≥ −30◦ (3π)  10,11  Pan-STARRS  y  961.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3 (910.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1–1083.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='9) nm  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='′′09  δ ≥ −30◦ (3π)  10,11  SkyMapper  u  350.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0 (306.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7–386.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7) nm  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='′′1  δ ≲ 0◦ (2π)  10,12,13  SkyMapper  v  387.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='9 (355.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0–421.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7) nm  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='′′9  δ ≲ 0◦ (2π)  10,12,13  SkyMapper  g  501.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6 (410.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3–657.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0) nm  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='′′6  δ ≲ 0◦ (2π)  10,12,13  SkyMapper  r  607.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7 (492.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5–723.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2) nm  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='′′4  δ ≲ 0◦ (2π)  10,12,13  SkyMapper  i  773.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3 (692.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='9–864.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7) nm  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='′′3  δ ≲ 0◦ (2π)  10,12,13  SkyMapper  z  912.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0 (815.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='9–1067.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='9) nm  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='′′3  δ ≲ 0◦ (2π)  10,12,13  SDSS  u  355.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1 nm  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='′′53  14,555 deg2  14,15  SDSS  g  468.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6 nm  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='′′44  14,555 deg2  14,15  SDSS  r  616.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5 nm  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='′′32  14,555 deg2  14,15  SDSS  i  748.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1 nm  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='′′26  14,555 deg2  14,15  SDSS  z  893.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1 nm  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='′′29  14,555 deg2  14,15  Near-IR  2MASS  J  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='235 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='081–1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='407) µm  ∼2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='′′5  All sky  10,16,17  2MASS  H  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='662 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='479–1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='823) µm  ∼2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='′′5  All sky  10,16,17  2MASS  Ks  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='159 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='954–2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='355) µm  ∼2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='′′5  All sky  10,16,17  Mid-IR  WISE  W1  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='353 (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='754–3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='872) µm  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='′′1  All sky  10,18  WISE  W2  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='603 (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='963–5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='341) µm  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='′′4  All sky  10,18  WISE  W3  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='56 (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='443–17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='261) µm  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='′′5  All sky  10,18  WISE  W4  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09 (19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='52–27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='91) µm  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='′′0  All sky  10,18  AKARI  S9W  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='228 (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='846–12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='188) µm  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='′′5  All sky  10,19,20  AKARI  L18W  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='61 (13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='61–28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='67) µm  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='′′7  All sky  10,19,20  Far-IR  Herschel  PACS blue  70 µm (60–85) µm  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='′′6  Targeted obs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='†  21,22  Herschel  PACS green  100 µm (85–130) µm  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='′′8  Targeted obs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='†  21,22  Herschel  PACS red  160 µm (130–210) µm  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='′′3  Targeted obs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='†  21,22  Herschel  PSW  250 µm  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='′′1  Targeted obs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='†  21,23  Herschel  PMW  350 µm  25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='′′2  Targeted obs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='†  21,23  Herschel  PLW  500 µm  36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='′′6  Targeted obs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='†  21,23  Radio  VLA (VLASS)  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0 GHz  99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='9 mm  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5′′  δ ≥ −40◦ (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3π)  24  VLA (NVSS)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4 GHz  214.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1 mm  45′′  δ ≥ −40◦ (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3π)  25  VLA (FIRST)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4 GHz  214.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1 mm  5′′  10,575 deg2  26  VLA (WENSS)  325.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='125 MHz  922.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1 mm  54′′  δ ≥ +30◦ (π)  27  VLA (VLSSr)  73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8 MHz  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06 m  75′′  δ ≥ −40◦ (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3π)  28  MOST (SUMSS)  843 MHz  355.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6 mm  45′′  δ ≤ −30◦ (π)  29,30  MWA (GLEAM)  170–231 MHz  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='50 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='30–1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='76) m  120′′  δ ≤ +30◦ (3π)  31,32  MWA (GLEAM)  147–154 MHz  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='99 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='95–2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04) m  120′′  δ ≤ +30◦ (3π)  31,32  MWA (GLEAM)  72–80 MHz  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='94 (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='75–4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='16) m  120′′  δ ≤ +30◦ (3π)  31,32  GMRT (TGSS)  147.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5 (140–156) MHz  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='03 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='92–2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='14) m  25′′  δ ≥ −53◦ (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6π)  33  Note—Comments: (1) wavelength class;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2–3) instrument and its wavelength band;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (4) wavelength range for the X-ray bands, effective  wavelength for the UV-to-far-IR bands, and the typical wavelength for the radio bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Bandwidth is denoted in parentheses;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (5)  angular resolution;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (6) area coverage of each survey;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (7) References of column (3)–(6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  References: (1) Gehrels et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2004);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2) Oh et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2018);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (3) Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2021) and the references therein;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (4) Harrison et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  (2013);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (5) Mitsuda et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2007);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (6) Jansen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2001);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (7) Garmire et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2003);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (8) Bianchi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2017);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (9) Morrissey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  (2007);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (10) Spanish Virtual Observatory (SVO) Filter Profile Servise (http://svo2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='cab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='inta-csic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='es/theory/fps/;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (11) Chambers et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  (2016);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (12) Wolf et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2018);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (13) Onken et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2019);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (14) Albareti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2017);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (15) Ahumada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2020) and the information  (scope and image quality) on the DR16 website (https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='sdss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='org/dr16/);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (16) Cohen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2003);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (17) Skrutskie et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2006);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  (18) Wright et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2010);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (19) Murakami et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2007);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (20) Ishihara et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2010);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (21) Chu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2017);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (22) Poglitsch et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  (2010);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (23) Griffin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2010);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (24) Gordon et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2021);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (25) Condon et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (1998);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (26) Helfand et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2015);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (27) Rengelink  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (1997);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (28) Lane et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2014);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (29) Mauch et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2003);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (30) Mauch et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2008);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (31) Hurley-Walker et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2017);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (32)  Hurley-Walker et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2019);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (33) Intema et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  † All of U/LIRGs in GOALS sample are mapped by the Herschel with both the PACS and SPIRE (see Chu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  8  Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' X-ray Spectra  Among 57 U/LIRGs, Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2021) carried out  the broadband X-ray spectral analysis for 49 U/LIRG  systems by using all of the available NuSTAR, Chan-  dra (Garmire et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2003), XMM-Newton (Jansen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2001), and Suzaku (Mitsuda et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2007) data observed  by 2020 April.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  They also performed the analysis of  Swift/X-Ray Telescope (XRT;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Burrows et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2005) data  when no other soft X-ray data were obtained, and uti-  lized the Swift/BAT spectra in the 105-month catalog  (Oh et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018) if detected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Considering that X-ray  spectral works support the clumpy nature of AGN tori  (see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Liu & Li 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Furui et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Tanimoto et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2018, 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Buchner et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019), these best-fitting mod-  els were provided with a Monte Carlo-based model from  a clumpy torus (XCLUMPY;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Tanimoto et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019),  which enables us to constrain the torus covering frac-  tions for individual AGNs (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Ogawa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019, 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Tanimoto et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020, 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020, 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Uematsu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Inaba et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The broadband  X-ray spectral analysis for three other sources UGC  2608, NGC 5135, and NGC 7469 was also conducted  with XCLUMPY (Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Ogawa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Therefore, we compiled these X-ray results of 52  U/LIRG systems with XCLUMPY to compare the re-  sults from the multiwavelength SED decomposition with  an updated CLUMPY model (Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  For the other five U/LIRGs, Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2021)  only analyzed the NuSTAR data because their spec-  tra show complex features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Instead of the XCLUMPY  model,  we  analyzed  their  NuSTAR  spectra  (∼3–  70 keV) by adopting the best-fitting models in pre-  vious works for three nonmerging LIRGs NGC 1068  (M2d in Bauer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2015), NGC 1275 (Model2 in Rani  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018), NGC 1365 (final model for Observation  4 in Rivers et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2015), and two dual-AGN systems  Mrk 266B/Mrk 266A (SW-R model in Iwasawa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2020)2 and NGC 6240S/NGC 6240N (sum of two AGN  models with MYtorus in Puccetti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2016), respec-  tively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The best-fitting spectral models were applied in the  multiwavelength SEDs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  By following the same man-  ner as Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2021), we calculated the 5σ up-  per limits in the 8–24 keV band from the NuSTAR  2 The torus reflection component reproduced by the SW-R model  (Ikeda et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2009) is defined only in the 1–100 keV band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' As-  suming the power-law model with the same slope as in the 80–  100 keV band, we approximately expanded the X-ray model to  the 100–200 keV spectra in Figures E1 and E7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  counts for the hard X-ray–undetected sources, by us-  ing the HEASARC tool WebPIMMS v4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11a assuming  a power law of Γ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8 (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Ueda et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Ricci  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017b) with Galactic absorption, whose hydro-  gen column density was fixed at the value of Willingale  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The 2–7 keV upper limits were provided  from the XMM-Newton/MOS (MOS1 and MOS2) for  IC 5283 and MCG+01-59-081, since their NuSTAR 8–  24 keV fluxes were smaller than those of the interacting  companion that causes the high contamination.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' UV Photometry  The far-UV (FUV;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' λeff ∼ 152.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8 nm) and near-UV  (NUV;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' λeff ∼ 231.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0 nm) photometries were compiled  from the latest version of the Galaxy Evolution Ex-  plore (GALEX;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Martin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2005;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Bianchi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2011)  satellite catalog (GR6plus7 data release;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Bianchi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3 The GALEX observation area covers almost all  of the sky (≳ 90%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Cross-matching the optical posi-  tions of the individual nuclei and the UV peak positions,  we extracted the GALEX photometries (FUV mag and  NUV mag).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' To ensure reliable data, we finally selected  the data with Fexf = 0 and Nexf = 0, where the Fexf  and Nexf represent the extended flags for FUV and NUV  bands, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Optical Photometry  The  optical  photometries  were  taken  from  the  large catalogs with three ground-base telescopes, Pan-  STARRS1 (PS1) DR2 (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Chambers et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Flewelling et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Magnier et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020a,b,c;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Waters  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020), SkyMapper Southern Survey DR1 and DR2  (Wolf et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Onken et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019), and SDSS DR16  (Ahumada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The current coverage areas are  ∼3/4 sky (north of δ = −30◦) for Pan-STARRS, ∼1/2  sky (south of δ = 0◦) for SkyMapper, and ∼1/3 sky (a  large part of the northern area) for SDSS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' We preferen-  tially used the Pan-STARRS mean object magnitudes  in g, r, i, z, and y bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Since most of our targets are  extended sources, we calculated the flux densities from  their Kron magnitudes (Kron 1980), which were cor-  rected for the missing fluxes (about 10%)4 by multiply-  ing 100/90 (or −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='115 mag).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' When the Pan-STARRS  data were not available, we applied the SkyMapper data  in u, v, g, r, i, and z bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Since the Petrosian magni-  tudes for extended sources were given in the SkyMapper  catalog, we adopted them and corrected for the missing  3 The GALEX observations utilized in this paper can be accessed  via 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='17909/t9-pyxy-kg53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  4 https://outerspace.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='stsci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='edu/display/PANSTARRS/PS1+  Kron+photometry+of+extended+sources  9  fluxes by −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='130 mag (Graham et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2005) assuming  the typical Sersic index to be 3 (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Haan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  We finally chose the SDSS photometry (cmodelMag) in  u, g, r, i, and z bands for the other sources, and for  NGC 4418/MCG+00-32-013 and Mrk 266B/Mrk 266A  because the Pan-STARRS photometries of these two  systems were >0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4 mag fainter than those of SDSS val-  ues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  We extracted the optical photometry from these cat-  alogs in each of three bins, u–v, g–z, and y bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The  averaged differences of the optical magnitudes, ∆Mag  (SkyMapper − Pan-STARRS) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11, −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='12,  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='16, and ∆Mag (SDSS − Pan-STARRS) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='14, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11,  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02, −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='19 for g, r, i, and z bands, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Here,  we systematically added the 10% uncertainties (∼0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='115  mag) for the whole optical flux densities as a systematic  error derived from the different measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' We ex-  cluded five pieces of the optical photometry for NGC 232  (SkyMapper v-band), ESO 374−IG032 (SkyMapper v-  band), IRAS F12112+0305 (Pan-STARRS y-band), and  NGC 6907/NGC 6908 (SkyMapper u–v bands) because  their flux densities were much smaller than those in  other optical bands by a factor of 3–10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Near-IR Photometry  In the near-IR bands, we utilized the data of the Two  Micron All Sky Survey (2MASS;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Skrutskie et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  The effective wavelengths of 2MASS filters are 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='235 µm,  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='662 µm, and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='159 µm for J, H, and Ks bands, re-  spectively (Turner 2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The data of our targets were  taken from the extended catalog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Since the values were  not presented only for IRAS F17138–1017, we took its  values from the point source catalog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Finally, we ex-  tracted the data with cc flg = “000” to avoid the effects  of artifacts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Mid-IR Photometry  The mid-IR data were compiled from the Wide-field  IR Survey Explorer (WISE;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Wright et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2010) and  AKARI (Murakami et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6 We employed the pho-  tometry in W1 (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4 µm), W2 (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6 µm), W3 (12 µm),  and W4 (22 µm) bands from the ALLWISE catalog  (Cutri et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021), or ALLSKY catalog (Cutri & et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2012) if not obtained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' We primarily utilized the “gmag”  (elliptical aperture magnitude), or secondarily “mpro”  (instrumental profile-fit photometry magnitude), with  w1-4sat=0 and w1-4cc map=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The AKARI fluxes in  5 The Digital Object Identifier (DOI) of the 2MASS catalog is  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='26131/IRSA2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  6 The DOIs of the WISE and AKARI catalogs are 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='26131/IRSA1  and 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='26131/IRSA181, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  S9W (9 µm) and L18W (18 µm) bands were obtained  from AKARI/IRC mid-IR all-sky Survey (Ishihara et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2010), where we selected the data with q S09=0 &  X09=0 for S9W, and q S18=0 & X18=0 for L18W, re-  spectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Far-IR Photometry  We applied the far-IR fluxes presented by Chu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  (2017), using the Herschel Space Observatory (Pilbratt  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2010) Photodetector Array Camera and Spec-  trometer (PACS;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Poglitsch et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2010) and the Spec-  tral and Photometric Imaging Receiver (SPIRE;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Griffin  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' For all the PACS bands (70 µm, 100 µm,  160 µm) and SPIRE bands (250 µm, 350 µm, 500 µm),  they computed the total system fluxes and component  fluxes of individual galaxies (where possible) for the en-  tire GOALS sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The aperture radius was set by the  band with the largest beam size for each instrument:  usually the 160 µm band for PACS, and the 500 µm  band for SPIRE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Radio Photometry  Radio surveys with large sky coverages have been per-  formed over a wide frequency range (see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Shimwell  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Stein et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' In our study, we utilized  eight kinds of wide-area radio catalogs, which have been  conducted with four main telescopes: Karl G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Jansky  Very Large Array (VLA), Molonglo Observatory Syn-  thesis Telescope (MOST;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Mills 1981;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Robertson 1991),  Murchison Widefield Array (MWA;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Lonsdale et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2009;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Tingay et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2013), and Giant Metrewave Radio  Telescope (GMRT;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Swarup 1991).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The catalogs are  described below:  The catalogs of the VLA observations:  (1) The Very Large Array Sky Survey (VLASS;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Gor-  don et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021), observing the entire sky north of  δ = −40◦ (82% sky region) at 3 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  (2) The NRAO VLA Sky Survey (NVSS;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Condon  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 1998) covering the sky north of δ = −40◦  at 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  (3) The Faint Images of the Radio Sky at Twenty-  centimeters (FIRST;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Helfand et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2015), observ-  ing in 10,575 deg2 of sky coverage (8,444 deg2  in the north Galactic cap and 2,131 deg2 in the  southern cap) at 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  (4) The Westerbork Northern Sky Survey (WENSS;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Rengelink et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 1997), a low-frequency radio sur-  vey that will cover the whole sky north of δ = +30◦  at 325.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='125 MHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  10  Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  (5) The  VLA  Low-frequency  Sky  Survey  Redux  (VLSSr;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Cohen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2007;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Lane et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2014), cov-  ering the sky north of δ = −40◦ at 73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8 MHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The catalogs of the other radio observations:  (6) The Sydney University Molonglo Sky Survey  (SUMSS) catalog, Version 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1r (updated in 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Mauch et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2003, 2008) with MOST, covering  the sky south of δ = −30◦ at 843 MHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The data  of IRAS F13120–5453 are not listed in the original  catalog but are obtained from Allison et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  (7) The GaLactic and Extragalactic All-sky MWA  (GLEAM;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Hurley-Walker et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017) survey, cov-  ering 24,831 deg2 over sky south of δ = +30◦  and Galactic latitudes outside 10◦ of the Galactic  plane, excluding some areas such as the Magellanic  Clouds, across 72–231 MHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Hurley-Walker et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  (2019) also presented the GLEAM catalog of the  Galactic plane (2,860 deg2);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' in which only the sys-  tem of MCG+04-48-002 and NGC 6921 was con-  tained, but their fluxes were not utilized because  both galaxies are not divided by the MWA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' To  get similar data from VLA catalogs for northern-  sky targets, we picked out the fluxes in the 170–  231 MHz, 147–154 MHz, and 72–80 MHz bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  (8) The TIFR GMRT Sky Survey (TGSS;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Intema  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017), observing 36,900 deg2 of the sky  north of δ = −53◦ (∼90% sky), at 147.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5 MHz  (with a bandwidth of 140–156 MHz).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  We basically utilized the integrated fluxes referred  from these radio catalogs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Although only the peaked  fluxes were presented in the VLSSr catalog, they should  be the same as integrated fluxes for unresolved point  sources because of the large beam size (75′′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' see Ta-  ble 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' To avoid flux underestimates due to the resolved-  out extended emission, we basically employed the radio  catalogs excluding the two catalogs observed with the  high-spatial-resolution instruments: VLASS (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='′′5) and  FIRST (5′′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7 For the faint sources that any data are  not obtained, we adopted the 5σ upper limits from the  TGSS catalog (<24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5 mJy at 150 MHz).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Additionally,  we used the fluxes of these faint sources from the VLASS  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0 GHz) and FIRST (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4 GHz) catalogs if detected  at the ≳5σ level8, or the 5σ upper limits (<0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='44 and  <1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='00 mJy, respectively).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  7 Since the uncertainties of FIRST flux densities were not provided,  we assume them as 10% uncertainties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  8 We utilized the VLASS fluxes for the low-significance radio  sources, NGC 833 (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3σ) and MCG+01-59-081 (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4σ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Correction for Galactic Extinction  The magnitudes in the FUV, NUV, u–y, J, H, Ks, W1  and W2 bands were corrected for the Galactic extinction  by following Schlegel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (1998), hereafter SFD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' We  adopted the correction factors, Rλ (= Aλ/E(B−V )SFD,  where Aλ is the extinction at the λ band in units of  magnitude, calculated by Aλ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='086τλ) from Bianchi  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2017) for GALEX, Schlafly & Finkbeiner (2011)  for Pan-STARRS, Wolf et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2018) for SkyMapper, and  Yuan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2013) for the other telescopes:  GALEX:  [RFUV, RNUV] = [8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='95]  Pan-STARRS:  [Rg, Rr, Ri, Rz, Ry]  = [3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='172, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='271, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='682, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='322, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='087]  SkyMapper:  [Ru, Rv, Rg, Rr, Ri, Rz]  = [4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='294, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='026, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='986, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='288, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='588, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='206]  SDSS:  [Ru, Rg, Rr, Ri, Rz]  = [4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='39, 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='30, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='31, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='71, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='29]  2MASS:  [RJ, RH, RKs] = [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='72, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='46, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='306]  WISE:  [RW1, RW2] = [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='18, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='16]  The magnitudes of E(B − V ) reddening and the flux  densities of the UV-to-radio photometries corrected for  the Galactic extinction in our sample are summarized  in Table E1 (λ < 1 µm), Table E2 (λ = 1–200 µm), and  Table E3 (λ > 200 µm).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' MULTIWAVELENGTH SED MODEL AND  BEST-FIT PARAMETERS  To best constrain the properties of polar dust, we  update the latest multiwavelength SED-fitting code X-  CIGALE (Yang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020a) by implementing the IR  CLUMPY model (Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1), whose geometry is the  same as in XCLUMPY.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The UV-to-IR SEDs are ana-  lyzed with the modified code for all targets (Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  For the radio data, we perform the fitting of radio pho-  tometry after the UV-to-IR SED decomposition (Sec-  tion 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' We finally combine the results of X-ray spec-  tral analysis (Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021), UV-to-IR SED de-  composition, and radio fitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The validity of the best-  fit parameters are evaluated in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  11  10  7  10  5  10  3  10  1  101  103  105  107  F  (mJy)  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  10  4  10  2  100  102  104  106  Observed  ( m)  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID01_NGC_34  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0196, reduced ²=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID01_NGC_34  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0196, reduced ²=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1)  Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' An example of the hard-X-ray-to-radio SED and best-fitting models for a stage-D merger NGC 34 (ID01).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Upper  panel: observed wavelength vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  flux density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Lower panel: rest-frame frequency vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  luminosity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The bottom panels show  the residuals in the UV-to-radio bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The individual curves show the SED models of radio non-thermal emission (pink  dashed), attenuated stellar emission (blue dash-dotted), nebular emission (gray), dust emission (red), AGN torus (green),  escaped AGN disk (cyan), polar dust (orange), absorption-corrected AGN X-ray emission (blue dotted), the X-ray emission  from AGN scatters and X-ray binaries (light green), and X-ray thermal emission (light purple).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Purple and red circles represent  the observed and model flux densities, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Red crosses in the X-ray band denote the NuSTAR spectra analyzed by  Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The results for all targets are given in Figures E1–E10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  12  Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The tables of best-fitting parameters and supple-  mental measurements of each target are listed in Ap-  pendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The results of a mock analysis (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', the test for  the reliability of the estimates, given the uncertainty of  the photometry) are shown in Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The compar-  ison of our results with the previous works is discussed  in Appendix C, and the comparison of the results with a  different AGN model (SKIRTOR;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Stalevski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2016)  is in Appendix D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The hard X-ray to radio multiwave-  length SEDs and their best-fitting models are presented  in Figure 1 and Figures E1–E10 (see Appendix E).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' New Implementation of CLUMPY for X-CIGALE  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' AGN Model in Multiwavelength SED  The combination of X-ray and IR data enables us to  constrain the distribution of the gas and dust in the  AGNs (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Hickox & Alexander 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' For making the  analysis consistent with the XCLUMPY X-ray spectra,  Miyaji et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2019) have modified the CIGALE package,  a fitting code to model the UV-to-radio SEDs of galax-  ies (Burgarella et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2005;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Noll et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2009;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Boquien  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019), to include an implementation of CLUMPY  (Nenkova et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2008a,b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' They conduct the X-ray spec-  tral analysis with XCLUMPY and the UV-to-IR SED  decomposition with CLUMPY as a module, and suc-  cessfully estimate the torus parameters of an AKARI-  selected CT AGN, such as X-ray absorbing column,  torus optical depth, torus angular width, and inclina-  tion angle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Recent works (Tanimoto et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Ogawa  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021) show that these clumpy torus models mostly  present the larger covering fraction in the IR band than  those in X-rays, consistent with the presence of the polar  dust (see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Asmus et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Asmus 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' L´opez-  Gonzaga et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' L´opez-Gonzaga & Jaffe 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' H¨onig  & Kishimoto 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' H¨onig 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Lyu & Rieke 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Buat  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Toba et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Andonie et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Yang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2020a) develop a new X-ray module for  CIGALE, allowing it to fit SEDs, named X-CIGALE  (but their X-ray model does not consider the absorption  from the target, our Galaxy, and/or the intergalactic  medium).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='9 Torus models are mainly classified by their  dust distribution such as smooth, clumpy, and two-phase  (clumpy and smooth) models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The current version of X-  CIGALE (CIGALE v2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0) includes two AGN mod-  els of a classical smooth torus model by Fritz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  (2006) and a modern two-phase model (SKIRTOR) by  Stalevski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2012, 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' They also implement the  9 Yang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2022) improve the X-CIGALE code mainly related  to AGN intrinsic X-ray anisotropy, X-ray binary emission, AGN  accretion-disk SED shape, and AGN radio emission (new version  as CIGALE v2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  model of polar-dust extinction (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Lyu & Rieke 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  H¨onig 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' For maintaining energy conservation in the  scheme of X-CIGALE, the polar dust model considers  the radiative energy absorbed by their dust.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The model  of polar dust assumes the isotropic dust re-radiation and  the “gray body” model (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Casey 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Since a clumpy distribution of the dust is neces-  sary to prevent the destruction of grains (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Krolik  & Begelman 1988), many works adopt the SKIRTOR  model in X-CIGALE (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Yang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020a, 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Buat et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  However, conducting the SED fit  by a self-consistent AGN model with X-CIGALE and  XCLUMPY is difficult because the torus component of  SKIRTOR has different geometry and parameter def-  initions from those of XCLUMPY.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Thus we use the  CLUMPY module by combining the SKIRTOR’s polar  dust component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Differences between CLUMPY and SKIRTOR  The CLUMPY model assumes an isotropic emission  of the central source commonly adopted in the litera-  ture (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Schartmann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2005;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' H¨onig et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Strong correlations between X-ray and nuclear 12 µm  fluxes (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', least biased by extra-nuclear emission) are  reported for both Seyfert 1 and 2 galaxies (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Gandhi  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2009;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Asmus et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' When taking the X-ray  emission as an isotropic tracer for the AGN luminosity,  the low scatter of the mid-IR/X-ray luminosity correla-  tion suggests that the mid-IR emission is also close to  isotropic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The reason is that the hollow cone is visible  to the observer at any inclination in the inflowing disk  and outflowing polar dust (H¨onig & Kishimoto 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  H¨onig 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The intrinsic SED of the central AGN  disk emission in CLUMPY follows the piecewise power-  law distribution in Rowan-Robinson (1995), where the  CLUMPY model adopts λRJ = 1 µm (wavelength mark-  ing the onset of the Rayleigh-Jeans tail).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  CLUMPY  model results in a Gaussian angular distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  A  density gradient along the polar angle is proportional  to exp(−θ2/σ2), where θ is the elevation angle and σ is  torus angular width (typically ∼20◦;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Ogawa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Whereas, SKIRTOR consid-  ers the anisotropy of the central source (Netzer 1987)  and employs larger λRJ = 5 µm than that in CLUMPY.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  SKIRTOR assumes a sharp-edged angular distribution  of high-density clumps embedded in a smooth compo-  nent with low density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  A density gradient along the  polar angle is proportional to exp(−x|cos(90◦ − θ)|) in  SKIRTOR, where x is a torus density angular parameter  typically fixed to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0 (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Yang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Stalevski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2016) demonstrate that the difference  in the input SED shape of the central engine (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', λRJ)  13  Disk  Torus  (τV ~ 400–1200)  (Escaped disk)  (Polar dust)  Polar dust  (τV ~ 0–3)  (Torus)  σ  i  Equ  X-ray Spectroscopy  Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' A schematic picture of the AGN structure assumed in the updated CLUMPY model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Central black circle and blue  bar represent the SMBH and accretion disk, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Brown circles show the clumps of torus, whose structure is constrained  by the X-ray spectroscopy with XCLUMPY.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Light-brown annular sector illustrates the polar dust.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Green arrays mark the torus  reflection emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Blue thick (solid and dotted) arrays are the AGN disk emission, while a blue thin array is the escaped disk  emission via the clump gaps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' These emissions are attenuated by the polar dust, marked as dashed lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Orange arrow shows the  dust re-radiation from the polar dust.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The symbols “σ” and “i” mean the torus angular width and inclination angle, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  has little effect on the resulting dust emission: what  matter is the total amount of emission from the central  engine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10 By comparing the results obtained with the  clumpy torus model of isotropic disk radiation, Stalevski  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2012) report that the anisotropic assumption only  reduces dust fluxes by a factor of at most 2, keeping  roughly the similar shape of IR SEDs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  On the other  hand, the smooth component in SKIRTOR can produce  a more attenuated silicate feature and have a stronger  near-IR emission than without the smoothly distributed  element (Stalevski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2012, 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' see also Efstathiou  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Moreover, the dependence of the dust dis-  tribution on θ in SKIRTOR tends to be less and may  cause a stronger near-IR emission than in CLUMPY  (Gaussian angular distribution).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Although we find such  a trend by examining how much of the differences in  the results derived from the fits with CLUMPY and  SKIRTOR (see Appendix D), both models consequently  present similar intrinsic AGN luminosities for almost  all of the U/LIRGs in our sample (Figure D1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Hence,  our multiwavelength SED analysis is less affected by the  model assumption between CLUMPY and SKIRTOR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Implementation of CLUMPY Model  Figure 2 shows a schematic picture of our updated  CLUMPY model containing the polar dust component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The model assumes the situation of an AGN structure  10 https://sites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='google.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='com/site/skirtorus/sed-library  consisting of (1) an accretion disk at ≪1 pc scale, (2)  a clumpy torus at ≲10 pc scale, and (3) polar dust at  ≳10 pc scale (see Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' In the torus model of  CLUMPY, the radial distribution of clumps is a power  law with an index of q (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', r−q), and the angular distri-  bution is a Gaussian distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The number of clumps  along a line-of-sight path (N LOS  clump) is described by:  N LOS  clump(θ) = N Equ  clump exp(−θ2/σ2),  (1)  where N Equ  clump is the number of clumps along the equa-  torial plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The updated CLUMPY considers dust  absorption, re-emission, and scattering (Nenkova et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2008a,b), except for the scattering effect in the smooth  polar-dust region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Since the total mass of polar dust  is much smaller than that contained in the torus, the  X-ray spectrum is almost unaffected by the polar dust  component at energies above a few keV (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Thus, the clump distribution derived from the X-  ray spectroscopy with XCLUMPY (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2021) traces the structure of the clumpy torus without  the polar dust.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' A part of the disk emission is escaped via  the clump gap, keeping the shape of its intrinsic AGN  SED.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Considering the optical depth of a single clump of  the torus with τV = 40–120 in this work (corresponds to  τλ > 1 in the UV-to-optical bands, the escape probabil-  ity, Pesc, is calculated by Pesc ≃ exp(−N LOS  clump) (see also  Equation A4 in Nenkova et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2008a and Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2 in  Nenkova et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2008b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The distribution of the polar dust is determined by the  region with θ ≥ σ (or the region with the angle between  14  Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  the polar axis and edge of the torus in SKIRTOR).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' By  limiting the range of the polar dust temperature between  100–250 K, the polar dust model in this work reflects the  extended dust at ≳10 pc (see Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3 and 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' We  allow the line-of-sight optical depth (τV) of polar dust  as a typical range in previous studies, τV ≲ 3 (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Buat  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Toba et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' see Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3 and 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The value is much smaller than the equatorial optical  depth of the torus (τ Equ  V  ∼ 400–1200), where the number  of clumps is 10 (Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Here, the distributions of  polar dust and the galaxy’s interstellar medium (ISM)  are not distinguished.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Finally, to keep energy conserva-  tion, the dust extinction and re-radiation of polar dust  in the UV-to-IR bands are included in the same manner  as the original X-CIGALE code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' UV-to-IR SED Fitting with CLUMPY  By using the X-CIGALE code with the CLUMPY im-  plementation, we conduct the UV-to-IR SED decom-  position, whose best-fit parameters are adopted for the  radio fitting (Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The details of the UV-to-  IR SED model are described for the host galaxy (stel-  lar emission, nebular emission, and dust emission;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Sec-  tion 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1), torus (torus and escaped disk emission;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2), and polar dust emission (Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3  and 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The models and parameters we adopted are  summarized in Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Host Galaxy Model  We utilize a delayed star formation history (SFH)  model to allow for an instantaneous burst of the star-  burst activities (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Ciesla et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Nersesian et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The parameter ranges of the SFH model are  mainly referred from the works with CIGALE code for  local Herschel-selected galaxies (Buat et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018) and  U/LIRGs (Paspaliaris et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The stellar emis-  sion is modeled as a 5 Gyr simple stellar population  (BC03;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Bruzual & Charlot 2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Here, the Chabrier  (2003) IMF, solar metallicity, and the standard nebu-  lar emission model (see Inoue 2011) are adopted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' We  consider the attenuation law for the stellar continuum  of Calzetti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2000), where the nebular emission is  reddened with a Milky Way extinction curve (Cardelli  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 1989).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The reddening of the nebular emission,  E(B − V )line is a free parameter, while the ratio of the  reddening of the emission lines and whole stellar contin-  uum, E(B−V )star/E(B−V )line, was found to be 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='44 for  local starbursts (Calzetti 2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Since the contribution  of the UV bump for local galaxies is small (∼1/3 of that  of the MW bump) and can be ignored as it affects the  near-UV magnitude by only 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1 mag (Salim et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018),  we fix the amplitude at zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Recent works report that  the extinction curves show a great diversity in power-law  slope (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Salim et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Salim & Narayanan 2020),  whose range of the slopes is covered from −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8 to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  We fit the cold dust emission from the host galaxy with  the physical dust model from Draine et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2014), the  updated model of the previous one (Draine & Li 2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The parameter ranges of qpah (qpah;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='47–2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='50), umin  (1–50) and alpha (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0 or 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5) are referred from recent  works (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Buat et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018, 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The dust fraction in  photo-dissociation regions (PDRs) is fixed to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02 (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=',  Draine & Li 2007;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Dale et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Magdis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Buat et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Torus Model (CLUMPY and SKIRTOR)  For the torus component, we adopt the CLUMPY  model implemented in the X-CIGALE code (Model I).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The number of clumps along the equator of N Equ  clump = 10,  the ratio of the outer to inner radii of Y = 20, and the  radial clumpy distribution index of q = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5 are assumed  to make the analysis consistent with XCLUMPY (Tani-  moto et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The torus optical depth in the V band  is a free parameter (τV;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 40, 80, or 120), while the torus  angular width (σ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 15◦ to 70◦ in steps of 5◦) and inclina-  tion angle (i;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 30◦, 60◦, or 80◦) are fixed as be the closest  values to the parameters of the best-fitting model in the  X-ray works (Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020, 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Ogawa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11 For the systems whose individual galaxies have  different inclinations (NGC 6921/MCG+04-48-002 and  NGC 7679/NGC 7682), we select σ = 20◦ and i = 60◦  as typical values in the X-ray results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The UV-to-IR  SEDs of starburst-dominant or hard X-ray–undetected  sources are modeled without AGN component (fAGN =  0), while allowing the AGN fraction in the IR band to  free between 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05–0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8 for AGNs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  We also perform the SED decomposition with the  SKIRTOR model (Model II;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' see Appendix D).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' A torus  density radial parameter (q) and torus density angular  parameter (x) are fixed to be 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0 (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Stalevski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Yang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='12 The equatorial optical depth  at 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7 µm (τ9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7) is a free parameter (5, 9, or 11).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The  angular distribution of clumps has a sharp edge corre-  sponding to the angle between the equatorial plane and  edge of the torus (∆).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Here, the unobscured and ob-  11 Since the reduced χ2 is larger than 10 for IRAS F08572+3915,  its inclination of 80◦ is chosen that present the smallest χ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' For  NGC 1068, NGC 1275, NGC 1365, Mrk 266B/Mrk 266A, and  NGC 6240S/NGC 6240N, we assume σ to be a typical value of  20◦ (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Ogawa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021), and select the  inclination angle showing the smallest χ2 from 30◦, 60◦, and 80◦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  12 We confirm that the results and discussion are unchanged even  if q = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5 to keep consistency with CLUMPY model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  15  Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Summary of Models and Input Parameters in the UV-to-IR SED Fitting  Model  Module  Parameter  Value  SFH model  shfdelayedbq  tau main (Myr)  1000, 3000, 5000  age main (Myr)  4500, 7000, 9500, 12000  age bq (Myr)  10, 20, 100  r sfr  1, 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='16, 10, 31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6, 100, 1000  Stellar emission  bc03  imf  1 (Chabrier)  metallicity  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  Nebular emission  nebular  logU  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  f esc  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  f dust  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  lines width (km s−1)  300  Attenuation law  dustatt modified starburst  E BV lines  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='25, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='75, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  E BV factor  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='44  uv bump wavelength (nm)  217.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  uv bump width (nm)  35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  uv bump amplitude  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  powerlaw slope  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8, −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  Ext law emission lines  1 (Milky Way)  Rv  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  Dust emission  dl2014  qpah (= qpah)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='47, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='12, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='50  umin  1, 5, 10, 25, 50  alpha  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  gamma  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  AGN (torus/disk)  CLUMPY (Model I)  Y ratio (= Y )  20  tau V (= τV)  40, 80, 120  N 0 (= N Equ  clump)  10  q (= q)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  sigma (= σ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' degree)  15 to 70 (per bin 5;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' fixed)  inclination (= i;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' degree)  30, 60, 80 (fixed)  fracAGN (= fAGN)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0 (for starburst-dominant sources), or  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4,  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8 (for AGNs)  SKIRTOR (Model II;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Appendix D)  R (= Y )  20  t (= τ9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7)  5, 9, 11  oa (= ∆;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' degree)  30, 40, 60 (fixed)  i (= i;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' degree)  30, 60, 80 (fixed)  fracAGN (= fAGN)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0 (for starburst-dominant sources), or  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4,  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8 (for AGNs)  AGN (polar)  CLUMPY/SKIRTOR  law  0 (SMC)  EBV (= E(B − V );' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' mag)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0 (fixed), or 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8  temperature (= Tpolar;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' K)  100, 150, 200, 250  emissivity (= β)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6  16  Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  scured AGNs are determined by the inclination angle  above i < 90◦ − ∆ or not, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' To keep fully  consistency between the SKIRTOR-based AGN classifi-  cation and X-ray classification in our sample (Table 1),  we convert the torus angular width (σ) of [10◦–15◦, 15◦–  25◦, 25◦–70◦] to the ∆ of [30◦, 40◦, 60◦], respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Polar Dust Model  In the polar dust model, we adopt the Small Magel-  lanic Cloud (SMC;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Prevot et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 1984) extinction curve,  which is preferred from AGN observations (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Hop-  kins et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2004;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Salvato et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2009;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Bongiorno et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Buat et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The reddening E(B −V ) is free  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3, and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Buat et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Paspaliaris  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Toba et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Yang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2022), or set-  ting E(B − V ) = 0 if no significant AGN contribution  (fAGN = 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The emissivity (β) is fixed at 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6 as a typical  value (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Draine & Lee 1984;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Casey 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Yang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2020a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The previous IR works indicate the tempera-  ture of polar dust (Tpolar) is ∼100–200 K (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Lopez-  Rodriguez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Lyu & Rieke 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' H¨onig 2019),  while the temperature of the torus is ≳300 K (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Tris-  tram et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2009;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Tristram & Schartmann 2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Recent  high-spatial-resolution mid-IR observation of the nearby  Seyfert 2 galaxy, the Circinus galaxy, with Very Large  Telescope Interferometer also supports the similar tem-  peratures (∼370 K within the subparsec-scale central  region and ∼200 K in outer polar dust regions;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Isbell  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' These temperatures are much larger than  those expected for a galaxy’s ISM heated only by star  formation (∼20–60 K;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Casey 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Clements et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' da Cunha et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Although the higher tem-  perature dust above 300 K should radiate the near-IR  emission from a ring-like dust structure on the subparsec  central region (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Krolik 2007;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Schartmann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Baba et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' H¨onig 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Lyu & Rieke 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' G´amez  Rosas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Matsumoto et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2022), the material  of the inner edge of a torus and accompanying polar dust  would be difficult to distinguish by both near-IR and X-  ray observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Therefore, we select the range of the  polar dust temperature within 100–250 K, and clarify  that (1) the estimates of the physical properties of ex-  tended (≳10 pc;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' see also Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5) polar dust that  are not taken into account for the hot (>300 K) dust  component on the subparsec region and (2) the central  hot dust emission are predominantly considered as the  torus emission in this study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Significance Test for Torus and Polar-dust Emission  We examine the Bayesian information criterion (BIC;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Schwarz 1978) for two kinds of fits with and without the  AGN (torus and polar dust) component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Using the χ2  statistics, the BIC is provided by the equation as BIC =  χ2+k×ln(N), where k is the number of free parameters  and N is the number of photometric data (Ciesla et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Buat et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Among the sources yielding a  poor fit with reduced χ2 above 6, the three galaxies,  ESO 350−38, ESO 374−IG032, and NGC 4418, show  the ∆BIC = BICwoAGN − BICwAGN > 6 (significantly  improvement with a posterior probability above 95%;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Raftery 1995).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Thus, we re-classify these three galax-  ies as AGN candidates and select the inclination angle  providing the smallest χ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Furthermore, we conduct the significance test for the  polar dust component in the UV-to-IR SED analy-  sis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The left panel of Figure 3 presents the fraction  of sources showing BIC > 6 for a polar dust compo-  nent with two kinds of torus models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  We find that  the analysis with SKIRTOR provides larger fractions  of the AGNs showing significant polar dust contribu-  tion than with CLUMPY.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' This stronger significance  of mid-IR polar dust emission can be explained by  the flatter SED slope of the torus component in the  SKIRTOR model due to the strong near-IR emission  from smooth low-density dust (Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2 and Ap-  pendix D).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Although the sample is quite limited to the  nine AGNs, the signatures of polar-dust radiation are  reported by high-resolution mid-IR images and inter-  ferometry (NGC 1068, NGC 1365, NGC 3690 West,  Mrk 231, MCG−03-34-064, NGC 5135, IC 4518W,  NGC 7469, and NGC 7674;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' L´opez-Gonzaga et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2014,  2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' L´opez-Gonzaga & Jaffe 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Asmus et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Asmus 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Lopez-Rodriguez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017, 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Mattila  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' G´amez Rosas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='13  Six of these  AGNs hosting polar dust emissions do not show any  significant BIC values with these torus models (right  panel of Figure 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' This is mainly because the available  photometries of them in the near-IR (2MASS) and/or  mid-IR (WISE and AKARI) bands are insufficient to  give a diagnosis, which may be derived by the artifacts  related to their IR emission from extended or compre-  hensive morphology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' So, we adopt the polar dust model  for the AGNs with one or more signs from mid-IR im-  ages, interferometry, and BIC tests by SED analysis  with CLUMPY and SKIRTOR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' For the seven AGNs  without any signs of polar dust contribution, most of  whose IR photometries are available, we treat them as  AGNs without polar dust emission by applying E(B−V )  = 0, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', returning to the original torus model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Impres-  13 The presence of polar dust in Mrk 231 is implied by near-to-mid-  IR polarimetry (Lopez-Rodriguez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017), and in NGC 3690  West by detecting the time variability of nucleus IR SED due  to the tidal disruption event radiating the polar dust emission  (Mattila et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  17  A  B  C  D  N  Merger Stage  0  20  40  60  80  100  Fraction of AGNs with polar dust [%]  Image, Interferometry  SED with CLUMPY  SED with SKIRTOR  Mixture of them  Image+Interferometry(9)  [only 9 sources in sub-sample]  CLUMPY(15)  SKIRTOR(26)  w/o Polar(7)  A(1)  A(1), B(1),  C(1), D(1), N(2)  C(1), D(1)  N(2)  A(2), B(2),  C(2), D(5), N(1)  A(1), B(1),  C(2), D(6), N(1)  A(4), B(2), N(1)  Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Left panel: Histogram of the fraction of the sources that shows some signatures of the presence of polar dust  emission for the AGNs with merger stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Each signature derived from the high-resolution image (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Asmus 2019) and  interferometry (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', L´opez-Gonzaga et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' L´opez-Gonzaga & Jaffe 2016) in the mid-IR band (blue), the UV-to-IR SED  decomposition with CLUMPY (black) and with SKIRTOR (red) are color-coded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Green histogram illustrates the fraction for  the AGNs with one or more signs of polar dust emission (green).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Right panel: Venn diagram of the sources with/without the  signs of polar dust emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The numbers of the sources for individual categories and merger stages are illustrated in parentheses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  sively, we find that these AGNs are in early mergers and  nonmergers, while all of the AGNs in late mergers show  the signatures of polar dust emission, as discussed in  Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Finally, we list the best fitting parame-  ters in the tables of Appendix A (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Table A1–A5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Radio Fitting  By fixing the best-fitting parameters obtained by the  UV-to-IR SED analysis, we finally conduct the radio  SED decomposition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The radio model is composed of  the continuum from the nebular emission (free-free, free-  bound, and two-photon continua)14, which also radi-  ates UV-to-IR emission (Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1), and indepen-  dent synchrotron emission from AGN and/or starburst  (Boquien et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' We parameterized a correlation  coefficient between total-IR luminosity and monochro-  matic radio luminosity of the synchrotron emission at  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4 GHz (qIR = logLIR/L1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4GHz), and the power-law  slope of synchrotron emission (αradio) derived from the  low-frequency radio emission in the 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1–4 m or 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07–  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0 GHz bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  We choose the parameter ranges of  qIR between −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='50 and +3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='50 with a step of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01 (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=',  Yun et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2001;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' U et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Vardoulaki et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2015),  and αradio between 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='00 and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='50 with a step of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Murphy 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Toba et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' If only a sin-  14 The model of the nebular component covers the UV to radio  1 m emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' To expand the available wavelength, we assume  the slope between the fluxes in the 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8 and 1 m bands to the 1–  10 m radio emission for the nebular component, where it is less  dominant than the synchrotron component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  gle radio photometry or upper limit values are available,  we fix αradio to be 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5, a median value in the <5 GHz  bands among local U/LIRGs (Murphy 2013), consistent  with the averaged value of the estimates in our study  (αradio =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='48±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='16).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The best-fitting parameters and  radio luminosities are listed in Table A3, and the com-  bined hard X-ray to radio multiwavelength SEDs and  their best-fitting models are shown in Figures 1 and Ap-  pendix E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Best-fit Parameters and Their Validity  We have performed the multiwavelength SED analysis  for the local U/LIRGs, covering the hard X-ray to radio  wavelength bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The best-fit parameters of individ-  ual sources are summarized in Tables A1–A5, and the  averaged values of these results are shown in Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The histogram of the reduced χ2 of the UV-to-IR SED  decomposition for the 72 individual targets in our sam-  ple is displayed in Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The SED decomposition of  some targets shows a relatively large χ2 above 5, which  is mainly caused by the noisy photometric data in the  UV or optical band (Figures E1–E10 in Appendix E).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Conducting a mock analysis, we confirm that the best-  fit parameters derived from our multiwavelength SED  decomposition are less affected by photometric uncer-  tainties (see Appendix B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' However, the SED fitting of  IRAS F08572+3915 shows a large reduced χ2 over 10  because the model presents weaker near-IR fluxes than  the photometric data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Its SED is moderately repro-  duced with SKIRTOR (with reduced χ2 of 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Al-  though its AGN luminosity may be underestimated (at  18  Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  0  2  4  6  8  10  12  Reduced  2  0  5  10  15  20  25  Number of sources  Total Number = 72  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Histogram of the reduced χ2 derived from the  UV-to-IR SED decomposition for the 72 individual targets  in our sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  worse ∼0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4 dex), the AGN luminosities for the other  sources derived with CLUMPY are well consistent with  the values with SKIRTOR (Appendix D).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Thus, we uti-  lize the results from the multiwavelength analysis with  CLUMPY for all targets to discuss their characteristics  of the host galaxy and AGN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Next, we investigate the significance of the AGN fea-  ture in the multiwavelength SED decomposition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Fig-  ure 5 shows the histogram of the ∆BIC on the different  fits with and without the AGN component for the 72  individual targets in our sample (see also Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Remarkably, most of the sources are distributed around  the threshold of ∆BIC = 6, regardless of whether the  sources are the AGNs (hard X-ray–detected AGNs and  three newly identified AGN candidates by the diag-  nostics of ∆BIC > 6) or the other sources (starburst-  dominant or hard X-ray–undetected sources).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' This in-  dicates that the AGNs in U/LIRGs are difficult to detect  only with the SED decomposition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Therefore, the strong  constraints on the AGN structure derived from the X-  ray spectral analysis will effectively solve the complex  SEDs in the IR band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  We evaluate the effects on the results if unresolved  photometries are utilized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  For the stellar mass (M∗)  and SFR, the comparison of our results and previous  works of SED analysis by using the photometry of total  systems are presented in Appendix E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Figure 6 presents  the differences in the results derived from the combined  photometry of a total system and the separated pho-  tometries of individual galaxies for the 13 resolved pairs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The stellar masses and SFRs are not affected by using  0  100  200  300  BIC (torus + polar dust)  0  5  10  Number of sources  BIC >  6  (Significant AGN comp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=')  AGN (41)  non-AGN (31)  Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Histogram of ∆BIC (= BICwoAGN−BICwAGN)  for the 72 individual targets in our sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The black solid  line shows the threshold of ∆BIC = 6 as the significant  differences (posterior probability above 95%) in two fits  with and without adding the AGN (torus and polar dust)  component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The red histogram shows the number of the  hard X-ray–detected AGNs and three newly identified  AGN candidates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The blue histogram is the number of  the other sources, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', starburst-dominant sources or hard  X-ray–undetected sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  the summed fluxes of individual galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' On the other  hand, for the 10 pairs hosting AGNs, the UV-to-IR  torus (Ltorus) and polar dust luminosities (Lpolar), and  intrinsic (bolometric) AGN disk luminosities (LAGN,int)  derived from the combined photometries become larger  than those from separated ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' According to the SED  models in Figures E1–E10, the slope of the IR SEDs  of the starburst component is similar to the one of the  AGN (see also Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' This makes it difficult to ac-  curately extract the AGN contribution from the IR SED  when the photometries of a starburst-dominant source  and a galaxy hosting an AGN are mixed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The overes-  timation of AGN luminosities for unresolved sources is  found to be ∼0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2 dex, which is a small effect on the  following discussion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' RESULTS: MULTIWAVELENGTH EMISSION  FROM U/LIRGS  Before the discussion on the properties of polar dust in  U/LIRGs (Section 6), we first study the characteristics  of the multiwavelength radiation, which are helpful to  understand the detailed environments from the nucleus  to galactic scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  We also aim to investigate unique  features for future works to explore buried AGNs in  19  M* t  SFR t  Ltorus  Lpolar  LAGN, int  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  X  [dex]  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  ||  X = logX (Total)  log[X (Target1) + X (Target2)]  Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The differences in M∗, SFR, Ltorus, Lpolar, and  LAGN,int derived from the UV-to-IR SED analysis by using  the combined photometry of a total system and separated  photometries of the individual galaxies for 13 resolved pairs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Diamonds and these uncertainties denote the averaged  values and 1σ dispersions, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  U/LIRGs at higher redshift.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' For these purposes, we here  examine the SFR–M∗ relation as an indicator of the host  galaxy’s properties (Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Next, we evaluate the  activities of AGNs and starbursts by focusing on the ra-  dio emission (Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2), WISE IR color (Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3),  and averaged multiwavelength SEDs (Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Fi-  nally, we discuss the properties of AGNs in U/LIRGs by  comparing the X-ray and other wavelength luminosities  corrected for the torus absorption (Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The  main findings are summarized in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Characteristics of Host Galaxies  We investigate the properties of host galaxies in  U/LIRGs by using the measurements of stellar masses  (M∗) and SFRs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  A strong correlation between these  quantities for the majority of star-forming galaxies has  been well reported (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Brinchmann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2004;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Noeske  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2007;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Elbaz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2007;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Speagle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Sain-  tonge et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Tomczak et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Pearson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2018), called the main sequence (MS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Generally, galax-  ies above the MS are qualified as “starburst”, while  galaxies below the relation are passive galaxies in terms  of their star-formation activity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Thus, the comparison  of these physical quantities enables us to understand the  galaxy’s evolution in the populations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Figure 7 shows the averaged values of M∗ and SFR  compared with merger stages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The M∗ is almost simi-  lar for all merger stages, while the SFR increases with  merger stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The left panel of Figure 8 presents the  SFR–M∗ relation obtained by the multiwavelength SED  analysis for our U/LIRGs color-coded by the merger  stages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' We overplot the values of Palmer–Green (PG)  quasars at z < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1 as gray diamonds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' For these quasars,  the SFRs are estimated by the UV-to-IR SED decompo-  sition (Lyu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017) and stellar masses are referred  from Xie et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2021) based on the high-resolution opti-  cal and near-IR images (Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2016) or the M∗–  MBH relation of Greene et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='15 For comparison,  we also plot some MS relations for SDSS star-forming  galaxies at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='015 ≤ z ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1 (Elbaz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2007), a large  homogeneous collection of star-forming galaxies out to  z ∼ 6 (the relation at z ≈ 0 is adopted;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Speagle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2014), and SDSS DR7 galaxies with 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01 < z < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  and M∗ > 108M⊙ on the basis of SFRs derived from  UV and mid-IR (12 or 22 µm) luminosities (Saintonge  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The previous IR SED analysis of local U/LIRGs using  the photometry of unresolved total systems by Shang-  guan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2019) decouples the contributions of AGN  and starburst emission and suggests the whole U/LIRGs  are above the MS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' On the other hand, using the sepa-  rated photometry of individual sources as possible in  the SED fitting, we find that some component sources  in early mergers sit on or lie below the MS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The early  mergers and PG quasars have wide ranges of SFRs above  and below the MS, while the late mergers have the high-  est SFRs above the MS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Except for some early merg-  ers, the distributions of the stellar masses are compa-  rable in both U/LIRGs and PG quasars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' As a result,  the average specific SFR, sSFR (= SFR/M∗), is much  larger in late mergers (log(sSFR/yr−1) = −8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='51±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='58)  than those in early mergers (−9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='58±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='98), nonmergers  (−9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='50±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='51), and PG quasars (−10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='16±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='64).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Inter-  estingly, this is well consistent with the recent high-  resolution simulations of gas-rich major mergers (Blecha  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018), which predicts the starbursts with the high-  est sSFR (−8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4 in a logarithmic scale) in the final phase  of mergers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Although the progenitor of quasars are not  necessarily triggered by mergers (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Xie et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021),  these results support that the starburst activities in  U/LIRGs are triggered in early mergers, and suppressed  after late mergers with high sSFR (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Di Matteo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2005;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Hopkins et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2008;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Ellison et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Barrera-  Ballesteros et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Shangguan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' U et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  15 The values of MBH are referred from Veilleux et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2009a)  by averaging the results from different measurements, including  spheroid luminosity, spheroid velocity dispersion, reverberation  mapping, and virial relation (see Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  20  Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Averaged Values of Best-fit Parameters and Accompanying Results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Parameter  Merger Stage  A  B  C  D  A–B  C–D  N  Free parameters (UV-to-IR SED analysis;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2)  1  log(tau main) (Myr)  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='38 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='23  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='42 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='22  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='50 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='12  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='53 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='40 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='23  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='52 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='38 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='19  2  log(age main) (Myr)  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='89 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='12  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='85 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='91 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='89 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='87 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='89 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='87 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  3  log(age bq) (Myr)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='65 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='22  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='68 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='21  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='55 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='32  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='39 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='31  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='67 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='22  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='44 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='32  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='61 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='16  4  log(r sfr)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='12 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='79  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='39 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='88  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='57 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='77  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='19 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='64  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='24 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='84  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='74  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='26 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='85  5  E BV lines  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='72 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='51  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='99 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='43  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='83 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='38  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='37 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='29  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='84 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='50  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='22 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='41  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='98 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='56  6  powerlaw slope  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='47 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='24  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='41 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='31  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='39 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='27  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='35 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='29  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='45 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='27  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='36 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='29  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='40 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='29  7  qpah  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='19 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='58  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='16 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='68  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='85 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='38  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='80 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='54  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='17 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='62  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='82 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='50  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='23 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='59  8  umin  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='18 ± 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='49 ± 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='15 ± 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='95  29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='93 ± 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='15  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='50 ± 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='25  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='57 ± 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='25  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='91 ± 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='52  9  alpha  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='19 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='20  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='20 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='23  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='18 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='22  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='31 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='22  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='19 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='22  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='27 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='23  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='17 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='20  10  τV  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='51 ± 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='95  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='26 ± 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='15  74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='31 ± 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='58  73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='37 ± 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='63  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01 ± 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='16  73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='67 ± 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='31  67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='56 ± 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='52  11  fAGN  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='16 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='13  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='26 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='18  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='18 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='19  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='14 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='20 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='19  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='36 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='26  12  E(B − V ) (mag)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='40 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='26  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='25 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='17  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='39 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='19  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='33 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='27  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='33 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='23  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='35 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='59 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='21  13  Tpolar (K)  164.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='03 ± 37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='97  173.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='29 ± 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='66  134.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10 ± 27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='44  132.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='57 ± 33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  168.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='15 ± 29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='25  133.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06 ± 31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='40  172.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='83 ± 59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='96  Fixed Parameters (UV-to-IR SED analysis;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2)  14  σ (degree)  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4 ± 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='9  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2 ± 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3 ± 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8 ± 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3 ± 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2  15  i (degree)  54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4 ± 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='9  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3 ± 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7 ± 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0 ± 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2  58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0 ± 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5 ± 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7  62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='9 ± 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='9  Free Parameters (radio fitting;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3)  16  α†  radio  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='54 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='16  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='52 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='52 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='14  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='38 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='54 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='13  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='43 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='16  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='52 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='16  17  q†  ir  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='39 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='41  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='26 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='29  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='50 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='19  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='57 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='27  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='34 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='37  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='55 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='25  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='94  Accompanying results  18  log(M∗) (M⊙)  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='23 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='91  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='42 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='39  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='43 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='35  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='35 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='52  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='31 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='74  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='37 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='48  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='54 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='45  19  log(SFR) (M⊙ yr−1)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='49 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='82  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='55  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='53 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='38  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='98 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='32  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='74 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='77  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='86 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='40  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='34  20  log(sSFR) (yr−1)  −9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='74 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  −9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='36 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='80  −8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='90 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='49  −8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='36 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='54  −9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='58 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='98  −8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='51 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='58  −9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='50 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='51  21  log(L1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4GHz)† (erg s−1)  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='19 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='88  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='75 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='52  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='30  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='47 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='44  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='44 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='80  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='36 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='44  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='97 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='90  22  q†  excess  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='12 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='03  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='03  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  23  log(L6,AGN) (erg s−1)  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='39 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='95  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='77 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='60  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='30 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='48  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='52 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='50  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='54 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='85  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='45 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='50  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='18 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='54  24  log(L12,t) (erg s−1)  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='03 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='83  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='31 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='49  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='93 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='50  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='52  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='14 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='73  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='52  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='74 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='51  25  log(L12,p) (erg s−1)  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='24 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='29  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='75  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='24  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='46 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='75  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='16 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='55  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='35 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='65  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='34 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='84  26  log(L12,AGN) (erg s−1)  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='21 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='85  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='52 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='53  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='40  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='23 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='53  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='34 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='75  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='17 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='50  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='98 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='56  27  log(Ltorus) (erg s−1)  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='18 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='80  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='43 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='44  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='98 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='45  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='14 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='50  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='28 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='69  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='49  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='80 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='51  28  log(Lpolar) (erg s−1)  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='62 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='54  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='40 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='18  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='39  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='29 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='59  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='53 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='43  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='22 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='55  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='99 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='46  29  log(LAGN,int) (erg s−1)  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='49 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='71  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='80 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='36  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='35 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='45  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='53 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='57  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='61 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='62  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='47 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='54  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='31 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='53  30  log(MBH) (M⊙)  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='80 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='41  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='83 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='24  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='34 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='28  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='83 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='46  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='81 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='35  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='67 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='47  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='79 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='25  31  log(λEdd)  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='43 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='17 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='47  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='15 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='45  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='29 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='67  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='33 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='85  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='24 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='61  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='63 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='75  32  log(Rpolar) (pc)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='77 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='59  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='56 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='24 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='45  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='35 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='40  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='68 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='45  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='32 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='42  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='90 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='55  Note—Comments: The table summarizes the averaged values of each parameter for individual merger stages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (1–13) Free parameters as listed in Table 3  (see Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (14–15) Two fixed parameters of torus angular width and inclination angle as listed in Table 3 (Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (16–17) free parameters  of the radio fitting (Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (18–20) stellar mass (M∗), SFR, and specific SFR (sSFR = SFR/M∗) as listed in Table A2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (21–22) rest-frame radio  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4 GHz luminosity and radio-excess parameter (qexcess) as listed in Table A3 (see Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (23–26) rest-frame 6 µm luminosity of AGN (torus and  polar dust) component, rest-frame 12 µm luminosities of the torus, polar dust, and total AGN component (see Table A4);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (27–32) UV-to-IR (mainly  IR) luminosities (torus, polar dust, and AGN components), SMBH mass, Eddington ratio, and physical sizes of the polar dust structure (Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5) as  listed in Table A5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  † The values of the sources whose αradio is fixed at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5 are excluded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The right panel of Figure 8 denotes the SFR–M∗ re-  lation for U/LIRGs with or without AGNs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Red stars  mark the hard X-ray–detected AGNs and three AGNs  that are re-classified by the significance test with BIC  values (Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4), while dark gray circles mark the  starburst-dominant or hard X-ray–undetected sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The U/LIRGs but several early mergers below the MS  show similar distributions regardless of the presence or  absence of AGNs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  About 50% of the AGNs in late  mergers are CT AGNs and, among the hard X-ray–  undetected sources, there are few CT AGN candidates  based on their 3σ upper limits in the 8–24 keV band  (Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' These results support that the  obscuration of the AGNs is not related to the difference  in the SFR–M∗ distribution with and without AGNs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  A similar result in the IR band for local U/LIRGs of  GOALS sample is reported by Shangguan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2019),  who evaluate the presence of AGNs when the IR SED  fit is significantly improved by adding the torus compo-  nent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Their AGN classification is based on the signa-  21  N  A  B  C  D  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  logM *   [M ]  N  A  B  C  D  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  logSFR  [M  yr  1]  Figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Left panel: averaged values of logarithmic M∗ compared with merger stages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Right panel: averaged values of  logarithmic SFR compared with merger stages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  7  8  9  10  11  12  logM *  2  1  0  1  2  3  logSFR  Speagle+14  Saintonge+16  Elbaz+07 (z<0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1 SDSS)  PG QSO (z<0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1)  Stage-A(Early)  Stage-B(Early)  Stage-C(Late)  Stage-D(Late)  Stage-N  7  8  9  10  11  12  logM *  2  1  0  1  2  3  logSFR  Speagle+14  Saintonge+16  Elbaz+07 (z<0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1 SDSS)  AGN (U/LIRG)  SB or HX nondet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (U/LIRG)  PG QSO (z<0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1)  Figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Left panel: logarithmic stellar mass in M⊙ vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' logarithmic SFR in M⊙ yr−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The blue circles, green triangles,  orange diamonds, red stars, and purple triangles represent the sources in stages A, B (early mergers), C, D (late mergers), and  N (nonmergers) U/LIRGs, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The gray diamonds illustrate the PG QSOs at z < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1, whose SFRs are estimated by  the UV-to-IR SED decomposition (Lyu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The black dotted curve and cyan area denote the MS and 1σ uncertain  reported by Speagle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2014), while the dashed solid curve and shading represent those reported by Saintonge et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The green dotted line is the MS among z < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1 SDSS galaxies Elbaz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Right panel: the same but the sources are  classified by AGNs in U/LIRGs (red star), starburst-dominant or hard X-ray–nondetected sources in U/LIRGs (gray circle),  and PG QSOs (gray diamond).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  ture of strong mid-IR emission from the AGNs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Thus,  no matter which classifications of hard X-ray or mid-IR  observations we select, the SFR–M∗ relation implies the  small influence of the AGN activities on the starburst  activities in the phase of U/LIRGs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Origin of Radio Emission from U/LIRGs  Radio observation is a potential approach to reveal a  mixture of starburst and AGN activities in U/LIRGs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  About 10% of AGNs radiate strong synchrotron emis-  sion primarily from the powerful relativistic jets in the  radio band, observable as radio-loud AGNs (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Begel-  man et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 1984).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The other AGNs are classified as radio-  quiet AGNs, whose radio emissions are derived from  a wide range of possible mechanisms: star formation,  AGN-driven wind, free-free emission from photoionized  gas, low power jets, and the innermost accretion disc  coronal activities (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Panessa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Kawamuro  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Thanks to the long wavelengths, radio ob-  servations can overcome the effects of dust obscuration  in U/LIRGs and investigate their central engines, par-  ticularly starbursts and/or AGNs (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Condon et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  22  Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  1991;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Lonsdale et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2003;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Murphy 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Vardoulaki  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Radio Slope  For star-forming galaxies, the radio emission typically  appears as a power law spectrum (Sν ∝ ν−α) from ther-  mal and non-thermal emission associated with the for-  mation of massive stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The thermal emission is pro-  duced by the young massive O/B stars dominating the  ionization in HII regions, and the non-thermal emission  is produced by supernova remnants of the more mas-  sive stars than ≳8 M⊙, accelerating cosmic-ray electrons  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Helou et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 1985;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Condon 1992).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Under such con-  ditions, the thermal bremsstrahlung free-free emission  from the HII regions has a flat slope (α ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1), while  the non-thermal free-free emission shows a steep slope  (α ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Niklas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 1997).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The contribution of  non-thermal emission is much larger at frequencies be-  low 10 GHz than the thermal emission, as confirmed by  the best-fit models of synchrotron (pink) and nebular  free-free (gray) emission in the radio band (see Figure 1  and Figures E1–E10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  However, since the AGNs also  radiate the synchrotron emission with a similar slope  to the starburst emission (α ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Krolik 1999;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Niklas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 1997;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' but see the study of radio-slope map  by Vardoulaki et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2015 and Linden et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019), this  makes difficult to separate the starburst and AGN ra-  dio emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' For U/LIRGs, the nuclear radio emission  should have flat spectra due to optically-thick free-free  absorption (Condon et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 1991;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Clemens et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2008;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Leroy et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Murphy et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Murphy 2013),  and thus the radio slope could not be a tracer of AGNs  but an indicator of the surrounding environment of the  nuclear starbursts and AGNs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The top panels of Figure 9 display the radio slope  within the 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07–3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0 GHz band, αradio, (Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3) as  a function of the SFR and the fraction of the AGN lu-  minosity in the IR band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The previous radio study of  U/LIRGs performed by Murphy (2013) reports that the  median value of the radio slope at ≲5 GHz for U/LIRGs  is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5, and the slopes decrease with merger stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The  values in our work are well consistent with their me-  dian value and decreasing trend.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The flat slope in late  mergers with high SFRs (αradio ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0–0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5) can be ex-  plained by the optically-thick free-free absorption due  to the rich environment of the nuclear region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='16 In the  right panel, the hard X-ray–detected AGNs and three  16 The AGNs with high-Eddington ratios also show the flat radio  slope (Laor et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Yang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020b), whose contribution  of the radio emission may be smaller than those of starbursts as  discussed on the correlation coefficient (qIR).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  newly-identified AGN candidates are characterized as  the positive values of the fraction of AGN luminosity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  As mentioned above, the AGN fraction (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', the domi-  nance of AGN activity) is not correlated with the radio  slope for U/LIRGs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Radio–IR Correlation Coefficient  Alternatively,  the correlation coefficient,  qIR  (=  logLIR/L1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4GHz;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' see Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3), can be a comple-  mentary parameter to unveil the presence of AGNs in  U/LIRGs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  For star-forming galaxies, a tight correla-  tion between radio and IR luminosities is reported (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=',  Kennicutt 1998;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Bonzini et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2015), whose luminos-  ity ratio is expressed by qIR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' For the AGN-dominant  sources, the value should be small due to the powerful  synchrotron emission from the AGN (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Yun et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2001;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' U et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  We investigate the distribution  of qIR as a function of the SFR and the fraction of the  AGN luminosity (bottom panels of Figure 9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Except for  three outliers below the criteria specified as radio-excess  (qIR < 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='64, marked by gray dotted line;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Yun et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2001), these U/LIRGs are distributed around the typi-  cal value of star-forming galaxies, ∼2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='64 (black dashed  line;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Bell 2003), without regard for merger stage and  SFR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Remarkably, the sources having larger fractions of  AGN luminosity tend to show smaller qIR, indicating the  strong radio emission due to the synchrotron radiation  from the AGNs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Not only the sources with qIR < 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='64  (Yun et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2001), but those with qIR < 2 have AGNs  for the U/LIRGs in our sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Radio Excess Parameter  In the left panel of Figure 10, we also compare  the SFR and radio 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4 GHz luminosities (L1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4GHz) for  U/LIRGs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The black dashed line is the empirical corre-  lation from the radio–far-IR luminosity relation and the  conversion factor between SFR and far-IR luminosity  for star-forming galaxies in Kennicutt (1998), assuming  Chabrier IMF (see also Bonzini et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2015):  log(L1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4GHz/erg s−1) = log(SFR) + 37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  (2)  Our targets roughly follow the empirical relation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Delvecchio et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2017) introduce a new diagnostics for  AGNs by using the radio excess parameter, qexcess =  log(L1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4GHz/SFR).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' They suggest that the sources hav-  ing qexcess > 38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='130×(1+z)0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='013 in (erg s−1)/(M⊙ yr−1)  are likely attributable to AGN activities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' As shown in  the right panel, the radio-excess sources in our samples  have fAGN > 0 (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', hosting AGNs) in the IR band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  As a whole, the radio-excess sources in U/LIRGs host  AGNs detected in the IR and X-ray bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Whereas,  the other major population of radio-quiet sources in  23  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  logSFR  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  radio  Murphy+13  Stage-A(Early)  Stage-B(Early)  Stage-C(Late)  Stage-D(Late)  Stage-N  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  fAGN (= LIR, AGN/LIR)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  radio  Murphy+13  Stage-A(Early)  Stage-B(Early)  Stage-C(Late)  Stage-D(Late)  Stage-N  2  1  0  1  2  3  logSFR  1  0  1  2  3  4  qir = log(LIR/L1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4GHz)  radio-excess (Yun+01)  Bell (2003)  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5 (fixed)  Stage-A(Early)  Stage-B(Early)  Stage-C(Late)  Stage-D(Late)  Stage-N  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  fAGN (= LIR, AGN/LIR)  1  0  1  2  3  4  qir = log(LIR/L1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4GHz)  radio-excess (Yun+01)  Bell (2003)  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5 (fixed)  Stage-A(Early)  Stage-B(Early)  Stage-C(Late)  Stage-D(Late)  Stage-N  Figure 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Top panels: logarithmic SFR vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' αradio (left) and fraction of AGN luminosity in the IR band vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' αradio (right),  excluding the sources whose αradio is fixed at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The sources with fAGN = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0 mean the U/LIRGs which do not have AGNs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The dashed line is the median of low-frequency (<5 GHz) αradio among U/LIRGs reported by Murphy (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Bottom panels:  logarithmic SFR vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' qIR (left) and fraction of AGN luminosity in the IR band vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' qIR (right).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The dashed line is the averaged  values reported in Bell (2003), and the dotted gray line illustrates the threshold for radio-excess (qIR < 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='64) as a tracer of an  AGN (Yun et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2001;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' U et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Large symbols are the same in Figure 8, while small crosses denote the sources where  αradio = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5 is assumed in the radio fitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2  1  0  1  2  3  logSFR  35  36  37  38  39  40  41  42  logL1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4GHz  [erg s  1]  Kennicutt+98  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5 (fixed)  Stage-A(Early)  Stage-B(Early)  Stage-C(Late)  Stage-D(Late)  Stage-N  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  fAGN (= LIR, AGN/LIR)  36  37  38  39  40  41  qexcess = log(L1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4GHz/SFR)  Delvecchio+17  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5 (fixed)  Stage-A(Early)  Stage-B(Early)  Stage-C(Late)  Stage-D(Late)  Stage-N  Figure 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Left panel: logarithmic SFR vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' logarithmic radio luminosity at 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The black dashed line is obtained by  the empirical radio-far-IR relation in star-forming galaxies in Kennicutt (1998), assuming Chabrier IMF (see Bonzini et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Right panel: fraction of AGN luminosity in the IR band (fAGN) vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' radio excess parameter (qexcess).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The sources with  fAGN = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0 mean the U/LIRGs which do not have AGNs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The black solid curve shows the threshold of radio-excess sources at  z ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0 (Delvecchio et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The symbols are the same in Figure 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  24  Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  U/LIRGs are indistinguishable from AGNs or not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The  same results are reported for AKARI-selected star-  forming galaxies with and without AGNs (Mori´c et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2010), indicating that the AGNs in U/LIRGs are typical  radio-quiet AGNs in star-forming galaxies (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', the large  contribution of the radio emission from the intense star-  bursts).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Therefore, although sources with high qexcess  values likely contain AGNs, the radio emission reflects  the intensity of the starburst activities (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', SFR) for  the majority of U/LIRGs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' WISE Color: New Wedge of Buried AGNs  Near-IR to mid-IR observations have been thought  of as a promising tool to detect the AGN emission in  U/LIRGs (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Veilleux et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2009b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Petric et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Imanishi & Saito 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Imanishi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' D´ıaz-Santos  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' A large part of the emission from central  AGNs in U/LIRGs is absorbed by the surrounding ma-  terials such as the torus with a large covering fraction  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Imanishi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2006, 2008;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Ricci et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Ya-  mada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019) and re-radiated chiefly in the mid-IR  wavelength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The ∼3–30 µm SEDs of the reprocessed  dust emission heated by the AGN is characterized as a  steep power-law slope (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Laurent et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2000;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Stern  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2005;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Assef et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Indeed, the IR color se-  lection with WISE has been exploited to search for the  optically obscured AGNs (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Jarrett et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Stern  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Mateos et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2012, 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Assef et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2013,  2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Secrest et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Toba et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Ellison et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Satyapal et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Weston et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Goulding  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Pfeifle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' W1–W2 Color  Figure 11 presents the WISE W1–W2 (or [3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4]–[4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6]  in Vega magnitude) color as a function of SFR (left)  and AGN fraction in the IR band (right).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='17  Here,  the WISE magnitudes are corrected for Galactic ex-  tinction (Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Stern et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2012) introduce a  simple mid-IR color criterion of [3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4] − [4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6] > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8 by  using the WISE-selected sources in the Cosmic Evo-  lution Survey (COSMOS;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Scoville et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Sim-  ilarly, Satyapal et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2014) report that a more in-  clusive [3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4] − [4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6] > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5 cut identifies AGNs in low-z  (z < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2) mergers selected from the SDSS survey (El-  lison et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' For our U/LIRGs, we find that all  late mergers have logSFR ≳ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5 and [3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4] − [4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6] ≳ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5,  while most early mergers and nonmergers have smaller  17 The WISE photometry of Mrk 231, a stage D merger hosting the  AGN with high λEdd, is not utilized in the SED analysis due to  the flag of w1-3sat ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06 (W1, W2, W3 = 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='80±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01, 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='58±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01,  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='54±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01, respectively), but is only provided in Figures 11–12  since it will be a small effect on the WISE colors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  SFRs and [3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4] − [4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6] ≲ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5, making it easy to select  the IR-luminous late mergers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  However, the compar-  ison between WISE color and AGN fraction suggests  that the hard X-ray–detected and newly-identified AGN  candidates (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', fAGN > 0) are not distinguished from  the other starburst-dominant or hard X-ray–undetected  sources by the [3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4]–[4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6] color.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' These results indicate  that for U/LIRGs, the [3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4]–[4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6] criteria could not nec-  essarily discriminate between the intense starbursts and  the AGNs discovered with the hard X-ray observations  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Ricci et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2016, 2017a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' WISE Color–color Diagram  Figure 12 shows the WISE color–color diagram ([3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4]–  [4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6] versus [4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6]–[12]) for our sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The AGN wedges  that have been well utilized for the low-z galaxies are  overplotted (Jarrett et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Mateos et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Blecha et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Almost all late mergers are lo-  cated within the AGN wedge that is based on the hy-  drodynamics and radiative transfer simulation of gas-  rich mergers (dashed line;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' see Equation (1) in Blecha  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' In late mergers, it is notable that the val-  ues of [4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6]–[12] magnitudes decrease with the values of  [3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4]–[4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6] magnitudes for the AGNs, while they increase  for the other sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Particularly, the AGNs with  [4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6]–[12] ≲ 3 in stage D mergers (IRAS F05189−2524,  IRAS F08572+3915, UGC 5101, ESO 374−IG032, and  Mrk 231) show the excess in the ∼3–10 µm wave-  length relative to the best-fit SED models with updated  CLUMPY model (Figures E1–E10), corresponding to  the dust emission at the temperature of ∼300–1000 K  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Lyu & Rieke 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The contribution of the near-  IR emission from the old stellar population (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Pol-  letta et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2007) is extracted by the multiwavelength  SED analysis, the origin of the ∼3–10 µm excess can be  explainable by the additional nuclear hot dust heated by  the AGNs, such as inner part of the dusty disk and/or  hot polar dust within the inner parsecs (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', H¨onig et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Garc´ıa-Bernete et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017, 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Lyu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Lyu & Rieke 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Mattila et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Mizukoshi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The near-IR excess in a sample of type 1 AGN is  well reported (Netzer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2007;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Mor et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2009;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Mor  & Netzer 2012) and this hot dust component can also  be part of the known outflows in Mrk 231 (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Feruglio  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Morganti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Veilleux et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The strong near-IR emission from the dusty disk, hot  polar dust, or both is a unique feature of buried AGNs  in late mergers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Although the complete selection of hard X-ray–  detected AGNs by the WISE color seems to be difficult,  some buried AGNs in local U/LIRGs are characterized  by the near-IR excess appearing in the improved AGN  25  2  1  0  1  2  3  logSFR  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  [3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4]  [4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6] in Vega mag  Satyapal+14  Stage-A(Early)  Stage-B(Early)  Stage-C(Late)  Stage-D(Late)  Stage-N  SB or HX nondet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  fAGN (= LIR, AGN/LIR)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  [3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4]  [4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6] in Vega mag  Satyapal+14  Stage-A(Early)  Stage-B(Early)  Stage-C(Late)  Stage-D(Late)  Stage-N  SB or HX nondet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Figure 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' WISE W1–W2 color as a function of SFR (left) and the fraction of AGN luminosity in the IR band (right).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Dashed  line illustrates the W1 − W2 > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5 threshold (Satyapal et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  [4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6]  [12] in Vega mag  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  [3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4]  [4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6] in Vega mag  UGC5101  F05189  F08572  ESO374  Mrk231  This Work  Jarrett+11  Mateos+12  Blecha+18  Stage-A(Early)  Stage-B(Early)  Stage-C(Late)  Stage-D(Late)  Stage-N  SB or HX nondet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Figure 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' WISE color–color diagram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The AGN selection wedges are illustrated as the areas within the dotted gray (Jarrett  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2011), dash-dotted gray (Mateos et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2012), and black dashed (Blecha et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018) boxes, and the pink shaded area is  presented in This work, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Large symbols are the same in Figure 8, while small circles illustrate the sources where  fAGN = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0 (starburst-dominant or hard X-ray–nondetected sources).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  color selection (pink shade);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2 < [4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6] − [12] < 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2, and  [3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4] − [4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6] > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1 × ([4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6] − [12]) + 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='38,  (3)  which are the combination of the previous AGN wedge  for QSOs, Seyfert galaxies, and obscured AGNs (dot-  ted line;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' see Equation (1) in Jarrett et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2011) and  the higher [3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4]–[4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6] region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Among our local U/LIRGs  within the new wedge, the selection purity of the AGNs  in stage C–D mergers is 72+11  −12% (9/12).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Here the frac-  tion and uncertainty are the 50th and 16th–84th quan-  tiles of a binomial distribution, respectively, calculated  with the beta function (Cameron 2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' By contrast,  the completeness of selecting AGNs with the new wedge  is low (40% ± 10%;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 9/23).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Considering that only the  most luminous AGNs (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', IRAS F05189−2524, IRAS  F08572+3915, and Mrk 231) tend to be selected, the low  completeness suggests the difficulty of the identification  of low-luminous AGNs in late mergers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' We also need  to keep in mind that this criterion should be adopted  for local U/LIRGs since it includes the typical criteria  for QSOs and normal AGNs (Jarrett et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Thus,  26  Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='100  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='102  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='104  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='106  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='Rest-frame wavelength [ m]  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='101  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='103  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='105  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='F  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='(normalized at Ks band)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='Stage-A (Early: 8)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='Stage-B (Early: 6)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='Stage-C (Late:  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='Stage-D (Late:12)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='Stage-N (7)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='Averaged SEDs for Hard X-ray Detected AGNs  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='100  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='102  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='104  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='106  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='Rest-frame wavelength [ m]  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='101  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='103  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='105  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='F  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='(normalized at Ks band)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='Stage-A (Early: 5)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='Stage-B (Early: 6)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='Stage-C (Late: 2)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='Stage-D (Late: 7)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='Stage-N (2)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='Averaged SEDs for Hard X-ray Nondetected Sources  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='Figure 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Top panel: rest-frame wavelength vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' flux density normalized at Ks band for the hard X-ray–detected AGNs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Bottom panel: the same but for the soft X-ray–detected galaxies among starburst-dominant or hard X-ray–nondetected sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The solid curves represent the averaged SEDs for the sources in stage A (blue), stage B (green), stage C (orange), stage D (red)  and stage N (purple) U/LIRGs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Values in parentheses are the number of sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The light-colored curves show the SEDs for  individual sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  this new WISE color–color diagram for local U/LIRGs  provides valuable information on the presence of the lu-  minous AGNs hosting the dusty disk, hot polar dust, or  both within the inner parsecs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Averaged SEDs in U/LIRGs  To further understand the characteristics of the hard  X-ray to radio emission in local U/LIRGs, in Figure 13  we illustrate the SEDs for all sources whose X-ray spec-  tra above ≳1 keV are analyzed by Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The Ks (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='159 µm) band (near the peak of the stel-  lar emission) is selected for the normalization since it is  less affected by dust extinction and contamination from  AGN-heated hot dust (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Kim et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2002;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Marconi  & Hunt 2003;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Skrutskie et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2006;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Vika et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='18  The left panel shows the best-fit models of 36 single  and two unresolved dual hard X-ray–detected AGNs  (Mrk 266B/Mrk 266A and NGC 6240S/NGC 6240N),  but excluding three newly identified AGN candidates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Here, the complex X-ray absorption lines in NGC 1365  are ignored as it is a dramatically variable feature,  mainly caused by highly ionized species of Fe in a high-  velocity outflow (Rivers et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' On the other hand,  the right panel shows those of two starburst-dominant  18 The results are almost unchanged even if the normalization is  chosen in the H band, which is also a reliable tracer of the stellar  luminosity (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Marconi & Hunt 2003;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Hainline et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='100  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='102  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='104  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='106  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='Rest-frame wavelength [ m]  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='101  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='103  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='105  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='F  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='(normalized at Ks band)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='Early Merger (NonX:  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='Early Merger (AGN: 14)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='Early Merger (SB:  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='Late Merger (AGN: 17)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='Late Merger (SB:  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='9)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='Averaged SEDs for Local U/LIRGs  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='109  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1011  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1013  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1015  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1017  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1019  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='Rest-frame frequency [Hz]  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='100  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='101  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='102  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='103  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='L  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='(normalized at Ks band)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='Early Merger (NonX:  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='Early Merger (AGN: 14)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='Early Merger (SB:  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='Late Merger (AGN: 17)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='Late Merger (SB:  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='9)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='Averaged SEDs for Local U/LIRGs  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='Figure 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Top panel: rest-frame wavelength vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' flux density normalized at Ks band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Bottom panel: rest-frame frequency  vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' luminosity normalized at Ks band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The dotted green curve shows the averaged SEDs for the sources whose X-ray spectra  above ≳1 keV are not obtained in stage A–B (early) mergers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The solid curves represent the averaged SEDs for the hard  X-ray–detected AGNs in stage A–B (early mergers;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' blue) and stage C–D (late mergers;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' red).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The dashed curves are the same  ones for the soft X-ray–detected galaxies among starburst-dominant or hard X-ray–nondetected sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Values in parentheses  are the number of sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' These SED templates are available in Table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  sources detected in the hard X-ray band (IC 1623A  and NGC 3256) and 20 hard X-ray–undetected sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Since the ≲3 keV spectra are complex due to the Galac-  tic extinction and the optically thin thermal emission in  the host galaxy, we plot the best-fit models of the X-ray  spectra in the 3–200 keV band for AGNs and 3–20 keV  for the other sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  These SEDs exhibit several common features in the  UV-to-radio bands regardless of the presence or absence  of AGNs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' First, they have a dip in the UV-to-optical  wavelength, even though the SEDs are corrected for  Galactic extinction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The UV emission from the stel-  lar populations and/or AGN disk is absorbed by the  gas and dust of the host galaxy, torus, and polar dust.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Second, the IR-to-radio fluxes relative to the Ks band  increase with merger stage due to the re-radiation from  the dust of AGNs and primarily intense starbursts (Sec-  tion 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1 and Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Third, the increase of the IR  emission causes the steep slope in the near-to-mid-IR  band to appear as the features in WISE [3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4]–[4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6] color  (Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Figure 14 presents the averaged SEDs for AGNs and  the other sources in both early and late mergers, whose  X-ray spectra above ≳1 keV are analyzed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' We also plot  the averaged UV-to-radio SEDs for the sources whose X-  ray spectra above ≳1 keV are not obtained, all of which  28  Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  100  101  102  Rest-frame wavelength [ m]  100  101  102  103  104  F  (normalized at Ks band)  Early Merger (Non-X: 6)  Early Merger (AGN: 14)  Early Merger (SB:  11)  Late Merger (AGN: 17)  Late Merger (SB:  9)  F08572 (WISE)  F08572 (others)  Averaged SEDs for Local U/LIRGs  Figure 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Enlarged picture of the IR (1–600 µm) wave-  length of the left panel in Figure 14 (rest-frame wavelength  vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' flux density normalized at Ks band).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Stars and squares  mark the photometry of WISE and other IR instruments  (2MASS, AKARI, and Herschel) for the AGN in IRAS  F08572+3915.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  are in early mergers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' These averaged SED templates in  Figure 14 are available in Table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' By comparing the  AGNs (solid curves) and the others (dashed and dot-  ted curves), we find that the averaged SEDs of the lat-  ter population show stronger far-IR fluxes than those of  the former.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' This support that the starburst-dominant  sources have cooler dust than AGNs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Whereas, the UV-  to-radio SEDs of AGNs and non-AGN sources holisti-  cally resemble each other, regardless of the merger stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The difference in the far-IR fluxes is smaller than the  scattering among the individual sources as shown in Fig-  ure 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' This resemblance makes it difficult to identify  the AGNs in U/LIRGs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  In Figure 15, we compare the averaged SEDs and the  photometry of the buried AGNs in IRAS F08572+3915,  which is one of the most luminous AGNs in our sam-  ple and is well selected by the WISE color–color di-  agram (Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  We find that the source shows  the flux peak at shorter IR wavelengths than in nor-  mal U/LIRGs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  This suggests the presence of a large  amount of hot dust, which can be a unique feature of  the luminous AGNs deeply hidden by gas and dust.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Re-  gardless of the presence of the IR-excess features, the  X-ray spectra of AGNs and others are completely dif-  ferent (Figure 14).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The AGNs have much larger X-ray  fluxes than those in the starburst-dominant or hard X-  ray–undetected sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' According to the X-ray spec-  tral analysis in Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2021), the observed X-  rays of AGNs become dimmed with merger stage due to  Table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Averaged SED Templates in Our Targets  Column Name  Format  Unit  Description  Class  LONG  Classification  Wavelength  DOUBLE  µm  Wavelength  Frequency  DOUBLE  Hz  Frequency  Normed FNU  DOUBLE  Flux density at each wavelength  Normed LNU  DOUBLE  Luminosity at each wavelength  (This table is available in its entirety in machine-readable form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=')  the increase of the hydrogen column density, while for  the starburst-dominant sources, the soft X-rays domi-  nated by the X-ray binary emission in the host galaxy  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Mineo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2012) become brighter in late merg-  ers with high SFRs than in early mergers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Overall, the  AGNs show a significant X-ray excess relative to the  other wavelength emission, as represented by the com-  parison between observed X-ray luminosity and SFR in  Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3 of Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Therefore, despite  the effects of the X-ray weakness (Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5), the ex-  cess of X-ray fluxes relative to the UV-to-radio SEDs  should be an incomparable characteristic enabling us to  reveal the true energy sources (intense starbursts and/or  buried AGNs) in U/LIRGs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' X-ray Weak AGNs in IR-luminous Galaxies  We finally investigate the multiwavelength AGN lumi-  nosities corrected for the absorption of the host galaxy,  torus, and polar dust.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2021) estimate the  de-absorbed 2–10 keV AGN luminosities and find that  the ratio of the bolometric AGN luminosity to the X-ray  luminosity is quite large for the AGNs in late mergers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  This X-ray weakness has been thought of as a particular  property of the AGNs in local U/LIRGs (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Teng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2014, 2015), and its origin (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', the optically thick failed  winds launched from an inner region of the disk) is dis-  cussed in Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' For understanding the  AGN activities in U/LIRGs through cosmic history, it is  at least necessary to probe whether the X-ray weakness  is a common feature for both low-z and high-z U/LIRGs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 6 µm Luminosity vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2–10 keV Luminosity  Figure 16 illustrates the relation between monochro-  matic luminosity of the AGN emission at rest-frame  6 µm derived from the multiwavelength SED decomposi-  tion (L6,AGN) and unabsorbed (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', de-absorbed) X-ray  luminosity in the rest-frame 2–10 keV band (LX,unabs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Many studies report that the mid-IR and X-ray lumi-  nosities of the AGN component are strongly correlated  over a wide luminosity ranges (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Lutz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2004;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  29  40  41  42  43  44  45  46  47  48  logL6, AGN [erg s  1]  40  41  42  43  44  45  46  47  logLX, unabs [erg s  1]  Stern (2015)  Mateos et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2015)  Toba et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2022)  This Work  ELIRG(z~2)  WISSH(z~2  4)  GOODS Herschel(z~1  3)  Extremely Red Quasar(z~2  3)  BL DOG(z~1)  IR-bright/Hot DOG(z~1-3)  Stage-A(Early)  Stage-B(Early)  Stage-C(Late)  Stage-D(Late)  Stage-N  Figure 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Rest-frame 6 µm luminosity contributed from AGNs vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' unabsorbed (absorption-corrected) rest-frame 2–10 keV  luminosity for AGNs in various IR-luminous galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The cyan triangle indicates an ELIRG at z ∼ 2 (Toba et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The yellow circles represent WISSH quasars at z ∼ 2–4 (Martocchia et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Zappacosta et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The pink circles  indicate mid-IR luminous quasars at z ∼ 1–3 in the GOODS–Herschel fields (Del Moro et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2016) while pink diamonds show  extremely red quasars at z ∼ 2–3 (Goulding et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The pink and red squares mark broad-line DOGs at z ∼ 1 (Zou  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020) and IR-bright/hot DOGs at z ∼ 1–3 (Ricci et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017c;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Vito et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Zappacosta et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Toba et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020a),  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Their colors (cyan, yellow, pink.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' and red) are largely categorized by the typical NH of the populations (see the  text).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The other symbols are the same in Figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The green dashed and blue dotted lines illustrate the linear relation using a  sample drawn from the eROSITA Final Equatorial Depth Survey (Toba et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2022a) and the Bright Ultra-hard XMM-Newton  Survey (Mateos et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2015), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The black solid curve denotes the 2D polynomial relations from Stern (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Red  dash-dotted line and the pink shaded area are the best-fitting relation and its 1σ dispersion among stage C–D mergers and the  high-z IR-luminous sources, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Ramos Almeida et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2007;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Gandhi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2009;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Ichikawa  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2012, 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Asmus et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Mateos et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Stern 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Garc´ıa-Bernete et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Toba et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019a, 2022a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Here, we plot the values  for local U/LIRGs color-coded by merger stages, and  overplot those for IR-luminous galaxies corresponding  to high-z U/LIRGs: an extremely luminous IR galaxy  (ELIRG) at z ∼ 2 (Toba et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021b);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' WISE/SDSS  selected hyper-luminous (WISSH) quasars at z ∼ 2–4  (Martocchia et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Zappacosta et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' mid-IR  luminous quasars at z ∼ 1–3 from the GOODS-Herschel  fields (Del Moro et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2016);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' extremely red quasars at  z ∼ 2–3 (Goulding et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018b);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' dust-obscured galax-  ies (DOGs) with broad optical/UV emission lines (BL  DOGs) at z ∼ 1 (Zou et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' and IR-bright DOGs  at z ∼ 1 (Toba et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020a) and hot DOGs at z ∼ 1–3  (Ricci et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017c;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Vito et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Zappacosta et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='19 The values of L6,AGN and LX,unabs for high-z  IR-luminous galaxies are presented in their references  mostly by the IR SED decomposition and X-ray spec-  tral analysis, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The AGNs are unobscured  19 The L6,AGN of extremely red quasars in Goulding et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2018b)  and hot DOGs in Ricci et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2017c) are provided by assuming  that the 6 µm emission is AGN-dominant (see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Del Moro  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2016 for extremely red quasars;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Stern et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Assef et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2016, 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Tsai et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Zappacosta et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018  for hot DOGs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  30  Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  (≲1022 cm−2) for an ELIRG (cyan), weakly obscured  (∼1021–1023 cm−2) for WISSH quasars (yellow), moder-  ately obscured (∼1022–1024 cm−2) for mid-IR luminous  quasars in the GOODS-Herschel fields, extremely red  quasars, and BL DOGs (pink), and heavily obscured  (≳1023 cm−2) for IR-bright/hot DOGs (red).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  More-  over, we compare these values with the typical relation  obtained from the SDSS-selected low-z Seyfert galaxies  (Stern 2015), the Bright Ultra-hard XMM-Newton Sur-  vey (BUXS;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Mateos et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2015), and the eROSITA Final  Equatorial Depth Survey (eFEDS;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Toba et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2022a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  We find that several late mergers of local U/LIRGs lie  below the typical L6,AGN–LX,unabs relation, supporting  the X-ray weakness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' For late mergers (stage C and D)  and high-z IR-luminous galaxies, we conduct a Bayesian  maximum likelihood method of Kelly (2007) between the  two parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The resulting linear function is  log(LX,unabs) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='80 log(L6,AGN) + 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='69,  (4)  and the 1σ dispersion is ±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='50 dex (red dashed line  and pink shaded area).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The correlation coefficient is  r = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='92 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02, confirming a tight correlation for low-  z and high-z IR-luminous sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' These AGNs in the  IR-luminous sources at z ∼ 0–4 are obscured sources  and show smaller de-absorbed X-ray luminosities rel-  ative to the mid-IR luminosities than the typical rela-  tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' In particular, most AGNs in IR-bright/hot DOGs  are heavily obscured (≳1023 cm−2) and explicitly X-ray  weak among them (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Ricci et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017c;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Toba et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2020a), sharing similarity with the X-ray weak AGNs in  late mergers for local U/LIRGs (Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Optical to X-ray Spectral Index  Additionally, we display the comparison between Ed-  dington ratio (λEdd) and the optical to X-ray spec-  tral index (αOX;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Tananbaum et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 1979) in Fig-  ure 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The definition of αOX is provided by using  the monochromatic luminosity at rest-frame 2500 ˚A of  the intrinsic AGN disk emission (L2500,disk) and the de-  absorbed monochromatic luminosity at rest-frame 2 keV  (L2keV,unabs) as below:  αOX = log(L2keV,unabs/L2500,disk)  log(ν2keV/ν2500)  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  (5)  The L2500,disk is obtained by multiwavelength SED anal-  ysis in this work, and L2keV,unabs is calculated from the  best-fit models of the broadband X-ray spectra (Sec-  tion 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The αOX probes the balance between the  accretion disk and hot corona activities, radiating op-  tical and X-ray emission respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Several works re-  port a moderate correlation between the Eddington ra-  tio and αOX (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Lusso et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Chiaraluce et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  4  3  2  1  0  1  log  Edd  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8  OX  Upper limit of z=7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2 ULIRG (GNz7q)  Mrk 231  F08572  Lusso+10  Stage-A(Early)  Stage-B(Early)  Stage-C(Late)  Stage-D(Late)  Stage-N  WISSH(z~2  4)  Figure 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Logarithmic Eddington ratio vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' αOX computed  using extinction-corrected 2500 ˚A and unabsorbed 2 keV  luminosities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The black solid curve represents the best-fit  relation among local and high-z AGNs, respectively (Lusso  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The gray shaded area shows its 1σ uncertainty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The upper limit of a ULIRG at z = 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2 (GNz7q;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Fujimoto  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2022) is shown as a red dashed line since its SMBH  mass and Eddington ratios are not constrained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Yellow  circles mark the WISSH quasars in z ∼ 2–4 (Zappacosta  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The other symbols are the same in Figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2018) for X-ray selected AGNs and a typical relation of  Lusso et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2010) is illustrated by a black solid line in  Figure 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' We overplot the values of WISSH quasars  (yellow circles;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Martocchia et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Zappacosta et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2020), and the upper limit of αOX (< −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='23) provided  with deep Chandra observation for a z = 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2 red quasar  GHz7q, classified as U/LIRG (red dashed line;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Fujimoto  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Although the Eddington ratios contain uncertainties  of about ±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5 dex originating from the MBH measure-  ments (Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021), some AGNs in stage D  mergers show much smaller αOX than the typical re-  lation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The distribution of αOX for X-ray selected  and optical-selected AGNs (Just et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2007;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Lusso  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Dong et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Martocchia et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Chiaraluce et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018) mostly covers from −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0 to  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Whereas, we find that the local stage-D merg-  ers with the largest AGN luminosities (Mrk 231 and  IRAS F08572+3915), many WISSH quasars, and GHz7q  lie αOX ≲ −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The caveat is that the X-ray lumi-  nosity of GHz7q is only corrected for Galactic absorp-  tion, but the Chandra observation of GHz7q confirms  the lack of rest-frame hard X-rays, and the signifi-  cant UV emission suggests the AGN is not heavily ob-  scured.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Its bolometric AGN luminosity estimated by  the optical-to-millimeter SED analysis is (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1) ×  31  1046 erg s−1, which is ∼7 times larger than that of IRAS  F08572+3915 (LAGN,int ∼ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5 × 1045 erg s−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Unless  the AGN of GHz7q has an extreme Eddington ratio  above λEdd ∼ 10, the upper limit of αOX suggests the  possibility that the AGN is also X-ray weak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' X-ray Weakness as a Common Feature  In  summary,  considering  the  small  values  of  LX,unabs/L6,AGN ratio and αOX, the de-absorbed multi-  wavelength SEDs support that the X-ray weakness may  be a common feature among the AGNs in IR-luminous  galaxies over cosmic history (z ∼ 0–7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Intriguingly,  the strong AGN-driven outflows have been discovered  from the z ≲ 1 U/LIRGs (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020) and  the high-z IR-luminous galaxies such as WISSH quasars  (Bischetti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Travascio et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Vietri et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2022), extremely red quasars (Zakamska et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Hamann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Goulding et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018b), and IR-  bright and hot DOGs (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Ricci et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017c;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Toba  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017a,b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Wu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Finnerty et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  As discussed in Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6 of Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2021)  for local late-stage U/LIRGs, the physical mechanism  of the extreme X-ray weakness (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', the X-ray attenu-  ation due to overionized optically-thick failed winds at  ∼102–103 rg) can enhance the UV-driven winds, which  may effectively trigger the massive outflows in low-z and  high-z U/LIRGs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Summary of Multiwavelength Features  Here, we summarize the multiwavelength features of  local U/LIRGs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The component galaxies in early merg-  ers have a wide range of SFRs above and below the MS,  while galaxies in late mergers have the highest SFRs  above the MS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Similar SFR–M∗ distributions of AGNs  and non-AGN sources imply the small influence of the  AGN activities on the star formation in the phase of  U/LIRGs (Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The flat slope of radio emission  in late mergers may be caused by the optically-thick  free-free absorption due to the rich environment of the  nuclear region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The SFRs are correlated with radio  luminosity, indicating the major origin of the radio  emission is from the starburst emission except for the  radio-excess AGNs (Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' In the WISE color–  color diagram, we propose a new wedge of the buried  AGNs in late mergers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The strong near-IR emission  of the hard X-ray–detected AGNs in late mergers sug-  gests that they host the dusty disk and/or hot polar  dust within the inner parsecs (Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The aver-  aged SEDs suggest that the excess of the X-rays is an  incomparable characteristic enabling us to reveal the  true energy sources (intense starbursts and/or buried  AGNs) in U/LIRGs (Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The absorption-  corrected AGN SEDs show the extreme X-ray weakness  relative to the other wavelengths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' This may be a com-  mon feature among the AGNs in IR-luminous galaxies  over the cosmic history (z ∼ 0–7), whose mechanism  will be related to their massive outflows (Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  In short, our results support that (1) the intense star-  burst and buried AGNs occur in late mergers and (2)  these buried AGNs may have dusty disks and/or hot  polar dust, whose X-ray weakness may be related to the  massive outflows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' DISCUSSION I: EVOLUTION OF POLAR DUST  IN U/LIRGS  In this Section, we investigate the structure of polar  dust in U/LIRGs based on the results of the multiwave-  length SED analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The detailed results of the polar  dust are discussed on the obscuration and luminosity  (Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1), gas-to-dust ratio (Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2), the contri-  bution to the IR AGN luminosity (Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3), polar  dust temperature (Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4), and the unified view of  the polar dust structure in U/LIRGs (Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Obscuration and Luminosity  The top left panel of Figure 18 presents the histograms  of the line-of-sight extinction in the V band by the torus  (A(LOS)  V ,torus), while the bottom left panel shows for po-  lar dust extinction (A(LOS)  V ,polar).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The dust extinction of  the polar dust is calculated with RV = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1 (Cardelli  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 1989) and given when 90◦ − i > σ (Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  We note that the values are much smaller than those  of torus due to the initial condition of E(B − V ) = 0–  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8 mag (Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2 and 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Buat et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' We compare the histograms of different groups  of unobscured, obscured, and CT AGNs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' As expected  from the dominance of the torus in the dust extinction,  the A(LOS)  V ,torus becomes larger with the line-of-sight AGN  obscuration in the X-ray band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Whereas, A(LOS)  V ,polar does  not show any positive correlation with the X-ray ob-  scuration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Considering that the hydrogen column den-  sities mainly reflect the absorption by the broad line  region and/or torus for obscured AGNs (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Tanimoto  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Ogawa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Andonie et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2022)20,  the decorrelation between A(LOS)  V ,polar and AGN types will  be derived by the difference in the scales of the torus  (∼1 pc) and the extended polar dust emission (∼10–  1000 pc;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' see Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5) whose typical temperatures  are allowed between 100–250 K (Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  20 Particularly for U/LIRGs, the AGNs show the dramatic vari-  ability in NH, supporting the presence of compact-scale (a few  parsecs) obscurer (Laha et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  32  Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  10  1  100  101  102  103  A(LOS)  V  [mag]  0  3  6  Number of sources  < 10  1  Torus: Unobscured  Torus: C-thin  Torus: CT  41  42  43  44  45  46  logLtorus [erg s  1]  0  4  8  Number of sources  10  1  100  101  102  103  A(LOS)  V  [mag]  0  3  6  Number of sources  < 10  1  Polar: Unobscured  Polar: C-thin  Polar: CT  42  43  44  45  46  logLpolar [erg s  1]  0  4  8  Number of sources  Non  Figure 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Top left panel: histogram of the line-of-sight extinction in the V band by the torus A(LOS)  V ,torus (top).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' These are divided  by the X-ray AGN classification (unobscured, Compton-thin, and CT AGNs;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Bottom left panel: the  same for the polar dust extinction, A(LOS)  V ,polar (bottom).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The seven sources showing 90◦ − i > σ (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', A(LOS)  V ,polar = 0) are excluded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Top right panel: histogram of the torus (top) luminosity in the UV-to-IR band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Bottom right panel: the same for polar  dust luminosity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The number of AGNs whose best-fit SED models do not include a polar dust component is shown on the left side.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  In the top right panel, we illustrate the distributions  of the integrated UV-to-IR (mainly IR) torus (Ltorus),  and in the bottom right panel for polar dust luminosities  (Lpolar).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' They cover the ranges of logLtorus/(erg s−1) ∼  42–45 and logLpolar/(erg s−1) ∼ 43–45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Although seven sources show no signatures of the polar  dust emission (Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4), the distribution of the po-  lar dust luminosities is larger than that of the torus ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  This is in agreement with the high-spatial-resolution  mid-IR imaging by Asmus (2019), who reports that a  large part of the mid-IR luminosities is derived from the  extended emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Gas-to-dust Ratio  The comparison between X-ray absorption and dust  extinction has been investigated to evaluate the gas-to-  dust ratio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The X-rays trace all material of gas and dust  (NH), and the optical-to-IR emission primarily traces  the dust component (AV ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Maiolino et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2001) re-  port that the NH/AV ratios are larger than the Galac-  tic value (NH/AV = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='87 × 1021 cm−2 mag−1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Draine  2003), while for unobscured AGNs those are smaller (see  also Burtscher et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Recent works with the torus  models of CLUMPY and XCLUMPY, but not including  the polar dust component, (Miyaji et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Tanimoto  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Ogawa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021) support that the NH/AV  values are higher than or similar to the Galactic value  for obscured AGNs, but smaller for unobscured AGNs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Ogawa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2021) suggest that the trend could be ex-  plained if the torus angular widths are overestimated in  the IR band due to the contamination from the polar  dust emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  33  1020  1021  1022  1023  1024  1025  N(LOS)  H  [cm  2]  100  101  102  103  A(LOS)  V, torus + A(LOS)  V, polar  [mag]  Galactic value  AV(Polar) >  AV(Torus)  Stage-A(Early)  Stage-B(Early)  Stage-C(Late)  Stage-D(Late)  Stage-N  Figure 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Line-of-sight hydrogen column density N (LOS)  H  derived from X-ray spectra vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  A(LOS)  V ,torus, and polar dust,  A(LOS)  V ,polar (if 90◦ − i > σ, A(LOS)  V ,polar = 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Solid line shows  the Galactic gas-to-dust ratio (NH/AV = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='87 × 1021 cm−2  mag−1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Draine 2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Large orange circles mark the AGNs  showing A(LOS)  V ,polar > A(LOS)  V ,torus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The other symbols are the  same in Figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Our  SED  decomposition  provides  the  values  of  A(LOS)  V ,torus and A(LOS)  V ,polar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' In Figure 19, we compare the X-  ray obscuration and dust extinction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The three AGNs  with A(LOS)  V ,torus < A(LOS)  V ,polar have a wide range of gas-to-  dust ratios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' As mentioned in Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1, both parame-  ters may trace the different regions of a compact torus  in X-rays and extended polar dust in the optical-to-IR  bands, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Except for them, the AGNs with  NH > 1022 cm−2 in our U/LIRGs show A(LOS)  V ,torus >  A(LOS)  V ,polar, meaning the small contribution of the polar  dust component to the dust extinction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' We find that  the obscured AGNs have similar or higher NH/AV ra-  tios than the Galactic one, indicating that the materials  on the compact (a few parsecs) scales in the U/LIRGs  show a large gas-to-dust ratio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Similarly, it is reported that the gas-to-dust mass ra-  tio (Mgas/Mdust) is ∼200–300 for local ULIRGs (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=',  Seaquist et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2004), which is larger than the Galactic  value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' These results may be explainable mainly by two  scenarios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The first scenario is that the AV decreases  by the destruction of the small dust grains by super-  nova shocks and/or expelled by strong AGN winds (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=',  Draine & Salpeter 1979;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Jones et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 1994;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Savage &  Sembach 1996;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Maiolino et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2001;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Gaskell et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2004;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Liang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2004;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Rupke et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2008;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Mannucci et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Roseboom et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Asano et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' R´emy-  Ruyer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The second is that the NH increases  by dust-free gas clouds covering the line-of-sight in BLR  of the AGN (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Granato et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 1997;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Burtscher et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Ichikawa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Ogawa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Mizukoshi  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' More investigations are needed to reveal  the origin of the large gas-to-dust ratios in U/LIRGs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Contribution to the IR AGN Luminosity  The torus and polar dust luminosities in the UV-to-IR  bands are primarily determined by the total AGN lumi-  nosity times their apparent covering fractions (and/or  large volumes).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Considering the averaged torus angu-  lar width is σ ∼ 20◦ (Ogawa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2021), the apparent covering fractions of polar dust can  be expected as Ω/4π = 1 − sin(20◦) ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The polar  dust luminosities are ∼2 times larger than those of the  torus component (left panel of Figure 20;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' see also Sec-  tion 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' If polar dust is likely the dust component of  the AGN-driven outflows, their activities should be cor-  related with the Eddington ratios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Although it is natural  under the situation that the polar dust luminosities are  proportional to the AGN luminosities, we confirm the  positive correlation between the polar dust luminosities  and Eddington ratios in our sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  In the X-rays, it is thought that the torus covering  fractions of Compton-thin matters becomes smaller with  larger Eddington ratios due to the radiation pressure  from the AGN (Ricci et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017d, 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' By analyzing  the broadband X-ray spectra with XCLUMPY, Yamada  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2021) find that the individual torus covering frac-  tion for AGNs in U/LIRGs follow the typical relation,  except for two buried AGNs with λEdd ∼ 1 in stage-D  mergers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' On the other hand, the torus angular width  (or covering fraction) in the IR band with CLUMPY  (Ichikawa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Garc´ıa-Bernete et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019) are  larger than those of X-ray results with XCLUMPY, sup-  porting the significant polar dust emission (Ogawa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Several works with other AGN models calculate the  torus covering fractions in the IR band by using the con-  version factor from the Ltorus/LAGN,int (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Stalevski  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Ichikawa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' However, consider-  ing that the polar dust is thought to be a hollow-cone  structure (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', H¨onig 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Isbell et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2022), it is diffi-  cult to calculate the true covering fractions of the polar  dust assuming the uniform conical distribution (Yang  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' In Figure 21, we investigate the UV-to-IR  luminosities relative to the intrinsic AGN disk luminos-  ity (LAGN,int) for the torus and polar dust components,  as a function of the Eddington ratio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' As noted above,  the Ltorus/LAGN,int ratios are smaller than those of po-  lar dust, and both simple luminosity ratios are not well  correlated with Eddington ratios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  34  Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  logLtorus [erg s  1]  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  logLpolar [erg s  1]  Stage-A(Early)  Stage-B(Early)  Stage-C(Late)  Stage-D(Late)  Stage-N  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  log  Edd  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  logLpolar [erg s  1]  Stage-A(Early)  Stage-B(Early)  Stage-C(Late)  Stage-D(Late)  Stage-N  Figure 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Left panel: logarithmic torus luminosity vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' logarithmic polar-dust luminosity in the UV-to-IR bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Right  panel: logarithmic Eddington ratio vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' logarithmic polar-dust luminosity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The symbols are the same in Figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  4  3  2  1  0  log  Edd  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  Ltorus / LAGN, int  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='47  Stage-A(Early)  Stage-B(Early)  Stage-C(Late)  Stage-D(Late)  Stage-N  4  3  2  1  0  log  Edd  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  Lpolar / LAGN, int  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='57  Stage-A(Early)  Stage-B(Early)  Stage-C(Late)  Stage-D(Late)  Stage-N  Figure 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Left panel: logarithmic Eddington ratio vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' ratio of the torus and intrinsic AGN luminosities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Two AGNs whose  luminosity ratio above 1 are plotted as Ltorus/LAGN,int = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Right panel: logarithmic Eddington ratio vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' ratio of polar dust  and intrinsic AGN luminosities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The symbols are the same in Figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  We find that the AGNs with Lpolar/LAGN,int > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  have the Eddington ratios of logλEdd ≳ −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' In the  X-ray band, Fabian et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2008) proposed the NH–  λEdd diagram to evaluate the presence of outflow, where  dusty clouds are pushed away by radiation pressure  against the gravitational force.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  In our sample, the  AGNs with higher Eddington ratios than the criteria  show multi-scale outflows, such as UFO, ionized out-  flow, and molecular outflows (Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Re-  cently, Venanzi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2020) compute similar diagnostics  for the IR-dominant outflows (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', polar dust).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' When  the AGN radiative acceleration and gravity are equal  (aAGN = ag), the dusty outflows are pushed away for the  AGNs with logλEdd ≳ −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5 assuming NH ≈ 1022 cm−2  or logλEdd ≳ −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0 assuming NH ≈ 1021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5 cm−2 (see also  Alonso-Herrero et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Thus, the decline of the po-  lar dust luminosity for low-Eddington AGNs is consis-  tent with the theoretical prediction of the IR-dominant  dusty winds caused by the radiation pressure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Polar Dust Temperature  In this study, we newly constrain the polar dust tem-  perature (Tpolar) for the AGNs in U/LIRGs, thanks to  the combination of X-ray spectroscopy and multiwave-  length SED analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Figure 22 provides the relation  between the polar dust luminosity and its temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  For these AGNs with signs of the polar dust emission,  we find that the averaged values of polar dust luminos-  ity increase from early mergers (log(Lpolar/erg s−1) =  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='53 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='43) to late mergers (44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='22 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='55;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' see Table 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  On the other hand, the polar dust temperature appears  to decrease with merger stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Here, it is notable that  the Tpolar mostly lie in the range of ∼100–200 K, which  are in good agreement with the researches of the IR in-  terferometric observations and IR SED analysis as listed  in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Even though the SED fitting with the  range of Tpolar within 100–300 K is examined, we con-  firm that the results are almost unchanged.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  35  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  logLpolar [erg s  1]  100  150  200  250  Tpolar [K]  Stage-A(Early)  Stage-B(Early)  Stage-C(Late)  Stage-D(Late)  Stage-N  Figure 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Logarithmic polar-dust luminosity vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' polar-  dust temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The symbols are the same in Figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  N  A  B  C  D  Merger Stage  Tpolar  [K]  100  150  200  Figure 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Differences in the polar-dust temperature with  merger stage, described in the logarithmic scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Diamonds  and uncertainties represent the averaged value and 1σ  dispersions, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  To confirm the trend of the polar dust temperature,  we also compare the averaged values with merger stages  as illustrated in Figure 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Notably, the temperatures of  late mergers (∼130 K) decline from the values of early  mergers or nonmergers (∼170 K).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Although the allowed  range is above 100 K, these averaged values are much  larger than the dust temperature of the ISM in local  U/LIRGs and high-z submillimeter galaxies (∼20–60 K;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Casey 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Clements et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' da Cunha et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' All AGNs in late mergers show significant signs  of the presence of polar dust emission (Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Taking into account the high AGN luminosities (pro-  portional to polar dust luminosity;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3) in late  mergers, the decline of the dust temperature within the  inner parsecs seems to be unlikely.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The preferable reason  is that the polar dust emission is radiated farther away  from the center (see also e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Lyu & Rieke 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Buat  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021), implying the development of the physical  size of the polar dust structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Polar Dust Structure  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Physical Size of the Polar Dust  Finally, we estimate the physical size of the polar dust  for local U/LIRGs by using the polar dust temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  For a simple analytic model, the luminosity absorbed  by dust grains at a distance (r) from the central radia-  tion source, Labs, is calculated by the following equation  (see also e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Barvainis 1987;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' H¨onig & Kishimoto 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Venanzi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020):  Labs = 16πr2Qabs;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='P(T)σSBT 4,  (6)  where Qabs;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='P(T) is the Planck mean absorption effi-  ciency and σSB is Stefan–Boltzmann constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The po-  lar dust model in our multiwavelength SED analysis as-  sumes the dust emissivity of β = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6 (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Draine & Lee  1984;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Casey 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Yang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020a), and the Qabs;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='P(T)  is proportional to T 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The typical scales of polar dust  (Rpolar) can be estimated by solving the equation:  Rpolar = rsub × (Tpolar/1500 K)−2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  (7)  The rsub is the sublimation radius at the temperature  of Tsub = 1500 K and can be calculated by rsub = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4 ×  (LAGN,int/1045 erg s−1)1/2 pc in the CLUMPY model  (Nenkova et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2008a,b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Table A5 lists the estimates  of Rpolar for the U/LIRGs in our sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  In the top panel of Figure 24, we present the relation  between the intrinsic (bolometric) AGN disk luminosity  and Rpolar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The linear regression analysis in log–log  space is performed for the targets by using the Bayesian  maximum-likelihood method (Kelly 2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The best-  fitting relation (red dashed line) is  log(Rpolar) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='78 log(LAGN,int/erg s−1) − 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  (8)  Its 1σ dispersion is ±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='35 dex and the correlation coef-  ficient is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='80, implying a tight relation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  It is notably that the radius of the polar dust emission  measured by the high-spatial-resolution imaging in the  mid-IR 12 µm band (Asmus 2019) for U/LIRGs (gray  diamond) and normal galaxies (gray square) are well  consistent with the best-fitting relation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' For NGC 1068,  the compact radius of the mid-IR emission (∼54 pc)  relative to the AGN luminosity is in good agreement  with our estimate (Rpolar ∼ 45 pc).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The distribution of  the Rpolar obtained from our methods and by the mid-IR  images (Asmus 2019) shows a steeper slope (∼0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8) than  the relationship with the constant temperature (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  This supports that the typical polar dust temperatures  36  Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  logLAGN, int  [erg s  1]  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  logRpolar  [pc]  NGC 1068  F08572  Mrk 231  Rpolar, SED = rsub × (Tpolar/1500 K)  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8  Tpolar=100K  Tpolar=150K  Tpolar=200K  This Work  MIR (U/LIRG;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Image)  MIR (normal;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Image)  Ion (U/LIRG;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Image)  Mol (U/LIRG;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Image)  Stage-A(Early;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' SED)  Stage-B(Early;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' SED)  Stage-C(Late;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' SED)  Stage-D(Late;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' SED)  Stage-N (SED)  ~10 pc  ~100 pc  ~10 pc  ~1 kpc  ~1500 K  (sublimation radius)  ~100 K (LAGN=1045.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5)  ~150 K (LAGN=1044)  ~200 K (LAGN=1043)  Evolution  Polar dust  NLR  t U/LIRG  ~ 30-100 Myr  Early Merger  Late Merger  Figure 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Top panel: logarithmic intrinsic AGN luminosity vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' logarithmic physical size of the dominant IR emission from  the polar dust, estimated from the sublimation radius and polar dust temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The dashed red line and pink shade show  the best-fitting linear relation and its 1σ dispersion among the AGNs, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The green circles illustrate the physical  size of ionized outflows measured with optical IFU observations, and light blue circles mark the size of molecular outflows  measured with submillimeter observations in the subsample of our U/LIRGs (Fluetsch et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019, 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The gray diamonds  and small circles denote the sizes of extended mid-IR emission for U/LIRGs and non-U/LIRG sources respectively (Asmus  2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  For the size of molecular outflows and extended mid-IR region, the bolometric AGN luminosities of U/LIRGs are  adopted to the estimates in this study, while those of non-U/LIRGs are calculated as the X-ray luminosity (Asmus 2019) times  20 (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Vasudevan & Fabian 2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The other symbols are the same in Figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Bottom panel: schematic picture of the AGN  structure (polar dust, NLR, torus, failed winds, accretion disk, and SMBH) in U/LIRGs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  37  decrease with AGN luminosity or physical size of the  polar dust (Rpolar).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  It should be emphasized that Equation (6) can be gen-  erally applied to an optically thin, continuous dust en-  vironment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Whereas, the extinction of the polar dust  in the V band is not (A(LOS)  V ,polar ∼ 1–3;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' see Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  A plausible explanation of this discrepancy is that the  polar dust consists of optically thin layers of other-  wise optically thick dust clouds, where the tempera-  ture and emission profile is dominated by direct heat-  ing from the central source (H¨onig & Kishimoto 2010,  2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='21 This is consistent with the radiative hydrody-  namic (RHD) simulations expecting that the polar dust  structure would be smoothly distributed with most sub-  structure being filamentary and/or clumpy (Wada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2009;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Wada 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Schartmann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Dorodnitsyn  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Chan & Krolik 2016, 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Dorodnitsyn &  Kallman 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Williamson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  If the polar dust structure is a bipolar hollow cone  with the opening angle of θ1–θ2, its volume (Vpolar) is  calculated by:  Vpolar = 2 × (4/3)πr3 × 2π[1 − (cos(θ2))]/4π  − 2 × (4/3)πr3 × 2π[1 − (cos(θ1))]/4π  = (4/3)πr3[cos(θ1) − cos(θ2)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  (9)  The conical structure of the polar dust model in our  study can be described as a simple case of θ1 = 0◦ and  θ2 = 90◦ − σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Lyu & Rieke (2018) introduce a power-  law dust density profile, ρ(r) ∝ r−α, and the value of  α is 0 < α ≲ 2 based on the previous observational  studies (Behar 2009;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Faucher-Gigu`ere & Quataert 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Feruglio et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Revalski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The total mass  of the extended (≳10 pc) polar dust within the radius  of r, Mpolar(r), follows the mass profile of dMpolar/dr ∝  (dVpolar/dr)ρ(r) ∝ r2−α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Assuming that the polar dust  emission depends on their mass, a large part of the polar  dust emission is derived from the large-scale structure  at r ∼ Rpolar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' However, the polar dust sizes for three  AGNs in NGC 1068, IRAS F08572+3915, and Mrk 231  are much smaller than the best-fitting relation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Interest-  ingly, Feruglio et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2015) investigate the spatial dis-  tribution of the intense molecular CO(2−1) outflows in  Mrk 231 with Atacama Large Millimeter/submillimeter  21 The polar dust temperature assuming the gray body model is  different from the inverse peak-wavelength temperature (Tpeak)  measured by Wein’s displacement law (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', λpeak = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='898 ×  103 µm K/Tpeak, which only applies to perfect black bodies;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Casey 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Though the assumption of the emitter (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', gray  body or smooth distribution with clumps) may cause a system-  atic uncertainty of the polar dust temperature, the results of the  decrease in Tpolar with merger stage will be almost unchanged.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Array (ALMA) and report that its mass profile (or the  outflow filling factor) follows α ≈ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' This suggests that  the polar dust emission in Mrk 231 is derived from the  whole structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Although the spatial distribution for  NGC 1068 and IRAS F08572+3915 is unclear, the den-  sity profile may cause the seemingly hot and compact  emission from the polar dust.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Except for these three  AGNs, the Rpolar is thought to be the spatial scale of  the polar dust detected in the mid-IR images (Asmus  2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Thus, the best-fitting relation between AGN lu-  minosity and Rpolar suggests that the IR-luminous po-  lar dust structure expands from a few tens parsec (early  mergers) to kiloparsec scales (late mergers).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Scenario of the Outflowing Polar Dust  To distinguish whether the polar dust is (1) the galac-  tic ISM or dust near the edge of NLR being illuminated  by the AGN or (2) the outflowing dusty winds launched  from the inner edge of the torus, we investigate the  spatial sizes of the ionized and molecular outflows for  our U/LIRGs (Table A5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Fluetsch et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2021) ana-  lyze the optical integral field unit (IFU) data of 26 lo-  cal U/LIRGs with Very Large Telescope (VLT)/Multi  Unit Spectroscopic Explorer (MUSE).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' From the liter-  ature, they also include 31 galaxies with spatially re-  solved multiphase outflow information (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Rupke &  Veilleux 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Rupke et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' For eight U/LIRGs  in our sample (small-green circles), they estimate the  radius of the ionized outflow based on the extent of the  broad Hα component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Fluetsch et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2019) investi-  gate the molecular outflows primarily by using CO data  from the ALMA archive in a sample of 45 local galax-  ies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The radius of the molecular outflows is measured  for nine U/LIRGs in our targets (light-blue circles).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' We  find that the sizes of ionized and molecular outflows are  similar to or larger than those of the polar dust size,  supporting that the materials outside the polar dust are  outflowing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Many works predict that the polar dusty outflows are  launched from the surface of the inner torus (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', H¨onig  & Kishimoto 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' H¨onig et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2012, 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Gallagher  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Ishibashi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The semi-analytical  disk and wind models suggest that the dusty winds can  be launched by the AGN radiation pressure and the  heated dust itself (Venanzi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Similarly, RHD  simulations also support that dusty winds are naturally  driven (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Schartmann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Wada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2016,  2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Williamson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019, 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Some observational  attempts to test this hypothesis have been performed by  analyzing the IR SEDs (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Lyu & Rieke 2018) and by  comparing the polar dust luminosities with the strength  38  Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  of the multiphase outflows (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Alonso-Herrero et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Since the polar dust emission does not show the emis-  sion/absorption lines, it is difficult to estimate its ve-  locity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' For the starburst galaxy M 82, Yoshida et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  (2011) carry out the spectropolarimetry of the optical  emission lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The outflowing dust grains are predicted  to polarize the continuum and emission lines emanating  from the nuclear starburst region, acting as “moving  mirrors” for nuclear light.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' By comparing the velocities  between the normal and polarized emission lines, they  find that the velocity of the polar dust (vpolar) decreases  from ∼200 km s−1 at a few hundred parsecs to ∼20–  30 km s−1 at 1–1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2 kpc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' For the U/LIRGs hosting nu-  clear starbursts and AGNs, the minimum velocity of the  polar dust should be ≳ 30 km s−1 at 1 kpc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The typ-  ical lifetime of the U/LIRGs containing submillimeter  galaxies at z ∼ 1–2 (tU/LIRG) are ∼30–100 Myr (Hop-  kins et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2006, 2008;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Meier et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Hickox et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Inayoshi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018) or at most 300 Myr (Swin-  bank et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2006;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Meng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Privon et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The migration length of the outflowing dusts can be  roughly estimated by the velocity (vpolar ≳ 30 km s−1)  times the U/LIRG lifetime (tU/LIRG ≳ 30 Myr), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=',  ≳1 kpc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The smaller fraction of the AGNs with signs of  polar dust emission for early mergers than that for late  mergers also supports the evolution of the polar dust  (Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Although the possible contribution of  the polar dust emission from the non-outflowing dust in  the NLR should not be rejected, the polar dust seems  to be dusty winds as expected by recent simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Thus, the polar dust size (Rpolar) increases from a few  tens of parsec (early mergers) to kiloparsec scales (late  mergers), indicating that the polar dust is likely the ex-  panding (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', evolving) dusty outflows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Unified View of the Polar Dust Structure in  U/LIRGs  In the bottom panel of Figure 24,  we present  the schematic picture of the polar dust structure in  U/LIRGs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The polar dust sizes, estimated from the po-  lar dust temperature and dust sublimation radius, in-  crease with AGN luminosity (or merger stage).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The po-  lar dust temperature decrease with the polar dust size  from ∼200 K (a few tens of parsec) to ∼100 K (kilopar-  sec scale).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Considering the typical dust density profile of  0 < α ≲ 2, their sizes corresponds to the outer structure  of the extended polar dust (Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The polar  dust sizes are smaller than those of ionized and molecu-  lar outflows, and their expansion with merger stage can  be explained by the polar dust velocity and U/LIRG  lifetime (Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  At the parsec-scale regions, RHD simulations show  that  the  innermost  torus  structure  is  formed  by  radiation-driven fountain-like outflows (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Wada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' A multiphase dynamic nature of torus (pink el-  lipses) and circumnuclear region (CND;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' yellow ocher) in  the r ≲ tens of parsecs torus region is confirmed by re-  cent ALMA observations (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Izumi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2016, 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  H¨onig (2019) mentions that the polar dust is expected  to be launched by the inner edge of the torus due to the  AGN radiation (coming from the AGN disk or vicin-  ity of the SMBH).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' As noted in Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1, the po-  lar dust structure would be smoothly distributed with  most substructure being filamentary and/or clumpy, as  expected by RHD simulations (Wada 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Schartmann  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Williamson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019), although we sim-  ply describe it by a smooth distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' According to  these results, the schematic picture illustrates the AGN  structures, containing the polar dust, NLR, torus, failed  winds around the torus, accretion disk, and SMBH in  the early-to-late merging U/LIRGs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Polar Dust vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Molecular Outflow  This study indicates that the multiwavelength SED  analysis is one of the key means to evaluate the ac-  tivities of the dust components of large-scale outflows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  In Figure 25, we compare the polar dust luminosities  with the molecular outflow velocity (Vout,mol;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' left panel)  and mass transfer rates ( ˙Mout,mol;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' right panel).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Yamada  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2021) lists the values of Vout,mol and  ˙Mout,mol for  local U/LIRGs by referring the previous works based on  the broad CO emission lines and OH absorption lines  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Gonz´alez-Alfonso et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Laha et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018 and  references therein).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' We find that the polar dust lumi-  nosity and Vout,mol show no significant relation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' This  may be due to the dispersion of the slope of the dust  density profiles (α), or the dispersion of the size of the  molecular outflows relative to the polar dust size (Fig-  ure 24).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Whereas, the polar dust luminosity and mass  transfer rates of the molecular outflows show a positive  correlation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' This may be a reasonable result by taking  into account that the polar dust luminosities depend  on their mass (particularly containing the large-scale  mass at r ∼ Rpolar;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  We calculate the  best-fitting relation by using the Bayesian maximum-  likelihood method as below:  log(Lpolar) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='77 log( ˙Mout,mol) + 42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='79,  (10)  where the 1σ dispersion is ±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='67 dex and the correla-  tion coefficient is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Since the sample is quite limited,  further studies using large samples are necessary to es-  tablish the general relation between polar dust (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=',  dusty winds) and molecular outflows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  39  0  200  400  600  800  1000  Vout, mol (AGN;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Yamada+21)  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  logLpolar  Stage-D(Late)  Stage-N  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  logMdotout, mol (AGN;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Yamada+21)  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  logLpolar  This Work  Stage-D(Late)  Stage-N  Figure 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Polar-dust luminosity as a function of molecular outflow velocity (left) and logarithmic mass transfer rate of  molecular outflow (right) referred from Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The red dashed line and pink shaded area mark the best-fitting  relation and its 1σ dispersion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The symbols are the same in Figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' DISCUSSION II: COEVOLUTION PROCESS OF  GALAXY, SMBH, AND OUTFLOW  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Activities of Starburst and AGN  To understand the origin of the coevolution of galaxies  and SMBHs, their growth rates are well studied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Numer-  ical simulations of galaxy mergers predict that the SFR,  AGN luminosities, and obscuration of the central AGN  increase with merger stage (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Di Matteo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2005;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Hopkins et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2006, 2008;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Narayanan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Angl´es-  Alc´azar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Blecha et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Kawaguchi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Yutani et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The observational studies us-  ing multiwavelength data support their increases with  merger stage (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Imanishi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Lee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Ellison et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Satyapal et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Ricci et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2017a, 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Koss et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Pfeifle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Shang-  guan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019, 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  By combining the broadband X-ray spectroscopy and  multiwavelength SED decomposition, this study esti-  mates the SFRs and AGN luminosities for a large sample  of 72 resolved sources in U/LIRGs, which are treated  separately divided into 41 hard X-ray–detected AGNs  (containing 36 single AGNs, 2 unresolved dual AGN  systems, and 3 newly identified AGNs) and 31 other  sources (starburst-dominant or hard X-ray–undetected  sources).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' In Figure 26, we investigate the distribution  of SFR (left) and intrinsic (bolometric) AGN luminos-  ity (right) as a function of projected separation between  two galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  For the starburst-dominant or hard X-  ray–undetected sources, we refer to the AGN luminosi-  ties estimated from the [O IV] 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='89 µm luminosity  (L[O IV];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' small crosses) in Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' They  confirm that these values are consistent with the 3σ up-  per limits of the predicted 2–10 keV AGN luminosity  from the X-ray counts by assuming NH ≤ 1025 cm−2  and LX,unabs–L[O IV] relation (Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' We note  that the dispersion of the low values of SFRs and AGN  luminosities for the early mergers with the ∼10–40 kpc  are caused by the faint companion galaxies that are not  IR-luminous galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Focusing on the largest values  of individual merger stages, our results support that the  SFRs and AGN luminosities increase with projected sep-  aration and merger stage, consistent with the results in  Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  In Figure 27, we compare the SFRs and bolometric  AGN luminosities in our sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' By the same method  in Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2021), we draw the galaxy–SMBH  “simultaneous evolution” relation (see also e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Ueda  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018), where the growing systems keeping the  SFR–LAGN,int relation are expected to establish the lo-  cal Mbulge–MBH relation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Here, the relation assumes the  fraction of stellar mass that are taken back to the ISM  (return fraction) as R = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='41 (Chabrier 2003), the ratio  of stellar masses to SMBH masses in the local universe  as A ∼ 200 (Kormendy & Ho 2013), and a radiative  efficiency as η = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05 (Ueda et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The detailed  explanations are presented in Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The  relation is described as  log(LAGN,int) = log(SFR/M⊙ yr−1) + 42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  (11)  The hard X-ray–detected and newly identified AGNs  in U/LIRGs follows the simultaneous coevolution re-  lation, consistent with the results by Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  For the AGNs in our sample excluding non-  mergers and outliers with logSFR < 0, we calculate the  best-fitting relation based on the Bayesian maximum-  likelihood method:  log(LAGN,int) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='89 log(SFR) + 42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  (12)  The 1σ uncertainty is ±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='66 dex and the correlation co-  efficient is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' As mentioned in Appendix C (see Fig-  ure C3), the AGN luminosities in Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2021)  40  Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  0  20  40  60  80  100  Separation [kpc]  2  1  0  1  2  3  logSFR  Stage-A(Early)  Stage-B(Early)  Stage-C(Late)  Stage-D(Late)  Stage-N  0  20  40  60  80  100  Separation [kpc]  41  42  43  44  45  46  logLAGN, int [erg s  1]  Stage-A(Early)  Stage-B(Early)  Stage-C(Late)  Stage-D(Late)  Stage-N  SB or HX nondet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Figure 26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  SFR and intrinsic AGN luminosity as a function of projected separation between two galaxies in units of  kiloparsecs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Single nuclei in merging (stage D) and nonmerging (stage N) sources are plotted on the left (negative value) and  right sides, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Large symbols are the same in Figure 8, while small crosses illustrate the starburst-dominant or hard  X-ray–nondetected sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2  1  0  1  2  3  logSFR  41  42  43  44  45  46  logLAGN, int  [erg s  1]  Trakhtenbrot+10  (Sy2,QSO)  This Work  local Mbulge-MBH  Stage-A(Early)  Stage-B(Early)  Stage-C(Late)  Stage-D(Late)  Stage-N  PG QSO (z<0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1)  SB or HX nondet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Figure 27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Logarithmic SFR vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' intrinsic AGN luminosity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Black dotted line denotes the typical relation among low-z Seyfert  2s, QUEST QSOs, and high-z QSOs (Trakhtenbrot & Netzer 2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The red dashed line and pink shaded area mark the  best-fitting relation and its 1σ dispersion for the AGNs in U/LIRGs, excluding the nonmergers and AGNs with logSFR < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The black solid line is the galaxy–SMBH “simultaneous evolution” line for A = 200 (see also Ueda et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The large  symbols are the same in Figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The small crosses mark the starburst-dominant or hard X-ray–nondetected sources, whose  LAGN,int values are derived from the [O IV] luminosities (Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  41  are larger than the values in this work, and then their  typical relation is ∼0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4 dex brighter in the AGN lumi-  nosity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Their AGN luminosities are derived from the  averages of four different measurements;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' the [O IV] lu-  minosity (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Gruppioni et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2016), bolometric AGN  fraction (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', D´ıaz-Santos et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017), and IR SED de-  composition and Spitzer/IRS spectral fitting (Alonso-  Herrero et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Shangguan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Its system-  atic scatter related to the application of the averaged  values is reported as about ±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='27 dex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Our best-fitting  relation with the 1σ uncertainty is overlapped on not  only the relation of Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2021) but the si-  multaneous coevolution relation (black solid line).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' This  supports that the AGNs in U/LIRGs are exactly in the  coevolution phase of galaxies and SMBHs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2021) report that the AGNs in stage D  mergers show the multiphase massive outflows at sub-  parsec to kiloparsec scales, that is, UFOs (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Feruglio  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Tombesi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Mizumoto et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Smith et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019), ionized outflows (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Fischer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Rich et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Kakkad et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Fluetsch et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Toba et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2022b), and molecular outflows with  velocities above 500 km s−1 (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Gonz´alez-Alfonso et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Laha et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Fluetsch et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' As dis-  cussed in Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3 and 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5, the polar dust luminosi-  ties are ∼ 2/3×LAGN,int, and the physical sizes increase  with AGN luminosities from a few tens of parsec to kilo-  parsec scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' In short, the polar dust luminosities and  sizes are the largest in the stage D mergers with high  AGN luminosities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Moreover, we plot the quantities of  PG quasars at z ≲ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1 (Lyu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017) and empirical re-  lation for local AGNs and quasars (Trakhtenbrot & Net-  zer 2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' They lie in the AGN-dominant region above  the coevolution relation, which should have strong gas  outflows (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Woo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The coexistence of in-  tense starbursts, luminous AGNs, and massive outflows  (UFOs, ionized outflows, molecular outflows, and dusty  winds) particularly in the phase of U/LIRGs support a  standard AGN feedback scenario that the AGN-driven  outflows suppress star-forming activities and ULIRGs  eventually transit to the unobscured quasars (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Di  Matteo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2005;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Hopkins et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2008;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Alexander &  Hickox 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Ananna et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' see also Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Mass Growth of Galaxy and SMBH  According to the obtained SFRs and AGN luminosi-  ties, we evaluate the total growth masses of galaxies and  SMBHs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The increase in the stellar mass (∆M∗) can  be calculated by the SFR times the growth timescale  (tgrowth).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The mass accretion rates ( ˙MBH) are estimated  by using a radiative efficiency (η = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Ueda et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2014) and the light speed (c) as  ˙MBH = LAGN,int × (1 − η)/(ηc2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  (13)  The increase in the SMBH mass (∆MBH) corresponds  to the  ˙MBH times tgrowth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Here, the multiwavelength  SED analysis presents the SFRs and AGN luminosities  for the U/LIRGs in the various merger stages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Since the  history of these quantities during the U/LIRG lifetime  (tU/LIRG ∼ 30–100 Myr;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2) is unclear, we  compute the increased masses assuming tgrowth is 30 Myr  as a time scale of early mergers or late mergers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' For the  three resolved dual AGN systems in stage A mergers  (NGC 833/NGC 835, NGC 6921/MCG+04-48-002, and  NGC 7679/NGC 7682), we also calculate the total mass  of the two galaxies and SMBHs after the galaxy collision,  containing the increased masses from their starburst and  AGN activities for 30 Myr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Figure 28 describes the relation between the stellar  masses and SMBH masses for the hard X-ray–detected  AGNs in our sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' We plot the local Mbulge–MBH re-  lation (Kormendy & Ho 2013), scaled relation assuming  Chabrier IMF, and a typical M∗–MBH relation for classi-  cal bulges and ellipticals (Reines & Volonteri 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The  stellar masses are obtained by our SED fitting, while the  SMBH masses are referred from Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The distributions of these masses in our U/LIRGs at  z < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1 are well consistent with the study of z < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3  U/LIRGs by Farrah et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The caveat is that  the SMBH masses we refer are derived from the av-  eraged values of the four kinds of different measure-  ments: stellar mass to SMBH mass relation (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Reines  & Volonteri 2015), M–σ∗ relation (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', G¨ultekin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2009), photometric bulge luminosity (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Veilleux et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2009a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Winter et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2009;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Haan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2011), and vari-  ous other methods such as the flux density of old stellar  emission at 2 µm (Caramete & Biermann 2010), veloc-  ity dispersion of [O III] emission (Alonso-Herrero et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2012), water masers (Lodato & Bertin 2003;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Kl¨ockner  & Baan 2004;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Izumi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2016), and so on.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Although  the systematic differences appear to depend on neither  the intrinsic AGN luminosity nor Eddington ratio (Ya-  mada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021), systematic uncertainties of the aver-  aged SMBH masses are not negligible (at most ±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5 dex;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  gray error bars).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Thus, the figure does not necessarily  indicate that the SMBH masses are a bit small relative  to the local relations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  We overplot the expected masses due to the star-  bursts and AGN activities for 30 Myr (arrows) and  the additional collision of two galaxies (empty stars).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  For the two stage-D mergers with low stellar masses  of log(M∗/M⊙) ∼ 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0–9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5 (IRAS F08572+3915 and  IRAS F17138−1017), their galaxies and SMBHs are  42  Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  logM *  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  logMBH  SB+AGN(30 Myr)  Collision  Kormendy13 (Mbulge-MBH)  Kormendy13 (scaled)  Reines+15 (M*-MBH)  Stage-A (Early;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' AGN)  Stage-B (Early;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' AGN)  Stage-C (Late;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' AGN)  Stage-D (Late;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' AGN)  Figure 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Logarithmic stellar mass vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' logarithmic SMBH mass referred from Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2021) for the AGNs in stage  C (orange diamond) and stage D (red star) U/LIRGs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Solid arrows represent the expected masses of the galaxy and SMBH if  they evolve with the constant growth rates (SFR and  ˙MBH) for 30 Myr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' For three dual-AGN systems in stage A mergers, the  merged masses of the two sources including the mass increase for 30 Myr are marked as empty blue stars with dotted lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The black solid line denotes the local bulge mass (Mbulge) and SMBH mass (MBH) relation for classical bulges and elliptical  galaxies (Kormendy & Ho 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The dashed line shows the scaled relation that has bulge masses scaled down by 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='33 dex  to consider the difference in the adopted mass-to-light ratios, and blue dotted line presents the typical M∗–MBH relation for  classical bulges and ellipticals (Reines & Volonteri 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  rapidly growing thanks to the starburst and AGN ac-  tivities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' We find that, however, the increased masses for  the other U/LIRGs are small by these activities even  though some of the stage-D U/LIRGs have the high-  est SFRs (∼100–300 M⊙ yr−1) and AGN luminosities  (logLAGN,int ∼ 45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0–45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Notably, the galaxy collision  causes rapid growth for these high-mass systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Soltan’s argument (Soltan 1982), one of the well-  known discussions on the cosmic growth of SMBHs, sug-  gests that the SMBHs are thought to have grown primar-  ily by the gas accretion, not SMBH–SMBH coalescence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  This requirement is imposed to explain the SMBH mass  density at redshift z and the accreting gas mass density  from z = ∞ to 0 (Yu & Tremaine 2002;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Shankar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Because the SMBH–SMBH coalescence conserves  the SMBH mass density, the argument does not reject  the presence of ubiquitous merger events (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Enoki  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2004;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Jahnke & Macci`o 2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' In this context, the  growth events keeping the balanced SFR–LAGN,int rela-  tion triggered by galaxy mergers (see Figure 27;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' see also  e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Di Matteo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2005) should be helpful to con-  struct the local Mbulge–MBH relation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Whereas we need  to keep in mind that, focusing on individual galaxies,  the galaxy collision generates such high-mass galaxies  with log(M∗/M⊙ ≳ 10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Therefore, our results indicate  that galaxy merger is a vital process to establish the  local Mbulge–MBH relation and build up the high-mass  galaxies such as local elliptical galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Perspective of the Galaxy–SMBH Coevolution in  Mergers  Finally, we summarize the perspective of the merger-  driven coevolution of galaxies and SMBHs as described  in the schematic picture of Figure 29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The SFRs and  intrinsic (bolometric) AGN luminosities increase with  merger stage, where the galaxy growth occurs first and  rapid mass accretion delivered from the host galaxy to  the SMBH is triggered later (Section 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The merger  process in the SFR–LAGN,int diagram should be a key  mechanism to drive the balanced growth of galaxies and  SMBHs in the cosmic history (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Madau & Dickinson  2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Ueda et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Aird et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2015) and then to es-  43  Stage A        ~        Stage D   Quasar   Elliptical  (Time)  Galaxy Evolution (Starburst)  SMBH Evolution (AGN)  Inflow  NGC 833/NGC 835 (SDSS)  NGC 3690 (SDSS)  Mrk 231 (SDSS)  M 87 (Pan-STARRS)  H1821+643 (Pan-STARRS)  Outflows  Merger-driven Growth  →  Cosmological  Coevolution  Collision    → Hierarchical Mass Growth  Figure 29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Schematic picture of merger-driven coevolution of galaxies and SMBHs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Middle panels are compiled from  Pan-STARRS DR2 and SDSS DR16 images (Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3), whose sources are merging U/LIRGs (NGC 833/NGC 835, NGC  3690, Mrk 231) and post-merger candidates (a quasar H1821+643, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Jadhav et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' and an elliptical galaxy M87, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=',  Longobardi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  tablish the local Mbulge–MBH relation (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Kormendy  & Ho 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Moreover, galaxy collision is another im-  portant process to induce hierarchical mass growth and  build up the high mass system such as local elliptical  galaxies (Section 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2021) find that the AGNs in stage  D mergers show the multiphase outflows at subparsec  to kiloparsec scales, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', UFOs, ionized outflows, and  molecular outflows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  They also unveil that the AGNs  with high Eddington ratios as λEdd ∼ 1 have moderate  NH (∼1023 cm−2), where dusty clouds at parsec scales  are pushed away by radiation pressure against the grav-  itational force as predicted with the NH–λEdd diagram  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Fabian et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2008, 2009;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Ricci et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017d, 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The recent high-spatial-resolution ALMA and Chandra  observations support the feedback effects on the torus  by evaporating a portion of the gas (Kawamuro et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2021), while the AGNs in U/LIRGs are deeply buried by  massive inflows and/or outflows (Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The X-ray weakness in U/LIRGs should make it easy to  launch the massive outflows efficiently (Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' By  combining the X-ray spectroscopy and multiwavelength  SED fitting, we constrain the physical parameters of po-  lar dust structure (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', IR luminosity, temperature, and  spatial scales) that is thought to be launched by the  AGN radiation pressure and the heated dust itself (Sec-  tion 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' see also Venanzi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Alonso-Herrero  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The polar dust emission may be negligible  for some low-Eddington AGNs (λEdd ≲ 10−3) in early  mergers (Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4 and 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' For the AGNs show-  ing significant polar dust emission, the physical size of  polar dust increases with merger stage from a few tens  of parsec to kiloparsec scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  These results indicate  that the massive outflows connecting to galaxy scales  44  Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  are nurtured by the rapid accretion SMBHs and rich  environments in U/LIRGs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The coexistence of intense starburst, AGNs, and large-  scale massive outflows in local U/LIRGs support a stan-  dard AGN feedback scenario (see also Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  According to the scenario, the U/LIRGs will transit to  the unobscured AGNs (Section 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' It is still unclear  whether the star-forming activities are quenched due  to the high specific SFRs (see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1) or the  AGN feedback by the massive outflows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Considering the  balanced starburst and AGN activities in the merger  sequence, the massive outflows would present some kind  of physical connection between galaxies and SMBHs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' To  completely understand the role of massive outflows in  late mergers, it is needed to more researches of the mass  transport mechanism and the effects on star formation  in the host galaxy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' In the near future, the high-spatial-  resolution IR images will be presented by the Mid-  InfraRed Instrument (MIRI;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Rieke et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Wright  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2015) onboard the James Webb Space Telescope  (5–28 µm), and The Mid-Infrared Multi-field Imager  for gaZing at the UnKnown Universe (MIMIZUKU;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Kamizuka et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020) on The University of Tokyo At-  acama Observatory (TAO;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Yoshii et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2010) 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5m  ground-based telescope (2–38 µm).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Combining the mul-  tiwavelength images with such as these telescopes and  ALMA will allow us to study the distribution of the  warm and cold outflowing matters, and better constrain  the relationship between the outflows and star-forming  activities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' CONCLUSION  The purpose of this work is (1) to understand the fea-  tures of multiwavelength emissions in U/LIRGs, (2) to  reveal the structure of the outflowing polar dust, and  (3) to investigate the activities of host galaxies, SMBHs,  and outflows for testing whether the merger process is a  vital factor to establish the local Mbulge–MBH relation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  To achieve these goals, we have performed a hard X-ray  to radio multiwavelength SED decomposition for the 57  local U/LIRGs (containing 84 individual galaxies) ob-  served with NuSTAR and/or Swift/BAT (Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  We compile the broadband X-ray spectra and  multiwavelength wide-survey catalogs in the UV to ra-  dio bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' After the cross-matching with them, we fi-  nally obtain the multiwavelength photometries of the  sample consisting of 72 resolved sources and 13 dupli-  cated systems of resolved pairs, which are spatially di-  vided in the Herschel PACS 70 µm bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' We modify  the latest SED-fitting code X-CIGALE by implementing  the infrared (IR) CLUMPY model, allowing the multi-  wavelength study with the consistent X-ray torus model  (XCLUMPY).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Adopting the torus parameters obtained  by the X-ray fitting (Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021), we constrain  the properties of host galaxies, AGN tori, and polar  dust.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Here, we described the main results as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The sample has 36 single and two unresolved dual  AGNs detected in the hard X-ray band (Yamada  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' For all targets, we perform the BIC  test for two kinds of UV-to-IR SED fitting with  and without AGN (torus and polar dust) compo-  nents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Although it is difficult to reliably identify  AGNs solely by the SED fitting, we newly iden-  tify three AGN candidates by the diagnostics of  ∆BIC > 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' We also examine the significance of the  polar dust component for these AGNs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The AGNs  in late mergers support the presence of polar dust  emission, while some AGNs in early mergers or  nonmergers show no signatures (Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The component galaxies in early mergers have a  wide range of SFRs above and below the main se-  quence (MS), while galaxies in late mergers have  the highest SFRs above the MS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Similar SFR–  M∗ distributions of AGNs and the others imply  that the small influence of the AGN activities on  the star formation in the phase of U/LIRGs (Sec-  tion 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The flat slope of radio emission in late mergers  may be caused by the optically-thick free-free ab-  sorption due to the rich environment of the nuclear  region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Most AGNs in U/LIRGs are radio-quiet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The SFRs are correlated with radio luminosity, in-  dicating that starburst emission is dominant (Sec-  tion 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' In the WISE color–color diagram, we propose a  new wedge of the buried AGNs in late mergers,  which show the ∼3–10 µm excess.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  This can be  explainable by the inner part of the dusty disk  and/or hot polar dust within the inner parsecs  (Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The averaged SEDs suggest that the strength of  the X-rays is the best means to reveal the true  energy sources (intense starbursts and/or buried  AGNs) in U/LIRGs (Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The absorption-  corrected AGN SEDs show X-ray weakness rel-  ative to the other wavelengths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  This may be a  common feature among the AGNs in IR-luminous  galaxies over the cosmic history (z ∼ 0–7), whose  mechanism will be related to their massive out-  flows (Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  45  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Although polar-dust extinction is much smaller  than torus extinction, the UV-to-IR (mainly IR)  polar dust luminosities are ∼2 times larger than  the torus ones because of the seemingly large cov-  ering fractions (and/or large volumes) of polar  dust.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The AGNs with the signs of polar dust  emission (Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4) have logλEdd ≳ −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0 (Sec-  tion 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The polar-dust temperature decreases with merger  stages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' We estimate the physical size of the po-  lar dust by the temperature and dust sublimation  radius, consistent with the high-spatial-resolution  mid-IR images (Asmus 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Their sizes increase  with AGN luminosity from a few tens of parsec  (early mergers) to kiloparsec scales (late mergers),  indicating that the polar dust is likely the expand-  ing (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', evolving) dusty outflows (Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The SFRs and intrinsic (bolometric) AGN lumi-  nosities increase with merger stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The compar-  ison between these quantities suggests that the  starbursts occur first and AGNs arise later, and  overall their growth rates follow the simultaneous  coevolution relation that can establish the local  Mbulge–MBH mass relation (Section 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Considering the Soltan argument, the balanced  SFR–LAGN,int relation helps the construction of  local Mbulge–MBH relation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Whereas, galaxy col-  lision is also a key process to build up high-  mass galaxies such as local elliptical galaxies (Sec-  tion 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2021) and this work suggest that  the AGNs in late mergers show the multiphase  outflows at subparsec to kiloparsec scales, that  is, UFOs, ionized outflows, molecular outflows,  and expanding dusty winds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The coexistence of  intense starburst, AGNs, and large-scale massive  outflows support a standard AGN feedback sce-  nario (Section 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  We thank the anonymous referee for constructive com-  ments and suggestions that helped improve the qual-  ity of the paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' acknowledges Dr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Taiki Kawa-  muro and Dr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Kohei Ichikawa for their helpful dis-  cussion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  This work is financially supported by JSPS  KAKENHI grant numbers 19J22216 and 22K20391  (S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' );' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  17K05384 and 20H01946 (Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' );' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  18J01050,  19K14759, and 22H01266 (Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' );' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  21J13894 (S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' );' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  22J22795 (R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' );' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' and 21K03632 (M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=').' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' is grate-  ful for support from RIKEN Special Postdoctoral Re-  searcher Program.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' acknowledge sup-  port by UNAM-DGAPA PAPIIT IN111319 and CONA-  CyT Investigaci´on Cient´ıfica B´asica 252531.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  also thanks support from a postdoctoral fellowship from  UNAM-DGAPA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' acknowledges support from the  Fondecyt Iniciacion grant 11190831 and ANID BASAL  project FB210003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  This research has made use of data and/or soft-  ware provided by the High Energy Astrophysics Sci-  ence Archive Research Center (HEASARC), which  is a service of the Astrophysics Science Division at  NASA/GSFC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' This work makes use of data obtained  from the NuSTAR Data Analysis Software (NuSTAR-  DAS) jointly developed by the ASI Science Data Center  (ASDC, Italy) and the California Institute of Technol-  ogy (USA).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' This publication makes use of data obtained  with Chandra, supported by the Chandra X-ray Obser-  vatory Center at the Smithsonian Astrophysical Obser-  vatory, and with XMM-Newton, an ESA science mission  with instruments and contributions directly funded by  ESA Member States and NASA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' This study makes use of  data obtained from the Suzaku satellite, a collaborative  mission between the space agencies of Japan (JAXA)  and the USA (NASA).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The scientific results reported in  this article are based on observations made by UK Swift  Science Data Centre at the University of Leicester.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  This research makes use of the SIMBAD database, op-  erated at CDS, Strasbourg, France (Wenger et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2000),  and the Aladin sky atlas, developed at CDS, Strasbourg  Observatory, France (Bonnarel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2000;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Boch & Fer-  nique 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Also, this research makes use of data  from the NASA/IPAC Extragalactic Database (NED)  and NASA/IPAC Infrared Science Archive (IRSA), op-  erated by JPL/California Institute of Technology under  contract with the National Aeronautics and Space Ad-  ministration (see also IPAC DOIs: Skrutskie et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2003;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Wright et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' AKARI Team 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  This research is based on observations with GALEX,  operated for NASA by the California Institute of  Technology under NASA contract NAS5-98034.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The  GALEX data presented in this paper were obtained from  the Mikulski Archive for Space Telescopes (MAST) at  the Space Telescope Science Institute (see also MAST  DOI: Bianchi 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The Pan-STARRS1 Surveys (PS1) and the PS1 public  science archive have been made possible through contri-  butions by the Institute for Astronomy, the University  of Hawaii, the Pan-STARRS Project Office, the Max-  Planck Society and its participating institutes, the Max  Planck Institute for Astronomy, Heidelberg and the Max  Planck Institute for Extraterrestrial Physics, Garching,  The Johns Hopkins University, Durham University, the  46  Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  University of Edinburgh, the Queen’s University Belfast,  the Harvard-Smithsonian Center for Astrophysics, the  Las Cumbres Observatory Global Telescope Network  Incorporated, the National Central University of Tai-  wan, the Space Telescope Science Institute, the National  Aeronautics and Space Administration under Grant No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  NNX08AR22G issued through the Planetary Science Di-  vision of the NASA Science Mission Directorate, the  National Science Foundation Grant No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' AST-1238877,  the University of Maryland, Eotvos Lorand University  (ELTE), the Los Alamos National Laboratory, and the  Gordon and Betty Moore Foundation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The national facility capability for SkyMapper has  been funded through ARC LIEF grant LE130100104  from the Australian Research Council, awarded to the  University of Sydney, the Australian National Univer-  sity, Swinburne University of Technology, the Univer-  sity of Queensland, the University of Western Australia,  the University of Melbourne, Curtin University of Tech-  nology, Monash University and the Australian Astro-  nomical Observatory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' SkyMapper is owned and oper-  ated by The Australian National University’s Research  School of Astronomy and Astrophysics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The survey data  were processed and provided by the SkyMapper Team  at ANU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The SkyMapper node of the All-Sky Virtual  Observatory (ASVO) is hosted at the National Compu-  tational Infrastructure (NCI).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Development and support  of the SkyMapper node of the ASVO have been funded  in part by Astronomy Australia Limited (AAL) and the  Australian Government through the Commonwealth’s  Education Investment Fund (EIF) and National Col-  laborative Research Infrastructure Strategy (NCRIS),  particularly the National eResearch Collaboration Tools  and Resources (NeCTAR) and the Australian National  Data Service Projects (ANDS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Funding for the SDSS IV has been provided by  the Alfred P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Sloan Foundation, the U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Depart-  ment of Energy Office of Science, and the Participat-  ing Institutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  SDSS acknowledges support and re-  sources from the Center for High-Performance Comput-  ing at the University of Utah.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The SDSS web site is  www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='sdss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='org.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' SDSS is managed by the Astrophysical  Research Consortium for the Participating Institutions  of the SDSS Collaboration including the Brazilian Par-  ticipation Group,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' the Carnegie Institution for Science,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Carnegie Mellon University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Center for Astrophysics —  Harvard & Smithsonian (CfA),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' the Chilean Participa-  tion Group,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' the French Participation Group,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Instituto  de Astrof´ısica de Canarias,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The Johns Hopkins Univer-  sity,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Kavli Institute for the Physics and Mathematics  of the Universe (IPMU) / University of Tokyo,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' the Ko-  rean Participation Group,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Lawrence Berkeley National  Laboratory,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Leibniz Institut f¨ur Astrophysik Potsdam  (AIP),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Max-Planck-Institut f¨ur Astronomie (MPIA Hei-  delberg),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Max-Planck-Institut f¨ur Astrophysik (MPA  Garching),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Max-Planck-Institut f¨ur Extraterrestrische  Physik (MPE),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' National Astronomical Observatories of  China,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' New Mexico State University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' New York Uni-  versity,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' University of Notre Dame,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Observat´orio Na-  cional / MCTI,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The Ohio State University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Pennsylva-  nia State University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Shanghai Astronomical Observa-  tory,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' United Kingdom Participation Group,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Universidad  Nacional Aut´onoma de M´exico,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' University of Arizona,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  University of Colorado Boulder,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' University of Oxford,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  University of Portsmouth,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' University of Utah,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Univer-  sity of Virginia,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' University of Washington,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' University of  Wisconsin,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Vanderbilt University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' and Yale University.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  This publication makes use of data products from the  2MASS, which is a joint project of the University of  Massachusetts and the Infrared Processing and Anal-  ysis Center/California Institute of Technology, funded  by the National Aeronautics and Space Administration  and the National Science Foundation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' This publication  makes use of data products from the WISE, which is  a joint project of the University of California, Los An-  geles, and the Jet Propulsion Laboratory/California In-  stitute of Technology, funded by the National Aeronau-  tics and Space Administration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' This research is based  on observations with AKARI, a JAXA project with the  participation of ESA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Herschel is an ESA space obser-  vatory with science instruments provided by European-  led Principal Investigator consortia and with important  participation from NASA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  This work makes use of the data from the VLA, op-  erated by the National Radio Astronomy Observatory  (NRAO).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The NRAO is a facility of the National Sci-  ence Foundation operated under a cooperative agree-  ment by Associated Universities, Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' This study makes  use of data obtained from the MOST, operated with  the support of the Australian Research Council and the  Science Foundation for Physics within the University of  Sydney.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' This scientific work makes use of the Murchison  Radio-astronomy Observatory, operated by CSIRO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' We  acknowledge the Wajarri Yamatji people as the tradi-  tional owners of the Observatory site.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Support for the  operation of the MWA is provided by the Australian  Government (NCRIS), under a contract to Curtin Uni-  versity administered by Astronomy Australia Limited.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  We acknowledge the Pawsey Supercomputing Centre  which is supported by the Western Australian and Aus-  tralian Governments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' We thank the staff of the GMRT  that made these observations possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' GMRT is run by  the National Centre for Radio Astrophysics of the Tata  Institute of Fundamental Research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  47  Facilities: NuSTAR, Swift, XMM-Newton, Chan-  dra,  Suzaku,  GALEX,  Pan-STARRS,  SkyMapper,  SDSS, 2MASS, WISE, AKARI, Herschel, VLA, MOST,  MWA, GMRT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Software: XCLUMPY (Tanimoto et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019), HEA-  soft (v6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='25), XSPEC(v12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Arnaud 1996), NuSTAR-  DAS(v1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0), CIAO(v4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11), SAS (v17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Gabriel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2004), TOPCAT (Taylor 2006), X-CIGALE (Boquien  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Yang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  APPENDIX  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' BEST-FITTING RESULTS  Here, we present the best-fit parameters derived from  the UV-to-IR SED decomposition, WISE W1–W4 mag-  nitude, (Table A1 and A2) and the results of the ra-  dio fitting (Table A3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  In Table A4 we list the loga-  rithmic AGN luminosities in the X-ray, optical, and IR  bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The obscuration and UV-to-IR luminosities for  the torus and polar dust component, Eddington ratios,  and the spatial scales of the multiphase outflows (Sec-  tion 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5) are summarized in Table A5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The multiwave-  length SEDs and the best-fit SED models are presented  in Appendix E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Table A1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Best-fitting Parameters of the UV-to-IR SED Decomposition  ID  Name  fAGN  τV  σ  i  E(B − V )polar  Tpolar  χ2  red  (◦)  (◦)  (mag)  (K)  (1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  ID01  NGC 34  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='03  95±28  20  60  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='12  170±54  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  ID02  MCG−02-01-052/MCG−02-01-051  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='00(f)  · ·  · ·  · ·  · ·  · ·  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  ID03  MCG−02-01-052  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='00(f)  · ·  · ·  · ·  · ·  · ·  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  ID04  MCG−02-01-051  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='00(f)  · ·  · ·  · ·  · ·  · ·  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6  ID05  ESO 350−38  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='60±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='03  41±7  20  80  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='17  100±1  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  ID06  NGC 232/NGC 235  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  93±28  20  60  · ·  · ·  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7  ID07  NGC 232  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='00(f)  · ·  · ·  · ·  · ·  · ·  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  ID08  NGC 235  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  87±29  20  60  · ·  · ·  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4  ID09  MCG+12-02-001  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  96±28  20  60  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='55±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='29  174±44  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8  ID10  IC 1623A/IC 1623B  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='00(f)  · ·  · ·  · ·  · ·  · ·  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3  ID11  NGC 833/NGC 835  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  87±31  15  60  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='55±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='29  201±52  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7  ID12  NGC 833  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='03  82±32  15  60  · ·  · ·  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7  ID13  NGC 835  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  91±30  15  60  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='16±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='26  190±48  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8  ID14  NGC 838  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='00(f)  · ·  · ·  · ·  · ·  · ·  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3  ID15  NGC 839  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='00(f)  · ·  · ·  · ·  · ·  · ·  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6  ID16  NGC 1068  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='49±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  79±33  20  80  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='39±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='31  250±5  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3  ID17  UGC 2608/UGC 2612  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='26±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  63±30  15  80  · ·  · ·  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8  ID18  UGC 2608  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='20±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  64±32  15  80  · ·  · ·  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  ID19  UGC 2612  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='00(f)  · ·  · ·  · ·  · ·  · ·  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  ID20  NGC 1275  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='80±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  41±8  20  30  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='80±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  100±1  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6  ID21  NGC 1365  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  83±32  20  30  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='80±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  235±25  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6  ID22  ESO 203−1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='00(f)  · ·  · ·  · ·  · ·  · ·  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4  ID23  CGCG 468-002W/CGCG 468-002E  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='17±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  81±32  15  60  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  126±35  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  ID24  CGCG 468-002W  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='20±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  85±32  15  60  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  162±36  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  ID25  CGCG 468-002E  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='00(f)  · ·  · ·  · ·  · ·  · ·  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  ID26  IRAS F05189−2524  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='70±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='03  40±3  15  60  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='80±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  100±1  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8  ID27  IRAS F06076−2139/  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  94±28  20  60  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='55±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='29  137±27  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8  2MASS 06094601−2140312  Table A1 continued  48  Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Table A1 (continued)  ID  Name  fAGN  τV  σ  i  E(B − V )polar  Tpolar  χ2  red  (◦)  (◦)  (mag)  (K)  (1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  ID28  NGC 2623  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  104±21  20  60  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  100±5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  ID29  ESO 060−IG016 West/East  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  80±31  20  60  · ·  · ·  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  ID30  IRAS F08572+3915  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='47±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  49±24  20  80  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  180±41  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8  ID31  UGC 5101  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  45±16  15  60  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='30±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  101±8  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7  ID32  MCG+08-18-012/MCG+08-18-013  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='00(f)  · ·  · ·  · ·  · ·  · ·  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  ID33  MCG+08-18-012  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='00(f)  · ·  · ·  · ·  · ·  · ·  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  ID34  MCG+08-18-013  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='00(f)  · ·  · ·  · ·  · ·  · ·  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4  ID35  MCG−01-26-013/NGC 3110  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='00(f)  · ·  · ·  · ·  · ·  · ·  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  ID36  MCG−01-26-013  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='00(f)  · ·  · ·  · ·  · ·  · ·  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3  ID37  NGC 3110  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='00(f)  · ·  · ·  · ·  · ·  · ·  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='9  ID38  ESO 374−IG032  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  54±25  20  30  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  172±45  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='9  ID39  NGC 3256  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='00(f)  · ·  · ·  · ·  · ·  · ·  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7  ID40  IRAS F10565+2448  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='00(f)  · ·  · ·  · ·  · ·  · ·  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2  ID41  NGC 3690 West/East  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='29±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11  88±31  45  30  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='58±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='31  158±57  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6  ID42  ESO 440−58/MCG−05-29-017  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='00(f)  · ·  · ·  · ·  · ·  · ·  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7  ID43  IRAS F12112+0305  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='00(f)  · ·  · ·  · ·  · ·  · ·  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7  ID44  NGC 4418/MCG+00-32-013  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='29±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='03  117±10  20  80  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='65±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='23  150±1  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2  ID45  NGC 4418  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  82±28  20  80  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='63±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='24  200±1  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4  ID46  MCG+00-32-013  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='00(f)  · ·  · ·  · ·  · ·  · ·  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='9  ID47  Mrk 231  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='28±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  79±33  25  60  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='42±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='29  186±55  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3  ID48  NGC 4922S/NGC 4922N  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='34±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  81±32  20  60  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='38±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='19  135±42  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8  ID49  IC 860  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='00(f)  · ·  · ·  · ·  · ·  · ·  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  ID50  IRAS 13120−5453  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  49±22  20  80  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='23±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='28  100±5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  ID51  NGC 5104  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='00(f)  · ·  · ·  · ·  · ·  · ·  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8  ID52  MCG−03-34-064  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='61±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  48±20  20  60  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='79±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  206±19  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8  ID53  NGC 5135  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  79±33  15  80  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='38±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='31  138±58  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  ID54  Mrk 266B/Mrk 266A  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  98±26  20  60  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='18  182±45  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6  ID55  Mrk 273  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  73±33  15  60  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='78±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09  101±6  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4  ID56  IRAS F14348−1447  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  71±33  20  80  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='40±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='31  102±11  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6  ID57  IRAS F14378−3651  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='00(f)  · ·  · ·  · ·  · ·  · ·  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4  ID58  IC 4518A/IC 4518B  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='13±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  79±33  20  60  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='39±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='31  181±58  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3  ID59  IRAS F15250+3608  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='00(f)  · ·  · ·  · ·  · ·  · ·  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8  ID60  Arp 220W/Arp 220E  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  110±18  20  60  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='72±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='18  141±20  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2  ID61  NGC 6240S/NGC 6240N  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  104±23  20  30  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  136±32  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4  ID62  NGC 6285/NGC 6286  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  82±33  20  80  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='38±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='31  172±74  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  ID63  NGC 6285  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='00(f)  · ·  · ·  · ·  · ·  · ·  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3  ID64  NGC 6286  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  82±33  20  80  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='44±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='31  168±75  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  ID65  IRAS F17138−1017  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='14±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  81±33  20  60  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='37±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='30  135±54  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  ID66  IRAS F18293−3413  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='00(f)  · ·  · ·  · ·  · ·  · ·  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='9  ID67  IRAS F19297−0406  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='00(f)  · ·  · ·  · ·  · ·  · ·  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  ID68  NGC 6907/NGC 6908  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='00(f)  · ·  · ·  · ·  · ·  · ·  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  ID69  NGC 6921/MCG+04-48-002  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  86±31  20  60  · ·  · ·  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4  ID70  NGC 6921  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  82±33  20  80  · ·  · ·  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8  ID71  MCG+04-48-002  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='03  91±29  20  60  · ·  · ·  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7  Table A1 continued  49  Table A1 (continued)  ID  Name  fAGN  τV  σ  i  E(B − V )polar  Tpolar  χ2  red  (◦)  (◦)  (mag)  (K)  (1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  ID72  II Zw 096/IRAS F20550+1655 SE  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='00(f)  · ·  · ·  · ·  · ·  · ·  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7  ID73  ESO 286−19  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='00(f)  · ·  · ·  · ·  · ·  · ·  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3  ID74  NGC 7130  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='24±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  79±32  25  80  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='38±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='31  109±32  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6  ID75  NGC 7469/IC 5283  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='34±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09  77±33  15  30  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='34±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='36  102±11  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4  ID76  NGC 7469  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='38±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  75±33  15  30  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='72±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='20  102±10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6  ID77  IC 5283  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='00(f)  · ·  · ·  · ·  · ·  · ·  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2  ID78  ESO 148−2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='22±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  45±18  20  80  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='16±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='24  100±3  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6  ID79  NGC 7591  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='00(f)  · ·  · ·  · ·  · ·  · ·  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3  ID80  NGC 7674/MCG+01-59-081  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='41±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  71±32  40  30  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  137±48  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7  ID81  NGC 7674  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='43±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  60±29  40  30  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  138±43  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6  ID82  MCG+01-59-081  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='00(f)  · ·  · ·  · ·  · ·  · ·  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3  ID83  NGC 7679/NGC 7682  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='03  90±30  20  60  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='49±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='31  181±57  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7  ID84  NGC 7679  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  88±31  15  30  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='44±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='32  190±63  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  ID85  NGC 7682  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='15±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  82±32  60  60  · ·  · ·  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7  Note—Comments: (1–2) ID and object name;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (3) fraction of AGN luminosity in the IR band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The symbol “(f)” means  that the value is fixed;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (4) optical depth of each clump at V band;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (5–6) torus angular width and inclination;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (7) E(B −V )  of the polar dust;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (8) temperature of the polar dust;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (9) reduced χ2 for the UV-to-IR SED decomposition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  (This table is available in its entirety in machine-readable form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=')  50  Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Table A2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Properties of Host Galaxies and WISE Color  ID  Name  logM∗  logSFR  logsSFR  W1  W2  W3  W4  (M⊙)  (M⊙ yr−1)  (yr)  (mag)  (mag)  (mag)  (mag)  (1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  ID01  NGC 34  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='31±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='13  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='51±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  −8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='80±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='14  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='82±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='35±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='25±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  ID02  MCG−02-01-052/MCG−02-01-051  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='37±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='13  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='47±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  −8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='90±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='14  · ·  · ·  · ·  · ·  ID03  MCG−02-01-052  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='85±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='57±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  −9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='29±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='25±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='17±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  · ·  · ·  ID04  MCG−02-01-051  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='22±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='15  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='42±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  −8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='80±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='17  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='80±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='35±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='89±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='95±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  ID05  ESO 350−38  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='74±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='16  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='95±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  −8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='79±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='17  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='79±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='50±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='49±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  ID06  NGC 232/NGC 235  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='35±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  −9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='72±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  · ·  · ·  · ·  · ·  ID07  NGC 232  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='73±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='13  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='35±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  −9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='38±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='15  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='66±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='32±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='40±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='71±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  ID08  NGC 235  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='93±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='03  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='55±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='03  −10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='38±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='03±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='47±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='44±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='71±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  ID09  MCG+12-02-001  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='34±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='41±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  −8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='93±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='12  · ·  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='92±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='49±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='45±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  ID10  IC 1623A/IC 1623B  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='64±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='82±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='03  −8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='82±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='22±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='21±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='52±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='54±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  ID11  NGC 833/NGC 835  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='16±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='37±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='24  −10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='80±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='25  · ·  · ·  · ·  · ·  ID12  NGC 833  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='76±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='78±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='34  −12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='54±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='34  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='50±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='49±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  · ·  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='71±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  ID13  NGC 835  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='95±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='59±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  −10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='36±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='91±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='77±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='33±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='32±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  ID14  NGC 838  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='36±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  −9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='26±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='32±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='00±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='70±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='14±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  ID15  NGC 839  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='19±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='91±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='03  −9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='27±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='60±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='91±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='81±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  ID16  NGC 1068  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='15  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='25±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  −8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='82±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='17  · ·  · ·  · ·  · ·  ID17  UGC 2608/UGC 2612  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='36±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  −9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='68±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='12  · ·  · ·  · ·  · ·  ID18  UGC 2608  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='75±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='24±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11  −9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='51±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='15  · ·  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='70±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='33±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  ID19  UGC 2612  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='64±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='13  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='53±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  −10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='14  · ·  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='39±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='55±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='88±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  ID20  NGC 1275  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='70±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='91±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  −8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='79±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='20  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='03±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='52±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  ID21  NGC 1365  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='94±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='93±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09  −10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='13  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='30±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='95±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='32±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  · ·  ID22  ESO 203−1  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='78±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='22  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='78±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  −8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='00±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='23  · ·  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='15±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='92±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='36±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  ID23  CGCG 468-002W/CGCG 468-002E  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='95±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='87±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='20  −10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='22  · ·  · ·  · ·  · ·  ID24  CGCG 468-002W  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='89±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='44±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='48  −11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='34±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='48  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='93±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='47±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='44±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  · ·  ID25  CGCG 468-002E  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='21±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  −8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='90±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  · ·  · ·  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='67±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  ID26  IRAS F05189−2524  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='72±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='56±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='12  −9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='16±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='16  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='77±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='65±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='79±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='77±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  ID27  IRAS F06076−2139/  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='41±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='19  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='65±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11  −8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='76±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='21  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='31±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='78±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='84±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='81±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  2MASS 06094601−2140312  ID28  NGC 2623  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='86±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='31  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='53±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  −8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='33±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='32  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='39±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='76±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='84±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='60±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  ID29  ESO 060−IG016 West/East  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='85±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='32  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='68±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  −8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='17±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='32  · ·  · ·  · ·  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='69±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  ID30  IRAS F08572+3915  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='18±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='25  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='89±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  −7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='28±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='25  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='25±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='94±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='90±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  ID31  UGC 5101  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='85±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='14  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='00±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09  −8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='86±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='16  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='46±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='20±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  ID32  MCG+08-18-012/MCG+08-18-013  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='28±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='30±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  −8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='98±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11  · ·  · ·  · ·  · ·  ID33  MCG+08-18-012  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  −8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='93±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='78±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='03  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='67±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='03  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='13±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  · ·  ID34  MCG+08-18-013  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='30±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='12  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='30±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09  −9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='00±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='15  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='84±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='44±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='36±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  · ·  ID35  MCG−01-26-013/NGC 3110  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='68±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='12  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='26±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09  −9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='42±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='15  · ·  · ·  · ·  · ·  ID36  MCG−01-26-013  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='24±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  −9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='82±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='42±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='24±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='64±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='15±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='03  ID37  NGC 3110  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='73±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='18±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  −9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='56±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='19±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='90±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='76±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='57±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  ID38  ESO 374−IG032  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='43±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='20  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='72±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  −8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='71±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='21  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='60±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='16±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='92±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='19±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  ID39  NGC 3256  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='67±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='12  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='81±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  −8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='86±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='13  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='58±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  · ·  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='44±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  ID40  IRAS F10565+2448  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='71±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='13  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='95±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09  −8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='76±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='16  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  · ·  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='24±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='17±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  ID41  NGC 3690 West/East  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='82±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='14  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='69±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  −9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='13±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='18  · ·  · ·  · ·  · ·  ID42  ESO 440−58/MCG−05-29-017  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='55±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='30±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  −9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='24±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  · ·  · ·  · ·  · ·  ID43  IRAS F12112+0305  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='95±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='39  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='35±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='03  −7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='60±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='39  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='36±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='63±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='57±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='28±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  ID44  NGC 4418/MCG+00-32-013  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='28±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='13  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='82±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  −8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='47±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='15  · ·  · ·  · ·  · ·  ID45  NGC 4418  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='97±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='23  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='96±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  −8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='24  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='15±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='32±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='40±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  ID46  MCG+00-32-013  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='32±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='19  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='80±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='03  −8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='19  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='03  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='89±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='34±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='77±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='16  ID47  Mrk 231  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='73±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='42  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='43±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  −8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='30±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='42  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='80±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='58±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='54±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='57±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  ID48  NGC 4922S/NGC 4922N  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='92±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='91±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  −10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='00±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  · ·  · ·  · ·  · ·  Table A2 continued  51  Table A2 (continued)  ID  Name  logM∗  logSFR  logsSFR  W1  W2  W3  W4  (M⊙)  (M⊙ yr−1)  (yr)  (mag)  (mag)  (mag)  (mag)  (1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  ID49  IC 860  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='68±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='85±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  −8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='82±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='62±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='51±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='17±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='93±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  ID50  IRAS 13120−5453  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='15±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='12  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='34±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  −8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='81±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='14  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='58±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='83±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='91±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  ID51  NGC 5104  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='68±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='97±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  −9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='71±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='62±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='38±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='74±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='18±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  ID52  MCG−03-34-064  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='71±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='47±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  −10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='24±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='14  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='20±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='92±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='17±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='53±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  ID53  NGC 5135  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='93±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='17  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='19±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  −9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='74±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='20  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='61±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='44±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='62±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  ID54  Mrk 266B/Mrk 266A  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='76±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='14  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='35±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  −9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='41±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='15  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='88±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='48±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='57±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='56±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  ID55  Mrk 273  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='52±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='22  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='24±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  −8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='28±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='22  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='50±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='37±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='85±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='16±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  ID56  IRAS F14348−1447  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='73±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='24  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='32±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  −8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='40±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='24  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='12±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='29±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='52±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='95±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  ID57  IRAS F14378−3651  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='29±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='21  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='33±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='03  −7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='96±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='21  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='24±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='37±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='42±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  ID58  IC 4518A/IC 4518B  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='78±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='16  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='24±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='22  −9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='55±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='27  · ·  · ·  · ·  · ·  ID59  IRAS F15250+3608  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='12  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='12±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  −7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='89±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='13  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='34±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='84±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='99±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='40±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  ID60  Arp 220W/Arp 220E  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='82±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='30  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='12±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  −7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='69±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='31  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='71±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='14±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='70±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='76±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  ID61  NGC 6240S/NGC 6240N  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='60±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  −9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='42±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='12  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='85±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='34±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='59±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='35±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  ID62  NGC 6285/NGC 6286  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='61±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='35±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='03  −9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='26±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  · ·  · ·  · ·  · ·  ID63  NGC 6285  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='25±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='19  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='61±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  −9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='63±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='20  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='89±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='66±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  · ·  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='62±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  ID64  NGC 6286  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='42±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  −9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='34±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='90±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='40±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='37±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='51±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  ID65  IRAS F17138−1017  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='40±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='29  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='48±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  −7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='92±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='30  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='63±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='66±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='84±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  ID66  IRAS F18293−3413  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='72±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='12  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='78±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  −8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='94±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='13  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='88±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='37±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='12±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='42±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  ID67  IRAS F19297−0406  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='60±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='22  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='39±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='16  −8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='21±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='27  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='94±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='19±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='85±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='46±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  ID68  NGC 6907/NGC 6908  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='73±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='14  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='03  −9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='66±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='15  · ·  · ·  · ·  · ·  ID69  NGC 6921/MCG+04-48-002  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='15±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='94±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='13  −10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='22±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='16  · ·  · ·  · ·  · ·  ID70  NGC 6921  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='20±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='33±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='25  −11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='54±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='25  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='67±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='62±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  · ·  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  ID71  MCG+04-48-002  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='42±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='17  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='88±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09  −9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='55±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='19  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='30±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='80±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='90±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  ID72  II Zw 096/IRAS F20550+1655 SE  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='35±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='90±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  −8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='45±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='37±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='38±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='35±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  · ·  ID73  ESO 286−19  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='94±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='97±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  −7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='97±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='30±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='96±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='78±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  · ·  ID74  NGC 7130  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='30±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  −9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='76±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='13  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='98±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='55±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='59±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='74±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  ID75  NGC 7469/IC 5283  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='83±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='17  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='49±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  −9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='34±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='19  · ·  · ·  · ·  · ·  ID76  NGC 7469  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='69±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='18  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='51±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  −9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='18±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='20  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='29±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  · ·  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='83±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='77±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  ID77  IC 5283  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='46±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='50±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='16  −9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='97±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='18  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='30±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  · ·  · ·  ID78  ESO 148−2  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='21±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='40  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='93±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  −8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='28±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='41  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='92±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='63±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  ID79  NGC 7591  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='62±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  −9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='58±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='54±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='33±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='54±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='91±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  ID80  NGC 7674/MCG+01-59-081  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='21±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='25±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  −9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='96±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11  · ·  · ·  · ·  · ·  ID81  NGC 7674  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='22±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09  −9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='88±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='12  · ·  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='66±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  ID82  MCG+01-59-081  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='61±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='33±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  −10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='28±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11  · ·  · ·  · ·  · ·  ID83  NGC 7679/NGC 7682  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='77±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='03  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  −9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='72±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  · ·  · ·  · ·  · ·  ID84  NGC 7679  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='33±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  −9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='28±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='63±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='30±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='75±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  ID85  NGC 7682  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='62±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='20±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='23  −10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='83±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='23  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='20±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='21±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='86±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='21±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='03  Note—Comments: (1–2) ID and object name;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (3) logarithmic stellar mass;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (4) logarithmic SFR;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (5) logarithmic specific SFR (sSFR);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (6)–(9) W1,  W2, W3, and W4 magnitudes (Vega) from ALLWISE catalog (Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5 and 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The W1 and W2 magnitudes are corrected for Galactic  extinction (Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  (This table is available in its entirety in machine-readable form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=')  52  Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Table A3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Results of the Radio Fitting  ID  Name  αradio  qir  logL1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4GHz  qexcess  χ2  red  (erg s−1)  (1)  (2)  (3)  (4)  (5)  (6)  (7)  ID01  NGC 34  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='41±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='77±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='91±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='25±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  ID02  MCG−02-01-052/MCG−02-01-051  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='44±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='54±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='03±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='42±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4  ID03  MCG−02-01-052  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5(f)  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='76±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='99±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='28±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2  ID04  MCG−02-01-051  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='49±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='50±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='99±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='42±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  ID05  ESO 350−38  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='56±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='36±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='54±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='44±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  ID06  NGC 232/NGC 235  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='68±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='43±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='20±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='70±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8  ID07  NGC 232  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='52±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='58±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='98±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='49±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8  ID08  NGC 235  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='57±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='93±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='81±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2  ID09  MCG+12-02-001  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='52±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='57±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='96±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='41±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7  ID10  IC 1623A/IC 1623B  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='67±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='25±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='52±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='56±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7  ID11  NGC 833/NGC 835  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='61±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='49±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='41±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='90±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='25  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6  ID12  NGC 833  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5(f)  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='59±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='66±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='34  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  ID13  NGC 835  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='60±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='46±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='43±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='70±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6  ID14  NGC 838  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='63±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='57±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='65±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='39±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2  ID15  NGC 839  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='51±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='98±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='24±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='18±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3  ID16  NGC 1068  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='56±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='23±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='83±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6  ID17  UGC 2608/UGC 2612  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='79±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='25±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='37±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='86±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8  ID18  UGC 2608  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='78±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='15±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='22±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='83±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  ID19  UGC 2612  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5(f)  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='47±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='03  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='40±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='72±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  ID20  NGC 1275  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='47±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='57±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='03  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='29±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='03  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='24±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6  ID21  NGC 1365  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='65±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='85±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='30±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='03  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='23±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3  ID22  ESO 203−1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5(f)  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='94±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3  ID23  CGCG 468-002W/CGCG 468-002E  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5(f)  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='76±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='47±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='45±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='20  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  ID24  CGCG 468-002W  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5(f)  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='79±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='84±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='14±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='48  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4  ID25  CGCG 468-002E  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5(f)  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='39±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='03  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='71±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3  ID26  IRAS F05189−2524  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5(f)  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='49±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='22±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='51±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='13  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7  ID27  IRAS F06076−2139/  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='36±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='67±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='97±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='18±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='12  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7  2MASS 06094601−2140312  ID28  NGC 2623  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='26±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='66±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='00±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='32±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  ID29  ESO 060−IG016 West/East  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5(f)  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='62±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='19±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='36±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  ID30  IRAS F08572+3915  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5(f)  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='40±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='69±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='65±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3  ID31  UGC 5101  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='22±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='14±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='92±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='78±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3  ID32  MCG+08-18-012/MCG+08-18-013  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='41±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='56±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='85±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='41±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7  ID33  MCG+08-18-012  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5(f)  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='20±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='19  36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='91±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='66±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='9  ID34  MCG+08-18-013  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='40±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='55±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='87±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='42±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3  ID35  MCG−01-26-013/NGC 3110  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='64±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='31±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='66±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4  ID36  MCG−01-26-013  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5(f)  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='45±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='82±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='43±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2  ID37  NGC 3110  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='64±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='32±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='74±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4  ID38  ESO 374−IG032  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='51±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='87±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='92±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3  ID39  NGC 3256  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='52±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='52±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='36±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='41±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3  ID40  IRAS F10565+2448  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='28±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='50±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='51±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='42±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8  ID41  NGC 3690 West/East  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='50±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='34±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='37±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='53±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2  ID42  ESO 440−58/MCG−05-29-017  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='58±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='53±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='95±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='03  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='49±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  ID43  IRAS F12112+0305  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='20±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='84±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='59±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2  ID44  NGC 4418/MCG+00-32-013  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5(f)  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='21±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='89±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='93±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  ID45  NGC 4418  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5(f)  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='42±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='91±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='03  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='80±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2  ID46  MCG+00-32-013  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5(f)  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='31±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='13  35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='98±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='63±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2  ID47  Mrk 231  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='37±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='27±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='25±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='67±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3  ID48  NGC 4922S/NGC 4922N  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='33±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='37±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='84±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='78±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='9  Table A3 continued  53  Table A3 (continued)  ID  Name  αradio  qir  logL1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4GHz  qexcess  χ2  red  (erg s−1)  (1)  (2)  (3)  (4)  (5)  (6)  (7)  ID49  IC 860  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='19±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='98±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8  ID50  IRAS 13120−5453  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5(f)  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='41±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='98±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='49±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='9  ID51  NGC 5104  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='60±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='60±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='63±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='52±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6  ID52  MCG−03-34-064  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='35±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='44±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='16±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='55±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  ID53  NGC 5135  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='60±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='31±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='75±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='9  ID54  Mrk 266B/Mrk 266A  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='60±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='50±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  ID55  Mrk 273  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='41±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='46±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='83±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='44±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2  ID56  IRAS F14348−1447  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='42±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='43±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='91±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='44±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3  ID57  IRAS F14378−3651  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='47±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='60±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='75±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='28±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  ID58  IC 4518A/IC 4518B  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='40±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='90±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='21±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='83±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='23  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7  ID59  IRAS F15250+3608  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='33±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='16  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='15±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='88±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6  ID60  Arp 220W/Arp 220E  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='59±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='51±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='24±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3  ID61  NGC 6240S/NGC 6240N  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='69±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='93±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='93±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='18±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  ID62  NGC 6285/NGC 6286  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='44±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='23±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='29±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='79±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2  ID63  NGC 6285  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5(f)  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='60±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='33±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  ID64  NGC 6286  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='46±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='25±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  ID65  IRAS F17138−1017  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='55±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='75±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='80±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='17±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6  ID66  IRAS F18293−3413  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='65±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='56±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='37±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='03  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='44±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8  ID67  IRAS F19297−0406  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='47±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='49±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='85±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='31±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='16  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='9  ID68  NGC 6907/NGC 6908  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='57±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='55±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='69±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='47±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8  ID69  NGC 6921/MCG+04-48-002  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='59±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='32±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='84±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='76±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='14  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4  ID70  NGC 6921  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='61±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='13±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='25±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='44±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7  ID71  MCG+04-48-002  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='58±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='36±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='70±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='68±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6  ID72  II Zw 096/IRAS F20550+1655 SE  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='77±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='65±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='23±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='18±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  ID73  ESO 286−19  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='24±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='82±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='32±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='20±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2  ID74  NGC 7130  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='38±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='19±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='03  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='74±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3  ID75  NGC 7469/IC 5283  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='53±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='37±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='19±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='56±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4  ID76  NGC 7469  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='50±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='42±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='17±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='51±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  ID77  IC 5283  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='86±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='72±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='38±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='17  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  ID78  ESO 148−2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='47±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='16  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='81±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='30±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='22±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4  ID79  NGC 7591  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='46±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='57±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='64±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='46±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  ID80  NGC 7674/MCG+01-59-081  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='43±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='73±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='75±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='36±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8  ID81  NGC 7674  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5(f)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='84±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='60±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='23±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6  ID82  MCG+01-59-081  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5(f)  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='21±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='39±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='92±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6  ID83  NGC 7679/NGC 7682  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='32±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='21±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='82±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  ID84  NGC 7679  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='44±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='51±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='70±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='51±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  ID85  NGC 7682  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='21±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='29±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='72±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='78±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='23  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  Note—Comments: (1–2) ID and object name;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (3) radio spectral index of the power-law synchrotron emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The symbol “(f)” means that the value is fixed;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (4) the far-IR/radio correlation coefficient;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (5) rest-frame radio  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4 GHz luminosity;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (6) radio-excess parameter qexcess = log(L1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4GHz/SFR);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (7) reduced χ2 for the combination  of the radio fitting and UV-to-IR SED decomposition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  (This table is available in its entirety in machine-readable form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=')  54  Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Table A4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Summary of the logarithmic AGN luminosities  ID  Name  L6,AGN  L12,t  L12,p  L12,AGN  L12,nuc  LX,unabs  L2keV,unabs  L2500,disk  αOX  (1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10)  (11)  ID01  NGC 34  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='14  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='46  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='70  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='89  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='90+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='63  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='55  ID05  ESO 350−38  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='23  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='87  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='93  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='92  · ·  · ·  · ·  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='84  · ·  ID06  NGC 232/NGC 235  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='59  · ·  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='59  · ·  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='28+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='18  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='16  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='98  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='24  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  ID08  NGC 235  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='68  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='25  · ·  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='25  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='29  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='28+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='18  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='16  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='97  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='84  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='95  ID09  MCG+12-02-001  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='54  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='15  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='42  · ·  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='75+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='33  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='48  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='88  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='54  ID11  NGC 833/NGC 835  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='49  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='77  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='32  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='43  · ·  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='33+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='28  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='24  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='54  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='19  ID12  NGC 833  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='37  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='95  · ·  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='95  · ·  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='99+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='25  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='24  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='78  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='51  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='89  ID13  NGC 835  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='31  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='89  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='75  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='13  · ·  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='13  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='03  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='67  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='59  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='35  ID16  NGC 1068  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='54  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='93  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='52  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='62  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='80  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='34+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  · ·  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='96  · ·  ID17  UGC 2608/UGC 2612  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='84  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='48  · ·  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='48  · ·  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='59+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='19  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='25  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='48  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='55  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='41  ID18  UGC 2608  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='49  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='12  · ·  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='12  · ·  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='59+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='19  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='25  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='33  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='26  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='36  ID20  NGC 1275†  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='88  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='43  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='45  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='21  · ·  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='19  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='84  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='25  ID21  NGC 1365  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='79  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='23  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='44  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='65  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='51  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='90+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='71  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='65  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='36  ID23  CGCG 468-002W/CGCG 468-002E  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='98  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='55  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='39  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='58  · ·  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='84+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='03  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='49  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='14  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='25  ID24  CGCG 468-002W  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='44  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='97  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='83  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='21  · ·  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='84+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='03  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='51  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='64  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  ID26  IRAS F05189−2524  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='38  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='92  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='89  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='95  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='87  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='42+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='30  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='60  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='50  ID27  IRAS F06076−2139/  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='94  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='55  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='50  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='82  · ·  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='18+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='15  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='14  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='92  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='14  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='47  2MASS 06094601−2140312  ID28  NGC 2623  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='77  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='37  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='39  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='61  40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='90+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11  40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='64  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='00  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='91  ID29  ESO 060−IG016 West/East  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='60  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='14  · ·  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='14  · ·  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='94+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='69  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='73  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='78  ID30  IRAS F08572+3915  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='70  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='79  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='13  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='77+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='52  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='61  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='19  ID31  UGC 5101  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='51  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='97  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='35  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='15+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='25  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='15  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='77  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='72  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='36  ID38  ESO 374−IG032  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='39  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='93  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='43  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  · ·  · ·  · ·  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='28  · ·  ID41  NGC 3690 West/East  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='70  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='89  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='70  · ·  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='66+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='34  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='32  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='55  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='80  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='48  ID44  NGC 4418/MCG+00-32-013  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='33  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='55  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='68  · ·  · ·  · ·  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='32  · ·  ID45  NGC 4418  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='24  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='75  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='49  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='56  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='70  · ·  · ·  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='89  · ·  ID47  Mrk 231  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='60  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='20  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='92  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='38  · ·  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='65+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='28  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='71  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='93  ID48  NGC 4922S/NGC 4922N  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='39  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='86  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  · ·  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='00+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='20  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='18  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='74  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='52  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='68  ID50  IRAS 13120−5453  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='29  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='94  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='00  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='99  · ·  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='17+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='59  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='91  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='88  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='76  ID52  MCG−03-34-064  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='49  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='95  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='18  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='38  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='00  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='27+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='53  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='17  ID53  NGC 5135  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='18  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='82  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='89  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='23  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='30+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='42  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='26  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='90  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='96  ID54  Mrk 266B/Mrk 266A  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='56  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='69  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='93  · ·  · ·  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='71  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='17  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='18  ID55  Mrk 273  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='41  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='94  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='91  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='98  · ·  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='21  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='21  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='78  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='73  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='36  ID56  IRAS F14348−1447  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='33  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='27  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='12  · ·  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='70+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='93  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='40  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='46  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='62  ID58  IC 4518A/IC 4518B  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='14  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='39  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='81  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='95  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='54  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='83+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='55  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='93  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='14  ID60  Arp 220W/Arp 220E  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='70  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='64  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='97  · ·  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='59+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='33  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='38  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='79  ID61  NGC 6240S/NGC 6240N  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='45  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='52  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='14  · ·  · ·  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='57  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='42  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='94  ID62  NGC 6285/NGC 6286  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='94  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='20  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  · ·  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='21  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='23  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='64  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='98  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='51  ID64  NGC 6286  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='71  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='54  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='96  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='64  · ·  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='21  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='23  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='63  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='80  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='45  ID65  IRAS F17138−1017  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='32  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='92  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='80  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='95  · ·  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='68+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='41  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='27  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='71  ID69  NGC 6921/MCG+04-48-002  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='96  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='52  · ·  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='52  · ·  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='96+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='40  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='46  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='64  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='12  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='19  ID70  NGC 6921  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='48  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='47  · ·  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='47  · ·  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='80+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='37  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='44  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='49  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='48  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='00  ID71  MCG+04-48-002  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='80  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='37  · ·  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='37  · ·  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='44+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='15  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='15  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='12  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='34  ID74  NGC 7130  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='91  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='71  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='75  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='75  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='18  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='87+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='31  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='25  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='55  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='58  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='39  ID75  NGC 7469/IC 5283  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='76  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='35  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='20  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='38  · ·  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='26+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='03  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='85  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='30  ID76  NGC 7469  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='63  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='21  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='24  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='83  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='26+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='03  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='84  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='29  ID78  ESO 148−2  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='65  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='29  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='35  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='34  · ·  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='38+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='24  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='28  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='13  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='25  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='81  ID80  NGC 7674/MCG+01-59-081  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='58  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='55  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='59  · ·  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='59+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='33  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='23  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='29  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='73  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='55  ID81  NGC 7674  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='03  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='54  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='53  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='58  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='26  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='59+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='33  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='23  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='28  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='71  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='55  Table A4 continued  55  Table A4 (continued)  ID  Name  L6,AGN  L12,t  L12,p  L12,AGN  L12,nuc  LX,unabs  L2keV,unabs  L2500,disk  αOX  (1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10)  (11)  ID83  NGC 7679/NGC 7682  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='67  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='16  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='47  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='65  · ·  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='49+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='21  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='70  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='19  ID84  NGC 7679  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='58  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='96  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='34  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='49  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='74  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='34+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='47  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='16  ID85  NGC 7682  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='13  · ·  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='13  · ·  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='94+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='68  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='94  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='00  Note—Comments: (1–2) ID and object name;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (3) logarithmic rest-frame 6 µm luminosity of AGN (torus and polar dust) component (L6,AGN);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  (4)–(6) logarithmic rest-frame 12 µm luminosities of torus component (L12,t), polar component (L12,p), and both components (L12,AGN);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (7)  logarithmic nuclear 12 µm luminosity (L12,nuc) referred from Asmus et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2014, 2015);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (8)–(9) logarithmic unabsorbed (absorption-corrected)  AGN luminosities in the rest-frame 2–10 keV (LX,unabs) and 2 keV bands (L2keV,unabs);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (10) logarithmic extinction-corrected intrinsic AGN disk  luminosity in the rest-frame 2500 ˚  A band (L2500,disk);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (11) X-ray to optical spectral index computed by αOX ≡ log(L′′  2keV/L′′  2500)/log(ν2keV/ν2500),  where L′′  2keV = L2keV,unabs/ν2keV and L′′  2500 = L2500,disk/ν2500.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  † Large fractions of the mid-IR and X-ray luminosities in NGC 1275 could be explained by the jet emission (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Hitomi Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Rani et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  (This table is available in its entirety in machine-readable form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=')  56  Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Table A5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Summary of the Extinction, AGN Luminosities, and Polar Dust Sizes  ID  Name  N (LOS)  H  A(LOS)  V ,torus  A(LOS)  V ,polar  logLtorus  logLpolar  logLAGN,int  logMBH  logλEdd  logRpolar  logR(mir/io/mo)  (1022 cm−2)  (mag)  (mag)  (erg s−1)  (erg s−1)  (erg s−1)  (M⊙)  (pc)  (pc)  (1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10)  (11)  (12)  ID01  NGC 34  50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3+10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3  −9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='9  108.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3±32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='54±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='16  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='53±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='16  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='84±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='16  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='82  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='16  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='67±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='40  · · /· · · /· · ·  ID05  ESO 350−38  · ·  346.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6±58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  0  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='96±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='30±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='62±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  · ·  · ·  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='71±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  · · /· · · /· · ·  ID06  NGC 232/NGC 235  51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4+8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3  −6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7±32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3  · ·  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='75±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  · ·  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='20  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='29±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  · ·  · · /· · · /· · ·  ID08  NGC 235  51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4+8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3  −6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4±33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7  · ·  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='35±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='03  · ·  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='61±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='03  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='20  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='69±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='03  · ·  · · /· · · /· · ·  ID09  MCG+12-02-001  707.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5+268.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4  −277.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  110.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3±31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='9  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='33±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='14  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='48±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='16  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='66±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='15  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='48±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='15  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='55±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='32  · · /· · · /· · ·  ID11  NGC 833/NGC 835  · ·  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4±6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='9  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='91±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='17±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='31±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  · ·  · ·  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='21±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='31  · · /· · · /· · ·  ID12  NGC 833  26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2±6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4  · ·  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='95±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='17  · ·  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='28±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='17  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='61  −4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='43±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='17  · ·  · · /· · · /· · ·  ID13  NGC 835  29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2±5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='9  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='99±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='12±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='37±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='85  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='58±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='30±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='31  · · /· · · /· · ·  ID16  NGC 1068  ∼1000  664.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8±278.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  0  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='49±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='74±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='35  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='71±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='65±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='73/· · · /2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='00  ID17  UGC 2608/UGC 2612  540+700  −310  436.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8±209.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2  · ·  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='52±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09  · ·  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='33±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='64  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='42±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09  · ·  · · /· · · /· · ·  ID18  UGC 2608  540+700  −310  447.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1±220.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  · ·  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='22±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='16  · ·  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='17  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='64  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='71±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='17  · ·  · · /· · · /· · ·  ID20  NGC 1275†  · ·  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='46±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='48±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='62±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  · ·  · ·  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='70±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  · · /· · · /· · ·  ID21  NGC 1365  ∼10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='28±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='30±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='43±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='13  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='80±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='13  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='74/· · · /· · ·  ID23  CGCG 468-002W/CGCG 468-002E  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2±6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='55±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='12  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='64±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='12  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='91±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='12  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='67  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='86±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='12  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='34  · · /· · · /· · ·  ID24  CGCG 468-002W  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='9±6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='15±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='13  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='41±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='67  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='36±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='52±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='28  · · /· · · /· · ·  ID26  IRAS F05189−2524  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='96±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='27±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='38±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='94  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='66±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  · · /3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='48/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='28  ID27  IRAS F06076−2139/  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2+24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  −12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  107.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7±31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='9  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='59±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='73±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='92±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='30  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='48±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='97±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='24  · · /· · · /· · ·  2MASS 06094601−2140312  ID28  NGC 2623  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0+4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  119.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3±23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='9  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='47±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='45±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='77±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='62  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='95±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='28±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  · · /· · · /· · ·  ID29  ESO 060−IG016 West/East  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4+4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='9  91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='9±35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7  · ·  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='25±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  · ·  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='51±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='79  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='38±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  · ·  · · /· · · /· · ·  ID30  IRAS F08572+3915  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6+129.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3  −28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3  417.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='9±199.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3  0  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='72±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='39±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='48  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='19±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='38±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='28  · · /3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='30/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='91  ID31  UGC 5101  96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3+4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='9±3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='9±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='35±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='50±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='17  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='77±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='64±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  · · /· · · /· · ·  ID38  ESO 374−IG032  · ·  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='95±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='03  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='75±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  · ·  · ·  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='77±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='32  · · /· · · /· · ·  ID41  NGC 3690 West/East  302.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6+60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6  −49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7  161.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0±56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='9  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8±1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='69±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='16  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='19  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='57±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='17  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='62±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='17  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='12±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='45  · · /· · · /· · ·  ID44  NGC 4418/MCG+00-32-013  · ·  991.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4±86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  0  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='38±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='03  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='90±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='03  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='03  · ·  · ·  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='95±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  · · /· · · /· · ·  ID45  NGC 4418  · ·  695.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0±238.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8  0  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='97±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='47±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='67±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  · ·  · ·  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='39±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  · · /· · · /2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='76  ID47  Mrk 231  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2  202.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3±83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='9  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='21±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='23±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='49±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='92  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='53±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='39±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='36  · · /3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='48/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='78  ID48  NGC 4922S/NGC 4922N  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='9+285.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  −21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6  93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1±37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='98±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='12  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='12  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='30±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='12  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='79  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='59±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='12  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='18±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='38  · · /· · · /· · ·  ID50  IRAS 13120−5453  164.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8+21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6  −20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  413.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0±183.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4  0  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='99±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='37±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='66±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='43  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='87±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='72±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  · · /2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='48/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='25  ID52  MCG−03-34-064  98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4+2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4  55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3±23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='97±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='14±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='30±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='95  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='75±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='67±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='33/· · · /· · ·  ID53  NGC 5135  670+1660  −280  548.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1±228.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  0  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='86±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='21  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='48±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='20  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='68±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='21  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='77  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='19±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='21  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='85±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='52  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='63/· · ·  ID54  Mrk 266B/Mrk 266A  700/6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8  111.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='9±30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='65±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='64±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='95±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  · ·  · ·  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='64±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='31  · · /· · · /· · ·  ID55  Mrk 273  49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6+5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4±6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='13  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='40±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='13  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='51±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='13  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='35  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='94±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='13  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='64±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  · · /3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='60/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='74  ID56  IRAS F14348−1447  128.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3+95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  −55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4  602.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6±277.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  0  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='15±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='15  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='61±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='18  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='84±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='17  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='84  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='17  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='79±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='15  · · /· · · /2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='55  ID58  IC 4518A/IC 4518B  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='9  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='9±37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2±1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='39±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='27  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='48±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='27  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='70±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='26  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='53  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='93±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='26  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='53±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='41  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='29/· · · /· · ·  Table A5 continued  57  Table A5 (continued)  ID  Name  N (LOS)  H  A(LOS)  V ,torus  A(LOS)  V ,polar  logLtorus  logLpolar  logLAGN,int  logMBH  logλEdd  logRpolar  logR(mir/io/mo)  (1022 cm−2)  (mag)  (mag)  (erg s−1)  (erg s−1)  (erg s−1)  (M⊙)  (pc)  (pc)  (1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10)  (11)  (12)  ID60  Arp 220W/Arp 220E  1000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0+n  −22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  126.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3±20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='81±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='99±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='03  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='15±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  · ·  · ·  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='17  · · /· · · /· · ·  ID61  NGC 6240S/NGC 6240N  147/155  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='89±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='20±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  · ·  · ·  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='12±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='28  · · /· · · /2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='81  ID62  NGC 6285/NGC 6286  140.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2+26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7  −34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6  690.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5±276.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  0  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='50±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='75±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='98  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='33±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='61±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='53  · · /· · · /· · ·  ID64  NGC 6286  140.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2+26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7  −34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6  694.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8±277.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4  0  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='88±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='35±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='58±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='98  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='50±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='55±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='54  · · /· · · /· · ·  ID65  IRAS F17138−1017  1000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0+n  −643.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2±38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='9  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='72±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='20  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='84±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='24  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='21  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='76  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='81±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='21  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='50  · · /· · · /· · ·  ID69  NGC 6921/MCG+04-48-002  · ·  98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='9±35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  · ·  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='63±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  · ·  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='89±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02  · ·  · ·  · ·  · · /· · · /· · ·  ID70  NGC 6921  173.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1+27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8  −31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='9  693.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8±275.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7  · ·  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='55±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='03  · ·  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='25±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='96±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04  · ·  · · /· · · /· · ·  ID71  MCG+04-48-002  72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7+14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8  −8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5±32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8  · ·  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='53±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11  · ·  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='80±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='64  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='94±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11  · ·  · · /· · · /· · ·  ID74  NGC 7130  413.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3+13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  −7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4  734.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0±292.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7  0  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='78±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='18  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='18  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='35±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='18  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='89  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='64±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='18  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='47±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='37  · · /3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08/· · ·  ID75  NGC 7469/IC 5283  <0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1±1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='36±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='44±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='14  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='63±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='30  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='77±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='68±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='14  · · /· · · /· · ·  ID76  NGC 7469  <0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='32±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='12  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='51±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='62±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='30  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='79±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='68±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='13  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='12/· · · /· · ·  ID78  ESO 148−2  158.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5+45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  −47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6  383.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4±151.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  0  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='36±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='72±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='03±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='49  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='57±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='91±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  · · /3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='41/· · ·  ID80  NGC 7674/MCG+01-59-081  29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6+2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='9  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1±36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='66±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='95±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='51±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='99  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='58±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='26±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='42  · · /· · · /· · ·  ID81  NGC 7674  29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6+2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='9  69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1±33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='64±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='93±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='49±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='99  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='60±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='25±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='38  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='59/· · · /· · ·  ID83  NGC 7679/NGC 7682  · ·  103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3±34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5±1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='15±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='16  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='28±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='18  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='48±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='16  · ·  · ·  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='42±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='39  · · /· · · /· · ·  ID84  NGC 7679  <0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4±1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='98±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='15  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='12  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='24±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='13  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='42  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='28±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='13  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='23±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='41  · · /· · · /· · ·  ID85  NGC 7682  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2+6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  −7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  691.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4±268.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8  · ·  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='67±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='22  · ·  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='72±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='21  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='48  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='86±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='21  · ·  · · /· · · /· · ·  Note—Comments: (1–2) ID and object name;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (3) line-of-sight hydrogen column density derived from X-ray spectral analysis (Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Yamada  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (4)–(5) line-of-sight extinction in the V  band due to torus, A(LOS)  V ,torus, and polar dust, A(LOS)  V ,torus;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (6)–(8) logarithmic UV-to-IR  luminosities of torus component (Ltorus), polar dust component (Lpolar), and intrinsic AGN disk component (LAGN,int);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (9) SMBH mass estimated  from the averaged value of four independent measurements in Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2021);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (10) logarithmic Eddington ratio (LAGN,int/LEdd).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The  Eddington luminosity is defined as LEdd = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='26 × 1038MBH/M⊙;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (11) physical size of polar dust, estimated by the polar dust temperature and  dust sublimation radius (Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (12) physical sizes of the polar dust emission detected in the mid-IR band (Rmir;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Asmus 2019), radius of  ionized outflows (Rio;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Fluetsch et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021), and radius of molecular outflows (Rmo;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Fluetsch et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  † Large fractions of the X-ray and mid-IR luminosities in NGC 1275 could be explained by the jet emission (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Hitomi Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Rani et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  (This table is available in its entirety in machine-readable form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=')  58  Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' MOCK ANALYSIS  We evaluate the constrainability of a model parame-  ter by the “mock analysis” of X-CIGALE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' This is im-  plemented in the previous version of CIGALE (see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=',  Buat et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2012, 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Ciesla et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Lo Faro et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Boquien et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Toba et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Yang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2020a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' X-CIGALE uses the photometric data for each  object based on the best-fit parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' It allows the  fluxes to vary within the uncertainties of the observa-  tions by adding a value taken from a Gaussian distribu-  tion with the same standard deviation as indicated by  the photometric data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Figure B1 shows the results of the mock analysis  with the best-fit values compared to the mock values  for the main parameters in this study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  We find that  the mean differences (the best-fit values − mock val-  ues) are small;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' ∆logM∗ = −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11, ∆logSFR =  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07, ∆fAGN = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='00 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='03, ∆logLAGN,int =  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08, ∆logLpolar = −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='01 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08, and ∆Tpolar =  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='21 ± 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The deviation of the differences in Tpolar  is relatively large but consistent with the range of 1σ  uncertainty of each object.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Therefore, we conclude that  these quantities are not sensitive to photometric un-  certainties thanks to the multiwavelength SED analysis  with the self-consistent AGN model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' COMPARISON WITH PREVIOUS SED STUDIES  Here, we examine the difference in the results of this  study and previous SED works.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' For the local U/LIRGs  in GOALS sample, Shangguan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2019) performed  the IR (1–500 µm) SED fitting and Paspaliaris et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  (2021) carried out the UV-to-submillimeter SED analy-  sis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Our estimates of the SFRs are well consistent with  their works (Figure C1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Whereas, we find that their  stellar mass is smaller than those of our results (Fig-  ure C2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' For the results of Shangguan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2019), this  may be explained by that the lack of optical photomet-  ric data that causes the overestimation of the fraction  of the old-stellar population.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' In this case, the estimates  of the luminosity from each star become small, and thus  the total stellar mass will be overestimated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Although it  is unclear why are the estimates of stellar mass by Pas-  paliaris et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2021) also larger, this may be affected by  the difference in the contribution of the IR polar dust  emission in our analysis that applies the torus parame-  ters obtained from the X-ray fitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  In the left panel of Figure C3, we compare the AGN  luminosities in this study and those in Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Their AGN luminosities are estimated by the av-  eraged values of four different methods (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', the [O IV]  luminosity, bolometric AGN fraction, and IR SED anal-  ysis).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Its typical scatter is reported as ∼0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='27 dex when  we adopt the averaged value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Particularly, the esti-  mates using the [O IV] luminosities may be larger than  those from other methods, which may be due to the  contamination from the intense starburst emission in  U/LIRGs (but see also Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Even if  the intrinsic AGN luminosities given by Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  (2021) are adopted, the main discussion on the SFR–  LAGN,int relation is unchanged (see Section 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The  right panel of Figure C3 presents the comparison be-  tween the 12 µm luminosity of the AGN component  (this study) and the nuclear 12 µm luminosities esti-  mated with the high-spatial-resolution mid-IR images  (Asmus 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Although there are a few differences,  the multiwavelength SED analysis extracts the AGN  emission that is consistent with the imaging studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' COMPARISON WITH THE RESULTS OF  SKIRTOR MODEL  In this study, we also performed the SED decom-  position by using the AGN model as the SKIRTOR  model (Stalevski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2016) instead of the CLUMPY  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The σ values are converted from torus angular  width (σ) of [10◦–15◦, 15◦–25◦, 25◦–70◦] to angle be-  tween the equatorial plane and edge of the torus (∆)  of [30◦, 40◦, 60◦], respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The smooth component  in the SKIRTOR model shields the AGN disk emission  at subparsec scales and re-radiates the strong near-IR  emission relative to the clumpy torus model (Stalevski  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2012, 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' In fact, the UV-to-IR SEDs of IRAS  F08572+3915 that is not reproduced with CLUMPY  (χ2  red = 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8) due to the near-IR bump (as illustrated in  the WISE color–color diagram in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3), while it  is well fitted with SKIRTOR model (χ2  red = 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The  intrinsic AGN luminosities of IRAS F08572+3915 es-  timated with CLUMPY (logLAGN,int = 45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='39 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06)  is smaller than that from SKIRTOR (45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='82 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='02).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  NGC 833, a stage A merger, is another outlier that  shows the gap between the estimates with CLUMPY  (logLAGN,int = 42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='28 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='17) and SKIRTOR (42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='91 ±  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='20;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' left panel of Figure D1), but the reason for the  difference should be the poor photometry in the 5–  70 µm band (see Figure E1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Except for the IRAS  F08572+3915 and NGC 833, all sources show similar  AGN luminosities with these models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Identically, the  polar dust luminosities constrained with the SKIRTOR  model are well consistent with the values with CLUMPY  (right panel of Figure D1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Additionally, we investigate the polar dust temper-  ature derived from the fits with SKIRTOR (left panel  of Figure D2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Due to the strong near-IR emission,  59  8  9  10  11  12  logM *  (Mock)  8  9  10  11  12  logM *  (This work)  F13120  Stage-A(Early)  Stage-B(Early)  Stage-C(Late)  Stage-D(Late)  Stage-N  2  1  0  1  2  3  logSFR (Mock)  2  1  0  1  2  3  logSFR (This work)  Stage-A(Early)  Stage-B(Early)  Stage-C(Late)  Stage-D(Late)  Stage-N  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  fAGN (= LIR, AGN/LIR) (Mock)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  fAGN (= LIR, AGN/LIR) (This Work)  Stage-A(Early)  Stage-B(Early)  Stage-C(Late)  Stage-D(Late)  Stage-N  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  logLAGN, int (Mock)  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  logLAGN, int (This work)  Stage-A(Early)  Stage-B(Early)  Stage-C(Late)  Stage-D(Late)  Stage-N  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  logLpolar (Mock)  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  logLpolar (This work)  Stage-A(Early)  Stage-B(Early)  Stage-C(Late)  Stage-D(Late)  Stage-N  100  150  200  250  Tpolar [K] (Mock)  100  150  200  250  Tpolar [K] (This work)  Stage-A(Early)  Stage-B(Early)  Stage-C(Late)  Stage-D(Late)  Stage-N  Figure B1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Comparison of the best-fit parameters and those derived from the mock analysis for the M∗ (top left), SFR (top  right), AGN fraction (middle left), intrinsic AGN luminosity (middle right), polar dust luminosity (bottom left), and polar  dust temperature (bottom right).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The symbols are the same in Figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  60  Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  logSFR (Shangguan+19)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  logSFR (This work)  Stage-A(Early)  Stage-B(Early)  Stage-C(Late)  Stage-D(Late)  Stage-N  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  logSFR (Paspaliaris+21)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  logSFR (This work)  Stage-A(Early)  Stage-B(Early)  Stage-C(Late)  Stage-D(Late)  Stage-N  Figure C1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Left panel: comparison of SFRs estimated in Shangguan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2019) and this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Right panel: comparison  of SFRs estimated in Paspaliaris et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2021) and this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The former values are converted from Salpeter (1955) IMF to  Chabrier (2003) IMF with 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='15 dex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The symbols are the same in Figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  logM *  (Shangguan+19)  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  logM *  (This work)  Stage-A(Early)  Stage-B(Early)  Stage-C(Late)  Stage-D(Late)  Stage-N  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  logM *  (Paspaliaris+21)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='24  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  logM *  (This work)  Stage-A(Early)  Stage-B(Early)  Stage-C(Late)  Stage-D(Late)  Stage-N  Figure C2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Left panel: comparison of M∗ estimated in Shangguan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2019) and this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Right panel: comparison of  M∗ estimated in Paspaliaris et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2021) and this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The former values are converted from Salpeter (1955) IMF to Chabrier  (2003) IMF with 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='24 dex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The symbols are the same in Figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  logLAGN, int (Yamada+21)  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  logLAGN, int (This work)  Stage-A(Early)  Stage-B(Early)  Stage-C(Late)  Stage-D(Late)  Stage-N  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  logL12, nuc (Asmus+15)  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  logL12, AGN (Torus + Polar)  Stage-A(Early)  Stage-B(Early)  Stage-C(Late)  Stage-D(Late)  Stage-N  Figure C3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Left panel: comparison of LAGN,int estimated in Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2021) and this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Right panel: comparison  with the AGN (torus and polar-dust components) 12 µm luminosity from UV-to-IR SED analysis (L12µm,AGN) and the nuclear  12 µm luminosity (L12µm,nuc;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Asmus et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  61  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  logLAGN, int (SKIRTOR)  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  logLAGN, int (CLUMPY)  Stage-A(Early)  Stage-B(Early)  Stage-C(Late)  Stage-D(Late)  Stage-N  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  logLpolar (SKIRTOR)  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  logLpolar (CLUMPY)  Stage-A(Early)  Stage-B(Early)  Stage-C(Late)  Stage-D(Late)  Stage-N  Figure D1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Left panel:  comparison of intrinsic (bolometric) AGN luminosities derived with the CLUMPY model and  SKIRTOR model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Right panel: comparison of polar-dust luminosities derived with CLUMPY model and SKIRTOR model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  The symbols are the same in Figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  100  150  200  250  300  Tpolar (SKIRTOR)  100  150  200  250  300  Tpolar (CLUMPY)  Stage-A(Early)  Stage-B(Early)  Stage-C(Late)  Stage-D(Late)  Stage-N  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0  logLpolar (SKIRTOR)  100  150  200  250  Tpolar [K] (SKIRTOR)  Stage-A(Early)  Stage-B(Early)  Stage-C(Late)  Stage-D(Late)  Stage-N  Figure D2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Left panel: comparison of polar dust temperatures derived with the CLUMPY model and SKIRTOR model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Right panel: logarithmic polar-dust luminosity vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' polar-dust temperature when SKIRTOR model is adopted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The symbols  are the same in Figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  the SEDs of the torus with SKIRTOR are flatter than  with CLUMPY.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' In this case, a large part of the mid-IR  emission will be modeled by the polar dust emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  This causes a larger fraction of the AGNs to show the  signs of polar dust emission with SKIRTOR than with  CLUMPY (Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Hence, the polar temper-  ature from the SKIRTOR model is larger than those  from the CLUMPY model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' In the right panel of Fig-  ure D2, we find that the results with SKIRTOR, that  is, the trends of the large polar dust luminosities and  low temperatures in late mergers, are consistent with  the results with CLUMPY.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' We note that the estimates  of the polar dust features by fixing the torus param-  eters with SKIRTOR are not self-consistent since the  geometry of the XCLUMPY and SKIRTOR is different.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Thus, it is preferred to adopt the results with CLUMPY  particularly when we discuss the polar dust structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' MULTIWAVELENGTH SED DECOMPOSITION  For convenience on the multiwavelength studies in our  sample, we present the hard-X-ray-to-radio SEDs and  the best fitting models at the observed frame in units of  flux density in Figures E1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' We also illustrate the SEDs  and the best fitting models at the rest frame in units  of luminosity in Figures E2–E10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The photometry data  are summarized in Table E1–E3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  62  Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  10  7  10  5  10  3  10  1  101  103  105  107  F  (mJy)  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  10  4  10  2  100  102  104  106  Observed  ( m)  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID01_NGC_34  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0196, reduced ²=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1)  10  7  10  5  10  3  10  1  101  103  105  107  F  (mJy)  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  10  4  10  2  100  102  104  106  Observed  ( m)  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID02_MCG-02-01-052_and_MCG-02-01-051  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0272, reduced ²=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4)  10  7  10  5  10  3  10  1  101  103  105  107  F  (mJy)  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  10  4  10  2  100  102  104  106  Observed  ( m)  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID03_MCG-02-01-052  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0273, reduced ²=4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2)  10  7  10  5  10  3  10  1  101  103  105  107  F  (mJy)  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  10  4  10  2  100  102  104  106  Observed  ( m)  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID04_MCG-02-01-051  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0271, reduced ²=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='51)  Figure E1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The hard-X-ray-to-radio SEDs and the best fitting models in units of flux density for our sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The bottom  panels show the residuals in the UV-to-radio bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The individual curves are the same as in Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Purple and red circles  represent the observed and model flux densities, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Red crosses in the X-ray band denote the NuSTAR spectra (or,  Swift/BAT for NGC 235 and XMM-Newton/MOS for IC 5283 and MCG+01-59-081).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The red arrow and green triangles mark  the 5σ upper limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  (The complete figure set of 85 images is available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=')  63  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID01_NGC_34  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0196, reduced ²=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID02_MCG-02-01-052_and_MCG-02-01-051  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0272, reduced ²=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID03_MCG-02-01-052  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0273, reduced ²=4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID04_MCG-02-01-051  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0271, reduced ²=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='51)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID05_ESO_350-38  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0206, reduced ²=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID06_NGC_232_and_NGC_235  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0224, reduced ²=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID07_NGC_232  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0226, reduced ²=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID08_NGC_235  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0222, reduced ²=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID09_MCG+12-02-001  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0157, reduced ²=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID10_IC_1623A_and_IC_1623B  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0202, reduced ²=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7)  Figure E2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The hard-X-ray-to-radio SEDs and the best fitting models in units of luminosity for the sample of ID=1–10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The  bottom panels show the residuals in the UV-to-radio bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The individual curves are the same as in Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Purple and red  circles represent the observed and model flux densities, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Red crosses in the X-ray band denote the NuSTAR spectra  (or, Swift/BAT for NGC 235 and XMM-Newton/MOS for IC 5283 and MCG+01-59-081).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The red arrow and green triangles  mark the 5σ upper limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  64  Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID11_NGC_833_and_NGC_835  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0132, reduced ²=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  Observed upper limits  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID12_NGC_833  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0129, reduced ²=3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID13_NGC_835  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0136, reduced ²=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID14_NGC_838  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0128, reduced ²=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID15_NGC_839  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0129, reduced ²=3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID16_NGC_1068  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0038, reduced ²=3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID17_UGC_2608_and_UGC_2612  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0276, reduced ²=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='82)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID18_UGC_2608  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0233, reduced ²=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='98)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  Observed upper limits  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID19_UGC_2612  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0318, reduced ²=4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID20_NGC_1275  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0176, reduced ²=3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6)  Figure E3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The same as in Figure E2 but for the sample of ID=11–20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  65  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID21_NGC_1365  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0055, reduced ²=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID22_ESO_203-1  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0529, reduced ²=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID23_CGCG_468-002W_and_CGCG_468-002E  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0171, reduced ²=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  Observed upper limits  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID24_CGCG_468-002W  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0175, reduced ²=3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  Observed upper limits  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID25_CGCG_468-002E  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0168, reduced ²=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID26_IRAS_F05189-2524  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0426, reduced ²=3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID27_IRAS_F06076-2139_and_2MASS_06094601-2140312  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0374, reduced ²=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='69)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID28_NGC_2623  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0185, reduced ²=3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID29_ESO_060-IG016_West_and_ESO_060-IG016_East  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0451, reduced ²=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='97)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID30_IRAS_F08572+3915  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='058, reduced ²=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1e+01)  Figure E4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The same as in Figure E2 but for the sample of ID=21–30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  66  Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID31_UGC_5101  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0394, reduced ²=3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID32_MCG+08-18-012_and_MCG+08-18-013  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0255, reduced ²=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  Observed upper limits  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID33_MCG+08-18-012  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0252, reduced ²=3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='9)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID34_MCG+08-18-013  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0259, reduced ²=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID35_MCG-01-26-013_and_NGC_3110  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0165, reduced ²=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID36_MCG-01-26-013  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0161, reduced ²=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID37_NGC_3110  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0169, reduced ²=3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID38_ESO_374-IG032  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='034, reduced ²=5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID39_NGC_3256  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0094, reduced ²=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID40_IRAS_F10565+2448  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0431, reduced ²=4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8)  Figure E5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The same as in Figure E2 but for the sample of ID=31–40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  67  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID41_NGC_3690_West_and_NGC_3690_East  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0103, reduced ²=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID42_ESO_440-58_and_MCG-05-29-017  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='023, reduced ²=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID43_IRAS_F12112+0305  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0733, reduced ²=5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID44_NGC_4418_and_MCG+00-32-013  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='00735, reduced ²=3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID45_NGC_4418  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0073, reduced ²=3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  Observed upper limits  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID46_MCG+00-32-013  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0074, reduced ²=4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID47_Mrk_231  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0422, reduced ²=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='31)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID48_NGC_4922S_and_NGC_4922N  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0238, reduced ²=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='9)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID49_IC_860  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0112, reduced ²=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID50_IRAS_13120-5453  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0308, reduced ²=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='9)  Figure E6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The same as in Figure E2 but for the sample of ID=41–50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  68  Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID51_NGC_5104  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0186, reduced ²=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID52_MCG-03-34-064  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0165, reduced ²=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID53_NGC_5135  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0137, reduced ²=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='92)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID54_Mrk_266B_and_Mrk_266A  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0278, reduced ²=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID55_Mrk_273  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0378, reduced ²=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID56_IRAS_F14348-1447  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0827, reduced ²=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID57_IRAS_F14378-3651  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0681, reduced ²=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID58_IC_4518A_and_IC_4518B  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0159, reduced ²=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='74)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID59_IRAS_F15250+3608  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0552, reduced ²=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID60_Arp_220W_and_Arp_220E  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0181, reduced ²=5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3)  Figure E7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The same as in Figure E2 but for the sample of ID=51–60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  69  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID61_NGC_6240S_and_NGC_6240N  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0245, reduced ²=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID62_NGC_6285_and_NGC_6286  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0186, reduced ²=4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID63_NGC_6285  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='019, reduced ²=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID64_NGC_6286  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0183, reduced ²=5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID65_IRAS_F17138-1017  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0173, reduced ²=4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID66_IRAS_F18293-3413  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0182, reduced ²=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='83)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID67_IRAS_F19297-0406  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0857, reduced ²=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='9)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID68_NGC_6907_and_NGC_6908  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0104, reduced ²=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID69_NGC_6921_and_MCG+04-48-002  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0142, reduced ²=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID70_NGC_6921  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0145, reduced ²=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7)  Figure E8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The same as in Figure E2 but for the sample of ID=61–70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  70  Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID71_MCG+04-48-002  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0139, reduced ²=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='63)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID72_II_Zw_096_and_IRAS_F20550+1655_SE  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0352, reduced ²=3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID73_ESO_286-19  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='043, reduced ²=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID74_NGC_7130  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0162, reduced ²=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID75_NGC_7469_and_IC_5283  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0162, reduced ²=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='38)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID76_NGC_7469  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0163, reduced ²=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='53)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID77_IC_5283  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='016, reduced ²=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID78_ESO_148-2  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0446, reduced ²=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID79_NGC_7591  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0165, reduced ²=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID80_NGC_7674_and_MCG+01-59-081  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0292, reduced ²=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='77)  Figure E9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The same as in Figure E2 but for the sample of ID=71–80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  71  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID81_NGC_7674  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0289, reduced ²=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='56)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  Observed upper limits  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID82_MCG+01-59-081  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0295, reduced ²=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='63)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID83_NGC_7679_and_NGC_7682  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0171, reduced ²=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID84_NGC_7679  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0171, reduced ²=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='99)  1037  1039  1041  1043  1045  1047  L  [erg/s]  Radio nonthermal  Stellar attenuated  Nebular emission  Dust emission  AGN torus  AGN disk  AGN polar  Abs-corrected AGN  XRB + AGN scattered  X-ray thermal  Model spectrum  Model fluxes  Observed fluxes  X-ray fluxes  109  1011  1013  1015  1017  1019  Rest-frame frequency [Hz]  1  0  1  Relative  residual  (Obs-Mod)/Obs  Best model for ID85_NGC_7682  (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0171, reduced ²=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5)  Figure E10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The same as in Figure E2 but for the sample of ID=81–85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  72  Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Table E1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Photometries of our targets in mJy (λ <1 µm)  ID  Name  E(B − V )  FUV  NUV  u  v  F uv  g  r  i  z  F griz  y  152.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8 nm  231.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0 nm  481.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1 nm  615.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6 nm  750.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4 nm  866.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='9 nm  P  961.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3 nm  350.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0 nm  387.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='9 nm  SM  501.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6 nm  607.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7 nm  773.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3 nm  912.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0 nm  SM  354.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3 nm  SD  477.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0 nm  623.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1 nm  762.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5 nm  913.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4 nm  SD  (1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10)  (11)  (12)  (13)  (14)  ID01  NGC 34  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0268  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='598  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='463  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='26  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='72  SM  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='22  23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='15  32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='59  SM  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='72  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='017  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='016  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='77  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='89  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='86  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='33  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='27  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='70  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='18  ID02  MCG-02-01-052/  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0361  · ·  · ·  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='72  · ·  SD  · ·  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='16  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='26  P  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  MCG-02-01-051  · ·  · ·  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='27  · ·  · ·  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='54  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='74  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='93  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='43  ID03  MCG-02-01-052  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0361  · ·  · ·  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='84  · ·  SD  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='44  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='15  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='41  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='37  P  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='95  · ·  · ·  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09  · ·  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='55  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='78  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='85  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='85  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='92  Note— Columns: (1) target ID;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2) target name;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (3) Galactic extinction estimated by Schlegel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (1998);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (4–5) FUV and NUV flux densities from  the GALEX database (GR6plus7;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Bianchi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (6–8) u-band and v-band flux densities, and the facility of these values, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The  adopted data of Pan-STARRS DR2 (P;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Chambers et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2016), SkyMapper DR1 and DR2 (SK;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Wolf et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018), and SDSS DR16 (SD;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Ahumada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020) are listed in Column (8);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (9–13) g-band, r-band, i-band, z-band flux densities and the facility of these values, respectively;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  (14) y-band flux density from Pan-STARRS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The Pan-STARRS photometries of g–y bands are converted from the original Kron magnitudes by  multiplying 100/90 (for 10% missing fluxes or 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='115 mag).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The SkyMapper photometries of u–z bands are converted from the original Petrosian  magnitudes by multiplying 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='127 (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='13 mag in case of typical Sersic index of 3;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Graham et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2005;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Haan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The flux densities are  in units of mJy, and corrected for the Galactic extinction of Column (3), by applying the band passes as noted in the text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Their 1σ uncertainties  are provided in the row just below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The uncertainties of u–y bands are corrected by adding 10% of their flux densities to consider the dispersions  among different kinds of measurements in their facilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  (This table is available in its entirety in machine-readable form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=')  73  Table E2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Photometries of our targets in mJy (λ =1–200 µm)  ID  Name  J  H  Ks  W1  W2  S9W  W3  L18W  W4  PACS blue  PACS green  PACS red  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='235 µm  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='662 µm  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='159 µm  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='353 µm  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='603 µm  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='228 µm  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='56 µm  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='61 µm  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09 µm  70 µm  100 µm  160 µm  (1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10)  (11)  (12)  (13)  (14)  ID01  NGC 34  · ·  · ·  · ·  35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='67  30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='43  269  245.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='26  · ·  1240.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='58  18210  17680  10650  · ·  · ·  · ·  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='17  26  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='36  · ·  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='86  840  810  480  ID02  MCG-02-01-052/  30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='59  33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='25  31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='82  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='32  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='43  178  · ·  517  · ·  8038  9876  7496  MCG-02-01-051  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='78  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='20  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='34  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09  11  · ·  33  · ·  403  495  375  ID03  MCG-02-01-052  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='53  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='78  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='44  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='82  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='27  · ·  · ·  · ·  · ·  1206  2081  1960  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='65  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='96  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05  · ·  · ·  · ·  · ·  62  105  99  Note—Columns: (1) target ID;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2) target name;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (3–5) J-band, H-band, and Ks-band flux densities from the 2MASS extended catalog, except for  IRAS F17138–1017 from point-source catalog (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Skrutskie et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2006);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (6–7), (9), and (11) W1, W2, W3, and W4 flux densities from ALLWISE  catalog (updated version on February 16, 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Cutri et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021) respectively;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (8) and (10) S9W and L18W flux densities from AKARI/IRC  mid-IR all-sky survey (Ishihara et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2010);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (12–14) flux densities in PACS blue, green, and red bands from Herschel/PACS data (Chu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2017);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The flux densities are in units of mJy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The Galactic extinction in J, H, Ks, W1, and W2 bands are corrected by applying the band passes  as noted in the text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Their 1σ uncertainties are provided in the row just below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  (This table is available in its entirety in machine-readable form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=')  74  Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Table E3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Photometries of our targets in mJy (λ >200 µm)  ID  Name  PSW  PMW  PLW  NVSS  SUMSS  WENSS  GLEAM1  GLEAM2  TGSS  GLEAM3  VLSSr  VLASS  FIRST  250 µm  350 µm  500 µm  214.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1 mm  355.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6 mm  922.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1 mm  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='50 m  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='99 m  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='03 m  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='94 m  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06 m  99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='9 mm  214.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1 mm  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4 GHz  843 MHz  325.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='125 MHz  200.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5 MHz  150.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5 MHz  147.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5 MHz  76 MHz  73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8 MHz  3 GHz  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4 GHz  (1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10)  (11)  (12)  (13)  (14)  (15)  ID01  NGC 34  3573  1239  339  66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='9  · ·  · ·  162.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1  212.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3  125.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  · ·  · ·  [41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3]  · ·  214  75  21  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  · ·  · ·  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6  26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3  · ·  · ·  [1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5]  · ·  ID02  MCG-02-01-052/  2862  1209  419  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7  · ·  · ·  · ·  · ·  123.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2  · ·  · ·  [12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7]  [33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6]  MCG-02-01-051  189  81  33  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8  · ·  · ·  · ·  · ·  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='6  · ·  · ·  [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4]  [3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4]  ID03  MCG-02-01-052  · ·  · ·  · ·  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3  · ·  · ·  · ·  · ·  · ·  · ·  · ·  [<0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='44]  [<1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0]  · ·  · ·  · ·  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  · ·  · ·  · ·  · ·  · ·  · ·  · ·  · ·  · ·  Note— Columns: (1) target ID;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (2) target name;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (3–5) flux densities in PSW, PMW, and PLW bands from Herschel/SPIRE data (Chu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  (6) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4 GHz flux densities from NVSS catalog (Condon et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 1998);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (7) 843 MHz flux densities from SUMSS catalog (Mauch et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2003);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (8)  325.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='125 MHz flux densities from WENSS catalog (Rengelink et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 1997);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (9–10) and (12) 200.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5 MHz (170–231 MHz), 150.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5 MHz (147–154 MHz),  and 76 MHz (72–80 MHz) flux densities from GLEAM catalog (Hurley-Walker et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The values of <5σ of GLEAM catalog are removed;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  (11) 147.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5 MHz flux densities from TGSS catalog (Intema et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (13) 73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='8 MHz flux densities from VLSSr (Lane et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2014);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (14) 3 GHz  flux densities with the high angular resolution (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='′′5) from VLASS catalog (Gordon et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' (15) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4 GHz flux densities with the high angular  resolution (5′′) from FIRST catalog (Becker et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 1995;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Helfand et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Since the uncertainties of FIRST flux densities were not provided, we  assume them as 10% uncertainties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The values in the square brackets for the VLASS and FIRST data represent the flux densities and uncertainties  that are not utilized in the radio fits (see Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='7 in details);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' The flux densities are in units of mJy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Their 1σ uncertainties are provided in the  row just below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  (This table is available in its entirety in machine-readable form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=')  75  REFERENCES  Ahumada, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Prieto, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Almeida, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020,  ApJS, 249, 3, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4365/ab929e  Aird, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Coil, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Georgakakis, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2015, MNRAS,  451, 1892, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1093/mnras/stv1062  AKARI Team.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020, AKARI/IRC Point Source Catalogue,  IPAC, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='26131/IRSA181  Albareti, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Allende Prieto, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Almeida, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017,  ApJS, 233, 25, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4365/aa8992  Alexander, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Hickox, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2012, NewAR, 56, 93,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='newar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='003  Allison, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Sadler, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Meekin, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2014,  MNRAS, 440, 696, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1093/mnras/stu289  Alonso-Herrero, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Pereira-Santaella, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Rieke, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', &  Rigopoulou, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2012, ApJ, 744, 2,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0004-637X/744/1/2  Alonso-Herrero, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Garc´ıa-Burillo, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', H¨onig, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2021, A&A, 652, A99, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361/202141219  Ananna, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Urry, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Ricci, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2022, ApJL,  939, L13, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/2041-8213/ac9979  Andonie, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Ricci, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Paltani, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2022, MNRAS,  511, 5768, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1093/mnras/stac403  Angl´es-Alc´azar, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Faucher-Gigu`ere, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='-A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Quataert, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=',  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017, MNRAS, 472, L109,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1093/mnrasl/slx161  Armus, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Mazzarella, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Evans, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2009,  PASP, 121, 559, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1086/600092  Arnaud, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 1996, Astronomical Society of the Pacific  Conference Series, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 101, XSPEC: The First Ten  Years, ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Jacoby & J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Barnes, 17  Asano, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Takeuchi, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Hirashita, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Nozawa, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2013, MNRAS, 432, 637, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1093/mnras/stt506  Asmus, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019, MNRAS, 489, 2177,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1093/mnras/stz2289  Asmus, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Gandhi, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', H¨onig, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Smette, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Duschl,  W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2015, MNRAS, 454, 766,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1093/mnras/stv1950  Asmus, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', H¨onig, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Gandhi, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2016, ApJ, 822, 109,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/0004-637X/822/2/109  Asmus, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', H¨onig, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Gandhi, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Smette, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Duschl,  W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2014, MNRAS, 439, 1648,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1093/mnras/stu041  Assef, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Stern, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Noirot, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018, ApJS, 234,  23, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4365/aaa00a  Assef, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Kochanek, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Brodwin, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2010,  ApJ, 713, 970, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0004-637X/713/2/970  Assef, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Stern, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Kochanek, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2013, ApJ,  772, 26, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0004-637X/772/1/26  Assef, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Walton, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Brightman, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2016,  ApJ, 819, 111, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/0004-637X/819/2/111  Assef, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Brightman, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Walton, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020,  ApJ, 897, 112, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/ab9814  Baba, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Nakagawa, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Isobe, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Shirahata, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018,  ApJ, 852, 83, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/aa9f25  Barrera-Ballesteros, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', S´anchez, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Garc´ıa-Lorenzo,  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2015, A&A, 579, A45,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361/201425397  Barvainis, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 1987, ApJ, 320, 537, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1086/165571  Bauer, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Ar´evalo, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Walton, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2015, ApJ,  812, 116, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0004-637X/812/2/116  Becker, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', White, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Helfand, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 1995, ApJ,  450, 559, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1086/176166  Begelman, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Blandford, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Rees, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 1984,  Reviews of Modern Physics, 56, 255,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1103/RevModPhys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='255  Behar, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2009, ApJ, 703, 1346,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0004-637X/703/2/1346  Bell, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2003, ApJ, 586, 794, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1086/367829  Bianchi, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020, GALEX UV Unique Source Catalogs  (”GUVcat”) and Cross-Matches With Gaia and SDSS  (”GUVmatch”), STScI/MAST,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='17909/T9-PYXY-KG53  Bianchi, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Herald, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Efremova, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2011, Ap&SS,  335, 161, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1007/s10509-010-0581-x  Bianchi, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Shiao, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Thilker, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017, ApJS, 230, 24,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4365/aa7053  Bischetti, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Piconcelli, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Vietri, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017, A&A,  598, A122, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361/201629301  Blecha, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Snyder, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Satyapal, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Ellison, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2018, MNRAS, 478, 3056, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1093/mnras/sty1274  Boch, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Fernique, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2014, in Astronomical Society of  the Pacific Conference Series, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 485, Astronomical  Data Analysis Software and Systems XXIII, ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Manset & P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Forshay, 277  Boettcher, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Gallagher, John S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Ohyama, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2020, A&A, 637, A17, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361/201834880  Bongiorno, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Merloni, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Brusa, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2012, MNRAS,  427, 3103, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1111/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1365-2966.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='22089.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='x  Bonnarel, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Fernique, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Bienaym´e, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2000,  A&AS, 143, 33, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/aas:2000331  Bonzini, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Mainieri, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Padovani, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2015,  MNRAS, 453, 1079, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1093/mnras/stv1675  Boquien, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Burgarella, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Roehlly, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019, A&A,  622, A103, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361/201834156  Brinchmann, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Charlot, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', White, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2004,  MNRAS, 351, 1151,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1111/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1365-2966.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07881.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='x  Bruzual, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Charlot, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2003, MNRAS, 344, 1000,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1046/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1365-8711.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06897.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='x  76  Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Buat, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Boquien, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Ma�lek, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018, A&A, 619,  A135, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361/201833841  Buat, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Ciesla, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Boquien, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Ma�lek, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Burgarella,  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019, A&A, 632, A79,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361/201936643  Buat, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Noll, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Burgarella, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2012, A&A, 545,  A141, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361/201219405  Buat, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Heinis, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Boquien, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2014, A&A, 561,  A39, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361/201322081  Buat, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Mountrichas, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Yang, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021, A&A,  654, A93, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361/202141797  Buchner, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Brightman, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Nandra, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Nikutta, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', &  Bauer, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019, A&A, 629, A16,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361/201834771  Burgarella, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Buat, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Small, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2005, ApJL, 619,  L63, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1086/423894  Burrows, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Hill, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Nousek, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2005,  SSRv, 120, 165, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1007/s11214-005-5097-2  Burtscher, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Davies, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Graci´a-Carpio, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2016,  A&A, 586, A28, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361/201527575  Calzetti, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2001, PASP, 113, 1449, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1086/324269  Calzetti, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Armus, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Bohlin, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2000, ApJ,  533, 682, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1086/308692  Cameron, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2011, PASA, 28, 128, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1071/AS10046  Caramete, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Biermann, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2010, A&A, 521, A55,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361/200913146  Cardelli, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Clayton, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Mathis, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 1989, ApJ,  345, 245, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1086/167900  Casey, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2012, MNRAS, 425, 3094,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1111/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1365-2966.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='21455.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='x  Chabrier, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2003, PASP, 115, 763, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1086/376392  Chambers, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Magnier, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Metcalfe, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2016,  arXiv e-prints, arXiv:1612.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05560.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  https://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='org/abs/1612.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05560  Chan, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Krolik, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2016, ApJ, 825, 67,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/0004-637X/825/1/67  —.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017, ApJ, 843, 58, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/aa76e4  Chen, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='-T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Hickox, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Goulding, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017,  ApJ, 837, 145, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/837/2/145  Chen, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Akiyama, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Ichikawa, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020, ApJ, 900,  51, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/aba599  Chiaraluce, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Vagnetti, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Tombesi, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Paolillo, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2018, A&A, 619, A95, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361/201833631  Chu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Sanders, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Larson, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017,  ApJS, 229, 25, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4365/aa5d15  Cicone, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Maiolino, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Sturm, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2014, A&A, 562,  A21, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361/201322464  Ciesla, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Elbaz, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Schreiber, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Daddi, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Wang, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2018, A&A, 615, A61, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361/201832715  Ciesla, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Charmandaris, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Georgakakis, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2015,  A&A, 576, A10, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361/201425252  Clemens, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Vega, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Bressan, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2008, A&A,  477, 95, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361:20077224  Clements, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Pearson, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Farrah, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018,  MNRAS, 475, 2097, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1093/mnras/stx3227  Cohen, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Lane, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Cotton, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2007, AJ,  134, 1245, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1086/520719  Cohen, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Wheaton, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Megeath, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2003, AJ,  126, 1090, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1086/376474  Condon, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 1992, ARA&A, 30, 575,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1146/annurev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='aa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='090192.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='003043  Condon, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Cotton, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Greisen, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 1998,  AJ, 115, 1693, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1086/300337  Condon, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Huang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Yin, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Thuan, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  1991, ApJ, 378, 65, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1086/170407  Cortijo-Ferrero, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Gonz´alez Delgado, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', P´erez, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=',  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017, A&A, 606, A95,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361/201730669  Cutri, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2012, VizieR Online Data Catalog,  II/311  Cutri, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Wright, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Conrow, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021, VizieR  Online Data Catalog, II/328  da Cunha, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Hodge, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Casey, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021, ApJ,  919, 30, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/ac0ae0  Dale, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Aniano, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Engelbracht, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2012,  ApJ, 745, 95, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0004-637X/745/1/95  Del Moro, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Alexander, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Bauer, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2016,  MNRAS, 456, 2105, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1093/mnras/stv2748  Delvecchio, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Smolˇci´c, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Zamorani, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017, A&A,  602, A3, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361/201629367  Di Matteo, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Springel, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Hernquist, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2005, Nature,  433, 604, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1038/nature03335  D´ıaz-Santos, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Charmandaris, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Armus, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2010,  ApJ, 723, 993, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0004-637X/723/2/993  D´ıaz-Santos, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Armus, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Charmandaris, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2013,  ApJ, 774, 68, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0004-637X/774/1/68  —.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2014, ApJL, 788, L17,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/2041-8205/788/1/L17  —.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017, ApJ, 846, 32, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/aa81d7  Dong, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Greene, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Ho, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2012, ApJ, 761, 73,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0004-637X/761/1/73  Dorodnitsyn, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Kallman, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017, ApJ, 842, 43,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/aa7264  Dorodnitsyn, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Kallman, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Bisnovatyi-Kogan, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2012, ApJ, 747, 8, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0004-637X/747/1/8  Draine, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2003, ARA&A, 41, 241,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1146/annurev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='astro.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='011802.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='094840  Draine, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Lee, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 1984, ApJ, 285, 89,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1086/162480  77  Draine, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Li, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2007, ApJ, 657, 810,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1086/511055  Draine, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Salpeter, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 1979, ApJ, 231, 438,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1086/157206  Draine, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Aniano, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Krause, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2014, ApJ,  780, 172, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0004-637X/780/2/172  Efstathiou, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Farrah, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Afonso, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2022, MNRAS,  512, 5183, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1093/mnras/stab3642  Elbaz, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Daddi, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Le Borgne, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2007, A&A, 468,  33, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361:20077525  Ellison, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Mendel, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Patton, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Scudder,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2013, MNRAS, 435, 3627,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1093/mnras/stt1562  Ellison, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Secrest, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Mendel, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Satyapal, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', &  Simard, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017, MNRAS, 470, L49,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1093/mnrasl/slx076  Enoki, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Inoue, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Nagashima, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Sugiyama, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2004, ApJ, 615, 19, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1086/424475  Fabian, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Vasudevan, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Gandhi, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2008,  MNRAS, 385, L43, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1111/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1745-3933.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='00430.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='x  Fabian, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Vasudevan, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Mushotzky, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=',  Winter, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Reynolds, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2009, MNRAS, 394,  L89, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1111/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1745-3933.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='00617.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='x  Farrah, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Efstathiou, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Afonso, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2022, MNRAS,  513, 4770, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1093/mnras/stac980  Faucher-Gigu`ere, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='-A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Quataert, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2012, MNRAS,  425, 605, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1111/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1365-2966.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='21512.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='x  Feruglio, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Fiore, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Carniani, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2015, A&A, 583,  A99, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361/201526020  Finnerty, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Larson, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Soifer, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020, ApJ,  905, 16, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/abc3bf  Fischer, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Crenshaw, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Kraemer, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', &  Schmitt, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2013, ApJS, 209, 1,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0067-0049/209/1/1  Flewelling, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Magnier, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Chambers, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2020, ApJS, 251, 7, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4365/abb82d  Fluetsch, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Maiolino, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Carniani, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019,  MNRAS, 483, 4586, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1093/mnras/sty3449  —.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021, MNRAS, 505, 5753, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1093/mnras/stab1666  Fritz, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Franceschini, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Hatziminaoglou, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2006,  MNRAS, 366, 767, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1111/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1365-2966.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='09866.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='x  Fujimoto, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Brammer, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Watson, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2022,  Nature, 604, 261, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1038/s41586-022-04454-1  Furui, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Fukazawa, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Odaka, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2016, ApJ, 818,  164, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/0004-637X/818/2/164  Gabriel, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Denby, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Fyfe, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2004,  Astronomical Society of the Pacific Conference Series,  Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 314, The XMM-Newton SAS - Distributed  Development and Maintenance of a Large Science  Analysis System: A Critical Analysis, ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Ochsenbein,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Allen, & D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Egret, 759  Gallagher, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Everett, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Abado, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Keating,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2015, MNRAS, 451, 2991,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1093/mnras/stv1126  G´amez Rosas, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Isbell, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Jaffe, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2022,  Nature, 602, 403, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1038/s41586-021-04311-7  Gandhi, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Horst, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Smette, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2009, A&A, 502,  457, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361/200811368  Garc´ıa-Bernete, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Ramos Almeida, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Landt, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2017, MNRAS, 469, 110, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1093/mnras/stx795  Garc´ıa-Bernete, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Ramos Almeida, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Acosta-Pulido,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2016, MNRAS, 463, 3531,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1093/mnras/stw2125  Garc´ıa-Bernete, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Ramos Almeida, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Alonso-Herrero, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=',  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019, MNRAS, 486, 4917,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1093/mnras/stz1003  Garc´ıa-Bernete, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Gonz´alez-Mart´ın, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Ramos Almeida,  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2022, A&A, 667, A140,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361/202244230  Garmire, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Bautz, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Ford, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Nousek, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=',  & Ricker, Jr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2003, in Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' SPIE, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 4851,  X-Ray and Gamma-Ray Telescopes and Instruments for  Astronomy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Truemper & H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Tananbaum,  28–44, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1117/12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='461599  Gaskell, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Goosmann, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Antonucci, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', &  Whysong, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2004, ApJ, 616, 147, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1086/423885  Gehrels, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Chincarini, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Giommi, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2004, ApJ,  611, 1005, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1086/422091  Gonz´alez-Alfonso, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Fischer, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Spoon, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2017, ApJ, 836, 11, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/836/1/11  Gordon, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Boyce, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', O’Dea, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021,  ApJS, 255, 30, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4365/ac05c0  Goulding, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Greene, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Bezanson, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018a,  PASJ, 70, S37, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1093/pasj/psx135  Goulding, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Zakamska, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Alexandroff, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=',  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018b, ApJ, 856, 4, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/aab040  Graham, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Driver, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Petrosian, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2005,  AJ, 130, 1535, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1086/444475  Granato, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Danese, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Franceschini, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 1997, ApJ,  486, 147, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1086/304502  Greene, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Strader, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Ho, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020, ARA&A, 58,  257, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1146/annurev-astro-032620-021835  Griffin, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Abergel, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Abreu, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2010, A&A,  518, L3, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361/201014519  78  Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Gruppioni, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Berta, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Spinoglio, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2016,  MNRAS, 458, 4297, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1093/mnras/stw577  G¨ultekin, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Richstone, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Gebhardt, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2009,  ApJ, 698, 198, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0004-637X/698/1/198  Haan, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Surace, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Armus, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2011, AJ, 141,  100, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0004-6256/141/3/100  Hainline, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Blain, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Smail, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2011, ApJ,  740, 96, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0004-637X/740/2/96  Hamann, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Zakamska, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Ross, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017,  MNRAS, 464, 3431, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1093/mnras/stw2387  Harrison, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Craig, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Christensen, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2013, ApJ, 770, 103, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0004-637X/770/2/103  Helfand, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', White, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Becker, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2015, ApJ,  801, 26, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0004-637X/801/1/26  Helou, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Soifer, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Rowan-Robinson, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 1985,  ApJL, 298, L7, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1086/184556  Hickox, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Alexander, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018, ARA&A, 56, 625,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1146/annurev-astro-081817-051803  Hickox, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Wardlow, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Smail, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2012,  MNRAS, 421, 284, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1111/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1365-2966.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='20303.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='x  Hitomi Collaboration, Aharonian, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Akamatsu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2018, PASJ, 70, 13, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1093/pasj/psx147  H¨onig, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019, ApJ, 884, 171,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/ab4591  H¨onig, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Beckert, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Ohnaka, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Weigelt, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2006,  A&A, 452, 459, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361:20054622  H¨onig, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Kishimoto, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2010, A&A, 523, A27,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361/200912676  —.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2011, A&A, 534, A121,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361/201117750  —.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017, ApJL, 838, L20, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/2041-8213/aa6838  H¨onig, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Kishimoto, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Antonucci, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2012,  ApJ, 755, 149, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0004-637X/755/2/149  H¨onig, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Kishimoto, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Tristram, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2013, ApJ, 771, 87, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0004-637X/771/2/87  Hopkins, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Hernquist, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Cox, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Kereˇs, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2008,  ApJS, 175, 356, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1086/524362  Hopkins, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Somerville, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Hernquist, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2006,  ApJ, 652, 864, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1086/508503  Hopkins, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Strauss, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Hall, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2004, AJ,  128, 1112, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1086/423291  Hurley-Walker, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Callingham, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Hancock, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2017, MNRAS, 464, 1146, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1093/mnras/stw2337  Hurley-Walker, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Hancock, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Franzen, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2019, PASA, 36, e047, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1017/pasa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='37  Ichikawa, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Ricci, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Ueda, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017, ApJ, 835, 74,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/835/1/74  Ichikawa, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Ueda, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Terashima, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2012, ApJ,  754, 45, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0004-637X/754/1/45  Ichikawa, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Packham, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Ramos Almeida, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2015,  ApJ, 803, 57, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0004-637X/803/2/57  Ichikawa, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Ricci, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Ueda, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019, ApJ, 870, 31,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/aaef8f  Ikeda, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Awaki, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Terashima, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2009, ApJ, 692, 608,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0004-637X/692/1/608  Imanishi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Dudley, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Maiolino, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2007,  ApJS, 171, 72, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1086/513715  Imanishi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Dudley, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Maloney, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2006, ApJ,  637, 114, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1086/498391  Imanishi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Kawamuro, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Kikuta, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Nakano, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', &  Saito, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020, ApJ, 891, 140,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/ab733e  Imanishi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Nakagawa, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Ohyama, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2008,  PASJ, 60, S489, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1093/pasj/60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='sp2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='S489  Imanishi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Nakagawa, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Shirahata, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Ohyama, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', &  Onaka, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2010, ApJ, 721, 1233,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0004-637X/721/2/1233  Imanishi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Saito, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2014, ApJ, 780, 106,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0004-637X/780/1/106  Inaba, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Ueda, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Yamada, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2022, ApJ, 939, 88,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/ac97ec  Inami, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Armus, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Charmandaris, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2013, ApJ,  777, 156, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0004-637X/777/2/156  Inami, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Armus, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Matsuhara, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018, A&A,  617, A130, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361/201833053  Inayoshi, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Ichikawa, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Haiman, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018, ApJL, 863,  L36, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/2041-8213/aad8ad  Inoue, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2011, MNRAS, 415, 2920,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1111/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1365-2966.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='18906.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='x  Intema, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Jagannathan, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Mooley, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Frail,  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017, A&A, 598, A78,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361/201628536  Isbell, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Meisenheimer, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Pott, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2022,  A&A, 663, A35, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361/202243271  Ishibashi, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Fabian, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Ricci, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Celotti, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018,  MNRAS, 479, 3335, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1093/mnras/sty1620  Ishihara, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Onaka, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Kataza, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2010, A&A, 514,  A1, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361/200913811  Iwasawa, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Sanders, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Teng, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2011, A&A,  529, A106, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361/201015264  Iwasawa, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Ricci, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Privon, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020, A&A,  640, A95, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361/202038513  Izumi, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Kawakatu, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Kohno, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2016, ApJ, 827, 81,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/0004-637X/827/1/81  Izumi, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Wada, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Fukushige, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Hamamura, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', &  Kohno, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018, ApJ, 867, 48,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/aae20b  79  Jadhav, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Robinson, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Almeyda, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Curran, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', &  Marconi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021, MNRAS, 507, 484,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1093/mnras/stab2176  Jahnke, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Macci`o, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2011, ApJ, 734, 92,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0004-637X/734/2/92  Jansen, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Lumb, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Altieri, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2001, A&A, 365,  L1, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361:20000036  Jarrett, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Cohen, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Masci, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2011, ApJ, 735,  112, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0004-637X/735/2/112  Jones, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Tielens, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Hollenbach, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', &  McKee, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 1994, ApJ, 433, 797, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1086/174689  Just, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Brandt, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Shemmer, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2007, ApJ,  665, 1004, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1086/519990  Kakkad, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Groves, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Dopita, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018, A&A, 618,  A6, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361/201832790  Kamizuka, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Miyata, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Sako, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020, in Society  of Photo-Optical Instrumentation Engineers (SPIE)  Conference Series, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 11447, Society of Photo-Optical  Instrumentation Engineers (SPIE) Conference Series,  114475X, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1117/12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2560789  Kawaguchi, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Yutani, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Wada, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020, ApJ, 890,  125, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/ab655a  Kawamuro, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Ricci, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Izumi, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021, ApJS, 257,  64, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4365/ac2891  Kawamuro, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Ricci, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Imanishi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2022, ApJ,  938, 87, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/ac8794  Kelly, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2007, ApJ, 665, 1489, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1086/519947  Kennicutt, Robert C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 1998, ARA&A, 36, 189,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1146/annurev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='astro.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='189  Kim, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Veilleux, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Sanders, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2002, ApJS, 143,  277, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1086/343843  Kl¨ockner, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Baan, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2004, A&A, 419, 887,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361:20040998  Kocevski, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Brightman, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Nandra, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2015,  ApJ, 814, 104, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0004-637X/814/2/104  Kormendy, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Ho, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2013, ARA&A, 51, 511,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1146/annurev-astro-082708-101811  Koss, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Mushotzky, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Treister, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2012, ApJL,  746, L22, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/2041-8205/746/2/L22  Koss, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Mushotzky, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Veilleux, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Winter, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2010,  ApJL, 716, L125, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/2041-8205/716/2/L125  Koss, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Blecha, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Bernhard, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018, Nature,  563, 214, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1038/s41586-018-0652-7  Krolik, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 1999, ApJL, 515, L73, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1086/311979  —.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2007, ApJ, 661, 52, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1086/515432  Krolik, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Begelman, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 1988, ApJ, 329, 702,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1086/166414  Kron, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 1980, ApJS, 43, 305, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1086/190669  Kroupa, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2001, MNRAS, 322, 231,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1046/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1365-8711.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='04022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='x  Laha, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Guainazzi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Piconcelli, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018, ApJ,  868, 10, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/aae390  Laha, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Markowitz, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Krumpe, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020, ApJ,  897, 66, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/ab92ab  Lane, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Cotton, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', van Velzen, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2014,  MNRAS, 440, 327, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1093/mnras/stu256  Lansbury, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Alexander, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Aird, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017,  ApJ, 846, 20, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/aa8176  Laor, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Baldi, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Behar, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019, MNRAS, 482,  5513, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1093/mnras/sty3098  Laurent, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Mirabel, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Charmandaris, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2000,  A&A, 359, 887.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' https://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='org/abs/astro-ph/0005376  Lee, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Hwang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Lee, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Kim, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Lee, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2012, ApJ, 756, 95, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0004-637X/756/1/95  Leroy, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Evans, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Momjian, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2011, ApJL,  739, L25, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/2041-8205/739/1/L25  Liang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Hammer, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Flores, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2004, A&A,  423, 867, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361:20035740  Linden, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Song, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Evans, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019, ApJ, 881,  70, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/ab2872  Liu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', H¨onig, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Ricci, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Paltani, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019,  MNRAS, 490, 4344, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1093/mnras/stz2908  Liu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Wang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='-X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Yang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Zhu, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='-F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Zhou, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2014, ApJ, 783, 106, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0004-637X/783/2/106  Liu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Li, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2014, ApJ, 787, 52,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0004-637X/787/1/52  Lo Faro, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Buat, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Roehlly, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017, MNRAS,  472, 1372, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1093/mnras/stx1901  Lodato, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Bertin, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2003, A&A, 398, 517,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361:20021672  Longobardi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Arnaboldi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Gerhard, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Mihos, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2015, A&A, 579, L3, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361/201526282  Lonsdale, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Lonsdale, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Smith, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Diamond,  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2003, ApJ, 592, 804, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1086/375778  Lonsdale, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Cappallo, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Morales, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2009,  IEEE Proceedings, 97, 1497,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1109/JPROC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2017564  L´opez-Gonzaga, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Burtscher, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Tristram, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=',  Meisenheimer, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Schartmann, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2016, A&A, 591,  A47, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361/201527590  L´opez-Gonzaga, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Jaffe, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2016, A&A, 591, A128,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361/201527149  L´opez-Gonzaga, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Jaffe, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Burtscher, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Tristram,  K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Meisenheimer, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2014, A&A, 565, A71,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361/201323002  Lopez-Rodriguez, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Packham, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Jones, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017,  MNRAS, 464, 1762, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1093/mnras/stw2491  Lopez-Rodriguez, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Fuller, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Alonso-Herrero, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2018, ApJ, 859, 99, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/aabd7b  80  Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Lu, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Zhao, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', D´ıaz-Santos, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017, ApJS, 230, 1,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4365/aa6476  Lusso, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Comastri, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Vignali, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2010, A&A, 512,  A34, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361/200913298  Lutz, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Maiolino, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Spoon, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Moorwood,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2004, A&A, 418, 465,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361:20035838  Lyu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Rieke, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018, ApJ, 866, 92,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/aae075  —.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021, ApJ, 912, 126, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/abee14  Lyu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Rieke, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Shi, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017, ApJ, 835, 257,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/835/2/257  Madau, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Dickinson, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2014, ARA&A, 52, 415,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1146/annurev-astro-081811-125615  Magdis, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Daddi, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', B´ethermin, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2012, ApJ,  760, 6, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0004-637X/760/1/6  Magnier, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Chambers, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Flewelling, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2020a, ApJS, 251, 3, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4365/abb829  Magnier, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Sweeney, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Chambers, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2020b, ApJS, 251, 5, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4365/abb82c  Magnier, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Schlafly, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Finkbeiner, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2020c, ApJS, 251, 6, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4365/abb82a  Maiolino, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Marconi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Oliva, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2001, A&A, 365, 37,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361:20000012  Mannucci, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Cresci, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Maiolino, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Marconi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', &  Gnerucci, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2010, MNRAS, 408, 2115,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1111/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1365-2966.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='17291.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='x  Marconi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Hunt, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2003, ApJL, 589, L21,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1086/375804  Martin, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Fanson, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Schiminovich, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2005,  ApJL, 619, L1, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1086/426387  Martocchia, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Piconcelli, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Zappacosta, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017,  A&A, 608, A51, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361/201731314  Mateos, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Alonso-Herrero, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Carrera, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2013,  MNRAS, 434, 941, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1093/mnras/stt953  —.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2012, MNRAS, 426, 3271,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1111/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1365-2966.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='21843.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='x  Mateos, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Carrera, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Alonso-Herrero, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2015,  MNRAS, 449, 1422, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1093/mnras/stv299  Matsumoto, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Nakagawa, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Wada, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2022, ApJ,  934, 25, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/ac755f  Mattila, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', P´erez-Torres, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Efstathiou, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018,  Science, 361, 482, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1126/science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='aao4669  Mauch, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Murphy, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Buttery, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2003,  MNRAS, 342, 1117,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1046/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1365-8711.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='06605.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='x  —.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2008, VizieR Online Data Catalog, VIII/81A  Mazzarella, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Iwasawa, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Vavilkin, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2012,  AJ, 144, 125, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0004-6256/144/5/125  Meier, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Turner, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Beck, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2010, AJ, 140,  1294, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0004-6256/140/5/1294  Meng, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='-M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Wu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Gu, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Wang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Cao, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2010,  ApJ, 718, 928, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0004-637X/718/2/928  Mills, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 1981, PASA, 4, 156,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1017/S1323358000016222  Mineo, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Gilfanov, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Sunyaev, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2012, MNRAS, 419,  2095, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1111/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1365-2966.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='19862.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='x  Mitsuda, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Bautz, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Inoue, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2007, PASJ, 59,  S1, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1093/pasj/59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='sp1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='S1  Miyaji, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Herrera-Endoqui, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Krumpe, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019,  ApJL, 884, L10, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/2041-8213/ab46bc  Mizukoshi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Minezaki, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Tsunetsugu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2022,  MNRAS, 516, 2876, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1093/mnras/stac2307  Mizumoto, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Izumi, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Kohno, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019, ApJ, 871,  156, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/aaf814  Mor, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Netzer, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2012, MNRAS, 420, 526,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1111/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1365-2966.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='20060.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='x  Mor, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Netzer, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Elitzur, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2009, ApJ, 705, 298,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0004-637X/705/1/298  Morganti, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Veilleux, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Oosterloo, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Teng, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', &  Rupke, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2016, A&A, 593, A30,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361/201628978  Mori´c, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Smolˇci´c, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Kimball, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2010, ApJ, 724,  779, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0004-637X/724/1/779  Morrissey, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Conrow, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Barlow, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2007,  ApJS, 173, 682, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1086/520512  Murakami, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Baba, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Barthel, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2007, PASJ, 59,  S369, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1093/pasj/59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='sp2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='S369  Murphy, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2013, ApJ, 777, 58,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0004-637X/777/1/58  Murphy, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Stierwalt, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Armus, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Condon, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', &  Evans, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2013, ApJ, 768, 2,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0004-637X/768/1/2  Narayanan, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Dey, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Hayward, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2010,  MNRAS, 407, 1701,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1111/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1365-2966.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='16997.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='x  Nenkova, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Sirocky, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Ivezi´c, ˇZ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Elitzur, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2008a, ApJ, 685, 147, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1086/590482  Nenkova, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Sirocky, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Nikutta, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Ivezi´c, ˇZ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', &  Elitzur, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2008b, ApJ, 685, 160, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1086/590483  Nersesian, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Xilouris, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Bianchi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019,  A&A, 624, A80, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361/201935118  Netzer, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 1987, MNRAS, 225, 55,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1093/mnras/225.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='55  Netzer, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Lutz, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Schweitzer, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2007, ApJ, 666,  806, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1086/520716  Niklas, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Klein, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Wielebinski, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 1997, A&A, 322, 19  Noeske, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Weiner, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Faber, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2007,  ApJL, 660, L43, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1086/517926  81  Noll, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Burgarella, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Giovannoli, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2009, A&A,  507, 1793, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361/200912497  Ogawa, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Ueda, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Tanimoto, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Yamada, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021,  ApJ, 906, 84, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/abccce  Ogawa, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Ueda, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Yamada, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Tanimoto, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', &  Kawaguchi, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019, ApJ, 875, 115,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/ab0e08  Oh, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Koss, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Markwardt, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018, ApJS,  235, 4, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4365/aaa7fd  Ohyama, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Sakamoto, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Aalto, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Gallagher, John S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=',  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019, ApJ, 871, 191, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/aaf9a5  Onken, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Wolf, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Bessell, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019, PASA,  36, e033, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1017/pasa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='27  Panessa, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Baldi, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Laor, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019, Nature  Astronomy, 3, 387, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1038/s41550-019-0765-4  Paspaliaris, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Xilouris, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Nersesian, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2021, A&A, 649, A137,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361/202038605  Pearson, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Wang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Hurley, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018, A&A,  615, A146, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361/201832821  Petric, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Armus, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Howell, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2011, ApJ, 730,  28, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0004-637X/730/1/28  Pfeifle, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Satyapal, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Secrest, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019, ApJ,  875, 117, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/ab07bc  Pfeifle, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Ricci, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Boorman, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2022, ApJS,  261, 3, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4365/ac5b65  Pilbratt, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Riedinger, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Passvogel, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2010,  A&A, 518, L1, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361/201014759  Poglitsch, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Waelkens, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Geis, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2010, A&A,  518, L2, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361/201014535  Polletta, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Tajer, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Maraschi, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2007, ApJ, 663,  81, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1086/518113  Prevot, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Lequeux, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Maurice, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Prevot, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', &  Rocca-Volmerange, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 1984, A&A, 132, 389  Privon, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Barnes, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Evans, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2013, ApJ,  771, 120, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0004-637X/771/2/120  Privon, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Ricci, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Aalto, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020, ApJ, 893,  149, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/ab8015  Puccetti, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Comastri, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Bauer, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2016, A&A,  585, A157, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361/201527189  Raftery, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 1995, Sociological Methodology, 25, 111.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  http://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='jstor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='org/stable/271063  Ramos Almeida, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', P´erez Garc´ıa, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Acosta-Pulido,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Rodr´ıguez Espinosa, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2007, AJ, 134, 2006,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1086/522625  Rani, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Madejski, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Mushotzky, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Reynolds, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=',  & Hodgson, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018, ApJL, 866, L13,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/2041-8213/aae48f  Reines, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Volonteri, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2015, ApJ, 813, 82,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0004-637X/813/2/82  R´emy-Ruyer, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Madden, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Galliano, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2014,  A&A, 563, A31, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361/201322803  Rengelink, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Tang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', de Bruyn, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 1997,  A&AS, 124, 259, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/aas:1997358  Revalski, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Crenshaw, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Kraemer, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018,  ApJ, 856, 46, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/aab107  Ricci, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Bauer, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Treister, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2016, ApJ, 819,  4, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/0004-637X/819/1/4  —.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017a, MNRAS, 468, 1273, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1093/mnras/stx173  Ricci, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Trakhtenbrot, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Koss, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017b, ApJS,  233, 17, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4365/aa96ad  Ricci, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Assef, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Stern, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017c, ApJ, 835,  105, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/835/1/105  Ricci, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Trakhtenbrot, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Koss, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017d,  Nature, 549, 488, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1038/nature23906  Ricci, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Privon, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Pfeifle, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021,  MNRAS, 506, 5935, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1093/mnras/stab2052  Ricci, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Ananna, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Temple, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2022, ApJ,  938, 67, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/ac8e67  Rich, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Kewley, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Dopita, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2015, ApJS,  221, 28, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0067-0049/221/2/28  Rieke, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Wright, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', B¨oker, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2015, PASP,  127, 584, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1086/682252  Rivers, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Risaliti, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Walton, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2015, ApJ, 804,  107, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0004-637X/804/2/107  Robertson, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 1991, Australian Journal of Physics, 44,  729, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1071/PH910729  Roseboom, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Bunker, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Sumiyoshi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2012,  MNRAS, 426, 1782,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1111/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1365-2966.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='21777.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='x  Rowan-Robinson, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 1995, MNRAS, 272, 737,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1093/mnras/272.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='737  Rupke, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', G¨ultekin, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Veilleux, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017, ApJ,  850, 40, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/aa94d1  Rupke, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Veilleux, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2013, ApJ, 768, 75,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0004-637X/768/1/75  Rupke, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Veilleux, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Baker, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2008, ApJ,  674, 172, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1086/522363  Saintonge, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Catinella, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Cortese, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2016,  MNRAS, 462, 1749, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1093/mnras/stw1715  Salim, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Boquien, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Lee, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018, ApJ, 859, 11,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/aabf3c  Salim, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Narayanan, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020, ARA&A, 58, 529,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1146/annurev-astro-032620-021933  Salpeter, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 1955, ApJ, 121, 161, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1086/145971  Salvato, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Hasinger, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Ilbert, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2009, ApJ, 690,  1250, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0004-637X/690/2/1250  Sanders, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Mazzarella, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Kim, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Surace,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Soifer, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2003, AJ, 126, 1607,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1086/376841  82  Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Sanders, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Mirabel, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 1996, ARA&A, 34, 749,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1146/annurev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='astro.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='749  Santini, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Maiolino, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Magnelli, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2014, A&A,  562, A30, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361/201322835  Satyapal, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Ellison, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', McAlpine, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2014,  MNRAS, 441, 1297, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1093/mnras/stu650  Satyapal, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Secrest, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Ricci, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017, ApJ, 848,  126, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/aa88ca  Savage, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Sembach, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 1996, ARA&A, 34, 279,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1146/annurev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='astro.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='279  Schartmann, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Krause, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Burkert, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2011, MNRAS,  415, 741, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1111/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1365-2966.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='18751.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='x  Schartmann, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Meisenheimer, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Camenzind, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Wolf,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Henning, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2005, A&A, 437, 861,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361:20042363  Schartmann, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Wada, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Prieto, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Burkert, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', &  Tristram, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2014, MNRAS, 445, 3878,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1093/mnras/stu2020  Schlafly, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Finkbeiner, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2011, ApJ, 737, 103,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0004-637X/737/2/103  Schlegel, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Finkbeiner, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Davis, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 1998, ApJ,  500, 525, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1086/305772  Schwarz, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 1978, Annals of Statistics, 6, 461  Scoville, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Abraham, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Aussel, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2007, ApJS,  172, 38, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1086/516580  Seaquist, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Yao, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Dunne, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Cameron, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2004,  MNRAS, 349, 1428,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1111/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1365-2966.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='07612.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='x  Secrest, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Dudik, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Dorland, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2015,  ApJS, 221, 12, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0067-0049/221/1/12  Shangguan, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Ho, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Li, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019, ApJ, 870, 104,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/aaf21a  Shankar, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Salucci, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Granato, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', De Zotti, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', &  Danese, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2004, MNRAS, 354, 1020,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1111/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1365-2966.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='08261.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='x  Shimwell, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Tasse, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Hardcastle, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019,  A&A, 622, A1, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361/201833559  Skrutskie, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Cutri, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Stiening, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2003,  2MASS All-Sky Point Source Catalog, IPAC,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='26131/IRSA2  —.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2006, AJ, 131, 1163, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1086/498708  Smith, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Tombesi, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Veilleux, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Lohfink, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', &  Luminari, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019, ApJ, 887, 69,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/ab4ef8  Soltan, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 1982, MNRAS, 200, 115,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1093/mnras/200.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='115  Speagle, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Steinhardt, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Capak, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', &  Silverman, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2014, ApJS, 214, 15,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0067-0049/214/2/15  Spoon, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Farrah, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Lebouteiller, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2013,  ApJ, 775, 127, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0004-637X/775/2/127  Stalevski, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Asmus, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Tristram, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017,  MNRAS, 472, 3854, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1093/mnras/stx2227  Stalevski, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Fritz, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Baes, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Nakos, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Popovi´c,  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' ˇC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2012, MNRAS, 420, 2756,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1111/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1365-2966.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='19775.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='x  Stalevski, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Ricci, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Ueda, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2016, MNRAS,  458, 2288, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1093/mnras/stw444  Stein, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Vollmer, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Boch, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021, A&A, 655,  A17, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361/202039659  Stern, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2015, ApJ, 807, 129,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0004-637X/807/2/129  Stern, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Eisenhardt, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Gorjian, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2005, ApJ, 631,  163, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1086/432523  Stern, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Assef, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Benford, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2012, ApJ,  753, 30, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0004-637X/753/1/30  Stern, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Lansbury, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Assef, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2014, ApJ,  794, 102, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0004-637X/794/2/102  Stierwalt, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Armus, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Surace, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2013, ApJS,  206, 1, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0067-0049/206/1/1  Swarup, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 1991, in Astronomical Society of the Pacific  Conference Series, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 19, IAU Colloq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 131: Radio  Interferometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Theory, Techniques, and Applications, ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Cornwell & R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Perley, 376–380  Swinbank, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Chapman, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Smail, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2006,  MNRAS, 371, 465, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1111/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1365-2966.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='10673.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='x  Tananbaum, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Avni, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Branduardi, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 1979,  ApJL, 234, L9, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1086/183100  Tanimoto, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Ueda, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Kawamuro, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018, ApJ,  853, 146, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/aaa47c  Tanimoto, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Ueda, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Odaka, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019, ApJ, 877,  95, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/ab1b20  —.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020, ApJ, 897, 2, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/ab96bc  Tanimoto, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Ueda, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Odaka, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Yamada, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Ricci,  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2022, ApJS, 260, 30, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4365/ac5f59  Taylor, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2006, in Astronomical Society of the Pacific  Conference Series, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 351, Astronomical Data Analysis  Software and Systems XV, ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Gabriel, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Arviset,  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Ponz, & S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Enrique, 666  Teng, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Brandt, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Harrison, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2014,  ApJ, 785, 19, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0004-637X/785/1/19  Teng, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Rigby, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Stern, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2015, ApJ, 814,  56, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0004-637X/814/1/56  Tingay, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Goeke, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Bowman, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2013,  PASA, 30, e007, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1017/pasa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='007  Toba, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Bae, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Nagao, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017a, ApJ, 850,  140, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/aa918a  Toba, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Komugi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Nagao, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017b, ApJ, 851,  98, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/aa9d17  83  Toba, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Ueda, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Matsuoka, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019a, MNRAS,  484, 196, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1093/mnras/sty3523  Toba, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Nagao, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Strauss, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2015, PASJ, 67,  86, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1093/pasj/psv057  Toba, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Yamashita, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Nagao, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019b, ApJS,  243, 15, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4365/ab238d  Toba, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Yamada, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Ueda, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020a, ApJ, 888, 8,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/ab5718  Toba, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Goto, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Oi, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020b, ApJ, 899, 35,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/ab9cb7  Toba, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Ueda, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Gandhi, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021a, ApJ, 912, 91,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/abe94a  Toba, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Brusa, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Liu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021b, A&A, 649, L11,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361/202140317  Toba, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Liu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Urrutia, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2022a, A&A, 661, A15,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361/202141547  Toba, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Yamada, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Matsubayashi, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2022b,  PASJ, 74, 1356, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1093/pasj/psac073  Tombesi, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Mel´endez, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Veilleux, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2015, Nature,  519, 436, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1038/nature14261  Tomczak, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Quadri, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Tran, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='-V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2016,  ApJ, 817, 118, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/0004-637X/817/2/118  Torres-Alb`a, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Iwasawa, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', D´ıaz-Santos, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018,  A&A, 620, A140, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361/201834105  Trakhtenbrot, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Netzer, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2010, MNRAS, 406, L35,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1111/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1745-3933.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='00876.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='x  Travascio, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Zappacosta, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Cantalupo, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020,  A&A, 635, A157, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361/201936197  Tristram, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Schartmann, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2011, A&A, 531,  A99, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361/201116867  Tristram, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Raban, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Meisenheimer, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2009, A&A, 502, 67, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361/200811607  Tsai, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='-W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Eisenhardt, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Jun, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018,  ApJ, 868, 15, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/aae698  Tully, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 1988, Nearby Galaxies Catalog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Cambridge  Univ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Press, Cambridge  Turner, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2011, RMxAA, 47, 127.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  https://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='org/abs/1102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='0347  U, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2022, Universe, 8, 392, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3390/universe8080392  U, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Sanders, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Mazzarella, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2012, ApJS,  203, 9, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0067-0049/203/1/9  U, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Medling, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Inami, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019, ApJ, 871,  166, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/aaf1c2  Ueda, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Akiyama, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Hasinger, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Miyaji, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', &  Watson, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2014, ApJ, 786, 104,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0004-637X/786/2/104  Ueda, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Hatsukade, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Kohno, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018, ApJ, 853,  24, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/aa9f10  Uematsu, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Ueda, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Tanimoto, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021, ApJ,  913, 17, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/abf0a2  Vardoulaki, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Charmandaris, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Murphy, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2015, A&A, 574, A4, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361/201424125  Vasudevan, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Fabian, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2007, MNRAS, 381,  1235, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1111/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1365-2966.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='12328.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='x  Veilleux, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Mel´endez, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Tripp, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Hamann, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', &  Rupke, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2016, ApJ, 825, 42,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/0004-637X/825/1/42  Veilleux, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Kim, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Rupke, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2009a, ApJ,  701, 587, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0004-637X/701/1/587  Veilleux, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Rupke, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Kim, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2009b,  ApJS, 182, 628, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0067-0049/182/2/628  Veilleux, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Mel´endez, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Sturm, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2013, ApJ, 776,  27, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0004-637X/776/1/27  Venanzi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', H¨onig, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Williamson, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020, ApJ, 900,  174, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/aba89f  Venturi, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Nardini, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Marconi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018, A&A,  619, A74, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361/201833668  Vietri, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Misawa, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Piconcelli, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2022, A&A,  668, A87, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361/202243285  Vika, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Driver, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Cameron, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Kelvin, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', &  Robotham, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2012, MNRAS, 419, 2264,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1111/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1365-2966.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='19881.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='x  Vito, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Brandt, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Stern, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018, MNRAS,  474, 4528, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1093/mnras/stx3120  Wada, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2012, ApJ, 758, 66,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0004-637X/758/1/66  Wada, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Fukushige, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Izumi, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Tomisaka, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018,  ApJ, 852, 88, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/aa9e53  Wada, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Papadopoulos, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Spaans, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2009, ApJ,  702, 63, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0004-637X/702/1/63  Wada, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Schartmann, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Meijerink, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2016, ApJL,  828, L19, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/2041-8205/828/2/L19  Waters, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Magnier, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Price, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020,  ApJS, 251, 4, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4365/abb82b  Wenger, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Ochsenbein, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Egret, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2000, A&AS,  143, 9, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/aas:2000332  Weston, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', McIntosh, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Brodwin, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2017,  MNRAS, 464, 3882, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1093/mnras/stw2620  Williamson, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', H¨onig, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Venanzi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019, ApJ, 876,  137, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/ab17d5  —.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020, ApJ, 897, 26, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/ab989e  Willingale, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Starling, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Beardmore, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Tanvir,  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & O’Brien, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2013, MNRAS, 431, 394,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1093/mnras/stt175  Winter, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Mushotzky, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Reynolds, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', &  Tueller, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2009, ApJ, 690, 1322,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0004-637X/690/2/1322  Wolf, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Onken, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Luvaul, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018, PASA,  35, e010, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1017/pasa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='5  84  Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Woo, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Son, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Rakshit, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020, ApJ, 901, 66,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/abad97  Wright, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Eisenhardt, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Mainzer, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  2010, AJ, 140, 1868, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1088/0004-6256/140/6/1868  —.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019, AllWISE Source Catalog, IPAC,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='26131/IRSA1  Wright, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Wright, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Goodson, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2015,  PASP, 127, 595, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1086/682253  Wu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Jun, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Assef, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018, ApJ, 852, 96,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/aa9ff3  Xie, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Ho, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Zhuang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Shangguan, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021,  ApJ, 910, 124, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/abe404  Yamada, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Ueda, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Oda, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018, ApJ, 858, 106,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/aabacb  Yamada, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Ueda, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Tanimoto, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2021, ApJS,  257, 61, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4365/ac17f5  —.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2019, ApJ, 876, 96, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/ab14f0  —.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020, ApJ, 897, 107, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/ab94b1  Yang, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Boquien, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Buat, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020a, MNRAS,  491, 740, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1093/mnras/stz3001  Yang, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Boquien, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Brandt, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2022, ApJ,  927, 192, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/ac4971  Yang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Yao, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Yang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020b, ApJ, 904, 200,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/abb775  Yoshida, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Kawabata, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Ohyama, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2011, PASJ,  63, 493, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1093/pasj/63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='sp2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='S493  Yoshii, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Aoki, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Doi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2010, in Society of  Photo-Optical Instrumentation Engineers (SPIE)  Conference Series, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 7733, Ground-based and Airborne  Telescopes III, ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Stepp, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' Gilmozzi, & H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='  Hall, 773308, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1117/12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='856680  Yu, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Tremaine, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2002, MNRAS, 335, 965,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1046/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1365-8711.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='05532.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='x  Yuan, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Liu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Xiang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2013, MNRAS,  430, 2188, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1093/mnras/stt039  Yun, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Reddy, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Condon, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2001, ApJ, 554,  803, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1086/323145  Yutani, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Toba, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Baba, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', & Wada, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2022, ApJ, 936,  118, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/1538-4357/ac87a2  Zakamska, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Hamann, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Pˆaris, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2016,  MNRAS, 459, 3144, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1093/mnras/stw718  Zappacosta, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Piconcelli, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Duras, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2018, A&A,  618, A28, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361/201732557  Zappacosta, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Piconcelli, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Giustini, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020,  A&A, 635, L5, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1051/0004-6361/201937292  Zhang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Shi, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Rieke, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2016, ApJL, 819,  L27, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='3847/2041-8205/819/2/L27  Zou, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Brandt, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', Vito, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content=' 2020, MNRAS, 499,  1823, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
+page_content='1093/mnras/staa2930' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE2T4oBgHgl3EQfCgYE/content/2301.03613v1.pdf'}
diff --git a/UNE4T4oBgHgl3EQfMAxr/vector_store/index.pkl b/UNE4T4oBgHgl3EQfMAxr/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..a914eadd74e50e211a252ea86cb2eadd25caa648
--- /dev/null
+++ b/UNE4T4oBgHgl3EQfMAxr/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:69d9e41138519db06ed53836b0eb2b96462d3c2b7387f01ba6cb1ffdd469107b
+size 124386
diff --git a/UtAyT4oBgHgl3EQfuvlU/content/tmp_files/2301.00618v1.pdf.txt b/UtAyT4oBgHgl3EQfuvlU/content/tmp_files/2301.00618v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..710b9780c24df91d849721bb50f1edd626eede44
--- /dev/null
+++ b/UtAyT4oBgHgl3EQfuvlU/content/tmp_files/2301.00618v1.pdf.txt
@@ -0,0 +1,1352 @@
+1
+An Event-based Algorithm for Simultaneous 6-DOF
+Camera Pose Tracking and Mapping
+Masoud Dayani Najafabadi, Mohammad Reza Ahmadzadeh
+Abstract—Compared to regular cameras, Dynamic Vision Sen-
+sors or Event Cameras can output compact visual data based on
+a change in the intensity in each pixel location asynchronously.
+In this paper, we study the application of current image-based
+SLAM techniques to these novel sensors. To this end, the
+information in adaptively selected event windows is processed to
+form motion-compensated images. These images are then used to
+reconstruct the scene and estimate the 6-DOF pose of the camera.
+We also propose an inertial version of the event-only pipeline
+to assess its capabilities. We compare the results of different
+configurations of the proposed algorithm against the ground truth
+for sequences of two publicly available event datasets. We also
+compare the results of the proposed event-inertial pipeline with
+the state-of-the-art and show it can produce comparable or more
+accurate results provided the map estimate is reliable.
+Index Terms—Event-based vision, event camera, KLT tracker,
+simultaneous localization and mapping (SLAM), state estimation.
+I. INTRODUCTION
+In applications such as robot navigation and control, aug-
+mented reality, and 3D reconstruction, we need to know a
+device’s location according to a map representation of the
+environment. Sometimes we are interested in estimating either
+the map or the robot’s pose. Localization or odometry is
+the problem of estimating the robot’s pose when the map is
+known. On the other hand, the general problem of estimating
+the device’s pose and the scene structure in parallel is called
+simultaneous localization and mapping (SLAM).
+The main challenge in an odometry/SLAM system is to
+achieve accurate and robust performance in real-time, no
+matter how severe the conditions are. Certain circumstances,
+including poor lighting, fast motion, dynamic scene, and
+long outdoor distances, can adversely complicate the problem.
+This problem is challenging because the estimation generally
+requires the optimization of nonlinear equations with a large
+number of unknown parameters.
+One way to address this issue is to use algorithmic tech-
+niques and constructs such as parallelization of different parts
+of the system or the use of efficient data structures [1],
+[2]. Another approach to achieve acceptable accuracy and
+robustness against various conditions is to use a range of
+complementary sensors.
+A Dynamic Vision Sensor (DVS) such as [3] is a visual
+sensor in which each pixel detects the log-intensity change
+at the pixel location and outputs an event independent of the
+The authors are with the Department of Electrical and Computer En-
+gineering, Isfahan University of Technology, Isfahan, Iran (e-mail: ma-
+soud.dayani@ec.iut.ac.ir; ahmadzadeh@iut.ac.ir).
+neighboring pixels. Event cameras are ideal for robotic appli-
+cations because they allow low latency, high event generation
+rates, high dynamic range, and low power consumption.
+After surveying the related work in Section II, a short
+review of event data and event generation mechanism is
+presented in Section III. We then explain different components
+of the proposed algorithm in Section IV in detail. Section V
+evaluates the performance of the proposed algorithm. Finally,
+we conclude our discussion in Section VI.
+II. RELATED WORK
+Because our algorithm first represents events as intensity
+images and then tracks detected features, we review both
+classical feature-based SLAM and event-based algorithms. Our
+aim here is to consider only the most relevant work rather than
+being comprehensive and complete.
+PTAM [1] is a feature-based algorithm that separates con-
+cepts of localization and mapping and parallelizes both tasks
+in concurrent threads. This technique not only improves the
+overall performance but also provides more flexibility; the
+estimated parameters from one module can be exploited in
+another without waiting for the process to finish.
+ORB-SLAM [2] gradually built on PTAM to address some
+issues. The last version of this algorithm at the time of
+this writing, ORB-SLAM3 [4], supports a range of sensors
+(regular cameras, IMU) with different configurations (monoc-
+ular, stereo, fisheye, distorted pinhole). This algorithm uses
+the estimated map to localize pose, supports multi-session
+mapping, can relocalize when tracking is lost, and reduce the
+accumulated error with the loop closing method. ORB-SLAM
+performance is limited due to the specifications of regular
+cameras, despite its robustness and accuracy.
+VINS-Mono [5] and its enhanced version, VINS-Fusion [6],
+are other feature-based methods that fuse different sensors
+to estimate the pose and structure using a window-based
+optimization scheme. Unlike ORB-SLAM, which associates
+features with their descriptors, VINS-Fusion is a KLT-based
+pipeline. Although it outperforms ORB-SLAM in some situ-
+ations [4], it still suffers from the same restrictions.
+In [7], Gallego et al. surveyed event-based vision and its
+applications. In the case of event-based odometry and SLAM,
+researchers have begun by simplifying assumptions for the
+camera motion or scene structure. For instance, Gallego et al.
+[8] proposed an algorithm for angular velocity estimation in
+which only pure 3D rotations were considered. However, most
+practical applications require more degrees of freedom, and a
+broader motion model should be considered.
+arXiv:2301.00618v1  [cs.CV]  2 Jan 2023
+
+2
+Mueggler et al. [9] proposed a continuous framework for
+pose estimation based on event data only. The information of
+every individual event is involved in state estimation. As noted
+in [10], each event contains little information, so it is better to
+process a group of events. Additionally, continuous algorithms
+demand estimating many parameters in a very narrow time
+window.
+In [11], Kim et al. reconstructed intensity images using
+event data and the features were detected and tracked in
+these frames. Although the algorithm performs well under fast
+motion and poor lighting conditions, it needs GPUs for real-
+time performance.
+Rebecq et al. [12] used IMU measurements and events to
+track 6-DOF camera motion in a window-based optimization
+framework. They reconstructed motion-compensated images
+from consecutive overlapped spatiotemporal event windows.
+Then the features were extracted and tracked using the KLT
+[13] method. Similarly, Vidal et al. [10] further utilized inten-
+sity images. Unlike [12], event windows were synchronized
+with the timestamp of intensity images. This synchronization
+can obscure the advantages of asynchronous low-latency event
+data. Both schemes require IMU measurements to initialize
+motion parameters and reconstruct frames. They also manually
+set the event window size for each sequence, which restricts
+the flexibility of their algorithm.
+Similar to our algorithm, the event-based visual-inertial
+odometry pipeline (EVIO) in [14] adaptively selects the best
+spatiotemporal event window length based on the events’
+optical flow. However, while our method, in its basic configu-
+ration, depends only on input events and addresses a range of
+conditions, EVIO relies on IMU readings for state estimation
+and does not explicitly consider situations where, for example,
+the camera is motionless.
+In this paper, we propose an event-based SLAM algorithm
+with the following features:
+• A novel image reconstruction algorithm adaptively selects
+the event window size based on camera motion and scene
+structure and converts them into a motion-compensated
+image.
+• A higher-level KLT-based localization and mapping mod-
+ule exploits map data derived from MC images to esti-
+mate the current pose of the camera.
+• An event-inertial version of the proposed event-only
+pipeline is presented to show how additional sensors can
+improve the algorithm.
+• Distorted pinhole and Kannala Brandt [15] camera mod-
+els are supported, the camera motion has six degrees of
+freedom (6-DOF), and there is no assumption about the
+type of scene.
+• The proposed algorithm has robust performance in dif-
+ferent conditions as long as the map estimate is reliable
+and there is relative motion between the camera and the
+scene.
+III. EVENT DATA
+If there is a relative motion between the DVS and the scene,
+the illumination I at each pixel location changes. When there
+is enough change in the log-intensity, L(tk) = log(I(tk)) at
+current time tk, relative to a reference time tr, it outputs an
+event at each pixel coordinate xxxk = (xk, yk). Formally, if the
+change in L is greater than a threshold, C,
+|∆L(tk, tr)| = |L(tk) − L(tr)| > C
+(1)
+there is an event
+eeek : {tk, xk, yk, pk}
+where pk shows the sign of change, i.e., if L(tk) is bigger
+than L(tr), pk is positive, and it is negative otherwise.
+Fig. 1 shows a slice of all events in the sequence
+shapes 6dof from the Public Event Dataset [16]. Each 3D
+point in the spatiotemporal space in Fig. 1(a) designates an
+event, color-coded based on event polarities. Each slice of this
+space represents a spatiotemporal event window.
+(a)
+(b)
+Fig. 1: Representation of a spatiotemporal event window from
+shapes 6dof [16]. (a) Spatiotemporal window of 2000 events
+starting from a specific timestamp. Blue points show events
+with positive polarity. (b) 2D view of (a) in the image (x-y)
+plane.
+Since event generation depends on intensity change in
+each pixel, there is no spatial correlation between adjacent
+pixels. Each pixel generates events asynchronously as soon
+as a change in its intensity value is detected. On the other
+hand, uniform areas in the image cannot contribute to event
+generation. This redundancy reduction allows lower latencies
+and faster event generation rates. Events compactly summarize
+information regarding the scene’s high-contrast areas.
+Note how the event generation rate depends on the relative
+motion between the camera and the scene and structure in
+normal illumination conditions. For a fixed threshold, C, if
+the camera traverses slowly through the environment, the event
+generation rate is low, and event data is noisy. On the other
+hand, in highly textured scenes, the event generation rate could
+be high at regular speeds. For specific camera settings, if
+the camera moves fast in a textured environment, the event
+generation rate eventually reaches the maximum allowable
+output bandwidth of the event camera.
+We can benefit from available image-based SLAM algo-
+rithms by representing event data as a 2D image. To produce
+the event histogram Ir for a specific event window Wr at
+reference time tr, all events in each pixel location are added
+Ir(xxx) =
+�
+eeek∈Wr
+pkδ(xxx − xxx′
+k),
+(2)
+
+0.46
+0.45
+0.44
+0.43
+0.42
+0.41
+200
+150
+250
+100
+200
+150
+50
+100
+50
+y
+0
+0
+X180
+160
+140
+120
+100
+80
+60
+40
+20
+0
+50
+100
+150
+200
+2503
+where δ(.) is the continuous Dirac’s delta kernel. It is common
+to replace the continuous delta operator with a discrete-time
+sampled Gaussian kernel with an arbitrary standard deviation
+σI. The parameter pk can be changed based on event polarity
+or set to constant 1 for all events in the window.
+Depending on the camera speed and the length of the
+event window, the event histograms may suffer from motion
+distortion. In this case, event coordinates can be corrected
+before reconstructing these images. The resulting image is
+called a Motion-Compensated Image or MCI for short.
+For a carefully selected event window, we can mitigate the
+motion distortion using a two-dimensional similarity or rigid
+body transformation [Sim(2) or SE(2)]. Assuming a constant
+rotational speed ω and translational speed vvv = (vx, vy) for
+each event eeek in the window, the warp
+�x′
+y′
+�
+= s
+�cos θk
+− sin θk
+sin θk
+cos θk
+� �x
+y
+�
++
+�tk,x
+tk,y
+�
+(3)
+maps the event location xxx at tk to xxx′ at time tr where θk =
+ω∆t, tttk = vvv∆t, s is the arbitrary scale, and ∆t = |tk − tr|.
+Event coordinates should be normalized based on the camera
+intrinsics beforehand.
+When the relative transform Ttr,tk and the depth Z(xxxk) of
+each event in the window are known, a SE(3) mapping can be
+used to warp events:
+xxx′
+k = π0(Ttr,tk[Z(xxxk)π−1
+0 (xxxk)]).
+(4)
+Here π0(.) projects the 3D point to the image plane viewed
+from the current pose, and π−1
+0 (.) is its inverse operation. In
+this case, we first retrieve the 3D feature point associated with
+each event, seen from the current camera position, and map it
+to a reference location.
+If we extract feature points from the reference reconstructed
+frame and track them across the current image, it is possible to
+estimate the parameters of (3) and (4) for all events between
+these frames. For this, we minimize the reprojection error
+between each warped reference feature location xxxi and the
+corresponding match xxxj in the current frame using
+θθθ∗ = argmin.
+θθθ∗
+�
+i,j∈J
+eeeT
+ij(xxx)ΩΩΩijeeeij(xxx),
+(5)
+where θθθ∗ is the transformation parameters, eeeij = xxxi − xxxj,
+ΩΩΩij is the information matrix, and J is the set containing all
+matched feature pairs between the two frames.
+To use the estimated parameters θθθ∗ to warp events in the
+current window, we first convert the relative transform to
+speed, ψψψ, using
+ψψψ = Log(θθθ∗)
+∆T
+,
+where ∆T is the length of the window in units of time and
+Log(.) is the inverse algebra that maps an element of SE(2)
+or SE(3) to a member of the corresponding tangent space. On
+the premise that the camera moves slow enough to assume
+constant speed for all events, the unknown transform between
+each event location and the reference timestamp, Ttr,tk, is
+Ttr,tk = Exp(ψψψ∆t),
+where ∆t = |tk − tr| and Exp(.) is the exponential map for
+the corresponding Lie group.
+We also distinguish the notion of an image and a frame.
+While an image is simply a two-dimensional array of numbers,
+a frame consists of other information, including the timestamp,
+camera pose, and key points beside the image.
+Interested readers can refer to [7] for an in-depth review of
+the event generation mechanism and event representation.
+IV. ALGORITHM
+Fig. 2 illustrates an overview of the proposed event-based
+SLAM algorithm. Our pipeline consists of two main compo-
+nents, which run concurrently in separate threads. The first part
+selects an appropriate spatiotemporal window of input events
+and reconstructs an image for each event window. The second
+part of the proposed algorithm extracts features from each
+input image and tracks them using the KLT method across
+the following frames. The 6-DOF pose of the camera is then
+estimated, and the local scene is reconstructed. Sections IV-A
+and IV-B discuss each component in more detail.
+A. Event Window Selection and Image Reconstruction
+The basic idea of the algorithm is to process events in
+small chunks and generate an MCI whenever there are enough
+events. The algorithm uses two sets of event windows to
+select the appropriate window size and reconstruct the MCI. It
+continually tracks and accumulates tiny windows to determine
+whether there are enough events. It reconstructs the MCI
+using the reconstruction window consisting of all previously
+collected events. Fig. 3 illustrates the relationship between the
+event stream, tiny windows, and reconstruction windows.
+This algorithm first selects a spatiotemporal window of
+input events. Initially, the length of the window, Ne, is selected
+arbitrarily and can be adjusted later. At this stage, consecutive
+event windows have no overlap. The proper event window size
+depends on the event generation rate. As discussed in Section
+III, the maximum bandwidth of the event camera limits the
+event generation rate. For example, in an event camera with
+a bandwidth of 1 million events per second and a resolution
+of 240 × 180 pixels, we can expect up to around 23 events
+per second per pixel. Thus the minimum event generation rate
+can be chosen based on the bandwidth of the event camera,
+e.g., one event per pixel per second. We select this threshold
+solely based on the event camera specifications agnostic to the
+camera motion and scene.
+Based on these observations, the event generation rate is
+calculated by
+r =
+Ne
+∆tWH
+(6)
+where ∆t = teNe −te1 is the difference between the first event
+timestamp, te1, and the last timestamp, teNe in the current
+window, and W and H are the width and height of the event
+image in pixels, respectively.
+If the camera does not move fast enough and the event
+generation rate is low then the event data will be noisy. The
+algorithm rejects most tiny windows with an event generation
+rate less than a threshold, the, and restarts from the initial state.
+
+4
+Input Events
+Event Window
+Selection
+Check Event
+Rate
+Update
+Window Size
+Reconstruct
+& Dispatch
+Tiny Frames
+Extract
+Features
+Reconstruct
+& Dispatch
+MCI
+Track (KLT)
+Initialize Map
+Event Window Selection &
+Image Reconstruction
+Event-based SLAM
+Parameters
+& Priors
+Map n
+Atlas
+Feature
+Tracks
+Feature
+Detection
+Track Local
+Map
+Local Mapping
+Key Frame
+Insertion
+Feature Tracking &
+Association (KLT)
+Fig. 2: An overview of the proposed event-based SLAM pipeline.
+Fig. 3: An illustration of the input event stream, tiny event
+windows, and non-overlapped reconstruction windows relative
+to each other.
+The only exception is when there are at least Nf frames. In this
+case, the algorithm restarts after it generates and dispatches the
+MCI.
+If the event generation rate of the current tiny window is
+acceptable, a tiny frame is reconstructed based on (2) without
+motion compensation. The following sections review the main
+components of the image reconstruction algorithm.
+1) KLT Optical Flow Initialization and Tracking: In each
+iteration, the algorithm detects FAST features [17] in the first
+tiny frame. Since we use image features to determine the
+displacement in event locations, fewer features are sufficient.
+If we cannot detect enough features, this step is repeated with
+the subsequent tiny frames; otherwise, we proceed to the next
+step.
+The algorithm then tracks the reference features in the
+subsequent frames. We can use the feature matches obtained
+from the feature tracks for the two-view reconstruction. The
+map initialization algorithm in [2] is used to estimate the
+relative pose between the current and the reference frames and
+the 3D map points corresponding to the feature matches. Due
+to the small baseline between consecutive frames, most scene
+reconstruction algorithms cannot yield reliable results. So, we
+relieve some of the stringent conditions in [2], i.e., the best
+model does not have to stand out by a large margin. Because
+most implementations use the RANSAC method internally,
+feature matches are still enhanced despite potential failures in
+scene reconstruction. If a successful reconstruction of the 3D
+structure is possible, this information is stored and used in the
+MCI reconstruction algorithm.
+We define the median feature displacement metric as the
+median distance of the tracked image features in pixels. When-
+ever the median feature displacement in the current tiny frame
+is higher than a threshold, e.g., five pixels, enough events have
+been accumulated, and the upcoming MCI reconstruction is
+commenced.
+Note that depending on the type of the scene, the number of
+detected features varies, but the median feature displacement
+is not affected. We select the feature displacement threshold
+based on how much distortion we can tolerate in event
+locations. This threshold is constant during the operation of
+the algorithm for all scenes.
+After the reconstruction and dispatching of the MCI, the
+algorithm restarts from the next iteration. Before it begins the
+next iteration, it updates the size of the tiny windows, Ne. If
+Nf is the number of processed frames and Nx is the number
+of expected frames per iteration, the new N ∗
+e is
+N ∗
+e =
+�NfNe
+Nx
+�
+,
+where ⌊x⌋ is the greatest integer less than or equal x.
+In this case, Ne is adjusted according to the camera speed
+automatically. If the camera speed increases, fewer events
+satisfy the feature displacement condition, and Ne decreases.
+On the other hand, if the camera moves slowly, we need
+more events for a defined feature displacement, and Ne
+
+Events
+TinyFrames
+Reconst.
+Frames
+W
+W
+.
+W
+k-2
+k-1
+k+15
+increases. Since we did not assume any scene structure, Ne is
+independent of the type of the scene.
+2) Motion Compensated Images: We use different warps
+to rectify motion distortion in events coordinates and use (2)
+to reconstruct the MCI. We consider the last event timestamp
+as the reference and project preceding events in the forward
+direction.
+If there is a reliable 3D reconstruction, we exploit this
+information in (4) to warp the event locations. As in [10], the
+median depth of 3D map points is used for all events in the
+window. Prior to this operation, motion and map parameters
+can be enhanced using the Bundle Adjustment (BA) method.
+On the other hand, if there exists no initial scene and motion
+estimate, but we have tracked the features across several tiny
+frames, we can still undistort events using a 2D optimization
+scheme. In this case, we first fit a Sim(2) or SE(2) motion
+model to the feature tracks and then reproject events to the
+reference frame according to (3). We also store this model as
+initialization parameters for the subsequent iterations.
+In some situations, we only know the relative motion
+estimate. For adequately small motion, we can integrate the
+IMU measurements to infer the camera motion. If the camera
+moves slow enough, we can also assume a constant speed and
+use the motion estimate from the previous iteration. In either
+case, an average scene depth can be estimated using the 3D
+motion model of (4) in (5) to minimize the reprojection error.
+We run each reconstruction method concurrently in parallel
+threads. Besides the MC images, we reconstruct the event
+histogram using (2) with no motion compensation. Finally, we
+score each image based on its contrast or sharpness [18]. To
+measure image sharpness, we first divide each image into non-
+overlapped patches and compute the local standard deviation
+(STD) for each patch. We select and dispatch the image with
+the highest average local STD. We choose the local STD
+because it yields more stable results than the global STD.
+The KLT algorithm has a poor performance when there is
+a large baseline between consecutive frames [13]. Although
+there is not much motion between tiny frames, the distance
+between the reconstructed frames can be much higher. One
+way to overcome this issue is to send these frames in addition
+to MCIs to the event-based tracking algorithm (Section IV-B).
+Another approach to ensure smooth transition between
+consecutive MC frames is to overlap the MC windows. Based
+on our experiments, this method yields more robust feature
+tracking in the second level, and hence, it is our preferred
+method.
+B. Event-based Localization and Mapping
+With the MCI from the previous step, the event-based
+localization module follows an image-based KLT optical flow
+scheme to estimate the 6-DOF pose of the camera and recon-
+struct the scene. The basic steps of this algorithm are almost
+similar to the reconstruction algorithm discussed in Section
+IV-A.
+1) Initialization: If there are not enough feature tracks, the
+algorithm detects new FAST features in the input MCI. It
+then creates and merges new feature tracks to manage feature
+locations across successive images. We use a bucketing grid
+scheme to ensure a uniform distribution of detected features
+across images.
+The last features are tracked in each subsequent image using
+the KLT method. If the map is not initialized, we use the
+two-view reconstruction algorithm between the current and
+reference frames to reconstruct the scene and recover the
+camera’s relative motion. As in Section IV-A, we use the map
+initialization algorithm in [2] for this step. After a successful
+reconstruction, we initialize the map and perform a global
+bundle adjustment optimization to enhance the estimate.
+2) Tracking The Local Map: Using feature tracks, we can
+identify feature associations and the corresponding map points
+across different frames. Therefore, the current pose of the
+camera is estimated using an optimization-based framework.
+To do this, the geometrical distance between the projected map
+points in the current frame and the corresponding key point
+observations is minimized.
+Due to the camera motion, we might lose track of some
+features. In this case, the algorithm fails to track features that
+are not visible in the subsequent frames.
+3) Key Frame Insertion and Local Mapping: The algorithm
+inserts a new keyframe whenever there is enough baseline
+between the current tracked frame and the last keyframe.
+We use several heuristics to decide when to spawn a new
+keyframe. Whenever the number of tracked map points falls
+below a threshold or the median pixel displacement between
+key points in the current frame and the preceding keyframe is
+greater than a certain limit, a new keyframe is created.
+The local mapping module is very similar to the method
+used in ORB-SLAM. While our algorithm uses the KLT
+method to track and associate features, ORB-SLAM detects
+new matches with descriptors.
+In local mapping, we first cull outlier map points based
+on their rate of observations. Additional map points are then
+triangulated for the new feature matches between the current
+and previous keyframes. Finally, a local bundle adjustment
+optimization enhances the map point estimates.
+C. IMU Measurements
+In this section, the necessary changes to incorporate IMU
+measurements are introduced to show how another sensor
+module can benefit the proposed algorithm. The preintegration
+theory and the IMU initialization module of [19] and [2] are
+used to accomplish this goal. These changes are as follows:
+• IMU measurements are integrated between the tiny
+frames, the reconstruction frames, and the keyframes.
+• In the MCI reconstruction module, using the initial pose
+from the IMU integrations and feature matches, we first
+find the average depth of the scene in the 3D warp
+(4) through the optimization framework of (5). We also
+consider IMU biases and the gravity direction as the
+state variables in this optimization. The initial gravity
+direction is evaluated using the first accelerometer reading
+for the current iteration. These parameters are stored for
+the subsequent iterations, and the MCI is reconstructed.
+• We use an inertial bundle adjustment optimization frame-
+work in the MCI generation step with a successfully
+
+6
+reconstructed scene. Besides IMU biases and the gravity
+direction, we also consider the relative scale.
+• We adapt the inertial local bundle adjustment and the
+mechanism of IMU initialization discussed in [2] in the
+local mapping algorithm. In summary, the IMU biases,
+the direction of the gravity, and the relative scale are
+estimated using an adequate number of keyframes. Such
+optimization and scale refinement are repeated for several
+predefined periods.
+V. EXPERIMENTS
+To evaluate the performance of the proposed pipeline, we
+use two publicly available event datasets, the Public Event
+Dataset [16] and the Multi-vehicle Stereo Event Dataset [20].
+The former includes short-duration sequences recorded in
+different scenes and challenging conditions by a monocular
+240×180 pixel DAVIS device. An embedded IMU measures
+acceleration and angular velocity along three axes of freedom.
+Most sequences include events, intensity images, IMU mea-
+surements, and the ground truth. We only consider the ones
+for which both the ground truth and IMU measurements are
+available; hence we exclude sequences from the “depth” group.
+Sequences of [20] are recorded with two similar DAVIS
+346×260 pixel cameras attached in the stereo configuration.
+It contains events and intensity images for both cameras, IMU
+measurements, and the ground truth for the trajectory and
+depth maps for each frame. We only use the left camera
+and several representative outdoor sequences, noting that the
+proposed pipeline is not designed to tackle the stereo case or
+track longer outdoor distances.
+We use several objective criteria to verify the results of
+the proposed algorithm quantitatively. Since our algorithm
+generally results in an atlas of multiple disconnected pose
+graphs, we extend the Relative Pose Error (RPE) in [21] to
+average the normalized relative errors as
+RPE(θθθ) =
+1
+|A|
+�
+G∈A
+1
+D|G|
+�
+i,j∈G
+θθθ(sss(∆T ∗
+i,j) ⊖ ∆Ti,j)
+(7)
+where A is the set of all pose graphs, G, ∆Ti,j = Ti ⊖ Tj
+is the relative transform between pairs of SE(3) poses in G,
+Ti and Tj, ⊖ is the inverse of SE(3) Lie algebra, D is the
+total traversed distance for the current graph, sss() is the scaling
+operation for monocular event-only tracking, θθθ() returns either
+rotational or translational component of error, and ∗ indicates
+the estimate. We normalize RPE by the total traversed distance
+to reflect the effects of variable length pieces. For the monoc-
+ular event-only configuration, we calculate the unknown scale
+by comparing the associated estimate and ground truth pairs
+and scale the estimate before computing the average error.
+Additionally, we consider measures to assess the stability of
+the pipeline. Total traversed distance or time is the sum of all
+distances or delta times between consecutive frames in each
+pose graph.
+Before the algorithm processes input events, lens distortions
+in event pixel locations are rectified using available calibration
+parameters for each sequence. We choose Nx = 3, and the
+initial value of Ne is 2000 events for sequences of [16] and
+6000 for [20]. Since the event frames in [20] have a higher
+resolution, a higher value for Ne helps the convergence speed,
+though starting from 2000 events should eventually converge
+to the optimal value. Motion-compensated windows have 50%
+overlap, and Event frames are reconstructed using a Gaussian
+kernel with σI = 1 in both tracking levels (tiny frames and
+MC images). The FAST feature detector threshold is set to
+a small amount (around zero) because this setting yields the
+most features and allows us to filter them by their response.
+We set the KLT tracker with two pyramid levels, a block size
+of 23×23 pixels, and a maximum bidirectional error of one.
+These settings are chosen arbitrarily based on our experiments.
+Table I summarizes the evaluation results for event-only
+(E-Only) and event-inertial (E-I-C1) sensor configurations.
+The stability column of this table is the multiplication of
+the total traversed distance in meters and time in seconds.
+Although event-only tracking shows similar or superior results
+in most cases, the inertial method is more stable. Since more
+challenging periods can be tracked in the inertial case, the
+errors grow accordingly. Furthermore, because we do not scale
+inertial pose graphs, the reported results also include scaling
+errors.
+Besides the challenging conditions of each sequence that
+can affect the quality of the event image reconstruction and the
+accuracy of pose estimates, we also note two degrading effects.
+For lower resolution images of [16], the rays connecting the
+map points with their respective observations in each frame are
+so close that the uncertainty in the depth of the subsequent map
+point estimates grows [22]. Since our pipeline estimates the
+following poses according to the map, the distance between
+consecutive poses diminishes, which in turn results in less
+accurate map estimates. This cycle continues until the tracking
+is lost. As discussed in [23], this situation can also happen
+for larger images of [20] recorded by the fisheye camera due
+to inaccurate translation estimates caused by far map points,
+especially for outdoor sequences.
+Although in the inertial case, the scale information embed-
+ded in IMU readings prevents the shrinking effect, inaccuracies
+due to IMU biases can affect map point estimates. If there
+are not enough map points, the following pose and map
+point estimates are affected by the growing bias of inertial
+measurements. In this case, subsequent map point estimates
+continue to expand after the insertion of each keyframe until
+the tracking is lost.
+The inertial configuration discussed in Table I (E-I-C1) still
+assumes that the tracking can be lost due to severe conditions,
+so it tries to reinitialize the map as soon as possible. To further
+assess the limitations of the proposed algorithm and compare
+it against the inertial state estimation in [10], we consider two
+other configurations (E-I-C2 and E-I-C3). We configure our
+pipeline to enforce continuous tracking without spawning and
+initializing new maps in unfavorable conditions. In both cases,
+we disallow the reinitialization of the map and continue to
+estimate 3D points using inertial readings and feature matches
+between nearby frames. In the last configuration (E-I-C3), we
+also fix the tiny event window size to a predefined value and
+restrict the withdrawal of noisy frames based on the event
+generation rate. Table II summarizes our preferences for the
+
+7
+TABLE I: Performance evaluation of the proposed algorithm for two event-based configurations compared against the ground
+truth for some sequences of [16] and [20].
+E-Only
+E-I-C1
+RPE
+RPE
+RPE
+RPE
+Dataset
+Sequence
+Position
+Rotation
+Stability
+Position
+Rotation
+Stability
+(-)
+(deg/m)
+(×103m.s)
+(-)
+(deg/m)
+(×103m.s)
+shapes 6dof
+0.048
+0.209
+2.31
+0.050
+0.114
+2.50
+shapes translation
+0.084
+0.186
+2.29
+0.092
+0.169
+2.62
+Public
+poster 6dof
+0.017
+0.062
+3.18
+0.018
+0.057
+3.14
+Event
+poster translation
+0.005
+0.006
+2.29
+0.005
+0.006
+2.33
+[16]
+hdr poster
+0.011
+0.025
+2.67
+0.002
+0.007
+2.73
+boxes 6dof
+0.002
+0.004
+3.91
+0.006
+0.008
+3.95
+boxes translation
+0.004
+0.004
+3.40
+0.004
+0.004
+3.46
+hdr boxes
+0.004
+0.007
+3.08
+0.004
+0.006
+3.07
+dynamic 6dof
+0.019
+0.041
+2.09
+0.032
+0.117
+2.11
+dynamic translation
+0.012
+0.018
+1.24
+0.034
+0.032
+1.38
+indoor flying1
+0.044
+0.041
+1.12
+0.080
+0.046
+1.34
+Multi-
+indoor flying2
+0.041
+0.032
+1.86
+0.029
+0.019
+2.11
+Vehicle
+indoor flying3
+0.018
+0.006
+3.23
+0.029
+0.008
+3.63
+Event
+indoor flying4
+0.038
+0.013
+0.11
+0.038
+0.016
+0.12
+Stereo
+outdoor day1
+0.889
+0.033
+3.14
+1.181
+0.041
+6.38
+[20]
+outdoor night1
+0.678
+0.003
+3.29
+1.131
+0.008
+3.94
+outdoor night3
+1.208
+0.009
+5.04
+1.406
+0.017
+8.95
+TABLE II: Fixed tiny event window size specification for each
+group of sequences in [16].
+Sequence
+Number of Events
+shapes
+2000
+dynamic
+8000
+poster
+10000
+boxes
+12000
+length of fixed tiny windows for each group of sequences in
+[16]. We select these values based on our experience of E-I-C1
+with variable window sizes.
+Table III compares different inertial configurations using
+the same RPE metrics of Table I. Both E-I-C2 and E-I-C3
+configurations show a significant performance boost to the E-
+I-C1 configuration. In this case, the prolonged tracking period
+of E-I-C2 and E-I-C3 configurations provokes more IMU
+initialization and refinement steps and improves the accuracy
+of the IMU parameters and the whole system.
+The last two columns of Table III also investigate the
+efficacy of the adaptive selection of the tiny window size.
+Although the results are similar in most sequences, noting
+that the window length in E-I-C3 is fixed to the optimal
+value, a wrongly selected size can impact the performance
+and accuracy of the system. Therefore, we report the E-I-C2
+configuration as our preferred method.
+Next, we compare our pipeline against the most relevant
+algorithm that provides a stable open-source implementation.
+For this reason, we exclude the methods that utilize the
+intensity images with the events.
+10
+20
+30
+40
+50
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+1.2
+Translation error [m]
+E-I [10]
+E-I-C2 (Proposed)
+shapes_6dof
+shapes_translation
+poster_translation
+hdr_poster
+boxes_6dof
+boxes_translation
+hdr_boxes
+dynamic_6dof
+dynamic_translation
+(a)
+10
+20
+30
+40
+50
+Distance traveled [m]
+0
+2
+4
+6
+8
+10
+Yaw error [deg]
+(b)
+Fig. 4: The comparison between the proposed algorithm and
+the event-inertial method of [10] in terms of the average
+relative pose error over a range of distances for the sequences
+of [16]: (a) average relative translation error, (b) average
+relative yaw error.
+
+8
+TABLE III: Comparison of the performance of different inertial configurations of the proposed algorithm for sequences of
+[16].
+E-I-C1
+E-I-C2
+E-I-C3
+RPE
+RPE
+RPE
+RPE
+RPE
+RPE
+Sequence
+Position
+Rotation
+Position
+Rotation
+Position
+Rotation
+(×10−3)
+(×10−3 deg/m)
+(×10−3)
+(×10−3 deg/m)
+(×10−3)
+(×10−3 deg/m)
+shapes 6dof
+50
+114
+1
+6
+2
+6
+shapes translation
+92
+169
+1
+3
+1
+2
+poster 6dof
+18
+57
+1
+6
+2
+7
+poster translation
+5
+6
+4
+5
+4
+5
+hdr poster
+2
+7
+3
+7
+3
+7
+boxes 6dof
+6
+8
+1
+3
+1
+2
+boxes translation
+4
+4
+2
+4
+2
+4
+hdr boxes
+4
+6
+2
+6
+2
+6
+dynamic 6dof
+32
+117
+2
+5
+2
+5
+dynamic translation
+34
+32
+4
+5
+4
+5
+Fig. 4 contrasts the E-I-C2 configuration of the proposed
+algorithm against the event-inertial method in [10]. We run
+the latest open-source release of their algorithm1 for each
+sequence in [16] using the default configurations (the sequence
+poster 6dof is excluded because this implementation of [10]
+fails to produce reliable results). Similar to [10], we measure
+and report the average relative translation and yaw error over a
+range of distances. We calculate the relative pose error between
+the first one hundred pairs that meet a specific distance range.
+Although the window-based state estimator of [10] estimates
+the pose of the camera and map points simultaneously, our
+algorithm relies on an accurate map to find the next pose. As
+a result, any condition that degrades map estimate accuracy
+will affect our results. For the sequence shapes 6dof, when
+the camera moves fast in front of a low-textured poster,
+the tracking fails due to the lack of detected features, and
+errors grow exponentially. Even though the scene in sequence
+dynamic 6dof is textured, the change in 3D feature locations
+affects the performance of the proposed method. Despite
+the poor lighting condition in boxes 6dof, there are enough
+reliable map points, and the proposed algorithm outperforms
+the state-of-the-art based on the translation errors.
+Based on our experiments, while the state estimator of
+[10] can produce more accurate results locally, the proposed
+algorithm can outperform over longer distances as long as the
+map estimates are reliable. As mentioned before, when the
+map estimates are valid, it will affect the subsequent pose
+estimates even when some map points are no longer visible.
+Consequently, although the results are not explicitly shown
+here, we claim that the proposed pipeline can reduce the
+absolute pose error (APE) when these conditions are met.
+Fig. 5 compares the absolute estimated position of the
+results of Fig. 4 for the sequence boxes 6dof. We use the
+APE tools in [2] to align the first 15 seconds of the estimates
+with the ground truth. In this case, the proposed method can
+track the ground truth more accurately.
+1https://github.com/uzh-rpg/rpg ultimate slam open
+X
+0.4
+0.2
+0.0
+0.2
+0.4
+0.6
+0.8
+Y
+0.8
+0.9
+1.0
+1.1
+1.2
+1.3
+1.4
+Z
+1.0
+1.1
+1.2
+1.3
+1.4
+1.5
+1.6
+1.7
+GT
+E-I-C2 (Proposed)
+E-I [10]
+Fig. 5: The absolute estimated positions of the proposed
+algorithm and the event-inertial method of [10] are compared
+against the ground truth in terms of the APE for the first 15
+seconds of the sequence boxes 6dof.
+Although we have not tried to optimize the performance of
+the proposed algorithm, we present the average tracking time
+statistics to contrast the computation cost of each module. In
+particular, we measure and report the performance of the main
+tracking thread (MTH), the first-level event image reconstruc-
+tion module (L1), and the second-level event frame tracking
+thread (L2). Since it almost takes several tiny frames in L1
+and one iteration of L2 for the main tracking thread to process
+input events, we include the timing as per motion-compensated
+frames (MCF) and as per tiny frame (TF). Assuming there are
+three TF for each MCF on average, we subtract double L1
+values from the MCF results and report the per TF results. The
+timing statistics for the local mapping thread are not reported
+here. We run our pipeline on a system with an Intel Core-i7
+9700K CPU, 64 GB RAM, and Ubuntu 20.04 LTS operating
+system.
+Table IV summarizes the timing results of different compo-
+nents of our pipeline for two sensor configurations and some
+
+9
+TABLE IV: Average tracking time statistics in milliseconds for three main modules of the proposed algorithm, calculated for
+representative sequences of [16] and [20].
+Event-Only
+Event-Inertial-C1
+MTH
+MTH
+L1
+L2
+MTH
+MTH
+L1
+L2
+Sequence
+/MCF
+/TF
+/TF
+/TF
+/MCF
+/TF
+/TF
+/TF
+shapes 6dof
+72
+48
+12
+6
+82
+56
+13
+7
+poster 6dof
+158
+106
+26
+7
+173
+119
+27
+9
+boxes 6dof
+158
+106
+26
+7
+174
+118
+28
+9
+dynamic 6dof
+138
+92
+23
+7
+157
+107
+25
+9
+indoor flying1
+139
+93
+23
+8
+147
+99
+24
+15
+outdoor day1
+171
+115
+28
+5
+185
+127
+29
+10
+outdoor night1
+187
+125
+31
+5
+202
+138
+32
+14
+representative sequences of both datasets [16] and [20]. The
+overall performance of our algorithm is several times lower
+than the real-time. Note that more textured sequences demand
+more processing power. The addition of the IMU slightly
+increases the performance cost of our method. Based on these
+results, the reconstruction of each MCF is generally the most
+costly operation. It takes about the same amount of time to
+reconstruct an MCF, around 28 ms on average, consistent
+across all configurations and datasets. The timing results of
+L2 are only comparable across the Public Event dataset. For
+sequences of [20], the cost of the inertial L2 module is almost
+twice the performance of the event-only case. One reason for
+this difference could be the high depth variation inherent in
+the fisheye camera and the difficulty of scale estimation and
+refinement involved in inertial tracking in this case (although
+the local mapping is performed in a separate thread, the inertial
+L2 must wait because of the map change).
+VI. CONCLUSION
+We proposed an algorithm that reconstructs MC images
+from the adaptively selected event windows and uses the event
+images to estimate the structure and trajectory. The first mod-
+ule tracks FAST features across multiple event histograms to
+choose the best event window size and resolve the parameters
+needed for MCI generation. After reconstruction, it sends the
+best MCI representation to an image-based SLAM to initialize
+the map and track the 6-DOF pose of the camera in it.
+Furthermore, we showed how to utilize inertial measurements
+to improve the performance of the event-only algorithm.
+We compared the estimated trajectory of different config-
+urations of the proposed pipeline with the ground truth for
+sequences of two publicly available event datasets. Although
+the algorithm produces accurate results in most cases, its
+performance depends on the reliability of the map estimate.
+We also showed that the proposed algorithm outperforms the
+state-of-the-art as long as a valid map estimate is available.
+Although the event window selection module is costly, it
+can still be used in most event-based algorithms to select
+the best event window without reconstructing the MCI. It is
+possible to use different techniques such as relocalization or
+loop-closing to improve the accuracy of the map, the overall
+performance, and the algorithm’s stability. These techniques
+generally extract and use descriptors to link different segments
+of a pose graph. One can consider event-based descriptors
+for that purpose or extract descriptors from regular intensity
+images, which are processed along with the event stream.
+REFERENCES
+[1] G. Klein and D. Murray, “Parallel tracking and mapping for small ar
+workspaces,” in 2007 6th IEEE and ACM International Symposium on
+Mixed and Augmented Reality, pp. 225–234, 2007.
+[2] R. Mur-Artal, J. M. M. Montiel, and J. D. Tardos, “ORB-SLAM: A
+versatile and accurate monocular SLAM system,” IEEE Transactions
+on Robotics, vol. 31, no. 5, p. 1147–1163, 2015.
+[3] P. Lichtsteiner, C. Posch, and T. Delbruck, “A 128×128 120 db 15 µs
+latency asynchronous temporal contrast vision sensor,” IEEE Journal of
+Solid-State Circuits, vol. 43, no. 2, pp. 566–576, 2008.
+[4] C. Campos, R. Elvira, J. J. G. Rodr´ıguez, J. M. M. Montiel, and
+J. D. Tard´os, “ORB-SLAM3: An accurate open-source library for visual,
+visual–inertial, and multimap SLAM,” IEEE Transactions on Robotics,
+vol. 37, no. 6, pp. 1874–1890, 2021.
+[5] T. Qin, P. Li, and S. Shen, “VINS-Mono: A robust and versatile monoc-
+ular visual-inertial state estimator,” IEEE Transactions on Robotics,
+vol. 34, no. 4, pp. 1004–1020, 2018.
+[6] T. Qin, J. Pan, S. Cao, and S. Shen, “A general optimization-based
+framework for local odometry estimation with multiple sensors,” 2019.
+[7] G. Gallego, T. Delbr¨uck, G. Orchard, C. Bartolozzi, B. Taba, A. Censi,
+S. Leutenegger, A. J. Davison, J. Conradt, K. Daniilidis, and D. Scara-
+muzza, “Event-based vision: A survey,” IEEE Transactions on Pattern
+Analysis and Machine Intelligence, vol. 44, no. 1, pp. 154–180, 2022.
+[8] G. Gallego and D. Scaramuzza, “Accurate angular velocity estimation
+with an event camera,” IEEE Robotics and Automation Letters, vol. 2,
+no. 2, pp. 632–639, 2017.
+[9] E. Mueggler, G. Gallego, and D. Scaramuzza, “Continuous-time trajec-
+tory estimation for event-based vision sensors,” in Robotics: Science and
+Systems, 2015.
+[10] A. R. Vidal, H. Rebecq, T. Horstschaefer, and D. Scaramuzza, “Ultimate
+SLAM? combining events, images, and IMU for robust visual SLAM in
+HDR and high-speed scenarios,” IEEE Robotics and Automation Letters,
+vol. 3, no. 2, pp. 994–1001, 2018.
+[11] H. Kim, A. Handa, R. Benosman, S.-H. Ieng, and A. Davison, “Simul-
+taneous mosaicing and tracking with an event camera,” in Proceedings
+of the British Machine Vision Conference, BMVA Press, 2014.
+[12] T. H. Henri Rebecq and D. Scaramuzza, “Real-time visual-inertial odom-
+etry for event cameras using keyframe-based nonlinear optimization,” in
+Proceedings of the British Machine Vision Conference (BMVC) (G. B.
+Tae-Kyun Kim, Stefanos Zafeiriou and K. Mikolajczyk, eds.), pp. 16.1–
+16.12, BMVA Press, September 2017.
+[13] B. D. Lucas and T. Kanade, “An iterative image registration technique
+with an application to stereo vision,” in Proceedings of the 7th Inter-
+national Joint Conference on Artificial Intelligence, vol. 2 of IJCAI’81,
+p. 674–679, Morgan Kaufmann Publishers Inc., 1981.
+[14] A. Z. Zhu, N. Atanasov, and K. Daniilidis, “Event-based visual inertial
+odometry,” in 2017 IEEE Conference on Computer Vision and Pattern
+Recognition (CVPR), pp. 5816–5824, 2017.
+
+10
+[15] J. Kannala and S. Brandt, “A generic camera model and calibration
+method for conventional, wide-angle, and fish-eye lenses,” IEEE Trans-
+actions on Pattern Analysis and Machine Intelligence, vol. 28, no. 8,
+pp. 1335–1340, 2006.
+[16] E. Mueggler, H. Rebecq, G. Gallego, T. Delbruck, and D. Scaramuzza,
+“The event-camera dataset and simulator: Event-based data for pose
+estimation, visual odometry, and SLAM,” The International Journal of
+Robotics Research, vol. 36, no. 2, p. 142–149, 2017.
+[17] P. Wyatt and H. Nakai, “Fast feature extraction using approximations to
+derivatives with summed-area images,” in Proceedings of the 7th Asian
+Conference on Computer Vision - Volume Part I, ACCV’06, (Berlin,
+Heidelberg), p. 776–786, Springer-Verlag, 2006.
+[18] G. Gallego, H. Rebecq, and D. Scaramuzza, “A unifying contrast
+maximization framework for event cameras, with applications to motion,
+depth, and optical flow estimation,” 2018 IEEE/CVF Conference on
+Computer Vision and Pattern Recognition, Jun 2018.
+[19] C. Forster, L. Carlone, F. Dellaert, and D. Scaramuzza, “On-manifold
+preintegration for real-time visual–inertial odometry,” IEEE Transactions
+on Robotics, vol. 33, no. 1, p. 1–21, 2017.
+[20] A. Z. Zhu, D. Thakur, T. Ozaslan, B. Pfrommer, V. Kumar, and
+K. Daniilidis, “The multivehicle stereo event camera dataset: An event
+camera dataset for 3D perception,” IEEE Robotics and Automation
+Letters, vol. 3, no. 3, p. 2032–2039, 2018.
+[21] J. Sturm, N. Engelhard, F. Endres, W. Burgard, and D. Cremers, “A
+benchmark for the evaluation of RGB-D SLAM Systems,” in Proc. of
+the International Conference on Intelligent Robot Systems (IROS), Oct.
+2012.
+[22] R. H. A. Zisserman, Multiple View Geometry in Computer Vision, 2nd
+Edition. 2 ed., 2004.
+[23] R. Mur-Artal and J. D. Tard´os, “ORB-SLAM2: an open-source SLAM
+system for monocular, stereo and RGB-D cameras,” IEEE Transactions
+on Robotics, vol. 33, no. 5, pp. 1255–1262, 2017.
+[24] A. Geiger, P. Lenz, and R. Urtasun, “Are we ready for autonomous
+driving? the KITTI vision benchmark suite,” in Conference on Computer
+Vision and Pattern Recognition (CVPR), 2012.
+
diff --git a/UtAyT4oBgHgl3EQfuvlU/content/tmp_files/load_file.txt b/UtAyT4oBgHgl3EQfuvlU/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c3add051150bee071d0469900891cb6317fb31d9
--- /dev/null
+++ b/UtAyT4oBgHgl3EQfuvlU/content/tmp_files/load_file.txt
@@ -0,0 +1,870 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf,len=869
+page_content='1  An Event-based Algorithm for Simultaneous 6-DOF  Camera Pose Tracking and Mapping  Masoud Dayani Najafabadi, Mohammad Reza Ahmadzadeh  Abstract—Compared to regular cameras, Dynamic Vision Sen-  sors or Event Cameras can output compact visual data based on  a change in the intensity in each pixel location asynchronously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  In this paper, we study the application of current image-based  SLAM techniques to these novel sensors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' To this end, the  information in adaptively selected event windows is processed to  form motion-compensated images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' These images are then used to  reconstruct the scene and estimate the 6-DOF pose of the camera.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  We also propose an inertial version of the event-only pipeline  to assess its capabilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' We compare the results of different  configurations of the proposed algorithm against the ground truth  for sequences of two publicly available event datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' We also  compare the results of the proposed event-inertial pipeline with  the state-of-the-art and show it can produce comparable or more  accurate results provided the map estimate is reliable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  Index Terms—Event-based vision, event camera, KLT tracker,  simultaneous localization and mapping (SLAM), state estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' INTRODUCTION  In applications such as robot navigation and control, aug-  mented reality, and 3D reconstruction, we need to know a  device’s location according to a map representation of the  environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Sometimes we are interested in estimating either  the map or the robot’s pose.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Localization or odometry is  the problem of estimating the robot’s pose when the map is  known.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' On the other hand, the general problem of estimating  the device’s pose and the scene structure in parallel is called  simultaneous localization and mapping (SLAM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  The main challenge in an odometry/SLAM system is to  achieve accurate and robust performance in real-time, no  matter how severe the conditions are.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Certain circumstances,  including poor lighting, fast motion, dynamic scene, and  long outdoor distances, can adversely complicate the problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  This problem is challenging because the estimation generally  requires the optimization of nonlinear equations with a large  number of unknown parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  One way to address this issue is to use algorithmic tech-  niques and constructs such as parallelization of different parts  of the system or the use of efficient data structures [1],  [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Another approach to achieve acceptable accuracy and  robustness against various conditions is to use a range of  complementary sensors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  A Dynamic Vision Sensor (DVS) such as [3] is a visual  sensor in which each pixel detects the log-intensity change  at the pixel location and outputs an event independent of the  The authors are with the Department of Electrical and Computer En-  gineering, Isfahan University of Technology, Isfahan, Iran (e-mail: ma-  soud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='dayani@ec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='iut.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='ir;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' ahmadzadeh@iut.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='ir).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  neighboring pixels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Event cameras are ideal for robotic appli-  cations because they allow low latency, high event generation  rates, high dynamic range, and low power consumption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  After surveying the related work in Section II, a short  review of event data and event generation mechanism is  presented in Section III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' We then explain different components  of the proposed algorithm in Section IV in detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Section V  evaluates the performance of the proposed algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Finally,  we conclude our discussion in Section VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' RELATED WORK  Because our algorithm first represents events as intensity  images and then tracks detected features, we review both  classical feature-based SLAM and event-based algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Our  aim here is to consider only the most relevant work rather than  being comprehensive and complete.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  PTAM [1] is a feature-based algorithm that separates con-  cepts of localization and mapping and parallelizes both tasks  in concurrent threads.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' This technique not only improves the  overall performance but also provides more flexibility;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' the  estimated parameters from one module can be exploited in  another without waiting for the process to finish.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  ORB-SLAM [2] gradually built on PTAM to address some  issues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' The last version of this algorithm at the time of  this writing, ORB-SLAM3 [4], supports a range of sensors  (regular cameras, IMU) with different configurations (monoc-  ular, stereo, fisheye, distorted pinhole).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' This algorithm uses  the estimated map to localize pose, supports multi-session  mapping, can relocalize when tracking is lost, and reduce the  accumulated error with the loop closing method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' ORB-SLAM  performance is limited due to the specifications of regular  cameras, despite its robustness and accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  VINS-Mono [5] and its enhanced version, VINS-Fusion [6],  are other feature-based methods that fuse different sensors  to estimate the pose and structure using a window-based  optimization scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Unlike ORB-SLAM, which associates  features with their descriptors, VINS-Fusion is a KLT-based  pipeline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Although it outperforms ORB-SLAM in some situ-  ations [4], it still suffers from the same restrictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  In [7], Gallego et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' surveyed event-based vision and its  applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' In the case of event-based odometry and SLAM,  researchers have begun by simplifying assumptions for the  camera motion or scene structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' For instance, Gallego et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  [8] proposed an algorithm for angular velocity estimation in  which only pure 3D rotations were considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' However, most  practical applications require more degrees of freedom, and a  broader motion model should be considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='00618v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='CV]  2 Jan 2023  2  Mueggler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' [9] proposed a continuous framework for  pose estimation based on event data only.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' The information of  every individual event is involved in state estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' As noted  in [10], each event contains little information, so it is better to  process a group of events.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Additionally, continuous algorithms  demand estimating many parameters in a very narrow time  window.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  In [11], Kim et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' reconstructed intensity images using  event data and the features were detected and tracked in  these frames.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Although the algorithm performs well under fast  motion and poor lighting conditions, it needs GPUs for real-  time performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  Rebecq et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' [12] used IMU measurements and events to  track 6-DOF camera motion in a window-based optimization  framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' They reconstructed motion-compensated images  from consecutive overlapped spatiotemporal event windows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  Then the features were extracted and tracked using the KLT  [13] method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Similarly, Vidal et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' [10] further utilized inten-  sity images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Unlike [12], event windows were synchronized  with the timestamp of intensity images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' This synchronization  can obscure the advantages of asynchronous low-latency event  data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Both schemes require IMU measurements to initialize  motion parameters and reconstruct frames.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' They also manually  set the event window size for each sequence, which restricts  the flexibility of their algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  Similar to our algorithm, the event-based visual-inertial  odometry pipeline (EVIO) in [14] adaptively selects the best  spatiotemporal event window length based on the events’  optical flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' However, while our method, in its basic configu-  ration, depends only on input events and addresses a range of  conditions, EVIO relies on IMU readings for state estimation  and does not explicitly consider situations where, for example,  the camera is motionless.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  In this paper, we propose an event-based SLAM algorithm  with the following features:  A novel image reconstruction algorithm adaptively selects  the event window size based on camera motion and scene  structure and converts them into a motion-compensated  image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  A higher-level KLT-based localization and mapping mod-  ule exploits map data derived from MC images to esti-  mate the current pose of the camera.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  An event-inertial version of the proposed event-only  pipeline is presented to show how additional sensors can  improve the algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  Distorted pinhole and Kannala Brandt [15] camera mod-  els are supported, the camera motion has six degrees of  freedom (6-DOF), and there is no assumption about the  type of scene.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  The proposed algorithm has robust performance in dif-  ferent conditions as long as the map estimate is reliable  and there is relative motion between the camera and the  scene.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' EVENT DATA  If there is a relative motion between the DVS and the scene,  the illumination I at each pixel location changes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' When there  is enough change in the log-intensity, L(tk) = log(I(tk)) at  current time tk, relative to a reference time tr, it outputs an  event at each pixel coordinate xxxk = (xk, yk).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Formally, if the  change in L is greater than a threshold, C,  |∆L(tk, tr)| = |L(tk) − L(tr)| > C  (1)  there is an event  eeek : {tk, xk, yk, pk}  where pk shows the sign of change, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=', if L(tk) is bigger  than L(tr), pk is positive, and it is negative otherwise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' 1 shows a slice of all events in the sequence  shapes 6dof from the Public Event Dataset [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Each 3D  point in the spatiotemporal space in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' 1(a) designates an  event, color-coded based on event polarities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Each slice of this  space represents a spatiotemporal event window.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  (a)  (b)  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' 1: Representation of a spatiotemporal event window from  shapes 6dof [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' (a) Spatiotemporal window of 2000 events  starting from a specific timestamp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Blue points show events  with positive polarity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' (b) 2D view of (a) in the image (x-y)  plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  Since event generation depends on intensity change in  each pixel, there is no spatial correlation between adjacent  pixels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Each pixel generates events asynchronously as soon  as a change in its intensity value is detected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' On the other  hand, uniform areas in the image cannot contribute to event  generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' This redundancy reduction allows lower latencies  and faster event generation rates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Events compactly summarize  information regarding the scene’s high-contrast areas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  Note how the event generation rate depends on the relative  motion between the camera and the scene and structure in  normal illumination conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' For a fixed threshold, C, if  the camera traverses slowly through the environment, the event  generation rate is low, and event data is noisy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' On the other  hand, in highly textured scenes, the event generation rate could  be high at regular speeds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' For specific camera settings, if  the camera moves fast in a textured environment, the event  generation rate eventually reaches the maximum allowable  output bandwidth of the event camera.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  We can benefit from available image-based SLAM algo-  rithms by representing event data as a 2D image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' To produce  the event histogram Ir for a specific event window Wr at  reference time tr, all events in each pixel location are added  Ir(xxx) =  �  eeek∈Wr  pkδ(xxx − xxx′  k),  (2)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='46  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='45  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='44  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='43  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='42  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='41  200  150  250  100  200  150  50  100  50  y  0  0  X180  160  140  120  100  80  60  40  20  0  50  100  150  200  2503  where δ(.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=') is the continuous Dirac’s delta kernel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' It is common  to replace the continuous delta operator with a discrete-time  sampled Gaussian kernel with an arbitrary standard deviation  σI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' The parameter pk can be changed based on event polarity  or set to constant 1 for all events in the window.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  Depending on the camera speed and the length of the  event window, the event histograms may suffer from motion  distortion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' In this case, event coordinates can be corrected  before reconstructing these images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' The resulting image is  called a Motion-Compensated Image or MCI for short.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  For a carefully selected event window, we can mitigate the  motion distortion using a two-dimensional similarity or rigid  body transformation [Sim(2) or SE(2)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Assuming a constant  rotational speed ω and translational speed vvv = (vx, vy) for  each event eeek in the window, the warp  �x′  y′  �  = s  �cos θk  − sin θk  sin θk  cos θk  � �x  y  �  +  �tk,x  tk,y  �  (3)  maps the event location xxx at tk to xxx′ at time tr where θk =  ω∆t, tttk = vvv∆t, s is the arbitrary scale, and ∆t = |tk − tr|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  Event coordinates should be normalized based on the camera  intrinsics beforehand.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  When the relative transform Ttr,tk and the depth Z(xxxk) of  each event in the window are known, a SE(3) mapping can be  used to warp events:  xxx′  k = π0(Ttr,tk[Z(xxxk)π−1  0 (xxxk)]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  (4)  Here π0(.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=') projects the 3D point to the image plane viewed  from the current pose, and π−1  0 (.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=') is its inverse operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' In  this case, we first retrieve the 3D feature point associated with  each event, seen from the current camera position, and map it  to a reference location.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  If we extract feature points from the reference reconstructed  frame and track them across the current image, it is possible to  estimate the parameters of (3) and (4) for all events between  these frames.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' For this, we minimize the reprojection error  between each warped reference feature location xxxi and the  corresponding match xxxj in the current frame using  θθθ∗ = argmin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  θθθ∗  �  i,j∈J  eeeT  ij(xxx)ΩΩΩijeeeij(xxx),  (5)  where θθθ∗ is the transformation parameters, eeeij = xxxi − xxxj,  ΩΩΩij is the information matrix, and J is the set containing all  matched feature pairs between the two frames.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  To use the estimated parameters θθθ∗ to warp events in the  current window, we first convert the relative transform to  speed, ψψψ, using  ψψψ = Log(θθθ∗)  ∆T  ,  where ∆T is the length of the window in units of time and  Log(.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=') is the inverse algebra that maps an element of SE(2)  or SE(3) to a member of the corresponding tangent space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' On  the premise that the camera moves slow enough to assume  constant speed for all events, the unknown transform between  each event location and the reference timestamp, Ttr,tk, is  Ttr,tk = Exp(ψψψ∆t),  where ∆t = |tk − tr| and Exp(.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=') is the exponential map for  the corresponding Lie group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  We also distinguish the notion of an image and a frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  While an image is simply a two-dimensional array of numbers,  a frame consists of other information, including the timestamp,  camera pose, and key points beside the image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  Interested readers can refer to [7] for an in-depth review of  the event generation mechanism and event representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' ALGORITHM  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' 2 illustrates an overview of the proposed event-based  SLAM algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Our pipeline consists of two main compo-  nents, which run concurrently in separate threads.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' The first part  selects an appropriate spatiotemporal window of input events  and reconstructs an image for each event window.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' The second  part of the proposed algorithm extracts features from each  input image and tracks them using the KLT method across  the following frames.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' The 6-DOF pose of the camera is then  estimated, and the local scene is reconstructed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Sections IV-A  and IV-B discuss each component in more detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Event Window Selection and Image Reconstruction  The basic idea of the algorithm is to process events in  small chunks and generate an MCI whenever there are enough  events.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' The algorithm uses two sets of event windows to  select the appropriate window size and reconstruct the MCI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' It  continually tracks and accumulates tiny windows to determine  whether there are enough events.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' It reconstructs the MCI  using the reconstruction window consisting of all previously  collected events.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' 3 illustrates the relationship between the  event stream, tiny windows, and reconstruction windows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  This algorithm first selects a spatiotemporal window of  input events.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Initially, the length of the window, Ne, is selected  arbitrarily and can be adjusted later.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' At this stage, consecutive  event windows have no overlap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' The proper event window size  depends on the event generation rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' As discussed in Section  III, the maximum bandwidth of the event camera limits the  event generation rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' For example, in an event camera with  a bandwidth of 1 million events per second and a resolution  of 240 × 180 pixels, we can expect up to around 23 events  per second per pixel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Thus the minimum event generation rate  can be chosen based on the bandwidth of the event camera,  e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=', one event per pixel per second.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' We select this threshold  solely based on the event camera specifications agnostic to the  camera motion and scene.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  Based on these observations, the event generation rate is  calculated by  r =  Ne  ∆tWH  (6)  where ∆t = teNe −te1 is the difference between the first event  timestamp, te1, and the last timestamp, teNe in the current  window, and W and H are the width and height of the event  image in pixels, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  If the camera does not move fast enough and the event  generation rate is low then the event data will be noisy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' The  algorithm rejects most tiny windows with an event generation  rate less than a threshold, the, and restarts from the initial state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  4  Input Events  Event Window  Selection  Check Event  Rate  Update  Window Size  Reconstruct  & Dispatch  Tiny Frames  Extract  Features  Reconstruct  & Dispatch  MCI  Track (KLT)  Initialize Map  Event Window Selection &  Image Reconstruction  Event-based SLAM  Parameters  & Priors  Map n  Atlas  Feature  Tracks  Feature  Detection  Track Local  Map  Local Mapping  Key Frame  Insertion  Feature Tracking &  Association (KLT)  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' 2: An overview of the proposed event-based SLAM pipeline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' 3: An illustration of the input event stream, tiny event  windows, and non-overlapped reconstruction windows relative  to each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  The only exception is when there are at least Nf frames.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' In this  case, the algorithm restarts after it generates and dispatches the  MCI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  If the event generation rate of the current tiny window is  acceptable, a tiny frame is reconstructed based on (2) without  motion compensation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' The following sections review the main  components of the image reconstruction algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  1) KLT Optical Flow Initialization and Tracking: In each  iteration, the algorithm detects FAST features [17] in the first  tiny frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Since we use image features to determine the  displacement in event locations, fewer features are sufficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  If we cannot detect enough features, this step is repeated with  the subsequent tiny frames;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' otherwise, we proceed to the next  step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  The algorithm then tracks the reference features in the  subsequent frames.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' We can use the feature matches obtained  from the feature tracks for the two-view reconstruction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' The  map initialization algorithm in [2] is used to estimate the  relative pose between the current and the reference frames and  the 3D map points corresponding to the feature matches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Due  to the small baseline between consecutive frames, most scene  reconstruction algorithms cannot yield reliable results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' So, we  relieve some of the stringent conditions in [2], i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=', the best  model does not have to stand out by a large margin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Because  most implementations use the RANSAC method internally,  feature matches are still enhanced despite potential failures in  scene reconstruction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' If a successful reconstruction of the 3D  structure is possible, this information is stored and used in the  MCI reconstruction algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  We define the median feature displacement metric as the  median distance of the tracked image features in pixels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' When-  ever the median feature displacement in the current tiny frame  is higher than a threshold, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=', five pixels, enough events have  been accumulated, and the upcoming MCI reconstruction is  commenced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  Note that depending on the type of the scene, the number of  detected features varies, but the median feature displacement  is not affected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' We select the feature displacement threshold  based on how much distortion we can tolerate in event  locations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' This threshold is constant during the operation of  the algorithm for all scenes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  After the reconstruction and dispatching of the MCI, the  algorithm restarts from the next iteration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Before it begins the  next iteration, it updates the size of the tiny windows, Ne.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' If  Nf is the number of processed frames and Nx is the number  of expected frames per iteration, the new N ∗  e is  N ∗  e =  �NfNe  Nx  �  ,  where ⌊x⌋ is the greatest integer less than or equal x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  In this case, Ne is adjusted according to the camera speed  automatically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' If the camera speed increases, fewer events  satisfy the feature displacement condition, and Ne decreases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  On the other hand, if the camera moves slowly, we need  more events for a defined feature displacement, and Ne  Events  TinyFrames  Reconst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  Frames  W  W  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  W  k-2  k-1  k+15  increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Since we did not assume any scene structure, Ne is  independent of the type of the scene.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  2) Motion Compensated Images: We use different warps  to rectify motion distortion in events coordinates and use (2)  to reconstruct the MCI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' We consider the last event timestamp  as the reference and project preceding events in the forward  direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  If there is a reliable 3D reconstruction, we exploit this  information in (4) to warp the event locations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' As in [10], the  median depth of 3D map points is used for all events in the  window.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Prior to this operation, motion and map parameters  can be enhanced using the Bundle Adjustment (BA) method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  On the other hand, if there exists no initial scene and motion  estimate, but we have tracked the features across several tiny  frames, we can still undistort events using a 2D optimization  scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' In this case, we first fit a Sim(2) or SE(2) motion  model to the feature tracks and then reproject events to the  reference frame according to (3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' We also store this model as  initialization parameters for the subsequent iterations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  In some situations, we only know the relative motion  estimate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' For adequately small motion, we can integrate the  IMU measurements to infer the camera motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' If the camera  moves slow enough, we can also assume a constant speed and  use the motion estimate from the previous iteration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' In either  case, an average scene depth can be estimated using the 3D  motion model of (4) in (5) to minimize the reprojection error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  We run each reconstruction method concurrently in parallel  threads.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Besides the MC images, we reconstruct the event  histogram using (2) with no motion compensation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Finally, we  score each image based on its contrast or sharpness [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' To  measure image sharpness, we first divide each image into non-  overlapped patches and compute the local standard deviation  (STD) for each patch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' We select and dispatch the image with  the highest average local STD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' We choose the local STD  because it yields more stable results than the global STD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  The KLT algorithm has a poor performance when there is  a large baseline between consecutive frames [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Although  there is not much motion between tiny frames, the distance  between the reconstructed frames can be much higher.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' One  way to overcome this issue is to send these frames in addition  to MCIs to the event-based tracking algorithm (Section IV-B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  Another approach to ensure smooth transition between  consecutive MC frames is to overlap the MC windows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Based  on our experiments, this method yields more robust feature  tracking in the second level, and hence, it is our preferred  method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Event-based Localization and Mapping  With the MCI from the previous step, the event-based  localization module follows an image-based KLT optical flow  scheme to estimate the 6-DOF pose of the camera and recon-  struct the scene.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' The basic steps of this algorithm are almost  similar to the reconstruction algorithm discussed in Section  IV-A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  1) Initialization: If there are not enough feature tracks, the  algorithm detects new FAST features in the input MCI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' It  then creates and merges new feature tracks to manage feature  locations across successive images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' We use a bucketing grid  scheme to ensure a uniform distribution of detected features  across images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  The last features are tracked in each subsequent image using  the KLT method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' If the map is not initialized, we use the  two-view reconstruction algorithm between the current and  reference frames to reconstruct the scene and recover the  camera’s relative motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' As in Section IV-A, we use the map  initialization algorithm in [2] for this step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' After a successful  reconstruction, we initialize the map and perform a global  bundle adjustment optimization to enhance the estimate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  2) Tracking The Local Map: Using feature tracks, we can  identify feature associations and the corresponding map points  across different frames.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Therefore, the current pose of the  camera is estimated using an optimization-based framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  To do this, the geometrical distance between the projected map  points in the current frame and the corresponding key point  observations is minimized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  Due to the camera motion, we might lose track of some  features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' In this case, the algorithm fails to track features that  are not visible in the subsequent frames.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  3) Key Frame Insertion and Local Mapping: The algorithm  inserts a new keyframe whenever there is enough baseline  between the current tracked frame and the last keyframe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  We use several heuristics to decide when to spawn a new  keyframe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Whenever the number of tracked map points falls  below a threshold or the median pixel displacement between  key points in the current frame and the preceding keyframe is  greater than a certain limit, a new keyframe is created.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  The local mapping module is very similar to the method  used in ORB-SLAM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' While our algorithm uses the KLT  method to track and associate features, ORB-SLAM detects  new matches with descriptors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  In local mapping, we first cull outlier map points based  on their rate of observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Additional map points are then  triangulated for the new feature matches between the current  and previous keyframes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Finally, a local bundle adjustment  optimization enhances the map point estimates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' IMU Measurements  In this section, the necessary changes to incorporate IMU  measurements are introduced to show how another sensor  module can benefit the proposed algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' The preintegration  theory and the IMU initialization module of [19] and [2] are  used to accomplish this goal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' These changes are as follows:  IMU measurements are integrated between the tiny  frames, the reconstruction frames, and the keyframes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  In the MCI reconstruction module, using the initial pose  from the IMU integrations and feature matches, we first  find the average depth of the scene in the 3D warp  (4) through the optimization framework of (5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' We also  consider IMU biases and the gravity direction as the  state variables in this optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' The initial gravity  direction is evaluated using the first accelerometer reading  for the current iteration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' These parameters are stored for  the subsequent iterations, and the MCI is reconstructed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  We use an inertial bundle adjustment optimization frame-  work in the MCI generation step with a successfully  6  reconstructed scene.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Besides IMU biases and the gravity  direction, we also consider the relative scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  We adapt the inertial local bundle adjustment and the  mechanism of IMU initialization discussed in [2] in the  local mapping algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' In summary, the IMU biases,  the direction of the gravity, and the relative scale are  estimated using an adequate number of keyframes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Such  optimization and scale refinement are repeated for several  predefined periods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' EXPERIMENTS  To evaluate the performance of the proposed pipeline, we  use two publicly available event datasets, the Public Event  Dataset [16] and the Multi-vehicle Stereo Event Dataset [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  The former includes short-duration sequences recorded in  different scenes and challenging conditions by a monocular  240×180 pixel DAVIS device.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' An embedded IMU measures  acceleration and angular velocity along three axes of freedom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  Most sequences include events, intensity images, IMU mea-  surements, and the ground truth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' We only consider the ones  for which both the ground truth and IMU measurements are  available;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' hence we exclude sequences from the “depth” group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  Sequences of [20] are recorded with two similar DAVIS  346×260 pixel cameras attached in the stereo configuration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  It contains events and intensity images for both cameras, IMU  measurements, and the ground truth for the trajectory and  depth maps for each frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' We only use the left camera  and several representative outdoor sequences, noting that the  proposed pipeline is not designed to tackle the stereo case or  track longer outdoor distances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  We use several objective criteria to verify the results of  the proposed algorithm quantitatively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Since our algorithm  generally results in an atlas of multiple disconnected pose  graphs,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' we extend the Relative Pose Error (RPE) in [21] to  average the normalized relative errors as  RPE(θθθ) =  1  |A|  �  G∈A  1  D|G|  �  i,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='j∈G  θθθ(sss(∆T ∗  i,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='j) ⊖ ∆Ti,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='j)  (7)  where A is the set of all pose graphs,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' ∆Ti,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='j = Ti ⊖ Tj  is the relative transform between pairs of SE(3) poses in G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  Ti and Tj,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' ⊖ is the inverse of SE(3) Lie algebra,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' D is the  total traversed distance for the current graph,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' sss() is the scaling  operation for monocular event-only tracking,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' θθθ() returns either  rotational or translational component of error,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' and ∗ indicates  the estimate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' We normalize RPE by the total traversed distance  to reflect the effects of variable length pieces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' For the monoc-  ular event-only configuration, we calculate the unknown scale  by comparing the associated estimate and ground truth pairs  and scale the estimate before computing the average error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  Additionally, we consider measures to assess the stability of  the pipeline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Total traversed distance or time is the sum of all  distances or delta times between consecutive frames in each  pose graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  Before the algorithm processes input events, lens distortions  in event pixel locations are rectified using available calibration  parameters for each sequence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' We choose Nx = 3, and the  initial value of Ne is 2000 events for sequences of [16] and  6000 for [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Since the event frames in [20] have a higher  resolution, a higher value for Ne helps the convergence speed,  though starting from 2000 events should eventually converge  to the optimal value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Motion-compensated windows have 50%  overlap, and Event frames are reconstructed using a Gaussian  kernel with σI = 1 in both tracking levels (tiny frames and  MC images).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' The FAST feature detector threshold is set to  a small amount (around zero) because this setting yields the  most features and allows us to filter them by their response.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  We set the KLT tracker with two pyramid levels, a block size  of 23×23 pixels, and a maximum bidirectional error of one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  These settings are chosen arbitrarily based on our experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  Table I summarizes the evaluation results for event-only  (E-Only) and event-inertial (E-I-C1) sensor configurations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  The stability column of this table is the multiplication of  the total traversed distance in meters and time in seconds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  Although event-only tracking shows similar or superior results  in most cases, the inertial method is more stable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Since more  challenging periods can be tracked in the inertial case, the  errors grow accordingly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Furthermore, because we do not scale  inertial pose graphs, the reported results also include scaling  errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  Besides the challenging conditions of each sequence that  can affect the quality of the event image reconstruction and the  accuracy of pose estimates, we also note two degrading effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  For lower resolution images of [16], the rays connecting the  map points with their respective observations in each frame are  so close that the uncertainty in the depth of the subsequent map  point estimates grows [22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Since our pipeline estimates the  following poses according to the map, the distance between  consecutive poses diminishes, which in turn results in less  accurate map estimates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' This cycle continues until the tracking  is lost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' As discussed in [23], this situation can also happen  for larger images of [20] recorded by the fisheye camera due  to inaccurate translation estimates caused by far map points,  especially for outdoor sequences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  Although in the inertial case, the scale information embed-  ded in IMU readings prevents the shrinking effect, inaccuracies  due to IMU biases can affect map point estimates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' If there  are not enough map points, the following pose and map  point estimates are affected by the growing bias of inertial  measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' In this case, subsequent map point estimates  continue to expand after the insertion of each keyframe until  the tracking is lost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  The inertial configuration discussed in Table I (E-I-C1) still  assumes that the tracking can be lost due to severe conditions,  so it tries to reinitialize the map as soon as possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' To further  assess the limitations of the proposed algorithm and compare  it against the inertial state estimation in [10], we consider two  other configurations (E-I-C2 and E-I-C3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' We configure our  pipeline to enforce continuous tracking without spawning and  initializing new maps in unfavorable conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' In both cases,  we disallow the reinitialization of the map and continue to  estimate 3D points using inertial readings and feature matches  between nearby frames.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' In the last configuration (E-I-C3), we  also fix the tiny event window size to a predefined value and  restrict the withdrawal of noisy frames based on the event  generation rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Table II summarizes our preferences for the  7  TABLE I: Performance evaluation of the proposed algorithm for two event-based configurations compared against the ground  truth for some sequences of [16] and [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  E-Only  E-I-C1  RPE  RPE  RPE  RPE  Dataset  Sequence  Position  Rotation  Stability  Position  Rotation  Stability  (-)  (deg/m)  (×103m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='s)  (-)  (deg/m)  (×103m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='s)  shapes 6dof  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='048  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='209  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='31  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='050  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='114  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='50  shapes translation  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='084  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='186  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='29  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='092  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='169  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='62  Public  poster 6dof  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='017  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='062  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='18  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='018  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='057  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='14  Event  poster translation  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='005  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='006  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='29  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='005  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='006  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='33  [16]  hdr poster  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='011  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='025  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='67  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='002  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='007  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='73  boxes 6dof  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='002  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='004  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='91  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='006  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='008  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='95  boxes translation  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='004  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='004  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='40  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='004  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='004  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='46  hdr boxes  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='004  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='007  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='08  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='004  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='006  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='07  dynamic 6dof  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='019  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='041  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='09  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='032  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='117  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='11  dynamic translation  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='012  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='018  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='24  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='034  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='032  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='38  indoor flying1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='044  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='041  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='12  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='080  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='046  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='34  Multi-  indoor flying2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='041  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='032  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='86  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='029  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='019  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='11  Vehicle  indoor flying3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='018  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='006  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='23  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='029  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='008  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='63  Event  indoor flying4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='038  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='013  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='11  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='038  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='016  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='12  Stereo  outdoor day1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='889  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='033  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='14  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='181  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='041  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='38  [20]  outdoor night1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='678  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='003  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='29  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='131  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='008  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='94  outdoor night3  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='208  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='009  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='04  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='406  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='017  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='95  TABLE II: Fixed tiny event window size specification for each  group of sequences in [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  Sequence  Number of Events  shapes  2000  dynamic  8000  poster  10000  boxes  12000  length of fixed tiny windows for each group of sequences in  [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' We select these values based on our experience of E-I-C1  with variable window sizes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  Table III compares different inertial configurations using  the same RPE metrics of Table I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Both E-I-C2 and E-I-C3  configurations show a significant performance boost to the E-  I-C1 configuration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' In this case, the prolonged tracking period  of E-I-C2 and E-I-C3 configurations provokes more IMU  initialization and refinement steps and improves the accuracy  of the IMU parameters and the whole system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  The last two columns of Table III also investigate the  efficacy of the adaptive selection of the tiny window size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  Although the results are similar in most sequences, noting  that the window length in E-I-C3 is fixed to the optimal  value, a wrongly selected size can impact the performance  and accuracy of the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Therefore, we report the E-I-C2  configuration as our preferred method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  Next, we compare our pipeline against the most relevant  algorithm that provides a stable open-source implementation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  For this reason, we exclude the methods that utilize the  intensity images with the events.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  10  20  30  40  50  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='2  Translation error [m]  E-I [10]  E-I-C2 (Proposed)  shapes_6dof  shapes_translation  poster_translation  hdr_poster  boxes_6dof  boxes_translation  hdr_boxes  dynamic_6dof  dynamic_translation  (a)  10  20  30  40  50  Distance traveled [m]  0  2  4  6  8  10  Yaw error [deg]  (b)  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' 4: The comparison between the proposed algorithm and  the event-inertial method of [10] in terms of the average  relative pose error over a range of distances for the sequences  of [16]: (a) average relative translation error, (b) average  relative yaw error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  8  TABLE III: Comparison of the performance of different inertial configurations of the proposed algorithm for sequences of  [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='E-I-C1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='E-I-C2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='E-I-C3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='RPE  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='RPE  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='RPE  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='RPE  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='RPE  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='RPE  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='Sequence  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='Position  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='Rotation  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='Position  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='Rotation  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='Position  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='Rotation  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='(×10−3)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='(×10−3 deg/m)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='(×10−3)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='(×10−3 deg/m)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='(×10−3)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='(×10−3 deg/m)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='shapes 6dof  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='50  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='114  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='shapes translation  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='92  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='169  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='poster 6dof  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='18  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='57  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='poster translation  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='hdr poster  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='boxes 6dof  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='boxes translation  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='hdr boxes  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='dynamic 6dof  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='32  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='117  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='dynamic translation  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='34  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='32  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' 4 contrasts the E-I-C2 configuration of the proposed  algorithm against the event-inertial method in [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' We run  the latest open-source release of their algorithm1 for each  sequence in [16] using the default configurations (the sequence  poster 6dof is excluded because this implementation of [10]  fails to produce reliable results).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Similar to [10], we measure  and report the average relative translation and yaw error over a  range of distances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' We calculate the relative pose error between  the first one hundred pairs that meet a specific distance range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  Although the window-based state estimator of [10] estimates  the pose of the camera and map points simultaneously, our  algorithm relies on an accurate map to find the next pose.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' As  a result, any condition that degrades map estimate accuracy  will affect our results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' For the sequence shapes 6dof, when  the camera moves fast in front of a low-textured poster,  the tracking fails due to the lack of detected features, and  errors grow exponentially.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Even though the scene in sequence  dynamic 6dof is textured, the change in 3D feature locations  affects the performance of the proposed method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Despite  the poor lighting condition in boxes 6dof, there are enough  reliable map points, and the proposed algorithm outperforms  the state-of-the-art based on the translation errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  Based on our experiments, while the state estimator of  [10] can produce more accurate results locally, the proposed  algorithm can outperform over longer distances as long as the  map estimates are reliable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' As mentioned before, when the  map estimates are valid, it will affect the subsequent pose  estimates even when some map points are no longer visible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  Consequently, although the results are not explicitly shown  here, we claim that the proposed pipeline can reduce the  absolute pose error (APE) when these conditions are met.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' 5 compares the absolute estimated position of the  results of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' 4 for the sequence boxes 6dof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' We use the  APE tools in [2] to align the first 15 seconds of the estimates  with the ground truth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' In this case, the proposed method can  track the ground truth more accurately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  1https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='com/uzh-rpg/rpg ultimate slam open  X  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='8  Y  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='9  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='3  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='4  Z  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='3  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='7  GT  E-I-C2 (Proposed)  E-I [10]  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' 5: The absolute estimated positions of the proposed  algorithm and the event-inertial method of [10] are compared  against the ground truth in terms of the APE for the first 15  seconds of the sequence boxes 6dof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  Although we have not tried to optimize the performance of  the proposed algorithm, we present the average tracking time  statistics to contrast the computation cost of each module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' In  particular, we measure and report the performance of the main  tracking thread (MTH), the first-level event image reconstruc-  tion module (L1), and the second-level event frame tracking  thread (L2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Since it almost takes several tiny frames in L1  and one iteration of L2 for the main tracking thread to process  input events, we include the timing as per motion-compensated  frames (MCF) and as per tiny frame (TF).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Assuming there are  three TF for each MCF on average, we subtract double L1  values from the MCF results and report the per TF results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' The  timing statistics for the local mapping thread are not reported  here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' We run our pipeline on a system with an Intel Core-i7  9700K CPU, 64 GB RAM, and Ubuntu 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='04 LTS operating  system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  Table IV summarizes the timing results of different compo-  nents of our pipeline for two sensor configurations and some  9  TABLE IV: Average tracking time statistics in milliseconds for three main modules of the proposed algorithm, calculated for  representative sequences of [16] and [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='Event-Only  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='Event-Inertial-C1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='MTH  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='MTH  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='L1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='L2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='MTH  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='MTH  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='L1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='L2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='Sequence  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='/MCF  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='/TF  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='/TF  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='/TF  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='/MCF  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='/TF  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='/TF  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='/TF  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='shapes 6dof  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='72  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='48  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='82  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='56  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='poster 6dof  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='158  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='106  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='26  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='173  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='119  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='boxes 6dof  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='158  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='106  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='26  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='174  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='118  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='dynamic 6dof  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='138  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='92  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='157  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='107  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='indoor flying1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='139  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='93  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='147  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='99  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='24  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='outdoor day1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='171  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='115  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='185  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='127  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='outdoor night1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='187  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='125  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='31  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='202  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='138  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='32  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='representative sequences of both datasets [16] and [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' The  overall performance of our algorithm is several times lower  than the real-time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Note that more textured sequences demand  more processing power.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' The addition of the IMU slightly  increases the performance cost of our method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Based on these  results, the reconstruction of each MCF is generally the most  costly operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' It takes about the same amount of time to  reconstruct an MCF, around 28 ms on average, consistent  across all configurations and datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' The timing results of  L2 are only comparable across the Public Event dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' For  sequences of [20], the cost of the inertial L2 module is almost  twice the performance of the event-only case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' One reason for  this difference could be the high depth variation inherent in  the fisheye camera and the difficulty of scale estimation and  refinement involved in inertial tracking in this case (although  the local mapping is performed in a separate thread, the inertial  L2 must wait because of the map change).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' CONCLUSION  We proposed an algorithm that reconstructs MC images  from the adaptively selected event windows and uses the event  images to estimate the structure and trajectory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' The first mod-  ule tracks FAST features across multiple event histograms to  choose the best event window size and resolve the parameters  needed for MCI generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' After reconstruction, it sends the  best MCI representation to an image-based SLAM to initialize  the map and track the 6-DOF pose of the camera in it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  Furthermore, we showed how to utilize inertial measurements  to improve the performance of the event-only algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  We compared the estimated trajectory of different config-  urations of the proposed pipeline with the ground truth for  sequences of two publicly available event datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Although  the algorithm produces accurate results in most cases, its  performance depends on the reliability of the map estimate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  We also showed that the proposed algorithm outperforms the  state-of-the-art as long as a valid map estimate is available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  Although the event window selection module is costly, it  can still be used in most event-based algorithms to select  the best event window without reconstructing the MCI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' It is  possible to use different techniques such as relocalization or  loop-closing to improve the accuracy of the map, the overall  performance, and the algorithm’s stability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' These techniques  generally extract and use descriptors to link different segments  of a pose graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' One can consider event-based descriptors  for that purpose or extract descriptors from regular intensity  images, which are processed along with the event stream.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  REFERENCES  [1] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Klein and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Murray, “Parallel tracking and mapping for small ar  workspaces,” in 2007 6th IEEE and ACM International Symposium on  Mixed and Augmented Reality, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' 225–234, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  [2] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Mur-Artal, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Montiel, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Tardos, “ORB-SLAM: A  versatile and accurate monocular SLAM system,” IEEE Transactions  on Robotics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' 31, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' 5, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' 1147–1163, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  [3] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Lichtsteiner, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Posch, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Delbruck, “A 128×128 120 db 15 µs  latency asynchronous temporal contrast vision sensor,” IEEE Journal of  Solid-State Circuits, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' 43, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' 566–576, 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  [4] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Campos, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Elvira, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Rodr´ıguez, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Montiel, and  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Tard´os, “ORB-SLAM3: An accurate open-source library for visual,  visual–inertial, and multimap SLAM,” IEEE Transactions on Robotics,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' 37, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' 6, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' 1874–1890, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  [5] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Qin, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Li, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Shen, “VINS-Mono: A robust and versatile monoc-  ular visual-inertial state estimator,” IEEE Transactions on Robotics,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' 34, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' 4, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' 1004–1020, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  [6] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Qin, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Pan, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Cao, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Shen, “A general optimization-based  framework for local odometry estimation with multiple sensors,” 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  [7] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Gallego, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Delbr¨uck, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Orchard, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Bartolozzi, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Taba, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Censi,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Leutenegger, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Davison, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Conradt, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Daniilidis, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Scara-  muzza, “Event-based vision: A survey,” IEEE Transactions on Pattern  Analysis and Machine Intelligence, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' 44, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' 154–180, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  [8] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Gallego and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Scaramuzza, “Accurate angular velocity estimation  with an event camera,” IEEE Robotics and Automation Letters, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' 2,  no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' 632–639, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  [9] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Mueggler, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Gallego, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Scaramuzza, “Continuous-time trajec-  tory estimation for event-based vision sensors,” in Robotics: Science and  Systems, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  [10] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Vidal, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Rebecq, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Horstschaefer, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Scaramuzza, “Ultimate  SLAM?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' combining events, images, and IMU for robust visual SLAM in  HDR and high-speed scenarios,” IEEE Robotics and Automation Letters,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' 3, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' 994–1001, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  [11] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Kim, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Handa, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Benosman, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Ieng, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Davison, “Simul-  taneous mosaicing and tracking with an event camera,” in Proceedings  of the British Machine Vision Conference, BMVA Press, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  [12] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Henri Rebecq and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Scaramuzza, “Real-time visual-inertial odom-  etry for event cameras using keyframe-based nonlinear optimization,” in  Proceedings of the British Machine Vision Conference (BMVC) (G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  Tae-Kyun Kim, Stefanos Zafeiriou and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Mikolajczyk, eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' ), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='1–  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='12, BMVA Press, September 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  [13] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Lucas and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Kanade, “An iterative image registration technique  with an application to stereo vision,” in Proceedings of the 7th Inter-  national Joint Conference on Artificial Intelligence, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' 2 of IJCAI’81,  p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' 674–679, Morgan Kaufmann Publishers Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=', 1981.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  [14] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Zhu, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Atanasov, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Daniilidis, “Event-based visual inertial  odometry,” in 2017 IEEE Conference on Computer Vision and Pattern  Recognition (CVPR), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' 5816–5824, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  10  [15] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Kannala and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Brandt, “A generic camera model and calibration  method for conventional, wide-angle, and fish-eye lenses,” IEEE Trans-  actions on Pattern Analysis and Machine Intelligence, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' 28, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' 8,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' 1335–1340, 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  [16] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Mueggler, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Rebecq, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Gallego, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Delbruck, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Scaramuzza,  “The event-camera dataset and simulator: Event-based data for pose  estimation, visual odometry, and SLAM,” The International Journal of  Robotics Research, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' 36, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' 2, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' 142–149, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  [17] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Wyatt and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Nakai, “Fast feature extraction using approximations to  derivatives with summed-area images,” in Proceedings of the 7th Asian  Conference on Computer Vision - Volume Part I, ACCV’06, (Berlin,  Heidelberg), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' 776–786, Springer-Verlag, 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  [18] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Gallego, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Rebecq, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Scaramuzza, “A unifying contrast  maximization framework for event cameras, with applications to motion,  depth, and optical flow estimation,” 2018 IEEE/CVF Conference on  Computer Vision and Pattern Recognition, Jun 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  [19] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Forster, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Carlone, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Dellaert, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Scaramuzza, “On-manifold  preintegration for real-time visual–inertial odometry,” IEEE Transactions  on Robotics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' 33, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' 1, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' 1–21, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  [20] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Zhu, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Thakur, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Ozaslan, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Pfrommer, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Kumar, and  K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Daniilidis, “The multivehicle stereo event camera dataset: An event  camera dataset for 3D perception,” IEEE Robotics and Automation  Letters, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' 3, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' 3, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' 2032–2039, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  [21] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Sturm, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Engelhard, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Endres, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Burgard, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Cremers, “A  benchmark for the evaluation of RGB-D SLAM Systems,” in Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' of  the International Conference on Intelligent Robot Systems (IROS), Oct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  [22] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Zisserman, Multiple View Geometry in Computer Vision, 2nd  Edition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' 2 ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=', 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  [23] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Mur-Artal and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Tard´os, “ORB-SLAM2: an open-source SLAM  system for monocular, stereo and RGB-D cameras,” IEEE Transactions  on Robotics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' 33, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' 5, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' 1255–1262, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content='  [24] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Geiger, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Lenz, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' Urtasun, “Are we ready for autonomous  driving?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
+page_content=' the KITTI vision benchmark suite,” in Conference on Computer  Vision and Pattern Recognition (CVPR), 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAyT4oBgHgl3EQfuvlU/content/2301.00618v1.pdf'}
diff --git a/VdAzT4oBgHgl3EQf1P6v/content/tmp_files/2301.01797v1.pdf.txt b/VdAzT4oBgHgl3EQf1P6v/content/tmp_files/2301.01797v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..8d18cf9ac8242eaf216363273ebf033ad74a8a8e
--- /dev/null
+++ b/VdAzT4oBgHgl3EQf1P6v/content/tmp_files/2301.01797v1.pdf.txt
@@ -0,0 +1,661 @@
+Dynamics of Argon Gas Bubbles Rising in Liquid Steel in the
+Presence of Transverse Magnetic Field
+Purushotam Kumar∗1 and Surya P. Vanka†2
+1Corning Incorporated, Manufacturing Technology & Engineering, Corning, NY 14830
+2Mechanical Science & Engineering, University of Illinois Urbana-Champaign, Urbana, IL
+61801
+January 6, 2023
+Abstract
+Bubbly flows are present in various industrial processes including metallurgical processes in
+which gas bubbles are injected at the bottom of bulk liquid metal to stir the liquid metal and
+homogenize the metal. Understanding the motion of such bubbles is essential, as it has been
+shown that bubble flotation can remove inclusions. In this work, we have numerically studied
+three-dimensional dynamics of a pair of inline Argon bubbles rising in molten steel under the
+influence of a transverse magnetic field. We have explored the effects of two transverse magnetic
+field strengths (Bx = 0 and 0.2 T). The bubbles’ motion and transient rise velocities are compared
+under different magnetic fields. The shape deformations and path of the bubbles are discussed.
+The flow structures behind the bubbles are analyzed. We found that structures are more organized
+and elongated under a magnetic field, whereas it is complex and intertwined when the magnetic
+field is not included. We have used a geometry construction-based volume of fluid (VOF) method
+to track interface, maintain mass balance and estimate the interface curvature. Additionally, we
+have incorporated a Sharp Surface Force Method (SSF) for surface tension forces. The algorithm
+is able to minimize the spurious velocities.
+Keywords: bubble dynamics; magneto convection; vortex interactions; bubble interactions; Volume
+of fluid (VOF) method; share surface force
+1
+INTRODUCTION
+Bubbly flows are encountered in various industrial processes and everyday life. To mix and homog-
+enize the metal in metallurgical processes, gas bubbles are injected at the bottom of bulk liquid
+metal to stir the liquid metal. In the process for continuous casting of steel, which is widely used
+∗pkumar8@illinois.edu
+†spvanka@illinois.edu
+1
+arXiv:2301.01797v1  [physics.flu-dyn]  4 Jan 2023
+
+for steel making, Argon bubbles are commonly injected during the casting process. Understanding
+the motion of such argon bubbles is essential as it has been shown that bubble flotation can remove
+inclusions. In addition, in order to improve the product quality frequently an external magnetic field
+is applied to control the fluid motion and bubble behavior. In the past several decades, numerous
+theoretical, experimental, and computational studies have been carried out on the dynamics of a
+rising bubble in transparent liquids (such as water and oils). However, only a few studies have been
+reported on bubble motion in liquids when subjected to an external magnetic field.
+Dynamics of a rising bubble are a function of the Eötvös number (Eo = ∆ρgd2σ−1, also referred
+as Bond number Bo = ρlgd2σ−1), Morton number (Mo = gµ4
+oρ−1
+l
+σ−3), confinement ratio (Cr =
+Wd−1), Hartmann number Ha = Bd
+�
+σ/µl (Jin et al., 2016; Kumar et al., 2015a). An exhaustive
+collection of experimental data for a bubble rising in an unconfined medium has been summarized
+in works of Grace (1973); Grace et al. (1976); Bhaga and Weber (1981), available as nomogram
+charts of the terminal Reynolds and bubble shape for combinations of Bond and Morton numbers.
+In addition, the proximity of the bubble to a wall alters the bubble rise velocity and shape and
+increases the shear force at the gas-liquid interface Figueroa-Espinoza et al. (2008); Kumar and
+Vanka (2015). Detailed reviews of bubble dynamics in Newtonian fluids are available in the works
+of Clift et al. (1978); DeKee (2002).
+The dynamics of multiple bubbles rising in Newtonian fluids without magnetic field has been studied
+by several authors (Abbassi et al., 2018; Gumulya et al., 2017; Watanabe and Sanada, 2006; Yuan
+and Prosperetti, 1994; Legendre et al., 2003; Yu et al., 2011; Katz and Meneveau, 1996; Ruzicka,
+2000) and have reported that flow structure around the bubble has an important impact on the
+interaction between leading and trailing bubbles. They have reported that wake in front of a trailing
+bubble plays an important role in reducing the drag around it. Due to reduced drag, the trailing
+bubble accelerates until it coalesces with the leading bubble.
+In the present paper, we have briefly discussed a numerical technique to simulate two-phase flows and
+used it to study the three-dimensional deformation and rise of two equally sized bubbles in molten
+steel under the influence of a transverse magnetic field for a given bubble size and center to center
+distance. Various quantities such as the bubble shape, rise velocity, and rise paths are investigated.
+The algorithm used for the computations is presented in the numerical method section. The problem
+description is provided in the computational details section. In the results and discussion section,
+we present the results of the simulations and discuss the critical findings. A summary of the present
+findings is given at the end.
+2
+
+2
+Problem Setup
+We consider a pair of deformable Argon bubbles rising in a rectangular column filled with liquid
+steel. The initial size (d) and shape of both bubbles are identical and spherical, and the initial
+distance between their centers (h) is adjusted. The trailing bubble is initially placed two diameters
+above the bottom boundary at the center of duct cross-section, and the leading bubble is placed
+at center to center distance of h. Both fluids (liquid in the column and bubbles) are stationary at
+the beginning of solution procedure. A constant transverse magnetic field of a given strength (Bx)
+is applied in the x− direction. The gravitational force acts downward along the negative z−axis.
+We have considered a three-dimensional domain of 4d × 4d × 24d along x, y and z directions with
+all boundaries of the domain to be no-slip, no-penetration and non-conductive walls. Based on a
+systematic grid refinement study, we have selected 32 control volumes per bubble diameter as an
+adequate resolution, with a grid of 128×128×768 (≈ 13 million) control volumes for current study.
+Figure 1 shows sketch of the computational domain.
+Fig. 1: Initial position of bubbles in liquid column
+Material properties for steel and Argon are taken as density: 7000 and 0.56 kg/m3, viscosity:
+6.3×10−3 and 7.42×10−5Pa s, and electrical conductivity: 714000 and 10−15 1/(Ω s). The surface
+tension (γ) is prescribed a value of 1.2 N/m.
+3
+Numerical method
+Governing equations
+We have used continuity, momentum and electromagnetic equations given by eq.(1), (2), and (3)-
+(4), to simulate bubble dynamics. We assumed the flow to be incompressible and isothermal (ignore
+3
+
+H
+g
+Z
+h
+x
+W
+Wany heat generation due to viscous dissipation or eddy currents).
+∇ · u = 0
+(1)
+∂ (ρu)
+∂t
++ ∇ · (ρuu) = −∇p + ∇ ·
+�
+µ
+�
+∇u + ∇uT ��
++ ρg + γκnδ (x − xf) + FL
+(2)
+J = σ (−∇Φ + u × B)
+(3)
+∇ · (σ∇Φ) = ∇ · [σ (u × B)]
+(4)
+In the above equations, u is fluid velocity, p is pressure, ρ is density, µ is dynamic viscosity, γ is
+surface tension coefficient, κ is interface curvature, n is interface normal, δ is the delta function, x is
+the spatial location where the equation is solved, xf is the position of the interface, g is acceleration
+due to gravity, J is electrical current density, B is external magnetic field, Φ is electric potential,
+and σ is electrical conductivity.
+FL is the Lorentz force and calculated as FL = J × B, the electrical current density J is calculated
+from Ohm’s law as given by eq. (3) and the electric potential (Φ) is calculated from the eq. (4).
+We also solve an equation to enforce divergence free condition (∇ · J = 0) for the current density
+and maintain the conservative properties of charge.
+The liquid and gas distribution is distinguished by liquid volume fraction (α). We solve an advection
+equation of α given by eq. (5) to capture the movement of interface between two fluids.
+∂α
+∂t + u · ∇α = 0
+(5)
+We use the linear weighting of the liquid volume fraction to calculate the mixture density, viscosity
+and electrical conductivity as,
+ρ = αρl + (1 − α)ρg
+(6)
+µ = αµl + (1 − α)µg
+(7)
+σ = ασl + (1 − α)σg
+(8)
+The subscripts l and g denote gas and liquid phases respectively.
+Solution procedure
+The accuracy and speed of a multiphase algorithm is dependent on methods to track the interface,
+model surface tension force, reduce momentum imbalance across the interface, handle property
+discontinuity, etc. In our current numerical procedure, we have used the geometry construction
+method Rider and Kothe (1998) to represent the interface inside a cell and to calculate volume
+fraction fluxes at the cell faces. The interface normals are calculated from α using second-order
+4
+
+central differencing scheme for derivatives. The second order operator split method of Noh and
+Woodward (1976); Li (1995); Ashgriz and Poo (1991) is used for solution of the VOF equation.
+Here, the advection along one direction (x, y or z) is done as a first step then the advection
+along remaining two directions are performed.
+We rotate the order of advection to reduce any
+directionally-biased errors introduced due to operator splitting approach. The advection term in
+the momentum equation (eq. (2)) is also calculated geometrically is ensure consistency between
+volume fraction and momentum advections. Kumar (2016); Kumar et al. (2015b) have provided
+more details about challenges and mitigation associated with implementation geometry construction
+method in three-dimensions.
+The γκnδ (x − xf) term in eq. (2) represents the surface tension force at the interface with γκ as
+the Laplace pressure jump. In our current algorithm, we have used the Sharp Surface Force (SSF)
+(Francois et al., 2006; Wang and Tong, 2008; Kumar et al., 2019) method to model the surface
+tension term in the Navier-Stokes equation. Here, the surface tension term is written as a pressure
+gradient term given by,
+γκnδ (x − xf) = −∇˜p
+(9)
+where ˜p is the pressure solely due to the surface tension force at the interface. We obtain a Poisson
+equation for ˜p from continuity and momentum equations,
+∇ ·
+�∇˜p
+ρ
+�
+= 0
+(10)
+The jump condition at the interface given by eq.(9) is used in the solution of eq.(10). This ensures
+the exact difference in pressure at the interface due to the surface tension. Using this method the
+spurious velocities are seen to reduce to machine zero for a static bubble with exact analytical
+curvature and to very small values when the curvature is numerically computed. We have used
+the height function method of Rudman (1998); Cummins et al. (2005) for curvature estimation.
+Admittedly, there are several methods to include the surface tension force in the Navier-stokes
+(Renardy and Renardy Renardy and Renardy (2002), Sussman et al. Sussman (2003); Sussman
+et al. (2007), Gueyffier et al.
+Gueyffier et al. (1999)), however, in our experience the current
+method is more accurate for reduction of spurious velocities and relatively easier to implement on
+GPUs.
+The momentum and continuity equations are discretized on a collocated Cartesian grid using a finite
+volume method. The terms in the momentum equation are integrated with a second-order accurate
+in time and space using Adams–Bashforth time advancement. The convection term(∇ · ρuu) is
+computed geometrically with linear interpolation for the face velocity. The pressure gradient term
+is written at cell faces and in the form of ∇p
+ρ . Coupling the pressure gradient and density together
+eliminates any ambiguity in density interpolation and leads to a robust method. The viscous term is
+5
+
+computed by second order central differencing scheme. Linear interpolation is used for face densities
+and viscosities.
+The electromagnetic equations given by eq. (3) and (4) are solved on the same grid as used for con-
+tinuity and momentum equations. The magnetic field strength (B), electric potential (Φ), current
+density (J) and thermal conductivity (σ) are stored at the cell centers and calculated at cell faces
+using linear averaging scheme.
+We solve three Poisson equations: pressure (p), surface tension pressure (˜p) and electric potential
+(Φ) in this numerical approach. These equations are efficiently solved using a geometric multigrid
+accelerated red black SOR relaxation scheme.
+All boundaries of the domain are considered wall, therefore no-slip, no-penetration and non-conducting
+boundary conditions are applied at them.
+uwall = vwall = wwall = 0
+(11)
+� ∂p
+∂ˆn
+�
+wall
+=
+� ∂˜p
+∂ˆn
+�
+wall
+= 0
+(12)
+Jwall = Jwall = Jwall = 0
+(13)
+�∂Φ
+∂ˆn
+�
+wall
+= 0
+(14)
+We have implemented this algorithm to run on multiple graphics processing units (GPU). We
+have used the CUDA-Fortran platform supported by the Portland group (PGI) Fortran compilers.
+Previously, we have validated the multiple GPU implementation (Kumar et al., 2015b; Vanka et al.,
+2016; Kumar, 2016) to study confinement effects on bubble dynamics (Kumar and Vanka, 2015),
+two-phase flows at T-juctions (Horwitz et al., 2012, 2013; Kumar et al., 2013), bubble dynamics in
+non-Newtonain fluids (Kumar et al., 2015a, 2019), droplet dynamics in square duct (Horwitz et al.,
+2014, 2019), Argon bubble rising in liquid steel (Vanka et al., 2015; Jin et al., 2016; Kumar and
+Vanka, 2022) and turbulent bubbly flow (Vanka et al., 2016; Kumar and Vanka, 2021).
+From analysis of the governing equations, we have identified that the dynamics of bubbles rising in
+a confined conducting liquid medium depends on these non-dimensional parameters.
+Bond number = Bo = ρlgd2/γ
+(15)
+Morton number = Mo = gµ4
+l /ρlγ3
+(16)
+Hartmann number = Ha = Bd
+�
+σ/µl
+(17)
+Confinement ratio = Cr = W/d
+(18)
+center to center distance = hd = h/d
+(19)
+6
+
+Grid refinement study
+We have conducted a systematic grid refinement study to understand the impact of grid size on
+the bubbles’ dynamics.
+For this grid refinement study, we have considered three grids namely:
+coarse (∆x = d/16 : 64 × 64 × 384), fine (∆x = d/32 : 128 × 128 × 768), and finer (∆x = d/64 :
+256 × 256 × 1536), and have analyzed the bubbles’ rise velocity and shapes for both leading and
+trailing bubbles.
+(a) Rise velocity of leading bubble
+(b) Rise velocity of trailing bubble
+Fig. 2: Rise velocity of leading and trailing bubbles for three grid sizes
+Figure 2 shows the rise velocities of the leading and trailing bubbles for three different grids. It
+can be noticed from the figure that both bubbles initially accelerate with faster rate then slows
+down to reach a steady state. For the total simulation time considered in this study, we notice that
+the leading bubble reach a steady state, however trailing bubble continues to accelerate. Further,
+we can observe that rise velocities of both leading and trailing bubbles for three grids are almost
+identical up to 15 ms and diverges afterwards. The velocities predicted on coarse grid is the lowest
+and increases with grid refinement. For leading bubble, rise velocities are 0.2848, 0.3434, and 0.3581
+m/s at t = 0.08 ms, for δx = 1/16, 1/32, and 1/64 grids respectively. The difference in rise velocities
+between finer and fine meshes is 4.1% and between finer and coarse meshes is 20.5%. Similarly, for
+trailing bubble, rise velocities are 0.2931, 0.3557, and 0.3654 m/s at t = 0.08 ms, for δx = 1/16,
+1/32, and 1/64 grids respectively. The difference in rise velocities between finer and fine meshes is
+2.6% and between finer and coarse meshes is 19.8%.
+Figure 3 shows the bubble shape on the central plane of the domain at a time when they leading
+7
+
+0.4
+0.3
+wb [m/s]
+0.2
+0.1
+LB, dx = 1/16
+LB, dx = 1/32
+LB, dx = 1/64
+0.02
+0.04
+0.06
+0.08
+time [s]0.4
+0.3
+wb [m/s]
+0.2
+0.1
+TB, dx = 1/16
+TB, dx = 1/32
+TB, dx = 1/64
+0.02
+0.04
+0.06
+0.08
+time [s](a) Shape of leading bubble
+(b) Shape of trailing bubble
+Fig. 3: Shape of leading and trailing bubbles for three grid sizes
+bubbles have reached steady state. For better comparison of the results, we have aligned bubble
+tops for all three grids. It can be noticed that bubbles become flatter as we refined the mesh, and
+∆x = 1/16 grid predicts largest height and smallest width for both leading and trailing bubbles.
+Both height and width converged as we refined the grid to ∆ = 1/32 and 1/64 with very small
+difference between fine and finer grids.
+From rise velocity and shape comparisons for three grids, we decided to use ∆x = 1/32 as a suitable
+grid that can give accurate result with moderate computational cost. The results discussed from
+here onward will be on fine (∆x = d/32 : 128 × 128 × 768) grid.
+4
+RESULTS AND DISCUSSION
+We now present the results of a study to analyze the effects of transverse magnetic field on the
+bubble deformation, rise velocity, rise path, and vortex shedding. We have considered bubbles of
+diameter 7 mm with the leading bubble placed 3 diameters above the trailing one, and have used
+two magnetic fields (0 and 0.2 T) to understand their effects. For these set of conditions, the key
+non-dimensional parameters are Bo = 2.8, Mo = 1.2 × 10−12, Cr = 4, hd = 3 and Ha = 14.9. It
+should be noted that the bubbles are initially placed at the center of cross-section, but they may
+come closer to the wall during their ascend. Hence, instantaneous confinement ratio is likely to
+change.
+We first look at the transient shapes of the bubbles as they travel upward. According to the Grace
+diagram Grace (1973), an initially spherical bubble of Bo = 2.8 rising in a liquid medium of Mo =
+8
+
+0.028
+dx=16-LB
+dx=32-LB
+0.0275
+dx=64-LB
+0.027
+0.0265
+0.026
+0.0255
+0.025
+0.0245
+0.004
+0.005
+0.006
+0.007
+0.008
+y0.013
+dx=16-TB
+dx=32-TB
+dx=64-TB
+0.012
+0.011
+0.01
+0.004
+0.005
+0.006
+0.007
+0.008
+y1.2×10−12 deforms into a flatter ellipsoidal shape with minimum surface oscillations. In our current
+consideration, due to additional forces introduced by magnetic field, bubbles’ dynamics (including
+shape and trajectory) are expected to be different.
+time (ms)
+B
+0
+80
+160
+240
+320
+0
+LB
+0
+TB
+0.2
+LB
+0.2
+TB
+Fig. 4: Transient three-dimensional front views of the bubbles for two magnetic fields
+Figure 4 shows the transient shapes of leading (LB) and trailing (TB) bubbles for B = 0 and 0.2.
+In absence of magnetic field, the leading bubble deforms from a spherical shape to an ellipsoidal
+shape with asymmetrical top and bottom surfaces by 80 ms and remains ellipsoidal for remaining of
+the simulation time. We can notice that for up to 160 ms, bubble’s major axes are horizontal and
+transitions to side-to-side oscillations (wobbling) between 160 - 240 ms. The trailing bubble also
+goes through similar transition from spherical to ellipsoidal by 80 ms, however it continues to deform
+afterwards. Shape oscillations of upper and lower surfaces: flatter-upper-surface (80 ms), rounder-
+upper-surface (160 ms), bulged-upper-surface (240 ms) to irregular upper surface afterwards.
+In the presence of magnetic field, deformation of both leading and trailing bubbles are less pro-
+nounced than in the absence of magnetic field, however the trailing bubble still goes through more
+deformation than the leading one. We can notice that leading bubble reached a steady-state shape
+by 80 ms and did not go through shape oscillations or wobble motion. The trailing bubble, however,
+continued to deform after 80 ms and did not achieve a steady-state shape for the time considered
+here.
+9
+
+Fig. 5: Rise velocity of leading and trailing bubbles for two magnetic fields
+Figure 5 shows the rise velocities of leading and trailing bubbles. Starting from stationary, rise
+velocity increases with time to go through fluctuations either to reach a steady state or continue to
+increase with time. The behavior of leading and trailing bubbles’ rise velocities are different and
+also depends on the applied magnetic field. In the absence of magnetic field, rise velocities of both
+leading and trailing bubbles are identical for up to t ≈ 75 ms. We can notice that the rise velocity
+of the leading bubble goes through rapid oscillations with the magnitude of oscillation is less than
+0.01m/s. It should also be noted that the mean velocity of leading bubble is almost unchanged
+after t ≈ 75 ms. On the other hand, the trailing bubble continues to accelerate for the total time
+considered in this study. Additionally, the trailing bubble’s rise velocity is always higher than that
+of the leading bubble.
+In the presence of a magnetic field, rise velocities of bubbles are identical for up to t ≈ 80 ms,
+and afterward, the curves diverge. Velocity of the leading bubble after 80 ms increases very slowly
+compared to before t = 80 ms and reaches almost a steady-state. On the other hand, trailing
+bubble continues to accelerate, although with smaller rate than initial acceleration, to achieve a
+higher velocity than the leading bubble. Comparing these curves, it is evident that the rise velocity
+and their oscillations in the presence of a magnetic field decreases.
+10
+
+0.45
+0.40
+0.35
+0.30
+Wb [m/s]
+0.25
+0.20
+0.15
+TB. h/d = 3. Bx = 0.0
+0.10
+LB. h/d = 3. Bx = 0.0
+TB. h/d = 3. Bx = 0.2
+LB, h/d = 3, Bx = 0.2
+0.05
+0.00
+0.00
+0.05
+0.10
+0.15
+0.20
+0.25
+time [s](a) B = 0
+(b) B = 0.2
+Fig. 6: Rise paths of leading and trailing bubbles for two magnetic fields
+Figure 6 shows the trajectory of leading and trailing bubbles as they ascend – red and black curves
+represent trajectories of trailing and leading bubbles, respectively. It can be noticed that in the
+absence of magnetic field both bubbles initially follow rectilinear paths turning into zigzags. Further,
+the trailing bubble deviates from rectilinear path earlier than the leading bubble. At the outset
+of ascend, trailing bubble has a smaller velocity and is away from the flow field modified by the
+leading bubble, therefore trailing bubble’s shape changes from the spherical to asymmetric ellipsoid
+and does not exhibit surface oscillations. This is the primary reason for the initial rectilinear path
+of the bubble. As bubbles accelerate and reach a certain critical speed (or Reynold number), they
+start to shed symmetric vortices which later grows into asymmetric. This leads to a non-uniform
+pressure distribution behind the bubble, which pushes bubbles away from liquid column’s center
+and migrates into a zigzag trajectory.
+When the magnetic field is included, both bubbles rise in the rectilinear paths for a longer time;
+however, towards the end of the simulation, they start to deviate and could potentially migrate
+into zigzag paths. This is in line with our observations from Fig. 4, the bubble reached a steady
+shape without any shape or orientation oscillations. To further understand the zigzag rise path and
+oscillatory rise velocity, we analyze the flow structures behind the bubbles.
+11
+
+(a) B = 0
+(b) B = 0.2
+Fig. 7: Iso-surfaces of ωz = ±25 at t = 240 ms for two magnetic fields
+Figure 7 shows the front view of the iso-surfaces of ωz at t = 240 ms (The blue and yellow represents
+iso-surfaces of ωz = 25 and ωz = −25 respectively). We can notice long elongated wake structures
+behind the bubbles with “tail-like” shape. In absence of the magnetic field, these structures are flatter
+and entangled which shows that these counter-rotating vortices are interacting with each other and
+can disintegrate into smaller vortical structures. We can further notice non-uniform vortex shed
+from the leading bubble – potentially modifying the flow-field observed by the trailing bubble.
+This explains why rise path of trailing bubble deviates from rectilinear trajectory earlier than the
+leading bubble. In presence of the magnetic field, we notice symmetrical and more organized vortex
+shedding from the leading bubble.
+These structures interact and surround the trailing bubble,
+however, symmetry of the flow structures remain intact. The vortex shedding from both leading
+and trailing bubbles applies lateral forces on them and can push them away from the duct centerline
+12
+
+which can result into zigzag trajectories. We can relate figures 4, 6 and 7 and infer that the non-
+rectilinear motion of bubbles is related to the structure of the wake formed behind the bubbles.
+These instabilities in the wake cause an asymmetrical flow behind the bubble and lead to a zigzag
+motion. Now we look at why vortical structures are more streamlined in presence of the magnetic
+field.
+(a) Vertical Lorentz force around leading bubble
+(b) Vertical Lorentz force around trailing bubble
+Fig. 8: Vertical Lorentz force distribution around bubbles on yz−plane at t = 160 ms for B = 0.2 T
+Figures 8(a) and 8(b) show the vertical Lorentz force Flz distribution overlaid with the Lorentz force
+vectors around leading and trailing bubbles on the yz−plane for a representative time of t = 160 ms.
+From these two figures, we can see that the Lorentz force acts in the negative z−direction on both
+bubbles. However, the magnitude of the force is higher on the trailing bubble than that on the
+leading bubble. This will act to decelerate the trailing bubble more than the leading bubble. We
+can also see that the Lorentz force is symmetric to the vertical centerline. Therefore, the magnetic
+force will act to reduce the bubble wobbling. In Fig. 5, we observed that the trailing bubble velocity
+is higher than that of the leading bubble, which indicates that the effects of flow modification by
+the leading bubble on drag force is higher than Lorentz force.
+5
+Conclusions
+We have studied the three-dimensional dynamics of two inline Argon bubbles rising in molten steel
+in the presence of a transverse magnetic field. We have used a VOF interface tracking method with
+the sharp surface force treatment to capture the interface and inclusion of surface tension forces
+accurately. The electromagnetic equations have been solved to capture the effects of the magnetic
+field. Then, we carried out two simulations of different magnetic fields for 7 mm bubbles placed 3d
+13
+
+Fz
+10000
+8000:
+6000:
+4000:
+2000:
+0:
+:2000:
+:4000:
+-60:00:
+80.00:
+:10000:
+12000:
+-14000:Z
+Fz:
+10000:
+8000:
+6000:
+4000:
+:2000:
+0:
+:2000:
+:4000:
+-60:00:
+8000:
+:10000:
+12000:
+14000:center-to-center distance apart. We analyzed the bubble deformation, rise path, rise velocity, and
+flow structures behind the bubbles.
+We observe that the magnetic field strongly influences bubble deformations. For B = 0.0, both
+leading and trailing bubbles deformed into flatter ellipsoid with asymmetric top and bottom surfaces
+and went through shape oscillations. For B = 0.2, the leading bubble reaches a steady-state shape
+of an ellipsoidal bubble, whereas the trailing bubble goes through mild shape oscillations. Further,
+we observe that for B = 0.0, the bubbles initially rose in a rectilinear path but migrated into a
+zigzag path, and the amplitude of the path is nearly twice the bubble diameter. For B = 0.2,
+bubbles rose in a linear path for most of their ascent and migrated away from the center towards
+the end.
+The rise velocity goes through oscillations in both magnetic field cases; however, in the absence
+of the magnetic field, the magnitude of the velocity is significantly larger. We found that these
+oscillations are related to the shape oscillation of the bubble and a zigzag rise path. In both cases,
+leading and trailing bubbles initially ascended with identical speeds. Once maximum deformation
+was achieved, the trailing bubble rose faster than the leading bubble.
+References
+K. Jin, P. Kumar, S. P. Vanka, and B. G. Thomas. Rise of an argon bubble in liquid steel in the
+presence of a transverse magnetic field. Physics of Fluids, 28(9), 2016. ISSN 10897666. doi:
+10.1063/1.4961561.
+Purushotam Kumar, Kai Jin, and S. Pratap Vanka. Bubble rise and deformation in a non-newtonian
+fluid in a square duct. Computational Methods and Tools in Thermal Fluids Sciences, pages 1–15,
+2015a.
+JR Grace. Shapes and velocities of bubbles rising in infinite liquids. Trans. Inst. Chem. Eng., 51
+(2):116–120, 1973.
+J.R. Grace, T. Wairegi, and T.H Nguyen. Shapes and velocities of single drops and bubbles moving
+freely through immiscible liquids. Chemical Engineering Research and Design, 54a:167–173, 1976.
+Dahya Bhaga and M.E. Weber. Bubbles in viscous liquids: shapes, wakes and velocities. Journal
+of Fluid Mechanics, 105:61–85, 1981.
+B. Figueroa-Espinoza, R. Zenit, and D. Legendre. The effect of confinement on the motion of a
+single clean bubble. Journal of Fluid Mechanics, 616:419–443, November 2008. ISSN 0022-1120.
+P. Kumar and S.P. Vanka. Effects of confinement on bubble dynamics in a square duct. International
+Journal of Multiphase Flow, 77:32 – 47, 2015. ISSN 0301-9322.
+14
+
+Roland Clift, John R Grace, and Martin E Weber. Bubbles, Drops and Particles. Academic Press,
+London, 1978.
+Daniel DeKee. Transport Processes in Bubbles, Drops and Particles. CRC Press, 2002.
+W. Abbassi, S. Besbes, M. Elhajem, H. Ben Aissia, and J.Y. Champagne. Numerical simulation
+of free ascension and coaxial coalescence of air bubbles using the volume of fluid method (vof).
+Computers & Fluids, 161:47–59, 2018. ISSN 0045-7930.
+M. Gumulya, R.P. Utikar, G.M. Evans, J.B. Joshi, and V. Pareek. Interaction of bubbles rising
+inline in quiescent liquid. Chemical Engineering Science, 166:1–10, 2017. ISSN 0009-2509.
+Masao Watanabe and Toshiyuki Sanada. In-line motion of a pair of bubbles in a viscous liquid.
+Jsme International Journal Series B-fluids and Thermal Engineering, 49:410–418, 2006.
+H. Yuan and A. Prosperetti. On the in-line motion of two spherical bubbles in a viscous fluid.
+Journal of Fluid Mechanics, 278:325–349, 1994.
+Dominique Legendre, Jacques Magnaudet, and Guillaume Mougin.
+Hydrodynamic interactions
+between two spherical bubbles rising side by side in a viscous liquid. Journal of Fluid Mechanics,
+497:133–166, 2003.
+Zhao Yu, Hui Yang, and Liang-Shih Fan. Numerical simulation of bubble interactions using an
+adaptive lattice boltzmann method.
+Chemical Engineering Science, 66(14):3441–3451, 2011.
+ISSN 0009-2509. 10th International Conference on Gas–Liquid and Gas–Liquid–Solid Reactor
+Engineering.
+J. Katz and C. Meneveau. Wake-induced relative motion of bubbles rising in line. International
+Journal of Multiphase Flow, 22(2):239–258, 1996. ISSN 0301-9322.
+M.C Ruzicka. On bubbles rising in line. International Journal of Multiphase Flow, 26(7):1141–1181,
+2000. ISSN 0301-9322.
+William J. Rider and Douglas B. Kothe. Reconstructing volume tracking. Journal of Computational
+Physics, 141(2):112–152, April 1998. ISSN 00219991.
+WF Noh and P Woodward. SLIC (simple line interface calculation). In Proceedings of the Fifth
+International Conference, pages 330–340, Berlin, 1976. Springer-Verlag.
+Jie Li. Calcul d’Interface Affine par Morceaux(piecewise linear interface calculation). C. R. Acad.
+Sci. Paris, 320(8):391–396, 1995.
+N Ashgriz and JY Poo. FLAIR: flux line-segment model for advection and interface reconstruction.
+Journal of Computational Physics, 93(2):449–468, April 1991. ISSN 00219991.
+15
+
+Purushotam Kumar. Development and application of Lattice Boltzmann and accurate volume of
+fluid numerical techniques on graphics processing units.
+PhD thesis, University of Illinois at
+Urbana-Champaign, 2016.
+Purushotam Kumar, Kai Jin, and S. Pratap Vanka. A multi-GPU based accurate algorithm for
+simulations of gas-liquid flows. Computational Methods and Tools in Thermal Fluids Sciences,
+pages 1–17, 2015b.
+Marianne M. Francois, Sharen J. Cummins, Edward D. Dendy, Douglas B. Kothe, James M. Sicilian,
+and Matthew W. Williams.
+A balanced-force algorithm for continuous and sharp interfacial
+surface tension models within a volume tracking framework. Journal of Computational Physics,
+213(1):141–173, March 2006. ISSN 00219991.
+Zhaoyuan Wang and Albert Y. Tong. Deformation and oscillations of a single gas bubble rising in
+a narrow vertical tube. International Journal of Thermal Sciences, 47(3):221–228, March 2008.
+ISSN 12900729.
+Purushotam Kumar, Kai Jin, and Surya Pratap Vanka. Numerical Simulation of a Gas Bubble
+Rising in Power-Law Fluids Using a Sharp Surface Force Implementation. Proceedings of the
+ASME-JSME-KSME 2019 8th Joint Fluids Engineering Conference. Volume 5: Multiphase Flow.
+San Francisco, California, USA, July 28-August 01, 2019.
+Murray Rudman. A volume-tracking method for incompressible multifluid flows with large density
+variations. International Journal for Numerical Methods in Fluids, 28(2):357–378, August 1998.
+ISSN 0271-2091.
+Sharen J. Cummins, Marianne M. Francois, and Douglas B. Kothe. Estimating curvature from
+volume fractions. Computers & Structures, 83(6-7):425 – 434, 2005. ISSN 0045-7949.
+Yuriko Renardy and Michael Renardy. PROST: a parabolic reconstruction of surface tension for
+the volume-of-fluid method. Journal of Computational Physics, 183(2):400–421, December 2002.
+ISSN 00219991.
+Mark Sussman. A second order coupled level set and volume-of-fluid method for computing growth
+and collapse of vapor bubbles. Journal of Computational Physics, 187(1):110–136, May 2003.
+ISSN 00219991.
+M. Sussman, K.M. Smith, M.Y. Hussaini, M. Ohta, and R. Zhi-Wei. A sharp interface method
+for incompressible two-phase flows. Journal of Computational Physics, 221(2):469–505, February
+2007. ISSN 00219991.
+16
+
+Denis Gueyffier, Jie Li, Ali Nadim, Ruben Scardovelli, and Stéphane Zaleski.
+Volume-of-Fluid
+interface tracking with smoothed surface stress methods for three-dimensional flows. Journal of
+Computational Physics, 152(2):423–456, July 1999. ISSN 00219991.
+S. P. Vanka, P. Kumar, K. Jin, and B. G. Thomas.
+Single and multiphase flow computations
+on graphics processing units. International Conference on Computational Methods for Thermal
+Problems, (217349), 2016. ISSN 2305-5995.
+Jeremy Horwitz, Purushotam Kumar, and Pratap Vanka.
+Simulations of multiphase flow in a
+t-junction and distributor header. Bulletin of the American Physical Society, 57, 2012.
+Jeremy Horwitz, Purushotam Kumar, and Pratap Vanka. Simulations of three-dimensional droplet
+deformation in a square-duct at moderate reynolds numbers. Bulletin of the American Physical
+Society, 58, 2013.
+Purushotam Kumar, Jeremy Horwitz, and Surya Vanka. A three-dimensional numerical study of
+immiscible droplet deformation in a right angle bend. Bulletin of the American Physical Society,
+58, 2013.
+JAK Horwitz, P Kumar, and SP Vanka. Three-dimensional deformation of a spherical droplet in
+a square duct flow at moderate reynolds numbers. International journal of multiphase flow, 67:
+10–24, 2014.
+Jeremy A. K. Horwitz, S. P. Vanka, and P. Kumar. Lbm simulations of dispersed multiphase flows
+in a channel: Role of a pressure poisson equation. Proceedings of the ASME-JSME-KSME 2019
+8th Joint Fluids Engineering Conference. Volume 5: Multiphase Flow. San Francisco, California,
+USA, July 28-August 01, 2019.
+Surya Pratap Vanka, Kai Jin, Purushotam Kumar, and Brian Thomas. Rise of an argon bubble
+in liquid steel in the presence of a transverse magnetic field. Bulletin of the American Physical
+Society, 60, 2015.
+Purushotam Kumar and Pratap Vanka. Dynamics of Argon Gas Bubble Pair Rising in Liquid Steel
+in the Presence of a Transverse Magnetic Field. Bulletin of the American Physical Society, 67,
+2022.
+Pratap Vanka, Purushotam Kumar, and Kai Jin. Numerical Simulation of Turbulent Bubbly Flow
+in a Vertical Square Duct. Bulletin of the American Physical Society, 61, 2016.
+Purushotam Kumar and Surya Pratap Vanka. Large scale gpu based simulations of turbulent bubbly
+flow in a square duct. arXiv preprint arXiv:2104.01636, 2021.
+17
+
diff --git a/VdAzT4oBgHgl3EQf1P6v/content/tmp_files/load_file.txt b/VdAzT4oBgHgl3EQf1P6v/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..7e20f595027ce7e45994099052e6281afbed8d9c
--- /dev/null
+++ b/VdAzT4oBgHgl3EQf1P6v/content/tmp_files/load_file.txt
@@ -0,0 +1,599 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf,len=598
+page_content='Dynamics of Argon Gas Bubbles Rising in Liquid Steel in the  Presence of Transverse Magnetic Field  Purushotam Kumar∗1 and Surya P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Vanka†2  1Corning Incorporated, Manufacturing Technology & Engineering, Corning, NY 14830  2Mechanical Science & Engineering, University of Illinois Urbana-Champaign, Urbana, IL  61801  January 6, 2023  Abstract  Bubbly flows are present in various industrial processes including metallurgical processes in  which gas bubbles are injected at the bottom of bulk liquid metal to stir the liquid metal and  homogenize the metal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Understanding the motion of such bubbles is essential, as it has been  shown that bubble flotation can remove inclusions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' In this work, we have numerically studied  three-dimensional dynamics of a pair of inline Argon bubbles rising in molten steel under the  influence of a transverse magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' We have explored the effects of two transverse magnetic  field strengths (Bx = 0 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='2 T).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' The bubbles’ motion and transient rise velocities are compared  under different magnetic fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' The shape deformations and path of the bubbles are discussed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  The flow structures behind the bubbles are analyzed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' We found that structures are more organized  and elongated under a magnetic field, whereas it is complex and intertwined when the magnetic  field is not included.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' We have used a geometry construction-based volume of fluid (VOF) method  to track interface, maintain mass balance and estimate the interface curvature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Additionally, we  have incorporated a Sharp Surface Force Method (SSF) for surface tension forces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' The algorithm  is able to minimize the spurious velocities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  Keywords: bubble dynamics;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' magneto convection;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' vortex interactions;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' bubble interactions;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Volume  of fluid (VOF) method;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' share surface force  1  INTRODUCTION  Bubbly flows are encountered in various industrial processes and everyday life.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' To mix and homog-  enize the metal in metallurgical processes, gas bubbles are injected at the bottom of bulk liquid  metal to stir the liquid metal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' In the process for continuous casting of steel, which is widely used  ∗pkumar8@illinois.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='edu  †spvanka@illinois.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='edu  1  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='01797v1  [physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='flu-dyn]  4 Jan 2023  for steel making, Argon bubbles are commonly injected during the casting process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Understanding  the motion of such argon bubbles is essential as it has been shown that bubble flotation can remove  inclusions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' In addition, in order to improve the product quality frequently an external magnetic field  is applied to control the fluid motion and bubble behavior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' In the past several decades, numerous  theoretical, experimental, and computational studies have been carried out on the dynamics of a  rising bubble in transparent liquids (such as water and oils).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' However, only a few studies have been  reported on bubble motion in liquids when subjected to an external magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  Dynamics of a rising bubble are a function of the Eötvös number (Eo = ∆ρgd2σ−1, also referred  as Bond number Bo = ρlgd2σ−1), Morton number (Mo = gµ4  oρ−1  l  σ−3), confinement ratio (Cr =  Wd−1), Hartmann number Ha = Bd  �  σ/µl (Jin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=', 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Kumar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=', 2015a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' An exhaustive  collection of experimental data for a bubble rising in an unconfined medium has been summarized  in works of Grace (1973);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Grace et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' (1976);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Bhaga and Weber (1981), available as nomogram  charts of the terminal Reynolds and bubble shape for combinations of Bond and Morton numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  In addition, the proximity of the bubble to a wall alters the bubble rise velocity and shape and  increases the shear force at the gas-liquid interface Figueroa-Espinoza et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' (2008);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Kumar and  Vanka (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Detailed reviews of bubble dynamics in Newtonian fluids are available in the works  of Clift et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' (1978);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' DeKee (2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  The dynamics of multiple bubbles rising in Newtonian fluids without magnetic field has been studied  by several authors (Abbassi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=', 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Gumulya et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=', 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Watanabe and Sanada, 2006;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Yuan  and Prosperetti, 1994;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Legendre et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=', 2003;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Yu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=', 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Katz and Meneveau, 1996;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Ruzicka,  2000) and have reported that flow structure around the bubble has an important impact on the  interaction between leading and trailing bubbles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' They have reported that wake in front of a trailing  bubble plays an important role in reducing the drag around it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Due to reduced drag, the trailing  bubble accelerates until it coalesces with the leading bubble.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  In the present paper, we have briefly discussed a numerical technique to simulate two-phase flows and  used it to study the three-dimensional deformation and rise of two equally sized bubbles in molten  steel under the influence of a transverse magnetic field for a given bubble size and center to center  distance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Various quantities such as the bubble shape, rise velocity, and rise paths are investigated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  The algorithm used for the computations is presented in the numerical method section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' The problem  description is provided in the computational details section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' In the results and discussion section,  we present the results of the simulations and discuss the critical findings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' A summary of the present  findings is given at the end.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  2  2  Problem Setup  We consider a pair of deformable Argon bubbles rising in a rectangular column filled with liquid  steel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' The initial size (d) and shape of both bubbles are identical and spherical, and the initial  distance between their centers (h) is adjusted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' The trailing bubble is initially placed two diameters  above the bottom boundary at the center of duct cross-section, and the leading bubble is placed  at center to center distance of h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Both fluids (liquid in the column and bubbles) are stationary at  the beginning of solution procedure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' A constant transverse magnetic field of a given strength (Bx)  is applied in the x− direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' The gravitational force acts downward along the negative z−axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  We have considered a three-dimensional domain of 4d × 4d × 24d along x, y and z directions with  all boundaries of the domain to be no-slip, no-penetration and non-conductive walls.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Based on a  systematic grid refinement study, we have selected 32 control volumes per bubble diameter as an  adequate resolution, with a grid of 128×128×768 (≈ 13 million) control volumes for current study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  Figure 1 shows sketch of the computational domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' 1: Initial position of bubbles in liquid column  Material properties for steel and Argon are taken as density: 7000 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='56 kg/m3, viscosity:  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='3×10−3 and 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='42×10−5Pa s, and electrical conductivity: 714000 and 10−15 1/(Ω s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' The surface  tension (γ) is prescribed a value of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='2 N/m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  3  Numerical method  Governing equations  We have used continuity, momentum and electromagnetic equations given by eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' (1), (2), and (3)-  (4), to simulate bubble dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' We assumed the flow to be incompressible and isothermal (ignore  3  H  g  Z  h  x  W  Wany heat generation due to viscous dissipation or eddy currents).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  ∇ · u = 0  (1)  ∂ (ρu)  ∂t  + ∇ · (ρuu) = −∇p + ∇ ·  �  µ  �  ∇u + ∇uT ��  + ρg + γκnδ (x − xf) + FL  (2)  J = σ (−∇Φ + u × B)  (3)  ∇ · (σ∇Φ) = ∇ · [σ (u × B)]  (4)  In the above equations,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' u is fluid velocity,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' p is pressure,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' ρ is density,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' µ is dynamic viscosity,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' γ is  surface tension coefficient,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' κ is interface curvature,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' n is interface normal,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' δ is the delta function,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' x is  the spatial location where the equation is solved,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' xf is the position of the interface,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' g is acceleration  due to gravity,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' J is electrical current density,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' B is external magnetic field,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Φ is electric potential,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  and σ is electrical conductivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  FL is the Lorentz force and calculated as FL = J × B, the electrical current density J is calculated  from Ohm’s law as given by eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' (3) and the electric potential (Φ) is calculated from the eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' (4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  We also solve an equation to enforce divergence free condition (∇ · J = 0) for the current density  and maintain the conservative properties of charge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  The liquid and gas distribution is distinguished by liquid volume fraction (α).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' We solve an advection  equation of α given by eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' (5) to capture the movement of interface between two fluids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  ∂α  ∂t + u · ∇α = 0  (5)  We use the linear weighting of the liquid volume fraction to calculate the mixture density, viscosity  and electrical conductivity as,  ρ = αρl + (1 − α)ρg  (6)  µ = αµl + (1 − α)µg  (7)  σ = ασl + (1 − α)σg  (8)  The subscripts l and g denote gas and liquid phases respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  Solution procedure  The accuracy and speed of a multiphase algorithm is dependent on methods to track the interface,  model surface tension force, reduce momentum imbalance across the interface, handle property  discontinuity, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' In our current numerical procedure, we have used the geometry construction  method Rider and Kothe (1998) to represent the interface inside a cell and to calculate volume  fraction fluxes at the cell faces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' The interface normals are calculated from α using second-order  4  central differencing scheme for derivatives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' The second order operator split method of Noh and  Woodward (1976);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Li (1995);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Ashgriz and Poo (1991) is used for solution of the VOF equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  Here, the advection along one direction (x, y or z) is done as a first step then the advection  along remaining two directions are performed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  We rotate the order of advection to reduce any  directionally-biased errors introduced due to operator splitting approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' The advection term in  the momentum equation (eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' (2)) is also calculated geometrically is ensure consistency between  volume fraction and momentum advections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Kumar (2016);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Kumar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' (2015b) have provided  more details about challenges and mitigation associated with implementation geometry construction  method in three-dimensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  The γκnδ (x − xf) term in eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' (2) represents the surface tension force at the interface with γκ as  the Laplace pressure jump.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' In our current algorithm, we have used the Sharp Surface Force (SSF)  (Francois et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=', 2006;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Wang and Tong, 2008;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Kumar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=', 2019) method to model the surface  tension term in the Navier-Stokes equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Here, the surface tension term is written as a pressure  gradient term given by,  γκnδ (x − xf) = −∇˜p  (9)  where ˜p is the pressure solely due to the surface tension force at the interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' We obtain a Poisson  equation for ˜p from continuity and momentum equations,  ∇ ·  �∇˜p  ρ  �  = 0  (10)  The jump condition at the interface given by eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' (9) is used in the solution of eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='(10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' This ensures  the exact difference in pressure at the interface due to the surface tension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Using this method the  spurious velocities are seen to reduce to machine zero for a static bubble with exact analytical  curvature and to very small values when the curvature is numerically computed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' We have used  the height function method of Rudman (1998);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Cummins et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' (2005) for curvature estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  Admittedly, there are several methods to include the surface tension force in the Navier-stokes  (Renardy and Renardy Renardy and Renardy (2002), Sussman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Sussman (2003);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Sussman  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' (2007), Gueyffier et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  Gueyffier et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' (1999)), however, in our experience the current  method is more accurate for reduction of spurious velocities and relatively easier to implement on  GPUs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  The momentum and continuity equations are discretized on a collocated Cartesian grid using a finite  volume method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' The terms in the momentum equation are integrated with a second-order accurate  in time and space using Adams–Bashforth time advancement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' The convection term(∇ · ρuu) is  computed geometrically with linear interpolation for the face velocity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' The pressure gradient term  is written at cell faces and in the form of ∇p  ρ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Coupling the pressure gradient and density together  eliminates any ambiguity in density interpolation and leads to a robust method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' The viscous term is  5  computed by second order central differencing scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Linear interpolation is used for face densities  and viscosities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  The electromagnetic equations given by eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' (3) and (4) are solved on the same grid as used for con-  tinuity and momentum equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' The magnetic field strength (B), electric potential (Φ), current  density (J) and thermal conductivity (σ) are stored at the cell centers and calculated at cell faces  using linear averaging scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  We solve three Poisson equations: pressure (p), surface tension pressure (˜p) and electric potential  (Φ) in this numerical approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' These equations are efficiently solved using a geometric multigrid  accelerated red black SOR relaxation scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  All boundaries of the domain are considered wall, therefore no-slip, no-penetration and non-conducting  boundary conditions are applied at them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  uwall = vwall = wwall = 0  (11)  � ∂p  ∂ˆn  �  wall  =  � ∂˜p  ∂ˆn  �  wall  = 0  (12)  Jwall = Jwall = Jwall = 0  (13)  �∂Φ  ∂ˆn  �  wall  = 0  (14)  We have implemented this algorithm to run on multiple graphics processing units (GPU).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' We  have used the CUDA-Fortran platform supported by the Portland group (PGI) Fortran compilers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  Previously, we have validated the multiple GPU implementation (Kumar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=', 2015b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Vanka et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=',  2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Kumar, 2016) to study confinement effects on bubble dynamics (Kumar and Vanka, 2015),  two-phase flows at T-juctions (Horwitz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=', 2012, 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Kumar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=', 2013), bubble dynamics in  non-Newtonain fluids (Kumar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=', 2015a, 2019), droplet dynamics in square duct (Horwitz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=',  2014, 2019), Argon bubble rising in liquid steel (Vanka et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=', 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Jin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=', 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Kumar and  Vanka, 2022) and turbulent bubbly flow (Vanka et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=', 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Kumar and Vanka, 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  From analysis of the governing equations, we have identified that the dynamics of bubbles rising in  a confined conducting liquid medium depends on these non-dimensional parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  Bond number = Bo = ρlgd2/γ  (15)  Morton number = Mo = gµ4  l /ρlγ3  (16)  Hartmann number = Ha = Bd  �  σ/µl  (17)  Confinement ratio = Cr = W/d  (18)  center to center distance = hd = h/d  (19)  6  Grid refinement study  We have conducted a systematic grid refinement study to understand the impact of grid size on  the bubbles’ dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  For this grid refinement study, we have considered three grids namely:  coarse (∆x = d/16 : 64 × 64 × 384), fine (∆x = d/32 : 128 × 128 × 768), and finer (∆x = d/64 :  256 × 256 × 1536), and have analyzed the bubbles’ rise velocity and shapes for both leading and  trailing bubbles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  (a) Rise velocity of leading bubble  (b) Rise velocity of trailing bubble  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' 2: Rise velocity of leading and trailing bubbles for three grid sizes  Figure 2 shows the rise velocities of the leading and trailing bubbles for three different grids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' It  can be noticed from the figure that both bubbles initially accelerate with faster rate then slows  down to reach a steady state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' For the total simulation time considered in this study, we notice that  the leading bubble reach a steady state, however trailing bubble continues to accelerate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Further,  we can observe that rise velocities of both leading and trailing bubbles for three grids are almost  identical up to 15 ms and diverges afterwards.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' The velocities predicted on coarse grid is the lowest  and increases with grid refinement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' For leading bubble, rise velocities are 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='2848, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='3434, and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='3581  m/s at t = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='08 ms, for δx = 1/16, 1/32, and 1/64 grids respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' The difference in rise velocities  between finer and fine meshes is 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='1% and between finer and coarse meshes is 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='5%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Similarly, for  trailing bubble, rise velocities are 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='2931, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='3557, and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='3654 m/s at t = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='08 ms, for δx = 1/16,  1/32, and 1/64 grids respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' The difference in rise velocities between finer and fine meshes is  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='6% and between finer and coarse meshes is 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='8%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  Figure 3 shows the bubble shape on the central plane of the domain at a time when they leading  7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='3  wb [m/s]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='1  LB, dx = 1/16  LB, dx = 1/32  LB, dx = 1/64  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='06  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='08  time [s]0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='3  wb [m/s]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='1  TB, dx = 1/16  TB, dx = 1/32  TB, dx = 1/64  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='06  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='08  time [s](a) Shape of leading bubble  (b) Shape of trailing bubble  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' 3: Shape of leading and trailing bubbles for three grid sizes  bubbles have reached steady state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' For better comparison of the results, we have aligned bubble  tops for all three grids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' It can be noticed that bubbles become flatter as we refined the mesh, and  ∆x = 1/16 grid predicts largest height and smallest width for both leading and trailing bubbles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  Both height and width converged as we refined the grid to ∆ = 1/32 and 1/64 with very small  difference between fine and finer grids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  From rise velocity and shape comparisons for three grids, we decided to use ∆x = 1/32 as a suitable  grid that can give accurate result with moderate computational cost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' The results discussed from  here onward will be on fine (∆x = d/32 : 128 × 128 × 768) grid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  4  RESULTS AND DISCUSSION  We now present the results of a study to analyze the effects of transverse magnetic field on the  bubble deformation, rise velocity, rise path, and vortex shedding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' We have considered bubbles of  diameter 7 mm with the leading bubble placed 3 diameters above the trailing one, and have used  two magnetic fields (0 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='2 T) to understand their effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' For these set of conditions, the key  non-dimensional parameters are Bo = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='8, Mo = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='2 × 10−12, Cr = 4, hd = 3 and Ha = 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' It  should be noted that the bubbles are initially placed at the center of cross-section, but they may  come closer to the wall during their ascend.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Hence, instantaneous confinement ratio is likely to  change.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  We first look at the transient shapes of the bubbles as they travel upward.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' According to the Grace  diagram Grace (1973), an initially spherical bubble of Bo = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='8 rising in a liquid medium of Mo =  8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='028  dx=16-LB  dx=32-LB  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='0275  dx=64-LB  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='027  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='0265  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='026  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='0255  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='025  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='0245  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='004  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='005  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='006  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='007  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='008  y0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='013  dx=16-TB  dx=32-TB  dx=64-TB  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='012  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='011  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='004  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='005  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='006  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='007  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='008  y1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='2×10−12 deforms into a flatter ellipsoidal shape with minimum surface oscillations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' In our current  consideration, due to additional forces introduced by magnetic field, bubbles’ dynamics (including  shape and trajectory) are expected to be different.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  time (ms)  B  0  80  160  240  320  0  LB  0  TB  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='2  LB  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='2  TB  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' 4: Transient three-dimensional front views of the bubbles for two magnetic fields  Figure 4 shows the transient shapes of leading (LB) and trailing (TB) bubbles for B = 0 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  In absence of magnetic field, the leading bubble deforms from a spherical shape to an ellipsoidal  shape with asymmetrical top and bottom surfaces by 80 ms and remains ellipsoidal for remaining of  the simulation time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' We can notice that for up to 160 ms, bubble’s major axes are horizontal and  transitions to side-to-side oscillations (wobbling) between 160 - 240 ms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' The trailing bubble also  goes through similar transition from spherical to ellipsoidal by 80 ms, however it continues to deform  afterwards.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Shape oscillations of upper and lower surfaces: flatter-upper-surface (80 ms), rounder-  upper-surface (160 ms), bulged-upper-surface (240 ms) to irregular upper surface afterwards.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  In the presence of magnetic field, deformation of both leading and trailing bubbles are less pro-  nounced than in the absence of magnetic field, however the trailing bubble still goes through more  deformation than the leading one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' We can notice that leading bubble reached a steady-state shape  by 80 ms and did not go through shape oscillations or wobble motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' The trailing bubble, however,  continued to deform after 80 ms and did not achieve a steady-state shape for the time considered  here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  9  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' 5: Rise velocity of leading and trailing bubbles for two magnetic fields  Figure 5 shows the rise velocities of leading and trailing bubbles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Starting from stationary, rise  velocity increases with time to go through fluctuations either to reach a steady state or continue to  increase with time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' The behavior of leading and trailing bubbles’ rise velocities are different and  also depends on the applied magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' In the absence of magnetic field, rise velocities of both  leading and trailing bubbles are identical for up to t ≈ 75 ms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' We can notice that the rise velocity  of the leading bubble goes through rapid oscillations with the magnitude of oscillation is less than  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='01m/s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' It should also be noted that the mean velocity of leading bubble is almost unchanged  after t ≈ 75 ms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' On the other hand, the trailing bubble continues to accelerate for the total time  considered in this study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Additionally, the trailing bubble’s rise velocity is always higher than that  of the leading bubble.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  In the presence of a magnetic field, rise velocities of bubbles are identical for up to t ≈ 80 ms,  and afterward, the curves diverge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Velocity of the leading bubble after 80 ms increases very slowly  compared to before t = 80 ms and reaches almost a steady-state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' On the other hand, trailing  bubble continues to accelerate, although with smaller rate than initial acceleration, to achieve a  higher velocity than the leading bubble.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Comparing these curves, it is evident that the rise velocity  and their oscillations in the presence of a magnetic field decreases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='45  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='40  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='35  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='30  Wb [m/s]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='15  TB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' h/d = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Bx = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='10  LB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' h/d = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Bx = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='0  TB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' h/d = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Bx = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='2  LB, h/d = 3, Bx = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='25  time [s](a) B = 0  (b) B = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='2  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' 6: Rise paths of leading and trailing bubbles for two magnetic fields  Figure 6 shows the trajectory of leading and trailing bubbles as they ascend – red and black curves  represent trajectories of trailing and leading bubbles, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' It can be noticed that in the  absence of magnetic field both bubbles initially follow rectilinear paths turning into zigzags.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Further,  the trailing bubble deviates from rectilinear path earlier than the leading bubble.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' At the outset  of ascend, trailing bubble has a smaller velocity and is away from the flow field modified by the  leading bubble, therefore trailing bubble’s shape changes from the spherical to asymmetric ellipsoid  and does not exhibit surface oscillations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' This is the primary reason for the initial rectilinear path  of the bubble.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' As bubbles accelerate and reach a certain critical speed (or Reynold number), they  start to shed symmetric vortices which later grows into asymmetric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' This leads to a non-uniform  pressure distribution behind the bubble, which pushes bubbles away from liquid column’s center  and migrates into a zigzag trajectory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  When the magnetic field is included, both bubbles rise in the rectilinear paths for a longer time;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  however, towards the end of the simulation, they start to deviate and could potentially migrate  into zigzag paths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' This is in line with our observations from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' 4, the bubble reached a steady  shape without any shape or orientation oscillations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' To further understand the zigzag rise path and  oscillatory rise velocity, we analyze the flow structures behind the bubbles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  11  (a) B = 0  (b) B = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='2  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' 7: Iso-surfaces of ωz = ±25 at t = 240 ms for two magnetic fields  Figure 7 shows the front view of the iso-surfaces of ωz at t = 240 ms (The blue and yellow represents  iso-surfaces of ωz = 25 and ωz = −25 respectively).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' We can notice long elongated wake structures  behind the bubbles with “tail-like” shape.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' In absence of the magnetic field, these structures are flatter  and entangled which shows that these counter-rotating vortices are interacting with each other and  can disintegrate into smaller vortical structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' We can further notice non-uniform vortex shed  from the leading bubble – potentially modifying the flow-field observed by the trailing bubble.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  This explains why rise path of trailing bubble deviates from rectilinear trajectory earlier than the  leading bubble.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' In presence of the magnetic field, we notice symmetrical and more organized vortex  shedding from the leading bubble.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  These structures interact and surround the trailing bubble,  however, symmetry of the flow structures remain intact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' The vortex shedding from both leading  and trailing bubbles applies lateral forces on them and can push them away from the duct centerline  12  which can result into zigzag trajectories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' We can relate figures 4, 6 and 7 and infer that the non-  rectilinear motion of bubbles is related to the structure of the wake formed behind the bubbles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  These instabilities in the wake cause an asymmetrical flow behind the bubble and lead to a zigzag  motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Now we look at why vortical structures are more streamlined in presence of the magnetic  field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  (a) Vertical Lorentz force around leading bubble  (b) Vertical Lorentz force around trailing bubble  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' 8: Vertical Lorentz force distribution around bubbles on yz−plane at t = 160 ms for B = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='2 T  Figures 8(a) and 8(b) show the vertical Lorentz force Flz distribution overlaid with the Lorentz force  vectors around leading and trailing bubbles on the yz−plane for a representative time of t = 160 ms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  From these two figures, we can see that the Lorentz force acts in the negative z−direction on both  bubbles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' However, the magnitude of the force is higher on the trailing bubble than that on the  leading bubble.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' This will act to decelerate the trailing bubble more than the leading bubble.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' We  can also see that the Lorentz force is symmetric to the vertical centerline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Therefore, the magnetic  force will act to reduce the bubble wobbling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' 5, we observed that the trailing bubble velocity  is higher than that of the leading bubble, which indicates that the effects of flow modification by  the leading bubble on drag force is higher than Lorentz force.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  5  Conclusions  We have studied the three-dimensional dynamics of two inline Argon bubbles rising in molten steel  in the presence of a transverse magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' We have used a VOF interface tracking method with  the sharp surface force treatment to capture the interface and inclusion of surface tension forces  accurately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' The electromagnetic equations have been solved to capture the effects of the magnetic  field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Then, we carried out two simulations of different magnetic fields for 7 mm bubbles placed 3d  13  Fz  10000  8000:  6000:  4000:  2000:  0:  :2000:  :4000:  60:00:  80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='00:  :10000:  12000:  14000:Z  Fz:  10000:  8000:  6000:  4000:  :2000:  0:  :2000:  :4000:  60:00:  8000:  :10000:  12000:  14000:center-to-center distance apart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' We analyzed the bubble deformation, rise path, rise velocity, and  flow structures behind the bubbles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  We observe that the magnetic field strongly influences bubble deformations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' For B = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='0, both  leading and trailing bubbles deformed into flatter ellipsoid with asymmetric top and bottom surfaces  and went through shape oscillations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' For B = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='2, the leading bubble reaches a steady-state shape  of an ellipsoidal bubble, whereas the trailing bubble goes through mild shape oscillations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Further,  we observe that for B = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='0, the bubbles initially rose in a rectilinear path but migrated into a  zigzag path, and the amplitude of the path is nearly twice the bubble diameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' For B = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='2,  bubbles rose in a linear path for most of their ascent and migrated away from the center towards  the end.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  The rise velocity goes through oscillations in both magnetic field cases;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' however, in the absence  of the magnetic field, the magnitude of the velocity is significantly larger.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' We found that these  oscillations are related to the shape oscillation of the bubble and a zigzag rise path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' In both cases,  leading and trailing bubbles initially ascended with identical speeds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Once maximum deformation  was achieved, the trailing bubble rose faster than the leading bubble.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  References  K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Jin, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Kumar, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Vanka, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Thomas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Rise of an argon bubble in liquid steel in the  presence of a transverse magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Physics of Fluids, 28(9), 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' ISSN 10897666.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' doi:  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='1063/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='4961561.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  Purushotam Kumar, Kai Jin, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Pratap Vanka.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Bubble rise and deformation in a non-newtonian  fluid in a square duct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Computational Methods and Tools in Thermal Fluids Sciences, pages 1–15,  2015a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  JR Grace.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Shapes and velocities of bubbles rising in infinite liquids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Inst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Eng.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=', 51  (2):116–120, 1973.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Grace, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Wairegi, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='H Nguyen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Shapes and velocities of single drops and bubbles moving  freely through immiscible liquids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Chemical Engineering Research and Design, 54a:167–173, 1976.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  Dahya Bhaga and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Weber.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Bubbles in viscous liquids: shapes, wakes and velocities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Journal  of Fluid Mechanics, 105:61–85, 1981.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Figueroa-Espinoza, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Zenit, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Legendre.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' The effect of confinement on the motion of a  single clean bubble.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Journal of Fluid Mechanics, 616:419–443, November 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' ISSN 0022-1120.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Kumar and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Vanka.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Effects of confinement on bubble dynamics in a square duct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' International  Journal of Multiphase Flow, 77:32 – 47, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' ISSN 0301-9322.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  14  Roland Clift, John R Grace, and Martin E Weber.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Bubbles, Drops and Particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Academic Press,  London, 1978.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  Daniel DeKee.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Transport Processes in Bubbles, Drops and Particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' CRC Press, 2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Abbassi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Besbes, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Elhajem, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Ben Aissia, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Champagne.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Numerical simulation  of free ascension and coaxial coalescence of air bubbles using the volume of fluid method (vof).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  Computers & Fluids, 161:47–59, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' ISSN 0045-7930.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Gumulya, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Utikar, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Evans, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Joshi, and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Pareek.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Interaction of bubbles rising  inline in quiescent liquid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Chemical Engineering Science, 166:1–10, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' ISSN 0009-2509.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  Masao Watanabe and Toshiyuki Sanada.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' In-line motion of a pair of bubbles in a viscous liquid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  Jsme International Journal Series B-fluids and Thermal Engineering, 49:410–418, 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Yuan and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Prosperetti.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' On the in-line motion of two spherical bubbles in a viscous fluid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  Journal of Fluid Mechanics, 278:325–349, 1994.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  Dominique Legendre, Jacques Magnaudet, and Guillaume Mougin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  Hydrodynamic interactions  between two spherical bubbles rising side by side in a viscous liquid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Journal of Fluid Mechanics,  497:133–166, 2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  Zhao Yu, Hui Yang, and Liang-Shih Fan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Numerical simulation of bubble interactions using an  adaptive lattice boltzmann method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  Chemical Engineering Science, 66(14):3441–3451, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  ISSN 0009-2509.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' 10th International Conference on Gas–Liquid and Gas–Liquid–Solid Reactor  Engineering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Katz and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Meneveau.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Wake-induced relative motion of bubbles rising in line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' International  Journal of Multiphase Flow, 22(2):239–258, 1996.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' ISSN 0301-9322.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='C Ruzicka.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' On bubbles rising in line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' International Journal of Multiphase Flow, 26(7):1141–1181,  2000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' ISSN 0301-9322.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  William J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Rider and Douglas B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Kothe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Reconstructing volume tracking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Journal of Computational  Physics, 141(2):112–152, April 1998.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' ISSN 00219991.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  WF Noh and P Woodward.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' SLIC (simple line interface calculation).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' In Proceedings of the Fifth  International Conference, pages 330–340, Berlin, 1976.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Springer-Verlag.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  Jie Li.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Calcul d’Interface Affine par Morceaux(piecewise linear interface calculation).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Acad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Paris, 320(8):391–396, 1995.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  N Ashgriz and JY Poo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' FLAIR: flux line-segment model for advection and interface reconstruction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  Journal of Computational Physics, 93(2):449–468, April 1991.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' ISSN 00219991.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  15  Purushotam Kumar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Development and application of Lattice Boltzmann and accurate volume of  fluid numerical techniques on graphics processing units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  PhD thesis, University of Illinois at  Urbana-Champaign, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  Purushotam Kumar, Kai Jin, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Pratap Vanka.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' A multi-GPU based accurate algorithm for  simulations of gas-liquid flows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Computational Methods and Tools in Thermal Fluids Sciences,  pages 1–17, 2015b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  Marianne M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Francois, Sharen J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Cummins, Edward D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Dendy, Douglas B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Kothe, James M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Sicilian,  and Matthew W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Williams.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  A balanced-force algorithm for continuous and sharp interfacial  surface tension models within a volume tracking framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Journal of Computational Physics,  213(1):141–173, March 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' ISSN 00219991.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  Zhaoyuan Wang and Albert Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Tong.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Deformation and oscillations of a single gas bubble rising in  a narrow vertical tube.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' International Journal of Thermal Sciences, 47(3):221–228, March 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  ISSN 12900729.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  Purushotam Kumar, Kai Jin, and Surya Pratap Vanka.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Numerical Simulation of a Gas Bubble  Rising in Power-Law Fluids Using a Sharp Surface Force Implementation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Proceedings of the  ASME-JSME-KSME 2019 8th Joint Fluids Engineering Conference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Volume 5: Multiphase Flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  San Francisco, California, USA, July 28-August 01, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  Murray Rudman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' A volume-tracking method for incompressible multifluid flows with large density  variations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' International Journal for Numerical Methods in Fluids, 28(2):357–378, August 1998.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  ISSN 0271-2091.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  Sharen J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Cummins, Marianne M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Francois, and Douglas B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Kothe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Estimating curvature from  volume fractions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Computers & Structures, 83(6-7):425 – 434, 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' ISSN 0045-7949.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  Yuriko Renardy and Michael Renardy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' PROST: a parabolic reconstruction of surface tension for  the volume-of-fluid method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Journal of Computational Physics, 183(2):400–421, December 2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  ISSN 00219991.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  Mark Sussman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' A second order coupled level set and volume-of-fluid method for computing growth  and collapse of vapor bubbles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Journal of Computational Physics, 187(1):110–136, May 2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  ISSN 00219991.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Sussman, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Smith, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Hussaini, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Ohta, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Zhi-Wei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' A sharp interface method  for incompressible two-phase flows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Journal of Computational Physics, 221(2):469–505, February  2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' ISSN 00219991.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  16  Denis Gueyffier, Jie Li, Ali Nadim, Ruben Scardovelli, and Stéphane Zaleski.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  Volume-of-Fluid  interface tracking with smoothed surface stress methods for three-dimensional flows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Journal of  Computational Physics, 152(2):423–456, July 1999.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' ISSN 00219991.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Vanka, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Kumar, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Jin, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Thomas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  Single and multiphase flow computations  on graphics processing units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' International Conference on Computational Methods for Thermal  Problems, (217349), 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' ISSN 2305-5995.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  Jeremy Horwitz, Purushotam Kumar, and Pratap Vanka.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  Simulations of multiphase flow in a  t-junction and distributor header.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Bulletin of the American Physical Society, 57, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  Jeremy Horwitz, Purushotam Kumar, and Pratap Vanka.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Simulations of three-dimensional droplet  deformation in a square-duct at moderate reynolds numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Bulletin of the American Physical  Society, 58, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  Purushotam Kumar, Jeremy Horwitz, and Surya Vanka.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' A three-dimensional numerical study of  immiscible droplet deformation in a right angle bend.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Bulletin of the American Physical Society,  58, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  JAK Horwitz, P Kumar, and SP Vanka.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Three-dimensional deformation of a spherical droplet in  a square duct flow at moderate reynolds numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' International journal of multiphase flow, 67:  10–24, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  Jeremy A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Horwitz, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Vanka, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Kumar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Lbm simulations of dispersed multiphase flows  in a channel: Role of a pressure poisson equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Proceedings of the ASME-JSME-KSME 2019  8th Joint Fluids Engineering Conference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Volume 5: Multiphase Flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' San Francisco, California,  USA, July 28-August 01, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  Surya Pratap Vanka, Kai Jin, Purushotam Kumar, and Brian Thomas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Rise of an argon bubble  in liquid steel in the presence of a transverse magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Bulletin of the American Physical  Society, 60, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  Purushotam Kumar and Pratap Vanka.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Dynamics of Argon Gas Bubble Pair Rising in Liquid Steel  in the Presence of a Transverse Magnetic Field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Bulletin of the American Physical Society, 67,  2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  Pratap Vanka, Purushotam Kumar, and Kai Jin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Numerical Simulation of Turbulent Bubbly Flow  in a Vertical Square Duct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Bulletin of the American Physical Society, 61, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  Purushotam Kumar and Surya Pratap Vanka.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' Large scale gpu based simulations of turbulent bubbly  flow in a square duct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content=' arXiv preprint arXiv:2104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='01636, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
+page_content='  17' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdAzT4oBgHgl3EQf1P6v/content/2301.01797v1.pdf'}
diff --git a/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf b/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..474af2d6225b05a37874f2d0ddb11494cc8d07aa
--- /dev/null
+++ b/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:a59f03ed8b7f674ed20cc68d3147b2d38a04c08061a7a5b9f5cf4402c154c162
+size 1082696
diff --git a/VdE0T4oBgHgl3EQf2wKz/vector_store/index.pkl b/VdE0T4oBgHgl3EQf2wKz/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..83ad0f30bbbc05adb8561f30706547fd6896bff9
--- /dev/null
+++ b/VdE0T4oBgHgl3EQf2wKz/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:6c09bb04de2881e94d736066d8768d94e03a4cdaba463d4ce9e68e5eaf55afb5
+size 173869
diff --git a/VtE4T4oBgHgl3EQfng0j/vector_store/index.faiss b/VtE4T4oBgHgl3EQfng0j/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..7853c3c4d4142a2450edac3a46e6b57a85909d0f
--- /dev/null
+++ b/VtE4T4oBgHgl3EQfng0j/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:d6a5bc299bc0fde445915f2f02005d961842b09b6da7440416e910ab6cedc57c
+size 3866669
diff --git a/XdE3T4oBgHgl3EQfbwqk/vector_store/index.faiss b/XdE3T4oBgHgl3EQfbwqk/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..89e80a08ebcde49aded0b3d211e923e904ef5729
--- /dev/null
+++ b/XdE3T4oBgHgl3EQfbwqk/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:2e7a551663a5467db918ec4670a8c9c7befb1963e33552567019d58443286dcc
+size 4325421
diff --git a/YdE1T4oBgHgl3EQfwAXq/content/tmp_files/2301.03407v1.pdf.txt b/YdE1T4oBgHgl3EQfwAXq/content/tmp_files/2301.03407v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b12ff32325da6718d7f9cf4591304b780d16e718
--- /dev/null
+++ b/YdE1T4oBgHgl3EQfwAXq/content/tmp_files/2301.03407v1.pdf.txt
@@ -0,0 +1,1358 @@
+On advantages of Mask-level Recognition for Open-set Segmentation in the Wild
+Matej Grci´c, Josip ˇSari´c, Siniˇsa ˇSegvi´c
+University of Zagreb, Faculty of Electrical Engineering and Computing
+Unska 3, 10000 Zagreb, Croatia
+{name.surname}@fer.hr
+Abstract
+Most dense recognition methods bring a separate de-
+cision in each particular pixel.
+This approach still de-
+livers competitive performance in usual closed-set setups
+with small taxonomies. However, important applications
+in the wild typically require strong open-set performance
+and large numbers of known classes. We show that these
+two demanding setups greatly benefit from mask-level pre-
+dictions, even in the case of non-finetuned baseline models.
+Moreover, we propose an alternative formulation of dense
+recognition uncertainty that effectively reduces false posi-
+tive responses at semantic borders. The proposed formu-
+lation produces a further improvement over a very strong
+baseline and sets the new state of the art in dense anomaly
+detection without training on negative data. Our contribu-
+tions also lead to a performance improvement in a recent
+open-set panoptic setup. In-depth experiments confirm that
+our approach succeeds due to implicit aggregation of pixel-
+level cues into mask-level predictions.
+1. Introduction
+Emergence of deep learning in the 2010s revolutionized
+the field of computer vision. Complex yet efficient deep net-
+works enabled advanced scene understanding in real time.
+Segmentation is a very important form of scene understand-
+ing due to its applications in medicine, agriculture, robotics
+and the automotive industry. In the last decade, segmenta-
+tion tasks were modeled as per-pixel classification [18,43].
+However, such approach assumes independence of neigh-
+bouring pixels, which does not hold in practice. Neigh-
+bouring pixels are usually strongly correlated due to be-
+longing to the same object or scene part. Albeit designed
+and trained with this false assumption, the obtained mod-
+els deliver competitive generalization performance in in-
+distribution scenes [13,14]. However, their real-world per-
+formance still leaves much to be desired due to insufficient
+handling of anomalies [5, 10] and inadequate learning on
+unbalanced datasets [31].
+A recent approach to per-pixel classification decouples
+localization from recognition [16]. The localization is car-
+ried out by assigning pixels to an abundant set of masks,
+each trained to capture semantically related regions (e.g. a
+pedestrian or a car). The recovered semantic regions are
+subsequently classified as a whole. The described approach
+is dubbed mask-level classification [15]. Decoupling local-
+ization from classification further enables utilizing the same
+model for semantic, instance and panoptic segmentation.
+The shared architecture performs competitively on standard
+segmentation benchmarks.
+However, prior work does not consider demanding ap-
+plications of mask-based approaches. Thus, we investigate
+the value of mask-level recognition in the contexts of two
+major remaining challenges towards scene understanding in
+the wild. These challenges involve dense anomaly detec-
+tion [6,10] for robust open-set operation [30] and semantic
+segmentation on large taxonomies with severe class imbal-
+ance [31]. Our experiments reveal strong performance of
+mask-classification baselines in all challenges. This work
+investigates the reasons behind such behaviour and con-
+tribute improvements that support important applications.
+Mask-level recognition has several interesting proper-
+ties. For instance, masks are classified into K known classes
+and the class void, while mask assignments are not mutu-
+ally exclusive. This provides the model plenty of oppor-
+tunity to reject prediction in certain pixels. On the other
+hand, standard per-pixel softmax-activated approaches tend
+to be overconfident even in out-of-distribution pixels [22].
+Furthermore, mask-level approaches can propagate mask-
+level uncertainty to the pixel-level. This is different from
+the standard approach which has to estimate independent
+anomaly scores in each pixel [27]. Obviously, the standard
+approach can easily ignore the local correlations in a pixel
+neighbourhood. Such behaviour does not seem desirable. In
+terms of scalability, mask-level recognition models do not
+require per-class feature maps at the output resolution. This
+allows designers to decrease the training footprint [7] and
+increase flexibility of training. All these properties make
+mask-level recognition a compelling research topic.
+1
+arXiv:2301.03407v1  [cs.CV]  9 Jan 2023
+
+Fishyscapes Static
+SMIYC ObstacleTrack
+Road Anomaly
+Fishyscapes LostAndFound
+Figure 1. Anomaly detection with the proposed mask-level approach. We present input images (top) and dense anomaly scores (bottom).
+This paper proposes the following contributions.
+We
+point out that mask-level classification delivers strong
+baseline performance on standard benchmarks for dense
+anomaly detection.
+We extend the baselines in order to
+further exploit the specific bias of mask-level classification.
+The novel formulation leads to further improvements over
+the strong baseline and outperforms the existing state of the
+art. We extend our contributions in order to enable com-
+petitive open-set panoptic performance on a recently pro-
+posed experimental setup. Furthermore, we reveal substan-
+tial improvements over the current state of the art in seman-
+tic segmentation on COCO+LVIS [31], the largest available
+taxonomy for dense supervised learning. Finally, our work
+opens a variety of exciting avenues for future applications
+of mask-level models for robust dense recognition.
+2. Related Work
+The related work considers models for mask-level recog-
+nition tasks (Sec. 2.1), open-set segmentation (Sec. 2.2) as
+well as segmentation over extreme class count (Sec. 2.3).
+2.1. Recognition of free-form regions
+Early approaches to mask-wide recognition relied on
+class-agnostic bottom-up proposals. They aggregated hand-
+crafted [8] or convolutional [17, 24, 46] features along the
+proposed regions and brought mask-wide decisions by clas-
+sifying pooled representations. Mask-RCNN extends this
+approach by sharing features across detection of propos-
+als and mask-wide classification, as well as by end-to-
+end training of all parameters. Recently, PointRend pro-
+poses to back-propagate the loss only through selected low-
+uncertainty predictions [35]. This allows to increase mask-
+RCNN resolution from 28×28 to 224×224 with a ne-
+glectable impact on the training footprint. Very recently,
+MaskFormer precludes dependence on bottom-up propos-
+als by directly assigning pixels to masks that span arbi-
+trary image regions [16]. Its key component is a hypernet-
+work [23] that produces the weights for two 1×1 convolu-
+tions that convert pixel-level embeddings into mask assign-
+ment scores and, subsequently, into semantic maps. This
+is the first architecture that succeeds to deliver competitive
+experimental performance on three dense recognition tasks:
+semantic segmentation, instance segmentation, and panop-
+tic segmentation. Mask2Former [15] further improves the
+mask hypernetwork by introducing a special kind of at-
+tention layer that promotes progressive focusing onto fore-
+ground pixels for a particular mask. Our work explores the
+Mask2Former performance in the context of open-set seg-
+mentation.
+2.2. Open-set segmentation
+Recognition over an open set of classes assumes pres-
+ence of test examples beyond the training taxonomy. Open-
+set models should reject the decision in such examples [51].
+This can be carried out by restricting the shape of the de-
+cision boundary [1, 52] or by complementing the classifier
+with an anomaly detector [28, 38]. The decision boundary
+can be restricted by thresholding distance from the learned
+class centers in the embedding space [9, 52]. This can be
+further improved by reciprocal-point learning [12] or by
+employing a stronger classifier [55].
+Image-wide anomaly detection approaches rely on pre-
+diction confidence [28], input perturbations [38], density es-
+timation [45] and Bayesian uncertainty [44]. Several stud-
+ies point out that semantic anomalies [50] may be especially
+hard to detect [34, 45, 53]. A promising approach involves
+multi-task joint learning in tandem with the discriminative
+task [36, 59]. Further empirical improvements have been
+achieved by mimicking anomalies with negative training
+data [29, 41]. However, this may lead to over-optimistic
+performance estimates due to overlap with test anomalies.
+Anomaly detection is especially interesting in the dense
+prediction context due to important applications in robust
+scene understanding [6, 10, 58]. However, straight-forward
+2
+
+T-
+lagerzeitadaptations of image-wide approaches experience two im-
+portant failure modes. First, they often fail to accurately
+localize anomalies in front of inlier backgrounds [3]. Sec-
+ond, they are prone to false positives in inlier pixels with
+high entropy predictions that occur regularly at semantic
+borders [49]. Hence, a large body of work proposes cus-
+tom designs for dense anomaly detection.
+Partially anomalous images can be accounted for by
+learning on mixed-content images [3, 4, 21, 54]. Correla-
+tion between neighbouring pixels can be addressed by ag-
+gregating evidence through meta-classification [49] or in-
+put pre-processing [38]. Our approach is most related to
+dense approaches that refrain from learning on real nega-
+tive data. Some of these approaches fit generative heads
+to pre-trained [6] or jointly trained [30, 37] features. An-
+other line of work trains on synthetic negatives correspond-
+ing to adversarial noise [2] or samples of a jointly trained
+generative model [19]. Finally, some approaches detect the
+discrepancy between the input and the resynthesised scene
+[4,40,56,57].
+Different than all previous works that do not train on
+real negative data, we formulate dense anomaly detection
+according to mask-wide predictions. Different than meta-
+classification approaches [11,49] our method requires only
+one learning episode and does not require negative data.
+Our method is orthogonal to most previous approaches and
+it, therefore, represents an exciting baseline for future work.
+2.3. Semantic segmentation beyond 1K classes
+Contemporary methods are able to detect over 9k ob-
+ject classess [47] and recognize more than 20k image-
+wide classes [48]. However, such taxonomies are not eas-
+ily handled in dense prediction setups due to huge train-
+ing footprint of the dense loss. Recent work trains 1284
+COCO+LVIS classes on a single GPU by reducing the di-
+mensionality of per-pixel activations through applying the
+dense loss only to the k nearest class embeddings [31].
+However, this requires k-NN search in each output pixel
+and fails to propagate the loss through the entire taxon-
+omy. Softmax dimensionality can also be reduced by se-
+lecting the subset of negative classes with a dedicate image-
+wide head [25]. However, this risks to overlook presence of
+small classes in image-wide representations and again fails
+in training on entire taxonomy.
+Contrary to previous approaches that rely on per-class
+logits, mask-level classification decouples dimensionality
+of latent activations from the number of classes. This ap-
+proach succeeds through ability to assign different classes to
+the same mask as long as these classes do not appear in the
+same image. Consequently, we were able to learn state-of-
+the-art segmentation into 1284 COCO+LVIS classes with
+only 100 feature maps on output resolution.
+3. Mask-level open-set recognition
+We present a novel open-set segmentation approach
+based on mask-wide anomaly detection. Our approach is
+based on Mask2Former - a recent architecture that intro-
+duces mask-level recognition into the field of scene under-
+standing [16]. We formulate a novel dense anomaly score
+by ensembling mask-wide anomaly scores. This improves
+dense anomaly detection on real datasets due to aggregating
+pixel-level evidence across image regions and decreasing
+sensitivity to semantic boundaries.
+3.1. Scene understanding with Mask2Former
+Mask level classification decouples classification from
+localization and models them with separate outputs [16].
+Localization is carried out according to a set of probabilistic
+assignments (masks) S = {mi | i = 1, . . . , N} that capture
+semantically related regions. Each mask mi is an H×W ar-
+ray of probabilistic assignments to the corresponding pixel.
+We can join masks into 3D tensor mN×H×W . Masks are re-
+covered by subjecting standard dense features E to inferred
+projection wloc and sigmoid activation:
+m = σ(conv1×1(E, wloc)).
+(1)
+Recognition is carried out by inferring N mask-wide cat-
+egorical distributions into K known classes and one void
+class that we denote as Pi(Y = k|x), i ∈ 1..N, k ∈ 1..K+1.
+Let us consider probabilities of non-void classes and ar-
+range them into a N × K matrix wcls. Then the tensor of
+closed-set semantic segmentation scores can be recovered
+by projecting masks according to wcls:
+Hclosed = conv1×1(m, wcls).
+(2)
+Note that this tensor does not contain distributions since
+�
+i mi[r, c] ̸= 1 and �
+k wcls[i, k] ̸= 1. The above con-
+volution can be interpreted as classifying each pixel (r,c)
+according to a weighted ensemble of per-mask classifiers
+where the weights correspond to dense mask assignments:
+ˆy[r, c] = argmax
+k=1...K
+�
+i
+mi[r, c] · Pi(Y = k|x) .
+(3)
+Figure 2 (left) shows that dense features E are produced
+in usual fashion, by connecting an off-the-shelf backbone,
+to an upsampling decoder with skip connections. The main
+novelty is a hypernetwork denoted as mask decoder that re-
+ceives latent features and infers image-wide weights wloc
+and wcls. The training fits mask assignments m and mask-
+level recognition Pi(Y = k|x) to the dense labels.
+3.2. Detecting anomalies in pixel-level predictions
+Dense anomaly detection requires a scoring function
+sood : [0, 255]3×H×W → RH×W that maps each pixel to
+3
+
++
+NxHxW
+ExN
+N x K
+Backbone
+Pixel decoder
+Mask decoder
+P(Y|x) 
+N x 1
+sood(x) 
+N
+queries
+Input
+x
++
+Mask2Former
+Open-set extension
+drop ∅ 
++
+Hclosed 
+ExHxW
+Anomaly score
+sood(x) > δ
+Fuse
+Hopen
+Hood
+Nx(K+1)
+m
+wcls
+wloc
+m
+KxHxW
+EAM
+Figure 2. We focus on three tensors that are produced by the standard M2F model (left) [15]: closed-set segmentation Hclosed (K×H×W),
+per-mask dense binary assignments m (N×H×W), and image-wide mask-level class scores wcls (N×K). We start our open-set extension
+(right) by quantifying uncertainty of mask-level predictions wcls. We recover the dense anomaly map sEAM
+OOD (H×W) by redistributing
+per-mask anomaly scores back to the pixels according to dense mask assignment m as shown in (7). We assemble open-set segmentation
+Hopen by thresholding sEAM
+OOD and fusing it with Hclosed. Note that �
+rc mi[r, c] ̸= 1.
+the corresponding anomaly score. Subsequently, we can de-
+tect anomalies by thresholding the anomaly score sood(x).
+We can recover open-set segmentation by fusing anomalies
+with closed-set segmentation.
+Several standard baselines detect anomalous regions ac-
+cording to uncertainty of pixel-level predictions [6,27]. The
+prediction uncertainty can be quantified as max-score [28],
+entropy [11], energy [41] etc. We shall evaluate that ap-
+proach by ablating the mask decoder from the standard
+Mask2Former architecture in Figure 2 (left).
+Such Per-
+Pixel baselines [16] shall employ the same backbone and
+the same pixel decoder as their mask-level counterparts, and
+train with standard cross-entropy.
+Pixel-level predictions can also be recovered with a
+mask-level model.
+The training procedure encourages
+masks mi to specialize for capturing specific visual con-
+cepts. Hence, one could define a pixel-level anomaly score
+which rejects pixels that are not claimed by any mask:
+sAM
+ood(x)[r, c] = − max
+i
+mi[r, c]
+(4)
+AM stands for Anomaly of the max-Mask. Accordingly,
+we shall have a high anomaly score where all masks have
+low confidence. Even though this approach outperforms
+anomaly detection in per-pixel predictions, it is far from
+perfect.
+Fig. 3 shows histograms of inliers and outliers
+on Fishyscapes L&F val according to max mi score. The
+left histogram reveals that almost all inliers have high-
+confidence mask assignments. On the other hand, the out-
+lier distribution is highly polarized.
+The left mode can
+be easily distinguished from inliers, but the right mode
+presents a tougher challenge. This suggests that pixel-level
+predictions may not be an optimal solution to our problem.
+Therefore, we consider to build on mask-level uncertainty.
+Figure 3. Relative pixel frequencies according to max mask prob-
+ability in inlier and outlier pixels on Fishyscapes L&F val.
+3.3. Detecting anomalies in mask-level predictions
+We first consider a method that recovers dense anomaly
+scores as mask-level uncertainty of the strongest mask. If
+we choose max-softmax as the uncertainty measure, we can
+formulate this score as:
+sAHM
+ood (x)[r, c] = − max
+k=1...K Pargmaximi[r,c](Y = k|x). (5)
+AHM stands for Anomaly score of Hard-assigned Masks.
+However, this approach completely ignores the uncertainty
+of the dominant mask assignment. This clearly feels sub-
+optimal, and our empirical results confirm this intuition.
+Therefore, we set out to combine uncertainties of pixel-level
+mask assignment and mask-level recognition.
+We introduce mask-level recognition into anomaly de-
+tection by considering closed-set semantic segmentation
+scores (3). We can quantify their uncertainty according to
+an arbitrary anomaly detector. If we choose max-logit de-
+4
+
+Inliers
+Outliers
+1.0
+0.8
+0.6
+pixel ratio
+0.4
+0.2
+max-mask probability max; mitector [27], we obtain the following:
+sAEM
+ood (x)[r, c] = − max
+k=1...K
+�
+i
+mi[r, c] · Pi(Y = k|x). (6)
+Closed-set semantic scores can be viewed as ensembled out-
+puts of per-mask classifiers, where mask assignments act
+as weights of the ensemble members. Hence, we denote
+this score as Anomaly of Ensembled Mask-wide predictions
+(AEM).
+Finally, we consider to apply anomaly detector directly
+to mask-level classification scores. We propose to aggregate
+the resulting evidence in each particular pixel according to
+its mask assignments m. This approach can be interpreted
+as an Ensemble over Anomaly scores of Mask-wide predic-
+tions (EAM). This approach has an intuitive appeal due to
+direct relation towards mask-level uncertainty. If we quan-
+tify mask-level uncertainty according to maximum per-class
+probability, we get a lower bound of the AEM score (6):
+sEAM
+ood (x)[r, c] =
+�
+i
+mi[r, c] · (− max
+k=1...K Pi(Y = k|x))
+≤ − max
+k=1...K
+�
+i
+mi[r, c] · Pi(Y = k|x)
+(7)
+Fig. 2 (right) illustrates steps to compute the EAM score
+from M2F outputs.
+We expect that the difference between the two ap-
+proaches should be best visible at semantic borders. Here
+adjacent masks often lower their pixel assignment confi-
+dence. In such situations our proposed EAM approach will
+correctly output a lower anomaly score than AEM. Fig. 4
+illustrates the differences between EAM and AEM scoring
+on two scenes from Fishyscapes L&F. We observe a similar
+behaviour in most of image pixels. However, the proposed
+EAM approach clearly outputs lower anomaly score on se-
+mantic boundaries. This can help by reducing false positive
+anomaly detections in inlier pixels at semantic boundaries.
+Input
+AEM
+EAM
+Figure 4. Pixel-level vs. mask-level anomaly detection. Mask-
+level anomaly detection alleviates the known issue of false posi-
+tives at semantic borders. Please zoom in for the details.
+4. Experiments
+Our experiments explore advantages of mask-level
+recognition for scene understanding in the wild. We focus
+on three distinct problems: open-set segmentation, open-set
+panoptics and semantic segmentation beyond 1K classes.
+4.1. Anomaly detection in road-driving images
+We evaluate open-set segmentation performance on
+standard benchmarks for dense anomaly detection.
+The
+Fishyscapes benchmark includes two tracks that focus on
+urban road driving [6]. The FS L&F track relabels a sub-
+set of the Lost and Found dataset.
+The FS Static track
+pastes anomalous objects in images from Cityscapes val.
+The SMIYC benchmark (Segment Me If You Can) includes
+two tracks with real-world anomalies in very diverse en-
+vironments. The Anomaly Track includes large anomalies
+that can occur anywhere in the image, while the Obstacle
+Track focuses on small anomalies on the road surface.
+We measure the performance of anomaly detection ac-
+cording to average precision (AP) and FPR at TPR of 95%
+(FPR95). We foster fair comparison with the previous work
+by experimenting with Swin-L [42] and ResNet-50 [26].
+For simplicity, we train all our models only on Cityscapes.
+This likely reduces our performance on SMIYC due to large
+domain shift [55]. We use standard hyper-parameters [15]
+except for the batch size, which we set to 18. The longest
+experiments last about 48 hours on 3×A6000.
+Table 1 compares the performance of our best approach
+(M2F-EAM) with the related work on SMIYC. The two
+sections organize the methods depending on whether they
+train on real negative data. Our method is a strong per-
+former in the bottom section and closes the gap with re-
+spect to top section. Our method achieves strong average
+precision in both tracks. High AP and comparatively poor
+FPR95 scores suggest rare occurrences of highly confident
+false negative detections. Analysis of the AUROC curve
+supports this hypothesis since we achieve FPR90 = 20%.
+Qualitative experiments on validation images confirm that
+our method recognizes a few anomalies as plausible known
+classes. We illustrate these experiments in the appendix.
+Method
+Aux
+AnomalyTrack
+ObstacleTrack
+data
+AP
+FPR95
+AP
+FPR95
+SynBoost [4]
+
+56.4
+61.9
+71.3
+3.2
+DenseHybrid [21]
+
+78.0
+9.8
+78.7
+2.1
+PEBAL [54]
+
+49.1
+40.8
+5.0
+12.7
+Void Classifier [6]
+
+36.6
+63.5
+10.4
+41.5
+Maxim. Ent. [11]
+
+85.5
+15.0
+85.1
+0.8
+Image Resyn. [40]
+
+52.3
+25.9
+37.7
+4.7
+Road Inpaint. [39]
+
+-
+-
+54.1
+47.1
+JSRNet [56]
+
+33.6
+43.9
+28.1
+28.9
+Max softmax [28]
+
+28.0
+72.1
+15.7
+16.6
+MC Dropout [33]
+
+28.9
+69.5
+4.9
+50.3
+ODIN [38]
+
+33.1
+71.7
+22.1
+15.3
+Embed. Dens. [6]
+
+37.5
+70.8
+0.8
+46.4
+M2F-EAM (ours)
+
+76.3
+93.9
+66.9
+17.9
+Table 1. Dense anomaly detection on SMIYC. Our AP perfor-
+mance outperforms all methods that do not train on negative data.
+5
+
+Table 2 evaluates dense anomaly detection on valida-
+tion subsets of Road Anomaly [40] and Fishyscapes [5].
+We compare our mask-level approaches with the pixel-level
+baseline (PerPixel) and the previous work. Again, meth-
+ods from top section train on auxiliary negative data while
+the others see only inliers. Our two mask-level approaches
+outperform the pixel-level baseline, all previous work from
+the bottom section, and many methods from the top sec-
+tion. Among the two mask-level approaches, ensemble over
+anomaly scores (M2F-EAM) outperforms anomaly score of
+the ensemble (M2F-AEM). We do not report experiments
+on Fishyscapes test due to the high latency of the evalua-
+tion procedure. We hope to include these experiments in
+the final version of the manuscript.
+Model
+Road Anomaly
+FS L&F
+FS Static
+AP
+FPR
+AP
+FPR
+AP
+FPR
+SynBoost [4]
+38.2
+64.8
+60.6
+31.0
+66.4
+25.6
+Energy [41]
+19.5
+70.2
+16.1
+41.8
+41.7
+17.8
+PEBAL [54]
+45.1
+44.6
+58.8
+4.8
+92.1
+1.5
+DHybrid [21]
+-
+-
+63.8
+6.1
+60.0
+4.9
+MSP [28]
+15.7
+71.4
+4.6
+40.6
+19.1
+24.0
+ML [27]
+19.0
+70.5
+14.6
+42.2
+38.6
+18.3
+NFlowJS [19]
+-
+-
+40.2
+18.7
+34.4
+11.2
+SML [32]
+25.8
+49.7
+36.6
+14.5
+48.7
+16.8
+SynthCP [57]
+24.9
+64.7
+6.5
+46.0
+23.2
+34.0
+Density [6]
+-
+-
+4.1
+22.3
+-
+-
+PerPixel
+49.3
+31.0
+2.5
+56.7
+11.5
+34.8
+M2F-AEM
+66.9
+15.3
+51.2
+28.0
+86.2
+3.5
+M2F-EAM
+66.7
+13.4
+52.0
+20.5
+87.3
+2.1
+Table 2. Comparison of our mask-level approaches (M2F-EAM,
+M2F-AEM) with the pixel-level baseline (PerPixel) and the previ-
+ous work on RoadAnomaly and Fishyscapes val.
+4.2. Open-set panoptic segmentation on COCO
+Mask-level anomaly detection can also be applied for
+open-set panoptic segmentation. We consider the hardest
+setup from a recent related work [30] that relabels 20% of
+thing classes from COCO as void pixels during training.
+These classes are dining table, banana, bicycle, cake, sink,
+cat, keyboard, and bear. During inference the model has
+to classify all pixels from these classes into the dedicated
+anomalous thing class. Open-set performance is measured
+according to standard metrics PQ, SQ, and RQ. Our models
+use a ResNet-50 backbone as in the previous work [30].
+Mask-level training encourages all masks to refrain from
+encompassing the void pixels. Our anomaly detectors are
+sensitive to the resulting lack of mask assignment. Hence,
+the intensity of our supervision is very similar to void-
+suppression [30]. Our inference recovers the dense anomaly
+map by thresholding the mask-level anomaly score.
+We
+validate the threshold for 95% TPR in anomaly detection
+on a held-out validation image. We assign each anomalous
+pixel to its prefered mask and form instances by keeping all
+masks with more than 200 pixels.
+Table 3 compares our method to several approaches from
+the EOPSN paper [30]. We outperform all previous work,
+in spite of much less supervision. Note that our method can
+easily accommodate anomalous stuff classes.
+Method
+Known
+Unknown
+PQ
+SQ
+RQ
+PQ
+SQ
+RQ
+Void-background
+37.7
+76.3
+46.6
+4.0
+71.1
+5.7
+Void-ignorance
+37.2
+76.3
+45.9
+3.7
+71.8
+5.2
+Void-suppression
+37.5
+75.9
+46.1
+7.2
+75.3
+9.6
+Void-train
+36.9
+76.4
+45.5
+7.8
+73.4
+10.7
+EOPSN [30]
+37.4
+76.2
+46.2
+11.3
+73.8
+15.3
+Open-M2F-AEM
+43.5
+82.0
+52.2
+11.3
+73.3
+15.3
+Open-M2F-EAM
+43.5
+82.0
+52.2
+13.2
+73.4
+18.0
+Table 3. Open-set panoptic segmentation on COCO. We relabel
+20% of thing classes to the unknown void class [30]. We outper-
+form other approaches both on known and unknown classes.
+Figure 5 shows qualitative results on three scenes from
+COCO val. The rows show: input image, ground truth, two
+results from [30] and finally our results. The results clearly
+illustrate improvements of our method over previous state
+of the art in open-set panoptic segmentation.
+Note finally that panoptic mask-level models can also be
+used for standard dense anomaly detection. In fact, panoptic
+models outperform their semantic counterparts in 3 out of 6
+metrics from Table 2.
+4.3. Semantic segmentation beyond 1K classes
+We investigate applicability of mask-level recognition
+for semantic segmentation over large taxonomies. We con-
+sider the COCO+LVIS dataset [31] that includes around
+100K train and 20K val images with dense labels.
+The
+combined COCO+LVIS taxonomy has 1284 classes and a
+long-tailed class-frequency distribution.
+We hypothesize
+that such setups do not affect mask-level models as much
+as per-pixel models for three reasons.
+First, classes are
+more disbalanced at the pixel-level than at the mask-level
+since frequent classes tend to occupy more pixels than rare
+classes. Thus, mask-level models get to ”see” rare classes
+more often than the usual models. Second, mask-level mod-
+els can operate with much fewer masks than classes. Conse-
+quently, training on large taxonomies incentivizes the model
+to economize mask assignment through unsupervised class
+clustering. The resulting class clusters are less imbalanced
+than raw classes. Third, mask-level models have a smaller
+training footprint again due to masks being less numerous
+classes. This allows to train on larger batches which stabi-
+lizes convergence on difficult taxonomies.
+We train our ResNet models for 160K iterations, and
+SWIN models for 200K iterations. We set batch size to 18,
+base learning rate to 3 · 10−4 and use ADAMW optimizer.
+We train on 512×512 crops from randomly resized images,
+and perform inference after resizing the shorter side to 512.
+6
+
+Input
+Ground Truth
+EOPSN
+Void train
+Ours
+Figure 5. Open-set panoptics with M2F-EAM. Stop sign, bananas,
+toilet and sink are considered unknown thing classes [30]. We
+detect all unknown classes and distinguish some instances.
+Table 4 compares our experiments with the previous
+work and per-pixel baseline. The results are organized into
+three sections according to the model backbone. We re-
+port frequency-weighted intersection-over-union (FWIoU)
+as well as standard mIoU.
+We observe that mask-level models (M2F) significantly
+outperform methods from the literature. Our models out-
+perform ESSnet [31] for 11.5 mIoU points and Upernet
++ RankSeg for 6.4 mIoU points [25].
+Additionally, we
+outperform the previously described per-pixel baseline by
+a wide margin. Finally, we set a new state-of-the-art on
+COCO-LVIS of 28.8 mIoU points. Note that previous meth-
+ods [25, 31] were specifically modified for this task, while
+we use the vanilla Mask2Former [15]. This suggests that
+mask-classification indeed is a very promising approach for
+large-vocabulary semantic segmentation.
+Figure 6 visualizes class-frequency histograms in pixel-
+level and mask-level models. We observe that mask-level
+histogram has a thicker tail. We come to the same conclu-
+sion by comparing Gini coefficients of the two histograms:
+Backbone
+Model
+FWIoU
+mIoU
+ResNet-50
+ESSNet [31]
+43.8
+8.8
+PerPixel
+48.2
+13.1
+M2F
+52.2
+20.3
+Swin-B
+UperNet + RankSeg [25]
+/
+20.8
+PerPixel
+51.8
+19.9
+M2F
+55.3
+27.2
+Swin-L
+M2F
+55.8
+28.8
+Table 4.
+Comparative evaluation of semantic segmentation on
+COCO+LVIS val. Mask-level classification outperforms both per-
+pixel baseline and all previous works [25,31].
+0.92 (per-pixel) vs 0.85 (mask level). This confirms our
+hypothesis that mask-level models train on more balanced
+class distributions.
+Figure 6. Per-pixel vs. mask-level class distribution on COCO-
+LVIS. For better visualization we show only top-500 classes.
+4.4. Ablations
+Table 5 considers several anomaly detectors that can
+be plugged into our methods. The five sections consider
+per-pixel baseline and the aforementioned M2F-AM, M2F-
+AHM, M2F-AEM, and M2F-EAM. We note that neither
+ensembles of mask scores nor the mask scores themselves
+are distributions. Hence we do not consider probabilistic
+anomaly detectors in the last four sections.
+Instead, we
+only consider simply taking the hard maximum (this is re-
+lated to max-softmax) or the energy score (log-sum-exp).
+The two options perform comparably so we choose to use
+hard maximum in our submissions to SMIYC as a sim-
+pler choice.
+As before, we observe slight advantage of
+M2F-EAM over M2F-AEM, as well as poor performance
+of per-pixel anomaly detection that is in line with previ-
+ous work [6, 27]. Additionally, we observe that ensemble-
+based methods outperform their simpler counterparts M2F-
+AM and M2F-AHM.
+Table 6 investigates anomaly detection performance of
+7
+
+pixels (gini=0.92)
+0.06
+masks (gini=0.85)
+0.02
+0
+100
+200
+300
+400
+500
+class rankGUINNESSSTOPTMethod
+Anomaly detector
+FS L&F
+FS Static
+PerPixel
+Entropy [29]
+2.9
+12.7
+KL div [20]
+4.1
+16.4
+Energy [41]
+2.4
+11.3
+Max-softmax [28]
+1.8
+8.9
+M2F-AM
+Max-score
+30.9
+30.2
+M2F-AHM
+Max-score
+3.5
+44.4
+M2F-AEM
+Energy
+51.1
+86.6
+Max-score
+51.2
+86.2
+M2F-EAM
+Energy
+48.5
+69.3
+Max-score
+52.0
+87.3
+Table 5. Validation of anomaly detectors that can plug-in into our
+methods. Energy score (log-sum-exp) performs similar to taking a
+hard maximum. Again, M2F-EAM outperforms M2F-AEM while
+both mask-level approaches outperform M2F-AM, M2F-AHM,
+and per-pixel baseline.
+per-pixel and mask-classification models with different
+backbones. We consider a convolutional ResNet-50 back-
+bone and a transformer-based backbone Swin-L. Addition-
+ally, we show results of DeepLabV3+ model with ResNet-
+50 backbone. Our per-pixel baseline and DLv3+ perform
+similarly while Mask2Former outperforms both methods.
+Strong performance of M2F models based on Swin-L sug-
+gests that large capacity and transformer architecture may
+be important for mask-based dense anomaly detection.
+Backbone
+Model
+FS L&F
+FS Static
+CS val
+AP
+FPR
+AP
+FPR
+mIoU
+ResNet-50
+DLv3+
+3.5
+45.0
+-
+-
+77.8
+PerPixel
+1.3
+64.0
+9.0
+42.9
+79.6
+M2F-EAM
+20.8
+22.7
+36.7
+23.8
+79.4
+Swin-L
+PerPixel
+2.5
+56.7
+11.5
+34.8
+83.2
+M2F-EAM
+52.0
+20.5
+87.3
+2.1
+83.5
+Table 6. Comparison of several models with different backbones
+on Fishyscapes val. Mask-level models outperform their per-pixel
+counterparts, and this is a major takeaway of our work.
+Table 7 explores the significance of the number of masks
+N for closed-set recognition and anomaly detection. We
+consider the case where the number of masks equals the
+number of classes (N=19) as well as two more abundant
+choices (N=50,100).
+These experiments reveal a very
+strong influence of N to anomaly detection performance, al-
+though both tasks profit from having many masks.
+5. Conclusion
+Robust open-set performance is an important prerequi-
+site for many exciting applications of scene understanding.
+Most previous dense open-set approaches build on pixel-
+level anomaly detection and thus fail to account for correla-
+Mask count
+FS L&F
+FS Static
+CS val
+AP
+FPR95
+AP
+FPR95
+mIoU
+19
+33.5
+18.7
+72.5
+6.8
+82.8
+50
+47.9
+24.7
+69.7
+4.8
+83.1
+100
+52.0
+20.5
+87.3
+2.1
+83.5
+Table 7. Impact of mask count to anomaly detection and closed-
+set segmentation with M2F-EAM. Abundant set of masks is more
+beneficial for anomaly detection than for semantic segmentation.
+tion between neighbouring pixels. We address this research
+problem by shifting anomaly detection from pixels to re-
+gions. The resulting mask-level predictions aggregate pixel-
+level evidence and thus increase the statistical power of the
+corresponding anomaly scores. Furthermore, we show that
+it is especially beneficial to perform anomaly detection be-
+fore ensembling decisions over particular masks. Finally,
+we also propose an extension of a standard mask-based
+model for open-set panoptic inference. Experiments reveal
+that mask-level anomaly detection outperforms pixel-level
+counterparts by a wide margin and achieves state-of-the-
+art AP performance among methods that do not train on
+real negative data. Furthermore, it also improves upon the
+previous state of the art in open-set panoptic segmentation
+in spite of requiring less supervision than previous work.
+The proposed formulation of mask-level open-set segmen-
+tation can accommodate any anomaly detector based on dis-
+criminative recognition score, and can be combined with
+most previous approaches. Promising directions for future
+work include learning with synthetic negatives and mod-
+elling probabilistic density of mask-wide descriptors. The
+source code will be available upon publication.
+6. Limitations
+In spite of accomplishing very competitive AP scores,
+our approach sometimes produces poor FPR95 perfor-
+mance. Analysis of ROC and PR curves for our SMIYC
+submission indicates that a small set of anomalies gets
+very low anomaly scores. Evidence from validation images
+suggests that these errors occur due to human-like over-
+generalization. For example, giraffe legs get recognized as
+a person’s legs. As expected, our FPR90 performance gets
+much better than FPR95. This limitation would likely be
+positively affected by training on negative data (either real
+or synthetic).
+8
+
+References
+[1] Abhijit Bendale and Terrance E. Boult. Towards open set
+deep networks. In IEEE Conference on Computer Vision and
+Pattern Recognition, CVPR, 2016. 2
+[2] Victor Besnier, Andrei Bursuc, David Picard, and Alexandre
+Briot. Triggering failures: Out-of-distribution detection by
+learning from local adversarial attacks in semantic segmen-
+tation. In ICCV, pages 15681–15690, 2021. 3
+[3] Petra Bevandic, Ivan Kreso, Marin Orsic, and Sinisa Segvic.
+Simultaneous semantic segmentation and outlier detection in
+presence of domain shift. In GCPR, 2019. 3
+[4] Giancarlo Di Biase, Hermann Blum, Roland Siegwart, and
+C´esar Cadena.
+Pixel-wise anomaly detection in complex
+driving scenes. In Computer Vision and Pattern Recognition,
+CVPR, 2021. 3, 5, 6
+[5] Hermann Blum, Paul-Edouard Sarlin, Juan I. Nieto, Roland
+Siegwart, and Cesar Cadena.
+Fishyscapes: A benchmark
+for safe semantic segmentation in autonomous driving. In
+2019 IEEE/CVF International Conference on Computer Vi-
+sion Workshops, pages 2403–2412. IEEE, 2019. 1, 6
+[6] Hermann Blum, Paul-Edouard Sarlin, Juan Nieto, Roland
+Siegwart, and Cesar Cadena. The fishyscapes benchmark:
+Measuring blind spots in semantic segmentation. Interna-
+tional Journal of Computer Vision, 2021. 1, 2, 3, 4, 5, 6,
+7
+[7] Samuel Rota Bul`o, Lorenzo Porzi, and Peter Kontschieder.
+In-place activated batchnorm for memory-optimized training
+of dnns. In 2018 IEEE Conference on Computer Vision and
+Pattern Recognition, CVPR 2018, Salt Lake City, UT, USA,
+June 18-22, 2018, pages 5639–5647. Computer Vision Foun-
+dation / IEEE Computer Society, 2018. 1
+[8] Jo˜ao Carreira, Rui Caseiro, Jorge P. Batista, and Cristian
+Sminchisescu.
+Semantic segmentation with second-order
+pooling.
+In ECCV 2012 - 12th European Conference on
+Computer Vision. Springer, 2012. 2
+[9] Jun Cen, Peng Yun, Junhao Cai, Michael Yu Wang, and Ming
+Liu.
+Deep metric learning for open world semantic seg-
+mentation. In 2021 IEEE/CVF International Conference on
+Computer Vision, ICCV 2021. IEEE, 2021. 2
+[10] Robin Chan, Krzysztof Lis, Svenja Uhlemeyer, Hermann
+Blum, Sina Honari, Roland Siegwart, Pascal Fua, Mathieu
+Salzmann, and Matthias Rottmann. Segmentmeifyoucan: A
+benchmark for anomaly segmentation. In NeurIPS Datasets
+and Benchmarks 1, 2021. 1, 2
+[11] Robin Chan, Matthias Rottmann, and Hanno Gottschalk.
+Entropy maximization and meta classification for out-of-
+distribution detection in semantic segmentation. In Interna-
+tional Conference on Computer Vision, ICCV, 2021. 3, 4,
+5
+[12] Guangyao Chen,
+Peixi Peng,
+Xiangqian Wang,
+and
+Yonghong Tian. Adversarial reciprocal points learning for
+open set recognition. IEEE Trans. Pattern Anal. Mach. In-
+tell., 2022. 2
+[13] Liang-Chieh Chen, Yukun Zhu, George Papandreou, Florian
+Schroff, and Hartwig Adam. Encoder-decoder with atrous
+separable convolution for semantic image segmentation. In
+ECCV, 2018. 1
+[14] Bowen Cheng, Maxwell D. Collins, Yukun Zhu, Ting Liu,
+Thomas S. Huang, Hartwig Adam, and Liang-Chieh Chen.
+Panoptic-deeplab: A simple, strong, and fast baseline for
+bottom-up panoptic segmentation. In IEEE/CVF Conference
+on Computer Vision and Pattern Recognition, 2020. 1
+[15] Bowen Cheng, Ishan Misra, Alexander G. Schwing, Alexan-
+der Kirillov, and Rohit Girdhar.
+Masked-attention mask
+transformer for universal image segmentation. In IEEE/CVF
+Conference on Computer Vision and Pattern Recognition,
+CVPR 2022, pages 1280–1289. IEEE, 2022. 1, 2, 4, 5, 7
+[16] Bowen Cheng, Alexander G. Schwing, and Alexander Kir-
+illov. Per-pixel classification is not all you need for semantic
+segmentation. In NeurIPS 2021, 2021. 1, 2, 3, 4
+[17] Jifeng Dai, Kaiming He, and Jian Sun. Convolutional feature
+masking for joint object and stuff segmentation. In CVPR,
+pages 3992–4000, 2015. 2
+[18] Cl´ement Farabet, Camille Couprie, Laurent Najman, and
+Yann LeCun.
+Learning hierarchical features for scene la-
+beling. IEEE Trans. Pattern Anal. Mach. Intell., 2013. 1
+[19] Matej Grcic, Petra Bevandic, Zoran Kalafatic, and Sinisa
+Segvic. Dense anomaly detection by robust learning on syn-
+thetic negative data. CoRR, abs/2112.12833, 2021. 3, 6
+[20] Matej Grcic, Petra Bevandic, and Sinisa Segvic.
+Dense
+open-set recognition with synthetic outliers generated by real
+NVP. In Proceedings of the 16th International Joint Confer-
+ence on Computer Vision, Imaging and Computer Graphics
+Theory and Applications. SCITEPRESS, 2021. 8
+[21] Matej Grcic, Petra Bevandic, and Sinisa Segvic. Densehy-
+brid: Hybrid anomaly detection for dense open-set recogni-
+tion. In ECCV 2022 - 17th European Conference. Springer,
+2022. 3, 5, 6
+[22] Chuan Guo, Geoff Pleiss, Yu Sun, and Kilian Q. Weinberger.
+On calibration of modern neural networks. In Proceedings
+of the 34th International Conference on Machine Learning,
+ICML 2017. PMLR, 2017. 1
+[23] David Ha, Andrew M. Dai, and Quoc V. Le. Hypernetworks.
+In ICLR, 2017. 2
+[24] Bharath Hariharan, Pablo Andr´es Arbel´aez, Ross B. Gir-
+shick, and Jitendra Malik. Simultaneous detection and seg-
+mentation.
+In ECCV 2014 - 13th European Conference.
+Springer, 2014. 2
+[25] Haodi He, Yuhui Yuan, Xiangyu Yue, and Han Hu. Rankseg:
+Adaptive pixel classification with image category ranking for
+segmentation. In ECCV 2022 - 17th European Conference.
+Springer, 2022. 3, 7
+[26] Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun.
+Deep residual learning for image recognition. In Proceed-
+ings of the IEEE Conference on Computer Vision and Pattern
+Recognition (CVPR), June 2016. 5
+[27] Dan Hendrycks, Steven Basart, Mantas Mazeika, Andy Zou,
+Joseph Kwon, Mohammadreza Mostajabi, Jacob Steinhardt,
+and Dawn Song.
+Scaling out-of-distribution detection for
+real-world settings. In International Conference on Machine
+Learning, ICML 2022. PMLR, 2022. 1, 4, 5, 6, 7
+[28] Dan Hendrycks and Kevin Gimpel. A baseline for detect-
+ing misclassified and out-of-distribution examples in neural
+networks. In ICLR, 2019. 2, 4, 5, 6, 8
+9
+
+[29] Dan Hendrycks, Mantas Mazeika, and Thomas G. Dietterich.
+Deep anomaly detection with outlier exposure.
+In ICLR,
+2019. 2, 8
+[30] Jaedong Hwang, Seoung Wug Oh, Joon-Young Lee, and Bo-
+hyung Han. Exemplar-based open-set panoptic segmentation
+network. In IEEE Conference on Computer Vision and Pat-
+tern Recognition, CVPR 2021, pages 1175–1184. Computer
+Vision Foundation / IEEE, 2021. 1, 3, 6, 7
+[31] Shipra Jain, Danda Pani Paudel, Martin Danelljan, and
+Luc Van Gool. Scaling semantic segmentation beyond 1k
+classes on a single GPU. In 2021 IEEE/CVF International
+Conference on Computer Vision, ICCV 2021, pages 7406–
+7416. IEEE, 2021. 1, 2, 3, 6, 7
+[32] Sanghun Jung, Jungsoo Lee, Daehoon Gwak, Sungha Choi,
+and Jaegul Choo. Standardized max logits: A simple yet
+effective approach for identifying unexpected road obstacles
+in urban-scene segmentation. In International Conference on
+Computer Vision, ICCV, 2021. 6
+[33] Alex Kendall and Yarin Gal. What uncertainties do we need
+in bayesian deep learning for computer vision?
+In Neural
+Information Processing Systems, 2017. 5
+[34] Polina Kirichenko, Pavel Izmailov, and Andrew Gordon Wil-
+son. Why normalizing flows fail to detect out-of-distribution
+data. In NeurIPS, 2020. 2
+[35] Alexander Kirillov, Yuxin Wu, Kaiming He, and Ross B.
+Girshick. Pointrend: Image segmentation as rendering. In
+CVPR, pages 9796–9805, 2020. 2
+[36] Kimin Lee, Honglak Lee, Kibok Lee, and Jinwoo Shin.
+Training confidence-calibrated classifiers for detecting out-
+of-distribution samples. In 6th International Conference on
+Learning Representations, ICLR, 2018. 2
+[37] Chen Liang, Wenguan Wang, Jiaxu Miao, and Yi Yang.
+Gmmseg: Gaussian mixture based generative semantic seg-
+mentation models. In NeurIPS, 2022. 3
+[38] Shiyu Liang, Yixuan Li, and R. Srikant. Enhancing the re-
+liability of out-of-distribution image detection in neural net-
+works. In ICLR, 2018. 2, 3, 5
+[39] Krzysztof Lis, Sina Honari, Pascal Fua, and Mathieu Salz-
+mann.
+Detecting road obstacles by erasing them.
+CoRR,
+abs/2012.13633, 2020. 5
+[40] Krzysztof Lis, Krishna Kanth Nakka, Pascal Fua, and Math-
+ieu Salzmann. Detecting the unexpected via image resynthe-
+sis. In International Conference on Computer Vision, ICCV,
+2019. 3, 5, 6
+[41] Weitang Liu, Xiaoyun Wang, John D. Owens, and Yixuan
+Li. Energy-based out-of-distribution detection. In NeurIPS
+2020, 2020. 2, 4, 6, 8
+[42] Ze Liu, Yutong Lin, Yue Cao, Han Hu, Yixuan Wei, Zheng
+Zhang, Stephen Lin, and Baining Guo. Swin transformer:
+Hierarchical vision transformer using shifted windows. In
+2021 IEEE/CVF International Conference on Computer Vi-
+sion, ICCV 2021, pages 9992–10002. IEEE, 2021. 5
+[43] Jonathan Long, Evan Shelhamer, and Trevor Darrell. Fully
+convolutional networks for semantic segmentation. In IEEE
+Conference on Computer Vision and Pattern Recognition,
+CVPR 2015. IEEE Computer Society, 2015. 1
+[44] Jishnu Mukhoti and Yarin Gal.
+Evaluating bayesian
+deep learning methods for semantic segmentation. CoRR,
+abs/1811.12709, 2018. 2
+[45] Eric T. Nalisnick, Akihiro Matsukawa, Yee Whye Teh, Dilan
+G¨or¨ur, and Balaji Lakshminarayanan. Do deep generative
+models know what they don’t know?
+In 7th International
+Conference on Learning Representations, ICLR, 2019. 2
+[46] Pedro Oliveira Pinheiro, Tsung-Yi Lin, Ronan Collobert, and
+Piotr Doll´ar. Learning to refine object segments. In ECCV,
+volume 9905 of Lecture Notes in Computer Science, pages
+75–91, 2016. 2
+[47] Joseph Redmon and Ali Farhadi. YOLO9000: better, faster,
+stronger. In 2017 IEEE Conference on Computer Vision and
+Pattern Recognition, CVPR 2017, Honolulu, HI, USA, July
+21-26, 2017. IEEE Computer Society, 2017. 3
+[48] Tal Ridnik, Emanuel Ben Baruch, Asaf Noy, and Lihi Zel-
+nik. Imagenet-21k pretraining for the masses. In Proceed-
+ings of the Neural Information Processing Systems Track on
+Datasets and Benchmarks 1, NeurIPS 2021, 2021. 3
+[49] Matthias Rottmann, Pascal Colling, Thomas-Paul Hack,
+Robin Chan, Fabian H¨uger, Peter Schlicht, and Hanno
+Gottschalk. Prediction error meta classification in semantic
+segmentation: Detection via aggregated dispersion measures
+of softmax probabilities. In IJCNN, pages 1–9, 2020. 3
+[50] Lukas Ruff, Jacob R. Kauffmann, Robert A. Vander-
+meulen, Gr´egoire Montavon, Wojciech Samek, Marius
+Kloft, Thomas G. Dietterich, and Klaus-Robert M¨uller. A
+unifying review of deep and shallow anomaly detection.
+Proc. IEEE, 109(5):756–795, 2021. 2
+[51] Walter J. Scheirer, Anderson de Rezende Rocha, Archana
+Sapkota, and Terrance E. Boult. Toward open set recogni-
+tion. IEEE Transactions on Pattern Analysis and Machine
+Intelligence, 35(7):1757–1772, 2013. 2
+[52] Walter J. Scheirer, Lalit P. Jain, and Terrance E. Boult. Prob-
+ability models for open set recognition. IEEE Trans. Pattern
+Anal. Mach. Intell., 36(11):2317–2324, 2014. 2
+[53] Joan Serr`a, David ´Alvarez, Vicenc¸ G´omez, Olga Slizovskaia,
+Jos´e F. N´u˜nez, and Jordi Luque.
+Input complexity and
+out-of-distribution detection with likelihood-based genera-
+tive models. In ICLR, 2020. 2
+[54] Yu Tian, Yuyuan Liu, Guansong Pang, Fengbei Liu, Yuan-
+hong Chen, and Gustavo Carneiro. Pixel-wise energy-biased
+abstention learning for anomaly segmentation on complex
+urban driving scenes. CoRR, abs/2111.12264, 2021. 3, 5, 6
+[55] Sagar Vaze, Kai Han, Andrea Vedaldi, and Andrew Zisser-
+man. Open-set recognition: A good closed-set classifier is all
+you need. In The Tenth International Conference on Learn-
+ing Representations, ICLR 2022, 2022. 2, 5
+[56] Tomas
+Vojir,
+Tom´aˇs
+ˇSipka,
+Rahaf
+Aljundi,
+Nikolay
+Chumerin, Daniel Olmeda Reino, and Jiri Matas.
+Road
+anomaly detection by partial image reconstruction with seg-
+mentation coupling. In International Conference on Com-
+puter Vision, ICCV, 2021. 3, 5
+[57] Yingda Xia, Yi Zhang, Fengze Liu, Wei Shen, and Alan L.
+Yuille.
+Synthesize then compare: Detecting failures and
+anomalies for semantic segmentation. In ECCV 2020 - 16th
+European Conference. Springer, 2020. 3, 6
+10
+
+[58] Oliver Zendel, Katrin Honauer, Markus Murschitz, Daniel
+Steininger, and Gustavo Fern´andez Dom´ınguez. Wilddash
+- creating hazard-aware benchmarks. In ECCV, pages 407–
+421, 2018. 2
+[59] Hongjie Zhang, Ang Li, Jie Guo, and Yanwen Guo. Hybrid
+models for open set recognition. In 16th European Confer-
+ence on Computer Vision ECCV, 2020. 2
+11
+
diff --git a/YdE1T4oBgHgl3EQfwAXq/content/tmp_files/load_file.txt b/YdE1T4oBgHgl3EQfwAXq/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..1f8ebaeb3796b18acea5b8b51ac276462ed6b8d1
--- /dev/null
+++ b/YdE1T4oBgHgl3EQfwAXq/content/tmp_files/load_file.txt
@@ -0,0 +1,851 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf,len=850
+page_content='On advantages of Mask-level Recognition for Open-set Segmentation in the Wild  Matej Grci´c, Josip ˇSari´c, Siniˇsa ˇSegvi´c  University of Zagreb, Faculty of Electrical Engineering and Computing  Unska 3, 10000 Zagreb, Croatia  {name.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='surname}@fer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='hr  Abstract  Most dense recognition methods bring a separate de-  cision in each particular pixel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  This approach still de-  livers competitive performance in usual closed-set setups  with small taxonomies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' However, important applications  in the wild typically require strong open-set performance  and large numbers of known classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' We show that these  two demanding setups greatly benefit from mask-level pre-  dictions, even in the case of non-finetuned baseline models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Moreover, we propose an alternative formulation of dense  recognition uncertainty that effectively reduces false posi-  tive responses at semantic borders.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' The proposed formu-  lation produces a further improvement over a very strong  baseline and sets the new state of the art in dense anomaly  detection without training on negative data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Our contribu-  tions also lead to a performance improvement in a recent  open-set panoptic setup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' In-depth experiments confirm that  our approach succeeds due to implicit aggregation of pixel-  level cues into mask-level predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Introduction  Emergence of deep learning in the 2010s revolutionized  the field of computer vision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Complex yet efficient deep net-  works enabled advanced scene understanding in real time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Segmentation is a very important form of scene understand-  ing due to its applications in medicine, agriculture, robotics  and the automotive industry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' In the last decade, segmenta-  tion tasks were modeled as per-pixel classification [18,43].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  However, such approach assumes independence of neigh-  bouring pixels, which does not hold in practice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Neigh-  bouring pixels are usually strongly correlated due to be-  longing to the same object or scene part.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Albeit designed  and trained with this false assumption, the obtained mod-  els deliver competitive generalization performance in in-  distribution scenes [13,14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' However, their real-world per-  formance still leaves much to be desired due to insufficient  handling of anomalies [5, 10] and inadequate learning on  unbalanced datasets [31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  A recent approach to per-pixel classification decouples  localization from recognition [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' The localization is car-  ried out by assigning pixels to an abundant set of masks,  each trained to capture semantically related regions (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' a  pedestrian or a car).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' The recovered semantic regions are  subsequently classified as a whole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' The described approach  is dubbed mask-level classification [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Decoupling local-  ization from classification further enables utilizing the same  model for semantic, instance and panoptic segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  The shared architecture performs competitively on standard  segmentation benchmarks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  However, prior work does not consider demanding ap-  plications of mask-based approaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Thus, we investigate  the value of mask-level recognition in the contexts of two  major remaining challenges towards scene understanding in  the wild.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' These challenges involve dense anomaly detec-  tion [6,10] for robust open-set operation [30] and semantic  segmentation on large taxonomies with severe class imbal-  ance [31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Our experiments reveal strong performance of  mask-classification baselines in all challenges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' This work  investigates the reasons behind such behaviour and con-  tribute improvements that support important applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Mask-level recognition has several interesting proper-  ties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' For instance, masks are classified into K known classes  and the class void, while mask assignments are not mutu-  ally exclusive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' This provides the model plenty of oppor-  tunity to reject prediction in certain pixels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' On the other  hand, standard per-pixel softmax-activated approaches tend  to be overconfident even in out-of-distribution pixels [22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Furthermore, mask-level approaches can propagate mask-  level uncertainty to the pixel-level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' This is different from  the standard approach which has to estimate independent  anomaly scores in each pixel [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Obviously, the standard  approach can easily ignore the local correlations in a pixel  neighbourhood.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Such behaviour does not seem desirable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' In  terms of scalability, mask-level recognition models do not  require per-class feature maps at the output resolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' This  allows designers to decrease the training footprint [7] and  increase flexibility of training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' All these properties make  mask-level recognition a compelling research topic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  1  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='03407v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='CV]  9 Jan 2023  Fishyscapes Static  SMIYC ObstacleTrack  Road Anomaly  Fishyscapes LostAndFound  Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Anomaly detection with the proposed mask-level approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' We present input images (top) and dense anomaly scores (bottom).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  This paper proposes the following contributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  We  point out that mask-level classification delivers strong  baseline performance on standard benchmarks for dense  anomaly detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  We extend the baselines in order to  further exploit the specific bias of mask-level classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  The novel formulation leads to further improvements over  the strong baseline and outperforms the existing state of the  art.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' We extend our contributions in order to enable com-  petitive open-set panoptic performance on a recently pro-  posed experimental setup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Furthermore, we reveal substan-  tial improvements over the current state of the art in seman-  tic segmentation on COCO+LVIS [31], the largest available  taxonomy for dense supervised learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Finally, our work  opens a variety of exciting avenues for future applications  of mask-level models for robust dense recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Related Work  The related work considers models for mask-level recog-  nition tasks (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='1), open-set segmentation (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='2) as  well as segmentation over extreme class count (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Recognition of free-form regions  Early approaches to mask-wide recognition relied on  class-agnostic bottom-up proposals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' They aggregated hand-  crafted [8] or convolutional [17, 24, 46] features along the  proposed regions and brought mask-wide decisions by clas-  sifying pooled representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Mask-RCNN extends this  approach by sharing features across detection of propos-  als and mask-wide classification, as well as by end-to-  end training of all parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Recently, PointRend pro-  poses to back-propagate the loss only through selected low-  uncertainty predictions [35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' This allows to increase mask-  RCNN resolution from 28×28 to 224×224 with a ne-  glectable impact on the training footprint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Very recently,  MaskFormer precludes dependence on bottom-up propos-  als by directly assigning pixels to masks that span arbi-  trary image regions [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Its key component is a hypernet-  work [23] that produces the weights for two 1×1 convolu-  tions that convert pixel-level embeddings into mask assign-  ment scores and, subsequently, into semantic maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' This  is the first architecture that succeeds to deliver competitive  experimental performance on three dense recognition tasks:  semantic segmentation, instance segmentation, and panop-  tic segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Mask2Former [15] further improves the  mask hypernetwork by introducing a special kind of at-  tention layer that promotes progressive focusing onto fore-  ground pixels for a particular mask.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Our work explores the  Mask2Former performance in the context of open-set seg-  mentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Open-set segmentation  Recognition over an open set of classes assumes pres-  ence of test examples beyond the training taxonomy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Open-  set models should reject the decision in such examples [51].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  This can be carried out by restricting the shape of the de-  cision boundary [1, 52] or by complementing the classifier  with an anomaly detector [28, 38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' The decision boundary  can be restricted by thresholding distance from the learned  class centers in the embedding space [9, 52].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' This can be  further improved by reciprocal-point learning [12] or by  employing a stronger classifier [55].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Image-wide anomaly detection approaches rely on pre-  diction confidence [28], input perturbations [38], density es-  timation [45] and Bayesian uncertainty [44].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Several stud-  ies point out that semantic anomalies [50] may be especially  hard to detect [34, 45, 53].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' A promising approach involves  multi-task joint learning in tandem with the discriminative  task [36, 59].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Further empirical improvements have been  achieved by mimicking anomalies with negative training  data [29, 41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' However, this may lead to over-optimistic  performance estimates due to overlap with test anomalies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Anomaly detection is especially interesting in the dense  prediction context due to important applications in robust  scene understanding [6, 10, 58].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' However, straight-forward  2  T-  lagerzeitadaptations of image-wide approaches experience two im-  portant failure modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' First, they often fail to accurately  localize anomalies in front of inlier backgrounds [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Sec-  ond, they are prone to false positives in inlier pixels with  high entropy predictions that occur regularly at semantic  borders [49].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Hence, a large body of work proposes cus-  tom designs for dense anomaly detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Partially anomalous images can be accounted for by  learning on mixed-content images [3, 4, 21, 54].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Correla-  tion between neighbouring pixels can be addressed by ag-  gregating evidence through meta-classification [49] or in-  put pre-processing [38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Our approach is most related to  dense approaches that refrain from learning on real nega-  tive data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Some of these approaches fit generative heads  to pre-trained [6] or jointly trained [30, 37] features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' An-  other line of work trains on synthetic negatives correspond-  ing to adversarial noise [2] or samples of a jointly trained  generative model [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Finally, some approaches detect the  discrepancy between the input and the resynthesised scene  [4,40,56,57].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Different than all previous works that do not train on  real negative data, we formulate dense anomaly detection  according to mask-wide predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Different than meta-  classification approaches [11,49] our method requires only  one learning episode and does not require negative data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Our method is orthogonal to most previous approaches and  it, therefore, represents an exciting baseline for future work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Semantic segmentation beyond 1K classes  Contemporary methods are able to detect over 9k ob-  ject classess [47] and recognize more than 20k image-  wide classes [48].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' However, such taxonomies are not eas-  ily handled in dense prediction setups due to huge train-  ing footprint of the dense loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Recent work trains 1284  COCO+LVIS classes on a single GPU by reducing the di-  mensionality of per-pixel activations through applying the  dense loss only to the k nearest class embeddings [31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  However, this requires k-NN search in each output pixel  and fails to propagate the loss through the entire taxon-  omy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Softmax dimensionality can also be reduced by se-  lecting the subset of negative classes with a dedicate image-  wide head [25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' However, this risks to overlook presence of  small classes in image-wide representations and again fails  in training on entire taxonomy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Contrary to previous approaches that rely on per-class  logits, mask-level classification decouples dimensionality  of latent activations from the number of classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' This ap-  proach succeeds through ability to assign different classes to  the same mask as long as these classes do not appear in the  same image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Consequently, we were able to learn state-of-  the-art segmentation into 1284 COCO+LVIS classes with  only 100 feature maps on output resolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Mask-level open-set recognition  We present a novel open-set segmentation approach  based on mask-wide anomaly detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Our approach is  based on Mask2Former - a recent architecture that intro-  duces mask-level recognition into the field of scene under-  standing [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' We formulate a novel dense anomaly score  by ensembling mask-wide anomaly scores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' This improves  dense anomaly detection on real datasets due to aggregating  pixel-level evidence across image regions and decreasing  sensitivity to semantic boundaries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Scene understanding with Mask2Former  Mask level classification decouples classification from  localization and models them with separate outputs [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Localization is carried out according to a set of probabilistic  assignments (masks) S = {mi | i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' , N} that capture  semantically related regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Each mask mi is an H×W ar-  ray of probabilistic assignments to the corresponding pixel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  We can join masks into 3D tensor mN×H×W .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Masks are re-  covered by subjecting standard dense features E to inferred  projection wloc and sigmoid activation:  m = σ(conv1×1(E, wloc)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  (1)  Recognition is carried out by inferring N mask-wide cat-  egorical distributions into K known classes and one void  class that we denote as Pi(Y = k|x), i ∈ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='.N, k ∈ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='.K+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Let us consider probabilities of non-void classes and ar-  range them into a N × K matrix wcls.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Then the tensor of  closed-set semantic segmentation scores can be recovered  by projecting masks according to wcls:  Hclosed = conv1×1(m, wcls).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  (2)  Note that this tensor does not contain distributions since  �  i mi[r, c] ̸= 1 and �  k wcls[i, k] ̸= 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' The above con-  volution can be interpreted as classifying each pixel (r,c)  according to a weighted ensemble of per-mask classifiers  where the weights correspond to dense mask assignments:  ˆy[r, c] = argmax  k=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='K  �  i  mi[r, c] · Pi(Y = k|x) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  (3)  Figure 2 (left) shows that dense features E are produced  in usual fashion, by connecting an off-the-shelf backbone,  to an upsampling decoder with skip connections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' The main  novelty is a hypernetwork denoted as mask decoder that re-  ceives latent features and infers image-wide weights wloc  and wcls.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' The training fits mask assignments m and mask-  level recognition Pi(Y = k|x) to the dense labels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Detecting anomalies in pixel-level predictions  Dense anomaly detection requires a scoring function  sood : [0, 255]3×H×W → RH×W that maps each pixel to  3  +  NxHxW  ExN  N x K  Backbone  Pixel decoder  Mask decoder  P(Y|x)  N x 1  sood(x)  N  queries  Input  x  +  Mask2Former  Open-set extension  drop ∅  +  Hclosed  ExHxW  Anomaly score  sood(x) > δ  Fuse  Hopen  Hood  Nx(K+1)  m  wcls  wloc  m  KxHxW  EAM  Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' We focus on three tensors that are produced by the standard M2F model (left) [15]: closed-set segmentation Hclosed (K×H×W),  per-mask dense binary assignments m (N×H×W), and image-wide mask-level class scores wcls (N×K).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' We start our open-set extension  (right) by quantifying uncertainty of mask-level predictions wcls.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' We recover the dense anomaly map sEAM  OOD (H×W) by redistributing  per-mask anomaly scores back to the pixels according to dense mask assignment m as shown in (7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' We assemble open-set segmentation  Hopen by thresholding sEAM  OOD and fusing it with Hclosed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Note that �  rc mi[r, c] ̸= 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  the corresponding anomaly score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Subsequently, we can de-  tect anomalies by thresholding the anomaly score sood(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  We can recover open-set segmentation by fusing anomalies  with closed-set segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Several standard baselines detect anomalous regions ac-  cording to uncertainty of pixel-level predictions [6,27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' The  prediction uncertainty can be quantified as max-score [28],  entropy [11], energy [41] etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' We shall evaluate that ap-  proach by ablating the mask decoder from the standard  Mask2Former architecture in Figure 2 (left).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Such Per-  Pixel baselines [16] shall employ the same backbone and  the same pixel decoder as their mask-level counterparts, and  train with standard cross-entropy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Pixel-level predictions can also be recovered with a  mask-level model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  The training procedure encourages  masks mi to specialize for capturing specific visual con-  cepts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Hence, one could define a pixel-level anomaly score  which rejects pixels that are not claimed by any mask:  sAM  ood(x)[r, c] = − max  i  mi[r, c]  (4)  AM stands for Anomaly of the max-Mask.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Accordingly,  we shall have a high anomaly score where all masks have  low confidence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Even though this approach outperforms  anomaly detection in per-pixel predictions, it is far from  perfect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 3 shows histograms of inliers and outliers  on Fishyscapes L&F val according to max mi score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' The  left histogram reveals that almost all inliers have high-  confidence mask assignments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' On the other hand, the out-  lier distribution is highly polarized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  The left mode can  be easily distinguished from inliers, but the right mode  presents a tougher challenge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' This suggests that pixel-level  predictions may not be an optimal solution to our problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Therefore, we consider to build on mask-level uncertainty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Relative pixel frequencies according to max mask prob-  ability in inlier and outlier pixels on Fishyscapes L&F val.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Detecting anomalies in mask-level predictions  We first consider a method that recovers dense anomaly  scores as mask-level uncertainty of the strongest mask.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' If  we choose max-softmax as the uncertainty measure, we can  formulate this score as:  sAHM  ood (x)[r, c] = − max  k=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='K Pargmaximi[r,c](Y = k|x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' (5)  AHM stands for Anomaly score of Hard-assigned Masks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  However, this approach completely ignores the uncertainty  of the dominant mask assignment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' This clearly feels sub-  optimal, and our empirical results confirm this intuition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Therefore, we set out to combine uncertainties of pixel-level  mask assignment and mask-level recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  We introduce mask-level recognition into anomaly de-  tection by considering closed-set semantic segmentation  scores (3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' We can quantify their uncertainty according to  an arbitrary anomaly detector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' If we choose max-logit de-  4  Inliers  Outliers  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='6  pixel ratio  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='2  max-mask probability max;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' mitector [27], we obtain the following:  sAEM  ood (x)[r, c] = − max  k=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='K  �  i  mi[r, c] · Pi(Y = k|x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' (6)  Closed-set semantic scores can be viewed as ensembled out-  puts of per-mask classifiers, where mask assignments act  as weights of the ensemble members.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Hence, we denote  this score as Anomaly of Ensembled Mask-wide predictions  (AEM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Finally, we consider to apply anomaly detector directly  to mask-level classification scores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' We propose to aggregate  the resulting evidence in each particular pixel according to  its mask assignments m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' This approach can be interpreted  as an Ensemble over Anomaly scores of Mask-wide predic-  tions (EAM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' This approach has an intuitive appeal due to  direct relation towards mask-level uncertainty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' If we quan-  tify mask-level uncertainty according to maximum per-class  probability, we get a lower bound of the AEM score (6):  sEAM  ood (x)[r, c] =  �  i  mi[r, c] · (− max  k=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='K Pi(Y = k|x))  ≤ − max  k=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='K  �  i  mi[r, c] · Pi(Y = k|x)  (7)  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 2 (right) illustrates steps to compute the EAM score  from M2F outputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  We expect that the difference between the two ap-  proaches should be best visible at semantic borders.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Here  adjacent masks often lower their pixel assignment confi-  dence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' In such situations our proposed EAM approach will  correctly output a lower anomaly score than AEM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 4  illustrates the differences between EAM and AEM scoring  on two scenes from Fishyscapes L&F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' We observe a similar  behaviour in most of image pixels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' However, the proposed  EAM approach clearly outputs lower anomaly score on se-  mantic boundaries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' This can help by reducing false positive  anomaly detections in inlier pixels at semantic boundaries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Input  AEM  EAM  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Pixel-level vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' mask-level anomaly detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Mask-  level anomaly detection alleviates the known issue of false posi-  tives at semantic borders.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Please zoom in for the details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Experiments  Our experiments explore advantages of mask-level  recognition for scene understanding in the wild.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' We focus  on three distinct problems: open-set segmentation, open-set  panoptics and semantic segmentation beyond 1K classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Anomaly detection in road-driving images  We evaluate open-set segmentation performance on  standard benchmarks for dense anomaly detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  The  Fishyscapes benchmark includes two tracks that focus on  urban road driving [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' The FS L&F track relabels a sub-  set of the Lost and Found dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  The FS Static track  pastes anomalous objects in images from Cityscapes val.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  The SMIYC benchmark (Segment Me If You Can) includes  two tracks with real-world anomalies in very diverse en-  vironments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' The Anomaly Track includes large anomalies  that can occur anywhere in the image, while the Obstacle  Track focuses on small anomalies on the road surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  We measure the performance of anomaly detection ac-  cording to average precision (AP) and FPR at TPR of 95%  (FPR95).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' We foster fair comparison with the previous work  by experimenting with Swin-L [42] and ResNet-50 [26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  For simplicity, we train all our models only on Cityscapes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  This likely reduces our performance on SMIYC due to large  domain shift [55].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' We use standard hyper-parameters [15]  except for the batch size, which we set to 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' The longest  experiments last about 48 hours on 3×A6000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Table 1 compares the performance of our best approach  (M2F-EAM) with the related work on SMIYC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' The two  sections organize the methods depending on whether they  train on real negative data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Our method is a strong per-  former in the bottom section and closes the gap with re-  spect to top section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Our method achieves strong average  precision in both tracks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' High AP and comparatively poor  FPR95 scores suggest rare occurrences of highly confident  false negative detections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Analysis of the AUROC curve  supports this hypothesis since we achieve FPR90 = 20%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Qualitative experiments on validation images confirm that  our method recognizes a few anomalies as plausible known  classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' We illustrate these experiments in the appendix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Method  Aux  AnomalyTrack  ObstacleTrack  data  AP  FPR95  AP  FPR95  SynBoost [4]  \x13  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='4  61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='9  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='3  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='2  DenseHybrid [21]  \x13  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='0  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='8  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='7  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='1  PEBAL [54]  \x13  49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='1  40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='8  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='0  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='7  Void Classifier [6]  \x13  36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='6  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='5  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='4  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='5  Maxim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Ent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' [11]  \x13  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='5  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='0  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='8  Image Resyn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' [40]  \x17  52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='3  25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='9  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='7  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='7  Road Inpaint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' [39]  \x17 54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='1  47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='1  JSRNet [56]  \x17  33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='6  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='9  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='1  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='9  Max softmax [28]  \x17  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='0  72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='1  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='7  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='6  MC Dropout [33]  \x17  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='9  69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='5  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='9  50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='3  ODIN [38]  \x17  33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='1  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='7  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='1  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='3  Embed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Dens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' [6]  \x17  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='5  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='8  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='4  M2F-EAM (ours)  \x17  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='3  93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='9  66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='9  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='9  Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Dense anomaly detection on SMIYC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Our AP perfor-  mance outperforms all methods that do not train on negative data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  5  Table 2 evaluates dense anomaly detection on valida-  tion subsets of Road Anomaly [40] and Fishyscapes [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  We compare our mask-level approaches with the pixel-level  baseline (PerPixel) and the previous work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Again, meth-  ods from top section train on auxiliary negative data while  the others see only inliers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Our two mask-level approaches  outperform the pixel-level baseline, all previous work from  the bottom section, and many methods from the top sec-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Among the two mask-level approaches, ensemble over  anomaly scores (M2F-EAM) outperforms anomaly score of  the ensemble (M2F-AEM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' We do not report experiments  on Fishyscapes test due to the high latency of the evalua-  tion procedure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' We hope to include these experiments in  the final version of the manuscript.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Model  Road Anomaly  FS L&F  FS Static  AP  FPR  AP  FPR  AP  FPR  SynBoost [4]  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='2  64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='8  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='6  31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='0  66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='4  25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='6  Energy [41]  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='5  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='2  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='1  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='8  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='7  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='8  PEBAL [54]  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='1  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='6  58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='8  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='8  92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='5  DHybrid [21] 63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='8  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='1  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='0  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='9  MSP [28]  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='7  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='4  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='6  40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='6  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='1  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='0  ML [27]  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='0  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='5  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='6  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='2  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='6  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='3  NFlowJS [19] 40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='2  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='7  34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='4  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='2  SML [32]  25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='8  49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='7  36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='6  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='5  48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='7  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='8  SynthCP [57]  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='9  64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='7  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='5  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='0  23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='2  34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='0  Density [6] 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='1  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='3 PerPixel  49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='3  31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='5  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='7  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='5  34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='8  M2F-AEM  66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='9  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='3  51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='2  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='0  86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='2  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='5  M2F-EAM  66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='7  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='4  52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='0  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='5  87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='3  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='1  Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Comparison of our mask-level approaches (M2F-EAM,  M2F-AEM) with the pixel-level baseline (PerPixel) and the previ-  ous work on RoadAnomaly and Fishyscapes val.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Open-set panoptic segmentation on COCO  Mask-level anomaly detection can also be applied for  open-set panoptic segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' We consider the hardest  setup from a recent related work [30] that relabels 20% of  thing classes from COCO as void pixels during training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  These classes are dining table, banana, bicycle, cake, sink,  cat, keyboard, and bear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' During inference the model has  to classify all pixels from these classes into the dedicated  anomalous thing class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Open-set performance is measured  according to standard metrics PQ, SQ, and RQ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Our models  use a ResNet-50 backbone as in the previous work [30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Mask-level training encourages all masks to refrain from  encompassing the void pixels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Our anomaly detectors are  sensitive to the resulting lack of mask assignment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Hence,  the intensity of our supervision is very similar to void-  suppression [30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Our inference recovers the dense anomaly  map by thresholding the mask-level anomaly score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  We  validate the threshold for 95% TPR in anomaly detection  on a held-out validation image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' We assign each anomalous  pixel to its prefered mask and form instances by keeping all  masks with more than 200 pixels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Table 3 compares our method to several approaches from  the EOPSN paper [30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' We outperform all previous work,  in spite of much less supervision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Note that our method can  easily accommodate anomalous stuff classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Method  Known  Unknown  PQ  SQ  RQ  PQ  SQ  RQ  Void-background  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='7  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='3  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='6  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='0  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='1  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='7  Void-ignorance  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='2  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='3  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='9  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='7  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='8  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='2  Void-suppression  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='5  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='9  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='1  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='2  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='3  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='6  Void-train  36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='9  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='4  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='5  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='8  73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='4  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='7  EOPSN [30]  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='4  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='2  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='2  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='3  73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='8  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='3  Open-M2F-AEM  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='5  82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='0  52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='2  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='3  73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='3  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='3  Open-M2F-EAM  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='5  82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='0  52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='2  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='2  73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='4  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='0  Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Open-set panoptic segmentation on COCO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' We relabel  20% of thing classes to the unknown void class [30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' We outper-  form other approaches both on known and unknown classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Figure 5 shows qualitative results on three scenes from  COCO val.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' The rows show: input image, ground truth, two  results from [30] and finally our results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' The results clearly  illustrate improvements of our method over previous state  of the art in open-set panoptic segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Note finally that panoptic mask-level models can also be  used for standard dense anomaly detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' In fact, panoptic  models outperform their semantic counterparts in 3 out of 6  metrics from Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Semantic segmentation beyond 1K classes  We investigate applicability of mask-level recognition  for semantic segmentation over large taxonomies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' We con-  sider the COCO+LVIS dataset [31] that includes around  100K train and 20K val images with dense labels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  The  combined COCO+LVIS taxonomy has 1284 classes and a  long-tailed class-frequency distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  We hypothesize  that such setups do not affect mask-level models as much  as per-pixel models for three reasons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  First, classes are  more disbalanced at the pixel-level than at the mask-level  since frequent classes tend to occupy more pixels than rare  classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Thus, mask-level models get to ”see” rare classes  more often than the usual models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Second, mask-level mod-  els can operate with much fewer masks than classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Conse-  quently, training on large taxonomies incentivizes the model  to economize mask assignment through unsupervised class  clustering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' The resulting class clusters are less imbalanced  than raw classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Third, mask-level models have a smaller  training footprint again due to masks being less numerous  classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' This allows to train on larger batches which stabi-  lizes convergence on difficult taxonomies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  We train our ResNet models for 160K iterations, and  SWIN models for 200K iterations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' We set batch size to 18,  base learning rate to 3 · 10−4 and use ADAMW optimizer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  We train on 512×512 crops from randomly resized images,  and perform inference after resizing the shorter side to 512.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  6  Input  Ground Truth  EOPSN  Void train  Ours  Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Open-set panoptics with M2F-EAM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Stop sign, bananas,  toilet and sink are considered unknown thing classes [30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' We  detect all unknown classes and distinguish some instances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Table 4 compares our experiments with the previous  work and per-pixel baseline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' The results are organized into  three sections according to the model backbone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' We re-  port frequency-weighted intersection-over-union (FWIoU)  as well as standard mIoU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  We observe that mask-level models (M2F) significantly  outperform methods from the literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Our models out-  perform ESSnet [31] for 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='5 mIoU points and Upernet  + RankSeg for 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='4 mIoU points [25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Additionally, we  outperform the previously described per-pixel baseline by  a wide margin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Finally, we set a new state-of-the-art on  COCO-LVIS of 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='8 mIoU points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Note that previous meth-  ods [25, 31] were specifically modified for this task, while  we use the vanilla Mask2Former [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' This suggests that  mask-classification indeed is a very promising approach for  large-vocabulary semantic segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Figure 6 visualizes class-frequency histograms in pixel-  level and mask-level models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' We observe that mask-level  histogram has a thicker tail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' We come to the same conclu-  sion by comparing Gini coefficients of the two histograms:  Backbone  Model  FWIoU  mIoU  ResNet-50  ESSNet [31]  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='8  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='8  PerPixel  48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='2  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='1  M2F  52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='2  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='3  Swin-B  UperNet + RankSeg [25]  /  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='8  PerPixel  51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='8  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='9  M2F  55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='3  27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='2  Swin-L  M2F  55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='8  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='8  Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Comparative evaluation of semantic segmentation on  COCO+LVIS val.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Mask-level classification outperforms both per-  pixel baseline and all previous works [25,31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='92 (per-pixel) vs 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='85 (mask level).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' This confirms our  hypothesis that mask-level models train on more balanced  class distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Per-pixel vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' mask-level class distribution on COCO-  LVIS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' For better visualization we show only top-500 classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Ablations  Table 5 considers several anomaly detectors that can  be plugged into our methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' The five sections consider  per-pixel baseline and the aforementioned M2F-AM, M2F-  AHM, M2F-AEM, and M2F-EAM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' We note that neither  ensembles of mask scores nor the mask scores themselves  are distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Hence we do not consider probabilistic  anomaly detectors in the last four sections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Instead, we  only consider simply taking the hard maximum (this is re-  lated to max-softmax) or the energy score (log-sum-exp).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  The two options perform comparably so we choose to use  hard maximum in our submissions to SMIYC as a sim-  pler choice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  As before, we observe slight advantage of  M2F-EAM over M2F-AEM, as well as poor performance  of per-pixel anomaly detection that is in line with previ-  ous work [6, 27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Additionally, we observe that ensemble-  based methods outperform their simpler counterparts M2F-  AM and M2F-AHM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Table 6 investigates anomaly detection performance of  7  pixels (gini=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='92)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='06  masks (gini=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='85)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='02  0  100  200  300  400  500  class rankGUINNESSSTOPTMethod  Anomaly detector  FS L&F  FS Static  PerPixel  Entropy [29]  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='9  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='7  KL div [20]  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='1  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='4  Energy [41]  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='4  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='3  Max-softmax [28]  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='8  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='9  M2F-AM  Max-score  30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='9  30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='2  M2F-AHM  Max-score  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='5  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='4  M2F-AEM  Energy  51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='1  86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='6  Max-score  51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='2  86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='2  M2F-EAM  Energy  48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='5  69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='3  Max-score  52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='0  87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='3  Table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Validation of anomaly detectors that can plug-in into our  methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Energy score (log-sum-exp) performs similar to taking a  hard maximum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Again, M2F-EAM outperforms M2F-AEM while  both mask-level approaches outperform M2F-AM, M2F-AHM,  and per-pixel baseline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  per-pixel and mask-classification models with different  backbones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' We consider a convolutional ResNet-50 back-  bone and a transformer-based backbone Swin-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Addition-  ally, we show results of DeepLabV3+ model with ResNet-  50 backbone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Our per-pixel baseline and DLv3+ perform  similarly while Mask2Former outperforms both methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Strong performance of M2F models based on Swin-L sug-  gests that large capacity and transformer architecture may  be important for mask-based dense anomaly detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Backbone  Model  FS L&F  FS Static  CS val  AP  FPR  AP  FPR  mIoU  ResNet-50  DLv3+  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='5  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='0 77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='8  PerPixel  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='3  64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='0  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='0  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='9  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='6  M2F-EAM  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='8  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='7  36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='7  23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='8  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='4  Swin-L  PerPixel  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='5  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='7  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='5  34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='8  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='2  M2F-EAM  52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='0  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='5  87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='3  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='1  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='5  Table 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Comparison of several models with different backbones  on Fishyscapes val.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Mask-level models outperform their per-pixel  counterparts, and this is a major takeaway of our work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Table 7 explores the significance of the number of masks  N for closed-set recognition and anomaly detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' We  consider the case where the number of masks equals the  number of classes (N=19) as well as two more abundant  choices (N=50,100).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  These experiments reveal a very  strong influence of N to anomaly detection performance, al-  though both tasks profit from having many masks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Conclusion  Robust open-set performance is an important prerequi-  site for many exciting applications of scene understanding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Most previous dense open-set approaches build on pixel-  level anomaly detection and thus fail to account for correla-  Mask count  FS L&F  FS Static  CS val  AP  FPR95  AP  FPR95  mIoU  19  33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='5  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='7  72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='5  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='8  82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='8  50  47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='9  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='7  69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='7  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='8  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='1  100  52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='0  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='5  87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='3  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='1  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='5  Table 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Impact of mask count to anomaly detection and closed-  set segmentation with M2F-EAM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Abundant set of masks is more  beneficial for anomaly detection than for semantic segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  tion between neighbouring pixels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' We address this research  problem by shifting anomaly detection from pixels to re-  gions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' The resulting mask-level predictions aggregate pixel-  level evidence and thus increase the statistical power of the  corresponding anomaly scores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Furthermore, we show that  it is especially beneficial to perform anomaly detection be-  fore ensembling decisions over particular masks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Finally,  we also propose an extension of a standard mask-based  model for open-set panoptic inference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Experiments reveal  that mask-level anomaly detection outperforms pixel-level  counterparts by a wide margin and achieves state-of-the-  art AP performance among methods that do not train on  real negative data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Furthermore, it also improves upon the  previous state of the art in open-set panoptic segmentation  in spite of requiring less supervision than previous work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  The proposed formulation of mask-level open-set segmen-  tation can accommodate any anomaly detector based on dis-  criminative recognition score, and can be combined with  most previous approaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Promising directions for future  work include learning with synthetic negatives and mod-  elling probabilistic density of mask-wide descriptors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' The  source code will be available upon publication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Limitations  In spite of accomplishing very competitive AP scores,  our approach sometimes produces poor FPR95 perfor-  mance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Analysis of ROC and PR curves for our SMIYC  submission indicates that a small set of anomalies gets  very low anomaly scores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Evidence from validation images  suggests that these errors occur due to human-like over-  generalization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' For example, giraffe legs get recognized as  a person’s legs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' As expected, our FPR90 performance gets  much better than FPR95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' This limitation would likely be  positively affected by training on negative data (either real  or synthetic).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  8  References  [1] Abhijit Bendale and Terrance E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Boult.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Towards open set  deep networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' In IEEE Conference on Computer Vision and  Pattern Recognition, CVPR, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 2  [2] Victor Besnier, Andrei Bursuc, David Picard, and Alexandre  Briot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Triggering failures: Out-of-distribution detection by  learning from local adversarial attacks in semantic segmen-  tation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' In ICCV, pages 15681–15690, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 3  [3] Petra Bevandic, Ivan Kreso, Marin Orsic, and Sinisa Segvic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Simultaneous semantic segmentation and outlier detection in  presence of domain shift.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' In GCPR, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 3  [4] Giancarlo Di Biase, Hermann Blum, Roland Siegwart, and  C´esar Cadena.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Pixel-wise anomaly detection in complex  driving scenes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' In Computer Vision and Pattern Recognition,  CVPR, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 3, 5, 6  [5] Hermann Blum, Paul-Edouard Sarlin, Juan I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Nieto, Roland  Siegwart, and Cesar Cadena.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Fishyscapes: A benchmark  for safe semantic segmentation in autonomous driving.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' In  2019 IEEE/CVF International Conference on Computer Vi-  sion Workshops, pages 2403–2412.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' IEEE, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 1, 6  [6] Hermann Blum, Paul-Edouard Sarlin, Juan Nieto, Roland  Siegwart, and Cesar Cadena.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' The fishyscapes benchmark:  Measuring blind spots in semantic segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Interna-  tional Journal of Computer Vision, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 1, 2, 3, 4, 5, 6,  7  [7] Samuel Rota Bul`o, Lorenzo Porzi, and Peter Kontschieder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  In-place activated batchnorm for memory-optimized training  of dnns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' In 2018 IEEE Conference on Computer Vision and  Pattern Recognition, CVPR 2018, Salt Lake City, UT, USA,  June 18-22, 2018, pages 5639–5647.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Computer Vision Foun-  dation / IEEE Computer Society, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 1  [8] Jo˜ao Carreira, Rui Caseiro, Jorge P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Batista, and Cristian  Sminchisescu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Semantic segmentation with second-order  pooling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  In ECCV 2012 - 12th European Conference on  Computer Vision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Springer, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 2  [9] Jun Cen, Peng Yun, Junhao Cai, Michael Yu Wang, and Ming  Liu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Deep metric learning for open world semantic seg-  mentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' In 2021 IEEE/CVF International Conference on  Computer Vision, ICCV 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' IEEE, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 2  [10] Robin Chan, Krzysztof Lis, Svenja Uhlemeyer, Hermann  Blum, Sina Honari, Roland Siegwart, Pascal Fua, Mathieu  Salzmann, and Matthias Rottmann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Segmentmeifyoucan: A  benchmark for anomaly segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' In NeurIPS Datasets  and Benchmarks 1, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 1, 2  [11] Robin Chan, Matthias Rottmann, and Hanno Gottschalk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Entropy maximization and meta classification for out-of-  distribution detection in semantic segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' In Interna-  tional Conference on Computer Vision, ICCV, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 3, 4,  5  [12] Guangyao Chen,  Peixi Peng,  Xiangqian Wang,  and  Yonghong Tian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Adversarial reciprocal points learning for  open set recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Pattern Anal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Mach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' In-  tell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=', 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 2  [13] Liang-Chieh Chen, Yukun Zhu, George Papandreou, Florian  Schroff, and Hartwig Adam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Encoder-decoder with atrous  separable convolution for semantic image segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' In  ECCV, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 1  [14] Bowen Cheng, Maxwell D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Collins, Yukun Zhu, Ting Liu,  Thomas S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Huang, Hartwig Adam, and Liang-Chieh Chen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Panoptic-deeplab: A simple, strong, and fast baseline for  bottom-up panoptic segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' In IEEE/CVF Conference  on Computer Vision and Pattern Recognition, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 1  [15] Bowen Cheng, Ishan Misra, Alexander G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Schwing, Alexan-  der Kirillov, and Rohit Girdhar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Masked-attention mask  transformer for universal image segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' In IEEE/CVF  Conference on Computer Vision and Pattern Recognition,  CVPR 2022, pages 1280–1289.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' IEEE, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 1, 2, 4, 5, 7  [16] Bowen Cheng, Alexander G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Schwing, and Alexander Kir-  illov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Per-pixel classification is not all you need for semantic  segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' In NeurIPS 2021, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 1, 2, 3, 4  [17] Jifeng Dai, Kaiming He, and Jian Sun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Convolutional feature  masking for joint object and stuff segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' In CVPR,  pages 3992–4000, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 2  [18] Cl´ement Farabet, Camille Couprie, Laurent Najman, and  Yann LeCun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Learning hierarchical features for scene la-  beling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Pattern Anal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Mach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Intell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=', 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 1  [19] Matej Grcic, Petra Bevandic, Zoran Kalafatic, and Sinisa  Segvic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Dense anomaly detection by robust learning on syn-  thetic negative data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' CoRR, abs/2112.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='12833, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 3, 6  [20] Matej Grcic, Petra Bevandic, and Sinisa Segvic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Dense  open-set recognition with synthetic outliers generated by real  NVP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' In Proceedings of the 16th International Joint Confer-  ence on Computer Vision, Imaging and Computer Graphics  Theory and Applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' SCITEPRESS, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 8  [21] Matej Grcic, Petra Bevandic, and Sinisa Segvic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Densehy-  brid: Hybrid anomaly detection for dense open-set recogni-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' In ECCV 2022 - 17th European Conference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Springer,  2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 3, 5, 6  [22] Chuan Guo, Geoff Pleiss, Yu Sun, and Kilian Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Weinberger.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  On calibration of modern neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' In Proceedings  of the 34th International Conference on Machine Learning,  ICML 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' PMLR, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 1  [23] David Ha, Andrew M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Dai, and Quoc V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Le.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Hypernetworks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  In ICLR, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 2  [24] Bharath Hariharan, Pablo Andr´es Arbel´aez, Ross B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Gir-  shick, and Jitendra Malik.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Simultaneous detection and seg-  mentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  In ECCV 2014 - 13th European Conference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Springer, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 2  [25] Haodi He, Yuhui Yuan, Xiangyu Yue, and Han Hu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Rankseg:  Adaptive pixel classification with image category ranking for  segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' In ECCV 2022 - 17th European Conference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Springer, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 3, 7  [26] Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Deep residual learning for image recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' In Proceed-  ings of the IEEE Conference on Computer Vision and Pattern  Recognition (CVPR), June 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 5  [27] Dan Hendrycks, Steven Basart, Mantas Mazeika, Andy Zou,  Joseph Kwon, Mohammadreza Mostajabi, Jacob Steinhardt,  and Dawn Song.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Scaling out-of-distribution detection for  real-world settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' In International Conference on Machine  Learning, ICML 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' PMLR, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 1, 4, 5, 6, 7  [28] Dan Hendrycks and Kevin Gimpel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' A baseline for detect-  ing misclassified and out-of-distribution examples in neural  networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' In ICLR, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 2, 4, 5, 6, 8  9  [29] Dan Hendrycks, Mantas Mazeika, and Thomas G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Dietterich.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Deep anomaly detection with outlier exposure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  In ICLR,  2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 2, 8  [30] Jaedong Hwang, Seoung Wug Oh, Joon-Young Lee, and Bo-  hyung Han.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Exemplar-based open-set panoptic segmentation  network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' In IEEE Conference on Computer Vision and Pat-  tern Recognition, CVPR 2021, pages 1175–1184.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Computer  Vision Foundation / IEEE, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 1, 3, 6, 7  [31] Shipra Jain, Danda Pani Paudel, Martin Danelljan, and  Luc Van Gool.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Scaling semantic segmentation beyond 1k  classes on a single GPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' In 2021 IEEE/CVF International  Conference on Computer Vision, ICCV 2021, pages 7406–  7416.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' IEEE, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 1, 2, 3, 6, 7  [32] Sanghun Jung, Jungsoo Lee, Daehoon Gwak, Sungha Choi,  and Jaegul Choo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Standardized max logits: A simple yet  effective approach for identifying unexpected road obstacles  in urban-scene segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' In International Conference on  Computer Vision, ICCV, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 6  [33] Alex Kendall and Yarin Gal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' What uncertainties do we need  in bayesian deep learning for computer vision?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  In Neural  Information Processing Systems, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 5  [34] Polina Kirichenko, Pavel Izmailov, and Andrew Gordon Wil-  son.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Why normalizing flows fail to detect out-of-distribution  data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' In NeurIPS, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 2  [35] Alexander Kirillov, Yuxin Wu, Kaiming He, and Ross B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Girshick.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Pointrend: Image segmentation as rendering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' In  CVPR, pages 9796–9805, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 2  [36] Kimin Lee, Honglak Lee, Kibok Lee, and Jinwoo Shin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Training confidence-calibrated classifiers for detecting out-  of-distribution samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' In 6th International Conference on  Learning Representations, ICLR, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 2  [37] Chen Liang, Wenguan Wang, Jiaxu Miao, and Yi Yang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Gmmseg: Gaussian mixture based generative semantic seg-  mentation models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' In NeurIPS, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 3  [38] Shiyu Liang, Yixuan Li, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Srikant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Enhancing the re-  liability of out-of-distribution image detection in neural net-  works.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' In ICLR, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 2, 3, 5  [39] Krzysztof Lis, Sina Honari, Pascal Fua, and Mathieu Salz-  mann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Detecting road obstacles by erasing them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  CoRR,  abs/2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='13633, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 5  [40] Krzysztof Lis, Krishna Kanth Nakka, Pascal Fua, and Math-  ieu Salzmann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Detecting the unexpected via image resynthe-  sis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' In International Conference on Computer Vision, ICCV,  2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 3, 5, 6  [41] Weitang Liu, Xiaoyun Wang, John D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Owens, and Yixuan  Li.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Energy-based out-of-distribution detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' In NeurIPS  2020, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 2, 4, 6, 8  [42] Ze Liu, Yutong Lin, Yue Cao, Han Hu, Yixuan Wei, Zheng  Zhang, Stephen Lin, and Baining Guo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Swin transformer:  Hierarchical vision transformer using shifted windows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' In  2021 IEEE/CVF International Conference on Computer Vi-  sion, ICCV 2021, pages 9992–10002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' IEEE, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 5  [43] Jonathan Long, Evan Shelhamer, and Trevor Darrell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Fully  convolutional networks for semantic segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' In IEEE  Conference on Computer Vision and Pattern Recognition,  CVPR 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' IEEE Computer Society, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 1  [44] Jishnu Mukhoti and Yarin Gal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Evaluating bayesian  deep learning methods for semantic segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' CoRR,  abs/1811.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='12709, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 2  [45] Eric T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Nalisnick, Akihiro Matsukawa, Yee Whye Teh, Dilan  G¨or¨ur, and Balaji Lakshminarayanan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Do deep generative  models know what they don’t know?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  In 7th International  Conference on Learning Representations, ICLR, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 2  [46] Pedro Oliveira Pinheiro, Tsung-Yi Lin, Ronan Collobert, and  Piotr Doll´ar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Learning to refine object segments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' In ECCV,  volume 9905 of Lecture Notes in Computer Science, pages  75–91, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 2  [47] Joseph Redmon and Ali Farhadi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' YOLO9000: better, faster,  stronger.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' In 2017 IEEE Conference on Computer Vision and  Pattern Recognition, CVPR 2017, Honolulu, HI, USA, July  21-26, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' IEEE Computer Society, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 3  [48] Tal Ridnik, Emanuel Ben Baruch, Asaf Noy, and Lihi Zel-  nik.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Imagenet-21k pretraining for the masses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' In Proceed-  ings of the Neural Information Processing Systems Track on  Datasets and Benchmarks 1, NeurIPS 2021, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 3  [49] Matthias Rottmann, Pascal Colling, Thomas-Paul Hack,  Robin Chan, Fabian H¨uger, Peter Schlicht, and Hanno  Gottschalk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Prediction error meta classification in semantic  segmentation: Detection via aggregated dispersion measures  of softmax probabilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' In IJCNN, pages 1–9, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 3  [50] Lukas Ruff, Jacob R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Kauffmann, Robert A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Vander-  meulen, Gr´egoire Montavon, Wojciech Samek, Marius  Kloft, Thomas G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Dietterich, and Klaus-Robert M¨uller.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' A  unifying review of deep and shallow anomaly detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' IEEE, 109(5):756–795, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 2  [51] Walter J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Scheirer, Anderson de Rezende Rocha, Archana  Sapkota, and Terrance E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Boult.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Toward open set recogni-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' IEEE Transactions on Pattern Analysis and Machine  Intelligence, 35(7):1757–1772, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 2  [52] Walter J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Scheirer, Lalit P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Jain, and Terrance E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Boult.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Prob-  ability models for open set recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Pattern  Anal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Mach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Intell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=', 36(11):2317–2324, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 2  [53] Joan Serr`a, David ´Alvarez, Vicenc¸ G´omez, Olga Slizovskaia,  Jos´e F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' N´u˜nez, and Jordi Luque.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Input complexity and  out-of-distribution detection with likelihood-based genera-  tive models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' In ICLR, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 2  [54] Yu Tian, Yuyuan Liu, Guansong Pang, Fengbei Liu, Yuan-  hong Chen, and Gustavo Carneiro.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Pixel-wise energy-biased  abstention learning for anomaly segmentation on complex  urban driving scenes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' CoRR, abs/2111.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='12264, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 3, 5, 6  [55] Sagar Vaze, Kai Han, Andrea Vedaldi, and Andrew Zisser-  man.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Open-set recognition: A good closed-set classifier is all  you need.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' In The Tenth International Conference on Learn-  ing Representations, ICLR 2022, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 2, 5  [56] Tomas  Vojir,  Tom´aˇs  ˇSipka,  Rahaf  Aljundi,  Nikolay  Chumerin, Daniel Olmeda Reino, and Jiri Matas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Road  anomaly detection by partial image reconstruction with seg-  mentation coupling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' In International Conference on Com-  puter Vision, ICCV, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 3, 5  [57] Yingda Xia, Yi Zhang, Fengze Liu, Wei Shen, and Alan L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Yuille.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content='  Synthesize then compare: Detecting failures and  anomalies for semantic segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' In ECCV 2020 - 16th  European Conference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Springer, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 3, 6  10  [58] Oliver Zendel, Katrin Honauer, Markus Murschitz, Daniel  Steininger, and Gustavo Fern´andez Dom´ınguez.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Wilddash  creating hazard-aware benchmarks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' In ECCV, pages 407–  421, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 2  [59] Hongjie Zhang, Ang Li, Jie Guo, and Yanwen Guo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' Hybrid  models for open set recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' In 16th European Confer-  ence on Computer Vision ECCV, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
+page_content=' 2  11' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE1T4oBgHgl3EQfwAXq/content/2301.03407v1.pdf'}
diff --git a/_tA0T4oBgHgl3EQfPf_J/vector_store/index.faiss b/_tA0T4oBgHgl3EQfPf_J/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..512c3c61bc9f4ef62d3ef75de30a48d9a4a10b07
--- /dev/null
+++ b/_tA0T4oBgHgl3EQfPf_J/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:77425411f68f27516d787ce776e7acc79bb7e486cf27abe2aa97d0ff064754c9
+size 2490413
diff --git a/a9FAT4oBgHgl3EQf4x7K/vector_store/index.pkl b/a9FAT4oBgHgl3EQf4x7K/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..7ec34a4a7954df337631a937cc684a79565876f1
--- /dev/null
+++ b/a9FAT4oBgHgl3EQf4x7K/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:60524298bb736fbc68488e0511f600a2dc839ffeba1a255dc3b1aecf803e01d3
+size 15203
diff --git a/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf b/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..7e88d775935b55074e58cfaa406ed7f91f2a3d92
--- /dev/null
+++ b/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:9692228a3ad05d83cb4317f7724014c4690027cda99ec2d349ecce6974facb2a
+size 1282493
diff --git a/aNFPT4oBgHgl3EQfvTWR/vector_store/index.pkl b/aNFPT4oBgHgl3EQfvTWR/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..1850a0400281d7315f12a5f8b6db194df5bad768
--- /dev/null
+++ b/aNFPT4oBgHgl3EQfvTWR/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:7ecab7cfa60893577c84c08d4fc832ef7b7ebe56ada0b23d63715904d0e026b2
+size 102103
diff --git a/adAyT4oBgHgl3EQfivgk/content/tmp_files/2301.00400v1.pdf.txt b/adAyT4oBgHgl3EQfivgk/content/tmp_files/2301.00400v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..9612beeb92a3205a14e95e30c9d30dddb51c0c0e
--- /dev/null
+++ b/adAyT4oBgHgl3EQfivgk/content/tmp_files/2301.00400v1.pdf.txt
@@ -0,0 +1,534 @@
+High-resistivity niobium nitride films for unity-efficiency SMSPDs at
+telecom wavelengths and beyond
+Philipp Zolotov∗1, Sergey Svyatodukh1,2, Alexander Divochiy3, Vitaliy Seleznev2,3,
+and Gregory Goltsman1,2,3
+1Moscow Institute of Electronics and Mathematics
+Tallinskaya Ulitsa 34, 123592, Moscow, Russia
+2Moscow Pedagogical State University
+Malaya Pirogovskaya Ulitsa 1/1, 119435, Moscow, Russia
+3Superconducting Nanotechnology (SCONTEL)
+Derbenevskaya Naberezhnaya 11kA, 115114, Moscow, Russia
+∗pizolotov@ya.ru
+Tuesday 3rd January, 2023
+Abstract
+The sensitive element of superconducting single-photon detectors made in the form of a microstrip promise to
+resolve significant limitations caused by their typical design. However, attention should be paid to the problem of
+deterioration of the detection efficiency of devices with an increase of the width of the superconducting strip from
+nano- to microscale.
+This article demonstrates a possibility of achieving highly saturated detection efficiency of
+superconducting microstrip single-photon detectors by using high-resistivity niobium nitride films.
+The approach
+opens the way for employing fundamentally improved experimental devices.
+Superconducting
+single-photon
+detectors
+(SSPDs)
+gained
+a
+significant
+attention
+soon
+after
+pioneering
+work back in 2001[1].
+Nowadays these detectors are
+known for their wide operation range from ultra-violet
+to mid-infrared, high counting rates of the order of 1
+GHz, 3 ps jitter, and low dark count rates as low as
+a count per day [2, 3, 4, 5, 6].
+However, in practical
+applications in fields of quantum optics, astronomy, and
+others, preference is usually given to another significant
+metric – photon detection efficiency (DE)[7, 8, 9, 10].
+Practical realizations of SSPDs require a specific design
+of the sensitive element of the detectors that is fabricated
+as a narrow and long meandering nano-sized strip or
+nanowire.
+Recently, Colangelo et al.
+demonstrated
+that superconducting nanowire single-photon detectors
+(SNSPDs) reach unity DE not only in near-, but also in
+middle-infrared range[11]. This achievement was granted
+by nanowires as narrow as 50 nm with a total length of
+the order of several hundred microns that were fabricated
+from tungsten silicide film.
+However, such a peculiar
+design
+significantly
+limits
+detector’s
+dead
+time
+and
+temporal resolution due to high kinetic inductance[12].
+Moreover, it restricts device fabrication capacities and
+raises the bar for technological requirements.
+The essence of SSPD’s photoresponse is the transition
+of the strip cross section from superconducting to normal
+state. Emerging after photon absorption hotspot, which
+initiates this transition, has a size of about several tens
+of nanometers, which explains the desire to maximize its
+influence by making narrow strips. However, upon closer
+examination, it turns out that a vortex – antivortex pair
+(or a single vortex that appears when a spot occurs at
+the edge of the strip) generated in the hotspot can lead
+to a formation of normal cross section almost without any
+reference to strip width. This conclusion was drawn by Zo-
+tova and Vodolazov in 2012 and launched a new branch of
+research involving micrometer-scale strips[13, 14]. Later,
+in 2018 a fundamentally new experimental results bode a
+solution to described downsides of the mainstream SNSPD
+design[15].
+Authors demonstrated that short structures
+as wide as 5 µm fabricated from niobium nitride (NbN)
+film preserved single-photon response at visible range and
+1
+arXiv:2301.00400v1  [physics.ins-det]  1 Jan 2023
+
+Figure 1: Scanning electron microscope image of device
+design. Single 75 µm strip is located in the center between
+two Ti/Au contact pads (in false color).
+Inset demon-
+strates a transition to bridge width with smooth rounding
+preventing current crowding.
+held short reset time (τd ≈ 5 ns), as well as large critical
+currents (IC ≈ 0.5 mA). This proof-of-principle devices
+showed great promise for superconducting single-photon
+detection technology, but demonstrated the presence of
+a drastic drop of DE in the near-infrared range for wide
+detectors. Subsequent works addressed the DE of super-
+conducting microstrip single-photon detectors (SMSPDs)
+by implementing WSi and MoSi superconducting ultra-
+thin films exhibiting transition temperatures (Tc) below
+5 K[16, 17]. However, the main downside of low-Tc ma-
+terials is a demand of sophisticated cryogenic apparatus
+required for their operation. As a result, such cryogenic
+systems partly exclude the possibility of wide spreading of
+the devices.
+Around the same time it was demonstrated that DE
+of superconducting single-photon detectors is highly de-
+pendent on normal state sheet resistance (Rs) of initial
+films[18, 19].
+For increasing sheet resistance saturation
+plateaus of the dependencies of detection efficiency on bias
+current extend. This extension, however, remains vulner-
+able to increase of detector’s operation temperature, pho-
+ton energy, or, as stated above, strip width. While dete-
+rioration of saturation in case of a higher operation tem-
+perature could be a result of significant drop of current
+density, and its decline for lower photon energies could be
+explained by less efficient gap suppression, its change with
+strip width is not fully understood and requires further
+experimental investigation[20, 19]. As it is anticipated by
+Vodolazov photon detection by a microstrip should not
+depend on its width when one key condition is met. This
+key condition is the ability of the strip to carry a super-
+conducting current larger than 0.7Id, where Id is depair-
+ing current that is related to critical supervelocity of the
+Cooper pairs. Therefore, the search of the optimal mate-
+rial for SMSPDs and its operating conditions should ref-
+erence these key aspects. A good candidate for such role
+is niobium nitride, which is a conventional material for
+SSPD fabrication, and is well suited for operation in a
+wide temperature range thanks to its relatively high crit-
+ical temperature of the order of 10 K obtained in a thin
+film. SNSPDs made from niobium nitride films reach sys-
+tem detection efficiencies above 90% in GM cryocoolers
+operated at 2.2 K and therefore are convenient both for re-
+search purposes, as well as in-field applications[21, 18, 22].
+In the field of SMSPDs niobium nitride devices demon-
+strated proximity to saturation of DE at 1064 nm in 1
+and 3 µm-wide bridges operated at 1.7 K[23]. At the same
+time, only near-unity detection efficiency was achieved at
+1550 nm for the same conditions.
+Similar results were
+independently obtained by implementing helium irradia-
+tion for post-fabrication treatment of the detectors and by
+cooling them to lower temperature of 0.84 K[24]. Missing
+plateaus at 1550 nm in results by Korneeva et al. could
+be attributed to low current density in fabricated struc-
+tures together with low values of Rs = 764Ω/□ (Tc = 9
+K) of initial film.
+Similar performance in work by Xu
+and co-authors may be explained by low critical tempera-
+ture (Tc = 6.4 K at Rs = 1036Ω/□), which might require
+lower operation temperature than was achieved in the ex-
+periment. Considering the above facts our main goal was
+to experimentally evaluate the performance of SMSPDs
+made out from niobium nitride film with Rs ≈ 1 kΩ/□
+and Tc ≥ 8 K, which are believed to be the key require-
+ments for high-performance SMSPDs. These values are
+in a optimal correspondence with experimental data for
+NbN films presented in our previous work[18]. As a result,
+we demonstrate microstrip devices operated in a Gifford
+– McMahon (GM) cryocooler and reaching unity DE at
+telecom wavelengths and beyond.
+Deposition runs of niobium nitride ultra-thin films
+was performed by reactive magnetron sputtering of nio-
+bium target onto sapphire substrates with additional
+Ti/Au/Si3N4 optical cavity that is often applied for fabri-
+cation of practical SNSPDs. During the process substrate
+was maintained at 300 °C. Before each film deposition the
+target was presputtered with a closed magnetron shutter
+for 3 minutes. Over the period of film growth, a negative
+250 V RF bias was delivered to the substrate. Argon to
+nitrogen flow ratio was fixed at 40:15 cm3/min resulting
+in operating pressure of 4 mTorr. Deposition rate was cal-
+ibrated using quartz crystal microbalance and controlled
+via film deposition time.
+Among deposited samples we
+chose the film which exhibited the highest critical temper-
+ature while holding close to desirable resistance per square.
+Estimated film thickness was 5 nm.
+It was found that
+substrate biasing allowed to increase Tc of deposited film
+by 0.5 K compared to bias-free deposition which agrees
+with results by Dane et al.[25].
+Design of our samples
+constituted of single bridges with dose-stabilization struc-
+tures – Fig 1. Devices had the same bridge length of 75
+2
+
+20 μmFigure 2: Detection probabilities for two samples with 0.5 and 1 µm strip width operating at 2.2 and 0.8 K. Curves
+presented for five wavelengths.
+Table 1: Parameters of studied devices. Table contains strip widths measured with scanning electron microscopy.
+Stated Rs and RRR values are measured on D1 and are also employed for D2. Rs is found as maximum value on
+Rs(T) curve.
+Device
+Strip width, µm
+I2.2K
+c
+, µA
+I0.8K
+c
+, µA
+Rs, kΩ/□
+Tc, K
+RRR
+I2.2K
+c
+/I2.2K
+d
+I0.8K
+c
+/I0.8K
+d
+D1
+0.43
+30.0
+35.5
+1.25
+8.3
+0.72
+0.62
+0.66
+D2
+0.89
+66.2
+80.0
+1.25
+8.3
+0.72
+0.61
+0.66
+µm and width of either 0.5 or 1 µm.
+Resulting bridge
+widths together with film parameters are combined in Ta-
+ble 1. Pattern files were generated using PHIDL package
+with some additional code supplement for obtaining dose-
+stabilization structures[26].
+Films were patterned using
+a 30 kV electron-beam lithography with PMMA A3 re-
+sist followed by plasma-etching in SF6 with Ar admixture.
+Fabricated structures were supplemented with Ti/Au con-
+tact pads and separated into chips.
+In order to evaluate the change of DE not only for two
+studied bridge widths, but also for two operation tempera-
+tures, measurements of fabricated devices were performed
+at 2.2 and 0.8 K in a GM closed-cycle refrigeration cryo-
+stat with additional sorption cooler module. Devices were
+installed on PCBs using varnish and wire bonding. Op-
+erating temperature of the detectors was measured with
+a diode thermometer installed in the same setup. Signal
+from devices was led from the cryostat via coaxial cables
+to the room temperature bias-tee followed by amplifier
+chain. Due to low inductance of the devices that leaded
+to latching a 470 nH SMD inductor coil was connected
+in series with each detector. Measurement routine con-
+sisted of recording photocounts dependence on bias cur-
+rent at various wavelengths (650, 900, 1310, 1550, 1700
+nm) fed into the cryostat via optical fiber. Devices were
+flood-illuminated while output power of the laser was at-
+tenuated to establish similar counting rate for each device
+at each wavelength. Radiation was generated by super-
+3
+
+650
+650
+900
+900
+1310
+1310
+1550
+1550
+1700
+1700Figure 3: Alteration of DE curves at 650 nm for D1 (top)
+and D2 (bottom). At lower temperatures the curves ex-
+tend to higher bias current values without any significant
+shift in terms of curve center values.
+continuum laser source (repetition rate was 20 MHz) with
+acousto-optic tunable filter providing a typical wavelength
+peak width of less than 5 nm. To avoid high heat loads
+of the cryogenic stage operating temperature was contin-
+uously monitored. Figure 2 presents performance of two
+selected from fabricated batch devices with different strip
+width values. Both devices reach unity DE at operating
+temperature of 2.2 K in a wide spectral range. When de-
+tectors are cooled down to 0.8 K they both demonstrate
+high saturation level of DE with saturation plateaus be-
+ginning at approximately 0.75Ic – 0.85Ic depending on the
+wavelength and width. To better visualize how DE evolves
+for various conditions we separately plot obtained curves
+of each detector at incident wavelength of 650 nm at both
+operating temperatures — Figure 3. As it follows from the
+graphs, when plotted in absolute values of the bias current,
+dependencies taken at 0.8 K are a direct continuation of
+those obtained at 2.2 K.
+To find out how obtained results relate to Vodolazov
+theory we estimate the relation between operating cur-
+rents of our detectors and depairing values. For that an
+additional experiment was made to measure critical tem-
+perature of fabricated devices along with residual resis-
+tivity ratio RRR found as R300K
+s
+/R20K
+s
+. For D1 we find
+Ic/Idep equal to 53.5 and 48.6 µA at 0.8 and 2.2 K corre-
+spondingly. And for D2 — 120.3 µA at 0.8 K and 109.4 µA
+at 2.2 K. The calculations were made under an assumption
+that diffusion coefficient in our films is equal to 0.5 cm/s2.
+It should be highlighted that obtained critical temperature
+of fabricated devices was within 0.1 K lower than that of
+as-deposited film. Interestingly, obtained RRR value was
+approximately 10% higher than the typical value for our
+films with similar Rs but deposited without RF bias. For
+convenience, measured values are added to Table 1.
+It appears from what has been demonstrated that
+NbN films preserve the desired properties for fabrica-
+tion of superconducting microstrip single-photon detectors
+that demonstrate saturated detection efficiency at telecom
+wavelengths and beyond. Such achievement is attributed
+to implementation of a film with high sheet resistance
+value that simultaneously preserve high critical temper-
+ature, which also allows device operation in conventional
+cryocoolers. Described technology may streamline fabrica-
+tion process of SMSPDs with the help of photolithography
+and still offer high performance. It is also believed that
+SMSPDs could become a helpful testbed for evaluation of
+the optimal thin superconducting films’ parameters.
+References
+[1] GN Gol’Tsman, O Okunev, G Chulkova, A Lipatov,
+A Semenov, K Smirnov, B Voronov, A Dzardanov,
+C Williams,
+and Roman Sobolewski.
+Picosec-
+ond superconducting single-photon optical detector.
+Applied physics letters, 79(6):705–707, 2001.
+[2] Emma E Wollman, Varun B Verma, Andrew D Beyer,
+Ryan M Briggs, B Korzh, Jason P Allmaras, F Mar-
+sili, Adriana E Lita, RP Mirin, SW Nam, et al. Uv su-
+perconducting nanowire single-photon detectors with
+high efficiency, low noise, and 4 k operating temper-
+ature. Optics express, 25(22):26792–26801, 2017.
+[3] Francesco Marsili, Francesco Bellei, Faraz Najafi, An-
+drew E Dane, Eric A Dauler, Richard J Molnar, and
+Karl K Berggren. Efficient single photon detection
+from 500 nm to 5 µm wavelength. Nano letters, 12
+(9):4799–4804, 2012.
+[4] Andreas Vetter, Simone Ferrari, Patrik Rath, Rasoul
+Alaee, Oliver Kahl, Vadim Kovalyuk, Silvia Diewald,
+Gregory N Goltsman, Alexander Korneev, Carsten
+Rockstuhl, et al. Cavity-enhanced and ultrafast su-
+perconducting single-photon detectors. Nano letters,
+16(11):7085–7092, 2016.
+[5] Boris Korzh, Qing-Yuan Zhao, Jason P Allmaras, Si-
+mone Frasca, Travis M Autry, Eric A Bersin, An-
+drew D Beyer, Ryan M Briggs, Bruce Bumble, Marco
+Colangelo, et al. Demonstration of sub-3 ps temporal
+resolution with a superconducting nanowire single-
+photon detector.
+Nature Photonics, 14(4):250–255,
+2020.
+[6] G Goltsman, A Korneev, V Izbenko, K Smirnov,
+P Kouminov, B Voronov, N Kaurova, A Verevkin,
+J Zhang,
+A Pearlman,
+et al.
+Nano-structured
+superconducting single-photon detectors.
+Nuclear
+Instruments
+and
+Methods
+in
+Physics
+Research
+Section A: Accelerators, Spectrometers, Detectors
+and Associated Equipment, 520(1-3):527–529, 2004.
+[7] Paul-Antoine Moreau, Ermes Toninelli, Thomas Gre-
+gory, and Miles J Padgett. Imaging with quantum
+states of light. Nature Reviews Physics, 1(6):367–380,
+2019.
+[8] Manuel Untern¨ahrer, B¨anz Bessire, Leonardo Gas-
+4
+
+D1 0.8 K
+D1 2.2 K
+D2 0.8 K
+D2 2.2 Kparini,
+Matteo Perenzoni,
+and Andr´e Stefanov.
+Super-resolution quantum imaging at the heisenberg
+limit. Optica, 5(9):1150–1154, 2018.
+[9] Nisan
+Ozana,
+Alexander
+I
+Zavriyev,
+Dibbyan
+Mazumder,
+Mitchell
+B
+Robinson,
+Kutlu
+Kaya,
+Megan H Blackwell, Stefan A Carp, and Maria An-
+gela
+Franceschini.
+Superconducting
+nanowire
+single-photon
+sensing
+of
+cerebral
+blood
+flow.
+Neurophotonics, 8(3):035006, 2021.
+[10] Shuang Wang, Zhen-Qiang Yin, De-Yong He, Wei
+Chen, Rui-Qiang Wang, Peng Ye, Yao Zhou, Guan-
+Jie Fan-Yuan, Fang-Xiang Wang, Yong-Gang Zhu,
+et al. Twin-field quantum key distribution over 830-
+km fibre. Nature Photonics, 16(2):154–161, 2022.
+[11] Marco Colangelo, Alexander B Walter, Boris A Ko-
+rzh, Ekkehart Schmidt, Bruce Bumble, Adriana E
+Lita, Andrew D Beyer, Jason P Allmaras, Ryan M
+Briggs, Alexander G Kozorezov, et al. Large-area su-
+perconducting nanowire single-photon detectors for
+operation at wavelengths up to 7.4 µm. Nano Letters,
+22(14):5667–5673, 2022.
+[12] Andrew J Kerman, Eric A Dauler, William E Keicher,
+Joel KW Yang, Karl K Berggren, G Gol’Tsman, and
+B Voronov. Kinetic-inductance-limited reset time of
+superconducting nanowire photon counters. Applied
+physics letters, 88(11):111116, 2006.
+[13] AN Zotova and D Yu Vodolazov.
+Photon detec-
+tion by current-carrying superconducting film:
+A
+time-dependent ginzburg-landau approach. Physical
+Review B, 85(2):024509, 2012.
+[14] D Yu Vodolazov. Single-photon detection by a dirty
+current-carrying superconducting strip based on the
+kinetic-equation approach. Physical Review Applied,
+7(3):034014, 2017.
+[15] Yu P Korneeva, D Yu Vodolazov, AV Semenov,
+IN Florya, N Simonov, E Baeva, AA Korneev,
+GN Goltsman, and TM Klapwijk.
+Optical single-
+photon detection in micrometer-scale nbn bridges.
+Physical Review Applied, 9(6):064037, 2018.
+[16] Ilya Charaev,
+Yukimi Morimoto,
+Andrew Dane,
+Akshay Agarwal, Marco Colangelo, and Karl K
+Berggren. Large-area microwire mosi single-photon
+detectors at 1550 nm wavelength. Applied Physics
+Letters, 116(24):242603, 2020.
+[17] Jeff Chiles, Sonia M Buckley, Adriana Lita, Varun B
+Verma, Jason Allmaras, Boris Korzh, Matthew D
+Shaw, Jeffrey M Shainline, Richard P Mirin, and
+Sae Woo Nam.
+Superconducting microwire detec-
+tors based on wsi with single-photon sensitivity in
+the near-infrared. Applied Physics Letters, 116(24):
+242602, 2020.
+[18] Philipp I Zolotov, Alexander V Semenov, Alexan-
+der V Divochiy, Gregory N Goltsman, Nikita R Ro-
+manov, and Teunis M Klapwijk. Dependence of pho-
+ton detection efficiency on normal-state sheet resis-
+tance in marginally superconducting films of nbn.
+IEEE Transactions on Applied Superconductivity, 31
+(5):1–5, 2021.
+[19] Alexej D Semenov.
+Superconducting nanostrip
+single-photon detectors some fundamental aspects
+in detection mechanism,
+technology and perfor-
+mance. Superconductor Science and Technology, 34
+(5):054002, 2021.
+[20] Jelmer Jan Renema.
+The physics of nanowire
+superconducting single-photon detectors. PhD the-
+sis, Leiden University, 2015.
+[21] Konstantin
+Smirnov,
+Alexander
+Divochiy,
+Yury
+Vakhtomin, Pavel Morozov, Philipp Zolotov, Andrey
+Antipov, and Vitaliy Seleznev.
+Nbn single-photon
+detectors with saturated dependence of quantum ef-
+ficiency. Superconductor Science and Technology, 31
+(3):035011, 2018.
+[22] Iman Esmaeil Zadeh, J Chang, Johannes WN Los,
+Samuel Gyger, Ali W Elshaari, Stephan Steinhauer,
+Sander N Dorenbos, and Val Zwiller. Superconduct-
+ing nanowire single-photon detectors: A perspective
+on evolution, state-of-the-art, future developments,
+and applications. Applied Physics Letters, 118(19):
+190502, 2021.
+[23] Yu P Korneeva, NN Manova, MA Dryazgov, NO Si-
+monov, Ph I Zolotov, and AA Korneev.
+Influence
+of sheet resistance and strip width on the detection
+efficiency saturation in micron-wide superconduct-
+ing strips and large-area meanders. Superconductor
+Science and Technology, 34(8):084001, 2021.
+[24] Guang-Zhao Xu, Wei-Jun Zhang, Li-Xing You, Jia-
+Min Xiong, Xing-Qu Sun, Hao Huang, Xin Ou, Yi-
+Ming Pan, Chao-Lin Lv, Hao Li, et al. Superconduct-
+ing microstrip single-photon detector with system de-
+tection efficiency over 90% at 1550 nm.
+Photonics
+Research, 9(6):958–967, 2021.
+[25] Andrew E Dane, Adam N McCaughan, Di Zhu,
+Qingyuan Zhao, Chung-Soo Kim, Niccolo Calan-
+dri, Akshay Agarwal, Francesco Bellei, and Karl K
+Berggren. Bias sputtered nbn and superconducting
+nanowire devices. Applied Physics Letters, 111(12):
+122601, 2017.
+[26] Adam N McCaughan, Alexander N Tait, Sonia M
+Buckley, Dylan M Oh, Jeffrey T Chiles, Jeffrey M
+Shainline, and Sae Woo Nam.
+Phidl:
+Python-
+based layout and geometry creation for nanolithog-
+raphy.
+Journal of Vacuum Science & Technology
+B, Nanotechnology and Microelectronics: Materials,
+Processing, Measurement, and Phenomena, 39(6):
+062601, 2021.
+5
+
diff --git a/adAyT4oBgHgl3EQfivgk/content/tmp_files/load_file.txt b/adAyT4oBgHgl3EQfivgk/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..42e1d6d47e724f8f035ec5f41e17d1417bf89a70
--- /dev/null
+++ b/adAyT4oBgHgl3EQfivgk/content/tmp_files/load_file.txt
@@ -0,0 +1,250 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf,len=249
+page_content='High-resistivity niobium nitride films for unity-efficiency SMSPDs at  telecom wavelengths and beyond  Philipp Zolotov∗1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Sergey Svyatodukh1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Alexander Divochiy3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Vitaliy Seleznev2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  and Gregory Goltsman1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='3  1Moscow Institute of Electronics and Mathematics  Tallinskaya Ulitsa 34,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' 123592,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Moscow,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Russia  2Moscow Pedagogical State University  Malaya Pirogovskaya Ulitsa 1/1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' 119435,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Moscow,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Russia  3Superconducting Nanotechnology (SCONTEL)  Derbenevskaya Naberezhnaya 11kA,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' 115114,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Moscow,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Russia  ∗pizolotov@ya.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='ru  Tuesday 3rd January, 2023  Abstract  The sensitive element of superconducting single-photon detectors made in the form of a microstrip promise to  resolve significant limitations caused by their typical design.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' However, attention should be paid to the problem of  deterioration of the detection efficiency of devices with an increase of the width of the superconducting strip from  nano- to microscale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  This article demonstrates a possibility of achieving highly saturated detection efficiency of  superconducting microstrip single-photon detectors by using high-resistivity niobium nitride films.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  The approach  opens the way for employing fundamentally improved experimental devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  Superconducting  single-photon  detectors  (SSPDs)  gained  a  significant  attention  soon  after  pioneering  work back in 2001[1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  Nowadays these detectors are  known for their wide operation range from ultra-violet  to mid-infrared, high counting rates of the order of 1  GHz, 3 ps jitter, and low dark count rates as low as  a count per day [2, 3, 4, 5, 6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  However, in practical  applications in fields of quantum optics, astronomy, and  others, preference is usually given to another significant  metric – photon detection efficiency (DE)[7, 8, 9, 10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  Practical realizations of SSPDs require a specific design  of the sensitive element of the detectors that is fabricated  as a narrow and long meandering nano-sized strip or  nanowire.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  Recently, Colangelo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  demonstrated  that superconducting nanowire single-photon detectors  (SNSPDs) reach unity DE not only in near-, but also in  middle-infrared range[11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' This achievement was granted  by nanowires as narrow as 50 nm with a total length of  the order of several hundred microns that were fabricated  from tungsten silicide film.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  However, such a peculiar  design  significantly  limits  detector’s  dead  time  and  temporal resolution due to high kinetic inductance[12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  Moreover, it restricts device fabrication capacities and  raises the bar for technological requirements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  The essence of SSPD’s photoresponse is the transition  of the strip cross section from superconducting to normal  state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Emerging after photon absorption hotspot, which  initiates this transition, has a size of about several tens  of nanometers, which explains the desire to maximize its  influence by making narrow strips.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' However, upon closer  examination, it turns out that a vortex – antivortex pair  (or a single vortex that appears when a spot occurs at  the edge of the strip) generated in the hotspot can lead  to a formation of normal cross section almost without any  reference to strip width.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' This conclusion was drawn by Zo-  tova and Vodolazov in 2012 and launched a new branch of  research involving micrometer-scale strips[13, 14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Later,  in 2018 a fundamentally new experimental results bode a  solution to described downsides of the mainstream SNSPD  design[15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  Authors demonstrated that short structures  as wide as 5 µm fabricated from niobium nitride (NbN)  film preserved single-photon response at visible range and  1  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='00400v1  [physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='ins-det]  1 Jan 2023  Figure 1: Scanning electron microscope image of device  design.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Single 75 µm strip is located in the center between  two Ti/Au contact pads (in false color).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  Inset demon-  strates a transition to bridge width with smooth rounding  preventing current crowding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  held short reset time (τd ≈ 5 ns), as well as large critical  currents (IC ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='5 mA).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' This proof-of-principle devices  showed great promise for superconducting single-photon  detection technology, but demonstrated the presence of  a drastic drop of DE in the near-infrared range for wide  detectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Subsequent works addressed the DE of super-  conducting microstrip single-photon detectors (SMSPDs)  by implementing WSi and MoSi superconducting ultra-  thin films exhibiting transition temperatures (Tc) below  5 K[16, 17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' However, the main downside of low-Tc ma-  terials is a demand of sophisticated cryogenic apparatus  required for their operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' As a result, such cryogenic  systems partly exclude the possibility of wide spreading of  the devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  Around the same time it was demonstrated that DE  of superconducting single-photon detectors is highly de-  pendent on normal state sheet resistance (Rs) of initial  films[18, 19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  For increasing sheet resistance saturation  plateaus of the dependencies of detection efficiency on bias  current extend.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' This extension, however, remains vulner-  able to increase of detector’s operation temperature, pho-  ton energy, or, as stated above, strip width.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' While dete-  rioration of saturation in case of a higher operation tem-  perature could be a result of significant drop of current  density, and its decline for lower photon energies could be  explained by less efficient gap suppression, its change with  strip width is not fully understood and requires further  experimental investigation[20, 19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' As it is anticipated by  Vodolazov photon detection by a microstrip should not  depend on its width when one key condition is met.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' This  key condition is the ability of the strip to carry a super-  conducting current larger than 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='7Id, where Id is depair-  ing current that is related to critical supervelocity of the  Cooper pairs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Therefore, the search of the optimal mate-  rial for SMSPDs and its operating conditions should ref-  erence these key aspects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' A good candidate for such role  is niobium nitride, which is a conventional material for  SSPD fabrication, and is well suited for operation in a  wide temperature range thanks to its relatively high crit-  ical temperature of the order of 10 K obtained in a thin  film.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' SNSPDs made from niobium nitride films reach sys-  tem detection efficiencies above 90% in GM cryocoolers  operated at 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='2 K and therefore are convenient both for re-  search purposes, as well as in-field applications[21, 18, 22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  In the field of SMSPDs niobium nitride devices demon-  strated proximity to saturation of DE at 1064 nm in 1  and 3 µm-wide bridges operated at 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='7 K[23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' At the same  time, only near-unity detection efficiency was achieved at  1550 nm for the same conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  Similar results were  independently obtained by implementing helium irradia-  tion for post-fabrication treatment of the detectors and by  cooling them to lower temperature of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='84 K[24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Missing  plateaus at 1550 nm in results by Korneeva et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' could  be attributed to low current density in fabricated struc-  tures together with low values of Rs = 764Ω/□ (Tc = 9  K) of initial film.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  Similar performance in work by Xu  and co-authors may be explained by low critical tempera-  ture (Tc = 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='4 K at Rs = 1036Ω/□), which might require  lower operation temperature than was achieved in the ex-  periment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Considering the above facts our main goal was  to experimentally evaluate the performance of SMSPDs  made out from niobium nitride film with Rs ≈ 1 kΩ/□  and Tc ≥ 8 K, which are believed to be the key require-  ments for high-performance SMSPDs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' These values are  in a optimal correspondence with experimental data for  NbN films presented in our previous work[18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' As a result,  we demonstrate microstrip devices operated in a Gifford  – McMahon (GM) cryocooler and reaching unity DE at  telecom wavelengths and beyond.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  Deposition runs of niobium nitride ultra-thin films  was performed by reactive magnetron sputtering of nio-  bium target onto sapphire substrates with additional  Ti/Au/Si3N4 optical cavity that is often applied for fabri-  cation of practical SNSPDs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' During the process substrate  was maintained at 300 °C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Before each film deposition the  target was presputtered with a closed magnetron shutter  for 3 minutes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Over the period of film growth, a negative  250 V RF bias was delivered to the substrate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Argon to  nitrogen flow ratio was fixed at 40:15 cm3/min resulting  in operating pressure of 4 mTorr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Deposition rate was cal-  ibrated using quartz crystal microbalance and controlled  via film deposition time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  Among deposited samples we  chose the film which exhibited the highest critical temper-  ature while holding close to desirable resistance per square.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  Estimated film thickness was 5 nm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  It was found that  substrate biasing allowed to increase Tc of deposited film  by 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='5 K compared to bias-free deposition which agrees  with results by Dane et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' [25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  Design of our samples  constituted of single bridges with dose-stabilization struc-  tures – Fig 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Devices had the same bridge length of 75  2  20 μmFigure 2: Detection probabilities for two samples with 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='5 and 1 µm strip width operating at 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='2 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='8 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Curves  presented for five wavelengths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  Table 1: Parameters of studied devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Table contains strip widths measured with scanning electron microscopy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  Stated Rs and RRR values are measured on D1 and are also employed for D2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Rs is found as maximum value on  Rs(T) curve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  Device  Strip width, µm  I2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='2K  c  , µA  I0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='8K  c  , µA  Rs, kΩ/□  Tc, K  RRR  I2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='2K  c  /I2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='2K  d  I0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='8K  c  /I0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='8K  d  D1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='43  30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='0  35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='25  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='72  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='62  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='66  D2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='89  66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='2  80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='25  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='72  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='61  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='66  µm and width of either 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='5 or 1 µm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  Resulting bridge  widths together with film parameters are combined in Ta-  ble 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Pattern files were generated using PHIDL package  with some additional code supplement for obtaining dose-  stabilization structures[26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  Films were patterned using  a 30 kV electron-beam lithography with PMMA A3 re-  sist followed by plasma-etching in SF6 with Ar admixture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  Fabricated structures were supplemented with Ti/Au con-  tact pads and separated into chips.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  In order to evaluate the change of DE not only for two  studied bridge widths, but also for two operation tempera-  tures, measurements of fabricated devices were performed  at 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='2 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='8 K in a GM closed-cycle refrigeration cryo-  stat with additional sorption cooler module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Devices were  installed on PCBs using varnish and wire bonding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Op-  erating temperature of the detectors was measured with  a diode thermometer installed in the same setup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Signal  from devices was led from the cryostat via coaxial cables  to the room temperature bias-tee followed by amplifier  chain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Due to low inductance of the devices that leaded  to latching a 470 nH SMD inductor coil was connected  in series with each detector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Measurement routine con-  sisted of recording photocounts dependence on bias cur-  rent at various wavelengths (650, 900, 1310, 1550, 1700  nm) fed into the cryostat via optical fiber.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Devices were  flood-illuminated while output power of the laser was at-  tenuated to establish similar counting rate for each device  at each wavelength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Radiation was generated by super-  3  650  650  900  900  1310  1310  1550  1550  1700  1700Figure 3: Alteration of DE curves at 650 nm for D1 (top)  and D2 (bottom).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' At lower temperatures the curves ex-  tend to higher bias current values without any significant  shift in terms of curve center values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  continuum laser source (repetition rate was 20 MHz) with  acousto-optic tunable filter providing a typical wavelength  peak width of less than 5 nm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' To avoid high heat loads  of the cryogenic stage operating temperature was contin-  uously monitored.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Figure 2 presents performance of two  selected from fabricated batch devices with different strip  width values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Both devices reach unity DE at operating  temperature of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='2 K in a wide spectral range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' When de-  tectors are cooled down to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='8 K they both demonstrate  high saturation level of DE with saturation plateaus be-  ginning at approximately 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='75Ic – 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='85Ic depending on the  wavelength and width.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' To better visualize how DE evolves  for various conditions we separately plot obtained curves  of each detector at incident wavelength of 650 nm at both  operating temperatures — Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' As it follows from the  graphs, when plotted in absolute values of the bias current,  dependencies taken at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='8 K are a direct continuation of  those obtained at 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='2 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  To find out how obtained results relate to Vodolazov  theory we estimate the relation between operating cur-  rents of our detectors and depairing values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' For that an  additional experiment was made to measure critical tem-  perature of fabricated devices along with residual resis-  tivity ratio RRR found as R300K  s  /R20K  s  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' For D1 we find  Ic/Idep equal to 53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='5 and 48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='6 µA at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='8 and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='2 K corre-  spondingly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' And for D2 — 120.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='3 µA at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='8 K and 109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='4 µA  at 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='2 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' The calculations were made under an assumption  that diffusion coefficient in our films is equal to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='5 cm/s2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  It should be highlighted that obtained critical temperature  of fabricated devices was within 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='1 K lower than that of  as-deposited film.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Interestingly, obtained RRR value was  approximately 10% higher than the typical value for our  films with similar Rs but deposited without RF bias.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' For  convenience, measured values are added to Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  It appears from what has been demonstrated that  NbN films preserve the desired properties for fabrica-  tion of superconducting microstrip single-photon detectors  that demonstrate saturated detection efficiency at telecom  wavelengths and beyond.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Such achievement is attributed  to implementation of a film with high sheet resistance  value that simultaneously preserve high critical temper-  ature, which also allows device operation in conventional  cryocoolers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Described technology may streamline fabrica-  tion process of SMSPDs with the help of photolithography  and still offer high performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' It is also believed that  SMSPDs could become a helpful testbed for evaluation of  the optimal thin superconducting films’ parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  References  [1] GN Gol’Tsman, O Okunev, G Chulkova, A Lipatov,  A Semenov, K Smirnov, B Voronov, A Dzardanov,  C Williams,  and Roman Sobolewski.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  Picosec-  ond superconducting single-photon optical detector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  Applied physics letters, 79(6):705–707, 2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  [2] Emma E Wollman, Varun B Verma, Andrew D Beyer,  Ryan M Briggs, B Korzh, Jason P Allmaras, F Mar-  sili, Adriana E Lita, RP Mirin, SW Nam, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Uv su-  perconducting nanowire single-photon detectors with  high efficiency, low noise, and 4 k operating temper-  ature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Optics express, 25(22):26792–26801, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  [3] Francesco Marsili, Francesco Bellei, Faraz Najafi, An-  drew E Dane, Eric A Dauler, Richard J Molnar, and  Karl K Berggren.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Efficient single photon detection  from 500 nm to 5 µm wavelength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Nano letters, 12  (9):4799–4804, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  [4] Andreas Vetter, Simone Ferrari, Patrik Rath, Rasoul  Alaee, Oliver Kahl, Vadim Kovalyuk, Silvia Diewald,  Gregory N Goltsman, Alexander Korneev, Carsten  Rockstuhl, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Cavity-enhanced and ultrafast su-  perconducting single-photon detectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Nano letters,  16(11):7085–7092, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  [5] Boris Korzh, Qing-Yuan Zhao, Jason P Allmaras, Si-  mone Frasca, Travis M Autry, Eric A Bersin, An-  drew D Beyer, Ryan M Briggs, Bruce Bumble, Marco  Colangelo, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Demonstration of sub-3 ps temporal  resolution with a superconducting nanowire single-  photon detector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  Nature Photonics, 14(4):250–255,  2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  [6] G Goltsman, A Korneev, V Izbenko, K Smirnov,  P Kouminov, B Voronov, N Kaurova, A Verevkin,  J Zhang,  A Pearlman,  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  Nano-structured  superconducting single-photon detectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  Nuclear  Instruments  and  Methods  in  Physics  Research  Section A: Accelerators, Spectrometers, Detectors  and Associated Equipment, 520(1-3):527–529, 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  [7] Paul-Antoine Moreau, Ermes Toninelli, Thomas Gre-  gory, and Miles J Padgett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Imaging with quantum  states of light.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Nature Reviews Physics, 1(6):367–380,  2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  [8] Manuel Untern¨ahrer, B¨anz Bessire, Leonardo Gas-  4  D1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='8 K  D1 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='2 K  D2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='8 K  D2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='2 Kparini,  Matteo Perenzoni,  and Andr´e Stefanov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  Super-resolution quantum imaging at the heisenberg  limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Optica, 5(9):1150–1154, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  [9] Nisan  Ozana,  Alexander  I  Zavriyev,  Dibbyan  Mazumder,  Mitchell  B  Robinson,  Kutlu  Kaya,  Megan H Blackwell, Stefan A Carp, and Maria An-  gela  Franceschini.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  Superconducting  nanowire  single-photon  sensing  of  cerebral  blood  flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  Neurophotonics, 8(3):035006, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  [10] Shuang Wang, Zhen-Qiang Yin, De-Yong He, Wei  Chen, Rui-Qiang Wang, Peng Ye, Yao Zhou, Guan-  Jie Fan-Yuan, Fang-Xiang Wang, Yong-Gang Zhu,  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Twin-field quantum key distribution over 830-  km fibre.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Nature Photonics, 16(2):154–161, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  [11] Marco Colangelo, Alexander B Walter, Boris A Ko-  rzh, Ekkehart Schmidt, Bruce Bumble, Adriana E  Lita, Andrew D Beyer, Jason P Allmaras, Ryan M  Briggs, Alexander G Kozorezov, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Large-area su-  perconducting nanowire single-photon detectors for  operation at wavelengths up to 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='4 µm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Nano Letters,  22(14):5667–5673, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  [12] Andrew J Kerman, Eric A Dauler, William E Keicher,  Joel KW Yang, Karl K Berggren, G Gol’Tsman, and  B Voronov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Kinetic-inductance-limited reset time of  superconducting nanowire photon counters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Applied  physics letters, 88(11):111116, 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  [13] AN Zotova and D Yu Vodolazov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  Photon detec-  tion by current-carrying superconducting film:  A  time-dependent ginzburg-landau approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Physical  Review B, 85(2):024509, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  [14] D Yu Vodolazov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Single-photon detection by a dirty  current-carrying superconducting strip based on the  kinetic-equation approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Physical Review Applied,  7(3):034014, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  [15] Yu P Korneeva, D Yu Vodolazov, AV Semenov,  IN Florya, N Simonov, E Baeva, AA Korneev,  GN Goltsman, and TM Klapwijk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  Optical single-  photon detection in micrometer-scale nbn bridges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  Physical Review Applied, 9(6):064037, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  [16] Ilya Charaev,  Yukimi Morimoto,  Andrew Dane,  Akshay Agarwal, Marco Colangelo, and Karl K  Berggren.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Large-area microwire mosi single-photon  detectors at 1550 nm wavelength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Applied Physics  Letters, 116(24):242603, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  [17] Jeff Chiles, Sonia M Buckley, Adriana Lita, Varun B  Verma, Jason Allmaras, Boris Korzh, Matthew D  Shaw, Jeffrey M Shainline, Richard P Mirin, and  Sae Woo Nam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  Superconducting microwire detec-  tors based on wsi with single-photon sensitivity in  the near-infrared.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Applied Physics Letters, 116(24):  242602, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  [18] Philipp I Zolotov, Alexander V Semenov, Alexan-  der V Divochiy, Gregory N Goltsman, Nikita R Ro-  manov, and Teunis M Klapwijk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Dependence of pho-  ton detection efficiency on normal-state sheet resis-  tance in marginally superconducting films of nbn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  IEEE Transactions on Applied Superconductivity, 31  (5):1–5, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  [19] Alexej D Semenov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  Superconducting nanostrip  single-photon detectors some fundamental aspects  in detection mechanism,  technology and perfor-  mance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Superconductor Science and Technology, 34  (5):054002, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  [20] Jelmer Jan Renema.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  The physics of nanowire  superconducting single-photon detectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' PhD the-  sis, Leiden University, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  [21] Konstantin  Smirnov,  Alexander  Divochiy,  Yury  Vakhtomin, Pavel Morozov, Philipp Zolotov, Andrey  Antipov, and Vitaliy Seleznev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  Nbn single-photon  detectors with saturated dependence of quantum ef-  ficiency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Superconductor Science and Technology, 31  (3):035011, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  [22] Iman Esmaeil Zadeh, J Chang, Johannes WN Los,  Samuel Gyger, Ali W Elshaari, Stephan Steinhauer,  Sander N Dorenbos, and Val Zwiller.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Superconduct-  ing nanowire single-photon detectors: A perspective  on evolution, state-of-the-art, future developments,  and applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Applied Physics Letters, 118(19):  190502, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  [23] Yu P Korneeva, NN Manova, MA Dryazgov, NO Si-  monov, Ph I Zolotov, and AA Korneev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  Influence  of sheet resistance and strip width on the detection  efficiency saturation in micron-wide superconduct-  ing strips and large-area meanders.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Superconductor  Science and Technology, 34(8):084001, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  [24] Guang-Zhao Xu, Wei-Jun Zhang, Li-Xing You, Jia-  Min Xiong, Xing-Qu Sun, Hao Huang, Xin Ou, Yi-  Ming Pan, Chao-Lin Lv, Hao Li, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Superconduct-  ing microstrip single-photon detector with system de-  tection efficiency over 90% at 1550 nm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  Photonics  Research, 9(6):958–967, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  [25] Andrew E Dane, Adam N McCaughan, Di Zhu,  Qingyuan Zhao, Chung-Soo Kim, Niccolo Calan-  dri, Akshay Agarwal, Francesco Bellei, and Karl K  Berggren.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Bias sputtered nbn and superconducting  nanowire devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content=' Applied Physics Letters, 111(12):  122601, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  [26] Adam N McCaughan, Alexander N Tait, Sonia M  Buckley, Dylan M Oh, Jeffrey T Chiles, Jeffrey M  Shainline, and Sae Woo Nam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  Phidl:  Python-  based layout and geometry creation for nanolithog-  raphy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  Journal of Vacuum Science & Technology  B, Nanotechnology and Microelectronics: Materials,  Processing, Measurement, and Phenomena, 39(6):  062601, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
+page_content='  5' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAyT4oBgHgl3EQfivgk/content/2301.00400v1.pdf'}
diff --git a/adE_T4oBgHgl3EQfyxwh/content/tmp_files/2301.08319v1.pdf.txt b/adE_T4oBgHgl3EQfyxwh/content/tmp_files/2301.08319v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..eb95ea1f9869240b61efb159f4deaab420088d95
--- /dev/null
+++ b/adE_T4oBgHgl3EQfyxwh/content/tmp_files/2301.08319v1.pdf.txt
@@ -0,0 +1,1227 @@
+Noncanonical inflation in f(R, T) gravity with Hamilton-Jacobi
+formalism
+Z. Ossoulian, Kh.
+Saaidi,∗ and S. Taghavi
+Department of Physics, Faculty of Science,
+University of Kurdistan, Sanandaj, Iran.
+(Dated: January 23, 2023)
+Abstract
+The scenario of slow-roll inflation is explored in the f(R, T) theory of gravity where a non-
+minimal coupling between matter and curvature is included. A noncanonical scalar field is assumed
+to play the role of inflaton which contains generalized kinetic energy. The study is performed by
+taking the Hamilton-Jacobi formalism where the Hubble parameter is taken as a function of the
+scalar field. In this regard, a power-law function and an exponential function of the scalar field are
+assumed for the Hubble parameter and the model is considered in detail. By performing Python
+coding and applying the observational data, the free parameters of the model are determined for
+which the model is put in perfect consistency with the data. Then, using the results, the validity
+of the swampland criteria and TCC is considered. It is realized that not only the model comes to
+a good agreement with data, but it also could satisfy the swampland criteria.
+∗ ksaaidi@uok.ac.ir
+1
+arXiv:2301.08319v1  [gr-qc]  18 Jan 2023
+
+I.
+INTRODUCTION
+Although the theory of general relativity has emerged successfully from many experi-
+ments, some challenging issues cannot be solved in the frame of general relativity. One of
+the main issues that the theory is faced with is the flatness and horizon problems. It could
+not provide a competent explanation for the problems. A possible solution is assuming an
+early exponential expansion phase, known as cosmic inflation, which has been developed by
+many scientists [1–3] since its first introduction [4, 5]. A common approach for studying
+inflation is by considering a single scalar field, known as inflaton, with a potential and
+imposing the slow-roll approximations [6–14]. The scenario shows an incredible consistency
+with data and it becomes the cornerstone of any cosmological model [15–17]. There are
+many different models of inflation based on the aforementioned suggestions [18–51].
+Another issue that the general theory of relativity encounters is the requirement of dark
+energy and dark matter to be able to fit the cosmological data. This issue became the
+main motivation for introducing alternative theories of gravity. The f(R, T) gravity theory
+is one of the alternative theories where R is the curvature scalar, T is the trace of the
+energy-momentum tensor, and f is an arbitrary function of R and T. The theory was first
+introduced by Harko et. al. [52]. It has been utilized to study different topics in cosmology
+including dark energy [53], dark matter [54], wormholes [55], gravitational waves [56]. The
+theory has also been used to investigate inflationary phase [57, 58], however, it has less
+attention in this area compared to other modified gravity theories such as f(R) theory and
+scalar-tensor theory. Most of these works only considered the canonical scalar field, and no
+work has been done using other fields such as the noncanonical scalar field which could be
+addressed as a subclasses of the k-essence scalar field.
+Investigating single field noncanonical inflation in f(R, T) gravity theory is the main
+aim that we are going to pursue. The work is followed using Hamilton-Jacobi formalism
+and for some types of Hubble parameter in detail. The free parameters are determined by
+using observational data. Besides the observational constraints, there are some theoretical
+constraints for inflationary models.
+One of these constraints is the swampland criteria
+which has been introduced recently in [59, 60] and refined in [61]. The swampland criteria
+2
+
+include two conjectures: first, the range of the inflationary field should satisfy the condition
+∆φ/Mp < c1, and the second conjecture concerns the gradient of the potential which is
+MpV ′/V > c2 (where both c1 and c2 are constants of the order of one) [62]. The other
+constraint is the trans-Planckian censorship conjecture (TCC) [63]. The conjecture states
+that no fluctuation with a wavelength less than the Planck length could cross the horizon,
+freeze, become classical, and lose its quantum nature. The conjecture puts a strong condi-
+tion on the energy scale of inflation and the tensor-to-scalar ratio and only a few models
+could survive [64, 65].
+The paper is organized as follows: the theory and its main dynamics equations are briefly
+introduced in Sec.II. In Sec.III, the noncanonical scalar field is brought up as the inflaton and
+the dynamical equations are rewritten under the approximations. Then the perturbation
+parameters are introduced.
+The model is considered in detail for some examples of the
+Hubble parameter in Sec.IV. Using data and by performing coding in Python, the free
+parameters of the model are determined. The swampland criteria and TCC are considered
+in Secs.V. Finally, the results are summarized in Sec.VI.
+II.
+BASIC EQUATIONS IN f(R, T) GRAVITY
+The general action in f(R, T) gravity theory is given as follows
+S =
+1
+2κ2
+�
+d4x√−g
+�
+f(R, T) + Lm
+�
+(1)
+where κ is defined as κ2 = 8πG and G is the Newtonian gravitational constant. R is the
+Ricci scalar constructed from the metric gµν with determinant g. The second term in the
+parenthesis, Lm is the Lagrangian of the matter field. T is the determinant of the energy-
+momentum tensor Tµν and f(R, T) is an arbitrary function of R and T.
+The field equation of the theory is obtained by taking variation of the above action with
+respect to the metric, which is read as
+Ξµνf,R(R, T) + f,RRµν − 1
+2gµνf(R, T) = κ2Tµν − f,T(R, T)
+�
+Tµν + Θµν
+�
+,
+(2)
+3
+
+where the operator Ξµν and Θµν are respectively defined as
+Ξµν = gµν□ − ∇µ∇ν,
+(3)
+Θµν = gαβ δTαβ
+δgµν .
+(4)
+The energy-mometum tensor is assumed to be played by a perfect fluid with the following
+form
+Tµν = (ρ + p)uµuν − pgµν
+(5)
+where ρ and p are the energy density and pressure of the fluid.
+To go further, f(R, T) is picked out as f(R, T) = R + ηT, where η is a constant. This
+choice for f(R, T) is one of the simplest and most common choices which has been studied
+in different topics [52, 66–74]. Taking a spatially flat FLRW metric, the friedmann equations
+are obtained as
+H2 = κ2
+3
+��3
+2λ + 1
+�
+ρ − λ
+2 p
+�
+,
+(6)
+−3H2 − 2 ˙H = κ2
+�
+−λ
+2 ρ +
+�3
+2λ + 1
+�
+p
+�
+,
+(7)
+where the constant λ comes from the definition η = λκ2. Combining these two equations,
+the time derivative of the Hubble parameter is acquired
+− 2 ˙H = κ2 (1 + λ) (ρ + p).
+(8)
+The consevation equation is obtained by taking the time derivative from Eq.(6) and using
+Eq.(8) as
+�3λ
+2 + 1
+�
+˙ρ − λ
+2 ˙p + 3H (1 + λ) (ρ + p) = 0.
+(9)
+All above equations return to the standard ones by imposing λ = 0.
+III.
+NONCANONICAL INFLATION
+The Lagrangian of the noncanonical scalar field is given by
+L(φ, X) = X
+� X
+M 4
+�α−1
+− V (φ)
+(10)
+4
+
+where X = ˙φ2/2. It returns to the canonical inflation for α = 1. The related energy density
+and pressure are
+ρ = (2α − 1)X
+� X
+M 4
+�α−1
++ V (φ)
+p = X
+� X
+M 4
+�α−1
+− V (φ).
+(11)
+Substituting the above energy density and pressure in the Friedmann equation (6) and (8),
+one arrives at
+H2 =
+1
+3M 2
+p
+��
+2α
+�3λ
+2 + 1
+�
+−
+�
+1 + 2λ
+�� � X
+M 4
+�α−1
+X + (1 + 2λ) V (φ)
+�
+˙H = −1
+2M 2
+p
+(1 + λ) 2α
+� X
+M 4
+�α−1
+X.
+(12)
+The field equation of motion is obtained by substituting Eqs.(11) in the modified conserva-
+tion equation (9), read as
+�
+2α
+�3λ
+2 + 1
+�
+−
+�
+1 + 2λ
+��
+¨φ + 3H
+�
+1 + 2λ
+� ˙φ + 1
+α
+�M 4
+X
+�α−1
+V ′(φ) = 0
+(13)
+where prime indicates derivatives with respect to the field. For α = 1 and λ = 0, the usual
+field equation for canonical scalar field is recovered.
+A.
+Hamilton-Jacobi formalism
+Following the Hamilton-Jacobi formalism, the Hubble parameter instead of the potential
+is introduced in terms of the scalar field, H = H(φ). Then, the time derivative of the Hubble
+parameter is rewritten as ˙H = ˙φH′(φ). Using it in Eq.(12), one has1
+H′(φ) = α(1 + λ)
+M 2
+pξ
+Xα −1
+˙φ
+(14)
+where the constant ξ is defined as ξ = M 4(α−1). The above equation is utilized to read ˙φ in
+terms of the Hubble parameter.
+1 From Eq.(12), there is Xα =
+�
+ξM 2
+p/α(1 + λ)
+�
+ϵ1H2 indicating that the coefficient α(1 + λ) should be
+positive if one takes ϵ1 as a positive value parameter. With this conclusion, from Eq.(14), it is found that
+H′ and ˙φ have opposite sign. Here, we assume that the term ˙φ is negative.
+5
+
+Reading the Kinetic term X from Eq.(12) and substituting it in the Friedmann equation,
+the potential is given as
+V (φ) =
+3M 2
+p
+(1 + 2λ) H2
+�
+�1 +
+2α
+�
+3λ
+2 + 1
+�
+−
+�
+1 + 2λ
+�
+3α(1 + λ)
+ϵ1
+�
+� ,
+(15)
+which is addressed as the Hamilton-Jacobi equation. The parameter ϵ1 in the above equation
+is known as the first slow-roll parameter defined as
+ϵ1 = − ˙H
+H2 =
+� 2αM 2
+pξ
+α(1 + λ)
+�
+1
+2α−1 H′
+2α
+2α−1
+H2
+.
+(16)
+The second slow-roll parameter is defined through a hierarchy approach as
+ϵ2 =
+˙ϵ1
+Hϵ1
+= 2 ϵ1 − 2α ηH
+(17)
+where
+ηH =
+1
+2α − 1
+� 2αM 2
+pξ
+α(1 + λ)
+�
+1
+2α−1 H′ 2−2α
+2α−1H′′
+H
+.
+(18)
+The amount of inflation is important for solving the problem of the hot big bang theory.
+The amount of inflation is measured by the parameter number of e-folds given by
+N =
+� te
+t⋆
+H dt =
+� φe
+φ⋆
+(19)
+where ” ⋆ ” and ”e” stand for the horizon crossing time and end of inflation.
+B.
+Perturbations
+To verify validity of any inflationary model, it is required to compared the predictions of
+the model with observational data. In the following lines, we are going to introduce some of
+these perturbation parameters which are essential for us in the next section where the model
+is considered for some specific types of the potentials. One of the important parameters is
+the amplitude of the scalar perturbations which is given by2
+Ps =
+1
+4π2
+H4
+cs
+�
+ρeff + peff
+�
+(20)
+2 From the action, it is realized that the combination of the trace of energy-momentum tensor T and the
+Lagrangian Lm is a combination of the scalar field kinetic term X = ˙φ2/2 and potential V (φ). Therefore,
+it could be addressed as a subclass of the k-essence model. The perturbation of such model has been
+studied in [75].
+6
+
+where
+ρeff =
+��3
+2λ + 1
+�
+ρ − λ
+2 p
+�
+peff =
+�
+−λ
+2 ρ +
+�3
+2λ + 1
+�
+p
+�
+with ρ and p are the energy density and pressure of tachyon field given by Eq.(11). The
+sound speed cs is obtained as3
+c2
+s = ˙peff
+˙ρeff
+=
+(1 + 2λ) − αλ
+2α
+�
+3λ
+2 + 1
+�
+−
+�
+1 + 2λ
+�.
+(21)
+which is constant.
+The scalar spectral index, which is defined through the amplitude of the scalar field, is given
+by
+ns = 1 − (2ϵ1 + ϵ2).
+(22)
+Regarding the tensor perturbations, there is the tensor-to-scalar ratio which is very essential
+in examining an inflationary model. The parameter is expressed as follows
+r = 16 cs ϵ1.
+(23)
+In the following section, we are going to examine the model for some specific types of the
+potential and compare the results with data.
+IV.
+TYPICAL EXAMPLES
+In this section, three types of potentials as power-law, T-mode, and exponential will be
+studied in detail.
+A.
+power-law case
+As the first case, the Hubble parameter is take as a power-law function of the scalar
+field, H(φ) = H0φn where H0 and n are two constants. Using this definition, the slow-roll
+3 In general the sound speed is defined as c2
+s = ˙p/ ˙ρ. But, in our case, the energy density and pressure in the
+relation are not the energy density and pressure defined through Eq.(11). In fact they are the effective
+energy density and pressure which is defined from the right hand side of Eqs.(6) and (7).
+7
+
+parameters are
+ϵ1 =
+� 2αM 2
+pξ
+α(1 + λ) n2α H2−2α
+0
+�
+1
+2α−1
+φ
+2n−2nα−2α
+2α−1
+(24)
+ηH = n(n − 1)
+2α − 1
+� 2αM 2
+pξ
+α(1 + λ) n2−2α H2−2α
+0
+�
+1
+2α−1
+φ
+2n−2nα−2α
+2α−1
+(25)
+Inflation ends as the first slow-roll parameter reaches one, ϵ1 = 1. The scalar field at the
+end of inflation is read from this relation that is
+φ
+2n−2nα−2α
+2α−1
+e
+=
+� 2αM 2
+pξ
+α(1 + λ) n2α H2−2α
+0
+�
+−1
+2α−1
+(26)
+We are going to determine the free parameters of the model by comparing its results with
+observational data. In this regard, we need to estimate the perturbation parameters at the
+time of horizon crossing. First, the scalar field is computed through the relation of the
+number of e-folds as
+φ
+2n−2nα−2α
+2α−1
+⋆
+=
+�� 2αM 2
+pξ
+α(1 + λ) n2α H2−2α
+0
+�
+1
+2α−1 �
+1 − 2n − 2nα − 2α
+n(2α − 1)
+N
+��−1
+(27)
+Inserting φ⋆ in the slow-roll parameters (16) and (17), one arrives at
+ϵ⋆
+1 =
+�
+1 − 2n − 2nα − 2α
+n(2α − 1)
+N
+�−1
+,
+(28)
+η⋆
+H =
+(n − 1)
+n(2α − 1)
+�
+1 − 2n − 2nα − 2α
+n(2α − 1)
+N
+�−1
+,
+(29)
+and returning to Eqs.(22) and (23), the scalar spectral index and the tensor-to-scalar ratio
+are obtained at horizon crossing. Fig.1(a) illustrates r−ns curves versus the parameter α for
+different values of λ. It is realized that the curve for n = 0.5 and 1 is out of the observational
+range and it enters the range for n = 1.5 and 2. The curves enter the observational range
+for higher values of α and they are out of range for smaller α. The r − ns curves versus
+n are plotted in Fig.1(b) for different values of α. It seems that the curves start from the
+same point and tend toward the smaller ns and bigger r by increasing α. It is relalized that
+the curves related to α = 1 and 1.5 do not cross our interest area. On the other hand, the
+curves related to α = 2 and 2.4 perfectly cross the observational area. To have a better
+view on the valid values of free parameters n and α, a parametric space is depicted in Fig.2.
+The blue area indicates a set of (α, n) points for which the model comes to good agreement
+8
+
+(a)
+(b)
+FIG. 1. The r − ns curves in terms of a) α and different values of n, b) n for different values of α.
+The constant λ is taken as λ = 2 and the curves are plotted for the number of e-folds N = 65.
+FIG. 2. The figure illustrates the parametric space of the parameter α and n so that for each point
+in the parameter the model remains in perfect agreement with data.
+with data.
+There is exact data about the amplitude of the scalar perturbations as well. Estimating
+the amplitude of the scalar perturbations at the time of the horizon crossing and applying
+the data for Ps, one could determine another free parameters of the model that is
+ξ2n =
+1
+H4α
+0
+��α(1 + λ)
+2αM 2
+p
+�
+1
+2α−1
+ϵ⋆
+1
+n
+2α
+2α−1
+�2n(2α−1) �
+1
+8π2M 2
+pcsϵ⋆
+1Ps
+�2n−2nα−2α
+(30)
+Table.I presents a brief results of the case and gives a better insight about the case. One
+could finds the model results for the scalar spectral index, the tensor-to-scalar ratio, the
+inflation energy scale and also anothe free parameters of the model M. These results are
+computed for different values of α and n so that some of them stand in the blue range of
+9
+
+0.10
+n= 0.5
+0.08 
+n= 1.0
+n= 1.5
+....
+n= 2.0
+0.05
+0.04 -
+:
+0.D2 -
+-
+0.D0 -
+0.950
+0.955
+0.960
+0.565
+0.970
+0860
+0.985
+Ns0.10
+1.0
+0.08
+α=2.4
+0.0-6
+0.D4 
+0.02 -
+0.00
+0.550
+0.5955
+0.960
+0.955
+0.580
+0.985
+Ns3.D
+25
+2D
+15 
+LD 
+0.5
+14
+16
+1B
+2D
+22
+24
+26
+aα
+n
+ns
+r
+M
+ES
+1.5
+1.0
+0.9695
+0.0653
+2.29 × 10−12
+4.47 × 10−3
+1.5
+1.5
+0.9645
+0.0868
+5.70 × 10−10
+4.80 × 10−3
+1.5
+2.0
+0.9605
+0.1040
+7.98 × 10−9
+5.02 × 10−3
+2.0
+1.0
+0.9695
+0.0368
+1.23 × 10−9
+3.88 × 10−3
+2.0
+1.5
+0.9652
+0.0472
+5.35 × 10−8
+4.12 × 10−3
+2.0
+2.0
+0.9620
+0.0550
+3.25 × 10−7
+4.28 × 10−3
+2.4
+1.0
+0.9695
+0.0145
+4.59 × 10−9
+3.07 × 10−3
+2.4
+1.5
+0.9655
+0.0183
+1.33 × 10−7
+3.25 × 10−3
+2.4
+2.0
+0.9626
+0.0211
+6.68 × 10−7
+3.37 × 10−3
+TABLE I. The numerical results for the case about the scalar spectral index, tensor-to-scalar ratio,
+constant M, and energy scale (ES) of inflation for different values of α and n taken from Fig.2,
+where number of e-folds is N = 65.
+Fig.2 and some do not.
+B.
+Exponential case
+The exponential function of the scalar field is picked out as the second case for the Hubble
+parameter, i.e. H(φ) = H0 exp(βφ) where H0 and β are two constant. Substituting this
+Hubble parameter in Eqs.(16) and (18), the slow-roll parameters are obtained as
+ϵ1 =
+� 2αM 2
+pξ
+α(1 + λ) β2α H2−2α
+0
+�
+1
+2α−1
+e
+2−2α
+2α−1 βφ,
+(31)
+ηH =
+1
+2α − 1
+� 2αM 2
+pξ
+α(1 + λ) β2α H2−2α
+0
+�
+1
+2α−1
+e
+2−2α
+2α−1 βφ.
+(32)
+Solving the relation ϵ1 = 1 in terms of φ, the field is estimated at the end of inflation
+e
+2α−2
+2α−1 β φe =
+� 2αM 2
+pξ
+α(1 + λ) β2α H2−2α
+0
+�
+1
+2α−1
+.
+(33)
+Applying this result on Eq.(19) and by integrating, the field at the time of the horizon
+crossing is given by
+e
+2α−2
+2α−1 β φ⋆ = e
+2α−2
+2α−1 β φ⋆
+�
+1 + 2α − 2
+2α − 1 N
+�
+.
+(34)
+10
+
+FIG. 3. The r − ns curves in terms of the α for different values of λ where the number of e-fold is
+N = 85.
+To estimate the scalar spectral index and the tensor-to-scalar ratio at the time of the horizon
+crossing, we first need to substitute the above field in the slow-roll parameters which leads
+to
+ϵ⋆
+1 =
+�
+1 + 2α − 2
+2α − 1 N
+�−1
+(35)
+η⋆
+H =
+1
+2α − 1 ϵ⋆
+1.
+(36)
+Using the slow-roll parameters in Eq.(22) and (23), ns and r are obtained at t⋆. The behavior
+of the parameters are described in Fig.3, where one finds r −ns curves versus the parameter
+α for different values of λ. For smaller values of λ, the curves comes to the observational
+range for larger values of α. In order to have a better understanding about the valid range of
+the parameters α and λ, we are going to run a Python code including the data for the scalar
+spectral index and the tensor-to-scalar ratio. The resulted parametric space is presented in
+Fig.4 that shows a set of (α, λ) for which the model is kept consistent with data. Also, one
+realizes that there is bigger range of λ for smaller values of α.
+Using the data about the amplitude of the scalar perturbations, another free parameter of
+the model is determined. From Eq.(20), it is found that
+ξ = α(1 + λ)
+2αM 2
+p
+ϵ2α−1
+1
+�
+8π2M 2
+pcsϵ1Ps
+�1−αβ2α
+(37)
+Table.II represents the value of the constant M = ξ1/4(α−1) for different choices of α and
+λ. The magnitude of the free parameter M is about O(105). Moreover, for each α and λ,
+the scalar spectral index, the tensor-to-scalar ration, and the energy scale of inflation are
+11
+
+0.16
+A = 0.10
+VO
+A = 0.30
+A = 0.50
+0.12
+入= 0.80
+0.10
+0.D8
+0.D6
+0.04
+0.D2
+O.DO
+0.552
+0.956
+0.958
+0.960
+0.962
+t960
+NsFIG. 4. The figure portrays a oarametric space for the free parameters α and λ where the number
+of e-folds is N = 85. For each point in the space the model comes to an agreement with data.
+α
+λ
+ns
+r
+ξ
+ES
+3.5
+0.1
+0.9606
+0.0785
+7.10 × −5
+1.03 × −2
+3.5
+0.2
+0.9606
+0.0672
+6.89 × −5
+9.84 × −3
+3.5
+0.3
+0.9606
+0.0565
+6.65 × −5
+9.44 × −3
+4.0
+0.1
+0.9613
+0.0685
+7.85 × −5
+4.12 × −2
+4.0
+0.2
+0.9613
+0.0559
+7.51 × −5
+3.94 × −2
+4.0
+0.3
+0.9613
+0.0433
+7.06 × −5
+3.78 × −2
+4.5
+0.1
+0.9619
+0.0608
+8.37 × −5
+1.11 × −1
+4.5
+0.2
+0.9619
+0.0468
+7.89 × −5
+1.06 × −1
+4.5
+0.3
+0.9619
+0.0314
+7.18 × −5
+1.02 × −1
+5.0
+0.1
+0.9623
+0.0545
+8.74 × −5
+2.34 × −1
+5.0
+0.2
+0.9623
+0.0388
+8.07 × −5
+2.23 × −1
+5.0
+0.3
+0.9623
+0.0184
+6.73 × −5
+2.15 × −1
+TABLE II. The numerical results for the scalar spectral index, tensor-to-scalar ratio, constant M,
+and the energy scale (ES) of inflation for different values of α and λ where the number of e-folds
+is N = 85.
+given as well. It is seen that the scalar spectal index and the tensor-to-scalar ratio stand in
+agreement with data. The enegy scale of inflation also increase by enhancement of α.
+12
+
+0.B
+0.6
+~ 0.4 -
+0.2
+0.D
+1+V.
+SWAMPLAND CRITERIA AND TCC
+String theory, which is known as one of the promising candidate for ultimate theory of
+quantum gravity, propounds a landscape which contains all consistent low-energy EFTs.
+Moreover, there are other low-energy EFTs which do not get along with string theory living
+on an area known as swampland. It is our desire to build our model based on a consistent low-
+energy EFT. Therefore, a mechanism is required to separate the consistent and inconsistent
+theories. over past years, several conjectures have been introduced in this matter and the
+most recent conjectures, which are known as swampland criteria, are
+• Distance conjecture: it puts an upper bound on the scalar field excursion in the field
+space
+∆φ ≤ c1
+(38)
+where c1 is a constant of the order of one, O(1) [59–61].
+• de Sitter conjecture: it stated that there should be a lower bound on the gradient of
+the potential as [60, 61]
+|V,φ|
+V
+≥ c2,
+(39)
+or as in the refined version of this criterion one of the following condition should
+satisfied
+|V,φ|
+V
+≥ c2,
+or|V,φφ|
+V
+≥ −c′
+2
+(40)
+The true order of the constant c1 depends on the detail of compaction. It is concluded
+that it is larger than
+√
+2. However, further consideration indicates that it could smaller,
+of the order of O(0.1) [60, 62]. In any case, the important criterium is that the constant
+must be positive.
+The conjecture are stated in Planck units, Mp = 1. Due to this believe that inflation occurs
+at energy scale below the Planck, it is expected to be describe by low-energy EFT. There-
+fore, it is interesting to consider the validation of the swampland criteria for an inflationary
+model.
+In the previous section, the free parameters of the model are determined using data. Now,
+we are going to use these results, the scalar field at the horizon crossing and the end of infla-
+tion is obtained and one could specify the field excursion and the gradient of the potential.
+13
+
+α
+n
+∆φ
+V ′/V
+1.5
+1.0
+1.18 × 10−5
+1.53 × 105
+1.5
+1.5
+5.28 × 10−4
+4.92 × 103
+1.5
+2.0
+3.35 × 10−3
+9.84 × 102
+2.0
+1.0
+8.89 × 10−6
+2.04 × 105
+2.0
+1.5
+4.27 × 10−4
+6.02 × 103
+2.0
+2.0
+2.80 × 10−3
+1.15 × 103
+2.4
+1.0
+5.57 × 10−6
+3.25 × 105
+2.4
+1.5
+3.10 × 10−4
+8.25 × 103
+2.4
+2.0
+2.19 × 10−3
+1.46 × 103
+TABLE III. Table shows the results for the field distance and potential gradient of the fisrt case
+for different values of α and n.
+Tables.III and IV display the results respectively for the first and second cases.
+The results clarify that both criteria could be satisfy in both cases. For the first case,
+for the specific parameter α, the field distance gets larger by increasing λ, however, the
+potential gradient decreases. Besides, there is a reverse situation for specific values of λ
+so that the field distance gets smaller by enhancement of α, while the potential gradient
+increase.
+For the second case, where the Hubble parameter is taken as an exponential
+function of the scalar field, the field distance could be smaller than one and the potential
+gradient larger. The point that one realizes from the table is that the field distance and the
+potential gradient are not sensitive to the varying of α and λ.
+Another conjecture which has been proposed recently is TCC. The TCC targets the
+fluctuations generated during inflation. These fluctuations are the origin of the universe
+structure. They are stretches with the expansion and cross the horizon, freeze and reenter
+the horizon after inflation, and today we could observe some of them. The crucial point
+is that the fluctuations have a quantum nature, however, they loss their nature as cross
+the horizon and freeze. At this point they become classical. Our main concern are the
+fluctuations with origin wavelength less than the Planck length. In this case, if inflation last
+long enough, they stretch and cross the horizon and become classical. This is known as the
+14
+
+α
+λ
+∆φ
+V ′/V
+3.5
+0.1
+0.4885
+20.927
+3.5
+0.2
+0.4885
+20.925
+3.5
+0.3
+0.4885
+20.923
+4.0
+0.1
+0.4780
+20.926
+4.0
+0.2
+0.4780
+20.923
+4.0
+0.3
+0.4780
+20.921
+4.5
+0.1
+0.4704
+20.924
+4.5
+0.2
+0.4704
+20.922
+4.5
+0.3
+0.4704
+20.920
+5.0
+0.1
+0.4647
+20.923
+5.0
+0.2
+0.4647
+20.921
+5.0
+0.3
+0.4647
+20.919
+TABLE IV. Table shows the results for the field distance and potential gradient of the second case
+for different values of α and λ.
+”trans-Planckian problem”. TCC states that no fluctuation with wavelength less than the
+Planck length should cross the horizon [39, 63, 64], and it is formulated as
+lp
+ai
+< H−1
+f
+af
+,
+(41)
+where lp is the Planck length, Hf is the Hubble parameter at the end of inflation. ai and af
+are the scale factor respectively at the beginning and the end of inflation.
+The quantity H−1
+f
+for both cases of Sec.IV is of the order of O(106). On the other hand,
+the term af/ai = eN is much higher than this magnitude. It implies that the condition
+eN < H−1
+f
+will never be satisfied.
+VI.
+CONCLUSION
+The scenario of slow-roll inflation was considered in the f(R, T) theory of gravity, which
+is known as a modified theory of gravity where the matter has a non-minimal coupling to the
+curvature. The inflaton was assumed to be played by a noncanonical scalar field including
+generalized kinetic energy, which is a subclass of the k-essence scalar field. After briefly
+15
+
+reviewing the model and its dynamical equations, the scenario of inflation is considering
+following Hamilton-Jacobi formalism. In this formalism, the Hubble parameter is introduced
+as a function of the scalar field instead of the potential. The investigation was pursued by
+considering two cases for the Hubble parameter as power-law and exponential functions of
+the scalar field. Utilizing observational data and performing a coding program, the free
+parameters of the model were determined.
+First, the Hubble parameter was assumed to be a power-law function of the scalar field.
+By estimating the scalar field at the time of the horizon crossing, we could compute the
+main perturbation parameters at this time.
+Next, by applying the data for the scalar
+spectral index and the tensor-to-scalar ratio, we could determine the valid range for the free
+parameters α and n. Then, the free parameter M was determined through the amplitude of
+the scalar perturbations. Following the obtained information about the free parameters of
+the model, the energy scale of inflation was computed that was of the order of 10−3Mp. Also,
+we considered the validity of the swampland criteria and TCC. Concerning the swampland
+criteria, the result implies that the two conjectures are perfectly satisfied. However, the
+TCC is not satisfied.
+In the next case, the Hubble parameter was picked as the exponential function of the scalar
+field.
+The same procedure was followed to determine the free parameters of the model
+for which to put the model in perfect agreement with the data. For the determined free
+parameters, the model could satisfy the swampland criteria, however, in contrast to the first
+case, they were not sensitive to the changes of the parameter λ.
+[1] A. Albrecht and P. J. Steinhardt, Cosmology for grand unified theories with radiatively induced
+symmetry breaking, Physical Review Letters 48, 1220 (1982).
+[2] A. D. Linde, A new inflationary universe scenario: a possible solution of the horizon, flatness,
+homogeneity, isotropy and primordial monopole problems, Physics Letters B 108, 389 (1982).
+[3] A. D. Linde, Chaotic inflation, Physics Letters B 129, 177 (1983).
+[4] A. A. Starobinsky, A new type of isotropic cosmological models without singularity, Physics
+Letters B 91, 99 (1980).
+16
+
+[5] A. H. Guth, The Inflationary Universe: A Possible Solution to the Horizon and Flatness
+Problems, Phys. Rev. D23, 347 (1981), [Adv. Ser. Astrophys. Cosmol.3,139(1987)].
+[6] A. D. Linde, Inflationary cosmology, Phys. Rept. 333, 575 (2000).
+[7] A. D. Linde, Particle physics and inflationary cosmology, Contemp. Concepts Phys. 5, 1
+(1990), arXiv:hep-th/0503203 [hep-th].
+[8] A. D. Linde, Current understanding of inflation, Proceedings, 6th UCLA Symposium on
+Sources and Detection of Dark Matter and Dark Energy in the Universe: Marina del Rey,
+CA, USA, February 18-20, 2004, New Astron. Rev. 49, 35 (2005).
+[9] A. D. Linde, Prospects of inflation, Proceedings, Nobel Symposium 127 on String theory and
+cosmology: Sigtuna, Sweden, August 14-19, 2003, Phys. Scripta T117, 40 (2005), arXiv:hep-
+th/0402051 [hep-th].
+[10] A. Riotto, Inflation and the theory of cosmological perturbations, Astroparticle physics and
+cosmology. Proceedings: Summer School, Trieste, Italy, Jun 17-Jul 5 2002, ICTP Lect. Notes
+Ser. 14, 317 (2003), arXiv:hep-ph/0210162 [hep-ph].
+[11] D. Baumann, TASI Lecture on Inflation, in Physics of the large and the small, TASI 09, pro-
+ceedings of the Theoretical Advanced Study Institute in Elementary Particle Physics, Boulder,
+Colorado, USA, 1-26 June 2009 (2011) pp. 523–686, arXiv:0907.5424 [hep-th].
+[12] S. Weinberg, Cosmology (2008).
+[13] D. H. Lyth and A. R. Liddle, The primordial density perturbation: Cosmology, inflation and
+the origin of structure (2009).
+[14] A. R. Liddle and D. H. Lyth, Cosmological inflation and large scale structure (2000).
+[15] P. A. R. Ade et al. (Planck), Planck 2013 results. XXII. Constraints on inflation, Astron.
+Astrophys. 571, A22 (2014), arXiv:arXiv:1303.5082 [astro-ph.CO].
+[16] P. A. R. Ade et al. (Planck), Planck 2015 results. XX. Constraints on inflation, Astron.
+Astrophys. 594, A20 (2016), arXiv:arXiv:1502.02114 [astro-ph.CO].
+[17] Y. Akrami et al. (Planck), Planck 2018 results. X. Constraints on inflation,
+(2018),
+arXiv:arXiv:1807.06211 [astro-ph.CO].
+[18] G. Barenboim and W. H. Kinney, Slow roll in simple non-canonical inflation, JCAP 0703,
+014, arXiv:astro-ph/0701343 [astro-ph].
+[19] P. Franche, R. Gwyn, B. Underwood, and A. Wissanji, Initial Conditions for Non-Canonical
+Inflation, Phys. Rev. D82, 063528 (2010), arXiv:1002.2639 [hep-th].
+17
+
+[20] S. Unnikrishnan, V. Sahni, and A. Toporensky, Refining inflation using non-canonical scalars,
+JCAP 1208, 018, arXiv:1205.0786 [astro-ph.CO].
+[21] K. Rezazadeh, K. Karami, and P. Karimi, Intermediate inflation from a non-canonical scalar
+field, JCAP 1509 (09), 053, arXiv:1411.7302 [gr-qc].
+[22] K. Saaidi, A. Mohammadi, and T. Golanbari, Light of Planck-2015 on Noncanonical Inflation,
+Adv. High Energy Phys. 2015, 926807 (2015), arXiv:1708.03675 [gr-qc].
+[23] M. Fairbairn and M. H. G. Tytgat, Inflation from a tachyon fluid?, Phys. Lett. B546, 1 (2002),
+arXiv:hep-th/0204070 [hep-th].
+[24] S. Mukohyama, Brane cosmology driven by the rolling tachyon, Phys. Rev. D66, 024009
+(2002), arXiv:hep-th/0204084 [hep-th].
+[25] A. Feinstein, Power law inflation from the rolling tachyon, Phys. Rev. D66, 063511 (2002),
+arXiv:hep-th/0204140 [hep-th].
+[26] T. Padmanabhan, Accelerated expansion of the universe driven by tachyonic matter, Phys.
+Rev. D66, 021301 (2002), arXiv:hep-th/0204150 [hep-th].
+[27] A. Aghamohammadi, A. Mohammadi, T. Golanbari, and K. Saaidi, Hamilton-Jacobi formal-
+ism for tachyon inflation, Phys. Rev. D90, 084028 (2014), arXiv:1502.07578 [gr-qc].
+[28] M. Spalinski, On Power law inflation in DBI models, JCAP 0705, 017, arXiv:hep-th/0702196
+[hep-th].
+[29] D. Bessada, W. H. Kinney, and K. Tzirakis, Inflationary potentials in DBI models, JCAP
+0909, 031, arXiv:0907.1311 [gr-qc].
+[30] J. M. Weller, C. van de Bruck, and D. F. Mota, Inflationary predictions in scalar-tensor DBI
+inflation, JCAP 1206, 002, arXiv:1111.0237 [astro-ph.CO].
+[31] N. Nazavari, A. Mohammadi, Z. Ossoulian, and K. Saaidi, Intermediate inflation driven by
+DBI scalar field, Phys. Rev. D93, 123504 (2016), arXiv:1708.03676 [gr-qc].
+[32] K.-i. Maeda and K. Yamamoto, Stability analysis of inflation with an su (2) gauge field,
+Journal of Cosmology and Astroparticle Physics 2013 (12), 018.
+[33] A. A. Abolhasani, R. Emami, and H. Firouzjahi, Primordial anisotropies in gauged hybrid
+inflation, Journal of Cosmology and Astroparticle Physics 2014 (05), 016.
+[34] S. Alexander, D. Jyoti, A. Kosowsky, and A. Marcian`o, Dynamics of gauge field inflation,
+Journal of Cosmology and Astroparticle Physics 2015 (05), 005.
+18
+
+[35] M. Tirandari and K. Saaidi, Anisotropic inflation in brans–dicke gravity, Nuclear Physics B
+925, 403 (2017).
+[36] R. Maartens, D. Wands, B. A. Bassett, and I. P. Heard, Chaotic inflation on the brane,
+Physical Review D 62, 041301 (2000).
+[37] T. Golanbari, A. Mohammadi, and K. Saaidi, Brane inflation driven by noncanonical scalar
+field, Physical Review D 89, 103529 (2014).
+[38] A. Mohammadi, T. Golanbari, S. Nasri, and K. Saaidi, Brane inflation: Swampland Criteria,
+TCC, and Reheating constraint, (2020), arXiv:2006.09489 [gr-qc].
+[39] A. Mohammadi, T. Golanbari, and J. Enayati, Brane inflation and Trans-Planckian censorship
+conjecture, (2020), arXiv:2012.01512 [hep-th].
+[40] A. Berera, Warm inflation, Physical Review Letters 75, 3218 (1995).
+[41] A. Berera, Warm inflation in the adiabatic regime—a model, an existence proof for inflationary
+dynamics in quantum field theory, Nuclear Physics B 585, 666 (2000).
+[42] L. M. Hall, I. G. Moss, and A. Berera, Scalar perturbation spectra from warm inflation,
+Physical Review D 69, 083525 (2004).
+[43] K. Sayar, A. Mohammadi, L. Akhtari, and K. Saaidi, Hamilton-Jacobi formalism to warm
+inflationary scenario, Phys. Rev. D95, 023501 (2017), arXiv:1708.01714 [gr-qc].
+[44] L. Akhtari, A. Mohammadi, K. Sayar, and K. Saaidi, Viscous warm inflation: Hamilton–Jacobi
+formalism, Astropart. Phys. 90, 28 (2017), arXiv:1710.05793 [astro-ph.CO].
+[45] H. Sheikhahmadi, A. Mohammadi, A. Aghamohammadi, T. Harko, R. Herrera, C. Corda,
+A. Abebe, and K. Saaidi, Constraining chameleon field driven warm inflation with Planck
+2018 data, Eur. Phys. J. C79, 1038 (2019), arXiv:1907.10966 [gr-qc].
+[46] A. Mohammadi, T. Golanbari, H. Sheikhahmadi, K. Sayar, L. Akhtari, M. Rasheed, and
+K. Saaidi, Warm tachyon inflation and swampland criteria, Chin. Phys. C 44, 095101 (2020),
+arXiv:2001.10042 [gr-qc].
+[47] A. Mohammadi, K. Saaidi, and T. Golanbari, Tachyon constant-roll inflation, Phys. Rev. D97,
+083006 (2018), arXiv:1801.03487 [hep-ph].
+[48] A. Mohammadi, K. Saaidi, and H. Sheikhahmadi, Constant-roll approach to non-canonical
+inflation, Phys. Rev. D100, 083520 (2019), arXiv:1803.01715 [astro-ph.CO].
+[49] T. Golanbari, A. Mohammadi, and K. Saaidi, Observational constraints on DBI constant-roll
+inflation, Phys. Dark Univ. 27, 100456 (2020), arXiv:1808.07246 [gr-qc].
+19
+
+[50] A. Mohammadi, T. Golanbari, and K. Saaidi, Beta-function formalism for k-essence constant-
+roll inflation, Phys. Dark Univ. 28, 100505 (2020), arXiv:1912.07006 [gr-qc].
+[51] .
+[52] T. Harko, F. S. N. Lobo, S. Nojiri, and S. D. Odintsov, f(R, T) gravity, Phys. Rev. D 84,
+024020 (2011), arXiv:1104.2669 [gr-qc].
+[53] M. Z.-U.-H. Bhatti and Z. Yousaf, Dynamical variables and evolution of the universe, Int. J.
+Mod. Phys. D 26, 1750029 (2016).
+[54] R. Zaregonbadi, M. Farhoudi, and N. Riazi, Dark Matter From f(R,T) Gravity, Phys. Rev. D
+94, 084052 (2016), arXiv:1608.00469 [gr-qc].
+[55] P. H. R. S. Moraes and P. K. Sahoo, Wormholes in exponential f(R, T) gravity, Eur. Phys.
+J. C 79, 677 (2019), arXiv:1903.03421 [gr-qc].
+[56] M. E. S. Alves, P. H. R. S. Moraes, J. C. N. de Araujo, and M. Malheiro, Gravitational waves
+in f(R, T) and f(R, T φ) theories of gravity, Phys. Rev. D 94, 024032 (2016), arXiv:1604.03874
+[gr-qc].
+[57] S. Bhattacharjee, J. R. L. Santos, P. H. R. S. Moraes, and P. K. Sahoo, Inflation in f(R, T)
+gravity, Eur. Phys. J. Plus 135, 576 (2020), arXiv:2006.04336 [gr-qc].
+[58] M. Gamonal, Slow-roll inflation in f(R, T) gravity and a modified Starobinsky-like inflationary
+model, Phys. Dark Univ. 31, 100768 (2021), arXiv:2010.03861 [gr-qc].
+[59] G. Obied, H. Ooguri, L. Spodyneiko, and C. Vafa, De Sitter Space and the Swampland, (2018),
+arXiv:1806.08362 [hep-th].
+[60] H. Ooguri, E. Palti, G. Shiu, and C. Vafa, Distance and de Sitter Conjectures on the Swamp-
+land, Phys. Lett. B788, 180 (2019), arXiv:1810.05506 [hep-th].
+[61] S. K. Garg and C. Krishnan, Bounds on Slow Roll and the de Sitter Swampland, JHEP 11,
+075, arXiv:1807.05193 [hep-th].
+[62] A. Kehagias and A. Riotto, A note on Inflation and the Swampland, Fortsch. Phys. 66, 1800052
+(2018), arXiv:1807.05445 [hep-th].
+[63] A. Bedroya and C. Vafa, Trans-Planckian Censorship and the Swampland, JHEP 09, 123,
+arXiv:1909.11063 [hep-th].
+[64] A. Bedroya, R. Brandenberger, M. Loverde, and C. Vafa, Trans-Planckian Censorship and
+Inflationary Cosmology, Phys. Rev. D 101, 103502 (2020), arXiv:1909.11106 [hep-th].
+20
+
+[65] R. Brandenberger and E. Wilson-Ewing, Strengthening the TCC Bound on Inflationary Cos-
+mology, JCAP 03, 047, arXiv:2001.00043 [hep-th].
+[66] P. H. R. S. Moraes, J. D. V. Arba˜nil, and M. Malheiro, Stellar equilibrium configurations of
+compact stars in f(R, T) gravity, JCAP 06, 005, arXiv:1511.06282 [gr-qc].
+[67] G. A. Carvalho, R. V. Lobato, P. H. R. S. Moraes, J. D. V. Arba˜nil, R. M. Marinho, E. Otoniel,
+and M. Malheiro, Stellar equilibrium configurations of white dwarfs in the f(R, T) gravity,
+Eur. Phys. J. C 77, 871 (2017), arXiv:1706.03596 [gr-qc].
+[68] P. H. R. S. Moraes, W. de Paula, and R. A. C. Correa, Charged wormholes in f(R,T) extended
+theory of gravity, Int. J. Mod. Phys. D 28, 1950098 (2019), arXiv:1710.07680 [gr-qc].
+[69] P. H. R. S. Moraes and P. K. Sahoo, Modelling wormholes in f(R, T) gravity, Phys. Rev. D
+96, 044038 (2017), arXiv:1707.06968 [gr-qc].
+[70] P. H. R. S. Moraes, R. A. C. Correa, and R. V. Lobato, Analytical general solutions for static
+wormholes in f(R, T) gravity, JCAP 07, 029, arXiv:1701.01028 [gr-qc].
+[71] T. Azizi, Wormhole Geometries In f(R, T) Gravity, Int. J. Theor. Phys. 52, 3486 (2013),
+arXiv:1205.6957 [gr-qc].
+[72] P. H. R. S. Moraes, Cosmology from induced matter model applied to 5D f(R, T) theory,
+Astrophys. Space Sci. 352, 273 (2014).
+[73] P. H. R. S. Moraes, Cosmological solutions from Induced Matter Model applied to 5D
+f(R, T) gravity and the shrinking of the extra coordinate, Eur. Phys. J. C 75, 168 (2015),
+arXiv:1502.02593 [gr-qc].
+[74] D. R. K. Reddy and R. Santhi Kumar, Some anisotropic cosmological models in a modified
+theory of gravitation, Astrophys. Space Sci. 344, 253 (2013).
+[75] J. Garriga and V. F. Mukhanov, Perturbations in k-inflation, Phys. Lett. B458, 219 (1999),
+arXiv:hep-th/9904176 [hep-th].
+21
+
diff --git a/adE_T4oBgHgl3EQfyxwh/content/tmp_files/load_file.txt b/adE_T4oBgHgl3EQfyxwh/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..49ae8c5ac7627e04a0fc8ade2557efcdf6626d8f
--- /dev/null
+++ b/adE_T4oBgHgl3EQfyxwh/content/tmp_files/load_file.txt
@@ -0,0 +1,1025 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf,len=1024
+page_content='Noncanonical inflation in f(R, T) gravity with Hamilton-Jacobi  formalism  Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Ossoulian, Kh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  Saaidi,∗ and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Taghavi  Department of Physics, Faculty of Science,  University of Kurdistan, Sanandaj, Iran.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  (Dated: January 23, 2023)  Abstract  The scenario of slow-roll inflation is explored in the f(R, T) theory of gravity where a non-  minimal coupling between matter and curvature is included.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' A noncanonical scalar field is assumed  to play the role of inflaton which contains generalized kinetic energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' The study is performed by  taking the Hamilton-Jacobi formalism where the Hubble parameter is taken as a function of the  scalar field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' In this regard, a power-law function and an exponential function of the scalar field are  assumed for the Hubble parameter and the model is considered in detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' By performing Python  coding and applying the observational data, the free parameters of the model are determined for  which the model is put in perfect consistency with the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Then, using the results, the validity  of the swampland criteria and TCC is considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' It is realized that not only the model comes to  a good agreement with data, but it also could satisfy the swampland criteria.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  ∗ ksaaidi@uok.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='ir  1  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='08319v1  [gr-qc]  18 Jan 2023  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  INTRODUCTION  Although the theory of general relativity has emerged successfully from many experi-  ments, some challenging issues cannot be solved in the frame of general relativity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' One of  the main issues that the theory is faced with is the flatness and horizon problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' It could  not provide a competent explanation for the problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' A possible solution is assuming an  early exponential expansion phase, known as cosmic inflation, which has been developed by  many scientists [1–3] since its first introduction [4, 5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' A common approach for studying  inflation is by considering a single scalar field, known as inflaton, with a potential and  imposing the slow-roll approximations [6–14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' The scenario shows an incredible consistency  with data and it becomes the cornerstone of any cosmological model [15–17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' There are  many different models of inflation based on the aforementioned suggestions [18–51].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  Another issue that the general theory of relativity encounters is the requirement of dark  energy and dark matter to be able to fit the cosmological data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' This issue became the  main motivation for introducing alternative theories of gravity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' The f(R, T) gravity theory  is one of the alternative theories where R is the curvature scalar, T is the trace of the  energy-momentum tensor, and f is an arbitrary function of R and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' The theory was first  introduced by Harko et.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' [52].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' It has been utilized to study different topics in cosmology  including dark energy [53], dark matter [54], wormholes [55], gravitational waves [56].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' The  theory has also been used to investigate inflationary phase [57, 58], however, it has less  attention in this area compared to other modified gravity theories such as f(R) theory and  scalar-tensor theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Most of these works only considered the canonical scalar field, and no  work has been done using other fields such as the noncanonical scalar field which could be  addressed as a subclasses of the k-essence scalar field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  Investigating single field noncanonical inflation in f(R, T) gravity theory is the main  aim that we are going to pursue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' The work is followed using Hamilton-Jacobi formalism  and for some types of Hubble parameter in detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' The free parameters are determined by  using observational data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Besides the observational constraints, there are some theoretical  constraints for inflationary models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  One of these constraints is the swampland criteria  which has been introduced recently in [59, 60] and refined in [61].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' The swampland criteria  2  include two conjectures: first, the range of the inflationary field should satisfy the condition  ∆φ/Mp < c1, and the second conjecture concerns the gradient of the potential which is  MpV ′/V > c2 (where both c1 and c2 are constants of the order of one) [62].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' The other  constraint is the trans-Planckian censorship conjecture (TCC) [63].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' The conjecture states  that no fluctuation with a wavelength less than the Planck length could cross the horizon,  freeze, become classical, and lose its quantum nature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' The conjecture puts a strong condi-  tion on the energy scale of inflation and the tensor-to-scalar ratio and only a few models  could survive [64, 65].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  The paper is organized as follows: the theory and its main dynamics equations are briefly  introduced in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' In Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='III, the noncanonical scalar field is brought up as the inflaton and  the dynamical equations are rewritten under the approximations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Then the perturbation  parameters are introduced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  The model is considered in detail for some examples of the  Hubble parameter in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Using data and by performing coding in Python, the free  parameters of the model are determined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' The swampland criteria and TCC are considered  in Secs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Finally, the results are summarized in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  BASIC EQUATIONS IN f(R, T) GRAVITY  The general action in f(R, T) gravity theory is given as follows  S =  1  2κ2  �  d4x√−g  �  f(R, T) + Lm  �  (1)  where κ is defined as κ2 = 8πG and G is the Newtonian gravitational constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' R is the  Ricci scalar constructed from the metric gµν with determinant g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' The second term in the  parenthesis, Lm is the Lagrangian of the matter field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' T is the determinant of the energy-  momentum tensor Tµν and f(R, T) is an arbitrary function of R and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  The field equation of the theory is obtained by taking variation of the above action with  respect to the metric, which is read as  Ξµνf,R(R, T) + f,RRµν − 1  2gµνf(R, T) = κ2Tµν − f,T(R, T)  �  Tµν + Θµν  �  ,  (2)  3  where the operator Ξµν and Θµν are respectively defined as  Ξµν = gµν□ − ∇µ∇ν,  (3)  Θµν = gαβ δTαβ  δgµν .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  (4)  The energy-mometum tensor is assumed to be played by a perfect fluid with the following  form  Tµν = (ρ + p)uµuν − pgµν  (5)  where ρ and p are the energy density and pressure of the fluid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  To go further, f(R, T) is picked out as f(R, T) = R + ηT, where η is a constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' This  choice for f(R, T) is one of the simplest and most common choices which has been studied  in different topics [52, 66–74].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Taking a spatially flat FLRW metric, the friedmann equations  are obtained as  H2 = κ2  3  ��3  2λ + 1  �  ρ − λ  2 p  �  ,  (6)  −3H2 − 2 ˙H = κ2  �  −λ  2 ρ +  �3  2λ + 1  �  p  �  ,  (7)  where the constant λ comes from the definition η = λκ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Combining these two equations,  the time derivative of the Hubble parameter is acquired  − 2 ˙H = κ2 (1 + λ) (ρ + p).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  (8)  The consevation equation is obtained by taking the time derivative from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' (6) and using  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' (8) as  �3λ  2 + 1  �  ˙ρ − λ  2 ˙p + 3H (1 + λ) (ρ + p) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  (9)  All above equations return to the standard ones by imposing λ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  NONCANONICAL INFLATION  The Lagrangian of the noncanonical scalar field is given by  L(φ, X) = X  � X  M 4  �α−1  − V (φ)  (10)  4  where X = ˙φ2/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' It returns to the canonical inflation for α = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' The related energy density  and pressure are  ρ = (2α − 1)X  � X  M 4  �α−1  + V (φ)  p = X  � X  M 4  �α−1  − V (φ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  (11)  Substituting the above energy density and pressure in the Friedmann equation (6) and (8),  one arrives at  H2 =  1  3M 2  p  ��  2α  �3λ  2 + 1  �  −  �  1 + 2λ  �� � X  M 4  �α−1  X + (1 + 2λ) V (φ)  �  ˙H = −1  2M 2  p  (1 + λ) 2α  � X  M 4  �α−1  X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  (12)  The field equation of motion is obtained by substituting Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' (11) in the modified conserva-  tion equation (9), read as  �  2α  �3λ  2 + 1  �  −  �  1 + 2λ  ��  ¨φ + 3H  �  1 + 2λ  � ˙φ + 1  α  �M 4  X  �α−1  V ′(φ) = 0  (13)  where prime indicates derivatives with respect to the field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' For α = 1 and λ = 0, the usual  field equation for canonical scalar field is recovered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  Hamilton-Jacobi formalism  Following the Hamilton-Jacobi formalism, the Hubble parameter instead of the potential  is introduced in terms of the scalar field, H = H(φ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Then, the time derivative of the Hubble  parameter is rewritten as ˙H = ˙φH′(φ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Using it in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' (12), one has1  H′(φ) = α(1 + λ)  M 2  pξ  Xα −1  ˙φ  (14)  where the constant ξ is defined as ξ = M 4(α−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' The above equation is utilized to read ˙φ in  terms of the Hubble parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  1 From Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' (12), there is Xα =  �  ξM 2  p/α(1 + λ)  �  ϵ1H2 indicating that the coefficient α(1 + λ) should be  positive if one takes ϵ1 as a positive value parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' With this conclusion, from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' (14), it is found that  H′ and ˙φ have opposite sign.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Here, we assume that the term ˙φ is negative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  5  Reading the Kinetic term X from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' (12) and substituting it in the Friedmann equation,  the potential is given as  V (φ) =  3M 2  p  (1 + 2λ) H2  �  �1 +  2α  �  3λ  2 + 1  �  −  �  1 + 2λ  �  3α(1 + λ)  ϵ1  �  � ,  (15)  which is addressed as the Hamilton-Jacobi equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' The parameter ϵ1 in the above equation  is known as the first slow-roll parameter defined as  ϵ1 = − ˙H  H2 =  � 2αM 2  pξ  α(1 + λ)  �  1  2α−1 H′  2α  2α−1  H2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  (16)  The second slow-roll parameter is defined through a hierarchy approach as  ϵ2 =  ˙ϵ1  Hϵ1  = 2 ϵ1 − 2α ηH  (17)  where  ηH =  1  2α − 1  � 2αM 2  pξ  α(1 + λ)  �  1  2α−1 H′ 2−2α  2α−1H′′  H  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  (18)  The amount of inflation is important for solving the problem of the hot big bang theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  The amount of inflation is measured by the parameter number of e-folds given by  N =  � te  t⋆  H dt =  � φe  φ⋆  (19)  where ” ⋆ ” and ”e” stand for the horizon crossing time and end of inflation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  Perturbations  To verify validity of any inflationary model, it is required to compared the predictions of  the model with observational data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' In the following lines, we are going to introduce some of  these perturbation parameters which are essential for us in the next section where the model  is considered for some specific types of the potentials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' One of the important parameters is  the amplitude of the scalar perturbations which is given by2  Ps =  1  4π2  H4  cs  �  ρeff + peff  �  (20)  2 From the action, it is realized that the combination of the trace of energy-momentum tensor T and the  Lagrangian Lm is a combination of the scalar field kinetic term X = ˙φ2/2 and potential V (φ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Therefore,  it could be addressed as a subclass of the k-essence model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' The perturbation of such model has been  studied in [75].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  6  where  ρeff =  ��3  2λ + 1  �  ρ − λ  2 p  �  peff =  �  −λ  2 ρ +  �3  2λ + 1  �  p  �  with ρ and p are the energy density and pressure of tachyon field given by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='(11).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' The  sound speed cs is obtained as3  c2  s = ˙peff  ˙ρeff  =  (1 + 2λ) − αλ  2α  �  3λ  2 + 1  �  −  �  1 + 2λ  �.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  (21)  which is constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  The scalar spectral index, which is defined through the amplitude of the scalar field, is given  by  ns = 1 − (2ϵ1 + ϵ2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  (22)  Regarding the tensor perturbations, there is the tensor-to-scalar ratio which is very essential  in examining an inflationary model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' The parameter is expressed as follows  r = 16 cs ϵ1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  (23)  In the following section, we are going to examine the model for some specific types of the  potential and compare the results with data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  TYPICAL EXAMPLES  In this section, three types of potentials as power-law, T-mode, and exponential will be  studied in detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  power-law case  As the first case, the Hubble parameter is take as a power-law function of the scalar  field, H(φ) = H0φn where H0 and n are two constants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Using this definition, the slow-roll  3 In general the sound speed is defined as c2  s = ˙p/ ˙ρ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' But, in our case, the energy density and pressure in the  relation are not the energy density and pressure defined through Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='(11).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' In fact they are the effective  energy density and pressure which is defined from the right hand side of Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' (6) and (7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  7  parameters are  ϵ1 =  � 2αM 2  pξ  α(1 + λ) n2α H2−2α  0  �  1  2α−1  φ  2n−2nα−2α  2α−1  (24)  ηH = n(n − 1)  2α − 1  � 2αM 2  pξ  α(1 + λ) n2−2α H2−2α  0  �  1  2α−1  φ  2n−2nα−2α  2α−1  (25)  Inflation ends as the first slow-roll parameter reaches one, ϵ1 = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' The scalar field at the  end of inflation is read from this relation that is  φ  2n−2nα−2α  2α−1  e  =  � 2αM 2  pξ  α(1 + λ) n2α H2−2α  0  �  −1  2α−1  (26)  We are going to determine the free parameters of the model by comparing its results with  observational data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' In this regard, we need to estimate the perturbation parameters at the  time of horizon crossing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' First, the scalar field is computed through the relation of the  number of e-folds as  φ  2n−2nα−2α  2α−1  ⋆  =  �� 2αM 2  pξ  α(1 + λ) n2α H2−2α  0  �  1  2α−1 �  1 − 2n − 2nα − 2α  n(2α − 1)  N  ��−1  (27)  Inserting φ⋆ in the slow-roll parameters (16) and (17), one arrives at  ϵ⋆  1 =  �  1 − 2n − 2nα − 2α  n(2α − 1)  N  �−1  ,  (28)  η⋆  H =  (n − 1)  n(2α − 1)  �  1 − 2n − 2nα − 2α  n(2α − 1)  N  �−1  ,  (29)  and returning to Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' (22) and (23), the scalar spectral index and the tensor-to-scalar ratio  are obtained at horizon crossing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='1(a) illustrates r−ns curves versus the parameter α for  different values of λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' It is realized that the curve for n = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='5 and 1 is out of the observational  range and it enters the range for n = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='5 and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' The curves enter the observational range  for higher values of α and they are out of range for smaller α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' The r − ns curves versus  n are plotted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='1(b) for different values of α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' It seems that the curves start from the  same point and tend toward the smaller ns and bigger r by increasing α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' It is relalized that  the curves related to α = 1 and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='5 do not cross our interest area.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' On the other hand, the  curves related to α = 2 and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='4 perfectly cross the observational area.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' To have a better  view on the valid values of free parameters n and α, a parametric space is depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  The blue area indicates a set of (α, n) points for which the model comes to good agreement  8  (a)  (b)  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' The r − ns curves in terms of a) α and different values of n, b) n for different values of α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  The constant λ is taken as λ = 2 and the curves are plotted for the number of e-folds N = 65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' The figure illustrates the parametric space of the parameter α and n so that for each point  in the parameter the model remains in perfect agreement with data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  with data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  There is exact data about the amplitude of the scalar perturbations as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Estimating  the amplitude of the scalar perturbations at the time of the horizon crossing and applying  the data for Ps, one could determine another free parameters of the model that is  ξ2n =  1  H4α  0  ��α(1 + λ)  2αM 2  p  �  1  2α−1  ϵ⋆  1  n  2α  2α−1  �2n(2α−1) �  1  8π2M 2  pcsϵ⋆  1Ps  �2n−2nα−2α  (30)  Table.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='I presents a brief results of the case and gives a better insight about the case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' One  could finds the model results for the scalar spectral index, the tensor-to-scalar ratio, the  inflation energy scale and also anothe free parameters of the model M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' These results are  computed for different values of α and n so that some of them stand in the blue range of  9  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='10  n= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='08  n= 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='0  n= 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='5  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='.  n= 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='04 -  :  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='D2 - 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='D0 -  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='950  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='955  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='960  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='565  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='970  0860  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='985  Ns0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='10  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='08  α=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='0-6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='D4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='02 -  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='550  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='5955  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='960  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='955  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='580  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='985  Ns3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='D  25  2D  15  LD  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='5  14  16  1B  2D  22  24  26  aα  n  ns  r  M  ES  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='9695  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='0653  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='29 × 10−12  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='47 × 10−3  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='9645  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='0868  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='70 × 10−10  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='80 × 10−3  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='9605  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='1040  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='98 × 10−9  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='02 × 10−3  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='9695  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='0368  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='23 × 10−9  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='88 × 10−3  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='9652  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='0472  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='35 × 10−8  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='12 × 10−3  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='9620  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='0550  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='25 × 10−7  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='28 × 10−3  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='9695  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='0145  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='59 × 10−9  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='07 × 10−3  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='9655  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='0183  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='33 × 10−7  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='25 × 10−3  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='4  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='9626  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='0211  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='68 × 10−7  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='37 × 10−3  TABLE I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' The numerical results for the case about the scalar spectral index, tensor-to-scalar ratio,  constant M, and energy scale (ES) of inflation for different values of α and n taken from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='2,  where number of e-folds is N = 65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='2 and some do not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  Exponential case  The exponential function of the scalar field is picked out as the second case for the Hubble  parameter, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' H(φ) = H0 exp(βφ) where H0 and β are two constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Substituting this  Hubble parameter in Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' (16) and (18), the slow-roll parameters are obtained as  ϵ1 =  � 2αM 2  pξ  α(1 + λ) β2α H2−2α  0  �  1  2α−1  e  2−2α  2α−1 βφ,  (31)  ηH =  1  2α − 1  � 2αM 2  pξ  α(1 + λ) β2α H2−2α  0  �  1  2α−1  e  2−2α  2α−1 βφ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  (32)  Solving the relation ϵ1 = 1 in terms of φ, the field is estimated at the end of inflation  e  2α−2  2α−1 β φe =  � 2αM 2  pξ  α(1 + λ) β2α H2−2α  0  �  1  2α−1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  (33)  Applying this result on Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' (19) and by integrating, the field at the time of the horizon  crossing is given by  e  2α−2  2α−1 β φ⋆ = e  2α−2  2α−1 β φ⋆  �  1 + 2α − 2  2α − 1 N  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  (34)  10  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' The r − ns curves in terms of the α for different values of λ where the number of e-fold is  N = 85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  To estimate the scalar spectral index and the tensor-to-scalar ratio at the time of the horizon  crossing, we first need to substitute the above field in the slow-roll parameters which leads  to  ϵ⋆  1 =  �  1 + 2α − 2  2α − 1 N  �−1  (35)  η⋆  H =  1  2α − 1 ϵ⋆  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  (36)  Using the slow-roll parameters in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' (22) and (23), ns and r are obtained at t⋆.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' The behavior  of the parameters are described in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='3, where one finds r −ns curves versus the parameter  α for different values of λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' For smaller values of λ, the curves comes to the observational  range for larger values of α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' In order to have a better understanding about the valid range of  the parameters α and λ, we are going to run a Python code including the data for the scalar  spectral index and the tensor-to-scalar ratio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' The resulted parametric space is presented in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='4 that shows a set of (α, λ) for which the model is kept consistent with data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Also, one  realizes that there is bigger range of λ for smaller values of α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  Using the data about the amplitude of the scalar perturbations, another free parameter of  the model is determined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' From Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' (20), it is found that  ξ = α(1 + λ)  2αM 2  p  ϵ2α−1  1  �  8π2M 2  pcsϵ1Ps  �1−αβ2α  (37)  Table.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='II represents the value of the constant M = ξ1/4(α−1) for different choices of α and  λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' The magnitude of the free parameter M is about O(105).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Moreover, for each α and λ,  the scalar spectral index, the tensor-to-scalar ration, and the energy scale of inflation are  11  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='16  A = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='10  VO  A = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='30  A = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='50  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='12  入= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='80  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='D8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='D6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='D2  O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='DO  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='552  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='956  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='958  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='960  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='962  t960  NsFIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' The figure portrays a oarametric space for the free parameters α and λ where the number  of e-folds is N = 85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' For each point in the space the model comes to an agreement with data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  α  λ  ns  r  ξ  ES  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='9606  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='0785  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='10 × −5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='03 × −2  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='9606  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='0672  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='89 × −5  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='84 × −3  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='9606  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='0565  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='65 × −5  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='44 × −3  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='9613  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='0685  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='85 × −5  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='12 × −2  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='9613  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='0559  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='51 × −5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='94 × −2  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='9613  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='0433  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='06 × −5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='78 × −2  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='9619  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='0608  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='37 × −5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='11 × −1  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='9619  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='0468  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='89 × −5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='06 × −1  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='9619  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='0314  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='18 × −5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='02 × −1  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='9623  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='0545  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='74 × −5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='34 × −1  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='9623  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='0388  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='07 × −5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='23 × −1  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='9623  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='0184  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='73 × −5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='15 × −1  TABLE II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' The numerical results for the scalar spectral index, tensor-to-scalar ratio, constant M,  and the energy scale (ES) of inflation for different values of α and λ where the number of e-folds  is N = 85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  given as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' It is seen that the scalar spectal index and the tensor-to-scalar ratio stand in  agreement with data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' The enegy scale of inflation also increase by enhancement of α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  12  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='B  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='6  ~ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='4 -  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='D  1+V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  SWAMPLAND CRITERIA AND TCC  String theory, which is known as one of the promising candidate for ultimate theory of  quantum gravity, propounds a landscape which contains all consistent low-energy EFTs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  Moreover, there are other low-energy EFTs which do not get along with string theory living  on an area known as swampland.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' It is our desire to build our model based on a consistent low-  energy EFT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Therefore, a mechanism is required to separate the consistent and inconsistent  theories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' over past years, several conjectures have been introduced in this matter and the  most recent conjectures, which are known as swampland criteria, are  Distance conjecture: it puts an upper bound on the scalar field excursion in the field  space  ∆φ ≤ c1  (38)  where c1 is a constant of the order of one, O(1) [59–61].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  de Sitter conjecture: it stated that there should be a lower bound on the gradient of  the potential as [60, 61]  |V,φ|  V  ≥ c2,  (39)  or as in the refined version of this criterion one of the following condition should  satisfied  |V,φ|  V  ≥ c2,  or|V,φφ|  V  ≥ −c′  2  (40)  The true order of the constant c1 depends on the detail of compaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' It is concluded  that it is larger than  √  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' However, further consideration indicates that it could smaller,  of the order of O(0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='1) [60, 62].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' In any case, the important criterium is that the constant  must be positive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  The conjecture are stated in Planck units, Mp = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Due to this believe that inflation occurs  at energy scale below the Planck, it is expected to be describe by low-energy EFT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' There-  fore, it is interesting to consider the validation of the swampland criteria for an inflationary  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  In the previous section, the free parameters of the model are determined using data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Now,  we are going to use these results, the scalar field at the horizon crossing and the end of infla-  tion is obtained and one could specify the field excursion and the gradient of the potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  13  α  n  ∆φ  V ′/V  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='18 × 10−5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='53 × 105  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='5  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='28 × 10−4  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='92 × 103  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='35 × 10−3  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='84 × 102  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='0  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='89 × 10−6  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='04 × 105  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='5  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='27 × 10−4  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='02 × 103  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='80 × 10−3  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='15 × 103  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='0  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='57 × 10−6  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='25 × 105  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='10 × 10−4  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='25 × 103  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='4  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='19 × 10−3  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='46 × 103  TABLE III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Table shows the results for the field distance and potential gradient of the fisrt case  for different values of α and n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  Tables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='III and IV display the results respectively for the first and second cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  The results clarify that both criteria could be satisfy in both cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' For the first case,  for the specific parameter α, the field distance gets larger by increasing λ, however, the  potential gradient decreases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Besides, there is a reverse situation for specific values of λ  so that the field distance gets smaller by enhancement of α, while the potential gradient  increase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  For the second case, where the Hubble parameter is taken as an exponential  function of the scalar field, the field distance could be smaller than one and the potential  gradient larger.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' The point that one realizes from the table is that the field distance and the  potential gradient are not sensitive to the varying of α and λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  Another conjecture which has been proposed recently is TCC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' The TCC targets the  fluctuations generated during inflation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' These fluctuations are the origin of the universe  structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' They are stretches with the expansion and cross the horizon, freeze and reenter  the horizon after inflation, and today we could observe some of them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' The crucial point  is that the fluctuations have a quantum nature, however, they loss their nature as cross  the horizon and freeze.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' At this point they become classical.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Our main concern are the  fluctuations with origin wavelength less than the Planck length.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' In this case, if inflation last  long enough, they stretch and cross the horizon and become classical.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' This is known as the  14  α  λ  ∆φ  V ′/V  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='4885  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='927  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='4885  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='925  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='4885  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='923  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='4780  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='926  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='4780  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='923  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='4780  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='921  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='4704  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='924  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='4704  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='922  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='4704  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='920  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='4647  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='923  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='4647  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='921  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='4647  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='919  TABLE IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Table shows the results for the field distance and potential gradient of the second case  for different values of α and λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  ”trans-Planckian problem”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' TCC states that no fluctuation with wavelength less than the  Planck length should cross the horizon [39, 63, 64], and it is formulated as  lp  ai  < H−1  f  af  ,  (41)  where lp is the Planck length, Hf is the Hubble parameter at the end of inflation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' ai and af  are the scale factor respectively at the beginning and the end of inflation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  The quantity H−1  f  for both cases of Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='IV is of the order of O(106).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' On the other hand,  the term af/ai = eN is much higher than this magnitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' It implies that the condition  eN < H−1  f  will never be satisfied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  CONCLUSION  The scenario of slow-roll inflation was considered in the f(R, T) theory of gravity, which  is known as a modified theory of gravity where the matter has a non-minimal coupling to the  curvature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' The inflaton was assumed to be played by a noncanonical scalar field including  generalized kinetic energy, which is a subclass of the k-essence scalar field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' After briefly  15  reviewing the model and its dynamical equations, the scenario of inflation is considering  following Hamilton-Jacobi formalism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' In this formalism, the Hubble parameter is introduced  as a function of the scalar field instead of the potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' The investigation was pursued by  considering two cases for the Hubble parameter as power-law and exponential functions of  the scalar field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Utilizing observational data and performing a coding program, the free  parameters of the model were determined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  First, the Hubble parameter was assumed to be a power-law function of the scalar field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  By estimating the scalar field at the time of the horizon crossing, we could compute the  main perturbation parameters at this time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  Next, by applying the data for the scalar  spectral index and the tensor-to-scalar ratio, we could determine the valid range for the free  parameters α and n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Then, the free parameter M was determined through the amplitude of  the scalar perturbations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Following the obtained information about the free parameters of  the model, the energy scale of inflation was computed that was of the order of 10−3Mp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Also,  we considered the validity of the swampland criteria and TCC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Concerning the swampland  criteria, the result implies that the two conjectures are perfectly satisfied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' However, the  TCC is not satisfied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  In the next case, the Hubble parameter was picked as the exponential function of the scalar  field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  The same procedure was followed to determine the free parameters of the model  for which to put the model in perfect agreement with the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' For the determined free  parameters, the model could satisfy the swampland criteria, however, in contrast to the first  case, they were not sensitive to the changes of the parameter λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [1] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Albrecht and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Steinhardt, Cosmology for grand unified theories with radiatively induced  symmetry breaking, Physical Review Letters 48, 1220 (1982).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [2] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Linde, A new inflationary universe scenario: a possible solution of the horizon, flatness,  homogeneity, isotropy and primordial monopole problems, Physics Letters B 108, 389 (1982).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [3] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Linde, Chaotic inflation, Physics Letters B 129, 177 (1983).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [4] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Starobinsky, A new type of isotropic cosmological models without singularity, Physics  Letters B 91, 99 (1980).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  16  [5] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Guth, The Inflationary Universe: A Possible Solution to the Horizon and Flatness  Problems, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' D23, 347 (1981), [Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Cosmol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='3,139(1987)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [6] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Linde, Inflationary cosmology, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Rept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' 333, 575 (2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [7] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Linde, Particle physics and inflationary cosmology, Contemp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Concepts Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' 5, 1  (1990), arXiv:hep-th/0503203 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [8] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Linde, Current understanding of inflation, Proceedings, 6th UCLA Symposium on  Sources and Detection of Dark Matter and Dark Energy in the Universe: Marina del Rey,  CA, USA, February 18-20, 2004, New Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' 49, 35 (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [9] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Linde, Prospects of inflation, Proceedings, Nobel Symposium 127 on String theory and  cosmology: Sigtuna, Sweden, August 14-19, 2003, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Scripta T117, 40 (2005), arXiv:hep-  th/0402051 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [10] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Riotto, Inflation and the theory of cosmological perturbations, Astroparticle physics and  cosmology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Proceedings: Summer School, Trieste, Italy, Jun 17-Jul 5 2002, ICTP Lect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Notes  Ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' 14, 317 (2003), arXiv:hep-ph/0210162 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [11] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Baumann, TASI Lecture on Inflation, in Physics of the large and the small, TASI 09, pro-  ceedings of the Theoretical Advanced Study Institute in Elementary Particle Physics, Boulder,  Colorado, USA, 1-26 June 2009 (2011) pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' 523–686, arXiv:0907.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='5424 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [12] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Weinberg, Cosmology (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [13] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Lyth and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Liddle, The primordial density perturbation: Cosmology, inflation and  the origin of structure (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [14] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Liddle and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Lyth, Cosmological inflation and large scale structure (2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [15] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Ade et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' (Planck), Planck 2013 results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' XXII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Constraints on inflation, Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' 571, A22 (2014), arXiv:arXiv:1303.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='5082 [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='CO].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [16] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Ade et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' (Planck), Planck 2015 results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' XX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Constraints on inflation, Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' 594, A20 (2016), arXiv:arXiv:1502.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='02114 [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='CO].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [17] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Akrami et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' (Planck), Planck 2018 results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Constraints on inflation,  (2018),  arXiv:arXiv:1807.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='06211 [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='CO].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [18] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Barenboim and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Kinney, Slow roll in simple non-canonical inflation, JCAP 0703,  014, arXiv:astro-ph/0701343 [astro-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [19] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Franche, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Gwyn, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Underwood, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Wissanji, Initial Conditions for Non-Canonical  Inflation, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' D82, 063528 (2010), arXiv:1002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='2639 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  17  [20] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Unnikrishnan, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Sahni, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Toporensky, Refining inflation using non-canonical scalars,  JCAP 1208, 018, arXiv:1205.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='0786 [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='CO].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [21] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Rezazadeh, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Karami, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Karimi, Intermediate inflation from a non-canonical scalar  field, JCAP 1509 (09), 053, arXiv:1411.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='7302 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [22] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Saaidi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Mohammadi, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Golanbari, Light of Planck-2015 on Noncanonical Inflation,  Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' High Energy Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' 2015, 926807 (2015), arXiv:1708.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='03675 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [23] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Fairbairn and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Tytgat, Inflation from a tachyon fluid?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=', Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' B546, 1 (2002),  arXiv:hep-th/0204070 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [24] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Mukohyama, Brane cosmology driven by the rolling tachyon, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' D66, 024009  (2002), arXiv:hep-th/0204084 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [25] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Feinstein, Power law inflation from the rolling tachyon, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' D66, 063511 (2002),  arXiv:hep-th/0204140 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [26] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Padmanabhan, Accelerated expansion of the universe driven by tachyonic matter, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' D66, 021301 (2002), arXiv:hep-th/0204150 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [27] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Aghamohammadi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Mohammadi, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Golanbari, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Saaidi, Hamilton-Jacobi formal-  ism for tachyon inflation, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' D90, 084028 (2014), arXiv:1502.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='07578 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [28] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Spalinski, On Power law inflation in DBI models, JCAP 0705, 017, arXiv:hep-th/0702196  [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [29] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Bessada, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Kinney, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Tzirakis, Inflationary potentials in DBI models, JCAP  0909, 031, arXiv:0907.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='1311 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [30] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Weller, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' van de Bruck, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Mota, Inflationary predictions in scalar-tensor DBI  inflation, JCAP 1206, 002, arXiv:1111.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='0237 [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='CO].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [31] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Nazavari, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Mohammadi, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Ossoulian, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Saaidi, Intermediate inflation driven by  DBI scalar field, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' D93, 123504 (2016), arXiv:1708.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='03676 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [32] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='-i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Maeda and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Yamamoto, Stability analysis of inflation with an su (2) gauge field,  Journal of Cosmology and Astroparticle Physics 2013 (12), 018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [33] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Abolhasani, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Emami, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Firouzjahi, Primordial anisotropies in gauged hybrid  inflation, Journal of Cosmology and Astroparticle Physics 2014 (05), 016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [34] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Alexander, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Jyoti, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Kosowsky, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Marcian`o, Dynamics of gauge field inflation,  Journal of Cosmology and Astroparticle Physics 2015 (05), 005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  18  [35] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Tirandari and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Saaidi, Anisotropic inflation in brans–dicke gravity, Nuclear Physics B  925, 403 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [36] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Maartens, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Wands, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Bassett, and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Heard, Chaotic inflation on the brane,  Physical Review D 62, 041301 (2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [37] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Golanbari, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Mohammadi, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Saaidi, Brane inflation driven by noncanonical scalar  field, Physical Review D 89, 103529 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [38] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Mohammadi, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Golanbari, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Nasri, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Saaidi, Brane inflation: Swampland Criteria,  TCC, and Reheating constraint, (2020), arXiv:2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='09489 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [39] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Mohammadi, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Golanbari, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Enayati, Brane inflation and Trans-Planckian censorship  conjecture, (2020), arXiv:2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='01512 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [40] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Berera, Warm inflation, Physical Review Letters 75, 3218 (1995).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [41] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Berera, Warm inflation in the adiabatic regime—a model, an existence proof for inflationary  dynamics in quantum field theory, Nuclear Physics B 585, 666 (2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [42] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Hall, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Moss, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Berera, Scalar perturbation spectra from warm inflation,  Physical Review D 69, 083525 (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [43] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Sayar, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Mohammadi, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Akhtari, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Saaidi, Hamilton-Jacobi formalism to warm  inflationary scenario, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' D95, 023501 (2017), arXiv:1708.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='01714 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [44] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Akhtari, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Mohammadi, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Sayar, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Saaidi, Viscous warm inflation: Hamilton–Jacobi  formalism, Astropart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' 90, 28 (2017), arXiv:1710.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='05793 [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='CO].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [45] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Sheikhahmadi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Mohammadi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Aghamohammadi, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Harko, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Herrera, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Corda,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Abebe, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Saaidi, Constraining chameleon field driven warm inflation with Planck  2018 data, Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' C79, 1038 (2019), arXiv:1907.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='10966 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [46] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Mohammadi, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Golanbari, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Sheikhahmadi, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Sayar, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Akhtari, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Rasheed, and  K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Saaidi, Warm tachyon inflation and swampland criteria, Chin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' C 44, 095101 (2020),  arXiv:2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='10042 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [47] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Mohammadi, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Saaidi, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Golanbari, Tachyon constant-roll inflation, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' D97,  083006 (2018), arXiv:1801.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='03487 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [48] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Mohammadi, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Saaidi, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Sheikhahmadi, Constant-roll approach to non-canonical  inflation, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' D100, 083520 (2019), arXiv:1803.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='01715 [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='CO].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [49] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Golanbari, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Mohammadi, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Saaidi, Observational constraints on DBI constant-roll  inflation, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Dark Univ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' 27, 100456 (2020), arXiv:1808.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='07246 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  19  [50] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Mohammadi, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Golanbari, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Saaidi, Beta-function formalism for k-essence constant-  roll inflation, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Dark Univ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' 28, 100505 (2020), arXiv:1912.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='07006 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [51] .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [52] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Harko, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Lobo, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Nojiri, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Odintsov, f(R, T) gravity, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' D 84,  024020 (2011), arXiv:1104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='2669 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [53] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='-U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Bhatti and Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Yousaf, Dynamical variables and evolution of the universe, Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' D 26, 1750029 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [54] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Zaregonbadi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Farhoudi, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Riazi, Dark Matter From f(R,T) Gravity, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' D  94, 084052 (2016), arXiv:1608.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='00469 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [55] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Moraes and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Sahoo, Wormholes in exponential f(R, T) gravity, Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' C 79, 677 (2019), arXiv:1903.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='03421 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [56] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Alves, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Moraes, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' de Araujo, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Malheiro, Gravitational waves  in f(R, T) and f(R, T φ) theories of gravity, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' D 94, 024032 (2016), arXiv:1604.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='03874  [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [57] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Bhattacharjee, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Santos, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Moraes, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Sahoo, Inflation in f(R, T)  gravity, Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Plus 135, 576 (2020), arXiv:2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='04336 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [58] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Gamonal, Slow-roll inflation in f(R, T) gravity and a modified Starobinsky-like inflationary  model, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Dark Univ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' 31, 100768 (2021), arXiv:2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='03861 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [59] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Obied, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Ooguri, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Spodyneiko, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Vafa, De Sitter Space and the Swampland, (2018),  arXiv:1806.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='08362 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [60] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Ooguri, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Palti, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Shiu, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Vafa, Distance and de Sitter Conjectures on the Swamp-  land, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' B788, 180 (2019), arXiv:1810.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='05506 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [61] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Garg and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Krishnan, Bounds on Slow Roll and the de Sitter Swampland, JHEP 11,  075, arXiv:1807.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='05193 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [62] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Kehagias and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Riotto, A note on Inflation and the Swampland, Fortsch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' 66, 1800052  (2018), arXiv:1807.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='05445 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [63] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Bedroya and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Vafa, Trans-Planckian Censorship and the Swampland, JHEP 09, 123,  arXiv:1909.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='11063 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [64] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Bedroya, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Brandenberger, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Loverde, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Vafa, Trans-Planckian Censorship and  Inflationary Cosmology, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' D 101, 103502 (2020), arXiv:1909.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='11106 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  20  [65] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Brandenberger and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Wilson-Ewing, Strengthening the TCC Bound on Inflationary Cos-  mology, JCAP 03, 047, arXiv:2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='00043 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [66] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Moraes, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Arba˜nil, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Malheiro, Stellar equilibrium configurations of  compact stars in f(R, T) gravity, JCAP 06, 005, arXiv:1511.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='06282 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [67] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Carvalho, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Lobato, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Moraes, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Arba˜nil, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Marinho, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Otoniel,  and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Malheiro, Stellar equilibrium configurations of white dwarfs in the f(R, T) gravity,  Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' C 77, 871 (2017), arXiv:1706.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='03596 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [68] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Moraes, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' de Paula, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Correa, Charged wormholes in f(R,T) extended  theory of gravity, Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' D 28, 1950098 (2019), arXiv:1710.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='07680 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [69] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Moraes and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Sahoo, Modelling wormholes in f(R, T) gravity, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' D  96, 044038 (2017), arXiv:1707.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='06968 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [70] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Moraes, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Correa, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Lobato, Analytical general solutions for static  wormholes in f(R, T) gravity, JCAP 07, 029, arXiv:1701.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='01028 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [71] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Azizi, Wormhole Geometries In f(R, T) Gravity, Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Theor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' 52, 3486 (2013),  arXiv:1205.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='6957 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [72] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Moraes, Cosmology from induced matter model applied to 5D f(R, T) theory,  Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Space Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' 352, 273 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [73] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Moraes, Cosmological solutions from Induced Matter Model applied to 5D  f(R, T) gravity and the shrinking of the extra coordinate, Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' C 75, 168 (2015),  arXiv:1502.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='02593 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [74] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Reddy and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Santhi Kumar, Some anisotropic cosmological models in a modified  theory of gravitation, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Space Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' 344, 253 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  [75] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Garriga and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Mukhanov, Perturbations in k-inflation, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content=' B458, 219 (1999),  arXiv:hep-th/9904176 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
+page_content='  21' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adE_T4oBgHgl3EQfyxwh/content/2301.08319v1.pdf'}
diff --git a/adFAT4oBgHgl3EQf4h70/content/2301.08727v1.pdf b/adFAT4oBgHgl3EQf4h70/content/2301.08727v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..b7992c3c8b67cc2089ec7efe702b6513d2ac1680
--- /dev/null
+++ b/adFAT4oBgHgl3EQf4h70/content/2301.08727v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:7e7bcd1e21d5d662d3bdf190b76162395b2e42b117ae68747fd6c4adab9f0001
+size 1719192
diff --git a/adFAT4oBgHgl3EQf4h70/vector_store/index.faiss b/adFAT4oBgHgl3EQf4h70/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..412423454885f21736af84c154cb9489ea001037
--- /dev/null
+++ b/adFAT4oBgHgl3EQf4h70/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:c6aea86c8d0f640f4f5f633c29d36189b0331b6ec4d874a78b2ac08e8226499c
+size 11993133
diff --git a/adFAT4oBgHgl3EQf4h70/vector_store/index.pkl b/adFAT4oBgHgl3EQf4h70/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..c1a7ea916cb59419b13dbbd490b2184bb6af27ac
--- /dev/null
+++ b/adFAT4oBgHgl3EQf4h70/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:9e3199acf06ad6b8ed0d1ffef1a6a49f2f57fe57025b5e7da10bf6c95d9340cd
+size 468302
diff --git a/b9AyT4oBgHgl3EQf-PqC/content/2301.00889v1.pdf b/b9AyT4oBgHgl3EQf-PqC/content/2301.00889v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..8f0efd6a73977788a29957003072ad94f71a448a
--- /dev/null
+++ b/b9AyT4oBgHgl3EQf-PqC/content/2301.00889v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:00b8b45101ce4f80357a0332bd8f8511a66d613e11adbeb2e07cd861b6ad74f5
+size 398263
diff --git a/b9AyT4oBgHgl3EQfi_hp/content/2301.00406v1.pdf b/b9AyT4oBgHgl3EQfi_hp/content/2301.00406v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..e35d988c01ad27c5845dfb41051e13645d33b4e9
--- /dev/null
+++ b/b9AyT4oBgHgl3EQfi_hp/content/2301.00406v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:ce7b629d18e9d042a7071d42d2b694f8e449bae876ccc6b8639f7a7ef66da034
+size 6786664
diff --git a/b9E2T4oBgHgl3EQfFgZ2/vector_store/index.faiss b/b9E2T4oBgHgl3EQfFgZ2/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..87f3f5d43c61f9e901c88ceb0f6043927c1ad901
--- /dev/null
+++ b/b9E2T4oBgHgl3EQfFgZ2/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:f0e62c4f3913a40ce444afe9cd896ae70425c17979653f6e2e88be689bff43ae
+size 8716333
diff --git a/bdFRT4oBgHgl3EQfRzcI/vector_store/index.faiss b/bdFRT4oBgHgl3EQfRzcI/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..0123181917b6dbcc1ab5f1ec7a0fc037d5db8c22
--- /dev/null
+++ b/bdFRT4oBgHgl3EQfRzcI/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:94ef93c576e6409361ae0d72fb4a24dcdf107a110eefde292c1f39d1552fa4c4
+size 2949165
diff --git a/bdFRT4oBgHgl3EQfRzcI/vector_store/index.pkl b/bdFRT4oBgHgl3EQfRzcI/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..4bba15f3c700395faf56a6fdf2ccbcb0c6c7ae71
--- /dev/null
+++ b/bdFRT4oBgHgl3EQfRzcI/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:33cae0f15b39ea6ac62ad7c3bf0c30dca43c705d59ca2a8c84366fbf1b9b1872
+size 106668
diff --git a/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf b/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..a0bd9deb92abff82554b68ca2f56a64ed60341ff
--- /dev/null
+++ b/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:d705050542bcafa6d7893b040f58ee357316cd0f96d6af9780a5e2481c35a035
+size 1122700
diff --git a/btFLT4oBgHgl3EQfYS80/vector_store/index.pkl b/btFLT4oBgHgl3EQfYS80/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..c7e03dee194fccce680f487f9d458b0ab105edcf
--- /dev/null
+++ b/btFLT4oBgHgl3EQfYS80/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:49cc9a0db9aa30068095eeacc721be8b8393a0db4beff1967ea940ff6a7825db
+size 158207
diff --git a/c9E2T4oBgHgl3EQfFwbt/content/tmp_files/load_file.txt b/c9E2T4oBgHgl3EQfFwbt/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..9cedfa7cd2ed21adbf8ca50949466cdd6d45270a
--- /dev/null
+++ b/c9E2T4oBgHgl3EQfFwbt/content/tmp_files/load_file.txt
@@ -0,0 +1,714 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf,len=713
+page_content='Astronomy & Astrophysics manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' ms_final  ©ESO 2023  January 11, 2023  Letter to the Editor  Atomic oxygen abundance toward Sagittarius B2⋆  Dariusz C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Lis1, Paul F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Goldsmith1, Rolf Güsten2, Peter Schilke3, Helmut Wiesemeyer2, Youngmin Seo1, and  Michael W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Werner1  1 Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Drove Drive, Pasadena, CA 91109, USA  2 Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, D-53121 Bonn, Germany  3 I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Physikalisches Institut, Universität zu Köln, Zülpicher Straße 77, D-50937 Köln, Germany  Received 11 November 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' accepted 23 December 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  ABSTRACT  A substantial fraction of oxygen in diffuse clouds is unaccounted for by observations and is postulated to be in an unknown refractory  form, referred to as unidentified depleted oxygen (UDO), which, depending on the local gas density, may contribute up to 50%  of the total oxygen content.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Previous Infrared Space Observatory (ISO) observations suggest that a significant fraction of oxygen  in even denser, translucent clouds may be in atomic form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' We have analyzed velocity-resolved archival SOFIA observations of  the 63 µm fine-structure [O i] transition toward the high-mass star-forming region Sgr B2(M) in the Central Molecular Zone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' The  foreground spiral-arm clouds as well as the extended Sgr B2 envelope between the Sun and the background dust continuum source  produce multiple [O i] absorption components, spectrally separated in velocity space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' The gas-phase atomic oxygen column density in  foreground clouds toward Sgr B2 is well correlated with the total hydrogen column density, with an average atomic oxygen abundance  of (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='51 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='69) × 10−4 with respect to hydrogen nuclei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' This value is in good agreement with the earlier ISO measurements on the  same line of sight, and is about 35% lower than the total interstellar medium oxygen abundance in the low-density warm gas, as  measured in the UV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' We find no evidence that a significant fraction of the oxygen on the line of sight toward Sagittarius B2 is in the  form of UDO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  Key words.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Astrochemistry – ISM: abundances – ISM: atoms – ISM: clouds – ISM: lines and bands – ISM: molecules  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Introduction  A long-standing problem in our understanding of the quiescent  dense interstellar medium (ISM) has been the difficulty of ac-  counting for the gas-phase abundances of carbon and oxygen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  Since the first calculations of ion-molecule reaction schemes  (Herbst & Klemperer 1973;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Dalgarno & Black 1976), there  have been theoretical predictions indicating that the fundamen-  tal reservoirs of these elements are the molecular species CO,  O2, and H2O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' The local gas-phase oxygen abundance is assumed  to be about twice that of carbon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' This comes from the observed  stellar values, modified by the depletion seen in local ISM dif-  fuse clouds, such as those toward ζ Ophiuchi and HD 154368  (Snow & Witt 1996;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Snow et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 1996;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Cardelli et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 1993),  that is, the carbon abundance [C] = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='66 × 10−4 and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='32 × 10−4,  respectively, and the oxygen abundance [O] = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='88×10−4, which  gives an average [C]/[O] = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' So, nearly all carbon should be  in CO, with plenty of oxygen left over for O2, and H2O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  Millimeter-wave measurements have indeed confirmed the  large abundance of CO at about 10−4 of H2 (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Lada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  1994).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' However, extensive Herschel observations (van Dishoeck  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2021) have shown that the H2O abundance is universally  low.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Even in warm outflows and shocks, the water abundance  is only ∼ 10−6 with respect to H2, much less than the expected  value of 4 × 10−4 if all volatile oxygen is in water.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Only in very  hot gas (> 1000 K) have water abundances close to 10−4 been  ⋆ We dedicate this manuscript to Tom Phillips, who was an inspira-  tion to all of us.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Tables with the data used for Figures 2 and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='3 are avail-  able at the CDS via anonymous ftp to cdsarc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='u-strasbg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='fr (130.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='128.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='5)  or via http://cdsarc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='u-strasbg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='fr/viz-bin/cat/J/A+A/XXX/XX  derived.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' For O2, low gas-phase abundances have been suggested  by early Submillimeter Wave Astronomy Satellite (SWAS) and  Odin observations (Goldsmith et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2000;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Larsson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  Herschel pushed the limits even lower, with O2 detections re-  ported only in the Orion shock (Goldsmith et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Chen  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2014) and in the ρ Ophiuchi cloud (Liseau et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  Larsson & Liseau 2017), where an abundance of 5 × 10−8 with  respect to H2 has been derived.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' In other sources, limits as low as  6 × 10−9 (3σ) were reported (NGC 1333 IRAS4A;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Yıldız et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  A combined analysis of water vapor, water ice, and O2 limits  in cold clouds thus indicates that a large fraction of the oxy-  gen is unaccounted for.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' A number of possible explanations have  been hypothesized (van Dishoeck et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Within the sim-  ple water chemistry models, the only solution is to have a short  pre-stellar stage of only 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='1 Myr to prevent all oxygen from be-  ing turned into water.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' An alternative is for dense cores to have  a small fraction of large grains (> 1 µm), which prevents more  than 50% of the water ice from being observed through infrared  absorption spectroscopy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' However, this solution does not apply  to hot cores and shocks, where the large icy grains should have  sublimated and where a large fraction of oxygen is also missing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  Another option is, therefore, that oxygen is in some refractory  form called unidentified depleted oxygen (UDO), which con-  sists of material that does not vaporize or atomize even in strong  shocks (up to 1000 K).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  A schematic overview of the oxygen budget in diffuse and  translucent clouds is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 3 of Whittet (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' In dif-  fuse clouds, most of the oxygen is in atomic form, with silicates  and oxides contributing up to about 100 pm (out of a total of 575  Article number, page 1 of 7  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='03651v1  [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='GA]  9 Jan 2023  A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' ms_final  ppm relative to H nuclei).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' The UDO wedge starts at hydrogen  nucleus densities of about 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='1 cm−3 and increases to about 150  ppm (∼ 25% of the total oxygen) at densities of about 7 cm−3,  corresponding to the effective observational limit on depletion  studies in the UV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' In higher-density clouds (nH ∼ 1000 cm−3),  gas-phase CO is expected to contribute at about 50 ppm, with  ices, and silicates and oxides contributing at about 100 ppm each.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  The atomic oxygen contribution is predicted to be small, leaving  about 300 ppm in the form of UDO (∼ 50% of the total oxygen).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  This denser gas is not accessible in the UV due to extinction, but  can be studied using far-infrared spectroscopy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  Atomic oxygen is an important part of the oxygen budget,  and a number of studies aimed at constraining its abundance  have been carried out.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' The [O i] 63 µm fine-structure line was ob-  served in the diffuse ISM using the Infrared Space Observatory  (ISO) Long Wavelength Spectrometer (LWS) by means of ab-  sorption spectroscopy against bright background dust continuum  sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Such studies were limited by the relatively low spectral  resolution of the LWS instrument (10 km s−1 in the Fabry-Perot  mode with the maximum entropy deconvolution).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' However, in  some sources, the foreground absorption is well separated in ve-  locity space from the background source, allowing a determina-  tion of the oxygen abundance in the foreground clouds (Vastel et  al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2000;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Lis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2001;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Vastel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  The [O i] 63 µm fine-structure line emission has been widely  used as a tracer of star formation both in Galactic sources (Liseau  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 1999;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Oberst et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2001;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Karska et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2014) and in exter-  nal galaxies (Malhotra et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2001;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Dale et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2004;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' González-  Alfonso et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Farrah et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Comparison of the  63 µm and 145 µm line intensities (Stacey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  1983) and  63 µm studies with higher spectral resolution (Kraemer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  1998;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Boreiko & Betz 1996;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Leurini et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Schneider et  al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Mookerjea et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2019) suggest that the lower-lying  63 µm line observed in emission is optically thick.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Goldsmith  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' (2021) find that approximately half of the 12 sources ob-  served with the German REceiver for Astronomy at Terahertz  Frequencies (GREAT) instrument on the Stratospheric Obser-  vatory for Infrared Astronomy (SOFIA) showed clear evidence  of self-absorption profiles, indicating the presence of large col-  umn densities of low-excitation atomic oxygen with N(O0  le) =  2 − 7 × 1018 cm−2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Much of this is in regions that would typi-  cally be assumed to be totally molecular, but which in fact have  X(Oo) ≃ 10−5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' The low-excitation foreground gas can be studied  by means of absorption spectroscopy toward bright background  dust continuum sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  Sgr B2 is one of the brightest far-infrared continuum sources  in the Galaxy, and thus an excellent target for absorption studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  The differential rotation of the Milky Way allows spectral fea-  tures from gas clouds at different galactocentric radii to be sepa-  rated in velocity (Greaves & Williams 1994;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Even at the  limited spectral resolution of the ISO LWS, the Sgr B2(M) [O i]  spectrum could be decomposed into three foreground velocity  components (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 3 of Lis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2001), and the atomic oxygen  column density was shown to be correlated with the CO column  density, as expected if the two species are well mixed spatially.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  An average atomic oxygen abundance of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='7 × 10−4 with respect  to hydrogen nuclei was derived in the molecular phase (Lis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  The ISO study was limited by the spectral resolution of the  LWS instrument, which resulted in blending of multiple ve-  locity components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' The GREAT instrument on SOFIA offers  tremendous improvements in sensitivity and spectral resolution  at 63 µm over ISO LWS (see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Wiesemeyer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  Goldsmith et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2021 for velocity-resolved [O i] observations of  other sources).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' In the present paper, we revisit the atomic oxygen  abundance in the foreground clouds on the sightline toward Sgr  B2 using archival SOFIA observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' The high spectral res-  olution of GREAT allows, for the first time, the [O i] emission  from individual line-of-sight clouds to be separated, velocity in-  tervals affected by saturated absorption to be correctly masked,  and accurate atomic oxygen column densities and abundances to  be derived.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Observations  We used publicly available SOFIA/GREAT (Heyminck et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  2012) observations of the 63 µm fine-structure [O i] line from the  NASA Infrared Processing and Analysis Center (IPAC) SOFIA  Science Archive1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' The data downloaded from the archive were  re-reduced using the latest version of the GREAT pipeline (see  Appendix A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' The [O i] spectrum is centered at the position of  Sgr B2M, 17h47m20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='16s;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' −28d23′04.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='5′′ (J2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  Figure 1 (upper panel) shows the final [O i] 63 µm spectrum  divided by the continuum, resampled to 1 km s−1 spectral res-  olution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Local standard of rest (LSR) velocities between −120  and +40 km s−1 correspond to the foreground gas, while those  greater than 40 km s−1 correspond to the envelope of the Sgr B2  cloud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' The higher gas densities present in this component make  the excitation and the resulting column densities uncertain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Con-  sequently, we excluded these velocities from the analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Ve-  locities between −6 and 0 km s−1, where the [O i] spectrum is  contaminated by telluric absorption, were also excluded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' To es-  timate the noise level in the [O i] absorption region, we split the  data into two independent subsets with comparable integration  times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' The lower histogram shows the difference spectrum be-  tween the two subsets divided by 2, which is a measure of the  uncertainty in the final [O i] spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' The difference spectrum  is flat over most velocities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' The rms computed in the −130 to 40  km s−1 velocity range is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='0193, and we used this value as the  uncertainty of the [O i] line-to-continuum ratio in the analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  The rms increases toward the edges, where the two local oscil-  lator (LO) settings used in the observations do not fully overlap,  resulting in an effectively shorter integration time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' In addition, a  higher rms is seen in the difference spectrum at positive veloc-  ities, where the foreground absorption may be contaminated by  wings of the [O i] emission from the Sgr B2 envelope.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' The full  width at half maximum (FWHM) SOFIA beam size at the [O i]  frequency is ∼ 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='6′′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  We used archival Herschel Heterodyne Instrument for the  Far-Infrared (HIFI) (de Graauw et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2010) observations of hy-  drogen fluoride (HF) to determine H2 column densities in the  various velocity components on the line of sight toward Sgr B2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  Two independent data sets were used in the analysis, which al-  lows an accurate quantification of the instrumental uncertain-  ties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Both data sets, reduced using the latest HIFI instrument  pipeline, were downloaded from the European Space Agency  Herschel Science Archive2 and imported into the Institut de  radioastronomie millimétrique (IRAM) Gildas3 software pack-  age for subsequent analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' The first observation is a Band 5A  spectral scan of Sgr B2(M), centered at the same position as  the O i spectrum (OBSID 1342204739).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' The second observation  is a 4′ long north-south strip taken in the double-beam-switch  (DBS) observing mode (OBSID 1342205881).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' The DBS refer-  ence beams lie approximately 3′ to the east and west (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', per-  1 https://irsa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='ipac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='caltech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='edu/Missions/sofia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='html;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' AOR ID 03_0088.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  2 https://archives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='esac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='esa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='int/hsa/whsa/  3 https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='iram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='fr/IRAMFR/GILDAS/  Article number, page 2 of 7  Lis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' : Atomic oxygen  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Spectra of [O i] and HF absorption toward Sgr B2(M) divided  by the corresponding continua.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' (Upper) SOFIA/GREAT [O i] spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  The lower histogram shows the difference between two independent  data subsets divided by 2, which is a measure of the uncertainty in the  [O i] spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Gray areas show velocities excluded from the analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  This includes the Sgr B2 envelope at velocities greater than 40 km s−1  and the region between -6 and 0 km s−1, where the [O i] spectrum is con-  taminated by telluric absorption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' (Lower) Average Herschel/HIFI spec-  trum of HF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' The lower histogram shows the difference between the two  independent observations divided by 2, which is a measure of the un-  certainty in the average spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  pendicular to the roughly north–south elongation of Sgr B2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  Two spectra in the strip closest to Sgr B2(M) (< 10′′ offsets)  were averaged with uniform weighting to produce the final spec-  trum used in the analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' We used spectra taken with the HIFI  wide band spectrometer, which provided a spectral resolution  of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='1 MHz over a 4 GHz intermediate frequency (IF) band-  width.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' The FWHM HIFI beam size at the HF frequency is ∼  18′′, about three times larger than the SOFIA beam size at the  [O i] frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' However, the foreground clouds are expected to  be extended on such angular scales and to fully cover the back-  ground continuum source.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' This conclusion is supported by the  good agreement between the two independent HF spectra taken  at positions offset by about half of the HIFI beam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  Figure 1 (lower panel) shows the final HF spectrum, an  equally weighted average of the two instrumental polarizations  and the two independent observations, resampled to a 1 km s−1  velocity resolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' The lower histogram shows the difference  between the spectral scan and DBS observations divided by 2,  which is a measure of the uncertainty in the final HF spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  The difference spectrum is very flat and shows no residuals, even  at positive velocities, where the background absorption may po-  tentially be contaminated by the Sgr B2 envelope emission (see  the HF emission wing at velocities greater than 85 km s−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' The  rms computed in the −130 to 40 km s−1 velocity range is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='0145,  and we used this value as the uncertainty of the HF line-to-  continuum ratio in the analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Results  To derive the oxygen optical depths and the corresponding col-  umn densities in the individual channels, we followed estab-  lished procedures commonly used in the analysis of HIFI ob-  servations of light hydrides (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Neufeld et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Lis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Monje et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' We first derived the optical depth  of the [O i] and HF lines (τ = −ln[1 − TL/TC], where TL/TC is  the line-to-continuum ratio), assuming that the foreground ab-  sorption completely covers the continuum source and that all  oxygen atoms are in the ground state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' The spiral arm clouds on  the line of sight toward Sgr B2 have moderate densities, up to a  few times 104 cm−3 (Greaves & Williams 1994).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' This is lower  than the critical density for the excitation of the 63 µm O i line  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='0 × 105 cm−3 for collisions with H2 and 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='8 × 105 cm−3 for  collisions with H;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Lique et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Goldsmith 2019);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' the as-  sumption that the entire population is in the ground state is thus  well justified.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Figure B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='1 shows the [O i] optical depths and the  corresponding column density as a function of velocity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  To determine the oxygen abundance, H2 and H column den-  sities in the line-of-sight clouds are required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Because of its  unique thermochemistry, HF has been shown to be an excellent  tracer of H2 (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Phillips et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Neufeld et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  Sonnentrucker et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Monje et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' The HF abun-  dance with respect to H2 in diffuse or translucent clouds, deter-  mined from a comparison with CH observations, is in the range  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='1 − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='6) × 10−8, with an average of (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='4 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='17) × 10−8 (mul-  tiple velocity components toward W51, W49N, and NGC6334I;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  Sonnentrucker et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Emprechtinger et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' We used  this value to convert the HF column density to the H2 column  density (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' To characterize the atomic gas component on  the line of sight toward Sgr B2, we used the H i column densities  of Winkel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Figure B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='3 shows the total hydrogen  nucleus column density as a function of velocity, along with the  molecular and atomic contributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  Figure 2 shows the gas-phase atomic oxygen abundance as  a function of velocity, derived from the observations of the  63 µm line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' The average abundance with respect to hydrogen  nuclei, computed over the −120 to +40 km s−1 velocity range,  is (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='51 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='69) × 10−4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' The ±1σ dispersion of the individual  measurements computed from the ensemble of 120 independent  velocity channels is shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Black error bars are the formal 1σ  uncertainties of the individual measurements, computed by com-  bining in quadrature corresponding uncertainties in the column  densities of the atomic oxygen, atomic, and molecular hydro-  gen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' They are typically smaller than the ensemble dispersion,  suggesting the presence of variations in the local atomic oxygen  abundance among different velocity components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Discussion  The average atomic oxygen abundance toward Sgr B2 derived  here, (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='51 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='69) × 10−4 with respect to hydrogen nuclei, is  in excellent agreement with the ISO value of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='7 × 10−4 (Lis  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2001), which was based on 13CO column density esti-  mates for the molecular gas component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Figure 3 shows a nor-  malized histogram of the O0 abundances in the 120 individual  velocity channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' The histogram is non-Gaussian and shows a  Article number, page 3 of 7  A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' ms_final  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Atomic oxygen abundance relative to hydrogen nuclei as a func-  tion of velocity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' The mean value of the 120 individual channels within  the −120 and 40 km s−1 velocity range is 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='51×10−4, and the dispersion  of the individual channels is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='65 × 10−4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' The horizontal dotted lines  mark the mean value and ±1σ dispersion computed from the ensemble  of individual measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' The black vertical error bars mark ±1σ un-  certainties in the individual channels, as described in the text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Color bars  mark velocity ranges corresponding to the 3 kpc, 5 kpc, Sagittarius, and  Scutum arms (red, magenta, blue, and yellow, respectively).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Velocities  corresponding to the Galactic center gas are marked in green and those  of the local gas in gray.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Channels with saturated absorption are masked.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  An electronic table with the data used for this figure is available at the  CDS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  narrow peak around 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='25 × 10−4 and a broader shoulder around  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='15 × 10−4, comparable to the values of 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='1 − 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='5 × 10−4 derived  by Wiesemeyer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' (2016) toward W31C, G34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='26, and W49N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  The origin of the variations in the derived atomic oxygen abun-  dance among different velocity components can be investigated  further by using independent observations of additional molec-  ular tracers, including the oxygen ions, CH as a proxy for H2  (Gerin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2010), argonium as a proxy for purely atomic gas  (Schilke et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2014), and ammonia as a tracer of high-density  gas;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' such analysis is beyond the scope of the present paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  As a reference, the cosmic standard abundance of oxygen is  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='75 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='4) × 10−4, as measured in a representative sample of  unevolved early B-type stars in nearby OB associations (Przy-  billa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' The latest solar photospheric abundance is  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='57 × 10−4 (Asplund et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2005), significantly lower than the  earlier Grevesse & Sauval (1998) value of 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='76 × 10−4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Car-  tledge et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' (2004) presented a comprehensive analysis of high-  resolution Hubble Space Telescope observations of O i and H i  Ly α UV absorption along 36 sight lines that probe a variety of  Galactic disk environments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' They derive an average O/H ratio of  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='90 × 10−4 in the low-density warm gas that should be least af-  fected by depletion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Sight lines of higher mean density are char-  acterized by a lower average O/H ratio of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='84×10−4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Taking the  higher value as a reference for the atomic oxygen abundance in  the ISM gas, our average abundance of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='51×10−4 on the line of  sight toward Sgr B2 corresponds to about 35% gas-phase oxygen  depletion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' CO will also contribute to the oxygen budget4 with a  typical abundance of 1 × 10−4 with respect to H2 in the molecu-  lar gas, which is dominant at most velocities on this line of sight  4 Other oxygen-bearing gas-phase species contribute at a much lower  level, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', the H2O fractional abundance with respect to H2 is in the  range 3 − 7 × 10−7 (Neufeld et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2000;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Lis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Normalized probability density function (PDF) of the O0 abun-  dances in 120 individual velocity channels toward Sgr B2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' The vertical  dashed black line shows the mean abundance, the gray shaded area ±1σ  departures from the mean, and the black arrow the corresponding ap-  proximate gas-phase oxygen content, including atomic oxygen and CO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  The vertical red line shows the cosmic standard abundance (Przybilla  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2008) and the magenta line the latest solar abundance (Asplund  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2005), with the magenta arrow pointing toward the earlier value  of Grevesse & Sauval (1998).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' The blue line is the average UV-derived  ISM abundance in the low-density warm gas that is least affected by de-  pletion, with the blue arrow showing the corresponding value for higher  mean density site lines (Cartledge et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Adding the two contributions, we derive an estimate  of the total gas-phase O0 + CO oxygen content toward Sgr B2  of ∼ 3 × 10−4 with respect to hydrogen nuclei, about 25% lower  than the O/H value derived in the low-density warm gas from the  UV measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  Figure 4 shows the good correlation between the atomic oxy-  gen and total hydrogen nucleus column densities (Pearson’s cor-  relation coefficient 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='85).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' The average abundance is 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='51 × 10−4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  Error bars mark the formal 1σ uncertainties of the individual  channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' We note that points with the highest O0 column den-  sities are located on average above the best-fit line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' However,  owing to the nonlinear dependence of the opacity on the line-  to-continuum ratio at such high column densities, these points  have large error bars and the result may not be significant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' If we  exclude points with the atomic oxygen column densities above  3 × 1017 cm−2, the resulting average atomic oxygen abundance  is lower by only 2%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Conclusions  We have presented an analysis of archival SOFIA/GREAT ob-  servations of the [O i] 63 µm absorption toward the Sagittar-  ius B2(M) continuum source in the Galactic center.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' The high  spectral resolution of the GREAT instrument allows, for the first  time, the [O i] absorption from individual line-of-sight clouds to  be separated, velocity intervals affected by saturated absorption  and telluric absorption to be masked, and accurate atomic oxy-  gen column densities and abundances to be derived.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' The atomic  oxygen column density in the foreground spiral arm clouds to-  ward Sgr B2 is well correlated with the total hydrogen column  density, as determined from HF and H i observations, with an  average abundance of (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='51 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='69) × 10−4 with respect to H  nuclei in individual 1 km s−1 velocity channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' This value is in  good agreement with the earlier ISO measurements on the same  Article number, page 4 of 7  Lis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' : Atomic oxygen  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Atomic oxygen column density as a function of total hydrogen  nucleus column density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Error bars are 1σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' The dotted line corresponds  to a fractional abundance of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='51 × 10−4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  line of sight, and about 35% lower than the average O/H ratio of  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='90 × 10−4 in low-density warm gas derived from UV measure-  ments (Cartledge et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' If we add a typical gas-phase CO  content at 1×10−4 with respect to H2 in the molecular gas, which  is dominant at most velocities on this line of sight (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='3), the  total gas-phase oxygen content (O0 + CO) on the line of sight  toward Sgr B2 is ∼ 3 × 10−4, or 300 ppm with respect to H,  about 25% lower than the low-density warm ISM oxygen abun-  dance derived from UV measurements (Cartledge et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  With silicates and oxides contributing another 100 ppm (Whittet  2010), the remaining oxygen fraction is about 175 ppm, which  can be viewed as an upper limit for UDO on the line of sight  toward Sagittarius B2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' However, the expected ice contribution in  this density regime is about 125 ppm (Whittet 2010), leaving  little room for UDO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  Acknowledgements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Based on observations made with the NASA/DLR Strato-  spheric Observatory for Infrared Astronomy (SOFIA).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' SOFIA is jointly oper-  ated by the Universities Space Research Association, Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' (USRA), under NASA  contract NAS2-97001, and the Deutsches SOFIA Institut (DSI) under DLR con-  tract 50 OK 0901 to the University of Stuttgart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' GREAT is a development by  the MPI für Radioastronomie and the KOSMA/Universität zu Köln, in cooper-  ation with the DLR Institut für Optische Sensorsysteme, financed by the par-  ticipating institutes, by the German Aerospace Center (DLR) under grants 50  OK 1102, 1103 and 1104, and within the Collaborative Research Centre 956,  funded by the Deutsche Forschungsgemeinschaft (DFG).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Part of this research  was carried out at the Jet Propulsion Laboratory, California Institute of Technol-  ogy, under a contract with the National Aeronautics and Space Administration  (80NM0018D0004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' We thank B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Winkel for providing us with the H i column  densities used in the analysis and an anonymous referee for helpful comments  regarding the overall oxygen budget.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' was supported by USRA through  a grant for SOFIA Program 08–0038 (HyGAL).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  References  Asplund, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Grevesse, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', & Sauval, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2005, Cosmic Abundances as  Records of Stellar Evolution and Nucleosynthesis in honor of David L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Lam-  bert, ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Barnes III & F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Bash.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' (ASP Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 336, San Fran-  cisco), 25  Boreiko, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', & Betz, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 1996, ApJ, 464, L83  Cartledge, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Lauroesch, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Meyer, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2004, ApJ, 613, 1037  Cardelli, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Ebbets, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', & Savage, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 1993, ApJ, 413, 401  Chen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Goldsmith, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Viti, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2014, ApJ, 793, 111  Dale, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Helou, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Brauher, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2004, ApJ, 604, 565  Dalgarno, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', & Black, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 1976, Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Prog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Phys, 39, 573  de Graauw, Th.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Helmich, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Phillips, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2010, A&A, 518, L6  Díaz-Santos, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Armus, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Charmandaris, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2017, ApJ, 846, 32  Emprechtinger, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Monje, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', van der Tak, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2012, ApJ, 756, 136  Farrah, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Lebouteiller, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Spoon, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2013, ApJ, 776, 38  Gerin, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', de Luca, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Goicoechea, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2010, A&A, 521, L16  Goldsmith, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2019, ApJ, 887, 54  Goldsmith, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Melnick, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Bergin, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2000, ApJ, 539, L123  Goldsmith, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Liseau, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Bell, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2011, ApJ, ApJ, 737, 96  Goldsmith, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Langer, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Sea, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2021, ApJ, 916, 6  González-Alfonso, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Fischer, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Graciá-Carpio, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2012, A&A, 541, A4  Greaves, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', & Williams, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 1994, A&A, 290, 259  Grevesse, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', & Sauval, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 1998, Space Scie.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', 130, 105  Herbst, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', & Klemperer, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 1973, ApJ, 185, 505  Heyminck, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Graf, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Güsten, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2012, A&A, 542, L1  Karska, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Herpin, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Bruderer, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2014, A&A, 562, A45  Kraemer, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Jackson, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', & Lane, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 1998, ApJ, 509, 931  Lada, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Lada, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Clemens, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 1994, ApJ, 429, 694  Larsson, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Liseau, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Pagani, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2007, A&A, 466, 999  Larsson, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', & Liseau, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2017, A&A, 608, A133  Leurini, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Wyrowski, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Wiesemeyer, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2015, A&A, 584, A70  Lique, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Kłos, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Le Picard, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2018, MNRAS, 474, 2313  Lis, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Keene, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Phillips, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2001, ApJ, 561, 823  Lis, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Phillips, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Goldsmith, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2010, A&A, 521, L26  Liseau, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', White, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Larsson, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 1999, A&A, 344, 342  Liseau, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Goldsmith, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Larsson, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2012, A&A, 541, A73  Oberst, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Parshley, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Nikola, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2011, ApJ, 739, 100  Malhotra, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Kaufman, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Hollenbach, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2001, ApJ, 561, 766  Monje, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Phillips, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Peng, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', 2011 ApJ, 734, L23  Mookerjea, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Sandell, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Güsten, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2019, A&A, 626, A131  Neufeld, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Asby, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Bergin, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2000, ApJ, 539, L111  Neufeld, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Sonnentrucker, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Phillips, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2010, A&A, 518, L108  Phillips, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Bergin, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Lis, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2010, A&A, 518, L109  Przybilla, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Nieva, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='-F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', & Butler, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2008, ApJ, 688, L103  Schilke, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Neufeld, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Müller, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2014, A&A, 566, A29  Schneider, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Röllig, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Simon, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2018, A&A, 617, A45  Snow, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', & Witt, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 1996, ApJ, 468, L65  Snow, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Black, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', van Dishoeck, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 1996, ApJ, 465, 245  Sonnentrucker, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Nefeld, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Phillips, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2010, A&A, 521, L12  Stacey, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Smyers, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Kurtz, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 1983, ApJ, 265, L7  van Dishoeck, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Kristensen, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Mottram, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2021, A&A, 648,  A24  Vastel, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Caux, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Ceccarelli, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2000, A&A, 357, 994  Vastel, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Polehampton, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Baluteau, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='-P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2002, ApJ, 581, 315  Whittet, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2010, ApJ, 710, 1009  Wiesemeyer, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Güsten, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Heyminck, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2016, A&A 585, A76  Winkel, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Wiesemeyer, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Menten, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2017, A&A, 600, A2  Yıldız, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Acharyya, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Goldsmith, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2013, A&A, 558, A58  Article number, page 5 of 7  A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' ms_final  Appendix A: SOFIA data reduction  The data were collected on 2015 July 19, on the southern hemi-  sphere deployment of SOFIA’s Cycle 1, at 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='3 to 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='5 km alti-  tude, under a precipitable water vapor column of typically 6 µm  at zenith.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' The high-frequency channel of GREAT was tuned to  the [O i] line, alternating between the lower and upper sideband,  so as to synthesize a sightline velocity interval from −200 to  +135 km s−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' In the velocity interval considered here, the median  single-sideband system temperatures at zenith were 2100 and  2400 K for lower-sideband and upper-sideband tuning, respec-  tively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Atmospheric and Galactic backgrounds were removed by  chopping to a reference position at 160′′ on both sides of Sgr  B2(M), at a position angle of 30◦ (east to south), that is to say,  perpendicular to the object’s elongation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' The FWHM beam size  of 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='6′′ was measured from cross-scans on Mars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  The spectra were calibrated to forward-beam brightness tem-  peratures (with a 97% forward efficiency) against loads at am-  bient and cold temperatures, and then to main-beam brightness  temperatures using a 67% main beam efficiency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' The 63 µm [OI]  transition is located in the wing of a broad water vapor ab-  sorption feature;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' the applied transmission correction was derived  from modeling the measured atmospheric total power emission  received in the signal and image bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' In order to minimize the  impact of mixer gain drifts, only the off-target spectra immedi-  ately following a calibration load measurement were used (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=',  the correction was determined scan-wise and then scaled to the  current elevation of each recorded spectrum).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  The continuum emission of Sgr B2(M) was obtained from  a dedicated double-sideband calibration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' While the signal-to-  image band gain ratio may deviate from unity (a standard de-  viation of 5%), the overall reliability of the calibration scheme  can be monitored with two tests: First, the saturation of the  [OI] line at the systemic velocity defines the zero level for the  single-sideband calibration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Second, the mesospheric [OI] line  serves as a “beacon” that undergoes the same attenuation in the  stratosphere as the astronomical signal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' With these precautions,  the calibrations and, consequently, the continuum levels of the  lower- and upper-sideband tunings were brought into agreement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  The spectra, s, of Sgr B2(M) in the lower- and upper-sideband  tuning are thus identical within the radiometric noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' The dif-  ference between the actually measured spectra (yL and yU for  lower- and upper-sideband tuning, respectively) displays a well-  defined linear baseline below 15 km s−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Instabilities that arise at  velocities above this baseline are from the upper-sideband tun-  ing and can be ignored there thanks to the redundancy with the  lower-sideband tuning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' The spectra from the two tunings can  then be expressed as yL = s + aLν, yU = s + aUν , where ν is  the frequency in the rest frame of Sgr B2(M).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Thanks to the lin-  ear baseline fit to the difference spectrum, only two parameters  (offset and slope) remained to be optimized, which was done in  a way that ensures equal continuum levels on both sides of the  line-free portion of the spectra and reproduces the saturated ab-  sorption at systemic velocity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' The good agreement between the  two tunings in the overlapping velocity interval, from −110 to  +15 km s−1, is taken as an assessment of the data processing al-  gorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  Appendix B: Atomic oxygen and HF column  densities  We converted the [O i] optical depth to the atomic oxygen col-  umn density assuming that the absorbing gas covers the back-  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' [O i] optical depth (left axis) and atomic oxygen column den-  sity (right axis) in 1 km s−1 channels as a function of velocity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Error bars  are 1σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' HF optical depth (left axis) and the H nucleus column den-  sity in the molecular component (right axis) in 1 km s−1 channels as a  function of velocity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Error bars are 1σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  ground continuum source and the entire population is in the  lower state (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=', Neufeld et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' 2010):  �  τdv = Aulguλ3  8πgl  N(O0) = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='365 × 10−18N(O0) cm2 km s−1,  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='1)  where Aul = 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='91−5 s−1 is the spontaneous radiative decay rate,  gu = 3 and gl = 5 are the degeneracies of the upper and lower  levels, and λ = 63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='184 µm is the transition wavelength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Fig-  ure B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='1 shows the [O i] optical depth (left vertical scale) and the  resulting atomic oxygen column density (right vertical scale) in  1 km s−1 velocity channels as a function of LSR velocity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  The corresponding formula for HF is  �  τdv = Aulguλ3  8πgl  N(HF) = 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='157 × 10−13N(HF) cm2 km s−1,  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='2)  with Aul = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='42−2 s−1, gu = 3, gl = 1, and λ = 243.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='2444 µm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  Figure B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='2 shows the HF optical depth and the resulting column  Article number, page 6 of 7  Lis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' : Atomic oxygen  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Total hydrogen nucleus column density toward Sgr B2(M) as  a function of velocity (black squares).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' The molecular, 2 × N(H2), and  atomic, N(H i), components are shown in cyan and green, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  Error bars are ±1σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' An electronic table with the data used for this figure  is available at the CDS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  density in 1 km s−1 velocity channels as a function of LSR veloc-  ity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content=' Figure B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='3 shows the total hydrogen nucleus column density  as a function of velocity, along with the molecular and atomic  contributions, as described in the text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
+page_content='  Article number, page 7 of 7' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/c9E2T4oBgHgl3EQfFwbt/content/2301.03651v1.pdf'}
diff --git a/cNAzT4oBgHgl3EQfnf3Z/vector_store/index.faiss b/cNAzT4oBgHgl3EQfnf3Z/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..22a60c060a721de1e2e3f6851f65591607a9e2f0
--- /dev/null
+++ b/cNAzT4oBgHgl3EQfnf3Z/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:4029ce8015ed0e02b6d988f2a2730f6ceddec484936cb63b4a75cc7bf367ca9b
+size 15401005
diff --git a/cNFJT4oBgHgl3EQfRCwA/content/tmp_files/2301.11493v1.pdf.txt b/cNFJT4oBgHgl3EQfRCwA/content/tmp_files/2301.11493v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..0562ea11034b6feccf2f5bf276b8e15cb440dac0
--- /dev/null
+++ b/cNFJT4oBgHgl3EQfRCwA/content/tmp_files/2301.11493v1.pdf.txt
@@ -0,0 +1,1220 @@
+arXiv:2301.11493v1  [math.AP]  27 Jan 2023
+THE EFFECT OF AN UNFAVORABLE REGION ON THE INVASION
+PROCESS OF A SPECIES§
+PENGCHAO LAI† AND JUNFAN LU†,∗
+Abstract. To model a propagating phenomena through the environment with an unfavorable
+region, we consider a reaction diffusion equation with negative growth rate in the unfavorable
+region and bistable reaction outside of it. We study rigorously the influence of L, the width of
+the unfavorable region, on the propagation of solutions. It turns out that there exists a critical
+value L∗ depending only on the reaction term such that, when L < L∗, spreading happens for
+any solution in the sense that it passes through the unfavorable region successfully and establish
+with minor defect in the region; when L = L∗, spreading happens only for a species with large
+initial population, while residue happens for a population with small initial data, in the sense
+that the solution converges to a small steady state; when L > L∗ we have a trichotomy result:
+spreading/residue happens for a species with large/small initial population, but, for a species
+with medium-sized initial data, it can not pass through the region either and converges to a
+transition steady state.
+1. Introduction
+In the field of mathematical biology, reaction diffusion equations like
+(1.1)
+ut = ∆u + f(u)
+are often used to describe the dynamics and the spreading phenomena of a species, where f(u)/u
+represents the growth rate of the species. Typical examples of f include the so-called monostable
+case like f(u) = u(1−u) and bistable case like f(u) = u(u− 1
+3)(1−u). These equations have been
+studied systematically in the last decades. For example, in the monostable case, Aronson and
+Weinberger [2, 3] proved a hair-trigger effect, which says that spreading (also called persistence
+or propagation: u converges to a positive stationary solution) happens for any positive solution.
+In the bistable case, [2, 3] gave sufficient conditions for spreading and that for vanishing (also
+called extinction: u → 0 as t → ∞). In 1977, Fife and McLeod [10] proved the existence and
+stability for the traveling wave solution of the bistable equation. In 2006, Zlatoˇs [15] gave a
+complete study on the bistable equation, and proved a trichotomy result on the asymptotic
+behavior for the solutions: there exists a sharp value L∗ > 0 such that when L > L∗ (resp.
+L < L∗), spreading (resp. vanishing) happens for the solution of the bistable equation with
+initial data u(x, 0) = χ[−L,L](x); when L = L∗, the solution develops to a transition ground
+2010 Mathematics Subject Classification. Primary 35B40, 92D25; Secondary 35K57.
+Key words and phrases. Population dynamics; reaction diffusion equation; unfavorable region; asymptotic
+behavior.
+§ This research was partly supported by the NSFC (No.
+12101413, 12071299), and the NSF of Shanghai
+(20JC1413800).
+† Mathematics and Science College, Shanghai Normal University, Shanghai 200234, China.
+∗ Corresponding author.
+Emails: laipchao@163.com (P. Lai), jlu@shnu.edu.cn (J. Lu).
+1
+
+2
+P. LAI AND J. LU
+state solution. In 2010, Du and Matano [8] extended these results to the Cauchy problem with
+general initial data like u(x, 0) = φλ(x). For bistable equations, they also proved the trichotomy
+and sharp transition results as in [15].
+In practical problems, however, a spreading process is generally not smooth due to the spatial
+and/or temporal heterogeneity. A favorable environment can accumulate the spreading while an
+unfavorable one will slow down or even block the spreading. For example, in the invasion process
+of a harmful species or infectious diseases, people often establish isolation zones to prevent the
+invasion by intensive elimination, or in the spreading process of a beneficial species, it may
+encounter adverse environments such as deserts, swamps, environmental pollution, etc..
+All
+of these unfavorable (for the species) environments can be regarded as desert regions for the
+propagation. (Note that, an unfavorable region we consider here is different from an obstacle
+area if the latter one is regarded as a region without population at all). In both ecology and
+mathematics, whether the species can pass through the region successfully or not is a problem
+that people are interested in (e.g., [11, 12, 13, 16] etc.).
+From mathematical point of view, if the spreading process of a species obeys the reaction
+diffusion equation as (1.1) before it encounters an unfavorable region, then the reaction term
+should be negative to the growth of the population when the species enters the unfavorable
+region, such as f = −ku + ε(u) for some small ε(u) (e.g., [14] etc.), or just f = −ku for
+simplicity. Intuitively, a species can passes though the unfavorable region easily when L (the
+width of the unfavorable region) and k (the death rate of the species in the unfavorable region)
+are small, but not when L, k are large. In this paper, we normalize the parameter k = 1, and
+study rigorously the influence of L on the propagation phenomena in one space dimension. We
+will show that there is a critical number L∗ such that, when L < L∗, spreading happens for a
+species in the sense that it passes through the unfavorable region successfully and establish with
+minor defect in the region; when L = L∗, we have a dichotomy result: spreading happens only
+for a species with large initial population, while residue happens for a species with small initial
+data, in the sense that the solution converges to a small steady state, which takes small value
+in the front area; when L > L∗, we have a trichotomy result: spreading or residue happens for
+a species with large or small initial population. For a species with medium-sized initial data,
+it can not pass through the region either, but converges to a transition steady state which lies
+between the final states of spreading and residue.
+Our mathematical model is the following Cauchy problem:
+(P)
+�
+ut = uxx + f(x, u),
+x ∈ R, t > 0,
+u(x, 0) = u0(x),
+x ∈ R,
+where the reaction term f(x, u) is defined as the following:
+(H)
+f(x, u) =
+�
+u(u − α)(1 − u),
+|x| ≥ L,
+−u,
+|x| < L.
+Here, α ∈ (0, 1
+2), and as we mentioned above, 2L is used to denote the width of the unfavorable
+region [−L, L], in which the environment is unfavorable for the species so that the growth rate
+is −1. We will see below that, as can be expected, the propagation will be more difficult than
+the original bistable equation, due to the destructiveness in the unfavorable region. This kind
+
+THE EFFECT OF AN UNFAVORABLE REGION
+3
+of model was also used by some authors to understand the phenomena of crime (e.g., [4, 5] and
+references therein). The unknown u(x, t) then denotes the population’s propensity to commit
+a crime, and the unfavorable region [−L, L] then denotes a prevention area of the invasions of
+crimes. Our background is different from theirs, but the mechanism is similar. As can be seen
+below, our results focus more on the convergence of solutions than theirs (see more in Remark
+1.5).
+We take initial data from L∞(R), then the well-posedness of W 2,1
+p,loc strong solution follows
+from the standard parabolic theory. We are then interested in the qualitative property of the
+solutions. We will show that any global solution of (P) will converge as t → ∞ to a stationary
+one, as in the typical reaction diffusion equations (e.g., [7, 8, 15]). Since we are studying a
+species with sufficient large population in the original habitat, and it tries to propagate further
+through an unfavorable region, it is natural to consider the initial data as the following:
+(I)
+
+
+
+u0(x) ∈ L∞(R), it is decreasing in R with u0(−∞) = 1, u0(∞) = 0,
+and
+lim
+x→−∞
+|1 − u0(x)|
+e
+√1−α x
+= 0 or ∞,
+lim
+x→+∞
+u0(x)
+e−√α x = 0 or ∞.
+The decay rates as x → ±∞ are imposed only for technical reasons when we use the zero number
+argument to prove a general convergence result. They are not essential and can be weakened
+(see more in Section 3 Remark 3.3). Clearly, the typical examples: H(a − x), U(x − ct − a)
+satisfy these conditions, where a ∈ R, H is the Heaviside function and U(x − ct) is the traveling
+wave solution of the bistable equation with U ′(z) < 0.
+Since the classification of the positive stationary solutions depends on the size of L, before
+we state our main theorems, it is necessary to specify the stationary solutions of (P) clearly.
+Stationary solutions solve the following equation:
+(1.2)
+v′′ + f(x, v) = 0,
+x ∈ R.
+By a careful phase plane analysis (see details in Section 2), we will see that there exists a critical
+value L∗ > 0 (which depends only on f), such that when L ∈ (0, L∗), (1.2) has exactly one
+positive stationary solution, denoted by Vb(x) ∈ W 2
+p,loc(R) for any p > 1, which satisfies
+(1.3)
+Vb(−x) = Vb(x),
+V′
+b(x) > 0 for x > 0,
+Vb(0) > 0,
+Vb(±∞) = 1.
+For convenience, we call Vb as a big stationary solution, and say spreading happens for a
+solution u of the problem (P) if
+lim
+t→∞ u(x, t) = Vb(x),
+in the topology of L∞
+loc(R).
+Then in case 0 < L < L∗ we have the following convergence result.
+Theorem 1.1 (Spreading result for small L). Assume L ∈ (0, L∗). Then for any u0 satisfying
+(I), spreading happens for the solution u of (P).
+In case L = L∗, the equation (1.2) has two positive stationary solutions: Vb as above and
+Vs ∈ W 2
+p,loc(R) for any p > 1, the latter satisfies
+(1.4)
+Vs(−∞) = 1,
+Vs(+∞) = 0,
+V′
+s(x) < 0 for x ∈ R.
+
+4
+P. LAI AND J. LU
+For convenience, we call Vs as a small stationary solution, and say that residue happens
+for the solution u if it converges to Vs(x) as t → ∞ in the topology of L∞
+loc(R).
+Theorem 1.2 (Dichotomy result for critical L∗). Assume L = L∗ and φ satisfies (I). For any
+σ ∈ R, let uσ(x, t) be the time-global solution of (P) with initial data u0 = φ(x−σ). Then either
+spreading happens as above for all σ ∈ R, or there exists σ∗ ∈ R such that
+(i) spreading happens when σ ∈ (σ∗, +∞);
+(ii) residue happens when σ ∈ (−∞, σ∗].
+When L > L∗, the equation (1.2) has exactly three positive stationary solutions: the big
+solution Vb and the small solution Vs as above, and another solution Vg ∈ W 2
+p,loc(R) for any
+p > 1 which lies between Vs and Vb, and
+(1.5)
+�
+Vg(−∞) = 1,
+Vg(+∞) = 0,
+Vs(x) < Vg(x) < Vb(x) for all x ∈ R,
+Vg has a unique local minimum x1 ∈ (−L, L) and a unique local maximum x2 > L.
+We call Vg a transition (stationary) solution, and say u is a transition solution of (P) if it
+converges to Vg in the topology of L∞
+loc(R). As we expect before, when L > L∗, the propagation
+is heavily effected by the unfavorable region and so residue happens easier. Nevertheless, we
+have complicated situations for the asymptotic behavior of the solutions in this case, that is, all
+of residue, transition and spreading are possible.
+Theorem 1.3 (Trichotomy result for large L). Assume L > L∗ and φ satisfies (I). For any
+σ ∈ R, let uσ(x, t) be a time-global solution of (P) with initial data u0 = φ(x − σ). Then there
+exist −∞ < σ∗ ≤ σ∗ < ∞ such that
+(i) spreading happens when σ ∈ (σ∗, +∞);
+(ii) residue happens when σ ∈ (−∞, σ∗);
+(iii) uσ is a transition solution when σ ∈ [σ∗, σ∗].
+By these results we know that, from a ecological point of view, an unfavorable region will
+definitely affect the propagation quantitatively, no matter how large the region is. On the other
+hand, whether the propagation is affected qualitatively depends on the size of the region. More
+precisely, when the width 2L of the region is smaller than the critical size 2L∗ depending on
+f, the effect is a quantitative one: propagation is always successful but with a defective limit,
+that is, the limit Vb < 1. When the width is larger than the critical value, the effect can be
+a qualitative one: small initial population may be blocked and can not propagate through the
+region successfully. As a result, it converges to a residue or transition stationary solution. Note
+that, these solutions remain positive on the right side with small value just because the problem
+is a Cauchy one, but not means the species can pass through the unfavorable region smoothly.
+For the clarity of our statements, in the previous theorems we adopted a cubic bistable
+nonlinearity and a constant death rate, outside of and in the unfavorable region, respectively.
+Of course, one can consider more general reaction terms.
+For example, f(x, u) is a general
+bistable nonlinearity fb(u) outside of the unfavorable region and a general negative growth rate
+fm(u) < 0 (u > 0) in the unfavorable region. In this case, analogue of our current conclusions can
+be derived in a similar way. More precisely, there are two positive real numbers L∗ ≥ L∗ > 0
+
+THE EFFECT OF AN UNFAVORABLE REGION
+5
+depending only on f such that the asymptotic behavior for the solutions of (P) are as the
+following.
+(1). When L < L∗, the equation (P) has only positive stationary solutions of Vb type (maybe
+not unique), spreading happens in the sense that each solution u converges to one of them.
+(2). When L ∈ [L∗, L∗) (or L = L∗ in case L∗ = L∗ as in our current case), the equation
+(P) has positive stationary solutions of both Vb and Vs types (maybe not unique), and
+a dichotomy results hold: a solution with large (resp. small) initial data converges to a
+stationary solution of the type Vb (resp. Vs).
+(3). When L ≥ L∗ (or L > L∗ in case L∗ = L∗ as in our current case), (P) has positive stationary
+solutions of Vb, Vg and Vs types (each type maybe not unique), a trichotomy results hold:
+a solution with large (resp. small, medium-sized) initial data converges to a stationary
+solution of the type Vb (resp. Vs, Vg).
+The proof of these results is similar as ours, and the details will be given in a forthcoming paper
+(see more in Remarks 2.4).
+Remark 1.4. If the reaction term is a monostable one like f(u) = u(1 − u), there is the so-
+called hair-trigger effect (e.g., [2, 3]), which says that any nonnegative, non-trivial solution will
+converge to 1, no matter how small the initial data is. Hence, if we use monostable model instead
+of the bistable one outside of the unfavorable region, then the asymptotic behavior will be very
+simple: spreading always happens.
+Remark 1.5. As we have mentioned above, Berestycki et al.
+[5] also studied the equation
+(P) as a model to understand the phenomena of crime. They proved that, when L < L∗, the
+wave propagates in the sense that u(x, t) > 1 − ε for any small ε > 0 and all large x, t; when
+L ≥ L∗, the propagation is blocked in the sense that there exists a stationary solution as our Vs.
+We see that these results correspond to our spreading and residue phenomena, but without the
+convergence to the corresponding stationary solutions. Moreover, we complete the dichotomy
+(in case L = L∗) and trichotomy (in case L > L∗) results, as well as the threshold for the initial
+data as in Theorem 1.3.
+The rest of the paper is organized as follows. In Section 2, we present the positive stationary
+solutions by using a phase plane analysis. In Section 3, we give a general convergence result for
+the solutions of (P) with initial data satisfying (I). In Section 4, we prove our main theorems
+on the dichotomy and trichotomy results.
+2. Positive Stationary Solutions
+In this section we will present the definition of the critical value L∗ of the unfavorable region
+width, and construct some useful positive stationary solutions by using the phase plane analysis.
+2.1. Phase plane. We will work on the equation of stationary solutions:
+(2.1)
+v′′ + f(x, v) = 0,
+x ∈ R,
+for f defined by (H). For convenience, in what follows we write
+fl(u) = fr(u) := u(u − α)(1 − u),
+fm(u) := −u,
+
+6
+P. LAI AND J. LU
+then f(x, u) = fl(u) = fr(u) when |x| ≥ L and f(x, u) = fm(u) when |x| < L. Each solution of
+equation (2.1) consists of three parts
+v =
+
+
+
+
+
+vl(x),
+x ≤ L,
+vm(x),
+|x| < L,
+vr(x),
+x ≥ L,
+which satisfies the following equations
+v′′
+l + fl(vl) = 0,
+x < −L,
+(2.2)
+v′′
+m + fm(vm) = 0,
+|x| < L,
+(2.3)
+v′′
+r + fr(vr) = 0,
+x > L,
+(2.4)
+with matching conditions on the boundaries of the unfavorable region:
+(2.5)
+�
+vl(−L − 0) = vm(−L + 0),
+v′
+l(−L − 0) = v′
+m(−L + 0),
+vm(L − 0) = vr(L + 0),
+v′
+m(L − 0) = v′
+r(L + 0).
+Now, we seek for solutions of the problems (2.2)-(2.4) by phase plane analysis. First, these
+equations can be converted into the following systems:
+(2.6)
+�
+v′
+i = wi,
+w′
+i = −fi(vi),
+for i = {l, m, r}. These systems are equivalent to the following first-order ordinary differential
+equations
+(2.7)
+widwi = −fi(vi)dvi.
+They are solved explicitly:
+(2.8)
+w2
+i = C − 2
+� vi
+0
+fi(s)ds,
+for some C to be determined. Taking different C we can sketch the phase diagram of (2.2)-(2.4)
+or (2.6) as in Figure 1. For convenience, we present some details here.
+Figure 1. Trajectories of the system (2.6).
+
+THE EFFECT OF AN UNFAVORABLE REGION
+7
+In Figure 1, the trajectory Γ1 is the graph of (2.8) with i = l and C = 2
+� 1
+0 fl(s)ds > 0. It
+corresponds to a solution V1 of (2.2) or (2.4), which takes 0 at some point x0 and is strictly
+increasing for x > x0 with
+0 < 1 − V1(x) ∼ e−√1−α x,
+x → ∞.
+Similarly, the trajectory Γ′
+1 corresponds to a solution ˜V1(x) ≡ V1(2x0 − x).
+Γ2 is the graph of (2.8) with i = l and C = 0. It is a homoclinic orbit, and corresponds to
+the so-called ground state solution V2 of (2.2) or (2.4), which satisfies
+V2(x) = V2(−x) and V ′
+2(x) < 0 for x > 0,
+V2(0) = θ,
+V2(x) ∼ e−√α x as x → +∞,
+where θ = θ(α) ∈ (α, 1) is defined by
+� θ
+0 fl(u)du =
+� θ
+0 fr(u)du = 0, that is,
+θ = θ(α) := 4(α + 1) −
+�
+16(α + 1)2 − 72α
+6
+.
+The trajectory Γ3 is the graph of (2.8) with i = l and C = 2
+� a
+0 fl(s)ds for any given a ∈ (θ, 1).
+It gives a compactly supported stationary solution Va of the bistable reaction diffusion equation,
+which satisfies, for some x0 ∈ (0, ∞) depending on a
+(2.9)
+Va(±x0) = 0,
+Va(0) = q0,
+Va(−x) = Va(x) and V ′
+a(x) < 0 in (0, x0].
+Such solutions will be used in Section 3 to give a sufficient condition for the spreading phenomena.
+The singular point (α, 0) is a center. For any a ∈ (0, α), there is a closed orbit Γ4 surrounding
+(α, 0), which is the graph of (2.8) with i = l and C = 2
+� a
+0 fl(s)ds, and corresponds to a periodic
+solution, denoted by V per
+a
+.
+For any small δ > 0, the trajectory Γ∗
+5 passing through F(1, −δ) is the graph of (2.8) with
+i = l and C = δ2 + 2
+� 1
+0 fl(s)ds. It corresponds to a solution V ∗
+5 which satisfies
+V ∗
+5 (x) < 0 for x < 0,
+V ∗
+5 (x) → +∞ as x → −∞,
+V ∗
+5 (0) = 0 and V ∗
+5 (x0) = 1,
+for some x0 < 0 (here we normalize the function as zero at x = 0).
+Finally, Γ0 is a trajectory of the system (2.6) for i = m. For any a ∈ (0, 1), there is a Γ0
+passing through A(a, 0), which is the graph of the function w2
+m = v2
+m − a2 (vm ≥ a). This
+trajectory gives a solution V0 of (2.1) in the interval [−L, L], and can be expressed explicitly as
+(2.10)
+V0(x; a) = a cosh(x) ≥ a.
+2.2. Trajectory pieces corresponding to the solutions on [−L, L]. We will combine suit-
+able trajectory pieces of (2.2)-(2.4) together to give solutions of the problem (2.1). Note that
+each one of such solutions satisfies (2.3) in a domain with exact width 2L.
+So we need to
+specify the relationship between the arc lengths of the trajectory pieces and the life spans of
+corresponding solutions.
+We introduce a notation. If AB is a trajectory piece in the phase plane corresponding to a
+solution V (x) of (2.1) such that
+(V (x1), V ′(x1)) = A,
+(V (x2), V ′(x2)) = B,
+then |x1 − x2| is the life span of the solution given by this piece AB. In what follows we use
+XAB to denote this span |x1 − x2|.
+
+8
+P. LAI AND J. LU
+In Figure 1, we see that if A = (a, 0) ∈ Γ0 lies between (0, 0) and (θ, 0), then Γ2 and Γ0
+has exactly two intersection points D2, D′
+2; if a = θ, then there is a unique intersection point
+A = (θ, 0) between them; if a ∈ (θ, 1), there is no intersection point between them. On the other
+hand, any Γ0 has a unique intersection point D1 with Γ1. Denote Di = (vi, wi) (i = 1, 2). Since
+the stationary solution corresponding to Γ0 is given by V0 in (2.10), we see that
+(2.11)
+V0(0) = a,
+V0(r) = v2,
+V0(R) = v1,
+for some R = R(a) > r = r(a) > 0, that is, XAD2 = r and XAD1 = R.
+We now study the monotonicity of R(a), r(a) and ℓ(a) := R(a) − r(a) = XD1D2.
+Lemma 2.1. All of R, r and ℓ given above are strictly decreasing in the parameter a ∈ (0, 1).
+Proof. (1). We first prove dR
+da < 0. Recall that the function of Γ0 is w2 = v2 − a2, and the
+function of Γ1 is w2 = 2
+� 1
+v fl(s)ds. Combining them together we obtain the v-coordinate v1 for
+D1:
+(2.12)
+v2
+1 − a2 = 2
+� 1
+v1
+fl(s)ds.
+Substituting the explicit formula (2.10) v1 = V0(R) = a cosh R into this equality we have
+(2.13)
+a2 cosh2(R) − a2 = 2
+� 1
+a cosh(R)
+fl(s)ds.
+Using the cubic bistable nonlinearity fl we can obtain
+(2.14)
+a2 d[cosh(R)]
+da
+=
+−2
+� 1
+v1 fl(s)ds − v1fl(v1)
+v1 + fl(v1)
+�����
+v1=a cosh(R)
+< 0.
+In fact, with
+F(v1, α) := 2
+� 1
+v1
+fl(s)ds + v1fl(v1) = −1
+2v4
+1 + 1
+3(1 + α)v3
+1 + 1 − 2α
+6
+,
+we have ∂F
+∂α = 1
+3v3
+1 − 1
+3 < 0 and F(v1, 1
+2) = − 1
+2v4
+1 + 1
+2v3
+1 > 0. Then (2.14) holds. This implies
+that
+dR
+da < 0.
+(2). In a similar way one can show that dr
+da < 0.
+(3). We now show that dℓ
+da = d(R−r)
+da
+< 0. Substituting fl(u) = u(u − α)(1 − u) into (2.12), we
+see that the v-coordinate of D1 is given by the root of
+(2.15)
+−1
+2v4
+1 + 2(α + 1)
+3
+v3
+1 + (1 − α)v2
+1 + 2α − 1
+6
+− a2 = 0.
+From the phase diagram we see that, for any a ∈ (0, θ(α)), this equation has a unique root
+v1(a; α) ∈ (a, 1). Similarly, the v-coordinate of D2 is given by the unique root v2(a; α) ∈ (a, θ)
+of following equation
+(2.16)
+−1
+2v4
+2 + 2(α + 1)
+3
+v3
+2 + (1 − α)v2
+2 − a2 = 0,
+
+THE EFFECT OF AN UNFAVORABLE REGION
+9
+Noticing that v1 = a cosh R(a) and v2 = a cosh r(a), we can conclude that
+(2.17)
+ℓ(a) = R(a) − r(a) = ln v1(a; α) +
+�
+v2
+1(a; α) − a2
+a
+− ln v2(a; α) +
+�
+v2
+2(a; α) − a2
+a
+.
+A tedious but trivial calculation gives the formulas of v1, v2 and ℓ(a), which shows that dℓ(a)
+da
+< 0
+for any given α ∈ (0, 1
+2) and any a ∈ (0, θ(α)]. A numerical simulation result is illustrated in
+Figure 2.
+0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+0.8
+0
+0.5
+1
+1.5
+2
+2.5
+3
+3.5
+4
+a
+l=R−r
+ 
+ 
+α=0.05
+α=0.1
+α=0.2
+α=0.3
+α=0.4
+α=0.45
+Figure 2. For each given α ∈ (0, 1
+2), ℓ(a) is strictly decreasing in a ∈ (0, θ(α)].
+The a-coordinate of the end point of each curve is θ(α).
+□
+2.3. Stationary solutions. For any given α ∈ (0, 1
+2), by the monotonicity of ℓ(a) on a, we see
+that
+(2.18)
+2L∗ := ℓ(θ(α)) =
+inf
+0<a<θ(α) ℓ(a) > 0.
+Clearly, this value depends only on f(x, u). This is the critical value of L appearing in our main
+theorems, and it plays a key role in the classification for the dynamics of the solutions.
+Based on the monotonicity of R, r, and ℓ, we can construct some positive solutions of (2.1)
+which will be used below.
+Proposition 2.2. Let L∗ be the critical value defined by (2.18).
+(a) In case 0 < L < L∗, the equation (2.1) has exactly one positive solution Vb ∈ C1(R) ∩
+C∞(R\{±L}) which satisfies (1.3) and
+(2.19)
+0 < 1 − Vb(x) ∼ e−√1−α |x| as |x| → ∞.
+(b) In case L = L∗, the equation (2.1) has at least two positive solutions, one is Vb as above,
+the other one Vs ∈ C1(R) ∩ C∞(R\{±L}) satisfies (1.4) and
+(2.20)
+0 < 1 − Vs(x) ∼ e
+√1−α x as x → −∞,
+0 < Vs(x) ∼ e−√α x as x → ∞.
+
+10
+P. LAI AND J. LU
+(c) In case L > L∗, the equation (2.1) has at least three positive solutions: Vb, Vs as above, and
+Vg ∈ C1(R) ∩ C∞(R\{±L}) which satisfies, for some x1, x2 with −L < x1 < L < x2,
+(2.21)
+
+
+
+V′
+g(x) < 0 for x ∈ (−∞, x1) ∪ (x2, ∞),
+V′
+g(x) > 0 for x ∈ (x1, x2),
+Vg(x1) ∈ (0, θ),
+Vg(x2) = θ,
+0 < 1 − Vg(x) ∼ e
+√1−α x as x → −∞,
+0 < Vg(x) ∼ e−√α x as x → ∞.
+Moreover, (2.1) has no other positive solutions satisfying v(−∞) = 1 and v(∞) = 0.
+(d) The solutions Vb, Vs, Vg are well-ordered, if they exist,
+(2.22)
+Vs(x) < Vg(x) < Vb(x),
+x ∈ R.
+Figure 3. Trajectories of the solutions of (2.1): the case L = L∗. (a). Trajectory of
+Vb; (b) Trajectory of Vs.
+Figure 4. Trajectories of the solutions of (2.1): the case L > L∗. (a) Trajectory of
+Vb; (b) Trajectory of Vg; (c) Trajectory of Vs.
+Proof. First, we construct solution Vb for any L > 0. In Figure 3 (a), we see that the combination
+of the trajectory pieces: (1, 0)-B-A-C-(1, 0) gives such a solution, as long as XBAC (which denotes
+the life span of the solution V0(x) given by the piece BAC) is 2L. From above we know that
+XBAC = 2R(a). Since
+R(a) → 0 as a → 1,
+R(a) → ∞ as a → 0,
+and since R(a) is strictly decreasing in a, there exists a unique a ∈ (0, 1) such that 2R(a) = 2L.
+For this choice of of a, the trajectory piece combination gives the solution Vb.
+Next, we construct Vs in case L ≥ L∗. It is easily seen that the combination of trajectory
+pieces: (1, 0)-B-C-(0, 0) in Figure 3 (b) or Figure 4 (c) gives a positive solution as Vs, as long
+
+THE EFFECT OF AN UNFAVORABLE REGION
+11
+as XBC = 2L. In case L = L∗, the unique suitable choice of C is (θ, 0) (see Figure 3 (b)). In
+case L > L∗, however, XBC = R(a) − r(a) = ℓ(a), which is also strictly decreasing in a with
+ℓ(a) → ∞ as a → 0,
+ℓ(a) → 2L∗ as a → θ.
+Hence, there exists a unique a such that ℓ(a) = 2L. The corresponding combination of trajectory
+pieces defines the solution Vs.
+We then construct Vg in case L > L∗. As in Figure 4 (b), the combination of trajectory
+pieces: (1, 0)-B-C′-A-C-(θ, 0)-(0, 0) gives a solution of type Vg. Note that, for this purpose, we
+require that XBAC = R(a) + r(a) = 2L. From the analysis in the previous subsection this span
+is strictly decreasing in a. Hence there is a unique a ∈ (0, θ) satisfies this requirement. This
+prove the existence and uniqueness of Vg.
+The regularities of these solutions follow from the fact that they are bounded in the W 2
+p,loc(R)
+topology, and smooth in the interior of R\{±L} by the interior estimates in the theory of elliptic
+equations. The decay rates in (2.19), (2.20), (2.21) can be shown by the corresponding solutions
+given by the trajectory pieces.
+Finally, we prove the ordering (2.22). We only consider the case L > L∗, since the proof for
+Vb > Vs in case L = L∗ is similar. In Figure 4 (a), we write the coordinates of the points A, B, C
+as (a1, 0), (vB
+1 , wB
+1 ), (vC
+1 , wC
+1 ), respectively, and write the coordinates of A, B, C in Figure 4 (b)
+and (c) similarly with subscripts 1 replaced by 2, 3, respectively.
+We first prove Vg > Vs. Recall that, the trajectory piece BC in Figure 4 (c) gives a solution
+V0(x; a3) = a3 cosh x, its shift a3 cosh(x − r(a3)+R(a3)
+2
+) coincides with Vs(x) in [−L, L], and
+ℓ(a3) = R(a3) − r(a3) = 2L. Similarly, the trajectory piece BC′AC in Figure 4 (b) gives the
+solution V0(x; a2) = a2 cosh x, its shift a2 cosh(x − ℓ(a2)
+2 ) coincides with Vg(x) in [−L, L], and
+ℓ(a2) + 2r(a2) = 2L. Hence,
+ℓ(a2) = 2L − 2r(a2) < 2L = ℓ(a3).
+By the monotonicity of ℓ we see that
+a3 < a2.
+Thus, the trajectory passing through (a3, 0) lies on the left of that passing through (a2, 0). This
+implies that (vB
+3 , wB
+3 ) lies on the left of (vB
+2 , wB
+2 ), (vC
+3 , wC
+3 ) lies on the left of (vC′
+2 , wC′
+2 ). Hence,
+vB
+3 < vB
+2 ,
+vC
+3 = vC′
+3
+< vC′
+2
+= vC
+2 ,
+that is,
+(2.23)
+a3 cosh
+�
+±L − r(a3) + R(a3)
+2
+�
+< a2 cosh
+�
+±L − ℓ(a2)
+2
+�
+.
+We now prove
+(2.24)
+a3 cosh
+�
+x − r(a3) + R(a3)
+2
+�
+< a2 cosh
+�
+x − ℓ(a2)
+2
+�
+,
+x ∈ [−L, L].
+By contradiction we assume this is not always true. Then combining with (2.23) we see that,
+there exists y ∈ (−L, L) such that
+a3 cosh
+�
+y − r(a3) + R(a3)
+2
+�
+= a2 cosh
+�
+y − ℓ(a2)
+2
+�
+,
+
+12
+P. LAI AND J. LU
+and the derivatives of them at this point y satisfy
+a3 sinh
+�
+y − r(a3) + R(a3)
+2
+�
+≤ a2 sinh
+�
+y − ℓ(a2)
+2
+�
+.
+This is impossible due to a3 < a2. This proves Vs < Vg in [−L, L].
+On the interval (−∞, −L], we have
+Vs(x) = ˜V1(x − x3),
+Vg(x) = ˜V1(x − x2)
+for some suitable x3, x2, where ˜V1(x) is the solution given by Γ′
+1. By vB
+3 < vB
+2 we have
+˜V1(−L − x3) = Vs(−L) = vB
+3 < vB
+2 = Vg(−L) = ˜V1(−L − x2).
+Hence x3 < x2 and so
+Vs(x) = ˜V1(x − x3) < Vg(x) = ˜V1(x − x2),
+x ≤ −L.
+In a similar way one can show that Vs < Vg in [L, ∞). In summary we obtain the the first
+inequality in (2.22).
+The second inequality of (2.22) is proved similarly.
+□
+Remark 2.3. We constructed three positive stationary solutions Vb, Vg, Vs in the previous
+proposition. For convenience, we call them the big, transition and small stationary solu-
+tions, respectively, and denote
+(2.25)
+S := {Vs, Vg, Vb}.
+In the next section we will show that any ω-limit of the solution of (P) with initial data satisfying
+(I) is an element in S, even though (P) has other positive stationary solutions. For example,
+the reflections of the solutions in S with respect to x = 0, and many other types of solutions,
+positive in the whole R, or compactly supported.
+Besides the positive stationary solutions mentioned above, we can construct some other upper
+and lower solutions which can be used for comparison. Here we give one of them. In Figure 4 (b),
+we see that the combination of the trajectory pieces F-D-B∗-E-Γ4 defines a function V (x). More
+precisely, denote D = (vD, wD), E = (vE, wE). Recall that we denote the solution corresponding
+to trajectory Γ∗
+5 by V ∗
+5 (x) in the previous subsection. Denote the solution corresponding to the
+combination D-B∗-E by V ∗
+0 (x), and the periodic solution corresponding to the Γ4 by V per(x).
+Combining them together we obtain the function V :
+V (x) =
+
+
+
+V ∗
+5 (x + x1),
+x ≤ −L,
+V ∗
+0 (x + x2),
+x ∈ [−L, L],
+V per(x + x3),
+x ≥ L,
+where the shifts x1, x2, x3 are chosen to satisfy the following matching conditions:
+V ∗
+5 (−L + x1) = vD = V ∗
+0 (−L + x2),
+V ∗
+0 (L + x2) = vE = V per(L + x3).
+
+THE EFFECT OF AN UNFAVORABLE REGION
+13
+Moreover, for any small ε0 > 0, there exists −L < −L such that V (x) = V ∗
+5 (x + x1) ≥ 1 + ε0
+for x ≤ −L. Now we define
+(2.26)
+V (x) :=
+
+
+
+
+
+
+
+1 + ε0,
+x ≤ −L,
+V ∗
+5 (x + x1),
+x ∈ [−L, −L],
+V ∗
+0 (x + x2),
+x ∈ [−L, L],
+V per(x + x3),
+x ≥ L.
+Note that this function is continuous in R and C1 in R\{−L}. In addition,
+V
+′(−L − 0) = 0 > V
+′(−L + 0),
+and
+V (x) ≥ ε1 := min
+�
+V ∗
+0 (0), min
+x∈R V per(x)
+�
+> 0,
+x ∈ R.
+In the Subsection 4.3 we will use this upper solution to separate Vs from Vg to give the trichotomy
+results.
+Remark 2.4. As we mentioned in Section 1, one may be interested in general reaction terms, to
+say, f is a bistable nonlinearity outside of the unfavorable region and a general negative growth
+rate in the region. In this case, the phase plane analysis we do in this section remains valid,
+but with more complicated situations. Now we give a sketch below. (1). We collect all possible
+trajectory pieces BC as in Figure 3(c) and 4(c), and define
+L∗ := min{XBC | B ∈ Γ′
+1, C lies on the lower half of Γ2};
+then collect all possible trajectory pieces BC′C as in Figure 4(b), and define
+L∗ := min{XBC′C | B ∈ Γ′
+1, C lies on the upper half of Γ2}.
+Then L∗ ≥ L∗ > 0. (Note that, in our current special case L∗ = L∗ = XBC for C = (θ, 0).) (2).
+If we consider only positive stationary solutions of (2.1) satisfying v(−∞) = 1, v(∞) = 0, then
+we can show the following results in a similar way as we do in this section: when L < L∗, (2.1)
+has only Vb type of solutions, which may be not unique but well-ordered; when L ∈ [L∗, L∗)
+(or L = L∗ when L∗ = L∗), (2.1) has two groups of solutions, one group is of the form Vs,
+the other is of the form Vb. Each group may be not unique but well-ordered; when L ≥ L∗
+(or L > L∗ when L∗ = L∗), (2.1) has three groups of solutions, they are of the form Vs, Vg, Vb,
+respectively. Each group may be not unique but well-ordered. (3). Though we can derive the
+order in each group, it is not easy to prove all the solutions are well-ordered. Even, we can
+not easily to show, by just analyzing the ODE (2.1), the existence of the smallest and largest
+stationary solution. However, it is remarkable to point out that, this last conclusion can be
+proved by a PDE approach. More precisely, we consider an initial data u0(x) which approaches
+1 as x → −∞ in a sufficiently slow decay rate, and it is decreasing and takes 0 at some point.
+If we shift this initial data leftward sufficiently far such that it is smaller than any stationary
+solution, then, by the general convergence result (which will be proved in the next section) the
+solution with this initial data converges to a positive stationary solution, which must be the
+smallest one. On the other hand, the solution with initial data u0 ≡ 1 must converges to the
+largest stationary solution.
+
+14
+P. LAI AND J. LU
+3. General Convergence Result
+In this section we use the so-called zero number argument to prove that, for any solution u
+of (P), its ω-limit set is contained in S. We first recall the typical zero number diminishing
+properties. Consider
+(3.1)
+ηt = a(x, t)ηxx + b(x, t)ηx + c(x, t)η
+in E0 := {(x, t) | x ∈ R, t ∈ (t1, t2)},
+where t2 > t1 ≥ 0. For each t ∈ (t1, t2), denote by
+Z(t) := ♯{x ∈ R | η(·, t) = 0}
+the number of zeroes of η(·, t) in R. A point x0 is called a multiple zero (or degenerate zero)
+of η(·, t) if η(x0, t) = ηx(x0, t) = 0. In 1988, Angenent [1] proved a zero number diminishing
+property, and in 1998, the conditions Angenent had used in [1] were weaken by Chen [6] for
+strong solutions in W 2,1
+p, loc(R × (0, ∞)). One of their results is summarized as the following:
+Lemma 3.1 ([1, 6]). Assume the coefficients in (3.1) satisfies
+(3.2)
+a, a−1, at, ax, b, c ∈ L∞.
+Let η be a nontrivial W 2,1
+p,loc solution of (3.1). Then
+(1) the zeros of η(·, t) are isolated;
+(2) if Z(t) < ∞ for some t0 ∈ (t1, t2), then it is decreasing in t ∈ (t0, t2).
+Moreover,
+if s ∈ (t0, t2) and x0 is a multiple zero of η(·, s), then Z(s1) > Z(s2) for all s1, s2
+satisfying t0 < s1 < s < s2 < t2.
+Using this lemma we can prove the following convergence result.
+Theorem 3.2. Assume (H), u0 satisfies (I).
+Then for any L > 0, the unique time-global
+solution u(x, t) converges as t → ∞ to an element in S, in the topology of L∞
+loc(R).
+Proof. First, one can derive the boundedness of u easily by the maximum principle. Then the
+existence and uniqueness of the strong solution in W 2,1
+p,loc(R × (0, ∞)) follows from the standard
+parabolic theory. By the standard Lp estimates, for any increasing time sequence {tn}, any
+p > 1, M > 0, there exists C = C(M, p) such that
+∥u(x, t + tn)∥W 2,1
+p
+([−M,M]2) ≤ C,
+therefore, for any ν ∈
+�
+0, 1 − 1
+p
+�
+, there exists a subsequence of {tn}, denoted it again by {tn},
+and a function w(x, t) ∈ C1+ν, 1+ν
+2 ([−M, M]2) such that
+∥u(x, t + tn) − w(x, t)∥
+C1+ν, 1+ν
+2
+([−M,M]2) → 0 as n → ∞.
+By Cantor’s diagonal argument, the ω-limit set of u(·, t) in the topology of C1+ν
+loc (R) is not empty,
+and by standard dynamics theory, compact, invariant and connected.
+We divide the rest proof into several steps.
+Step 1. A quasi-convergence result: any ω-limit of u is a stationary solution. We follow the
+idea in [7, 8] and use the zero number argument. We show that, for any t ∈ R, w(·, t) is actually
+a stationary solution. We only need to prove w(·, 0) is so. By contradiction, we assume that
+
+THE EFFECT OF AN UNFAVORABLE REGION
+15
+w(x, 0) is not a stationary solution, so w(x, 0) ̸≡ 0. Assume without loss of generality that
+w(0, 0) > 0. Using w(x, 0) we construct a real stationary solution:
+(3.3)
+�
+v′′ + f(x, v) = 0,
+x ∈ R,
+v(0) = w(0, 0) > 0,
+v′(0) = wx(0, 0).
+By the phase plane analysis in the previous section we see that, the bounded W 2
+p solution of
+(3.3) must be less than 1 and positive in some open interval (l0, r0) with −l0, r0 ∈ (0, ∞]. In
+addition, it has the following cases:
+(1). v = v1 satisfies v1(l0) = v2(r0) = 0 for l0 < 0 < r0;
+(2). v = v2 satisfies v2(l0) = 0 for l0 < 0, v2(x) > 0 for x > l0 and v2 satisfies (3.4) as x → ∞;
+(3). v = v3 satisfies v3(l0) = 0 for l0 < 0, v3(x) > 0 for x > l0 and v3 satisfies (3.5) for x > L;
+(4). v = v4 satisfies v4(l0) = 0 for l0 < 0, v4(x) > 0 for x > l0 and v4 satisfies (3.6) as x → ∞;
+(5). v = v5 satisfies v5(r0) = 0 for r0 > 0, v5(x) > 0 for x < r0 and v5 satisfies (3.4) as x → −∞;
+(6). v = v6 satisfies v6(r0) = 0 for r0 > 0, v6(x) > 0 for x < r0 and v6 satisfies (3.5) for x < −L;
+(7). v = v7 satisfies v7(r0) = 0 for r0 > 0, v7(x) > 0 for x < r0 and v7 satisfies (3.6) as x → −∞;
+(8). v = v8 satisfies v8(x) > 0 for all x ∈ R. Moreover, it satisfies (3.4) as x → −∞; and satisfies
+(3.4) or (3.6) as x → ∞. Note that such solutions ar nothing but Vb, Vg, Vs constructed in
+the previous section, and each of them is unique if it exists;
+(9). v = v9 satisfies v9(x) > 0 for all x ∈ R. Moreover, it satisfies (3.4) as x → −∞; and satisfies
+(3.5) for x > L. (Note that V per we constructed in the previous section belongs to this
+type, and only exist in case L > L∗);
+(10). v = v10 satisfies v10(x) > 0 for all x ∈ R. Moreover, it satisfies (3.5) for x < −L, or satisfies
+(3.6) as x → −∞; and satisfies one of the following decay rates on the right side:
+(3.4)
+0 < 1 − v(x) ∼ e−√1−α|x|;
+(3.5)
+v(x) = V per(x) for some positive periodic solution V per with 0 < V per(x) < θ;
+(3.6)
+0 < v(x) ∼ e−√α|x|.
+For any of the above stationary solution vi, we set η(x, t) := u(x, t)−vi(x) for x ∈ (l0, r0), t ≥
+0. Then η satisfies
+ηt = ηxx + c(x, t)η,
+(l0, r0), t > 0,
+where
+c(x, t) :=
+
+
+
+f(x, u) − f(x, vi)
+η(x, t)
+,
+when η(x, t) ̸= 0,
+0,
+when η(x, t) = 0
+is bounded. Hence, the zero number diminishing property Lemma 3.1 is applicable. On the
+other hand, the decay rates to 1 and/or to 0 for u0 in (I) is imposed in order to separate u0 with
+any one of the stationary solutions: for any choice of i ∈ {1, 2, · · · , 10}, the function η satisfies
+η(l0, t1) ̸= 0,
+η(r0, t1) ̸= 0,
+
+16
+P. LAI AND J. LU
+for any sufficiently small t1 > 0. Moreover, when l0 = −∞ we have η(x, t1) ̸= 0 for all x ≪ −1,
+and when r0 = ∞ we have η(x, t1) ̸= 0 for all x ≫ 1. Therefore, the zero number property
+implies that the number of zeros, denoted by Z(t), of η(·, t) in (l0, r0) is finite for all t > t1:
+Z(t) < ∞. In addition, it is decreasing in t and strictly decreasing in t when it passes a moment
+when there is degenerate zeros. Consequently, after some time, to say, when t ≥ T for some
+large T, η(·, t) not longer has degenerate zeros. As it was shown in [8, Lemma 2.6], this implies
+that any ω-limit of η(·, t) either is identical 0, or has only simple zeros. Especially, the limit
+w(x, 0) − vi(x) of η(x, tn) is identical zero, this is what we desired, or it has only simple zeros.
+The latter, however, contradicts the initial conditions in (3.3). This proves the quasi-convergence
+in Step 1.
+Step 2. To show ω(u) ⊂ S. By our assumption (I) we see that for any a ∈ (θ, 1) and any
+x1 ≪ −1,
+u0(x) > Va(x − x1),
+x ∈ [x1 − x0, x1 + x0],
+for the compactly supported stationary solution Va(x) given in (2.9). By comparison we have
+u(x, t) ≥ Va(x−x1) for all t > 0. So the possible choices of the ω-limits of u are as v5, v6, v7, v8, v9.
+On the other hand, u is bounded in the topology of W 2,1
+p,loc(R × (0, ∞)) and so the ω-limits can
+be taken in the topology of C
+1+ν, 1+ν
+2
+loc
+(R × (0, ∞)) for any ν ∈ (0, 1). This implies that any
+ω-limit must be a C1+ν(R) function. Hence, v5, v6 and v7 are excluded from the candidates of
+the ω-limits since they are not C1 function at x = r0.
+We finally exclude the possibility of v9. By contradiction, assume v9(x) is an ω-limit of u. As
+we mentioned in the previous section, once a solution of v9 type exists, there must be a small
+family of such type of solutions. We choose one of them, to say, ˜v9 such that
+max v9 ̸= max ˜v9,
+min v9 ̸= min ˜v9.
+Now we consider the number of zeros Z9(t) of η9(x, t) := u(x, t) − ˜v9(x). On the one hand,
+as before we know by the assumption for u0 that Z9(t) < ∞ and is decreasing in t. On the
+other hand, the assumption v9 is an ω-limit of u implies that Z9(t) tends to the number of the
+zeros of v9(x) − ˜v9(x), which is infinite, a contradiction. Therefore, any ω-limit of u must be a
+stationary solution of type v8, which are nothing but one of Vb, Vg, Vs in ω(u) ⊂ S. This proves
+the conclusion in Step 2.
+Step 3. To show the convergence. Since ω(u) ⊂ S and S has only three isolated element, we
+conclude that each solution u of (P) with initial data satisfying (I) must converges to Vb, Vg or
+Vs.
+This proves Theorem 3.2.
+□
+Remark 3.3. From the proof of the above theorem we see that the key point to use the zero
+number argument is to guarantee the number of the intersection points between the initial data
+u0 and any one of vi, denoted it by Z[u0 − vi], is finite. We impose decay rates for u0 in (I)
+to ensure this is true. We remark that this is the only place to use the decay rate assumption.
+Clearly, this condition can be extended. For example, if the initial data u0 satisfies
+h :=
+lim
+x→−∞ u0(x) ∈ (α, 1),
+
+THE EFFECT OF AN UNFAVORABLE REGION
+17
+and satisfies similar conditions on the right hand side, then the zero number argument is applica-
+ble as before. In fact, in case h ∈ [θ, 1), the finiteness of Z[u0 − vi] is obvious; in case h ∈ (α, θ),
+then one can show that u(x, t) > θ for all large t and x ≪ −1 by a similar argument as in [9, 10],
+and so it has at most finite number of intersection points with any stationary solution.
+4. Asymptotic Behavior of the Solutions
+In this section we consider the asymptotic behavior for the solutions based on the general
+convergence result in Theorem 3.2, and prove our main theorems.
+4.1. Convergence result for small L.
+Proof of Theorem 1.1. When L < L∗, we have only one stationary solution Vb in S. Hence, by
+the general result in Theorem 3.2 we see that spreading happens for all u.
+□
+4.2. Dichotomy result for critical L∗. First, we give a sufficient condition for spreading.
+Lemma 4.1. Assume (H), u0 satisfies (I). Assume further that, for some a ∈ (θ, 1),
+(4.1)
+u0(x) ≥ Va(x − x1),
+x ∈ [x1 − x0, x1 + x0],
+where Va is the compactly supported stationary solution in (2.9) with support [−x0, x0], x1 >
+x0 + L. Then spreading happens for u.
+Proof. Sine Va(x − x1) is a stationary solution, by comparison we have
+u(x, t) > Va(x − x1),
+x ∈ [x1 − x0, x1 + x0], t > 0.
+Hence the ω-limit of u is also larger than Va(x − x1). By the previous theorem, suitable choice
+for such ω-limit must be Vb.
+□
+Proof of Theorem 1.2. Since S = {Vb, Vs} in the current case, we have either spreading or residue
+happens.
+The prove the theorem we first show that spreading happens for large σ. In fact, by φ(−∞) = 1
+in (I) we see that, when σ ≫ 1 we have
+φ(x − σ) ≥ Va(x − x0 − L),
+x ∈ [L, L + 2x0],
+for some stationary solution Va constructed in (2.9). Therefore spreading happens for uσ by
+Lemma 4.1.
+Denote
+Σ1 := {σ ∈ R | spreading happens for uσ(x, t)}.
+Then Σ1 is nonempty. By the assumption that φ(x) is decreasing function, so φ(x − σ) and uσ
+are increasing in σ. Hence Σ1 is an interval. Moreover, for any σ1 ∈ Σ1, uσ1 converges as t → ∞
+in the L∞
+loc(R) topology to Vb. Hence, there exists T1 large such that
+uσ1(x, T1) > Va(x − x0 − L),
+x ∈ [L, L + 2x0].
+By the continuously dependence for the solution uσ on its initial data φ(x − σ), we see that, for
+any σ satisfying 0 < σ1 − σ ≪ 1, we have
+uσ(x, T1) ≥ Va(x − x0 − L),
+x ∈ [L, L + 2x0].
+
+18
+P. LAI AND J. LU
+Therefore, spreading also happens for uσ. This proves that Σ1 is an open interval (σ∗, ∞) for
+some σ∗ ∈ [−∞, ∞).
+If σ∗ = −∞, then there is nothing left to prove. If σ∗ ∈ R, then, for any σ > σ∗, spreading
+happens for uσ; for any σ ∈ (−∞, σ∗], the only ω-limit of uσ is Vs, that is, residue happens.
+This proves Theorem 1.2.
+□
+4.3. Trichotomy result for large L: Proof of Theorem 1.3. .
+By Proposition 2.2 and Theorem 3.2, in case L > L∗, any solution of (P) with initial data
+satisfying (I) must converges to one element in S.
+Denote
+Σ1 :={σ ∈ R | spreading happens for uσ};
+Σ2 :={σ ∈ R | uσ is a transition solution};
+Σ3 :={σ ∈ R | residue happens for uσ}.
+As in the proof of the previous theorem, one can show that Σ1 is a nonempty open interval
+(σ∗, ∞) for some σ∗ ∈ [−∞, ∞). In what follows we show Σ3 is not empty and so σ∗ ∈ R. The
+proof is divided into several steps.
+Step 1. To show Σ3 is not empty. We will use the the weak upper solution V of (P) constructed
+at the end of Section 2. Recall that, for some ε0 > 0,
+(4.2)
+V ≡ 1 + ε0,
+x ≤ −L,
+and, for some ε ∈ (0, ε0],
+(4.3)
+V (x) − Vs(x) ≥ 3ε,
+x ∈ R.
+By our assumption (I) we see that, when σ ≪ −1, the function φ(x − σ) < V (x). Since V is
+a weak upper solution, by comparison, any ω-limit of uσ(x, t) = u(x, t; φ(x − σ)) is less than V ,
+which is nothing but Vs. This proves that Σ3 is not empty.
+Step 2. To show Σ3 is an open set. Assume σ1 ∈ Σ3, we now show that σ2 ∈ Σ3 when
+0 < σ2 − σ1 ≪ 1.
+This implies that Σ3 in open.
+For simplicity, denote the corresponding
+solutions of (P) with initial data φ(x − σi) by ui (i = 1, 2). By the definition, u1(·, t) converges
+as t → ∞ to Vs in the L∞
+loc(R) topology. Hence, there exists T > 0 such that
+∥u1(x, t) − Vs(x)∥L∞([−L,L]) ≤ ε,
+t ≥ T.
+By parabolic estimate, for any ν ∈ (0, 1), we actually have
+∥u1(x, t) − Vs(x)∥C1+ν([−L,L]) ≤ ε1,
+t ≥ T,
+for some small ε1 > 0. Taking ε smaller if necessary we see that ε1 is also small and so
+(4.4)
+u1x(L, t) < V′
+s(L) + ε1 < 0,
+t ≥ T.
+Moreover, by (4.2) we have
+(4.5)
+∥u1(x, t) − Vs(x)∥L∞((−∞,L]) ≤ ε,
+t ≥ T.
+Note that this inequality is not necessarily true in J := [L, ∞) since, till now, we have no
+monotonicity in this interval. Actually, a solution u can really be not monotonically decreasing
+
+THE EFFECT OF AN UNFAVORABLE REGION
+19
+in this interval, especially for the spreading and transition solutions. Nevertheless, we can claim
+that u1 is monotonically decreasing for x ≫ 1 and all large t. This is proved in two claims.
+Claim 1. There exists M1 = M1(T) > L + 1 such that u1x(x, T) < 0 for x ≥ M1.
+In fact, due to the monotonicity of φ(x − σ1), by using the zero number argument in J we
+see that any local maximum points of u1 in J must first arise at x = L and then propagates
+rightward to the interior of J. Denote the right-most maximum point by ξ(t), that is,
+u1x(ξ(t), t) = 0,
+u1x(x, t) < 0 for x > ξ(t), t > T0,
+where T0 is the first time when ξ(t) appears in J. Since u1x satisfies a linear parabolic equation,
+by a simple estimate for linear equation we can derive that
+ξ(t) ≤ M1(T),
+t ∈ [T0, T].
+This proves Claim 1.
+Claim 2. There exists M2 > M1 such that u1x(x, t) < 0 for all x ≥ M2, t ≥ T.
+In fact, by Claim 1, there exists M2 > M1, such that
+(4.6)
+Vs(x) < ε,
+x ≥ M2,
+and
+u1(x, T) > ˜u1(x, T),
+x ∈ [L, M2),
+where ˜u1(x, t) := u1(2M2 − x, t) for x ∈ [L, M2], t ≥ T denotes the reflection of u1 with respect
+to M2, and so η(x, t) := u1(x, t) − ˜u1(x, t) satisfies
+
+
+
+ηt = ηxx + c(x, t)η,
+x ∈ [L, M2], t ≥ T,
+ηx(L, t) < 0,
+η(M2, t) = 0,
+t ≥ T,
+η(x, T) > 0,
+x ∈ [L, M2),
+for some bounded function c. By the maximum principle we have η(x, t) > 0 for all x ∈ [L, M2)
+and t ≥ T. If the right-most maximum ξ(t) of u1 moves to M2 at some time T1 > T, then we
+have
+η(M2, T1) = 0,
+ηx(M2, T1) = 2u1x(M2, T1) = 2u1x(ξ(T1), T1) = 0,
+this, however, contradicts the Hopf lemma. Thus ξ(t) will never move rightward through M2.
+Now using the L∞
+loc(R) convergence of u1 to Vs we conclude that, for some large T2 > T1,
+∥u1(x, t) − Vs(x)∥L∞((−∞,M2]) ≤ ε,
+t ≥ T2.
+Consequently, by Claim 2 and (4.6) we have
+u1(x, t) ≤ u1(M2, t) ≤ Vs(M2) + ε ≤ 2ε,
+x ≥ M2, t ≥ T2.
+Together with (4.3) we conclude that
+u1(x, T2) ≤ V (x) − ε,
+x ∈ R.
+By the continuous dependence of the solution uσ on its initial data φ(x−σ), we see that when
+σ2 > σ1 with σ2 − σ1 sufficiently small we have
+u2(x, T2) ≤ V (x),
+x ∈ R.
+
+20
+P. LAI AND J. LU
+This indicates that residue happens for u2. This proves the openness of Σ3 in Step 1. Further-
+more, by comparison, there exists −∞ < σ∗ ≤ σ∗ such that Σ3 := (−∞, σ∗).
+Step 3. To complete the proof of Theorem 1.3. From above we have
+Σ1 = (σ∗, ∞),
+Σ3 = (−∞, σ∗).
+Therefore, Σ2 = [σ∗, σ∗] is a nonempty closed set.
+This proves Theorem 1.3.
+□
+References
+[1] S. B. Angenent, The zero set of a solution of a parabolic equation, J. reine angew. Math., 390 (1988), 79-96.
+[2] D. G. Aronson and H. F. Weinberger, Nonlinear diffusion in population genetics, combustion, and nerve pulse
+propagation, Lect. Notes Math., 446 (1975), 5-49.
+[3] D. G. Aronson and H. F. Weinberger, Multidimensional nonlinear diffusion arising in population genetics,
+Adv. Math., 30 (1978), 33-76.
+[4] H. Berestycki and J.-P. Nadal, Self-organised critical hot spots of criminal activity, European J. Appl. Math.,
+21 (2010), 371-399.
+[5] H. Berestycki, N. Rodr´ıguez and L. Ryzhik, Traveling wave solutions in a reaction-diffusion model for criminal
+activity, Multiscale Model. Simul., 11 (2013), 1097-1126.
+[6] X. Y. Chen, A strong unique continuation theorem for parabolic equations, Math. Ann., 311 (1998), 603-630.
+[7] Y. Du and B. Lou, Spreading and vanishing in nonlinear diffusion problems with free boundaries, J. Eur. Math.
+Soc., 17 (2015), 2673-2724.
+[8] Y. Du and H. Matano, Convergence and sharp thresholds for propagation in nonlinear diffusion problems, J.
+Eur. Math. Soc., 12 (2010), 279-312.
+[9] E. Feireisl and P. Pol´aˇcik, Structure of periodic solutions and asymptotic behavior for time-periodic reac-
+tion–diffusion equations on R, Adv. Differential Equations, 5 (2000), 583-622.
+[10] P. C. Fife and J. B. McLeod, The approach of solutions of nonlinear diffusion equations to travelling front
+solutions, Arch. Ration. Mech. Anal., 65 (1977), 335-361.
+[11] G. Lan, C. Wei and S. Zhang, Long time behaviors of single-species population models with psychological
+effect and impulsive toxicant in polluted environments, Phys. A, 521 (2019), 828-842.
+[12] B. Li, M. Zhang and B. Coffman, Can a barrier zone stop invasion of a population?, J. Math. Biol., 81
+(2020), 1193-1216.
+[13] G. A. Maciel and F. Lutscher, Allee effects and population spread in patchy landscapes, J. Biol. Dyn., 9
+(2015), 109-123.
+[14] M. Wang, The diffusive logistic equation with a free boundary and sign-changing coefficient, J. Differential
+Equations, 258 (2015), 1252-1266.
+[15] A. Zlatoˇs, Sharp transition between extinction and propagation of reaction, J. Amer. Math. Soc., 19 (2006),
+251-263.
+[16] N. Zaker, L. Ketchemen and F. Lutscher, The effect of movement behavior on population density in patchy
+landscapes, Bull. Math. Biol., 82 (2020), 1-24.
+
diff --git a/cNFJT4oBgHgl3EQfRCwA/content/tmp_files/load_file.txt b/cNFJT4oBgHgl3EQfRCwA/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..97df2a8cf92efff4d31f182bf3885fed970dae25
--- /dev/null
+++ b/cNFJT4oBgHgl3EQfRCwA/content/tmp_files/load_file.txt
@@ -0,0 +1,813 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf,len=812
+page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='11493v1  [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='AP]  27 Jan 2023  THE EFFECT OF AN UNFAVORABLE REGION ON THE INVASION  PROCESS OF A SPECIES§  PENGCHAO LAI† AND JUNFAN LU†,∗  Abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' To model a propagating phenomena through the environment with an unfavorable  region, we consider a reaction diffusion equation with negative growth rate in the unfavorable  region and bistable reaction outside of it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' We study rigorously the influence of L, the width of  the unfavorable region, on the propagation of solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' It turns out that there exists a critical  value L∗ depending only on the reaction term such that, when L < L∗, spreading happens for  any solution in the sense that it passes through the unfavorable region successfully and establish  with minor defect in the region;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' when L = L∗, spreading happens only for a species with large  initial population, while residue happens for a population with small initial data, in the sense  that the solution converges to a small steady state;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' when L > L∗ we have a trichotomy result:  spreading/residue happens for a species with large/small initial population, but, for a species  with medium-sized initial data, it can not pass through the region either and converges to a  transition steady state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Introduction  In the field of mathematical biology, reaction diffusion equations like  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='1)  ut = ∆u + f(u)  are often used to describe the dynamics and the spreading phenomena of a species, where f(u)/u  represents the growth rate of the species.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Typical examples of f include the so-called monostable  case like f(u) = u(1−u) and bistable case like f(u) = u(u− 1  3)(1−u).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' These equations have been  studied systematically in the last decades.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' For example, in the monostable case, Aronson and  Weinberger [2, 3] proved a hair-trigger effect, which says that spreading (also called persistence  or propagation: u converges to a positive stationary solution) happens for any positive solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  In the bistable case, [2, 3] gave sufficient conditions for spreading and that for vanishing (also  called extinction: u → 0 as t → ∞).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' In 1977, Fife and McLeod [10] proved the existence and  stability for the traveling wave solution of the bistable equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' In 2006, Zlatoˇs [15] gave a  complete study on the bistable equation, and proved a trichotomy result on the asymptotic  behavior for the solutions: there exists a sharp value L∗ > 0 such that when L > L∗ (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  L < L∗), spreading (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' vanishing) happens for the solution of the bistable equation with  initial data u(x, 0) = χ[−L,L](x);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' when L = L∗, the solution develops to a transition ground  2010 Mathematics Subject Classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Primary 35B40, 92D25;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Secondary 35K57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Key words and phrases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Population dynamics;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' reaction diffusion equation;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' unfavorable region;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' asymptotic  behavior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  § This research was partly supported by the NSFC (No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  12101413, 12071299), and the NSF of Shanghai  (20JC1413800).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  † Mathematics and Science College, Shanghai Normal University, Shanghai 200234, China.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  ∗ Corresponding author.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Emails: laipchao@163.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='com (P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Lai), jlu@shnu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='cn (J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Lu).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  1  2  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' LAI AND J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' LU  state solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' In 2010, Du and Matano [8] extended these results to the Cauchy problem with  general initial data like u(x, 0) = φλ(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' For bistable equations, they also proved the trichotomy  and sharp transition results as in [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  In practical problems, however, a spreading process is generally not smooth due to the spatial  and/or temporal heterogeneity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' A favorable environment can accumulate the spreading while an  unfavorable one will slow down or even block the spreading.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' For example, in the invasion process  of a harmful species or infectious diseases, people often establish isolation zones to prevent the  invasion by intensive elimination, or in the spreading process of a beneficial species, it may  encounter adverse environments such as deserts, swamps, environmental pollution, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='.  All  of these unfavorable (for the species) environments can be regarded as desert regions for the  propagation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' (Note that, an unfavorable region we consider here is different from an obstacle  area if the latter one is regarded as a region without population at all).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' In both ecology and  mathematics, whether the species can pass through the region successfully or not is a problem  that people are interested in (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=', [11, 12, 13, 16] etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  From mathematical point of view, if the spreading process of a species obeys the reaction  diffusion equation as (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='1) before it encounters an unfavorable region, then the reaction term  should be negative to the growth of the population when the species enters the unfavorable  region, such as f = −ku + ε(u) for some small ε(u) (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=', [14] etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' ), or just f = −ku for  simplicity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Intuitively, a species can passes though the unfavorable region easily when L (the  width of the unfavorable region) and k (the death rate of the species in the unfavorable region)  are small, but not when L, k are large.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' In this paper, we normalize the parameter k = 1, and  study rigorously the influence of L on the propagation phenomena in one space dimension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' We  will show that there is a critical number L∗ such that, when L < L∗, spreading happens for a  species in the sense that it passes through the unfavorable region successfully and establish with  minor defect in the region;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' when L = L∗, we have a dichotomy result: spreading happens only  for a species with large initial population, while residue happens for a species with small initial  data, in the sense that the solution converges to a small steady state, which takes small value  in the front area;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' when L > L∗, we have a trichotomy result: spreading or residue happens for  a species with large or small initial population.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' For a species with medium-sized initial data,  it can not pass through the region either, but converges to a transition steady state which lies  between the final states of spreading and residue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Our mathematical model is the following Cauchy problem:  (P)  �  ut = uxx + f(x, u),  x ∈ R, t > 0,  u(x, 0) = u0(x),  x ∈ R,  where the reaction term f(x, u) is defined as the following:  (H)  f(x, u) =  �  u(u − α)(1 − u),  |x| ≥ L,  −u,  |x| < L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Here, α ∈ (0, 1  2), and as we mentioned above, 2L is used to denote the width of the unfavorable  region [−L, L], in which the environment is unfavorable for the species so that the growth rate  is −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' We will see below that, as can be expected, the propagation will be more difficult than  the original bistable equation, due to the destructiveness in the unfavorable region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' This kind  THE EFFECT OF AN UNFAVORABLE REGION  3  of model was also used by some authors to understand the phenomena of crime (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=', [4, 5] and  references therein).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' The unknown u(x, t) then denotes the population’s propensity to commit  a crime, and the unfavorable region [−L, L] then denotes a prevention area of the invasions of  crimes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Our background is different from theirs, but the mechanism is similar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' As can be seen  below, our results focus more on the convergence of solutions than theirs (see more in Remark  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  We take initial data from L∞(R), then the well-posedness of W 2,1  p,loc strong solution follows  from the standard parabolic theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' We are then interested in the qualitative property of the  solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' We will show that any global solution of (P) will converge as t → ∞ to a stationary  one, as in the typical reaction diffusion equations (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=', [7, 8, 15]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Since we are studying a  species with sufficient large population in the original habitat, and it tries to propagate further  through an unfavorable region, it is natural to consider the initial data as the following:  (I)  \uf8f1  \uf8f2  \uf8f3  u0(x) ∈ L∞(R), it is decreasing in R with u0(−∞) = 1, u0(∞) = 0,  and  lim  x→−∞  |1 − u0(x)|  e  √1−α x  = 0 or ∞,  lim  x→+∞  u0(x)  e−√α x = 0 or ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  The decay rates as x → ±∞ are imposed only for technical reasons when we use the zero number  argument to prove a general convergence result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' They are not essential and can be weakened  (see more in Section 3 Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Clearly, the typical examples: H(a − x), U(x − ct − a)  satisfy these conditions, where a ∈ R, H is the Heaviside function and U(x − ct) is the traveling  wave solution of the bistable equation with U ′(z) < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Since the classification of the positive stationary solutions depends on the size of L, before  we state our main theorems, it is necessary to specify the stationary solutions of (P) clearly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Stationary solutions solve the following equation:  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='2)  v′′ + f(x, v) = 0,  x ∈ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  By a careful phase plane analysis (see details in Section 2), we will see that there exists a critical  value L∗ > 0 (which depends only on f), such that when L ∈ (0, L∗), (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='2) has exactly one  positive stationary solution, denoted by Vb(x) ∈ W 2  p,loc(R) for any p > 1, which satisfies  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='3)  Vb(−x) = Vb(x),  V′  b(x) > 0 for x > 0,  Vb(0) > 0,  Vb(±∞) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  For convenience, we call Vb as a big stationary solution, and say spreading happens for a  solution u of the problem (P) if  lim  t→∞ u(x, t) = Vb(x),  in the topology of L∞  loc(R).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Then in case 0 < L < L∗ we have the following convergence result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='1 (Spreading result for small L).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Assume L ∈ (0, L∗).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Then for any u0 satisfying  (I), spreading happens for the solution u of (P).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  In case L = L∗, the equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='2) has two positive stationary solutions: Vb as above and  Vs ∈ W 2  p,loc(R) for any p > 1, the latter satisfies  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='4)  Vs(−∞) = 1,  Vs(+∞) = 0,  V′  s(x) < 0 for x ∈ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  4  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' LAI AND J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' LU  For convenience, we call Vs as a small stationary solution, and say that residue happens  for the solution u if it converges to Vs(x) as t → ∞ in the topology of L∞  loc(R).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='2 (Dichotomy result for critical L∗).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Assume L = L∗ and φ satisfies (I).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' For any  σ ∈ R, let uσ(x, t) be the time-global solution of (P) with initial data u0 = φ(x−σ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Then either  spreading happens as above for all σ ∈ R, or there exists σ∗ ∈ R such that  (i) spreading happens when σ ∈ (σ∗, +∞);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  (ii) residue happens when σ ∈ (−∞, σ∗].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  When L > L∗, the equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='2) has exactly three positive stationary solutions: the big  solution Vb and the small solution Vs as above, and another solution Vg ∈ W 2  p,loc(R) for any  p > 1 which lies between Vs and Vb, and  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='5)  �  Vg(−∞) = 1,  Vg(+∞) = 0,  Vs(x) < Vg(x) < Vb(x) for all x ∈ R,  Vg has a unique local minimum x1 ∈ (−L, L) and a unique local maximum x2 > L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  We call Vg a transition (stationary) solution, and say u is a transition solution of (P) if it  converges to Vg in the topology of L∞  loc(R).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' As we expect before, when L > L∗, the propagation  is heavily effected by the unfavorable region and so residue happens easier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Nevertheless, we  have complicated situations for the asymptotic behavior of the solutions in this case, that is, all  of residue, transition and spreading are possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='3 (Trichotomy result for large L).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Assume L > L∗ and φ satisfies (I).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' For any  σ ∈ R, let uσ(x, t) be a time-global solution of (P) with initial data u0 = φ(x − σ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Then there  exist −∞ < σ∗ ≤ σ∗ < ∞ such that  (i) spreading happens when σ ∈ (σ∗, +∞);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  (ii) residue happens when σ ∈ (−∞, σ∗);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  (iii) uσ is a transition solution when σ ∈ [σ∗, σ∗].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  By these results we know that, from a ecological point of view, an unfavorable region will  definitely affect the propagation quantitatively, no matter how large the region is.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' On the other  hand, whether the propagation is affected qualitatively depends on the size of the region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' More  precisely, when the width 2L of the region is smaller than the critical size 2L∗ depending on  f, the effect is a quantitative one: propagation is always successful but with a defective limit,  that is, the limit Vb < 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' When the width is larger than the critical value, the effect can be  a qualitative one: small initial population may be blocked and can not propagate through the  region successfully.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' As a result, it converges to a residue or transition stationary solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Note  that, these solutions remain positive on the right side with small value just because the problem  is a Cauchy one, but not means the species can pass through the unfavorable region smoothly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  For the clarity of our statements, in the previous theorems we adopted a cubic bistable  nonlinearity and a constant death rate, outside of and in the unfavorable region, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Of course, one can consider more general reaction terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  For example, f(x, u) is a general  bistable nonlinearity fb(u) outside of the unfavorable region and a general negative growth rate  fm(u) < 0 (u > 0) in the unfavorable region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' In this case, analogue of our current conclusions can  be derived in a similar way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' More precisely, there are two positive real numbers L∗ ≥ L∗ > 0  THE EFFECT OF AN UNFAVORABLE REGION  5  depending only on f such that the asymptotic behavior for the solutions of (P) are as the  following.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  (1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' When L < L∗, the equation (P) has only positive stationary solutions of Vb type (maybe  not unique), spreading happens in the sense that each solution u converges to one of them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  (2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' When L ∈ [L∗, L∗) (or L = L∗ in case L∗ = L∗ as in our current case), the equation  (P) has positive stationary solutions of both Vb and Vs types (maybe not unique), and  a dichotomy results hold: a solution with large (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' small) initial data converges to a  stationary solution of the type Vb (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Vs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  (3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' When L ≥ L∗ (or L > L∗ in case L∗ = L∗ as in our current case), (P) has positive stationary  solutions of Vb, Vg and Vs types (each type maybe not unique), a trichotomy results hold:  a solution with large (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' small, medium-sized) initial data converges to a stationary  solution of the type Vb (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Vs, Vg).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  The proof of these results is similar as ours, and the details will be given in a forthcoming paper  (see more in Remarks 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Remark 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' If the reaction term is a monostable one like f(u) = u(1 − u), there is the so-  called hair-trigger effect (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=', [2, 3]), which says that any nonnegative, non-trivial solution will  converge to 1, no matter how small the initial data is.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Hence, if we use monostable model instead  of the bistable one outside of the unfavorable region, then the asymptotic behavior will be very  simple: spreading always happens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Remark 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' As we have mentioned above, Berestycki et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  [5] also studied the equation  (P) as a model to understand the phenomena of crime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' They proved that, when L < L∗, the  wave propagates in the sense that u(x, t) > 1 − ε for any small ε > 0 and all large x, t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' when  L ≥ L∗, the propagation is blocked in the sense that there exists a stationary solution as our Vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  We see that these results correspond to our spreading and residue phenomena, but without the  convergence to the corresponding stationary solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Moreover, we complete the dichotomy  (in case L = L∗) and trichotomy (in case L > L∗) results, as well as the threshold for the initial  data as in Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  The rest of the paper is organized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' In Section 2, we present the positive stationary  solutions by using a phase plane analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' In Section 3, we give a general convergence result for  the solutions of (P) with initial data satisfying (I).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' In Section 4, we prove our main theorems  on the dichotomy and trichotomy results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Positive Stationary Solutions  In this section we will present the definition of the critical value L∗ of the unfavorable region  width, and construct some useful positive stationary solutions by using the phase plane analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Phase plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' We will work on the equation of stationary solutions:  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='1)  v′′ + f(x, v) = 0,  x ∈ R,  for f defined by (H).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' For convenience, in what follows we write  fl(u) = fr(u) := u(u − α)(1 − u),  fm(u) := −u,  6  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' LAI AND J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' LU  then f(x, u) = fl(u) = fr(u) when |x| ≥ L and f(x, u) = fm(u) when |x| < L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Each solution of  equation (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='1) consists of three parts  v =  \uf8f1  \uf8f4  \uf8f2  \uf8f4  \uf8f3  vl(x),  x ≤ L,  vm(x),  |x| < L,  vr(x),  x ≥ L,  which satisfies the following equations  v′′  l + fl(vl) = 0,  x < −L,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='2)  v′′  m + fm(vm) = 0,  |x| < L,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='3)  v′′  r + fr(vr) = 0,  x > L,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='4)  with matching conditions on the boundaries of the unfavorable region:  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='5)  �  vl(−L − 0) = vm(−L + 0),  v′  l(−L − 0) = v′  m(−L + 0),  vm(L − 0) = vr(L + 0),  v′  m(L − 0) = v′  r(L + 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Now, we seek for solutions of the problems (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='2)-(2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='4) by phase plane analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' First, these  equations can be converted into the following systems:  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='6)  �  v′  i = wi,  w′  i = −fi(vi),  for i = {l, m, r}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' These systems are equivalent to the following first-order ordinary differential  equations  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='7)  widwi = −fi(vi)dvi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  They are solved explicitly:  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='8)  w2  i = C − 2  � vi  0  fi(s)ds,  for some C to be determined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Taking different C we can sketch the phase diagram of (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='2)-(2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='4)  or (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='6) as in Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' For convenience, we present some details here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Trajectories of the system (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  THE EFFECT OF AN UNFAVORABLE REGION  7  In Figure 1, the trajectory Γ1 is the graph of (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='8) with i = l and C = 2  � 1  0 fl(s)ds > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' It  corresponds to a solution V1 of (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='2) or (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='4), which takes 0 at some point x0 and is strictly  increasing for x > x0 with  0 < 1 − V1(x) ∼ e−√1−α x,  x → ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Similarly, the trajectory Γ′  1 corresponds to a solution ˜V1(x) ≡ V1(2x0 − x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Γ2 is the graph of (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='8) with i = l and C = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' It is a homoclinic orbit, and corresponds to  the so-called ground state solution V2 of (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='2) or (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='4), which satisfies  V2(x) = V2(−x) and V ′  2(x) < 0 for x > 0,  V2(0) = θ,  V2(x) ∼ e−√α x as x → +∞,  where θ = θ(α) ∈ (α, 1) is defined by  � θ  0 fl(u)du =  � θ  0 fr(u)du = 0, that is,  θ = θ(α) := 4(α + 1) −  �  16(α + 1)2 − 72α  6  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  The trajectory Γ3 is the graph of (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='8) with i = l and C = 2  � a  0 fl(s)ds for any given a ∈ (θ, 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  It gives a compactly supported stationary solution Va of the bistable reaction diffusion equation,  which satisfies, for some x0 ∈ (0, ∞) depending on a  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='9)  Va(±x0) = 0,  Va(0) = q0,  Va(−x) = Va(x) and V ′  a(x) < 0 in (0, x0].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Such solutions will be used in Section 3 to give a sufficient condition for the spreading phenomena.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  The singular point (α, 0) is a center.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' For any a ∈ (0, α), there is a closed orbit Γ4 surrounding  (α, 0), which is the graph of (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='8) with i = l and C = 2  � a  0 fl(s)ds, and corresponds to a periodic  solution, denoted by V per  a  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  For any small δ > 0, the trajectory Γ∗  5 passing through F(1, −δ) is the graph of (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='8) with  i = l and C = δ2 + 2  � 1  0 fl(s)ds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' It corresponds to a solution V ∗  5 which satisfies  V ∗  5 (x) < 0 for x < 0,  V ∗  5 (x) → +∞ as x → −∞,  V ∗  5 (0) = 0 and V ∗  5 (x0) = 1,  for some x0 < 0 (here we normalize the function as zero at x = 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Finally, Γ0 is a trajectory of the system (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='6) for i = m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' For any a ∈ (0, 1), there is a Γ0  passing through A(a, 0), which is the graph of the function w2  m = v2  m − a2 (vm ≥ a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' This  trajectory gives a solution V0 of (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='1) in the interval [−L, L], and can be expressed explicitly as  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='10)  V0(x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' a) = a cosh(x) ≥ a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Trajectory pieces corresponding to the solutions on [−L, L].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' We will combine suit-  able trajectory pieces of (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='2)-(2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='4) together to give solutions of the problem (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Note that  each one of such solutions satisfies (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='3) in a domain with exact width 2L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  So we need to  specify the relationship between the arc lengths of the trajectory pieces and the life spans of  corresponding solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  We introduce a notation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' If AB is a trajectory piece in the phase plane corresponding to a  solution V (x) of (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='1) such that  (V (x1), V ′(x1)) = A,  (V (x2), V ′(x2)) = B,  then |x1 − x2| is the life span of the solution given by this piece AB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' In what follows we use  XAB to denote this span |x1 − x2|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  8  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' LAI AND J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' LU  In Figure 1, we see that if A = (a, 0) ∈ Γ0 lies between (0, 0) and (θ, 0), then Γ2 and Γ0  has exactly two intersection points D2, D′  2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' if a = θ, then there is a unique intersection point  A = (θ, 0) between them;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' if a ∈ (θ, 1), there is no intersection point between them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' On the other  hand, any Γ0 has a unique intersection point D1 with Γ1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Denote Di = (vi, wi) (i = 1, 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Since  the stationary solution corresponding to Γ0 is given by V0 in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='10), we see that  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='11)  V0(0) = a,  V0(r) = v2,  V0(R) = v1,  for some R = R(a) > r = r(a) > 0, that is, XAD2 = r and XAD1 = R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  We now study the monotonicity of R(a), r(a) and ℓ(a) := R(a) − r(a) = XD1D2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' All of R, r and ℓ given above are strictly decreasing in the parameter a ∈ (0, 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' (1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' We first prove dR  da < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Recall that the function of Γ0 is w2 = v2 − a2, and the  function of Γ1 is w2 = 2  � 1  v fl(s)ds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Combining them together we obtain the v-coordinate v1 for  D1:  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='12)  v2  1 − a2 = 2  � 1  v1  fl(s)ds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Substituting the explicit formula (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='10) v1 = V0(R) = a cosh R into this equality we have  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='13)  a2 cosh2(R) − a2 = 2  � 1  a cosh(R)  fl(s)ds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Using the cubic bistable nonlinearity fl we can obtain  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='14)  a2 d[cosh(R)]  da  =  −2  � 1  v1 fl(s)ds − v1fl(v1)  v1 + fl(v1)  �����  v1=a cosh(R)  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  In fact, with  F(v1, α) := 2  � 1  v1  fl(s)ds + v1fl(v1) = −1  2v4  1 + 1  3(1 + α)v3  1 + 1 − 2α  6  ,  we have ∂F  ∂α = 1  3v3  1 − 1  3 < 0 and F(v1, 1  2) = − 1  2v4  1 + 1  2v3  1 > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Then (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='14) holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' This implies  that  dR  da < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  (2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' In a similar way one can show that dr  da < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  (3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' We now show that dℓ  da = d(R−r)  da  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Substituting fl(u) = u(u − α)(1 − u) into (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='12), we  see that the v-coordinate of D1 is given by the root of  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='15)  −1  2v4  1 + 2(α + 1)  3  v3  1 + (1 − α)v2  1 + 2α − 1  6  − a2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  From the phase diagram we see that, for any a ∈ (0, θ(α)), this equation has a unique root  v1(a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' α) ∈ (a, 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Similarly, the v-coordinate of D2 is given by the unique root v2(a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' α) ∈ (a, θ)  of following equation  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='16)  −1  2v4  2 + 2(α + 1)  3  v3  2 + (1 − α)v2  2 − a2 = 0,  THE EFFECT OF AN UNFAVORABLE REGION  9  Noticing that v1 = a cosh R(a) and v2 = a cosh r(a), we can conclude that  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='17)  ℓ(a) = R(a) − r(a) = ln v1(a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' α) +  �  v2  1(a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' α) − a2  a  − ln v2(a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' α) +  �  v2  2(a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' α) − a2  a  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  A tedious but trivial calculation gives the formulas of v1, v2 and ℓ(a), which shows that dℓ(a)  da  < 0  for any given α ∈ (0, 1  2) and any a ∈ (0, θ(α)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' A numerical simulation result is illustrated in  Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='8  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='5  2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='5  3  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='5  4  a  l=R−r  α=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='05  α=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='1  α=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='2  α=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='3  α=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='4  α=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='45  Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' For each given α ∈ (0, 1  2), ℓ(a) is strictly decreasing in a ∈ (0, θ(α)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  The a-coordinate of the end point of each curve is θ(α).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  □  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Stationary solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' For any given α ∈ (0, 1  2), by the monotonicity of ℓ(a) on a, we see  that  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='18)  2L∗ := ℓ(θ(α)) =  inf  0<a<θ(α) ℓ(a) > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Clearly, this value depends only on f(x, u).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' This is the critical value of L appearing in our main  theorems, and it plays a key role in the classification for the dynamics of the solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Based on the monotonicity of R, r, and ℓ, we can construct some positive solutions of (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='1)  which will be used below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Let L∗ be the critical value defined by (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='18).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  (a) In case 0 < L < L∗, the equation (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='1) has exactly one positive solution Vb ∈ C1(R) ∩  C∞(R\\{±L}) which satisfies (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='3) and  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='19)  0 < 1 − Vb(x) ∼ e−√1−α |x| as |x| → ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  (b) In case L = L∗, the equation (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='1) has at least two positive solutions, one is Vb as above,  the other one Vs ∈ C1(R) ∩ C∞(R\\{±L}) satisfies (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='4) and  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='20)  0 < 1 − Vs(x) ∼ e  √1−α x as x → −∞,  0 < Vs(x) ∼ e−√α x as x → ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  10  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' LAI AND J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' LU  (c) In case L > L∗, the equation (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='1) has at least three positive solutions: Vb, Vs as above, and  Vg ∈ C1(R) ∩ C∞(R\\{±L}) which satisfies, for some x1, x2 with −L < x1 < L < x2,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='21)  \uf8f1  \uf8f2  \uf8f3  V′  g(x) < 0 for x ∈ (−∞, x1) ∪ (x2, ∞),  V′  g(x) > 0 for x ∈ (x1, x2),  Vg(x1) ∈ (0, θ),  Vg(x2) = θ,  0 < 1 − Vg(x) ∼ e  √1−α x as x → −∞,  0 < Vg(x) ∼ e−√α x as x → ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Moreover, (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='1) has no other positive solutions satisfying v(−∞) = 1 and v(∞) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  (d) The solutions Vb, Vs, Vg are well-ordered, if they exist,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='22)  Vs(x) < Vg(x) < Vb(x),  x ∈ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Trajectories of the solutions of (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='1): the case L = L∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' (a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Trajectory of  Vb;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' (b) Trajectory of Vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Trajectories of the solutions of (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='1): the case L > L∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' (a) Trajectory of  Vb;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' (b) Trajectory of Vg;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' (c) Trajectory of Vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' First, we construct solution Vb for any L > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' In Figure 3 (a), we see that the combination  of the trajectory pieces: (1, 0)-B-A-C-(1, 0) gives such a solution, as long as XBAC (which denotes  the life span of the solution V0(x) given by the piece BAC) is 2L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' From above we know that  XBAC = 2R(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Since  R(a) → 0 as a → 1,  R(a) → ∞ as a → 0,  and since R(a) is strictly decreasing in a, there exists a unique a ∈ (0, 1) such that 2R(a) = 2L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  For this choice of of a, the trajectory piece combination gives the solution Vb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Next, we construct Vs in case L ≥ L∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' It is easily seen that the combination of trajectory  pieces: (1, 0)-B-C-(0, 0) in Figure 3 (b) or Figure 4 (c) gives a positive solution as Vs, as long  THE EFFECT OF AN UNFAVORABLE REGION  11  as XBC = 2L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' In case L = L∗, the unique suitable choice of C is (θ, 0) (see Figure 3 (b)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' In  case L > L∗, however, XBC = R(a) − r(a) = ℓ(a), which is also strictly decreasing in a with  ℓ(a) → ∞ as a → 0,  ℓ(a) → 2L∗ as a → θ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Hence, there exists a unique a such that ℓ(a) = 2L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' The corresponding combination of trajectory  pieces defines the solution Vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  We then construct Vg in case L > L∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' As in Figure 4 (b), the combination of trajectory  pieces: (1, 0)-B-C′-A-C-(θ, 0)-(0, 0) gives a solution of type Vg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Note that, for this purpose, we  require that XBAC = R(a) + r(a) = 2L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' From the analysis in the previous subsection this span  is strictly decreasing in a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Hence there is a unique a ∈ (0, θ) satisfies this requirement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' This  prove the existence and uniqueness of Vg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  The regularities of these solutions follow from the fact that they are bounded in the W 2  p,loc(R)  topology, and smooth in the interior of R\\{±L} by the interior estimates in the theory of elliptic  equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' The decay rates in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='19), (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='20), (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='21) can be shown by the corresponding solutions  given by the trajectory pieces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Finally, we prove the ordering (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='22).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' We only consider the case L > L∗, since the proof for  Vb > Vs in case L = L∗ is similar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' In Figure 4 (a), we write the coordinates of the points A, B, C  as (a1, 0), (vB  1 , wB  1 ), (vC  1 , wC  1 ), respectively, and write the coordinates of A, B, C in Figure 4 (b)  and (c) similarly with subscripts 1 replaced by 2, 3, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  We first prove Vg > Vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Recall that, the trajectory piece BC in Figure 4 (c) gives a solution  V0(x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' a3) = a3 cosh x, its shift a3 cosh(x − r(a3)+R(a3)  2  ) coincides with Vs(x) in [−L, L], and  ℓ(a3) = R(a3) − r(a3) = 2L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Similarly, the trajectory piece BC′AC in Figure 4 (b) gives the  solution V0(x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' a2) = a2 cosh x, its shift a2 cosh(x − ℓ(a2)  2 ) coincides with Vg(x) in [−L, L], and  ℓ(a2) + 2r(a2) = 2L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Hence,  ℓ(a2) = 2L − 2r(a2) < 2L = ℓ(a3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  By the monotonicity of ℓ we see that  a3 < a2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Thus, the trajectory passing through (a3, 0) lies on the left of that passing through (a2, 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' This  implies that (vB  3 , wB  3 ) lies on the left of (vB  2 , wB  2 ), (vC  3 , wC  3 ) lies on the left of (vC′  2 , wC′  2 ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Hence,  vB  3 < vB  2 ,  vC  3 = vC′  3  < vC′  2  = vC  2 ,  that is,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='23)  a3 cosh  �  ±L − r(a3) + R(a3)  2  �  < a2 cosh  �  ±L − ℓ(a2)  2  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  We now prove  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='24)  a3 cosh  �  x − r(a3) + R(a3)  2  �  < a2 cosh  �  x − ℓ(a2)  2  �  ,  x ∈ [−L, L].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  By contradiction we assume this is not always true.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Then combining with (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='23) we see that,  there exists y ∈ (−L, L) such that  a3 cosh  �  y − r(a3) + R(a3)  2  �  = a2 cosh  �  y − ℓ(a2)  2  �  ,  12  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' LAI AND J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' LU  and the derivatives of them at this point y satisfy  a3 sinh  �  y − r(a3) + R(a3)  2  �  ≤ a2 sinh  �  y − ℓ(a2)  2  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  This is impossible due to a3 < a2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' This proves Vs < Vg in [−L, L].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  On the interval (−∞, −L], we have  Vs(x) = ˜V1(x − x3),  Vg(x) = ˜V1(x − x2)  for some suitable x3, x2, where ˜V1(x) is the solution given by Γ′  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' By vB  3 < vB  2 we have  ˜V1(−L − x3) = Vs(−L) = vB  3 < vB  2 = Vg(−L) = ˜V1(−L − x2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Hence x3 < x2 and so  Vs(x) = ˜V1(x − x3) < Vg(x) = ˜V1(x − x2),  x ≤ −L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  In a similar way one can show that Vs < Vg in [L, ∞).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' In summary we obtain the the first  inequality in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='22).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  The second inequality of (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='22) is proved similarly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  □  Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' We constructed three positive stationary solutions Vb, Vg, Vs in the previous  proposition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' For convenience, we call them the big, transition and small stationary solu-  tions, respectively, and denote  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='25)  S := {Vs, Vg, Vb}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  In the next section we will show that any ω-limit of the solution of (P) with initial data satisfying  (I) is an element in S, even though (P) has other positive stationary solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' For example,  the reflections of the solutions in S with respect to x = 0, and many other types of solutions,  positive in the whole R, or compactly supported.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Besides the positive stationary solutions mentioned above, we can construct some other upper  and lower solutions which can be used for comparison.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Here we give one of them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' In Figure 4 (b),  we see that the combination of the trajectory pieces F-D-B∗-E-Γ4 defines a function V (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' More  precisely, denote D = (vD, wD), E = (vE, wE).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Recall that we denote the solution corresponding  to trajectory Γ∗  5 by V ∗  5 (x) in the previous subsection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Denote the solution corresponding to the  combination D-B∗-E by V ∗  0 (x), and the periodic solution corresponding to the Γ4 by V per(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Combining them together we obtain the function V :  V (x) =  \uf8f1  \uf8f2  \uf8f3  V ∗  5 (x + x1),  x ≤ −L,  V ∗  0 (x + x2),  x ∈ [−L, L],  V per(x + x3),  x ≥ L,  where the shifts x1, x2, x3 are chosen to satisfy the following matching conditions:  V ∗  5 (−L + x1) = vD = V ∗  0 (−L + x2),  V ∗  0 (L + x2) = vE = V per(L + x3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  THE EFFECT OF AN UNFAVORABLE REGION  13  Moreover, for any small ε0 > 0, there exists −L < −L such that V (x) = V ∗  5 (x + x1) ≥ 1 + ε0  for x ≤ −L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Now we define  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='26)  V (x) :=  \uf8f1  \uf8f4  \uf8f4  \uf8f2  \uf8f4  \uf8f4  \uf8f3  1 + ε0,  x ≤ −L,  V ∗  5 (x + x1),  x ∈ [−L, −L],  V ∗  0 (x + x2),  x ∈ [−L, L],  V per(x + x3),  x ≥ L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Note that this function is continuous in R and C1 in R\\{−L}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' In addition,  V  ′(−L − 0) = 0 > V  ′(−L + 0),  and  V (x) ≥ ε1 := min  �  V ∗  0 (0), min  x∈R V per(x)  �  > 0,  x ∈ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  In the Subsection 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='3 we will use this upper solution to separate Vs from Vg to give the trichotomy  results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' As we mentioned in Section 1, one may be interested in general reaction terms, to  say, f is a bistable nonlinearity outside of the unfavorable region and a general negative growth  rate in the region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' In this case, the phase plane analysis we do in this section remains valid,  but with more complicated situations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Now we give a sketch below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' (1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' We collect all possible  trajectory pieces BC as in Figure 3(c) and 4(c), and define  L∗ := min{XBC | B ∈ Γ′  1, C lies on the lower half of Γ2};' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  then collect all possible trajectory pieces BC′C as in Figure 4(b), and define  L∗ := min{XBC′C | B ∈ Γ′  1, C lies on the upper half of Γ2}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Then L∗ ≥ L∗ > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' (Note that, in our current special case L∗ = L∗ = XBC for C = (θ, 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=') (2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  If we consider only positive stationary solutions of (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='1) satisfying v(−∞) = 1, v(∞) = 0, then  we can show the following results in a similar way as we do in this section: when L < L∗, (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='1)  has only Vb type of solutions, which may be not unique but well-ordered;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' when L ∈ [L∗, L∗)  (or L = L∗ when L∗ = L∗), (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='1) has two groups of solutions, one group is of the form Vs,  the other is of the form Vb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Each group may be not unique but well-ordered;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' when L ≥ L∗  (or L > L∗ when L∗ = L∗), (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='1) has three groups of solutions, they are of the form Vs, Vg, Vb,  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Each group may be not unique but well-ordered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' (3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Though we can derive the  order in each group, it is not easy to prove all the solutions are well-ordered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Even, we can  not easily to show, by just analyzing the ODE (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='1), the existence of the smallest and largest  stationary solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' However, it is remarkable to point out that, this last conclusion can be  proved by a PDE approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' More precisely, we consider an initial data u0(x) which approaches  1 as x → −∞ in a sufficiently slow decay rate, and it is decreasing and takes 0 at some point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  If we shift this initial data leftward sufficiently far such that it is smaller than any stationary  solution, then, by the general convergence result (which will be proved in the next section) the  solution with this initial data converges to a positive stationary solution, which must be the  smallest one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' On the other hand, the solution with initial data u0 ≡ 1 must converges to the  largest stationary solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  14  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' LAI AND J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' LU  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' General Convergence Result  In this section we use the so-called zero number argument to prove that, for any solution u  of (P), its ω-limit set is contained in S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' We first recall the typical zero number diminishing  properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Consider  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='1)  ηt = a(x, t)ηxx + b(x, t)ηx + c(x, t)η  in E0 := {(x, t) | x ∈ R, t ∈ (t1, t2)},  where t2 > t1 ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' For each t ∈ (t1, t2), denote by  Z(t) := ♯{x ∈ R | η(·, t) = 0}  the number of zeroes of η(·, t) in R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' A point x0 is called a multiple zero (or degenerate zero)  of η(·, t) if η(x0, t) = ηx(x0, t) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' In 1988, Angenent [1] proved a zero number diminishing  property, and in 1998, the conditions Angenent had used in [1] were weaken by Chen [6] for  strong solutions in W 2,1  p, loc(R × (0, ∞)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' One of their results is summarized as the following:  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='1 ([1, 6]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Assume the coefficients in (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='1) satisfies  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='2)  a, a−1, at, ax, b, c ∈ L∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Let η be a nontrivial W 2,1  p,loc solution of (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Then  (1) the zeros of η(·, t) are isolated;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  (2) if Z(t) < ∞ for some t0 ∈ (t1, t2), then it is decreasing in t ∈ (t0, t2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Moreover,  if s ∈ (t0, t2) and x0 is a multiple zero of η(·, s), then Z(s1) > Z(s2) for all s1, s2  satisfying t0 < s1 < s < s2 < t2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Using this lemma we can prove the following convergence result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Assume (H), u0 satisfies (I).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Then for any L > 0, the unique time-global  solution u(x, t) converges as t → ∞ to an element in S, in the topology of L∞  loc(R).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' First, one can derive the boundedness of u easily by the maximum principle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Then the  existence and uniqueness of the strong solution in W 2,1  p,loc(R × (0, ∞)) follows from the standard  parabolic theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' By the standard Lp estimates, for any increasing time sequence {tn}, any  p > 1, M > 0, there exists C = C(M, p) such that  ∥u(x, t + tn)∥W 2,1  p  ([−M,M]2) ≤ C,  therefore, for any ν ∈  �  0, 1 − 1  p  �  , there exists a subsequence of {tn}, denoted it again by {tn},  and a function w(x, t) ∈ C1+ν, 1+ν  2 ([−M, M]2) such that  ∥u(x, t + tn) − w(x, t)∥  C1+ν, 1+ν  2  ([−M,M]2) → 0 as n → ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  By Cantor’s diagonal argument, the ω-limit set of u(·, t) in the topology of C1+ν  loc (R) is not empty,  and by standard dynamics theory, compact, invariant and connected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  We divide the rest proof into several steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Step 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' A quasi-convergence result: any ω-limit of u is a stationary solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' We follow the  idea in [7, 8] and use the zero number argument.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' We show that, for any t ∈ R, w(·, t) is actually  a stationary solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' We only need to prove w(·, 0) is so.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' By contradiction, we assume that  THE EFFECT OF AN UNFAVORABLE REGION  15  w(x, 0) is not a stationary solution, so w(x, 0) ̸≡ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Assume without loss of generality that  w(0, 0) > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Using w(x, 0) we construct a real stationary solution:  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='3)  �  v′′ + f(x, v) = 0,  x ∈ R,  v(0) = w(0, 0) > 0,  v′(0) = wx(0, 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  By the phase plane analysis in the previous section we see that, the bounded W 2  p solution of  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='3) must be less than 1 and positive in some open interval (l0, r0) with −l0, r0 ∈ (0, ∞].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' In  addition, it has the following cases:  (1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' v = v1 satisfies v1(l0) = v2(r0) = 0 for l0 < 0 < r0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  (2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' v = v2 satisfies v2(l0) = 0 for l0 < 0, v2(x) > 0 for x > l0 and v2 satisfies (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='4) as x → ∞;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  (3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' v = v3 satisfies v3(l0) = 0 for l0 < 0, v3(x) > 0 for x > l0 and v3 satisfies (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='5) for x > L;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  (4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' v = v4 satisfies v4(l0) = 0 for l0 < 0, v4(x) > 0 for x > l0 and v4 satisfies (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='6) as x → ∞;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  (5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' v = v5 satisfies v5(r0) = 0 for r0 > 0, v5(x) > 0 for x < r0 and v5 satisfies (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='4) as x → −∞;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  (6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' v = v6 satisfies v6(r0) = 0 for r0 > 0, v6(x) > 0 for x < r0 and v6 satisfies (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='5) for x < −L;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  (7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' v = v7 satisfies v7(r0) = 0 for r0 > 0, v7(x) > 0 for x < r0 and v7 satisfies (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='6) as x → −∞;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  (8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' v = v8 satisfies v8(x) > 0 for all x ∈ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Moreover, it satisfies (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='4) as x → −∞;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' and satisfies  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='4) or (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='6) as x → ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Note that such solutions ar nothing but Vb, Vg, Vs constructed in  the previous section, and each of them is unique if it exists;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  (9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' v = v9 satisfies v9(x) > 0 for all x ∈ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Moreover, it satisfies (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='4) as x → −∞;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' and satisfies  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='5) for x > L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' (Note that V per we constructed in the previous section belongs to this  type, and only exist in case L > L∗);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  (10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' v = v10 satisfies v10(x) > 0 for all x ∈ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Moreover, it satisfies (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='5) for x < −L, or satisfies  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='6) as x → −∞;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' and satisfies one of the following decay rates on the right side:  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='4)  0 < 1 − v(x) ∼ e−√1−α|x|;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='5)  v(x) = V per(x) for some positive periodic solution V per with 0 < V per(x) < θ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='6)  0 < v(x) ∼ e−√α|x|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  For any of the above stationary solution vi, we set η(x, t) := u(x, t)−vi(x) for x ∈ (l0, r0), t ≥  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Then η satisfies  ηt = ηxx + c(x, t)η,  (l0, r0), t > 0,  where  c(x, t) :=  \uf8f1  \uf8f2  \uf8f3  f(x, u) − f(x, vi)  η(x, t)  ,  when η(x, t) ̸= 0,  0,  when η(x, t) = 0  is bounded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Hence, the zero number diminishing property Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='1 is applicable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' On the  other hand, the decay rates to 1 and/or to 0 for u0 in (I) is imposed in order to separate u0 with  any one of the stationary solutions: for any choice of i ∈ {1, 2, · · · , 10}, the function η satisfies  η(l0, t1) ̸= 0,  η(r0, t1) ̸= 0,  16  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' LAI AND J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' LU  for any sufficiently small t1 > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Moreover, when l0 = −∞ we have η(x, t1) ̸= 0 for all x ≪ −1,  and when r0 = ∞ we have η(x, t1) ̸= 0 for all x ≫ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Therefore, the zero number property  implies that the number of zeros, denoted by Z(t), of η(·, t) in (l0, r0) is finite for all t > t1:  Z(t) < ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' In addition, it is decreasing in t and strictly decreasing in t when it passes a moment  when there is degenerate zeros.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Consequently, after some time, to say, when t ≥ T for some  large T, η(·, t) not longer has degenerate zeros.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' As it was shown in [8, Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='6], this implies  that any ω-limit of η(·, t) either is identical 0, or has only simple zeros.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Especially, the limit  w(x, 0) − vi(x) of η(x, tn) is identical zero, this is what we desired, or it has only simple zeros.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  The latter, however, contradicts the initial conditions in (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' This proves the quasi-convergence  in Step 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Step 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' To show ω(u) ⊂ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' By our assumption (I) we see that for any a ∈ (θ, 1) and any  x1 ≪ −1,  u0(x) > Va(x − x1),  x ∈ [x1 − x0, x1 + x0],  for the compactly supported stationary solution Va(x) given in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' By comparison we have  u(x, t) ≥ Va(x−x1) for all t > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' So the possible choices of the ω-limits of u are as v5, v6, v7, v8, v9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  On the other hand, u is bounded in the topology of W 2,1  p,loc(R × (0, ∞)) and so the ω-limits can  be taken in the topology of C  1+ν, 1+ν  2  loc  (R × (0, ∞)) for any ν ∈ (0, 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' This implies that any  ω-limit must be a C1+ν(R) function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Hence, v5, v6 and v7 are excluded from the candidates of  the ω-limits since they are not C1 function at x = r0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  We finally exclude the possibility of v9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' By contradiction, assume v9(x) is an ω-limit of u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' As  we mentioned in the previous section, once a solution of v9 type exists, there must be a small  family of such type of solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' We choose one of them, to say, ˜v9 such that  max v9 ̸= max ˜v9,  min v9 ̸= min ˜v9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Now we consider the number of zeros Z9(t) of η9(x, t) := u(x, t) − ˜v9(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' On the one hand,  as before we know by the assumption for u0 that Z9(t) < ∞ and is decreasing in t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' On the  other hand, the assumption v9 is an ω-limit of u implies that Z9(t) tends to the number of the  zeros of v9(x) − ˜v9(x), which is infinite, a contradiction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Therefore, any ω-limit of u must be a  stationary solution of type v8, which are nothing but one of Vb, Vg, Vs in ω(u) ⊂ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' This proves  the conclusion in Step 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Step 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' To show the convergence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Since ω(u) ⊂ S and S has only three isolated element, we  conclude that each solution u of (P) with initial data satisfying (I) must converges to Vb, Vg or  Vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  This proves Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  □  Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' From the proof of the above theorem we see that the key point to use the zero  number argument is to guarantee the number of the intersection points between the initial data  u0 and any one of vi, denoted it by Z[u0 − vi], is finite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' We impose decay rates for u0 in (I)  to ensure this is true.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' We remark that this is the only place to use the decay rate assumption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Clearly, this condition can be extended.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' For example, if the initial data u0 satisfies  h :=  lim  x→−∞ u0(x) ∈ (α, 1),  THE EFFECT OF AN UNFAVORABLE REGION  17  and satisfies similar conditions on the right hand side, then the zero number argument is applica-  ble as before.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' In fact, in case h ∈ [θ, 1), the finiteness of Z[u0 − vi] is obvious;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' in case h ∈ (α, θ),  then one can show that u(x, t) > θ for all large t and x ≪ −1 by a similar argument as in [9, 10],  and so it has at most finite number of intersection points with any stationary solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Asymptotic Behavior of the Solutions  In this section we consider the asymptotic behavior for the solutions based on the general  convergence result in Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='2, and prove our main theorems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Convergence result for small L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Proof of Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' When L < L∗, we have only one stationary solution Vb in S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Hence, by  the general result in Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='2 we see that spreading happens for all u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  □  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Dichotomy result for critical L∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' First, we give a sufficient condition for spreading.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Assume (H), u0 satisfies (I).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Assume further that, for some a ∈ (θ, 1),  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='1)  u0(x) ≥ Va(x − x1),  x ∈ [x1 − x0, x1 + x0],  where Va is the compactly supported stationary solution in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='9) with support [−x0, x0], x1 >  x0 + L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Then spreading happens for u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Sine Va(x − x1) is a stationary solution, by comparison we have  u(x, t) > Va(x − x1),  x ∈ [x1 − x0, x1 + x0], t > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Hence the ω-limit of u is also larger than Va(x − x1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' By the previous theorem, suitable choice  for such ω-limit must be Vb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  □  Proof of Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Since S = {Vb, Vs} in the current case, we have either spreading or residue  happens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  The prove the theorem we first show that spreading happens for large σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' In fact, by φ(−∞) = 1  in (I) we see that, when σ ≫ 1 we have  φ(x − σ) ≥ Va(x − x0 − L),  x ∈ [L, L + 2x0],  for some stationary solution Va constructed in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Therefore spreading happens for uσ by  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Denote  Σ1 := {σ ∈ R | spreading happens for uσ(x, t)}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Then Σ1 is nonempty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' By the assumption that φ(x) is decreasing function, so φ(x − σ) and uσ  are increasing in σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Hence Σ1 is an interval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Moreover, for any σ1 ∈ Σ1, uσ1 converges as t → ∞  in the L∞  loc(R) topology to Vb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Hence, there exists T1 large such that  uσ1(x, T1) > Va(x − x0 − L),  x ∈ [L, L + 2x0].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  By the continuously dependence for the solution uσ on its initial data φ(x − σ), we see that, for  any σ satisfying 0 < σ1 − σ ≪ 1, we have  uσ(x, T1) ≥ Va(x − x0 − L),  x ∈ [L, L + 2x0].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  18  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' LAI AND J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' LU  Therefore, spreading also happens for uσ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' This proves that Σ1 is an open interval (σ∗, ∞) for  some σ∗ ∈ [−∞, ∞).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  If σ∗ = −∞, then there is nothing left to prove.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' If σ∗ ∈ R, then, for any σ > σ∗, spreading  happens for uσ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' for any σ ∈ (−∞, σ∗], the only ω-limit of uσ is Vs, that is, residue happens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  This proves Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  □  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Trichotomy result for large L: Proof of Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  By Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='2 and Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='2, in case L > L∗, any solution of (P) with initial data  satisfying (I) must converges to one element in S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Denote  Σ1 :={σ ∈ R | spreading happens for uσ};' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Σ2 :={σ ∈ R | uσ is a transition solution};' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Σ3 :={σ ∈ R | residue happens for uσ}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  As in the proof of the previous theorem, one can show that Σ1 is a nonempty open interval  (σ∗, ∞) for some σ∗ ∈ [−∞, ∞).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' In what follows we show Σ3 is not empty and so σ∗ ∈ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' The  proof is divided into several steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Step 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' To show Σ3 is not empty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' We will use the the weak upper solution V of (P) constructed  at the end of Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Recall that, for some ε0 > 0,  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='2)  V ≡ 1 + ε0,  x ≤ −L,  and, for some ε ∈ (0, ε0],  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='3)  V (x) − Vs(x) ≥ 3ε,  x ∈ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  By our assumption (I) we see that, when σ ≪ −1, the function φ(x − σ) < V (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Since V is  a weak upper solution, by comparison, any ω-limit of uσ(x, t) = u(x, t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' φ(x − σ)) is less than V ,  which is nothing but Vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' This proves that Σ3 is not empty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Step 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' To show Σ3 is an open set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Assume σ1 ∈ Σ3, we now show that σ2 ∈ Σ3 when  0 < σ2 − σ1 ≪ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  This implies that Σ3 in open.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  For simplicity, denote the corresponding  solutions of (P) with initial data φ(x − σi) by ui (i = 1, 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' By the definition, u1(·, t) converges  as t → ∞ to Vs in the L∞  loc(R) topology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Hence, there exists T > 0 such that  ∥u1(x, t) − Vs(x)∥L∞([−L,L]) ≤ ε,  t ≥ T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  By parabolic estimate, for any ν ∈ (0, 1), we actually have  ∥u1(x, t) − Vs(x)∥C1+ν([−L,L]) ≤ ε1,  t ≥ T,  for some small ε1 > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Taking ε smaller if necessary we see that ε1 is also small and so  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='4)  u1x(L, t) < V′  s(L) + ε1 < 0,  t ≥ T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Moreover, by (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='2) we have  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='5)  ∥u1(x, t) − Vs(x)∥L∞((−∞,L]) ≤ ε,  t ≥ T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Note that this inequality is not necessarily true in J := [L, ∞) since, till now, we have no  monotonicity in this interval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Actually, a solution u can really be not monotonically decreasing  THE EFFECT OF AN UNFAVORABLE REGION  19  in this interval, especially for the spreading and transition solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Nevertheless, we can claim  that u1 is monotonically decreasing for x ≫ 1 and all large t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' This is proved in two claims.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Claim 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' There exists M1 = M1(T) > L + 1 such that u1x(x, T) < 0 for x ≥ M1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  In fact, due to the monotonicity of φ(x − σ1), by using the zero number argument in J we  see that any local maximum points of u1 in J must first arise at x = L and then propagates  rightward to the interior of J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Denote the right-most maximum point by ξ(t), that is,  u1x(ξ(t), t) = 0,  u1x(x, t) < 0 for x > ξ(t), t > T0,  where T0 is the first time when ξ(t) appears in J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Since u1x satisfies a linear parabolic equation,  by a simple estimate for linear equation we can derive that  ξ(t) ≤ M1(T),  t ∈ [T0, T].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  This proves Claim 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Claim 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' There exists M2 > M1 such that u1x(x, t) < 0 for all x ≥ M2, t ≥ T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  In fact, by Claim 1, there exists M2 > M1, such that  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='6)  Vs(x) < ε,  x ≥ M2,  and  u1(x, T) > ˜u1(x, T),  x ∈ [L, M2),  where ˜u1(x, t) := u1(2M2 − x, t) for x ∈ [L, M2], t ≥ T denotes the reflection of u1 with respect  to M2, and so η(x, t) := u1(x, t) − ˜u1(x, t) satisfies  \uf8f1  \uf8f2  \uf8f3  ηt = ηxx + c(x, t)η,  x ∈ [L, M2], t ≥ T,  ηx(L, t) < 0,  η(M2, t) = 0,  t ≥ T,  η(x, T) > 0,  x ∈ [L, M2),  for some bounded function c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' By the maximum principle we have η(x, t) > 0 for all x ∈ [L, M2)  and t ≥ T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' If the right-most maximum ξ(t) of u1 moves to M2 at some time T1 > T, then we  have  η(M2, T1) = 0,  ηx(M2, T1) = 2u1x(M2, T1) = 2u1x(ξ(T1), T1) = 0,  this, however, contradicts the Hopf lemma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Thus ξ(t) will never move rightward through M2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Now using the L∞  loc(R) convergence of u1 to Vs we conclude that, for some large T2 > T1,  ∥u1(x, t) − Vs(x)∥L∞((−∞,M2]) ≤ ε,  t ≥ T2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Consequently, by Claim 2 and (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='6) we have  u1(x, t) ≤ u1(M2, t) ≤ Vs(M2) + ε ≤ 2ε,  x ≥ M2, t ≥ T2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Together with (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='3) we conclude that  u1(x, T2) ≤ V (x) − ε,  x ∈ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  By the continuous dependence of the solution uσ on its initial data φ(x−σ), we see that when  σ2 > σ1 with σ2 − σ1 sufficiently small we have  u2(x, T2) ≤ V (x),  x ∈ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  20  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' LAI AND J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' LU  This indicates that residue happens for u2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' This proves the openness of Σ3 in Step 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Further-  more, by comparison, there exists −∞ < σ∗ ≤ σ∗ such that Σ3 := (−∞, σ∗).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Step 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' To complete the proof of Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' From above we have  Σ1 = (σ∗, ∞),  Σ3 = (−∞, σ∗).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Therefore, Σ2 = [σ∗, σ∗] is a nonempty closed set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  This proves Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  □  References  [1] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Angenent, The zero set of a solution of a parabolic equation, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' reine angew.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=', 390 (1988), 79-96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  [2] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Aronson and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Weinberger, Nonlinear diffusion in population genetics, combustion, and nerve pulse  propagation, Lect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Notes Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=', 446 (1975), 5-49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  [3] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Aronson and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Weinberger, Multidimensional nonlinear diffusion arising in population genetics,  Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=', 30 (1978), 33-76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  [4] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Berestycki and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='-P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Nadal, Self-organised critical hot spots of criminal activity, European J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=',  21 (2010), 371-399.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  [5] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Berestycki, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Rodr´ıguez and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Ryzhik, Traveling wave solutions in a reaction-diffusion model for criminal  activity, Multiscale Model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Simul.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=', 11 (2013), 1097-1126.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  [6] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Chen, A strong unique continuation theorem for parabolic equations, Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Ann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=', 311 (1998), 603-630.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  [7] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Du and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Lou, Spreading and vanishing in nonlinear diffusion problems with free boundaries, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=', 17 (2015), 2673-2724.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  [8] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Du and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Matano, Convergence and sharp thresholds for propagation in nonlinear diffusion problems, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=', 12 (2010), 279-312.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  [9] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Feireisl and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Pol´aˇcik, Structure of periodic solutions and asymptotic behavior for time-periodic reac-  tion–diffusion equations on R, Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Differential Equations, 5 (2000), 583-622.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  [10] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Fife and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' McLeod, The approach of solutions of nonlinear diffusion equations to travelling front  solutions, Arch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Ration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Mech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Anal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=', 65 (1977), 335-361.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  [11] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Lan, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Wei and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Zhang, Long time behaviors of single-species population models with psychological  effect and impulsive toxicant in polluted environments, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' A, 521 (2019), 828-842.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  [12] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Li, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Zhang and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Coffman, Can a barrier zone stop invasion of a population?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=', J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Biol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=', 81  (2020), 1193-1216.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  [13] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Maciel and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Lutscher, Allee effects and population spread in patchy landscapes, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Biol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Dyn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=', 9  (2015), 109-123.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  [14] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Wang, The diffusive logistic equation with a free boundary and sign-changing coefficient, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Differential  Equations, 258 (2015), 1252-1266.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  [15] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Zlatoˇs, Sharp transition between extinction and propagation of reaction, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Amer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=', 19 (2006),  251-263.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content='  [16] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Zaker, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Ketchemen and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Lutscher, The effect of movement behavior on population density in patchy  landscapes, Bull.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=' Biol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
+page_content=', 82 (2020), 1-24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNFJT4oBgHgl3EQfRCwA/content/2301.11493v1.pdf'}
diff --git a/dNFAT4oBgHgl3EQfYx1Q/vector_store/index.faiss b/dNFAT4oBgHgl3EQfYx1Q/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..60b8cd875c6ad4e68aa5ff4f28de601f494e2705
--- /dev/null
+++ b/dNFAT4oBgHgl3EQfYx1Q/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:f5b0a96ba396d5cf077c2c707814f8d26a973ce56768421dc2e38734caa9d1a6
+size 14876717
diff --git a/ddFST4oBgHgl3EQfEzgN/vector_store/index.faiss b/ddFST4oBgHgl3EQfEzgN/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..91454fa28fd51b13ce84393bc1a1b793ce1dc3bc
--- /dev/null
+++ b/ddFST4oBgHgl3EQfEzgN/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:5d5e3e6dd754512939bcf9bd3be4486cd7b7888f4b2aca662f3060d9bf13b997
+size 4063277
diff --git a/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf b/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..cdd13cb70bbf12007fd36eca3145ed7408f7d2a4
--- /dev/null
+++ b/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:3b755a5c91531e8efec1a9d608d826ca2215a20196ffdf1c42390357a24e43c5
+size 576011
diff --git a/dtFJT4oBgHgl3EQf_i1w/vector_store/index.pkl b/dtFJT4oBgHgl3EQf_i1w/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..5040d07842d06c20add9014cf69a6851842d4864
--- /dev/null
+++ b/dtFJT4oBgHgl3EQf_i1w/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:17cd026151e5533368c73e37ad9cc900ae1cf67663c4c49c0dea15ceeff59e0d
+size 150068
diff --git a/eNE1T4oBgHgl3EQfeQRR/vector_store/index.faiss b/eNE1T4oBgHgl3EQfeQRR/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..575b05b3b94d70e135689fd11ddcd4f0e30929c6
--- /dev/null
+++ b/eNE1T4oBgHgl3EQfeQRR/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:59198926e064a4187853c56c9d7f7ff3e645d496be7af95d41bf8b23b30da485
+size 1966125
diff --git a/eNE2T4oBgHgl3EQfbQcn/vector_store/index.faiss b/eNE2T4oBgHgl3EQfbQcn/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..d4d94b4503d426738093017a391f0e48be0a96ae
--- /dev/null
+++ b/eNE2T4oBgHgl3EQfbQcn/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:752e32f2565f957f5eb993116cde555e14bcfd00c0e2d3b890a84f66709f1000
+size 3604525
diff --git a/eNE2T4oBgHgl3EQfbQcn/vector_store/index.pkl b/eNE2T4oBgHgl3EQfbQcn/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..d5e172a1b88d7386f41539c6351e350845135a6e
--- /dev/null
+++ b/eNE2T4oBgHgl3EQfbQcn/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:893e676ca395fd29ac1a253e040ab1ef9a693d5c208f6397e98b89faee4c1b4d
+size 146173
diff --git a/gdE0T4oBgHgl3EQfXgBN/content/2301.02293v1.pdf b/gdE0T4oBgHgl3EQfXgBN/content/2301.02293v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..deed14278516393e49ff6df1c2c0233e019be19e
--- /dev/null
+++ b/gdE0T4oBgHgl3EQfXgBN/content/2301.02293v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:c6a35d86a1a4c90451f73c55199e87a6a66dac8b1390a8fa906691480030cdeb
+size 240290
diff --git a/gdE0T4oBgHgl3EQfXgBN/vector_store/index.faiss b/gdE0T4oBgHgl3EQfXgBN/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..ca00fdf611fa3d0f0c8f81c7f70221b221a64461
--- /dev/null
+++ b/gdE0T4oBgHgl3EQfXgBN/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:fd13e5bc58907dce6a4d573d9eb037e1d518531dcd442916ca87ad22419dcd61
+size 1638445
diff --git a/gdE0T4oBgHgl3EQfXgBN/vector_store/index.pkl b/gdE0T4oBgHgl3EQfXgBN/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..3b83a32d97293b97ef3570a29059f604ccebc899
--- /dev/null
+++ b/gdE0T4oBgHgl3EQfXgBN/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:3d23248a662dfbcd5116b14c64d03ef98026abf27f179671027e50536ae6edb7
+size 54469
diff --git a/htAyT4oBgHgl3EQfXvc6/vector_store/index.faiss b/htAyT4oBgHgl3EQfXvc6/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..1e013902c61a753bd371e87b89be8dad32c045f5
--- /dev/null
+++ b/htAyT4oBgHgl3EQfXvc6/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:cc223588b672f3eeae4bffbb74e7b0ce94674be86734677a5299ad2f866557e5
+size 6357037
diff --git a/idE_T4oBgHgl3EQf4Rxl/vector_store/index.pkl b/idE_T4oBgHgl3EQf4Rxl/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..6aa794e5e9ade00cbb296970e4032e93f959b27c
--- /dev/null
+++ b/idE_T4oBgHgl3EQf4Rxl/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:ee33b38d829f9d479399556df5d1c21dd13c2cb87e8911aa5c6c02ac343a20b0
+size 264616
diff --git a/idFJT4oBgHgl3EQfWizT/vector_store/index.faiss b/idFJT4oBgHgl3EQfWizT/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..4fdd8ffb2bd75377798325ec4f03974e32bec475
--- /dev/null
+++ b/idFJT4oBgHgl3EQfWizT/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:862a0e8764dfc83adbee0950f500981270c8df5e2835d3db0c261c7c9064ea10
+size 2752557
diff --git a/jtFPT4oBgHgl3EQfFzRC/content/tmp_files/2301.13001v1.pdf.txt b/jtFPT4oBgHgl3EQfFzRC/content/tmp_files/2301.13001v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f904f1c8bec7f9cd8cb5bff59bb3553a102ebe50
--- /dev/null
+++ b/jtFPT4oBgHgl3EQfFzRC/content/tmp_files/2301.13001v1.pdf.txt
@@ -0,0 +1,1362 @@
+arXiv:2301.13001v1  [math.CO]  30 Jan 2023
+On the minimum size of linear sets
+Sam Adriaensen
+Vrije Universiteit Brussel
+Paolo Santonastaso
+Universit`a degli Studi della Campania
+“Luigi Vanvitelli”
+Abstract
+Recently, a lower bound was established on the size of linear sets in projective spaces, that
+intersect a hyperplane in a canonical subgeometry. There are several constructions showing
+that this bound is tight. In this paper, we generalize this bound to linear sets meeting some
+subspace π in a canonical subgeometry. We also give constructions of linear sets attaining
+equality in this bound, both in the case that π is a hyperplane, and in the case that π is a
+lower dimensional subspace.
+Keywords: Projective geometry, Linear set, Subgeometry.
+MSC2020: 51E20, 05B25.
+1
+Introduction
+Linear sets are certain point sets in projective spaces, generalizing the notion of a subgeometry.
+They have proven themselves to be very useful in constructing interesting objects in projective
+spaces, such as blocking sets [26] and KM-arcs [9], and have been used to construct Hamming
+and rank metric codes [1, 18, 20, 23–25, 27]. For a survey on linear sets, we refer the reader to
+[13,19].
+Given the usefulness of linear sets, their recent spurt in popularity within the field of finite
+geometry is far from surprising. One of the most natural questions arising in the study of linear
+sets is establishing lower and upper bounds on their size. There is a quite trivial upper bound
+on the size of linear sets, and the study of linear sets attaining equality in this bound can be
+traced back to a paper by Blokhuis and Lavrauw [5]. However, finding good lower bounds on
+the size of linear sets seems to be a harder problem. Yet it is an interesting endeavor, e.g. due
+to its connection with the weight distribution of linear rank metric codes [21].
+As a consequence of the celebrated result on the number of directions determined by a
+function over finite field [2, 4], Bonoli and Polverino established a lower bound on the size of
+certain linear sets on a projective line. More specifically, they proved the following result (for
+the definitions, we refer to Section 2).
+Result 1.1 ([6, Lemma 2.2]). If LU is an Fq-linear set of rank n on PG(1, qn), and LU contains
+at least one point of weight 1, then |LU| ≥ qn−1 + 1.
+De Beule and Van de Voorde managed to remove the condition on the rank from this bound.
+We note that linear sets of rank greater than n on PG(1, qn) are not interesting to study, since
+they necessarily contain all the points of the projective line. Hence it is natural to limit the
+study to linear sets whose rank is at most n.
+Result 1.2 ([8, Theorem 1.2]). If LU is an Fq-linear set of rank k, with 1 < k ≤ n on PG(1, qn),
+and LU contains at least one point of weight 1, then |LU| ≥ qk−1 + 1.
+Using an inductive argument, they obtained a bound on the size of a linear set in a higher
+dimensional projective space.
+Using Lemma 3.2, which we prove later in this paper, this is
+equivalent to the following result.
+1
+
+Result 1.3 ([8, Theorem 4.4]). Let LU be an Fq-linear set of rank k > d in PG(d, qn). If LU
+meets some hyperplane Ω in a canonical Fq-subgeometry of Ω, then
+|LU| ≥ qk−1 + qk−2 + . . . + qk−d + 1.
+De Beule and Van de Voorde note directly after their statement of the above result that they
+would like to find lower bounds on linear sets satisfying less restrictive conditions. Furthermore,
+Jena and Van de Voorde [11, §2.5 (B)] state that they believe the above lower bound to hold for
+all Fq-linear sets of rank k that span PG(d, qn), if n is prime and k ≤ d + n.
+In this article we will generalize the above result by dropping the condition that Ω is a
+hyperplane.
+Theorem 1.4. Let LU be an Fq-linear set of rank k in PG(d, qn). Suppose that there exists
+some (r − 1)-space Ω, with r < k, such that LU meets Ω in a canonical Fq-subgeometry of Ω.
+Then
+|LU| ≥ qk−1 + . . . + qk−r + IΩ,
+where IΩ denotes the number of r-spaces through Ω, containing a point of LU \ Ω.
+This yields the following recursive lower bound on the size of a linear set.
+Theorem 1.5. Let Bq,n(r, k, d) denote the minimum size of an Fq-linear set of rank k that spans
+PG(d, qn) and intersects an (r − 1)-space in a canonical subgeometry. Then
+Bq,n(r, k, d) ≥
+�
+qk−1 + Bq,n(r − 1, k − 1, d − 1)
+if r > 0,
+qk−⌊
+k
+d+1⌋ + Bq,n
+�
+0, k −
+�
+k
+d+1
+�
+, d − 1
+�
+if r = 0.
+Note in particular that for the linear set LU in Theorem 1.4, this implies that
+|LU| ≥ qk−1 + . . . + qk−r + qk−r−⌊
+k−r
+d−r+1⌋ + Bq,n
+�
+0, k − r −
+�
+k − r
+d − r + 1
+�
+, d − r − 1
+�
+.
+In PG(1, qn), the bound of De Beule and Van de Voorde is tight. For every rank k ≤ n, there
+exist so-called (k − 1)-clubs of rank k. These linear sets contain (an abundance of) points of
+weight 1, and their size matches the bound in Result 1.2. Lunardon and Polverino [15] provided
+the first less trivial family of linear sets of rank n reaching equality in Result 1.1. Their example
+was extended by Jena and Van de Voorde [11] to a very large family of linear sets of general
+rank, attaining equality in Result 1.2. More recently, there have been other constructions of such
+linear sets, and partial classification results, see Napolitano et al. [16]. Moreover, Jena and Van
+de Voorde generalized their constructions to higher dimensions, to obtain linear sets attaining
+equality in the bound of Result 1.3, some of which also satisfy the conditions of Result 1.3
+[11, §2.5 (B)].
+In this article, we study the construction by Jena and Van de Voorde in general dimension,
+and we provide a sufficient condition for these linear sets to satisfy the hypothesis of Result 1.3.
+We also generalize the construction of Napolitano et al. to higher dimensions. Furthermore,
+we construct linear sets in PG(d, qn) satisfying the conditions of Theorem 1.4, and attaining
+equality in the corresponding bound, where n is not prime.
+The size of these linear sets is
+smaller than the bound from Result 1.3, hence this illustrates the necessity of the conditions
+imposed in Result 1.3 in case n is not prime.
+Structure of the paper. Section 2 contains preliminary results on linear sets. Section 3
+contains the proof of Theorems 1.4 and 1.5. We also discuss some sufficient conditions on linear
+sets for the hypothesis of Result 1.3 to hold. In addition, we deduce from Theorem 1.4 that the
+rank of a linear set is determined by its size and the minimum weight of its points, and that
+it is spanned by its points of minimum weight. In Section 4 we discuss linear sets attaining
+2
+
+equality in Result 1.3. More specifically, we show a sufficient condition for the minimum size
+linear sets of [11] to satisfy the hypothesis of Result 1.3, and we generalize the construction from
+[16] to higher dimension. Section 5 contains constructions of linear sets attaining equality in
+Theorem 1.4. Finally, Section 6 contains some concluding remarks.
+2
+Preliminaries
+Throughout this article, q will always denote a prime power, and Fq will denote the finite field
+of order q. The d-dimensional projective space over Fq will be denoted by PG(d, q).
+If the
+projective space is constructed from a (d + 1)-dimensional Fq-vector space V , and we want to
+emphasize the underlying vector space, we might also denote the projective space as PG(V, Fq).
+We note that the number of points in PG(d, q) equals qd+1−1
+q−1
+= qd + qd−1 + . . . + q + 1.
+Notation 2.1. Throughout the article, when working in PG(d, q) = PG(Fd+1
+q
+, Fq), we denote
+the vectors of Fd+1
+q
+as (x0, . . . , xd), i.e. we label the coordinate positions from 0 to d. The ith
+standard basis vector will be denoted as
+ei = (0, . . . , 0,
+1
+����
+ith position
+, 0 . . . , 0),
+and the corresponding point in PG(d, q) will be denoted as Ei.
+2.1
+Linear sets
+Let V be a (d + 1)-dimensional vector space over Fqn. Then V is also a (d + 1)n-dimensional
+vector space over Fq. Let U denote an Fq-subspace of V . Then
+LU = {⟨u⟩Fqn : u ∈ U \ {0}}
+is a set of points in PG(d, qn). Sets of this type are called Fq-linear sets, and the Fq-dimension
+of U is called the rank of LU.
+We note that if U1 and U2 are Fq-subspaces, and LU1 and LU2 are equal as point set in
+PG(d, qn), this need not imply that dimFq U1 = dimFq U2. Hence, the rank of a linear set LU
+is generally not unambiguously defined by LU as point set in PG(d, qn), without taking into
+account the underlying subspace U.
+Given an Fqn-subspace W ≤ V , we define the weight of Ω = PG(W, Fqn) to be
+wLU (Ω) = dimFq(U ∩ W).
+Note that wLU (Ω) equals the rank of the linear set LU∩W = LU ∩ Ω.
+For each i ∈ {1, . . . , n}, let Ni(LU) denote the number of points in PG(d, qn) of weight i.
+We will simply denote this as Ni if LU is clear from context. The numbers N1, . . . , Nn are called
+the weight distribution of LU. In addition, the weight spectrum of LU is the vector (i1, . . . , it)
+with i1 ≤ . . . ≤ it and
+{i1, . . . , it} = {wLU(P) : P ∈ LU} = {i ∈ {1, . . . , n} : Ni > 0}.
+Let k > 0 denote the rank of LU. Then the weight distribution satisfies the following properties.
+|LU| = N1 + . . . + Nn,
+(1)
+n
+�
+i=1
+Ni
+qi − 1
+q − 1 = qk − 1
+q − 1 ,
+(2)
+3
+
+|LU| ≤ qk − 1
+q − 1 ,
+(3)
+|LU| ≡ 1 (mod q).
+(4)
+Let T be an Fq-subspace of V with dimFq(T) = r ≤ d + 1.
+If dimFqn(⟨T⟩Fqn) = r, we
+will say that LT ∼= PG(T, Fq) = PG(r − 1, q) is an Fq-subgeometry of PG(V, Fqn) and r is the
+rank of the subgeometry LT. When r = d + 1, we say that LT is a canonical subgeometry of
+PG(V, Fqn) = PG(d, qn). Note that each point of a subgeometry LT has weight 1 and hence
+|LT | = qr−1
+q−1 , if LT has rank r.
+Regarding the linearity of a linear set, we recall these definitions explored in [12].
+Definition 2.2 ([12, Definitions 1.1, 1.2]). An Fq-linear set LU is an Fqs-linear set if U is also
+an Fqs-vector space. We say that Fqs is the maximum field of linearity of LU if s is the largest
+exponent such that LU is Fqs-linear.
+Definition 2.3 ([12, Definitions 1.3, 1.4]). An Fq-linear set LU has geometric field of linearity
+Fqs if there exists an Fqs-linear set LU′ such that LU = LU′. An Fq-linear set LU has maximum
+geometric field of linearity Fqs if s is the largest integer such that LU has geometric field of
+linearity Fqs.
+The maximum field of linearity and the maximum geometric field of linearity do not always
+coincide. Clearly if LU is an Fqs-linear set, it has geometric field of linearity Fqs, but the converse
+need not hold, see e.g. [12, Example 1.5].
+Remark 2.4. Note that if there exists a line ℓ that is (q + 1)-secant to a linear set LU, then by
+(4) LU has maximum geometric field of linearity Fq, see also [12].
+We refer to [19] and [13] for comprehensive references on linear sets.
+2.2
+Subspaces of complementary weights
+Recently, there has been an interest in linear sets admitting subspaces of complementary weights
+(see below for the definition), due to their application in coding theory, see e.g. [18,20,28]. Linear
+sets on the projective line admitting two points of complementary weights have been studied in
+[17] (see also [12,16]). The higher dimensional analogue has been studied in [28]. For the sake
+of completeness, we state the definition and prove the structural description of such linear sets
+here in full generality.
+Call subspaces W1, . . . , Wm ≤qn Fd+1
+qn
+independent if each subspace Wi intersects ⟨Wj : j ̸=
+i⟩Fqn trivially, or equivalently if dimFqn⟨Wi : i = 1, . . . , m⟩ = dimFqn W1 + . . . + dimFqn Wm.
+Lemma 2.5. Let W1, . . . , Wm be independent subspaces in Fd+1
+qn , and let LU be an Fq-linear set
+in PG(d, qn) of rank k, that spans the entire space. Then
+wLU (PG(W1, Fqn)) + . . . + wLU (PG(Wm, Fqn)) ≤ k.
+If equality holds, then Fd+1
+qn
+= W1 ⊕ . . . ⊕ Wm.
+Proof. Since no Wi intersects the span of the others, it is permitted to consider the direct sum
+W1 ⊕ . . . ⊕ Wm. Then
+k = dimFq U ≥ dimFq(U ∩ (W1 ⊕ . . . ⊕ Wm)) ≥ dimFq(U ∩ W1) + . . . + dimFq(U ∩ Wm)
+= wLU(PG(W1, Fqn)) + . . . + wLU(PG(Wm, Fqn))
+If equality holds, then
+U ∩ (W1 ⊕ . . . ⊕ Wm) = U.
+Since W1 ⊕ . . . ⊕ Wm is an Fqn-subspace, and ⟨U⟩Fqn = Fd+1
+qn , we get that
+W1 ⊕ . . . ⊕ Wm = Fd+1
+qn .
+4
+
+Definition 2.6. If the subspaces W1, . . . , Wm attain equality in Lemma 2.5, we say that
+PG(W1, Fqn), . . . , PG(Wm, Fqn) are subspaces of complementary weight (w.r.t. LU).
+Lemma 2.7. Let LU be an Fq-linear set spanning PG(d, qn).
+Then there exist subspaces
+Ω1, . . . , Ωm in PG(d, qn) of complementary weight, with dim Ωi = di and wLU (Ωi) = ki, if
+and only if U is GL(d + 1, qn)-equivalent to an Fq-subspace U1 × . . . × Um, with each Ui a
+ki-dimensional Fq-subspace of Fdi+1
+qn
+satisfying ⟨Ui⟩Fqn = Fdi+1
+qn
+.
+Proof. First suppose that such subspaces Ωi = PG(Wi, Fqn) exist. Then there exists a map
+ϕ ∈ GL(d + 1, qn) such that ϕ(W1) = ⟨e0, . . . , ed1⟩Fqn, ϕ(W2) = ⟨ed1+1, . . . , ed1+d2+1⟩Fqn, and so
+on. As can be seen in the proof of the previous lemma,
+ϕ(U) = ϕ(U ∩ W1) ⊕ . . . ⊕ ϕ(U ∩ Wm),
+which equals U1 × . . . × Um, with
+Ui = {u ∈ Fdi+1
+qn
+: (0, . . . , 0, u, 0, . . . , 0) ∈ ϕ(U) ∩ ϕ(Wi)}.
+Clearly,
+dimFq Ui = dimFq ϕ(U ∩ Wi) = dimFq U ∩ Wi = wLU(Ωi) = ki.
+Vice versa, suppose that ϕ(U) = U1 ×. . .×Um, with each Ui a ki-dimensional Fq-subspace of
+Fdi+1
+qn
+, for some ϕ ∈ GL(d+1, qn). Then define W1 = ⟨e0, . . . , ed1⟩Fqn, W2 = ⟨ed1+1, . . . , ed1+d2+1⟩Fqn,
+and so on. Then clearly PG(W1, Fqn), . . . , PG(Wm, Fqn) are subspaces of complementary weights
+w.r.t. LU. Having subspaces of complementary weights is GL(d+1, qn)-invariant, which finishes
+the proof.
+3
+General bounds
+This section is devoted to prove Theorem 1.4. Afterwards, we provide some sufficient conditions
+on linear sets for the hypothesis of Result 1.3 to hold. Lastly, from Theorem 1.4 we derive that
+if a linear set LU contains a point of weight 1, its rank equals ⌈logq(|LU|)⌉, and ⟨LU⟩ is spanned
+by the points of LU of weight 1.
+3.1
+Proof of Theorems 1.4 and 1.5
+De Beule and Van de Voorde proved the following bound.
+Result 3.1 ([8, Theorem 4.4]). Let LU be an Fq-linear set spanning PG(d, qn) of rank k. Suppose
+that LU meets some hyperplane Ω in exactly qd−1
+q−1 points, spanning Ω. Then
+|LU| ≥ qk−1 + qk−2 + . . . + qk−d + 1.
+Note that if d = 1, this result is exactly Result 1.2.
+We now prove that this result is
+equivalent to Result 1.3. This follows directly from the following lemma.
+Lemma 3.2. Let LU be an Fq-linear set in PG(d − 1, qn), with d ≥ 2. Then LU spans PG(d −
+1, qn) and satisfies |LU| = qd−1
+q−1 if and only if LU is a canonical Fq-subgeometry.
+Proof. If LU is a canonical subgeometry, then it immediately follows that LU spans the entire
+space, and |LU| = qd−1
+q−1 . So suppose that LU spans the space, and that |LU| = qd−1
+q−1 . We need
+to prove that all points of LU have weight 1. Indeed in that case, by equations (1) and (2), LU
+must then have rank d, which proves that LU is a canonical subgeometry. So suppose by way
+5
+
+of contradiction that LU has points of weight greater than 1. Note that by Equations (1) and
+(2), the rank of LU is some number k > d. Let
+σ = ⟨P ∈ LU : wLU(P) > 1⟩
+denote the subspace of PG(d − 1, qn) spanned by points of weight greater than 1.
+Suppose that σ is not PG(d − 1, qn). Then LU ̸⊆ σ, and every point in LU \ σ is a point of
+weight 1. Hence, there are at least qk−1 points in LU \ σ corresponding to (necessarily distinct)
+points of weight 1 of LU. Thus, |LU| > qk−1 > qd−1
+q−1 since k > d, a contradiction.
+Hence σ equals PG(d − 1, qn). Let
+m = max
+P ∈LU wLU(P)
+denote the maximum weight of the points of LU. Then we can choose d independent points
+P1, . . . , Pd in LU such that wLU(P1) = m, and wLU(Pi) ≥ 2 for each i. By Lemma 2.5,
+k ≥
+d
+�
+i=1
+wLU(Pi) ≥ m + 2(d − 1).
+Let N1, . . . , Nm denote the weight distribution of LU. Then by Equations (1) and (2),
+qm − 1
+q − 1 |LU| =
+m
+�
+i=1
+Ni
+qm − 1
+q − 1 ≥
+m
+�
+i=1
+Ni
+qi − 1
+q − 1 = qk − 1
+q − 1 ≥ qm+2(d−1) − 1
+q − 1
+.
+This implies that
+qd − 1
+q − 1 = |LU| ≥ qm+2(d−1) − 1
+qm − 1
+,
+which yields a contradiction if d ≥ 2.
+We will now prove Theorem 1.4.
+Proof of Theorem 1.4. Consider the r-spaces Π1, Π2, . . . of PG(d, qn) through Ω = PG(W, Fqn),
+with Πi = PG(Wi, Fqn), for each i. We can order the r-spaces in such a way that Πi contains a
+point of LU \ Ω if and only if i ≤ IΩ. Let
+ki = dimFq(U ∩ Wi)
+denote the rank of the Fq-linear set LU∩Wi. Then the sets Wi ∩ U \ W partition the vectors in
+U \ W. Since LU intersects Ω in a canonical subgeometry, dimFq W = r. This yields
+qk − qr =
+IΩ
+�
+i=1
+(qki − qr)
+=⇒
+qk−r = 1 +
+IΩ
+�
+i=1
+(qki−r − 1).
+(5)
+Analogously, the points of Πi \ Ω partition the points of LU \ Ω. Note that for i ≤ IΩ, we
+have that LU ∩ Πi = LU∩Wi is an Fq-linear set in Πi of rank ki, satisfying the hypothesis of
+Result 1.3. Hence,
+|LU| = |LU ∩ Ω| +
+IΩ
+�
+i=1
+(|LU ∩ Πi| − |LU ∩ Ω|)
+≥ qr − 1
+q − 1 +
+IΩ
+�
+i=1
+�
+(qki−1 + . . . + qki−r + 1) − qr − 1
+q − 1
+�
+6
+
+= qr − 1
+q − 1 +
+IΩ
+�
+i=1
+�
+qki−r qr − 1
+q − 1 − qr − 1
+q − 1 + 1
+�
+= qr − 1
+q − 1
+�
+1 +
+IΩ
+�
+i=1
+(qki−r − 1)
+�
++ IΩ.
+Using Equation (5) this implies that
+|LU| ≥ qr − 1
+q − 1 qk−r + IΩ = qk−1 + qk−2 + . . . + qk−r + IΩ.
+Remark 3.3. If one wants to apply Theorem 1.4 to a particular linear set LU, different choices
+of the (r − 1)-space Ω can yield different bounds. In other words, IΩ need not be the same for
+all (r − 1)-spaces meeting LU in a canonical Fq-subgeometry. This is illustrated in the example
+below.
+Example 3.4. Consider the (n + 1)-dimensional Fq-subspace
+U = {(x, xq) : x ∈ Fqn} × Fq
+of F3
+qn. Consider the corresponding Fq-linear set LU of rank n + 1 in PG(2, qn). Every point of
+LU has weight 1, so we can apply Theorem 1.4 with Ω any point of LU. However, for a point
+P ∈ LU, IP = qn−1 + 1 if P lies on the line X2 = 0, and IP = qn−1
+q−1 if P does not lie on X2 = 0.
+These numbers are distinct if n > 2.
+We also remark that in Theorem 1.4 the number IΩ of r-spaces through Ω containing a point
+of LU \ Ω equals the size of a certain linear set.
+Definition 3.5. Consider an Fq-linear set LU in PG(V, Fqn) and a subspace Ω = PG(W, Fqn).
+Let U denote the subspace (U + W)/W of the quotient space V/W. Then the projection of LU
+from Ω is the Fq-linear set LU of PG(V/W, Fqn).
+Lemma 3.6. Suppose that LU is an Fq-linear set of rank k in PG(V, Fqn) and let LU be the
+projection of LU from an (r − 1)-space Ω = PG(W, Fqn). Then for each Fqn-subspace W ′ ≤ V
+through W,
+wLU (PG((W ′ + W)/W, Fqn)) = wLU(PG(W ′, Fqn)) − wLU (Ω).
+In particular, LU has rank k − wLU (Ω), and |LU| equals the number of r-spaces in PG(V, Fqn)
+through Ω that contain a point of LU \ Ω. Furthermore, if LU spans PG(V, Fqn), then LU spans
+PG(V/W, Fqn).
+Proof. We can find Fq-subspaces U1, U2, U3 of U such that
+U1 = W ∩ U,
+U1 ⊕ U2 = W ′ ∩ U,
+U1 ⊕ U2 ⊕ U3 = U.
+Then
+wLU (PG((W ′ + W)/W, Fqn)) = dimFq(U ∩ ((W ′ + W)/W)) = dimFq(⟨U, W⟩Fq ∩ W ′) − dimFq W
+= dimFq(W ⊕ U2) − dimFq(W) = dimFq(U2)
+= dimFq(U1 ⊕ U2) − dimFq(U1) = wLU(PG(W ′, Fqn)) − wLU(Ω).
+If we put W ′ = V , we see that LU has rank k − wLU(Ω). It also follows that the points of LU
+are in 1-1 correspondence with the (r + 1)-spaces W ′ of V with wLU(PG(W, Fqn)) > wLU(Ω),
+which are exactly the r-spaces through Ω in PG(V, Fqn) containing a point of LU \ Ω.
+7
+
+This tells us the following about the quantity IΩ in Theorem 1.4.
+Proposition 3.7. In the hypothesis of Theorem 1.4, let LU be the projection of LU from Ω.
+Then
+|LU| ≥ qk−1 + qk−2 + . . . + qk−r + |LU|.
+Moreover, LU has rank k − r.
+Together with the following lemma, we can now prove Theorem 1.5.
+Lemma 3.8. Suppose that LU is an Fq-linear set of rank k of PG(n, q). Let m = min{wLU (P) :
+P ∈ LU} denote the minimum weight of the points of LU. Then there exists an Fq-linear set
+LU′ of rank k − m + 1 in PG(n, q) containing points of weight 1 such that LU and LU′ coincide
+as point sets.
+Proof. Take a vector u ∈ U such that P = ⟨u⟩Fqn has weight m in LU. Then there exists a
+(k − m + 1)-dimensional Fq-subspace U ′ of U that intersects ⟨u⟩Fqn in a 1-dimensional subspace.
+Then wLU′(P) = 1. It remains to show that LU and LU′ coincide as points sets. The inclusion
+LU′ ⊆ LU is evident. On the other hand, take a non-zero v ∈ U. Then, by Grassmann’s identity
+wLU′(⟨v⟩Fqn ) = dimFq(⟨v⟩Fqn ∩ U ′) = dimFq((⟨v⟩Fqn ∩ U) ∩ U ′)
+= dimFq(⟨v⟩Fqn ∩ U) + dimFq(U ′) − dimFq(⟨⟨v⟩Fqn ∩ U, U ′⟩Fq)
+≥ m + (k − m + 1) − dimFq(U) = 1.
+This shows that LU ⊆ LU′. Thus, LU and LU′ coincide as point sets.
+Proof of Theorem 1.5.
+Let LU be an Fq-linear set spanning PG(d, qn) and intersecting an
+(r − 1)-space PG(W, Fqn) in a canonical Fq-subgeometry. If r > 0, then LU contains a point
+P = ⟨u⟩Fqn ∈ PG(W, Fqn) of weight 1. By Proposition 3.7,
+|LU| ≥ qk−1 + |LU|,
+where LU is the projection of LU from P. Then LU is an Fq-linear set of rank k − 1 spanning
+PG(d − 1, qn). Furthermore, W + ⟨u⟩Fqn is an (r − 2)-space in the quotient space, containing
+points of complementary weights, all weights equal to 1. Hence, it intersects LU in a canonical
+Fq-subgeometry. This proves that Bq,n(r, k, d) ≥ qk−1 + Bq,n(r − 1, k − 1, d − 1) if r > 0.
+Now suppose that r = 0. Then the minimum of the minimum weight of the points of LU,
+which we will denote by m, is at least 2. By Lemma 3.8, |LU| ≥ Bq,n(1, k − m + 1, d). Since this
+lower bound on |LU| is decreasing in m, we need to find an upper bound on m. There are d + 1
+independent points in LU, since LU spans PG(d, qn). Lemma 2.5 then tells us that m(d+1) ≤ k,
+which implies
+m ≤
+�
+k
+d + 1
+�
+.
+Hence,
+|LU| ≥ Bq,n
+�
+1, k −
+�
+k
+d + 1
+�
++ 1, d
+�
+≥ qk−⌊
+k
+d+1⌋ + Bq,n
+�
+0, k −
+�
+k
+d + 1
+�
+, d − 1
+�
+.
+In the next sections, we will investigate linear sets attaining equality in the bound of Theo-
+rem 1.4. To this end, we introduce some relevant terminology.
+Definition 3.9. Let LU be an Fq-linear set of rank k in PG(d, qn). If
+|LU| = qk−1 + . . . + qk−d + 1,
+8
+
+we say that LU is of d-minimum size. If there is some (r−1)-space Ω such that LU and Ω satisfy
+the hypothesis of Theorem 1.4, and
+|LU| = qk−1 + . . . + qk−r + IΩ ≤ qk−1 + . . . + qk−d + 1,
+then we say that LU is of (r, d, Ω)-minimum size, or simply of (r, d)-minimum size. A linear set
+of (d, d)-minimum size, will also be called of proper d-minimum size.
+Remark 3.10. By Remark 2.4, an (r, d)-minimum size linear set has maximum field of linearity
+Fq whenever r ≥ 2.
+In the next proposition, we also prove that if a linear set is of (r, d)-minimum size, it is of
+(r′, d)-minimum size for every r′ ≤ r.
+Proposition 3.11. Let LU be an (r, d)-minimum size Fq-linear set of rank k in PG(d, qn). Then
+LU is of (r′, d)-minimum size as well, for every 0 < r′ ≤ r.
+Proof. It is enough to prove the statement for r′ = r − 1. By hypothesis, we know that there is
+some (r − 1)-space Ω = PG(W, Fqn) of PG(d, qn) meeting LU in a canonical subgeometry, such
+that
+|LU| = qk−1 + qk−2 + . . . + qk−r + |LU|,
+(6)
+where LU is the Fq-linear set in PG(V/W, Fqn) = PG(d − r, qn) defined by U = U + W ⊆ V/W.
+Let Ω′ = PG(W ′, Fqn) be an (r − 2)-space of Ω that meets LU in a canonical subgeometry. So,
+by Proposition 3.7, we have that
+|LU| ≥ qk−1 + qk−2 + . . . + qk−r+1 + |LU′|,
+(7)
+where LU′ is the Fq-linear set of rank k − r + 1 in PG(V/W ′, Fqn) = PG(d − r + 1, qn) defined
+by U ′ = U + W ′ ⊆ V/W ′. Therefore, by (6), it follows qk−r + |LU| ≥ |LU′|. On the other hand,
+since wLU(Ω) = r, we get wLU′(PG(W/W ′, Fqn)) = 1 and so LU′ has a point of weight 1. Now,
+by Proposition 3.7, we get that
+|LU′| ≥ qk−r +
+���LU′
+���
+with U ′ = U/W ′ + W/W ′ ≤ (V/W ′)/W, which is equal to U = U + W ≤ V/W. Hence,
+|LU′| ≥ qk−r + |LU|.
+Then, by (6), equality holds in (7) and so LU is of (r − 1, d, Ω′)-minimum size.
+3.2
+Sufficient conditions to apply Result 1.3
+In this part of the section, we show some conditions on a linear set that ensure the existence of
+at least one hyperplane meeting the linear set in a canonical subgeometry.
+Theorem 3.12. Let k, d and r be non negative integers with r < k, d. Let LU be an Fq-linear
+set in PG(d, qn) of rank k + d − r spanning PG(d, qn). Suppose that there is an r-space Ω of
+PG(d, qn) such that wLU(Ω) = k, and Ω contains an (r−1)-space Ω′ that meets LU in a canonical
+Fq-subgeometry. Then some hyperplane Π of PG(d, qn) meets LU in a canonical Fq-subgeometry,
+implying |LU| ≥ qk+d−r−1 + qk+d−r−2 + . . . + qk−r + 1.
+Proof. Suppose that PG(d, qn) = PG(V, Fqn), Ω = PG(W, Fqn), and Ω′ = PG(W ′, Fqn). Con-
+sider the projection of LU from Ω′, which equals the linear set LU, with U = U + W ′ ⊆ V/W ′.
+Write P0 = W/W ′, and choose any point P1 ∈ LU \ {P0}. Since LU spans PG(d, qn), we can ex-
+tend P0, P1 to a subset P0, P1, . . . , Pd−r of LU that spans PG(V/W ′, Fqn). Also, wLU(P0) = k−r,
+and the rank of LU equals k + d − 2r = (k − r) + (d − r). Hence, by Lemma 2.5,
+(k − r) + (d − r) ≥
+d−r
+�
+i=0
+wLU (Pi) = (k − r) +
+d−r
+�
+i=1
+wLU (Pi),
+9
+
+which implies that wLU(Pi) = 1 for all i ≥ 1, and P0, . . . , Pd−r are points of complementary
+weights. Therefore, LU meets ⟨P1, . . . , Pd−r⟩ in a canonical subgeometry. There is a unique
+Fqn-space W ′′ through W ′ such that ⟨P1, . . . , Pd−r⟩ = PG(W ′′ + W ′, Fqn).
+It follows that
+PG(W ′′, Fqn) meets LU in a canonical subgeometry.
+For linear sets on a projective line PG(1, qn) of rank n, the notion of maximum field of
+linearity and maximum geometric field of linearity coincide.
+Result 3.13 ([7, Proposition 2.3] [12, Proposition 1.10]). Let LU be an Fq-linear set on PG(1, qn)
+of rank n. Define s = minP ∈LU wLU (P). Then the maximum field of linearity and the maximum
+geometric field of linearity are both Fqs.
+In particular, when n is prime, the above result implies the existence of a point of weight 1.
+Corollary 3.14. Assume that n is prime and d ≥ 2. Let LU be an Fq-linear set in PG(d, qn)
+of rank n + d − 1 spanning PG(d, qn). Suppose that there is a line ℓ of PG(d, qn) such that
+wLU (ℓ) = n. Then |LU| ≥ qn+d−2 + qn+d−3 + . . . + qn−1 + 1.
+Proof. On the one hand, n is prime, so the maximum field of linearity of LU ∩ ℓ is Fq. On the
+other hand, wLU (ℓ) = n and by Result 3.13, the maximum field of linearity of LU ∩ ℓ is Fqs with
+s = minP ∈LU∩ℓ wLU(P). Hence,
+min
+P ∈LU∩ℓ wLU (P) = 1,
+and ℓ contains a point of weight 1. The statement now follows from Theorem 3.12.
+Also when n is a prime and the rank of the linear set is n+d−1, in order to have the bound
+from Result 1.3, it is enough to impose the existence of a (d − 2)-space meeting the linear set in
+a canonical subgeometry of this space.
+Corollary 3.15. Assume that n is prime and d ≥ 2. Let LU be an Fq-linear set in PG(d, qn) of
+rank k = n+d−1 spanning PG(d, qn). Suppose that some (d−2)-space meets LU in a canonical
+subgeometry. Then |LU| ≥ qk−1 + qk−2 + . . . + qk−d + 1.
+Proof. Let Ω = PG(W, Fqn) be the (d − 2)-space of PG(d, qn) meeting LU in a canonical subge-
+ometry. By Proposition 3.7, we know that
+|LU| ≥ qk−1 + qk−2 + . . . + qk−d+1 + |LU|,
+where U = U + W is an Fq-subspace of the quotient V/W. Since LU has rank n + d − 1 and
+dimFq(U ∩ W) = d − 1, then LU is an Fq-linear set of rank n in PG(1, qn) spanning the whole
+line. Therefore, since n is a prime, by Result 3.13 it follows that LU has at least one point of
+weight 1 and so |LU| ≥ qn−1 + 1 and the assertion follows.
+3.3
+Consequences of Theorem 1.4
+When r = 1, Theorem 1.4 looks as follows.
+Corollary 3.16. Let LU be an Fq-linear set of rank k ≥ 2 in PG(d, qn), admitting at least one
+point of weight 1. Let I be the number of secant lines through some point of weight 1. Then
+|LU| ≥ qk−1 + I.
+In particular, this result implies that the rank of a linear set is determined by its size and
+the minimum weight of its points.
+10
+
+Proposition 3.17. Let LU be an Fq-linear set spanning PG(d, qn), containing more than one
+point. Denote m = minP ∈LU wLU(P). Then the rank of LU is the unique integer k satisfying
+qk−m + Bq,n(0, k − m, d − 1) ≤ |LU| ≤ qk − 1
+qm − 1,
+i.e. k = ⌈logq(|LU|)⌉ + m − 1 = ⌊logq(|LU|)⌋ + m.
+Proof. As in the proof of Theorem 1.5, we have that |LU| ≥ Bq,n(1, k − m + 1, d) ≥ qk−m +
+Bq,n(0, k − m, d − 1). The lower bound follows from Lemma 3.8 and Corollary 3.16. By Equa-
+tion (2),
+(qm − 1)|LU| = (qm − 1)
+n
+�
+i=m
+Ni ≤
+n
+�
+i=m
+Ni(qi − 1) = qk − 1.
+Another consequence of Corollary 3.16 is that any Fq-linear set is spanned by its points of
+minimum weight, (cf. [6, Lemma 2.2] for linear sets on PG(1, qn)).
+Proposition 3.18. If an Fq-linear LU spans PG(d, qn), then its points of minimum weight also
+span PG(d, qn).
+Proof. Suppose that LU is an Fq-linear set of rank k, spanning PG(d, qn), and denote m =
+minP ∈LU wLU (P). By Corollary 3.16, |LU| > qk−m. Now assume that the points of weight m
+of LU lie in a hyperplane π = PG(W, Fqn) of PG(d, qn). Suppose that U1 = U ∩ W. Then
+there exits a subspace U2 of U such that U = U1 ⊕ U2. Now let U ′
+1 be an Fq-subspace of U1 of
+codimension m − 1, and let U ′
+2 be an Fq-subspace of U2 of codimension 1. Let U ′ = U ′
+1 ⊕ U ′
+2,
+then LU′ and LU coincide as point sets. Indeed, if P ∈ LU ∩ π, then wLU (P) = wLU1(P) ≥ m.
+As in the proof of Lemma 3.8, this implies that wLU′(P) = wLU′
+1(P) ≥ 1. If P ∈ LU \ π, then
+wLU (P) ≥ m + 1, and as in the proof of Lemma 3.8, wLU′(P) ≥ 1. But
+dimq U ′ = (dimq U1 − (m − 1)) + (dimq U2 − 1) = k − m.
+Hence, by Equation (3), |LU| = |LU′| ≤ qk−m−1
+q−1
+< qk−m, a contradiction.
+4
+Constructions of d-minimum size linear sets
+4.1
+Exploring the Jena-Van de Voorde construction
+Recently, Jena and Van de Voorde constructed d-minimum size linear sets admitting points
+of complementary weights, and they completely determined their weight spectrum and weight
+distribution. Recall that if λ ∈ Fqn, then the degree of λ over Fq equals the degree of the minimal
+polynomial of λ over Fq, or equivalently the smallest integer t such that λ ∈ Fqt.
+Construction 4.1 ([11, Theorem 2.17]). Suppose that λ ∈ Fqn has degree t > 1 over Fq. Choose
+positive integers k0 ≥ . . . ≥ kd such that k0 + k1 ≤ t + 1. Define
+JVq,n(λ, t; k0, . . . , kd) = ⟨1, λ, . . . , λk0−1⟩Fq × . . . × ⟨1, λ, . . . , λkd−1⟩Fq
+= {(f0(λ), . . . , fd(λ)): fi ∈ Fq[X], deg(fi) < ki}.
+Then LJVq,n(λ,t;k0,...,kd) is a d-minimum size Fq-linear set in PG(d, qn) of rank k0 + . . . + kd−1.
+Note that since JVq,n(λ, t; k0, . . . , kd) is a Cartesian product of Fq-subspaces of Fqn, it indeed
+admits points of complementary weights.
+Before proceeding, we make some conventions regarding polynomials.
+11
+
+Definition 4.2. Given two polynomials f, g ∈ Fq[X], let gcd(f, g) denote the unique monic
+polynomial of maximal degree that divides f and g. We call f and g coprime if gcd(f, g) = 1.
+Furthermore, we will use the convention that the degree of the zero polynomial is −∞, so that
+the equality deg(f · g) = deg f + deg g still holds if f or g is the zero polynomial.
+Remark 4.3 ([11, Remark 2.19]). Jena and Van de Voorde also determined the weight spectrum
+of the above linear set. It is (1, . . . , k0) if k1 = k0, and (1, . . . , k1, k0) if k1 < k0, in which case
+E0 is the unique point of weight k0. They also described the weight distribution, but since it
+is rather involved, we omit it here. It follows from their arguments that if gcd(f0, . . . , fd) = 1,
+then
+wLU
+�
+⟨f0(λ), . . . , fd(λ)⟩Fqn
+�
+= min
+0≤i≤d{ki − deg(fi)}.
+(8)
+This makes it relatively easy to determine Ni for some large values of i. For instance, let
+U = JVq,n(λ, t; k0, . . . , kd) ⊆ Fd+1
+qn ,
+and assume that k1 < k0.
+As stated above, E0 is the unique point of weight k0, and the
+second largest weight of LU is k1. We can determine Nk1(LU). Let m denote the number of
+indices j with kj = k1, i.e. k1 = . . . = km > km+1.
+Let P = ⟨f0(λ), . . . , fd(λ)⟩Fqn ∈ LU,
+with gcd(f0, . . . , fd) = 1.
+Then, by (8), P has weight k1 if and only if deg(f0) ≤ k0 − k1,
+deg(fi) ≤ 0, for i = 1, . . . , m and fi = 0, for i > m and there exists some j ∈ {1, . . . , m} such
+that deg(fj) > 0. Then,
+Nk1(LU) = qk0−k1+1 qm − 1
+q − 1 .
+The above construction has the following consequence on the existence of d-minimum size
+linear sets in PG(d, qn).
+Corollary 4.4 ([11, Corollary 2.18]). There exists a d-minimum size Fq-linear set of rank k in
+PG(d, qn) whenever
+d < k ≤
+�
+(d + 1)n+1
+2
+if n is odd,
+(d + 1)n
+2 + 1
+if n is even.
+We now present a sufficient condition for the linear set of Construction 4.1 to be of proper
+d-minimum size.
+Theorem 4.5. Consider U = JVq,n(λ, t; k0, . . . , kd) as in Construction 4.1. Suppose that there
+exist pairwise coprime polynomials g0, . . . , gd ∈ Fq[X] such that for each i, deg gi = ki − 1. If
+k0 + . . . + kd ≤ t + d, then LU is of proper d-minimum size.
+Proof. By Construction 4.1, we know that LU is an Fq-linear set in PG(d, qn) of rank k =
+k0 + . . . + kd of d-minimum size.
+So it remains to prove that there exists a hyperplane of
+PG(d, qn) meeting LU in a canonical subgeometry. Consider the points Pi = ⟨e0 + gi(λ)ei⟩Fqn
+for i = 1, . . . , d. Clearly, P1, . . . , Pd are independent, hence they span a hyperplane. Define the
+polynomial
+G(X) =
+d
+�
+i=1
+gi(X).
+Note that for each i ≥ 1, the polynomial
+�G
+gi
+�
+(X) =
+d
+�
+j=1
+j̸=i
+gj(X)
+12
+
+is well-defined. Then the equation of the hyperplane Π = ⟨P1, . . . , Pd⟩Fqn of PG(d, qn) is
+G(λ)X0 =
+d
+�
+i=1
+�G
+gi
+�
+(λ)Xi.
+(9)
+Let k = k0 + . . . + kd denote the rank of LU. Then
+deg G =
+d
+�
+i=1
+(ki − 1) = k − k0 − d < t,
+hence G(λ) ̸= 0, and Equation (9) does indeed define a hyperplane. Now take a non-zero vector
+v = (f0(λ), . . . , fd(λ)) ∈ U, and suppose that ⟨v⟩Fqn ∈ Π. Then
+G(λ)f0(λ) =
+d
+�
+i=1
+�G
+gi
+�
+(λ)fi(λ).
+(10)
+Every term in Equation (10) is a polynomial in λ, and
+deg(Gf0) = deg G + deg f0 = (k − k0 − d) + deg f0 < t,
+deg((G/gi)fi) = deg G + deg fi − deg(gi) ≤ deg(G) < t.
+Since 1, λ, . . . , λt−1 are Fq-linearly independent, Equation (10) implies that
+G(X)f0(X) =
+d
+�
+i=1
+�G
+gi
+�
+(X)fi(X).
+On the one hand, this implies that f0 is a constant polynomial. Otherwise, the left-hand
+side has degree greater than deg(G), but the degree of the right-hand side is at most deg(G), a
+contradiction. On the other hand, for each i,
+gi(X) |
+
+G(X)f0(X) −
+�
+1≤j̸=i
+� G
+gj
+�
+(X)fj(X)
+
+ =
+�G
+gi
+�
+(X)fi(X).
+Since G/gi is coprime with gi, and deg(fi) ≤ deg(gi) this is only possible if fi is a multiple of
+gi. Hence,
+v = (α0, α1g1(λ), . . . , αdgd(λ)),
+for some scalars α0, . . . , αd ∈ Fq. Moreover, since ⟨v⟩Fqn ∈ Π, α0 = α1 + . . . + αd. Hence, LU
+intersects Π in the linear set LW , with
+W =
+� d
+�
+i=1
+αi(e0 + gi(λ)ei): αi ∈ Fq
+�
+.
+Therefore, LU intersects Π in a canonical subgeometry.
+A sufficient condition to ensure the existence of pairwise coprime polynomials g0, . . . , gd ∈
+Fq[X] such that deg(gi) = ki − 1, is to choose the size of the ground field large enough.
+Proposition 4.6. Consider U = JVq,n(λ, t; k0, . . . , kd) as in Construction 4.1, with k0 + . . . +
+kd ≤ t + d. Assume that
+d
+�
+i=0
+ki − d − 1 ≤ q.
+Then LU is of proper d-minimum size.
+13
+
+Proof. By the hypothesis, we can consider d+1 subsets S0, . . . , Sd of Fq that are pairwise disjoint
+and such that |Si| = ki − 1, for each i ∈ {0, . . . , d}. Then, we can define gi(x) = �
+α∈Si(x − αi).
+So the assertion follows by Theorem 4.5.
+Another sufficient condition to ensure the existence of pairwise coprime polynomials g0, . . . , gd ∈
+Fq[X] such that deg(gi) = ki − 1, is that the gi’s are different monic irreducible polynomials
+over Fq. It is well known, see e.g. [14, Theorem 3.25], that the number of monic irreducible
+polynomials of degree s over the finite field Fq is given by Gauss’s formula
+1
+s
+�
+h|s
+µ(s/h)qh,
+where h runs over the set of all positive divisors of s and µ denotes the M¨obius function.
+Remark 4.7. We note the following lower bound on the number of monic irreducible polyno-
+mials of degree s over Fq, see e.g. [3]:
+1
+s
+�
+h|s
+µ (s/h) qh ≥ qs − 2qs/2
+s
+.
+So we get the following corollary.
+Corollary 4.8. Consider U = JVq,n(λ, t; k0, . . . , kd) as in Construction 4.1, with k0 +. . .+kd ≤
+t + d. For each s = 1, . . . , t, suppose that
+|{i: ki − 1 = s}| ≤ qs − 2qs/2
+s
+.
+Then LU is of proper d-minimum size.
+Clearly, if the rank of a linear set LU obtained from Construction 4.1 is greater than n + d,
+then every hyperplane has weight at least d + 1 in LU, so LU cannot be of proper d-minimum
+size. In case the rank exceeds n + d, we can prove that LU is of (1, d)-minimum size under some
+constraints on the rank.
+Proposition 4.9. Let U = JVq,n(λ, t; k0, . . . , kd) be as in Construction 4.1. If k0 + kd−1 + kd ≤
+t + 2, then LU is a (1, d)-minimum size Fq-linear set.
+Proof. Let
+U ′ = {(f0(λ), . . . , fd−1(λ) + λkd−1−1fd(λ), fd(λ)): fi ∈ Fq[X], deg(fi) < ki}.
+Then U ′ is GL(d + 1, qn)-equivalent to U via the Fqn-linear map
+ϕ : v = (v0, . . . , vd) �→ v + vdλkd−1−1ed−1.
+The point ⟨(0, . . . , 0, −λkd−1−1, 1)⟩Fqn has weight 1 in LU and it is mapped to point Ed by ϕ. So
+Ed has weight 1 in LU′. We prove that |LU′| = qk−1 + |LU|, where U = U ′ + Ed ≤q Fd+1
+qn /Ed.
+Note that Fd+1
+qn /Ed can be identified with Fd
+qn and U = U ′ + Ed ≤q Fd+1
+qn /Ed with
+U = JVq,n(λ, t; k0, . . . , kd−2, kd−1 + kd − 1).
+By hypothesis k0 + kd−1 + kd − 1 ≤ t + 1, and so k0, . . . , kd−2, kd−1 + kd − 1 indeed satisfy
+the hypothesis of Construction 4.1 when rearranged in descending order. Therefore, |LU| =
+qk−2 + . . . + qk−d + 1. Since |LU| = |LU′| = qk−1 + . . . + qk−d + 1 = qk−1 + |LU|, we have the
+assertion.
+14
+
+The above proposition together with Corollary 4.4, allows to construct (1, d)-minimum size
+linear sets whose ranks exceed n + d.
+Corollary 4.10. There exist (1, d)-minimum size Fq-linear sets in PG(d, qn), d ≥ 2, of rank k,
+whenever
+d < k ≤
+�
+dn+1
+2
++ 1
+if n is odd,
+dn
+2 + 2
+if n is even.
+4.2
+Generalizing the Caserta construction
+In [16, Theorem 4.1], a construction is given of linear sets on the projective line, based on the
+more general framework exploited in [10] and [22].
+In this subsection, we generalize this to
+higher dimensions. The construction starts from an Fq-linear set LU′ in PG(d, qt), and yields an
+Fq-linear set in PG(d, qst). Moreover, the weight distribution of LU is completely determined
+by the weight distribution of LU′.
+Construction 4.11. Suppose that n = st with s, t > 1. Let U ′ be an Fq-subspace of Fd+1
+qt
+⊆ Fd+1
+qn
+with dimFq(U ′) = k′ > 0. Let Z be an Fqt-subspace of Fqn of dimension r > 0, such that 1 /∈ Z.
+Define
+Cq,s,t(Z, U ′) := {(z + u0, u1, . . . , ud): z ∈ Z, (u0, . . . , ud) ∈ U ′} ⊆ Fd+1
+qn ,
+which we will simply denote by U. Then
+(1) the Fq-linear set LU ⊆ PG(d, qn) has rank rt + k′,
+(2) |LU| = qrt|LU′ \ {E0}| + 1,
+(3) wLU(E0) = rt + wLU′(E0),
+(4) Ni(LU) = qrt(Ni(LU′) − δi,wLU′ (E0)) + δi,wLU (E0),
+where δi,j denotes the Kronecker symbol.
+Proof. (1) Since Z is an Fqt-subspace of Fqn, and 1 /∈ Z, Z ∩ Fqt = {0}. Furthermore, since U ′
+is an Fq-subspace of Fd+1
+qt
+, Z ∩ {u0 : (u0, . . . , ud) ∈ U ′} = {0}. Hence,
+U = (Z × {0}d) ⊕Fq U ′.
+Therefore,
+dimFq U = dimFq Z + dimFq U ′ = rt + k′.
+(3) Similarly,
+wLU(E0) = dimFq
+�
+Z ⊕Fq {u0 : u0e0 ∈ U ′}
+�
+= dimFq Z + dimFq({u0 : u0e0 ∈ U ′})
+= rt + wLU′(E0).
+(2,4) Suppose that
+⟨ze0 + u⟩Fqn = ⟨z′e0 + v⟩Fqn ,
+with z, z′ ∈ Z, and u, v ∈ U ′ \ ⟨e0⟩Fqn. Then ze0 + u = α(z′e0 + v) for some α ∈ Fqn. Since u, v
+are not multiples of e0, there must exist some position j > 0 such that uj, vj ̸= 0. This implies
+that α = vj/uj ∈ Fqt. We also have that z + u0 = α(z′ + v0), hence
+z − αz′ = αv0 − u0
+Recall that Z is an Fqt-subspace, and that u0, v0, α ∈ Fqt. Therefore, the left-hand side of the
+above equality is in Z, and the right-hand side is in Fqt. Since Z ∩ Fqt = {0}, this implies that
+z = αz′ and therefore u = αv.
+15
+
+Vice versa, if z ∈ Z, u ∈ U ′ \ ⟨e0⟩Fqn and αu ∈ U ′ for some α ∈ Fqt, then ⟨ze0 + u⟩Fqn =
+⟨αze0 + αu⟩Fqn . This proves that
+wLU (⟨z + u⟩Fqn) = dimFq{α ∈ Fqt : αu ∈ U ′} = wLU′(⟨u⟩Fqn).
+Hence, varying z, we see that every point of LU′ \ {E0} gives rise to |Z| points of LU \ {E0} of
+the same weight, and this accounts for all points of LU \{E0}. Points (2) and (4) follow directly
+from this observation and the fact that E0 ∈ LU.
+Remark 4.12. We remark that LU′ is contained in LU and the weight distribution and rank
+of LU in the above construction only depends on the weight distribution of LU′ and wLU′(E0),
+but not on the specific structure of U ′. In particular, if ϕ ∈ ΓL(d + 1, qt), and ϕ fixes ⟨e0⟩, then
+Cq,s,t(Z, U ′) and Cq,s,t(Z, ϕ(U ′)) have the same rank and weight distribution.
+Given some minor conditions, the above construction preserves the property of being (r, d)-
+minimum size.
+Proposition 4.13. Let U = Cq,s,t(Z, U ′) be as in Construction 4.11. If LU′ is an Fq-linear set
+of (r, d, Ω)-minimum size, and E0 ∈ LU′ \ Ω, then LU is also of (r, d, Ω)-minimum size.
+Proof. Suppose that Ω = PG(W, Fqn), and that the rank of LU′ is k′. Since LU′ is of (r, d, Ω)-
+minimum size, LU′ meets Ω in a canonical subgeometry of Ω, and
+|LU′| = qk′−1 + . . . + qk′−r + |LU′|,
+where U ′ := U ′ + W ≤q Fd+1
+qn /W.
+Since E0 /∈ Ω, up to GL(d + 1, qn)-equivalence, we can
+suppose that Ω is defined by the equations X0 = . . . = Xd−r = 0.
+Hence Fd+1
+qn /W can be
+identified with Fd−r+1
+qn
+in an obvious way. Now, an element z +u ∈ U belongs to W if and only if
+z+u0 = u1 = . . . = ud−r = 0 if and only if z = u0 = . . . = ud−r = 0. Therefore, U ∩W = U ′ ∩W
+and so Ω also meets LU in a canonical subgeometry. Moreover, by Construction 4.11,
+U = U + W = {z + u: u ∈ U ′} ⊆ Fd+1
+qn /W,
+has size qrt(|LU′| − 1) + 1. Therefore we have
+|LU| = qrt(|LU′| − 1) + 1 = qrt(qk′−1 + . . . + qk′−r + |LU′| − 1) + 1
+= qk−1 + . . . + qk−r + |LU|,
+with k = rt + k′ the rank of LU.
+We can apply Construction 4.11 with U ′ as in Construction 4.1, obtaining the following
+families of d-minimum size linear sets.
+Theorem 4.14. Consider U ′ = JVq,t(λ, t′; k0, . . . , kd) where t′ | t as in Construction 4.1, and
+choose ϕ ∈ GL(d+1, qt) such that E0 ∈ Lϕ(U′). Now define U = Cq,s,t(Z, ϕ(U ′)) as in Construc-
+tion 4.11, with Z an Fqt-subspace of rank r > 0, not containing 1. Then LU is a d-minimum
+size Fq-linear set of rank k = rt + k0 + . . . + kd. Moreover, the weight spectrum of LU is
+
+
+
+�
+1, . . . , k1, k0, rt + wLϕ(U′)(E0)
+�
+if wLϕ(U′)(E0) < k0 and k1 < k0,
+�
+1, . . . , k1, rt + wLϕ(U′)(E0)
+�
+otherwise.
+Proof. The Fq-linear set Lϕ(U′) has the same weight spectrum, weight distribution, and size as
+LU′. So the assertions follow by applying Construction 4.11 and Remark 4.3.
+16
+
+Remark 4.15. Using [11, Remark 2.19] and Construction 4.11 (3,4), one could in fact also
+determine the weight distribution of the linear set in the above theorem.
+The above construction gives new examples of proper d-minimum size linear sets.
+Corollary 4.16. In the hypothesis of Theorem 4.14, suppose that LU′ is a (d, d, Π)-minimum
+size Fq-linear set, with Π = PG(W, Fqn). Suppose that E0 ∈ Lϕ(U′)\˜Π, with ˜Π = PG(ϕ(W), Fqn).
+Then LU is a proper d-minimum size Fq-linear set in PG(d, qn).
+Proof. The linear set LU′ is of (d, d, Π)-minimum size, so the hyperplane Π = PG(W, Fqn) of
+PG(d, qn) meets LU′ in a canonical subgeometry of Π and
+|LU′| = qm−1 + . . . + qm−d + 1.
+It follows that ˜Π also meets Lϕ(U′) in a canonical subgeometry of ˜Π, that is Lϕ(U′) is of proper
+d-minimum size as well. The assertion follows by Proposition 4.13.
+Construction 4.1 provides constructions of d-minimum size linear sets admitting points of
+complementary weights. Using Theorem 4.14, it is possible to construct proper d-minimum size
+linear sets that do not have this property, as we will see in the next example. This proves that
+in general a d-minimum size linear set need not contain independent points whose weights sum
+to the rank of the linear set. So in general, as already observed in [16] for the projective line,
+being minimum size does not determine the weight spectrum and distribution of a linear set.
+Example 4.17. Consider
+U ′ = JVq,6(λ, 6; 2, 2, 2)
+as in Construction 4.1. Then LU′ is an Fq-linear set of rank 6 in PG(2, q6) having size q5 +q4 +1
+and points of weight at most 2. Moreover, wLU′(E0) + wLU′(E1) + wLU′(E2) = 2 + 2 + 2 = 6 is
+equal to the rank of LU′. Define
+ϕ ∈ GL(3, q6) : (x, y, z) �→ (x, y − λx, z).
+Then the Fq-linear set LU′′ in PG(2, q6), with
+U ′′ = ϕ(U ′) = {(α0 + α1λ, β0 + β1λ − α1λ2, γ0 + γ1λ): αi, βi, γi ∈ Fq} ⊆ F3
+q6
+has the same rank, weight spectrum and weight distribution as LU′. Note that wLU′′(E0) = 1.
+Choose a 1-dimensional Fq6-subspace Z ̸= Fq6 of Fq12. By Theorem 4.14, the Fq-linear set LU
+of PG(2, q12), with
+U = Cq,2,6(Z, U ′′)
+has rank 12 and size q11 + q10 + 1. So, it is a 2-minimum size linear set. Note that the weight
+spectrum of LU is (1, 2, 7), and so there do not three points of complementary weights.
+In
+particular, LU cannot be obtained from Construction 4.1.
+In some cases, Theorem 4.14 gives us linear sets admitting points of complementary weights,
+but with a different weight distribution than those of Construction 4.1, as stated in the following
+theorem.
+Theorem 4.18. Consider
+U ′ = JVq,t(λ, t; k0, . . . , kd)
+and let ϕi be the linear map swapping coordinates 0 and i ∈ {0, . . . , d} (with ϕ0 = id). Consider
+U = Cq,s,t(Z, ϕi(U ′)),
+17
+
+(1) If ki = k0, then there exists an Fq-linear set obtained from Construction 4.1 with the same
+weight distribution as LU.
+(2) If ki < k0 − 1, then there does not exist an Fq-linear set obtained from Construction 4.1
+with the same weight distribution as LU.
+Proof. Write n = st.
+(1) If ki = k0, choose a primitive element µ of Fqn.
+Consider U2 = JVq,n(µ, n; k0 +
+rt, k1, . . . , kd). Then LU and LU2 have the same weight distribution by Remark 4.3 (see also
+[11, Remark 2.19]) and Construction 4.11 (3,4).
+(2) Now assume that ki < k0 − 1, and suppose that there exists some Fq-subspace
+U3 = JVq,n(µ, t′; k′
+0, . . . , k′
+d) ⊆ Fd+1
+qn
+such that LU and LU3 have the same weight distribution. Since LU has a unique point of weight
+rt + ki by Construction 4.11 (3,4), we see that by Remark 4.3, k′
+0 = rt + ki. Furthermore, the
+second largest weight of LU and LU3 is respectively k0 and k′
+1, hence k0 = k′
+1. Let m′ denote
+the number of indices j with k′
+j = k0, i.e. k′
+1 = . . . = k′
+m′ > k′
+m′+1. Then, using Remark 4.3 (see
+also [11, Remark 2.19]),
+Nk0(LU3) = qk′
+0−k′
+1+1 qm′ − 1
+q − 1
+= qrt+ki−k0+1 qm′ − 1
+q − 1 .
+On the other hand, by Construction 4.11 (4) and Remark 4.3 (see also [11, Remark 2.19]),
+Nk0(LU) = qrtNk0(LU′) = qrtqm − 1
+q − 1 ,
+with m the number indices j with kj = k0. Therefore,
+qrt+ki−k0+1 qm′ − 1
+q − 1
+= qrtqm − 1
+q − 1 .
+Since qm−1
+q−1 and qm′−1
+q−1
+are coprime with q, this implies that ki = k0 − 1.
+4.3
+Regarding equivalence
+We show that the two different types of Fq-subspaces that define the d-minimum size linear
+sets defined in Construction 4.1 and Theorem 4.14 are ΓL(d + 1, qn)-inequivalent, even if the
+associated linear sets have the same weight spectrum and distribution (see Theorem 4.18 (1)),
+when the dimension of Z is the maximum possible. The trace function Trqn/q of Fqn over Fq,
+defines a non-degenerate symmetric bilinear form as follows:
+(a, b) ∈ Fqn × Fqn �→ Trqn/q(ab) ∈ Fq.
+Hence, for any subset S of Fqn we can define the orthogonal complement as
+S⊥ = {a ∈ Fqn : Trqn/q(ab) = 0, ∀b ∈ S}.
+Note that if S is an Fqt-subspace of Fqn, then S⊥ is an Fqt-subspace as well.
+Given an ordered Fq-basis B = (ξ0, . . . , ξn−1) of Fqn, there exists a unique ordered Fq-basis
+B∗ = (ξ∗
+0, . . . , ξ∗
+n−1) of Fqn such that Trqn/q(ξiξ∗
+j ) = δij, for i, j ∈ {0, . . . , n − 1}, called the dual
+basis of B, see e.g. [14, Definition 2.30].
+18
+
+Lemma 4.19 ([17, Corollary 2.7]). Let λ ∈ Fqn and suppose that B = (1, λ, . . . , λn−1) is an
+ordered Fq-basis of Fqn. Let f(x) = a0 + a1x + . . . + an−1xn−1 + xn be the minimal polynomial
+of λ over Fq. Then the dual basis B∗ of B is
+B∗ = (δ−1γ0, . . . , δ−1γn−1),
+where δ = f ′(λ) and γi = �n−i
+j=1 λj−1ai+j, for every i ∈ {0, . . . , n − 1}.
+Theorem 4.20. Suppose that n = (s + 1)t, with s, t > 1. Consider U ′ = JVq,t(µ, t; k0, . . . , kd)
+as in Construction 4.1, with k0 < t − 1. Let ϕi be the linear map swapping coordinates 0 and
+i ∈ {0, . . . , d} (with ϕ0 = id) and define
+U1 = Cq,s,t(Z, ϕi(U ′)),
+as in Construction 4.11, with Z an Fqt-subspace of dimension s, not containing 1. Consider
+U2 = JVq,n(λ, n; h0, k1, . . . , kd) as in Construction 4.1, with h0 = st+k0. Then the Fq-subspaces
+U1 are U2 are ΓL(d + 1, qn)-inequivalent.
+Proof. Suppose that ki < k0 − 1. Then, by Theorem 4.18, LU1 and LU2 have a distinct weight
+distribution, hence U1 and U2 cannot be ΓL(d + 1, qn)-equivalent. So suppose that ki ∈ {k0 −
+1, k0} and suppose by contradiction that U1 and U2 are ΓL(d + 1, qn)-equivalent via an element
+ϕ. Since h0 > ki, for every i ∈ {1, . . . , d}, the point E0 is the only point in LU1 and in LU2 of
+weight h0. So, we have that ϕ(U1 ∩ E0) = U2 ∩ E0, that is
+aSρ
+1 = S2,
+some a ∈ F∗
+qn and ρ ∈ Aut(Fqn), with S1 = Z ⊕ ⟨1, µ, . . . , µk0−1⟩Fq and S2 = ⟨1, λ, . . . , λh0−1⟩Fq.
+In particular, we have that aZρ ⊆ S2 and so (aZρ)⊥ ⊇ S⊥
+2 .
+Note that dimFqt(aZρ) =
+dimFqt(Z) = s. This implies that dimFq((aZρ)⊥) = n − st = t and hence (aZρ)⊥ is an Fqt-
+subspace of Fqn of dimension one. Consider the ordered Fq basis B = (1, λ, . . . , λn−1) of Fqn and
+its dual basis B∗ = (λ∗
+0, . . . , λ∗
+n−1). So we have that S⊥
+2 = ⟨λ∗
+h0, . . . , λ∗
+n−1⟩Fq and since k0 < t−1,
+we have that h0 < n − 1. By Lemma 4.19 it follows that
+λ∗
+n−2 = δ−1(an−1 + λ),
+and
+λ∗
+n−1 = δ−1,
+where f(x) = a0+a1x+. . .+an−1xn−1+xn is the minimal polynomial of λ over Fq and δ = f ′(λ).
+Now, since λ∗
+n−2, λ∗
+n−1 ∈ (aZρ)⊥ and since (aZρ)⊥ has dimension one over Fqt, it follows
+λ∗
+n−2
+λ∗
+n−1
+= an−1 + λ ∈ Fqt,
+that is λ ∈ Fqt, a contradiction.
+5
+Below the De Beule-Van de Voorde bound
+In this section, we will provide constructions of linear sets LU that in PG(d, qn), with d > 2,
+that are of (r, d)-minimum size but not of d-minimum size. They have maximum geometric field
+of linearity Fq, and admit two subspaces of complementary weights.
+For our aims, we will suppose that one of these subspaces intersects LU in a linear set with
+greater field of linearity. This gives us the following constructions.
+Theorem 5.1. Let n = st, with s, t > 1, and suppose that
+19
+
+U1 is a k1-dimensional Fqt-subspace of Fd1+1
+qn
+,
+U2 is a k2-dimensional Fq-subspace of Fd2+1
+qt
+⊆ Fd2+1
+qn
+.
+Define U = U1 × U2, and d = d1 + d2 + 1. Then LU is an Fq-linear set of PG(d, qn) of rank
+k1t + k2, with
+|LU| = |LU1| + qk1t|LU2|.
+Moreover, its weight distribution satisfies
+Ni(LU) = Ni(LU1) + qk1tNi(LU2).
+Proof. Take a vector u ∈ U1 and v ∈ U2 with (u, v) ̸= 0. Then
+wLU(⟨(u, v)⟩Fqn ) = dimFq{α ∈ Fqn : α(u, v) ∈ U}.
+Evidently, α(u, v) ∈ U if and only if αu ∈ U1 and αv ∈ U2. If v ̸= 0, then αv ∈ U2 implies
+that α ∈ Fqt, and since U1 is an Fqt-subspace, αu is automatically in U1. Therefore, every point
+⟨v⟩Fqn of LU2 gives rise to the qk1t points {⟨(u, v)⟩Fqn : u ∈ U1} of LU with the same weight. If
+v = 0, then we just need that αu ∈ U1, hence in this way, every point of LU1 gives rise to one
+point of LU of the same weight. Since this accounts for all points of LU, the statement of the
+theorem follows.
+Using the above theorem, we are able to obtain constructions of linear sets in PG(d, qn),
+with d ≥ 3, having maximum geometric field of linearity Fq that are (r, d)-minimum size with
+2 ≤ r < d and that are not d-minimum size.
+Theorem 5.2. Let n = st, with s, t > 1, and suppose that
+U1 is a k1-dimensional Fqt-subspace of Fd1+1
+qn
+, with k1 ≤ d1s,
+U2 is a k2-dimensional Fq-subspace of Fd2+1
+qt
+, such that LU2 is a proper d2-minimum size
+Fq-linear set.
+Define U = U1 × U2, d = d1 + d2 + 1, and k = k1t + k2. Then LU is a (d2, d)-minimum size
+Fq-linear set of size
+|LU| = qk−1 + qk−2 + . . . + qk−d2 + qk1t + |LU1|.
+Hence, LU is not d-minimum size if k2 ≥ d2+2. Furthermore, if d2 ≥ 2, then Fq is the maximum
+geometric field of linearity of LU.
+Proof. The Fq-linear set LU2 ⊆ PG(d2, qn) is of proper d2-minimum size, and so its size is
+|LU2| = qk2−1 + . . . + qk2−d2 + 1.
+By Theorem 5.1, LU has rank k = k1t + k2 and size
+|LU1| + qk1t(qk2−1 + . . . + qk2−d2 + 1) = |LU1| + qk−1 + qk−2 + . . . + qk−d2 + qk1t.
+Moreover there exists a (d2 − 1)-space Γ = PG(W, Fqn) of PG(d2, qn), with W ⊆ Fd2+1
+qn
+, meeting
+LU2 in a canonical subgeometry. Now, let W ′ = {0}d1+1 × W. Then W ′ defines a d2-space of
+PG(d, qn) meeting LU in a canonical subgeometry. Identifying Fd+1
+qn /W with Fd1+1
+qn
+we have that
+U = U1 + W ≤q Fd+1
+qn /W with
+U = U1 × U ′,
+where U ′ is an Fq-subspace of Fqn of dimension k2 − d2. So again, by Theorem 5.1, we have
+|LU| = qk1t + |LU1|. Moreover, by (3), |LU1| ≤ q(k1−1)t + . . . + qt + 1, and since k2 > d2 + 1 it
+follows that
+|LU1| < qk−d2−1 + . . . + qk−d + 1 − qk1t.
+This implies that LU is not of d-minimum size. Finally, the assertion on the geometric field of
+linearity follows from Remark 3.10.
+20
+
+By the above corollary and Proposition 4.5, we get the following construction.
+Corollary 5.3. Let n = st, with s, t > 1, and suppose that
+U1 = JVqt,n(λ, n; l0, . . . , ld1), and denote k1 = l0 + . . . + ld1,
+U2 = JVq,t(µ, t; m0, . . . , md2), and denote k2 = m0 + . . . + md2,
+with LU2 satisfying the condition of Theorem 4.5. Define U = U1 × U2. Then LU is a (d2, d)-
+minimum size Fq-linear set, but not of d-minimum size. Moreover, if d2 ≥ 2, then Fq is the
+maximum geometric field of linearity of LU.
+Proof. Note that
+|LU1| = q(k1−1)t + . . . + q(k1−d1)t + 1 < qk−d2−1 + . . . + qk−d + 1 − qk1t,
+and then the assertion follows by Theorem 5.2.
+Remark 5.4. Other examples of (d2, d)-minimum size linear set can be obtained by using as
+LU1 or LU2 in Theorem 5.2 the minimum size linear sets constructed in Corollary 4.14.
+Remark 5.5. It is natural to consider PG(d, qn), n not prime, and wonder what the maximal
+value of d2 is such that the above corollary implies the existence of an Fq-linear set in PG(d, qn)
+that is of (d2, d)-minimum size, but not of d-minimum size, and has maximum geometric field of
+linearity Fq. So let t be the largest proper divisor of n. Note that t ≥ √n. We want to construct
+a set U2 = JVq,t(µ, t; m0, . . . , md2) with d2 maximal, such that it satisfies the conditions of
+Theorem 4.5. Hence, there must exist pairwise coprime polynomials gi of degree mi − 1 such
+that (m0 − 1) + . . . + (md2 − 1) ≤ t − 1. Let δ(x) denote the maximum number of distinct monic
+irreducible polynomials over Fq such that the sum of their degrees is smaller than x. Then for
+any m ≥ 1, δ(qm) ≥ qm−1
+m . Indeed, consider the minimal polynomials of the elements of F∗
+qm.
+Since every element of F∗
+qm is the root of a unique such polynomial, their degrees sum to qm − 1.
+Furthermore, the maximum degree equals m, so there are at least qm−1
+m
+such polynomials. Hence,
+to answer the original question, asymptotically, d2 = Ω(t/ logq(t)) = Ω(√n/ logq(n)).
+We conclude this subsection with examples of linear sets of (1, 2)-minimum size that are not
+of (2, 2)-minimum size and have maximum geometric field of linearity Fq.
+Proposition 5.6. Let n = st, with s > 1, and t > 2 prime. Suppose that the smallest prime
+that divides s is at least t. Let
+U1 be a k1-dimensional Fqt-subspace of Fqn,
+U2 = JVq,t(µ, t; m0, m1), with t = m0 + m1.
+Define U = U1 × U2. Then LU is a (1, 2)-minimum size Fq-linear set, but not of 2-minimum
+size. Moreover, Fq is the maximum geometric field of linearity of LU.
+Proof. By Theorem 5.1, LU is an Fq-linear set of PG(2, qn) of rank (k1 + 1)t having size
+|LU| = q(k1+1)t−1 + qk1t + 1,
+that is not of 2-minimum size. Since LU2 has a point of weight 1, there exists ϕ ∈ GL(2, qt), such
+that the Fq-linear set LU′, with U ′ = U1×ϕ(U2) has E2 as a point of weight 1. Hence F3
+qn/E2 can
+be identified with F2
+qn in an obvious way. Clearly, LU and LU′ are GL(3, qn)-equivalent. In this
+way, U ′/E2 can be identified as an Fq-subspace U = U1 × U ′
+2, where U ′
+2 is an (t − 1)-dimensional
+Fq-subspace of Fqt. Again, by Theorem 5.1, we have that |LU| = qk1t + 1 and hence LU is a
+(1, 2)-minimum size Fq-linear set. Suppose now, that LU = LW for some Fqr-linear set LW . If
+r < t, then by our hypothesis, r is coprime with s and t, hence r is coprime with n = st, and
+Fqr is not a subfield of Fqn. Therefore, r ≥ t. Let ℓ be the line of PG(2, qn) having equation
+X0 = 0. Then
+qt−1 + 1 = |LU2| = |ℓ ∩ LU| = |ℓ ∩ LW |.
+Since ℓ∩LW is an Fqr-linear set we have that |ℓ∩LW| ≥ qr +1. So t−1 ≥ r, a contradiction.
+21
+
+6
+Conclusion
+De Beule and Van de Voorde [8] provided a lower bound on the size of an Fq-linear set LU
+in PG(d, qn) that intersects some hyperplane Ω in a canonical subgeometry. In this paper, we
+generalized their result by allowing Ω to be an (r − 1)-space, with 1 ≤ r ≤ d. Our bound looks
+like
+|LU| ≥ qk−1 + . . . + qk−r + |LU|,
+where k is the rank of LU, and LU is the projection of LU from Ω. Unfortunately, the bound
+still depends on the size of the linear set LU. This raises the question what the minimum size of
+LU is. Taking r as large as possible, we may assume that LU does not have any points of weight
+1. We presented a recursive lower bound on the size of linear sets without points of weight 1.
+Since we recursively use a rather naive upper bound on the minimum weight of the points of
+LU, one should not expect this bound to be tight, except for some particular cases.
+Open problem 1. Find a good lower bound on the size of an Fq-linear set of rank k−r spanning
+PG(d − r, qn), containing no points of weight 1.
+The rest of the paper was concerned with finding examples of linear sets that attain equality
+in the bound. We note that all constructions but the one of Jena and Van de Voorde [11] use a
+subfield in between Fq and Fqn. So it looks like the most restrictive setting to study linear sets
+of minimum size is the case where such a subfield does not exist, i.e. the case where n is prime.
+We reiterate that for n prime, Jena and Van de Voorde [11, §2.5 (B)] stated their belief that the
+bound of Result 1.3 is still correct with less restrictive conditions.
+Open problem 2. Is it true that if n is prime, all Fq-linear sets LU in PG(d, qn) of rank
+k ≤ d + n satisfy |LU| ≥ qk−1 + . . . + qk−d + 1? If so, can we classify the linear sets attaining
+equality in this bound?
+Acknowledgment
+We would like to thank Jan De Beule, Olga Polverino and Ferdinando Zullo for fruitful discus-
+sions. Paolo Santonastaso is very grateful for the hospitality of the Department of Mathematics
+and Data Science, Vrije Universiteit Brussel, Brussels, Belgium, where he was a visiting PhD
+student for 2 months during the preparation of this paper. Paolo Santonastaso was supported
+by the project “VALERE: VAnviteLli pEr la RicErca” of the University of Campania “Luigi
+Vanvitelli” and by the Italian National Group for Algebraic and Geometric Structures and their
+Applications (GNSAGA - INdAM).
+References
+[1] G. N. Alfarano, M. Borello, A. Neri, and A. Ravagnani. Linear cutting blocking sets and
+minimal codes in the rank metric. Journal of Combinatorial Theory, Series A, 192:105658,
+2022.
+[2] S. Ball. The number of directions determined by a function over a finite field. Journal of
+Combinatorial Theory, Series A, 104(2):341–350, 2003.
+[3] M. Blaser and C. Saha.
+Computational number theory and algebra,
+lecture 9.
+https://www.csa.iisc.ac.in/~chandan/courses/CNT/notes/lec9.pdf, 2012.
+[4] A. Blokhuis, S. Ball, A. E. Brouwer, L. Storme, and T. Sz˝onyi. On the number of slopes of
+the graph of a function defined on a finite field. Journal of Combinatorial Theory, Series
+A, 86(1):187–196, 1999.
+22
+
+[5] A. Blokhuis and M. Lavrauw.
+Scattered spaces with respect to a spread in PG(n, q).
+Geometriae Dedicata, 81(1):231–243, 2000.
+[6] G. Bonoli and O. Polverino. Fq-linear blocking sets in PG(2, q4). Innovations in Incidence
+Geometry Algebraic Topological and Combinatorial, 2(1):35–56, 2005.
+[7] B. Csajb´ok, G. Marino, and O. Polverino. Classes and equivalence of linear sets in PG(1, qn).
+Journal of Combinatorial Theory, Series A, 157:402–426, 2018.
+[8] J. De Beule and G. Van de Voorde. The minimum size of a linear set. Journal of Combi-
+natorial Theory, Series A, 164:109–124, 2019.
+[9] M. De Boeck and G. Van de Voorde. A linear set view on KM-arcs. Journal of Algebraic
+Combinatorics, 44(1):131–164, 2016.
+[10] A. G´acs and Z. Weiner. On (q+t, t)-arcs of type (0, 2, t). Designs, Codes and Cryptography,
+29, 2003.
+[11] D. Jena and G. Van de Voorde. On linear sets of minimum size. Discrete Mathematics,
+344(3):112230, 2021.
+[12] D. Jena and G. Van de Voorde. The geometric field of linearity of linear sets. Designs,
+Codes and Cryptography, 90(3):779–799, 2022.
+[13] M. Lavrauw and G. Van de Voorde. Field reduction and linear sets in finite geometry.
+Topics in finite fields, 632:271–293, 2015.
+[14] R. Lidl and H. Niederreiter. Finite Fields. Cambridge University Press, 1997.
+[15] G. Lunardon and O. Polverino. Blocking sets of size qt +qt−1 +1. Journal of Combinatorial
+Theory, Series A, 90(1):148–158, 2000.
+[16] V. Napolitano, O. Polverino, P. Santonastaso, and F. Zullo. Classifications and construc-
+tions of minimum size linear sets. arXiv:2201.02003, 2022.
+[17] V. Napolitano, O. Polverino, P. Santonastaso, and F. Zullo. Linear sets on the projective
+line with complementary weights. Discrete Mathematics, 345(7):112890, 2022.
+[18] V. Napolitano, O. Polverino, P. Santonastaso, and F. Zullo. Two pointsets in PG(2, qn) and
+the associated codes. Advances in Mathematics of Communications, 17(1):227–245, 2023.
+[19] O. Polverino. Linear sets in finite projective spaces. Discrete Mathematics, 310(22):3096–
+3107, 2010.
+[20] O. Polverino, P. Santonastaso, J. Sheekey, and F. Zullo. Divisible linear rank metric codes.
+to appear in IEEE Transactions on Information Theory, 2023.
+[21] O. Polverino, P. Santonastaso, and F. Zullo. Maximum weight codewords of a linear rank
+metric code. in preparation, 2023.
+[22] O. Polverino, T. Sz˝onyi, and Z. Weiner. Blocking sets in galois planes of square order. Acta
+Scientiarum Mathematicarum (Szeged), 65, 1999.
+[23] O. Polverino and F. Zullo.
+Connections between scattered linear sets and MRD-codes.
+Bulletin of the Institute of Combinatorics and its Applications, 89:46–74, 2020.
+[24] J. Sheekey. A new family of linear maximum rank distance codes. Advances in Mathematics
+of Communications, 10(3):475, 2016.
+23
+
+[25] J. Sheekey and G. Van de Voorde. Rank-metric codes, linear sets, and their duality. Designs,
+Codes and Cryptography, 88:655–675, 2020.
+[26] P. Sziklai. On small blocking sets and their linearity. Journal of Combinatorial Theory,
+Series A, 115(7):1167–1182, 2008.
+[27] G. Zini and F. Zullo. Scattered subspaces and related codes. Designs, Codes and Cryptog-
+raphy, pages 1–21, 2021.
+[28] F. Zullo. Multi-orbit cyclic subspace codes and linear sets. Finite Fields and Their Appli-
+cations, 87:102153, 2023.
+Sam Adriaensen
+Vrije Universiteit Brussel
+Department of Mathematics and Data Science
+Pleinlaan 2, 1050 Elsene, Belgium
+sam.adriaensen@vub.be
+Paolo Santonastaso
+Universit`a degli Studi della Campania “Luigi Vanvitelli”
+Dipartimento di Matematica e Fisica
+Viale Lincoln, 5, I– 81100 Caserta, Italy
+paolo.santonastaso@unicampania.it
+24
+
diff --git a/k9FPT4oBgHgl3EQf2jWr/content/tmp_files/2301.13187v1.pdf.txt b/k9FPT4oBgHgl3EQf2jWr/content/tmp_files/2301.13187v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a1a75ee25720a1ad46dc566e3fdf2d91f194446f
--- /dev/null
+++ b/k9FPT4oBgHgl3EQf2jWr/content/tmp_files/2301.13187v1.pdf.txt
@@ -0,0 +1,2150 @@
+Weighted flow diffusion for local graph clustering with node
+attributes: an algorithm and statistical guarantees
+Shenghao Yang∗
+Kimon Fountoulakis∗
+Abstract
+Local graph clustering methods aim to detect small clusters in very large graphs without the need to
+process the whole graph. They are fundamental and scalable tools for a wide range of tasks such as local
+community detection, node ranking and node embedding. While prior work on local graph clustering
+mainly focuses on graphs without node attributes, modern real-world graph datasets typically come with
+node attributes that provide valuable additional information. We present a simple local graph clustering
+algorithm for graphs with node attributes, based on the idea of diffusing mass locally in the graph while
+accounting for both structural and attribute proximities. Using high-dimensional concentration results,
+we provide statistical guarantees on the performance of the algorithm for the recovery of a target cluster
+with a single seed node. We give conditions under which a target cluster generated from a fairly general
+contextual random graph model, which includes both the stochastic block model and the planted cluster
+model as special cases, can be fully recovered with bounded false positives. Empirically, we validate all
+theoretical claims using synthetic data, and we show that incorporating node attributes leads to superior
+local clustering performances using real-world graph datasets.
+1
+Introduction
+Given a graph G and a seed node in that graph, a local graph clustering algorithm finds a good small cluster
+that contains the seed node without looking at the whole graph [3, 25]. Because the graphs arising from
+modern applications are massive in size and yet are rich in small-scale local structures [18, 16], local graph
+clustering has become an important scalable tool for probing large-scale graph datasets with a wide range of
+applications in machine learning and data analytics [14, 13, 20].
+Traditional local graph clustering algorithms primarily focus on the structural properties of a graph dataset, i.e.
+nodes and edges, and consequently the analyses of these algorithms are often concerned with the combinatorial
+properties of the output cluster. For example, in most previous studies one is interested in the conductance
+of a cluster and define a good cluster as one that has low conductance [25, 3, 22, 2, 4, 24, 28, 13, 19]. In
+this case, the objective of local graph clustering is thus detecting a low conductance cluster around the
+seed. With the increasing availability of multi-modal datasets, it is now very common for a graph dataset to
+contain additional sources of information such as node attributes, which may prove to be crucial for correctly
+identifying clusters with rather noisy edge connections. However, nearly all existing local graph clustering
+algorithms do not work with attributed graphs. Moreover, in the presence of node attributes, the objective
+and analysis of a local graph clustering algorithm should also adjust to take into account both sources of
+information (i.e. graph structure and attributes) as opposed to focus solely on the combinatorial notion of
+conductance.
+*David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, Canada.
+Emails: shenghao.yang@uwaterloo.ca, kimon.fountoulakis@uwaterloo.ca
+1
+arXiv:2301.13187v1  [cs.SI]  30 Jan 2023
+
+1.1
+Our contributions
+We propose a simple local graph clustering algorithm that simultaneously considers both graph structural
+and node attribute information. We analyze the performance of the proposed algorithm from a statistical
+perspective where we assume that the target cluster and the node attributes have been generated from a
+random data model. We provide conditions under which the algorithm is guaranteed to fully recover the
+target cluster with bounded false positives.
+Our local graph clustering algorithm uses the recently proposed flow diffusion model on graphs [13, 8]. The
+original flow diffusion is proposed to solve the local graph clustering problem on unweighted graphs without
+node attributes. In this work we consider flow diffusion on weighted graphs where the edge weights are
+designed to reflect the proximity between node attributes. A distinct characteristic of the proposed algorithm
+is its simplicity and flexibility. On one hand, the algorithm has few hyperparameters and thus it does
+not require much tuning; while on the other hand, it allows flexible initialization of source mass and sink
+capacities, which enables us to obtain different types of recovery guarantees.
+Our main contribution is the analyses of the algorithm for the recovery of a target cluster with a single seed
+node. We provide high probability guarantees on the performance of the algorithm under a certain type of
+contextual random graph model. The data model we consider is fairly general. On the structural side, it only
+concerns the connectivity of nodes within the target cluster and its adjacent nodes, and hence it encompasses
+the stochastic block model (SBM) and the planted cluster model as special cases; on the node attribute
+side, it allows an attribute be modelled by a sub-Gaussian random variable, and this includes Gaussian,
+uniform, Bernoulli, and any discrete or continuous random variables over a finite domain. Depending on a
+signal-to-noise ratio of the node attributes, we present two recovery results. Informally, if we have very good
+node attributes, then with overwhelming probability the algorithm fully recovers the target cluster with nearly
+zero false positives, irrespective of the interval connectivity of the target cluster (as long as it is connected);
+on the other hand, if we have good, but not too good, node attributes, then with overwhelming probability
+the algorithm fully recovers the target cluster, with the size of the false positives jointly controlled by both
+the combinatorial conductance of the target cluster and the signal-to-noise ratio of the node attributes.
+Finally, we carry out experiments on synthetic data to verify all theoretical claims and on real-world data to
+demonstrate the advantage of incorporating node attributes.
+1.2
+Previous work
+The local graph clustering problem is first introduced by [25] where the authors proposed a random-walk
+based algorithm with early termination. Later [3] studied the same problem using approximate personalized
+PageRank vectors. There is a long line of work on local graph clustering where the analysis of the algorithm
+concerns the conductance of the output cluster [3, 22, 25, 2, 4, 24, 28, 13, 19]. The first statistical analysis
+of local graph clustering is considered in [15] where the authors analyze the average-case performance of
+the ℓ1-regularized PageRank [12] over a random data model. None of these work studies local clustering in
+attributed graphs.
+The idea to utilize both structural and node attribute information has been applied in the context of
+community detection, where the goal is to detect all clusters in a graph [30, 17, 31, 26]. These methods
+require processing the whole graph and hence are not suitable for local graph clustering.
+Recently, contextual random graph models are been used in the literature for analyzing the performance
+of certain algorithms for attributed graphs. [10, 29, 7, 1] study algorithms for community detection in the
+contextual stochastic block model (CSBM). [5, 11, 6] analyze the separability of nodes in CSBM by functions
+that are representable by graph neural networks. The random model we consider in this work is more general
+and we are the first to consider statistical performance of a local graph clustering algorithm in contextual
+2
+
+random models.
+2
+Weighted flow diffusion and local graph clustering with node
+attributes
+In this section, we start by providing an overview of flow diffusion on graphs, describing its physical
+interpretation as spreading mass in a graph along edges, and disucssing some important algorithmic properties.
+Then, we present an algorithm that uses edge-weighted flow diffusion for local graph clustering with node
+attributes.
+2.1
+Notations and basic properties of flow diffusion
+We consider undirected, weighted and connected graph G = (A, W) which consists of n nodes and m edges,
+where A ∈ {0, 1}n×n is the combinatorial adjacency matrix, i.e., Aij = 1 if node i is adjacent to node j and
+0 otherwise, W ∈ Rm×m is a diagonal matrix of edge weights. We write wij = W(i,j),(i,j) as the weight of
+an edge (i, j). If W = I then G reduces to an unweighted graph. We denote V = {1, 2, . . . , n} as the set of
+nodes and E as the set of edges, i ∼ j if (i, j) ∈ E. The combinatorial degree degG(i) of a node i ∈ V is the
+number of edges incident to it. For a subset C ⊆ V , the volume of C is given by volG(C) = �
+i∈C degG(i).
+We use subscripts to indicate the graph we are working with, and we omit them when the graph is clear from
+context. We denote B ∈ Rm×n as the combinatorial signed incidence matrix under an arbitrary orientation
+of the graph, where the row that corresponds to the oriented edge (i, j) has two nonzero entries, with −1 at
+column i and 1 at column j. The support of a vector x is supp(x) = {i : xi ̸= 0}. We use standard notations
+On, Ωn, Θn, on, ωn for asymptotic behaviors of a function with respect to n, and we omit the subscript when
+it is clear.
+Given a source vector ∆ ∈ Rn and a sink capacity vector T ∈ Rn, a flow diffusion on G is formulated as the
+following optimization problem:
+min
+f
+1
+2f T Wf
+s.t. ∆ + BT Wf ≤ T,
+(1)
+where W is restricted to be the identity matrix in the original formulation [13]. The flow variables f ∈ Rm
+determine the amount of mass that moves between nodes i and j for every edge (i, j) ∈ E. More precisely,
+wijfij specifies the amount of mass that travels along (i, j). We abuse the notation and use fij = −fji for
+an edge (i, j), so wijfij is the amount of mass that moves from node i to node j. In a flow diffusion, we
+assign ∆i source mass to node i and enforce a constraint that node i can hold up to Ti mass. Because one
+may always scale ∆ and T by the same constant, we assume without loss of generality that Ti ≥ 1 for all
+i. If Ti > ∆i at some node i, then we need to spread the source mass along edges in the graph to satisfy
+the capacity constraint. The vector ∆ + BT Wf measures the final mass at each node if we spread the mass
+according to f. Therefore, the goal of the flow diffusion problem (1) is to find a feasible way to spread the
+mass while minimizing the cost of flow f T Wf. In this work we allow different edge weights as long as they
+are positive, i.e., W consists of positive diagonal entries. In the context of flow diffusion, edge weights define
+the efficiencies at which mass can spread over edges. To see this, simply note that wijfij determines the
+amount of mass that moves along the edge (i, j), and thus for fixed fij, the higher wij is the more mass we
+can move along (i, j).
+For local graph clustering, it is usually more convenient to consider the dual problem of (1):
+min
+x≥0
+1
+2xT Lx + xT (T − ∆)
+(2)
+3
+
+Algorithm 1 Flow diffusion (algorithmic form)
+Input: graph G, source ∆ and sink T
+1. Initialize xi = 0 and mi = ∆i for all i ∈ V .
+2. For t = 1, 2, . . . do
+(a) Pick i ∈ {j : mj > Tj} uniformly at random.
+(b) Apply push(i).
+3. Return x.
+push(i):
+Make the following updates:
+1. xi ← xi + (mi − Ti)/wi where wi = �
+j∼i wij.
+2. mi ← Ti.
+3. For each node j ∼ i: mj ← mj + (mi − Ti)wij/wi.
+where L = BT WB is the weighted Laplacian matrix of G. Throughout this work we use f ∗ and x∗ to denote
+the optimal solutions of (1) and (2), respectively. The solution x∗ ∈ Rn
++ embeds the nodes on the nonnegative
+real line. In [13] the authors apply a sweep-cut rounding procedure for local graph clustering without node
+attributes, and they obtain a combinatorial guarantee in terms of the conductance of a cluster. In this work,
+with the presence of node attributes which may come from some unknown distributions, we take a natural
+statistical perspective and show how supp(x∗) recovers a target cluster generated from a contextual random
+graph model.
+In order to compute the solution to (2) one may extend the iterative coordinate method in [13] to work with
+weighted edges. We layout the algorithmic steps in Algorithm 1, where we describe each coordinate-wise
+gradient update (i.e., push(i)) using its combinatorial interpretation as spreading mass from a node to its
+neighbors. In Algorithm 1, mi represents the current mass at node i. At every iteration, we pick a node
+i whose current mass mi exceeds its capacity Ti, and we remove the excess amount mi − Ti by sending it
+to the neighbors. Algorithm 1 may be viewed as an equivalent algorithmic form of flow diffusion since the
+iterates converge to x∗ [13]. An important property of Algorithm 1 is that it updates xi only if x∗
+i > 0, and
+it updates mj only if j ∼ i for some i such that x∗
+i > 0. This means that the algorithm will not explore the
+whole graph if x∗ is sparse, which is usually the case in applications such local clustering and node ranking.
+We state this local property in Proposition 2.1 and provide a running time bound in Proposition 2.2. Both
+propositions can be proved by simply including edge weights in the original arguments from [13] and our
+assumption that Ti ≥ 1 for all i.
+Proposition 2.1 ([13]). Let xt for t ≥ 1 be iterates generated by Algorithm 1, then supp(xt) ⊆ supp(x∗).
+Moreover, |supp(x∗)| ≤ ∥∆∥1.
+Proposition 2.2 ([13]). Assuming |supp(x∗)| < n, then after τ = O(∥∆∥1 α
+β log 1
+ϵ ) iterations, where α =
+maxi∈supp(x∗) wi where wi = �
+j∼i wij, and β ≥ min(i,j)∈supp(Bx∗) wij, one has E[F(xτ)] − F(x∗) ≤ ϵ, where
+F denotes the objective function of (2).
+Let ¯d denote the maximum degree of a node in supp(x∗). Since each iteration of Algorithm 1 only touches a
+node i ∈ supp(x∗) and its neighbors, Proposition 2.1 implies that the total number of nodes (except their
+neighbors j such that x∗
+j = 0) that Algorithm 1 will ever look at is upper bounded by the total amount
+of source mass ∥∆∥1. Therefore, if the source mass is small and ¯d does not scale linearly with n, then
+Algorithm 1 would only explore locally in the graph, and the size of the subgraph which Algorithm 1 explores
+is controlled by ∥∆∥1. Proposition 2.2 implies that the total running time of Algorithm 1 for computing
+an ϵ-accurate solution is O( ¯d∥∆∥1 α
+β log 1
+ϵ ). Therefore, if ¯d, ∥∆∥1, α
+β are all sublinear in n, then Algorithm 1
+takes sublinear time.
+4
+
+Algorithm 2 Local graph clustering with node attributes
+Input: unweighted graph G = (A, I), node attributes Xi for all i ∈ V , seed node s ∈ V , hyperparameter
+γ ≥ 0.
+Output: a cluster C ⊆ V
+1. Define weighted graph G′ = (A, W) whose edge weights are given by wij = exp(−γ∥Xi − Xj∥2
+2).
+2. Set source mass ∆s > 0 and ∆i = 0 for i ̸= s, set sink capacity Ti.
+3. Run flow diffusion (Algorithm 1) with input G′, ∆, T and obtain output xτ.
+4. Return supp(xτ)
+2.2
+Local clustering with node attributes
+In local graph clustering, we are given a seed node s ∈ V and the goal is to identify a good cluster that
+contains the seed. Existing methods mostly focus on the setting where one only has access to the structural
+information, i.e. nodes and edges of a graph, and they do not take into account node attributes. However,
+it is reasonable to expect that informative node attributes should help improve the performance of a local
+clustering algorithm. For example, the original flow diffusion solves the local graph clustering problem by
+spreading source mass from the seed node to nearby nodes, and an output cluster is obtained based on where
+in the graph the mass diffuse to [13]. In this case, node attributes may be used to guide the spread of mass so
+that more mass are trapped inside the ground-truth target cluster, and consequently, improve the accuracy of
+the algorithm.
+The idea to guide the diffusion by using node attributes can be easily realized by relating edge weights to
+node attributes, which we describe in the next. Given a graph G = (A, W) with a set of node attributes
+Xi ∈ Rd for i ∈ V , and given a seed node s from an unknown target cluster K, the goal is to recover
+K. To do so, we construct a new graph G′ = (A, W ′) having the same structure but new edge weights
+w′
+ij = h(wij, Xi, Xj) where h is some function that should improve diffusion. For example, one may set
+h(wij, Xi, Xj) = wijρ(Xi, Xj) where ρ(Xi, Xj) measures the proximity between Xi and Xj. This means that,
+for a flow diffusion in G′, if two adjacent nodes i and j have similar attributes, then it is easier to send a lot
+of mass along the edge (i, j). In particular, when one removes the excess mass from a node i by sending it
+to the neighbors, the amount of mass that a neighbor j receives is proportional to w′
+ij (cf. push(i)), and
+hence more mass will be sent to a neighbor whose attributes also bear close proximity. Therefore, if nodes
+within the target cluster K share similar attributes, then a flow diffusion in G′, which starts from a seed
+node s ∈ K, would force more mass to spread within K than a flow diffusion in the original graph G.
+In this work, we focus on a particular choice of h given by w′
+ij = h(wij, Xi, Xj) = wij exp(−γ∥Xi − Xj∥2
+2)
+where γ ≥ 0 is a hyperparameter. For simplicity we will assume that wij = 1 for all (i, j) ∈ E. In this case, h
+is the Gaussian kernel of node attributes and has proved useful in many applications, e.g., spectral clustering.
+In the next section we provide rigorous statistical guarantees on the performance of local graph clustering with
+node attributes by using the optimal solution of weighted flow diffusion (2), where edge weights are defined
+by the Gaussian kernel for an appropriately chosen γ > 0. We summarize the local clustering procedure in
+Algorithm 2. As we show in the next section, suitable choices for T include Ti = 1 or Ti = degG(i) for all i,
+and one may correspondingly set ∆s = α �
+i∈K Ti for α > 1 where K is the target cluster.
+3
+Statistical guarantees under contextual random graph model
+We assume that the node attributes and a target cluster are generated from the following random model.
+Definition 3.1 (Contextual local random model). Given a set of nodes V , let K ⊆ V be a target cluster
+with cardinality |K| = k. For every pair of nodes i and j, if i, j ∈ K then we draw an edge (i, j) with
+5
+
+probability p; if i ∈ K and j /∈ K then we draw an edge (i, j) with probability q; otherwise, we allow
+any (deterministic or random) model to draw an edge. The node attributes Xi for a node i are given as
+Xi = µi +Zi, where µi ∈ Rd is a fixed signal vector and Zi ∈ Rd is a random noise vector whose ℓth coordinate
+Ziℓ follows independent mean zero sub-Gaussian distribution with variance proxy σℓ, i.e., for any t ≥ 0 we
+have P(|Ziℓ| ≥ t) ≤ 2 exp(− t2
+2σ2
+ℓ ). Though not necessary, to simplify the discussion we require µi = µj for
+i, j ∈ K .
+This random model is fairly general. For example, if the edges that connect nodes in V \K have been
+generated from the SBM, µi = µj for every i, j that belong to the same block, and all Zi’s follow the
+same isotropic Gaussian distribution, then we obtain the CSBM which has been extensively used in the
+analyses of algorithms for attributed graphs [10, 5, 29]. On the other hand, if the edges that connect nodes
+in V \K have been generated from the Erd˝os-Renyi model with probability q, µi = µj for i, j ∈ K and
+µi = 0 for i ̸∈ K, and all Zi’s follow the same isotropic Gaussian distribution, then we obtain a natural
+coupling of the planted densest subgraph problem and the submatrix localization problem [9]. In terms of
+modelling the noise of node attributes, sub-Gaussian distributions include Gaussian, Bernoulli, and any other
+continuous or discrete distribution over finite domains. Therefore the random model allows different types of
+coordinate-wise noise (and different level of noise controlled by σℓ) which could depend on the nature of the
+specific attribute. For example, the noise of a continuous attribute may be Gaussian or uniform, whereas the
+noise of a binary-encoded categorical attribute may be Bernoulli.
+In order for node attributes to provide useful information, nodes inside K should have distinguishable
+attributes compared to nodes not in K. Denote
+ˆµ :=
+min
+i∈K,j̸∈K ∥µi − µj∥2,
+ˆσ := max
+1≤ℓ≤d σℓ.
+We make Assumption 3.2 which states that the relative signal ˆµ dominates the maximum coordinate-wise
+noise ˆσ, and that the sum of normalized noises does not grow faster than log n. The later assumption is
+easily satisfied, e.g., when the dimension d of node attributes does not scale with the number of nodes n. In
+practice, when the set of available or measurable attributes are fixed a priori, one always has d = On(1). This
+is particularly relevant in the context of local clustering where it is desirable to have sublinear algorithms,
+since if d = Ω(n) then even computing a single edge weight wij would take time at least linear in n.
+Assumption 3.2. ˆµ = ω(ˆσ√λ log n) for some λ = Ωn(1); �d
+ℓ=1 σ2
+ℓ/ˆσ2 = O(log n).
+Before we move on to discuss how exactly node attributes help to recover K, we need to talk about the signal
+and noise from the graph structure. For a node i ∈ K, the expected number of neighbors in K is p(k − 1),
+and the expected number of neighbors not in K is q(n − k). Since mass spread along edges, if there are too
+many edges connecting K to V \K, it may become difficult to prevent a lot of mass from spreading out of K.
+The consequence of having too much mass which start in K to leak out of K is that supp(x∗) may have little
+overlap with K, and consequently Algorithm 2 would have poor performance.
+Fortunately, node attributes may be very helpful when the structural information is not strong enough, e.g.,
+when q(n − k) > p(k − 1). As discussed earlier, informative node attributes should be able to guide the spread
+of mass in the graph. In a flow diffusion, where the mass get spread to from the source node depends on the
+edge weights. The higher weight an edge has, the easier to send mass along that edge. Therefore, in order
+to keep as much mass as possible inside the target cluster K, an ideal situation would be that edges inside
+K have significantly more weights than an edge that connects K to V \K. It turns out that this is exactly
+the case when we have good node attributes. By applying concentration results on the sum of squares of
+sub-Gaussian random variables, Lemma 3.3 says that, with overwhelming probability, one obtains a desirable
+separation of edge weights as a consequence of node attributes having more signal than noise (i.e. when
+Assumption 3.2 holds).
+6
+
+Lemma 3.3. Under Assumption 3.2, one may pick γ such that γˆσ2 = o(log−1 n) and γˆµ2 = ωn(λ).
+Consequently, with probability at least 1 − on(1), the edge weight wij = exp(−γ∥Xi − Xj∥2
+2) satisfies wij ≥
+1 − on(1) for all i, j ∈ K, and wij ≤ exp(−ωn(λ)) for all i ∈ K, j ̸∈ K.
+Not surprisingly, Lemma 3.3 implies that the gap between edge weights is controlled by λ which, according
+to Assumption 3.2, measures how strong the attribute signal is. If λ is sufficiently large, then naturally
+one would expect an algorithm that uses the node attributes to nearly perfectly recover K, irrespective
+of how noisy the graph is. Otherwise, the performance to recover K would depend on a combination of
+both structural and attribute information. In what follows we present two recovery results which precisely
+correspond to these two scenarios. In all probability bounds, we keep explicit dependence on the cluster size
+k because, for local graph clustering, k may be a large constant and does not necessarily scale with n.
+Theorem 3.4 (Recovery with very good node attributes). Under Assumption 3.2, for any γ satisfying
+γˆσ2 = o(log−1 n) and γˆµ2 = ωn(λ), with source mass ∆s = (1 + β) �
+i∈K Ti for any β > 0, we have that for
+large enough n,
+1. if K is connected and λ = Ωn(log k+log(q(n−k))+log(1/β)), then with probability at least 1−on(1)−k−1/3,
+for every seed node s ∈ K we have K ⊆ supp(x∗) and �
+i∈supp(x∗)\K Ti ≤ β �
+i∈K Ti;
+2. if p ≥ (4+ϵ)
+δ2
+log k
+k−1 for some 0 < δ < 1 and ϵ > 0, and λ = Ωn(log k + log( q(n−k)
+p(k−1) ) + log(1/β) + log(1 − δ)),
+then with probability at least 1 − on(1) − k−1/3 − ek−ϵ/2, for every seed node s ∈ K we have K ⊆ supp(x∗)
+and �
+i∈supp(x∗)\K Ti ≤ β �
+i∈K Ti.
+In particular, we obtain the following bounds on false positives: if Ti = 1 for all i ∈ V then
+|supp(x∗)\K| ≤ β|K|;
+if Ti = degG(i) for all i ∈ V then
+volG(supp(x∗)\K) ≤ βvolG(K).
+Some discussions are in order. The first part of Theorem 3.4 does not assume anything about the internal
+connectivity of K. It applies as long as K is connected, and this includes the extreme case when the induced
+subgraph on K is a tree but each node in K is also connected to many other nodes not in K. The second
+part of Theorem 3.4 requires a weaker condition on the strength of attribute signal ˆµ. The additive term
+log(q(n − k)) from part 1 is weakened to log( q(n−k)
+p(k−1) ) due to the improved connectivity of K, under the
+additional assumption that p ≥ Ω(log k/k). We consider two specific choices of T. The first choice gives the
+exact bound on the number of false positives, and the second choice bounds the size of false positives in terms
+of volume [15]. Note that even in the case where the node attributes alone provide sufficient signal, the graph
+structure still plays a very important role as it allows the possibility that an algorithm would return a good
+output without having to explore all data points. For example, during the execution of Algorithm 2, one only
+needs to query the attributes of a node whenever they are required for subsequent computations.
+Let us introduce one more notion before presenting the recovery guarantee with good, but not too good,
+node attributes. Given the contextual random model described in Definition 3.1, consider a “population”
+graph ¯G = ( ¯A, ¯W) where ¯Aij = 1 for every pair i, j such that i ̸= j, and the edge weight ¯wij satisfies
+¯wij = p exp(−γ∥E[Xi] − E[Xj]∥2
+2) = p if i, j ∈ K, ¯wij = q exp(−γ∥E[Xi] − E[Xj]∥2
+2) ≤ qe−γ ˆµ2 if i ∈ K, j /∈ K.
+A frequently used measure of cluster quality is conductance which quantifies the ratio between external and
+internal connectivity. For a set of nodes C in ¯G, its conductance is defined as �
+i∈C,j /∈C ¯wij/ �
+i∈C
+�
+j∼i ¯wij.
+For 0 ≤ c ≤ 1 denote
+η(c) :=
+p(k − 1)
+p(k − 1) + q(n − k)e−cγ ˆµ2 .
+One may easily verify that the conductance of K in ¯G is upper bounded by 1 − η(1). Therefore, the higher
+η(1) is the lower conductance K may have in ¯G. On the other hand, in the absence of node attributes,
+7
+
+or if all nodes share identical attributes, then the conductance of K in ¯G is exactly 1 − η(0). Note that
+1 − η(c) ≥ 1 − η(0) for any c ≥ 0. Intuitively, a low conductance cluster is better connected internally than
+externally, and thus it should be easier to detect. Therefore, the advantage of having node attributes is
+that they help reduce the conductance of the target cluster, making it easier to recover from the population
+graph. While in practice one never works with the population graph, our next theorem indicates that, with
+overwhelming probability, the recoverability of K in the population graph transfers to an realization of the
+random model in Definition 3.1. More specifically, Theorem 3.5 says that when the node attributes are good,
+i.e. Assumption 3.2 holds, but not too good, i.e. conditions required in Theorem 3.4 may not hold, then
+Algorithm 2 still fully recovers K as long as there is sufficient internal connection. Moreover, the relative size
+of false positives (compared to the size of K) is upper bounded by O(1/η(c)2) − 1 for any c < 1 and large
+enough n. Denote
+m(δ1, δ2) =
+(1 + 3δ1 +
+1
+p(k−1))2
+(1 − δ1)(1 − δ2)
+,
+Tmax = max
+i∈K Ti.
+Theorem 3.5 (Recovery with good node attributes). Under Assumption 3.2, if p ≥ max( (3+ϵ1)
+δ2
+1
+log k
+k−1 ,
+(2+ϵ2)
+δ2
+√1−δ1
+√log k
+√k−1 )
+where 0 < δ1, δ2 ≤ 1 and ϵ1, ϵ2 > 0, then with probability at least 1 − on(1) − 4k−ϵ1/3 − k−2ϵ2, for every seed
+node s ∈ K with source mass
+∆s = c1Tmax
+m(δ1, δ2)k
+η(c2)2
+for any constants c1 > 1 and c2 < 1, it holds that for all large enough n, K ⊆ supp(x∗). Moreover, if Ti = 1
+for all i ∈ V then
+|supp(x∗)\K| ≤
+�c1m(δ1, δ2)
+η(c2)2
+− 1
+�
+|K|;
+if Ti = degG(i) for all i ∈ V
+volG(supp(x∗)\K) ≤
+�c1m(δ1, δ2)
+η(c2)2
+(1 + δ1)
+(1 − δ1) − 1
+�
+volG(K).
+In the special case where there is no node attribute, we may simply take ˆµ = 0 and Theorem 3.5 still holds.
+For this specific setting we obtain a nearly identical recovery guarantee (i.e. same assumption and same
+result) that has been previously obtained for local graph clustering using PageRank vectors without node
+attributes [15], where the relative size of false positives is O(1/η(0)2 − 1). This comparison quantifies the
+advantage of having good node attributes as they reduce the bound to O(1/η(c)2 − 1) for any c < 1, which
+can be substantially smaller. Note that the expression 1/η(c)2 is jointly controlled by the combinatorial
+conductance of K and the attribute signal ˆµ.
+4
+Experiments
+We evaluate the performance of Algorithm 2 for local graph clustering with node attributes. First, we
+investigate empirically our theoretical results over synthetic data generated from a specification of the random
+model described in Definition 3.1. We use the synthetic experiments to demonstrate (i) the distinction
+between having weak and strong graph structural information, and (ii) the distinction between having very
+good and moderately good node attributes. In addition, the synthetic experiments indicates the necessity of
+Assumption 3.2 in order for Algorithm 2 to have notable performance improvement against method that does
+not use node attributes. Second, we carry out experiments using real-world data. We show that incorporating
+node attributes improves the F1 scores by an average of 4.3% over 20 clusters from two academic co-authorship
+networks.
+8
+
+4.1
+Simulated data and results
+The generative model. We generate random graphs using the stochastic block model with block size
+k = 500 and the total number of clusters r = 20. The total number of nodes is n = kr = 10, 000. Two nodes
+within the same cluster are connected with probability p, and two nodes from different clusters are connected
+with probability q. We fix q = 0.002 and vary p to control the strength of the structural signal. We randomly
+pick one of the clusters as the target cluster K. The dimension of the node attributes is set to d = 100. For
+node attributes Xi = µi + Zi, we sample Zi from Gaussian distribution with mean 0 and identity covariance.
+Therefore σℓ = 1 for all ℓ = 1, 2, . . . , d, and hence ˆσ = 1. We set µiℓ = aˆσ√log n/2
+√
+d for all ℓ if i ∈ K, and
+µiℓ = −aˆσ√log n/2
+√
+d for all ℓ if i ̸∈ K. In this way, we get that ˆµ = maxi∈K,j̸∈K ∥µi − µj∥2 = aˆσ√log n.
+We vary a to control the strength of node attribute signal.
+Setup and evaluation metric. We set the sink capacity Ti = 1 for all i. We set the source mass ∆s = αk
+and we allow α to vary. We set γ = (log−3/2 n)/4ˆσ2 so that γˆσ2 = o(log−1 n) as required by Theorem 3.4 and
+Theorem 3.5. To measure the quality of an output cluster C := supp(xτ), we use precision and recall which
+are defined as |C ∩ K|/|C| and |C ∩ K|/|K|, respectively. The F1 score is the harmonic mean of precision and
+recall given by 2/(Precision−1 + Recall−1). For comparison we also consider the performance of unweighted
+flow diffusion which does not use node attributes. There are other methods for local graph clustering without
+node attributes, such as the ℓ1-regularized PageRank [3, 15]. We did not consider other methods because the
+unweighted flow diffusion is shown to achieve state-of-the-art performance [13]. Moreover, the comparison
+between weighted and unweighted flow diffusions, which either use or does not use node attributes, allows us
+to obtain a fair estimate on the benefits of node attributes.
+Results. Figure 1 shows detailed views of the performance of Algorithm 2 as we vary α between [0.1, 5]
+with 0.1 increments.
+It is used to demonstrate the two claims of Theorem 3.4.
+In Figure 1a, we set
+p = 0.01 < log k/k, so the target cluster K is very sparse. On average, each node i ∈ K only has 5 neighbors
+inside K while it has 19 neighbors outside of K. This means that the graph structural information alone is not
+very helpful for recovering K. On the other hand, we set a = 3√log n so ˆµ = 3ˆσ log n. This means that the
+node attributes contain very strong signal. In this case, observe that as soon as α becomes strictly larger than
+1, the output cluster C fully recovers K, i.e. Recall = 1. This demonstrates the first claim of Theorem 3.4.
+As a comparison, the unweighted flow diffusion which does not use node attributes has very poor performance
+for every choice of α. This is expected because edge connectivity reveals very little clustering information.
+In Figure 1b, we keep the same graph structure but slightly weaken the node attributes to ˆµ = 5
+2 ˆσ log n by
+reducing a. This stops the output cluster C from fully recovering K for small α larger than 1. The algorithm
+still has a good performance if one chooses α properly. This scenario is covered by Theorem 3.5 and we will
+discuss more about it later. In Figure 1c, we keep the same node attributes as in Figure 1b but increase p
+from 0.01 to 0.03 which is slightly larger than 2 log k/k. In this case, the output cluster C again fully recovers
+K as soon as α is strictly larger than 1. The distinction between Figure 1b and Figure 1c means that the
+required threshold for ˆµ to fully recover K at any α > 1 decreases as p increases. This demonstrates the
+second claim of Theorem 3.4.
+In Figure 2 we consider a more realistic setting where one may not know the size of the target cluster K
+and the node attributes may be noisy. We keep the same graph connectivity (i.e. p = 0.03 and q = 0.002)
+and vary a between [0, 8] with 0.5 increments. Recall that the node attributes are set in a way such that
+ˆµ = aˆσ√log n, therefore the strength of node attributes increases as a increases. For each choice of a, given a
+seed node s, we run Algorithm 2 multiple times with source mass αk for α ∈ {1.1, 1.6, . . . , 10.1}. This gives
+multiple output clusters, one from each choice of α. We consider two cases for selecting a final cluster. The
+first case is a best-case scenario where we pick the cluster that achieves the best F1 score, the second case is
+a more realistic case where we pick the cluster that has the minimum conductance.1 Figure 2 illustrates the
+performance of Algorithm 2 in these two cases. The x-axis of Figure 2 is the value of a where ˆµ = aˆσ√log n.
+Overall, the performance improves as ˆµ increases. When the node attributes are reasonably strong, e.g.
+1Given edge weights wij and a cluster C, we consider weighted conductance which is the ratio �
+i∈C,j̸∈C wij/ �
+i∈C
+�
+j∼i wij.
+9
+
+0
+1
+2
+3
+4
+5
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Recall
+Precision
+= 1.1
+Recall (no attributes)
+Precision (no attributes)
+(a) p = 0.01, q = 0.002, ˆµ = 3ˆσ log n
+0
+1
+2
+3
+4
+5
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+(b) p = 0.01, q = 0.002, ˆµ = 5
+2 ˆσ log n
+0
+1
+2
+3
+4
+5
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+(c) p = 0.03, q = 0.002, ˆµ = 5
+2 ˆσ log n
+Figure 1: Demonstration of Theorem 3.4. The lines show average performance over 100 trails. In each trial
+we randomly pick a seed node s from the target cluster K. The error bars show standard deviation. Figure 1a
+and Figure 1c show full recovery of K as soon as α > 1 (i.e. as soon as β > 0, see first part of Theorem 3.4).
+The distinction between Figure 1b and Figure 1c demonstrate that the required threshold for ˆµ depends on p
+(cf. second part of Theorem 3.4). With very good node attributes, the performance of flow diffusion that
+uses node attributes is significantly better than the performance of flow diffusion that does not use node
+attributes.
+a ≥ 4, the scenario where we select a cluster based on minimum conductance matches with the best-case
+performance. Note that, the higher ˆµ is, the lower η(c) is for any 0 < c ≤ 1, and according to Theorem 3.5,
+there should be less false positives and hence a higher F1 score. This is exactly what Figure 2 shows. In
+Figure 2 we also plot the best-case performance of unweighted flow diffusion without node attributes. When
+the node attributes are very noisy, and in particular, when ˆµ ≤ ˆσ√log n where Assumption 3.2 clearly fails,
+we see that using node attributes can be harmful as it can lead to worse performance than not using node
+attributes at all. On the other hand, once the node attributes become strong enough, e.g., a ≥ 4, using node
+attributes start to yield much better outcome.
+10
+
+0
+1
+2
+3
+4
+5
+6
+7
+8
+Strength of node attributes
+0.3
+0.4
+0.5
+0.6
+0.7
+0.8
+0.9
+1.0
+F1 score
+Best performance
+Perf. for min conductance
+Best perf. without attributes
+=
+logn
+Figure 2: Performance of Algorithm 2 as ˆµ increases. ˆµ needs to be larger than ˆσ√log n in order for node
+attributes to be useful. The x-axis shows the value of a where ˆµ = aˆσ√log n. We average over 100 trials,
+each trial uses a randomly selected seed node.
+4.2
+Real-world graphs and results
+We evaluate the performance of Algorithm 2 on two co-authorship graphs based on the Microsoft Academic
+Graph from the KDD Cup 2016 challenge [23].2 In these graphs, nodes are authors, and two nodes are
+connected by an edge if they have coauthored a paper. The clusters are defined according to the most
+active research field of each author. The node attributes represent paper keywords for each author’s papers.
+The first graph consists of 18,333 computer science researchers and 81,894 connections among them. Each
+computer science researcher belongs to one of the 15 ground-truth clusters. The second graph consists of
+34,493 physics researchers and 247,962 connections among them. Each physics researcher belongs to one of
+the 5 ground-truth clusters. Details of node attributes and cluster sizes are found in Appendix D.
+We consider two choices for the sink capacities T. The first is Ti = degG(i) for all i and the second is Ti = 1
+for all i. For each cluster K in a graph, given a seed node s ∈ K, we run Algorithm 2 with source mass
+∆s = α �
+i∈K Ti for α ∈ {1.5, 1.75, 2, . . . , 5}. We select the output cluster that has the minimum conductance
+and measure the recovery quality using the F1 score. For each of the 20 target clusters we run 100 trials and
+each trial uses a different seed node. We report the average F1 scores using the first choice for T in Table 1.
+Additional results using the second choice for T, along with more details on parameter choices, are found in
+Appendix D. In most cases, incorporating node attributes improves recovery accuracy. Over the total 20
+clusters in the two co-authorship networks, using node attributes increases the F1 score by 4.3% on average.
+5
+Conclusion and future work
+In this work we propose and analyze a simple algorithm for local graph clustering with node attributes. We
+provide conditions under which the algorithm is guaranteed to work well. We empirically demonstrate the
+advantage of incorporating node attributes over both synthetic and real-world datasets. To the best of our
+knowledge, this is the first local graph clustering algorithm for attributed graphs that also have provable
+guarantees. The current work is the first step towards building principled tools for local learning on graphs
+2In Appendix D.1 we include additional experiments using Amazon co-purchase graph [21] and demonstrate the performance
+of Algorithm 2 when the node attributes are not strong enough. (F1 only increases by 1% on average.)
+11
+
+Table 1: F1 scores for local clustering in co-authorship networks
+Network
+Cluster
+No attr.
+Use attr.
+Improv.
+Computer Science
+Bioinformatics
+32.1
+39.3
+7.2
+Machine Learning
+30.9
+37.3
+6.4
+Computer Vision
+37.6
+35.5
+-2.1
+NLP
+45.2
+52.3
+7.1
+Graphics
+38.6
+49.2
+10.6
+Networks
+44.1
+47.0
+2.9
+Security
+29.9
+35.7
+5.8
+Databases
+48.5
+58.1
+9.6
+Data Mining
+27.5
+28.8
+1.3
+Game Theory
+60.6
+66.0
+5.4
+HCI
+70.0
+77.6
+7.6
+Information Theory
+47.4
+46.9
+-0.5
+Medical Informatics
+65.7
+70.3
+4.6
+Robotics
+59.9
+59.9
+0.0
+Theoretical CS
+66.3
+70.7
+4.4
+Physics
+Phys. Rev. A
+69.4
+70.9
+1.5
+Phys. Rev. B
+41.4
+42.3
+0.9
+Phys. Rev. C
+79.3
+82.1
+2.8
+Phys. Rev. D
+62.3
+68.9
+6.6
+Phys. Rev. E
+49.5
+53.7
+4.2
+AVERAGE
+50.3
+54.6
+4.3
+using both structural and attribute information without processing the whole graph. An interesting future
+direction is to incorporate node embedding and parameter learning into local diffusion, where the attributes
+and their relative importance may be optimized simultaneously alongside the local diffusion process.
+12
+
+References
+[1] E. Abbe, J. Fan, and K. Wang. An ℓp theory of pca and spectral clustering. The Annals of Statistics,
+50(4):2359–2385, 2022.
+[2] Z. Allen-Zhu, L. Silvio, and S. M. Vahab. A local algorithm for finding well-connected clusters. In
+Proceedings of the 30th International Conference on Machine Learning (ICML), pages 396–404, 2013.
+[3] R. Andersen, F. Chung, and K. Lang. Local graph partitioning using pagerank vectors. Proceedings of
+the 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS), pages 475–486, 2006.
+[4] R. Andersen, S. O. Gharan, Y. Peres, and L. Trevisan. Almost optimal local graph clustering using
+evolving sets. Journal of the ACM, 63(2), 2016.
+[5] A. Baranwal, K. Fountoulakis, and A. Jagannath. Graph convolution for semi-supervised classifica-
+tion: Improved linear separability and out-of-distribution generalization. In Proceedings of the 38th
+International Conference on Machine Learning (ICML), volume 139, pages 684–693, 2021.
+[6] A. Baranwal, K. Fountoulakis, and A. Jagannath. Effects of graph convolutions in multi-layer networks.
+In International Conference on Learning Representations (ICLR), 2023.
+[7] G. Braun, H. Tyagi, and C. Biernacki. An iterative clustering algorithm for the contextual stochastic
+block model with optimality guarantees. In Proceedings of the 39th International Conference on Machine
+Learning (ICML), pages 2257–2291. PMLR, 2022.
+[8] L. Chen, R. Peng, and D. Wang. 2-norm flow diffusion in near-linear time. In IEEE 62nd Annual
+Symposium on Foundations of Computer Science (FOCS), pages 540–549, 2022.
+[9] Yudong Chen and Jiaming Xu. Statistical-computational tradeoffs in planted problems and submatrix
+localization with a growing number of clusters and submatrices. The Journal of Machine Learning
+Research, 17(1):882–938, 2016.
+[10] Y. Deshpande, S. Sen, A. Montanari, and E. Mossel. Contextual stochastic block models. Advances in
+Neural Information Processing Systems (NeurIPS), 31, 2018.
+[11] K. Fountoulakis, A. Levi, S. Yang, A. Baranwal, and A. Jagannath. Graph attention retrospective, 2022.
+[12] K. Fountoulakis, F. Roosta-Khorasani, J. Shun, X. Cheng, and M. W. Mahoney. Variational perspective
+on local graph clustering. Mathematical Programming, 174:553–573, 2017.
+[13] K. Fountoulakis, D. Wang, and S. Yang. p-norm flow diffusion for local graph clustering. Proceedings of
+the 37th International Conference on Machine Learning (ICML), 2020.
+[14] D. F. Gleich. Pagerank beyond the web. SIAM Review, 57(3):321–363, 2015.
+[15] W. Ha, K. Fountoulakis, and M. W. Mahoney. Statistical guarantees for local graph clustering. The
+Journal of Machine Learning Research, 22(1):6538–6591, 2021.
+[16] L. G. S. Jeub, P. Balachandran, M. A. Porter, P. J. Mucha, and M. W. Mahoney. Think locally, act
+locally: Detection of small, medium-sized, and large communities in large networks. Physical Review E,
+91:012821, 2015.
+[17] Caiyan Jia, Yafang Li, Matthew B Carson, Xiaoyang Wang, and Jian Yu. Node attribute-enhanced
+community detection in complex networks. Scientific reports, 7(1):1–15, 2017.
+[18] J. Leskovec, K.J. Lang, A. Dasgupta, and M.W. Mahoney. Community structure in large networks:
+Natural cluster sizes and the absence of large well-defined clusters. Internet Mathematics, 6(1):29–123,
+2009.
+13
+
+[19] M. Liu and D. F. Gleich. Strongly local p-norm-cut algorithms for semi-supervised learning and local
+graph clustering. In Advances in Neural Information Processing Systems (NeurIPS), volume 33, pages
+5023–5035, 2020.
+[20] P. Macgregor and H. Sun. Local algorithms for finding densely connected clusters. In Proceedings of the
+38th International Conference on Machine Learning (ICML), pages 7268–7278. PMLR, 2021.
+[21] J. McAuley, C. Targett, Q. Shi, and A. Van Den Hengel. Image-based recommendations on styles
+and substitutes. In Proceedings of the 38th ACM SIGIR International Conference on Research and
+Development in Information Retrieval, pages 43–52, 2015.
+[22] A. Reid and P. Yuval. Finding sparse cuts locally using evolving sets. In Proceedings of the 41st ACM
+Symposium on Theory of Computing (STOC), pages 235–244, 2009.
+[23] O. Shchur, M. Mumme, A. Bojchevski, and S. G¨unnemann. Pitfalls of graph neural network evaluation.
+Relational Representation Learning Workshop, NeurIPS 2018, 2018.
+[24] P. Shi, K. He, D. Bindel, and J. Hopcroft. Local Lanczos spectral approximation for community
+detection. In Proceedings of the European Conference on Machine Learning and Principles and Practice
+of Knowledge Discovery in Databases (ECML-PKDD), September 2017.
+[25] D. A. Spielman and S.-H. Teng. A local clustering algorithm for massive graphs and its application to
+nearly linear time graph partitioning. SIAM Journal on computing, 42(1):1–26, 2013.
+[26] Heli Sun, Fang He, Jianbin Huang, Yizhou Sun, Yang Li, Chenyu Wang, Liang He, Zhongbin Sun, and
+Xiaolin Jia. Network embedding for community detection in attributed networks. ACM Transactions on
+Knowledge Discovery from Data (TKDD), 14(3):1–25, 2020.
+[27] R. Vershynin. High-dimensional probability: An introduction with applications in data science, volume 47.
+Cambridge university press, 2018.
+[28] D. Wang, K. Fountoulakis, M. Henzinger, M. W. Mahoney, and S. Rao. Capacity releasing diffusion
+for speed and locality. Proceedings of the 34th International Conference on Machine Learning (ICML),
+70:3607–2017, 2017.
+[29] B. Yan and P. Sarkar. Covariate regularized community detection in sparse graphs. Journal of the
+American Statistical Association, 116(534):734–745, 2021.
+[30] J. Yang, J. McAuley, and J. Leskovec. Community detection in networks with node attributes. In IEEE
+13th International Conference on Data Mining (ICDM), pages 1151–1156. IEEE, 2013.
+[31] Chen Zhe, Aixin Sun, and Xiaokui Xiao. Community detection on large complex attribute network. In
+Proceedings of the 25th ACM SIGKDD international conference on knowledge discovery & data mining,
+pages 2041–2049, 2019.
+14
+
+A
+Primal-dual solutions of flow diffusion
+Recall that we denote f ∗ and x∗ as the optimal solutions of the primal and dual flow diffusion problem (1)
+and (2), respectively. We derive two useful properties of x∗ based on the primal-dual relationships between
+f ∗ and x∗. In Appendix B when we analyze the support of x∗, we will repeatedly use these properties to
+characterize the nodes covered by supp(x∗). Note that
+min
+f
+1
+2f T Wf
+s.t. ∆ + BT Wf ≤ T
+= min
+f
+max
+x≥0
+1
+2f T Wf + xT (∆ + BT Wf − T)
+= max
+x≥0 min
+f
+1
+2f T Wf + xT (∆ + BT Wf − T)
+= max
+x≥0 −1
+2xT BT WBx + xT (∆ − T),
+therefore the optimal solutions f ∗ and x∗ are related by f ∗ = −Bx∗. According to the physical interpretation
+of the flow variables f, this means that, in an optimal flow diffusion, the amount of mass that moves from
+node i to node j is precisely wij(x∗
+i − x∗
+j) where wij is the weight for the edge (i, j). Moreover, we have
+x∗
+i > 0 only if ∆i + [BT Wf ∗]i = Ti. Recall that the quantity ∆i + [BT Wf ∗]i represents the amount of mass
+at node i after spreading mass according to f ∗, therefore, we get that x∗
+i > 0 only if the final mass at node i
+equals exactly to its sink capacity Ti. In this case, we say that node i is saturated.
+B
+Proofs
+B.1
+Proof of Lemma 3.3
+We have that
+∥Xi − Xj∥2
+2 =
+� ∥Zi − Zj∥2
+2,
+if i, j ∈ K,
+∥Zi − Zj∥2
+2 + ∥µi − µj∥2
+2 + (µi − µj)T (Zi − Zj),
+if i ∈ K, j ̸∈ K.
+(3)
+Consider the random variable
+∥Zi − Zj∥2
+2 − E[∥Zi − Zj∥2
+2] =
+d
+�
+ℓ=1
+�
+(Ziℓ − Zjℓ)2 − E[(Ziℓ − Zjℓ)2]
+�
+.
+Each term in the summation is sub-exponential and satisfies
+∥(Ziℓ − Zjℓ)2 − E[(Ziℓ − Zjℓ)2]∥ψ1 ≤ C∥(Ziℓ − Zjℓ)2∥ψ1 = C∥Ziℓ − Zjℓ∥2
+ψ2 ≤ 2C∥Ziℓ∥2
+ψ2 ≤ C′σ2
+ℓ
+for some absolute constants C, C′, where ∥ · ∥ψ1 and ∥ · ∥ψ2 denote the sub-exponential norm and the
+sub-Gaussian norm, respectively [27]. The first inequality follows from standard centering inequality for the
+sub-exponential norm (e.g. see Lemma 2.6.8 and Exercise 2.7.10 in [27]), and the second equality follows from
+Lemma 2.7.6 in [27]. Therefore, we may apply a Bernstein-type inequality for the sum of sub-exponential
+15
+
+random variables (e.g. see Theorem 2.8.1 in [27]) and get
+P
+����∥Zi − Zj∥2
+2 − E∥Zi − Zj∥2
+2
+��� > t
+�
+≤ exp
+�
+− min
+�
+t2
+c �d
+ℓ=1 ∥(Ziℓ − Zjℓ)2 − E[(Ziℓ − Zjℓ)2]∥2
+ψ1
+,
+t
+c′ maxℓ ∥(Ziℓ − Zjℓ)2 − E[(Ziℓ − Zjℓ)2]∥ψ1
+��
+= exp
+�
+− min
+�
+t2
+c′ �d
+ℓ=1 σ4
+ℓ
+,
+t
+c′′ˆσ2
+��
+for some absolute constants c, c′. Set t = c′′ˆσ2 log n for a large enough constant c′′, use �d
+ℓ=1(σℓ/ˆσ)4 ≤
+�d
+ℓ=1(σℓ/ˆσ)2 = O(log n) which follows from Assumption 3.2, and take a union bound over all i, j ∈ V , we
+get that with probability at least 1 − on(1), for all i, j ∈ V it holds that
+∥Zi − Zj∥2
+2 ≤ E∥Zi − Zj∥2
+2 + O(ˆσ2 log n)
+≤ ˜c
+d
+�
+ℓ=1
+∥Ziℓ − Zjℓ∥2
+ψ2 + O(ˆσ2 log n)
+≤ ˜c′
+d
+�
+ℓ=1
+σ2
+ℓ + O(ˆσ2 log n)
+= O(ˆσ2 log n),
+(4)
+where ˜c, ˜c′ are absolute constants.
+For i ∈ K and j /∈ K, the term (µi − µj)T (Zi − Zj) = �d
+ℓ=1(µiℓ − µjℓ)(Ziℓ − Zjℓ) is a sum of independent
+and mean zero sub-Gaussian random variables. We may apply a general Hoeffding’s inequality (see Lemma
+2.6.3 in [27]) and get that
+P(|(µi − µj)T (Zi − Zj)| ≥ t) ≤ 2 exp
+�
+ct2
+maxℓ ∥Ziℓ − Zjℓ∥2
+ψ2∥µi − µj∥2
+2
+�
+≤ 2 exp
+�
+−
+c′t2
+ˆσ2∥µi − µj∥2
+2
+�
+,
+and hence by setting t = c′′ˆσ√log n∥µi − µj∥2 for a large enough constant c′′ we get that with probability at
+least 1 − on(1),
+(µi − µj)T (Zi − Zj) ≥ −O(ˆσ
+�
+log n∥µi − µj∥2), ∀i ∈ K, j /∈ K.
+(5)
+Combining (3), (4), (5), and using ∥µi − µj∥2 ≥ ˆµ = ω(ˆσ√log n), we get that with probability at least
+1 − on(1),
+∥Xi − Xj∥2
+2 ≤ O(ˆσ2 log n), ∀i ∈ K, ∀j ∈ K,
+∥Xi − Xj∥2
+2 ≥ ∥µi − µj∥2
+2 − O(ˆσ
+�
+log n∥µi − µj∥2)
+= ∥µi − µj∥2
+2(1 − on(1)) ≥ ˆµ2(1 − on(1)), ∀i ∈ K, ∀j ̸∈ K.
+By Assumption 3.2, we may pick γ that satisfies γˆσ2 = o(log−1 n) and γˆµ2 = ωn(λ), and for any such γ we
+have
+exp(−γ∥Xi − Xj∥2
+2) ≥ exp(−on(1)), ∀i ∈ K, ∀j ∈ K,
+exp(−γ∥Xi − Xj∥2
+2) ≤ exp(−γˆµ2(1 − on(1))), ∀i ∈ K, ∀j ̸∈ K,
+as required.
+16
+
+B.2
+Proof of Theorem 3.4
+We start with part 1 of the theorem. Without loss of generality let us assume that the node indices are
+such that K = {1, 2, . . . , k} and that x∗
+1 ≥ x∗
+2 ≥ . . . ≥ x∗
+k. In order to show that K ⊆ supp(x∗), it suffices
+to show that x∗
+k > 0. Assume for the sake of contradiction that x∗
+k = 0. Note that since the initial mass is
+(1 + β) �
+i∈K Ti, in an optimal flow routing, the amount of mass that flows over an edge cannot be greater
+than (1 + β) �
+i∈K Ti. This means that wij|x∗
+i − x∗
+j| ≤ (1 + β) �
+i′∈K Ti′ for all i, j ∈ V (recall the basic
+properties of x∗ provided in Section A). Therefore we have that
+x∗
+1 ≤
+k−1
+�
+i=1
+(1 + β) �
+i′∈K Ti′
+wi(i+1)
++ x∗
+k =
+k−1
+�
+i=1
+(1 + β) �
+i′∈K Ti′
+wi(i+1)
+.
+It then follows from Lemma 3.3 that with probability at least 1 − on(1),
+x∗
+1 ≤ (1 + β)k(1 + on(1))
+�
+i∈K
+Ti.
+On the other hand, the total amount of mass that leaves K is
+k
+�
+i=1
+�
+j≥k+1
+j∼i
+wij(x∗
+i − x∗
+j) ≤
+k
+�
+i=1
+x∗
+i
+�
+j≥k+1
+j∼i
+wij ≤ x∗
+1
+�
+(i,j)∈cutG(K)
+wij.
+Apply Lemma 3.3, Lemma C.2 and pick ϵ = δ = 1 there, and use the above bound on x∗
+1, we get that, with
+probability at least 1 − on(1) − k−1/3,
+k
+�
+i=1
+�
+j≥k+1
+j∼i
+wij(x∗
+i − x∗
+j) ≤ (1 + β)k2(1 + on(1))(2q(n − k) + 4 log k/k) exp(−γˆµ2(1 − on(1)))
+�
+i∈K
+Ti.
+Since we started with (1 + β) �
+i∈K Ti initial mass inside K, nodes in K can settle at most �
+i∈K Ti units
+of mass, we know that at least β �
+i∈K Ti amount of mass must leave K. In what follows we show that
+this cannot be the case for appropriately chosen γ, and hence arriving at the desired contradiction. Since
+ˆµ = ω(ˆσ
+�
+log n(1 + λ)), we may pick γ such that γˆσ2 = o(log−1 n) to satisfy the assumption required for
+Lemma 3.3, and at the same time γˆµ2 = ω(1 + λ). Since λ = Ω(log k + log(q(n − k)) + log(1/β)), we know
+that for any terms an = on(1) and bn = on(1) and for sufficiently large n,
+γˆµ2(1 − an) > 2 log k + log(2q(n − k) + 4 log k/k) + log(1/β + 1) + log(1 + bn),
+which implies that, for sufficiently large n,
+(1 + β)k2(1 + on(1))(2q(n − k) + 4 log k/k) exp(−γˆµ2(1 − on(1))) < β,
+and hence
+k
+�
+i=1
+�
+j≥k+1
+j∼i
+wij(x∗
+i − x∗
+j) < β
+�
+i∈K
+Ti,
+which is the desired contradiction. Therefore we must have that x∗
+k > 0 and consequently K ⊆ supp(x∗).
+Now, since x∗
+i > 0 for all i ∈ K, this means that nodes inside K settles exactly �
+i∈K Ti units mass, and
+hence exactly β �
+i∈K Ti mass leaves K. Because x∗
+i > 0 only if node j is saturated with Ti unit mass, we
+get that �
+i∈supp(x∗
+i )\K Ti ≤ β �
+i∈K Ti.
+Part 2 of the theorem is prove by following the same reasoning. Assume for the sake of contradiction
+that x∗
+k = 0. Since p ≥ (4+ϵ)
+δ2
+log k
+k−1 , we apply Lemma C.1 and get that with probability at least 1 − ek−ϵ/2,
+17
+
+cutK(C) ≥ (1 − δ)p(k − 1) for every C ⊆ K such that 1 ≤ |C| ≤ k − 1. We will assume that this event holds.
+Moreover, for any 1 ≤ i ≤ k − 1, the total amount of mass that moves from {1, 2, . . . , i} to {i + 1, i + 2, . . . , k}
+cannot be greater than (1 + β) �
+i∈K Ti. Since there are at least (1 − δ)p(k − 1) edges between {1, 2, . . . , i}
+and {i + 1, i + 2, . . . , k}, we must have that
+x∗
+i − x∗
+i+1 ≤
+(1 + β) �
+i′∈K Ti′
+(1 − δ)p(k − 1) minj,j′∈K,j∼j′ wjj′ , ∀i = 1, 2, . . . , k − 1,
+because, otherwise, there would be more than (1 + β) �
+i∈K Ti mass that moves from {1, 2, . . . , i} to
+{i + 1, i + 2, . . . , k}. Apply Lemma 3.3 we have that, with probability at least 1 − on(1) − ek−ϵ/2,
+x∗
+1 ≤
+k−1
+�
+i=1
+(1 + β) �
+i′∈K Ti′
+(1 − δ)p(k − 1) minj,j′∈K,j∼j′ wjj′ ≤ (1 + β)k(1 + on(1)) �
+i′∈K Ti′
+(1 − δ)p(k − 1)
+.
+The rest of the proof proceeds as the proof of part 1.
+B.3
+Proof of Theorem 3.5
+To see that K ⊆ supp(x∗), let us assume for the sake of contradiction that x∗
+i = 0 for some i ∈ K. This
+means that node i receives at most Ti ≤ Tmax mass, because otherwise we would have x∗
+i > 0. We also know
+that i ̸= s because Tmax < ∆s. Denote F := {j ∈ K : j ∼ s}. We will consider two cases depending on if
+i ∈ F or not. If i ∈ F, then we must have that, with probability at least 1 − on(1),
+wis(x∗
+s − x∗
+i ) ≤ Tmax ⇐⇒ x∗
+s ≤ Tmax/wis + x∗
+i = Tmax(1 + an)
+for some an = on(1), where the last equality follows Lemma 3.3. Moreover, since c2 < 1 we have that
+p(k − 1)
+η(c2)
+= p(k − 1) + q(n − k)e−c2γ ˆµ2 > p(k − 1) + q(n − k)e−γ ˆµ2(1−bn)
+(6)
+for any bn = on(1) and for all sufficiently large n. Therefore, with probability at least 1 − on(1) − 4k−ϵ1/3
+and for all sufficiently large n, the total amount of mass that is sent out from node s is
+�
+ℓ∼s
+wis(x∗
+s − x∗
+ℓ) =
+�
+ℓ∼s
+ℓ∈K
+wis(x∗
+s − x∗
+ℓ) +
+�
+ℓ∼s
+ℓ/∈K
+wis(x∗
+s − x∗
+ℓ)
+(i)
+≤
+�
+ℓ∼s
+ℓ∈K
+x∗
+s +
+�
+ℓ∼s
+ℓ/∈K
+e−γ ˆµ2(1−bn)x∗
+s
+for some bn = on(1)
+(ii)
+≤ (1 + δ1)p(k − 1)x∗
+s + ((1 + δ1)q(n − k) + 2δ1p(k − 1))e−γ ˆµ2(1−bn)x∗
+s
+≤ (1 + 3δ1)
+�
+p(k − 1) + q(n − k)e−γ ˆµ2(1−bn)�
+x∗
+s
+(iii)
+< (1 + 3δ1)p(k − 1)
+η(c2)
+x∗
+s
+≤ (1 + 3δ1)p(k − 1)
+η(c2)
+Tmax(1 + an)
+(iv)
+< c1(1 + 3δ1)p(k − 1)
+η(c2)
+Tmax,
+where (i) follows from Lemma 3.3 and x∗ ≥ 0, (ii) follows from Lemma C.3, (iii) follows from (6), (iv) follows
+from the assumption that c1 > 1 and hence for all sufficiently large n we have c1 ≥ (1 + an) where an = on(1).
+18
+
+Since the initial mass equals the sum of Ts and the total amount of mass that is sent out from s, we get that
+the total amount of initial mass is
+∆s < c1(1 + 3δ1)p(k − 1)
+η(c2)
+Tmax + Tmax < c1Tmax
+�
+(1 + 3δ1)(1 +
+1
+k−1)k
+η(c2)
+�
+< c1Tmax
+m(δ1, δ2)k
+η(c2)2
+= ∆s,
+which is a contradiction. Therefore, we must have i ̸∈ F.
+Suppose now that i ̸∈ F. Then we know that node i receives at most Ti ≤ Tmax mass from its neighbors. In
+particular, node i receives at most Tmax mass from nodes in F, that is, �
+j∈F
+j∼i
+wijx∗
+j ≤ Tmax. By Lemma C.4,
+we know that with probability at least 1 − 2k−ϵ1/3 − k−2ϵ2, node i has at least (1 − δ1)(1 − δ2)p2(k − 1)
+neighbors in F. Apply Lemma 3.3 we get that, with probability at least 1 − on(1) − 2k−ϵ1/3 − k−2ϵ2,
+�
+j∈F
+j∼i
+wijx∗
+j ≤ Ti =⇒ (1 − δ1)(1 − δ2)p2(k − 1) · min
+j∈F
+j∼i
+x∗
+j ≤ Tmax · max
+j∈F
+j∼i
+1
+wij
+=⇒ min
+j∈F
+j∼i
+≤
+Tmax(1 + an)
+(1 − δ1)(1 − δ2)p2(k − 1)
+=⇒ min
+j∈F ≤
+Tmax(1 + an)
+(1 − δ1)(1 − δ2)p2(k − 1)
+for some an = on(1). Let j ∈ F a node such that x∗
+j ≤ x∗
+ℓ for all ℓ ∈ F, then
+x∗
+j ≤
+Tmax(1 + an)
+(1 − δ1)(1 − δ2)p2(k − 1).
+(7)
+By Lemma C.4, with probability at least 1 − 2k−ϵ1/3 − k−2ϵ2, node j has at least (1 − δ1)(1 − δ2)p2(k − 1) − 1
+neighbors in F. Since x∗
+j ≤ x∗
+ℓ for all ℓ ∈ F and x∗
+j ≤ x∗
+s, we know that
+|{ℓ ∈ K : x∗
+ℓ ≥ x∗
+j}| ≥ (1 − δ1)(1 − δ2)p2(k − 1)
+(8)
+Therefore, for all sufficiently large n, with probability at least 1 − on(1) − 4k−ϵ1/3 − k−2ϵ2, the maximum
+amount of mass that node j can send out is
+�
+ℓ∼j
+wjℓ(x∗
+j − x∗
+ℓ) =
+�
+ℓ∼j
+ℓ∈K
+wjℓ(x∗
+j − x∗
+ℓ) +
+�
+ℓ∼j
+ℓ̸∈K
+wjℓ(x∗
+j − x∗
+ℓ)
+(i)
+≤
+�
+ℓ∼j
+ℓ∈K
+wjℓ(x∗
+j − x∗
+ℓ) +
+�
+ℓ∼j
+ℓ̸∈K
+e−γ ˆµ2(1−bn)(x∗
+j − x∗
+ℓ)
+for some bn = on(1)
+(ii)
+≤
+�
+(1 + δ1)p(k − 1) − (1 − δ1)(1 − δ2)p2(k − 1)
+�
+x∗
+j
++
+�
+(1 + δ1)q(n − k) + 2δ1p(k − 1)
+�
+e−γ ˆµ2(1−bn)x∗
+j
+≤
+�
+(1 + 3δ1)
+�
+p(k − 1) + q(n − k)e−γ ˆµ2(1−bn)�
+− (1 − δ1)(1 − δ2)p2(k − 1)
+�
+x∗
+j
+(iii)
+≤
+�
+(1 + 3δ1)p(k − 1)
+η(c2)
+− (1 − δ1)(1 − δ2)p2(k − 1)
+�
+x∗
+j
+(iv)
+≤
+�
+(1 + 3δ1)p(k − 1)
+η(c2)
+− (1 − δ1)(1 − δ2)p2(k − 1)
+�
+Tmax(1 + an)
+(1 − δ1)(1 − δ2)p2(k − 1)
+≤ Tmax(1 + an)
+(1 + 3δ1)
+(1 − δ1)(1 − δ2)
+1
+pη(c2) − Tmax,
+19
+
+where (i) follows from Lemma 3.3, (ii) follows from Lemma C.3 and (8), (iii) follows from (6) and (iv) follows
+from (7). Now, since node j settles at most Tj ≤ Tmax mass, the maximum amount of mass that node j
+receives is
+Tmax(1 + an)
+(1 + 3δ1)
+(1 − δ1)(1 − δ2)
+1
+pη(c2) − Tmax + Tmax = Tmax(1 + an)
+(1 + 3δ1)
+(1 − δ1)(1 − δ2)
+1
+pη(c2).
+This means that
+wjs(x∗
+s − x∗
+j) ≤ Tmax(1 + an)
+(1 + 3δ1)
+(1 − δ1)(1 − δ2)
+1
+pη(c2)
+=⇒ x∗
+s ≤
+Tmax(1 + a′
+n)
+(1 − δ1)(1 − δ2)
+�
+1
+p2(k − 1) + (1 + 3δ1)
+pη(c2)
+�
+for some a′
+n = on(1), where we have applied Lemma 3.3 for wjs. Apply the same reasoning as before, we get
+that with probability at least 1 − on(1) − 4k−ϵ1/3 − k−2ϵ2 for all sufficiently large n, the total amount of mass
+that is sent out from node s is
+�
+ℓ∼s
+wis(x∗
+s − x∗
+ℓ) < (1 + 3δ1)p(k − 1)
+η(c2)
+x∗
+s
+≤
+Tmax(1 + a′
+n)
+(1 − δ1)(1 − δ2)
+�(1 + 3δ1)
+pη(c2)
++ (1 + 3δ1)2(k − 1)
+η(c2)2
+�
+≤ c1Tmax
+(1 + 3δ1)
+(1 − δ1)(1 − δ2)
+(1 + 3δ2 +
+1
+p(k−1))
+η(c2)2
+(k − 1)
+≤ c1Tmax
+m(δ1, δ2)(k − 1)
+η(c2)2
+,
+but then this means that the total amount of initial mass is
+∆s < c1Tmax
+m(δ1, δ2)(k − 1)
+η(c2)2
++ Tmax < c1Tmax
+m(δ1, δ2)k
+η(c2)2
+= ∆s
+which is a contradiction. Therefore we must have i ̸∈ K, but then this contradicts our assumption that i ∈ K.
+Since our choice of i, s ∈ K were arbitrary, this means that x∗
+i > 0 for all i ∈ K and for all s ∈ K.
+Finally, the upper bound on the false positives follows directly from the fact that x∗
+i > 0 only if node i is
+saturated with exactly Ti mass. When Ti = 1 for all i the result follows directly from ∆s = c1m(δ1, δ2)k/η(c2)2.
+When Ti = deg(i) for all i, we may apply Lemma C.3 and get that
+∆s ≤ c1m(δ1, δ2)
+η(c2)2
+(1 + δ1)k(p(k − 1) + q(n − k)) ≤ c1m(δ1, δ2)
+η(c2)2
+(1 + δ1)
+(1 − δ1)vol(K)
+from which the result follows.
+C
+Technical lemmas
+Lemma C.1 (Lower bound of internal cut). For any 0 < δ ≤ 1 and ϵ > 0, if p ≥ (4+ϵ)
+δ2
+log k
+k−1 and k ≥ 20, then
+with probability at least 1 − ek−ϵ/2 we have that cutK(C) ≥ (1 − δ)p(k − 1) for all proper subsets C ⊂ K.
+Proof. Consider integers j such that 1 ≤ j ≤ k/2. First fix some j and let C ⊂ K be such that |C| = j. Note
+that cut(C) is the sum of j(k − j) independent Bernoulli random variables with expectation E(cut(C)) =
+20
+
+pj(k − j). Therefore we may apply the Chernoff bound and get
+P(cutK(C) ≤ (1 − δ)p(k − 1)) ≤ e−pj(k−j)
+�
+ej(k − j)
+(1 − δ)(k − 1)
+�(1−δ)p(k−1)
+.
+By a union bound over all subsets C ⊂ K such that |C| = j we get that
+P (cutK(C) ≤ (1 − δ)p(k − 1), ∀C ⊂ K s.t. |C| = j)
+≤
+�k
+j
+�
+e−pj(k−j)
+�
+ej(k − j)
+(1 − δ)(k − 1)
+�(1−δ)p(k−1)
+≤
+�ek
+j
+�j
+exp
+�
+−pj(k − j) + (1 − δ)p(k − 1) + (1 − δ)p(k − 1) log
+�
+j(k − j)
+(1 − δ)(k − 1)
+��
+= exp
+�
+−pj(k − j) + (1 − δ)p(k − 1) + (1 − δ)p(k − 1) log
+�
+j(k − j)
+(1 − δ)(k − 1)
+�
++ j + j log
+�k
+j
+��
+.
+(9)
+Now consider the exponent in (9),
+f(j) = −pj(k − j) + (1 − δ)p(k − 1) + (1 − δ)p(k − 1) log
+�
+j(k − j)
+(1 − δ)(k − 1)
+�
++ j + j log
+�k
+j
+�
+,
+we will show that f(j) ≤ −(1 + ϵ/2) log k + 1 for all 1 ≤ j ≤ k/2 and k ≥ 20. Let us first consider the interval
+[1, 3k/8]. The derivative of f(j) with respect to j is
+f ′(j) = −p(k − 2j) + (1 − δ)p(k − 1)(k − 2j)
+j(k − j) + log
+�k
+j
+�
+,
+and we have that f ′(j) ≤ 0 for all 1 ≤ j ≤ 3k/8. To see this, for 1 ≤ j ≤ k/2 we have
+(k − 1)
+j(k − j) ≤ 1 ⇐⇒ (1 − δ)p(k − 1)(k − 2j)
+j(k − j)
+≤ (1 − δ)p(k − 2j)
+⇐⇒ −p(k − 2j) + (1 − δ)p(k − 1)(k − 2j)
+j(k − j) ≤ −δp(k − 2j),
+(10)
+moreover, since p ≥ (4+ϵ)
+δ2
+log k
+k−1 , for 1 ≤ j ≤ 3k/8 and k ≥ 2 we have
+− δp(k − 2j) ≤ −δpk
+4
+≤ − (4 + ϵ)k
+4δ(k − 1) log k ≤ − log k ≤ − log(k/j),
+(11)
+and thus by combining (10) and (11) we get f ′(j) ≤ −δp(k − 2j) + log(k/j) ≤ 0 for all 1 ≤ j ≤ 3k/8. This
+implies that f(j) achieves maximum at j = 1 over the interval [1, 3k/8]. Therefore, for all 1 ≤ j ≤ 3k/8,
+f(j) ≤ f(1) = −p(k − 1) + (1 − δ)p(k − 1) − (1 − δ)p(k − 1) log(1 − δ) + 1 + log k
+= −p(k − 1)(δ + (1 − δ) log(1 − δ)) + 1 + log k
+≤ −p(k − 1)δ2/2 + 1 + log k
+≤ −(2 + ϵ/2) log k + 1 + log k
+= −(1 + ϵ/2) log k + 1
+where the second inequality follows from the numeric inequality δ + (1 − δ) log(1 − δ) ≥ δ2/2 for δ ∈ (0, 1),
+and the third inequality follows from the assumption that p ≥ (4+ϵ)
+δ2
+log k
+k−1 .
+21
+
+Next, consider the value of f(j) over the interval [3k/8, k/2]. We have that for 3k/8 ≤ j ≤ k/2 and k ≥ 20,
+f(j) ≤ −p
+�3k
+8
+� �5k
+8
+�
++ (1 − δ)p(k − 1)
+�
+1 + log
+�
+k2/4
+(1 − δ)(k − 1)
+��
++ k
+2 + 3k
+8 log
+�8
+3
+�
+≤ −15
+64pk2 + p(k − 1)
+�
+1 + (1 − δ) log
+� k2/4
+k − 1
+��
++ 22
+25k
+≤ −pk
+� 41
+256k − 1 − log
+� k2/4
+k − 1
+��
+− k
+� 19
+256pk − 22
+25
+�
+≤ −1
+2pk
+≤ −(2 + ϵ/2) log k.
+In the above, the first inequality follows from the fact that the term j log(k/j) is decreasing over the interval
+[3k/8, k/2], the second inequality follows from the numeric inequality (1 − δ) − (1 − δ) log(1 − δ) ≤ 1 for
+δ ∈ (0, 1) which follows from the fact that log x ≥ 1 − 1/x for x > 0, the forth inequality follows from k ≥ 20.
+Therefore, the exponent in (9) satisfies f(j) ≤ −(1 + ϵ/2) log k + 1 for all 1 ≤ j ≤ k/2 and k ≥ 20. Finally,
+apply a union bound we get that
+P(cutK(C) ≤ (1 − δ)p(k − 1), ∀C ⊂ K s.t. 1 ≤ |C| ≤ k − 1)
+=
+⌊k/2⌋
+�
+j=1
+P(cutK(C) ≤ (1 − δ)p(k − 1), ∀C ⊂ K s.t. |C| = j)
+≤ exp(f(j) + log k) ≤ exp
+�
+− ϵ
+2 log k + 1
+�
+= ek−ϵ/2
+which proves the required result.
+Lemma C.2 (Upper bound of external cut). For any 0 < δ ≤ 1 and ϵ > 0 with probability at least 1 − k−ϵ/3
+we have that cutG(K) ≤ (1 + δ)qk(n − k) + (eϵ/δ2 + ϵ/3) log k.
+Proof. Note that cutG(K) is the sum of k(n − k) independent Bernoulli random variables with mean
+E[cutG(K)] = qk(n−k). We consider two cases depending on the value of qk(n−k). If qk(n−k) ≥ ϵ log k/δ2,
+then by the multiplicative Chernoff bound we have that,
+P(cutG(K) ≥ (1 + δ)qk(n − k)) ≤ exp
+�
+−δ2
+3 qk(n − k)
+�
+≤ exp (−ϵ log k/3) .
+(12)
+Next consider the case qk(n − k) ≤ ϵ log k/δ2. Denote c(ϵ, δ) := eϵ/δ2 + ϵ/3 and observe that
+ϵ
+δ2 = c(ϵ, δ) − ϵ/3
+e
+=
+�
+1 −
+ϵ/3
+c(ϵ, δ)
+� c(ϵ, δ)
+e
+≤ exp
+�
+− ϵ/3
+c(ϵ, δ)
+� c(ϵ, δ)
+e
+.
+This means that
+qk(n − k) ≤ ϵ
+δ2 log k ≤ exp
+�
+− ϵ/3
+c(ϵ, δ) − 1
+�
+c(ϵ, δ) log k,
+and thus
+qk(n − k)
+c(ϵ, δ) log k ≤ exp
+�
+− ϵ/3
+c(ϵ, δ) − 1
+�
+⇐⇒
+c(ϵ, δ) + c(ϵ, δ) log
+� qk(n − k)
+c(ϵ, δ) log k
+�
+≤ −ϵ/3.
+22
+
+Therefore the Chernoff bound yields
+P (cutG(K) ≥ c(ϵ, δ) log k) ≤ e−qk(n−k)
+� eqk(n − k)
+c(ϵ, δ) log k
+�c(ϵ,δ) log k
+= exp
+�
+−qk(n − k) + c(ϵ, δ) log k
+�
+1 + log
+� qk(n − k)
+c(ϵ, δ) log k
+���
+≤ exp
+�
+log k
+�
+c(ϵ, δ) + c(ϵ, δ) log
+� qk(n − k)
+c(ϵ, δ) log k
+���
+≤ exp(−ϵ log k/3).
+(13)
+Combining (12) and (13) gives the required result.
+Lemma C.3 (Concentration of degrees). If p ≥ (3+ϵ)
+δ2
+log k
+k−1 for some ϵ > 0 and 0 < δ ≤ 1, then with probability
+at least 1 − 2k−ϵ/3 we have that
+(1 − δ)p(k − 1) ≤ degK(i) ≤ (1 + δ)p(k − 1), ∀i ∈ K.
+Similarly, with probability at least 1 − 2k−ϵ/3 we have that
+(1 − δ)(p(k − 1) + q(n − k)) ≤ degG(i) ≤ (1 + δ)(p(k − 1) + q(n − k)), ∀i ∈ K.
+Proof. For each node i ∈ K, degK(i) is the sum of independent Bernoulli random variables with mean
+E[degK(i)] = p(k − 1), therefore, apply the multiplicative Chernoff bound we have
+P(| degK(i) − p(k − 1)| ≥ δp(k − 1)) ≤ 2 exp(−δ2p(k − 1)/3) ≤ 2 exp(−(1 + ϵ) log k/3).
+By taking a union bound over all i ∈ K we obtain the required concentration result for degK(i) for all i ∈ K.
+The result for degG(i) for all i ∈ K is obtained similarly.
+Lemma C.4 (Well-connected cluster). If p ≥ max( (3+ϵ1)
+δ2
+1
+log k
+k−1 ,
+(2+ϵ2)
+δ2
+√1−δ1
+√log k
+√k−1 ), then with probability at least
+1 − 2k−ϵ1/3 − k−2ϵ2 we have that for all s ∈ K, for all i ∈ K\{s}, there are at least (1 − δ1)(1 − δ2)p2(k − 1)
+paths connecting node i to node s such that, the path lengths are at most 2 and the paths are mutually
+non-overlapping, i.e., an edge appears in at most one of the paths.
+Proof. Let s ∈ K and denote F the set of neighbors of s in K. By Lemma C.3 and our assumption on p we
+know that |F| ≥ (1 − δ1)p(k − 1) with probability at least 1 − 2k−ϵ1/3. Let us denote E(A, B) the set of edges
+between A ⊆ K and B ⊆ K. Let i ∈ K\{s}. If i ̸∈ F, then |E({i}, F)| is the sum of independent Bernoulli
+random variables with mean E[|E({i}, F)|] = |F|p. Apply the multiplicative Chernoff bound we get that
+P(|E({i}, F)| ≤ (1 − δ2)|F|p) ≤ exp
+�
+−δ2
+2
+2 |F|p
+�
+≤ exp
+�
+−δ2
+2(1 − δ1)
+2
+p2(k − 1)
+�
+≤ exp(−(2 + 2ϵ2) log k)
+where the last inequality is due to our assumption that p ≥
+(2+ϵ2)
+δ2
+√1−δ1
+√log k
+√k−1 . If i ∈ F, then the edge (i, s) is a
+path of length 1 between node i and node s, moreover,
+P(|E({i}, F\{i})| + 1 ≤ (1 − δ2)|F|p) ≤ P(|E(i′, F)| ≤ (1 − δ2)|F|p)
+for any node i′ ∈ K\F and i′ ̸= s. Note that, for i ∈ K\{s}, each edge (i, j) in E({i}, F\{i}) identifies a
+unique path (i, j, s) and all these paths do not have overlapping edges. Therefore, denote P(i, s) the set
+of mutually non-overlapping paths of length at most 2 between i and s. and take union bounds over all
+i ∈ K\{s} and then over all s ∈ K, we get that
+P(P(i, s) ≤ (1 − δ2)|F|p, ∀s ∈ K, ∀i ∈ K\{s}) ≤ k−2ϵ2.
+Finally, a union bound over the above event and the event that |F| ≤ (1 − δ1)p(k − 1) gives the required
+result.
+23
+
+D
+Dataset details, empirical setup and additional results
+The co-authorship graphs are based on the Microsoft Academic Graph from the KDD Cup 2016 challenge [23].
+In these graphs, nodes are authors, and two nodes are connected by an edge if they have coauthored a paper.
+The clusters are defined according to the most active research field of each author. The node attributes
+represent paper keywords for each author’s papers. The first graph consists of 18,333 computer science
+researchers and 81,894 connections among them. Each computer science researcher belongs to one of the 15
+ground-truth clusters. The node attributes consists of 6,805 key words. The second graph consists of 34,493
+physics researchers and 247,962 connections among them. Each physics researcher belongs to one of the 5
+ground-truth clusters. The node attributes consists of 8,415 key words. The cluster sizes are given in Table 2.
+Table 2: Cluster statistics in co-authorship graphs
+Network Cluster
+Number of nodes Volume
+Computer Science
+Bioinformatics
+708
+3767
+Machine Learning
+462
+4387
+Computer Vision
+2050
+20384
+NLP
+429
+2476
+Graphics
+1394
+15429
+Networks
+2193
+18364
+Security
+371
+2493
+Databases
+924
+9954
+Data Mining
+775
+7573
+Game Theory
+118
+362
+HCI
+1444
+15145
+Information Theory
+2033
+16007
+Medical Informatics
+420
+3838
+Robotics
+4136
+33708
+Theoretical CS
+876
+9901
+TOTAL
+18333 163788
+Physics
+Phys. Rev. A
+5750
+52151
+Phys. Rev. B
+5045
+54853
+Phys. Rev. C
+17426 325475
+Phys. Rev. D
+2753
+40451
+Phys. Rev. E
+3519
+22994
+TOTAL
+34493 495924
+For both datasets, we preprocess the node attributes by applying PCA to reduce the dimension to 128. In
+addition, for each node we enhance its attributes by taking a uniform average over its own attributes and
+the neighbors’ attributes. Uniform averaging of neighborhood attributes has been shown to improve the
+signal-to-noise ratio in CSBM [5]. This operation does not break the local nature of Algorithm 2 because
+it only needs to be done whenever it becomes necessary for subsequent computations, i.e., when a node is
+looked at by Algorithm 2.
+We consider two ways for setting the sink capacities. The first is Ti = degG(i) for all i. The corresponding
+local clustering results are reported in Table 1 in the main text. The second is Ti = 1 for all i. The additional
+results are presented in Table 3. For each cluster K in a graph, given a seed node s ∈ K, we run Algorithm 2
+with source mass ∆s = α �
+i∈K Ti for α ∈ {1.5, 1.75, 2, . . . , 5}. We select the cluster that has the minimum
+edge-weighted conductance. Given edge weights wij for (i, j) ∈ E and a cluster C ⊆ V , the edge-weighted
+24
+
+conductance of C is the ratio
+�
+i∈C,j̸∈C wij
+�
+i∈C
+�
+j∼i wij
+.
+We measure recovery quality using the F1 score. For each cluster we run 100 trials, for each trial we randomly
+select a seed node from the target cluster. We report average F1 scores over 100 trials. We set γ = 0.02 so
+that the edge weights are reasonably distributed between 0 and 1, that is, not all edges weights are arbitrarily
+close to 1, and not all edge weights are arbitrarily close 0. We find that the results do not change much when
+we use other choices for γ within a reasonable range, e.g. γ ∈ [0.005, 0.1]. For both choices of T, using node
+attributes generally improves the recovery accuracy. Overall, setting the sink capacities to Ti = degG(i) leads
+to higher F1 scores than setting Ti = 1.
+Table 3: F1 scores for local clustering in co-authorship networks under different settings of flow diffusion
+Ti = degG(i) for all i
+Ti = 1 for all i
+Network
+Cluster
+No attr.
+Ues attr.
+Improv.
+No attr.
+Ues attr.
+Improv.
+Computer Science
+Bioinformatics
+32.1
+39.3
+7.2
+23.5
+31.7
+8.2
+Machine Learning
+30.9
+37.3
+6.4
+27.5
+34.4
+6.9
+Computer Vision
+37.6
+35.5
+-2.1
+40.4
+37.8
+-2.6
+NLP
+45.2
+52.3
+7.1
+34.3
+37.2
+2.9
+Graphics
+38.6
+49.2
+10.6
+39.1
+41.3
+2.2
+Networks
+44.1
+47.0
+2.9
+43.0
+44.1
+1.1
+Security
+29.9
+35.7
+5.8
+23.0
+26.2
+3.2
+Databases
+48.5
+58.1
+9.6
+41.9
+42.6
+0.7
+Data Mining
+27.5
+28.8
+1.3
+26.2
+28.6
+2.4
+Game Theory
+60.6
+66.0
+5.4
+56.9
+62.6
+5.7
+HCI
+70.0
+77.6
+7.6
+44.0
+63.1
+19.1
+Information Theory
+47.4
+46.9
+-0.5
+41.6
+41.4
+-0.2
+Medical Informatics
+65.7
+70.3
+4.6
+62.7
+68.1
+5.4
+Robotics
+59.9
+59.9
+0.0
+58.8
+55.9
+-2.9
+Theoretical CS
+66.3
+70.7
+4.4
+54.9
+59.1
+4.2
+Physics
+Phys. Rev. A
+69.4
+70.9
+1.5
+53.5
+60.9
+7.4
+Phys. Rev. B
+41.4
+42.3
+0.9
+40.4
+41.1
+0.7
+Phys. Rev. C
+79.3
+82.1
+2.8
+84.9
+85.9
+1.0
+Phys. Rev. D
+62.3
+68.9
+6.6
+63.6
+70.0
+6.4
+Phys. Rev. E
+49.5
+53.7
+4.2
+30.1
+34.9
+4.8
+AVERAGE
+50.3
+54.6
+4.3
+44.5
+48.3
+3.8
+D.1
+Additional experiments with Amazon co-purchase graph
+We carry out additional experiments using a segment of the Amazon co-purchase graph [21, 23]. In this
+graph, nodes represent products, and two products are connected by an edge if they are frequently bought
+together. The clusters are defined according to the product category. The node attributes are bag-of-words
+encoded product reviews. The cluster sizes are given in Table 4. We use exactly the same empirical settings
+as before. The local clustering results are reported in Table 5.
+We estimate an average signal-to-noise ratio in each dataset as follows. Let K1, K2, . . . , KC denote a partition
+25
+
+Table 4: Cluster statistics in the Amazon co-purchase graph
+Cluster
+Number of nodes Volume
+Film Photography
+365
+13383
+Digital Cameras
+1634
+32208
+Binoculars & Scopes
+686
+21611
+Lenses
+901
+26479
+Tripods & Monopods
+872
+26133
+Video Surveillance
+798
+17959
+Lighting & Studio
+1900
+86989
+Flashes
+331
+13324
+TOTAL
+18333 163788
+Table 5: F1 scores for local clustering in a segment of the Amazon co-purchase graph
+Ti = degG(i) for all i
+Ti = 1 for all i
+Cluster
+No attr.
+Ues attr.
+Improv.
+No attr.
+Ues attr.
+Improv.
+Film Photography
+69.0
+71.9
+2.9
+70.4
+74.0
+3.6
+Digital Cameras
+54.4
+56.0
+1.6
+42.7
+43.1
+0.4
+Binoculars
+83.3
+85.1
+1.8
+81.8
+82.7
+0.9
+Lenses
+39.0
+40.4
+1.4
+32.2
+32.9
+0.7
+Tripods & Monopods
+46.3
+47.8
+1.5
+37.9
+38.1
+0.2
+Video Surveillance
+94.7
+94.9
+0.2
+94.0
+93.8
+-0.2
+Lighting & Studio
+49.6
+49.5
+-0.1
+53.7
+53.5
+-0.2
+Flashes
+33.3
+32.7
+-0.6
+27.0
+25.8
+-1.2
+AVERAGE
+58.7
+59.8
+1.1
+55.0
+55.5
+0.5
+of nodes into distinct clusters. Let Xi be the node attributes of node i. For 1 ≤ r ≤ C let
+¯µr :=
+1
+|Kr|
+�
+i∈Kr
+Xi
+be the empirical mean of node attributes in the cluster Kr. Denote
+¯λr :=
+min
+1≤s≤C,s̸=r ∥¯µr − ¯µs∥2
+the empirical minimum pairwise mean distance between cluster Kr and other clusters. Let ¯σℓ denote the
+empirical standard deviation for the ℓth attribute and let ¯σ = 1
+d
+�d
+ℓ=1 ¯σℓ, where d is the dimension of node
+attributes. Then we compute an average relative signal strength for the entire dataset as
+ratio :=
+1
+|C|
+C
+�
+r=1
+¯λr/¯σ.
+The computed results are shown in Table 6. Observe that the ratio is much smaller for the Amazon co-purchase
+graph than the two co-authorships graphs. This means that the relative strength of attribute signal is much
+smaller for the Amazon co-purchase graph, and it explains why there is only a very small improvement when
+using node attributes.
+The results we observe in the experiments with real-world datasets indicate that, an very interesting future
+work is to incorporate node embedding and parameter learning into the local flow diffusion pipeline (to
+26
+
+Table 6: Relative signal strength for each dataset
+graph
+ratio
+Co-authorship (Computer Science)
+41.69
+Co-authorship (Physics)
+77.09
+Amazon co-purchase
+7.58
+improve signal-to-noise ratio of node attributes), where the attributes and their relative importance may be
+optimized simultaneously alongside the local diffusion process.
+27
+
diff --git a/k9FPT4oBgHgl3EQf2jWr/content/tmp_files/load_file.txt b/k9FPT4oBgHgl3EQf2jWr/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c38ba0e375fff63beee294fa0975086cce12ab2d
--- /dev/null
+++ b/k9FPT4oBgHgl3EQf2jWr/content/tmp_files/load_file.txt
@@ -0,0 +1,1463 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf,len=1462
+page_content='Weighted flow diffusion for local graph clustering with node  attributes: an algorithm and statistical guarantees  Shenghao Yang∗  Kimon Fountoulakis∗  Abstract  Local graph clustering methods aim to detect small clusters in very large graphs without the need to  process the whole graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' They are fundamental and scalable tools for a wide range of tasks such as local  community detection, node ranking and node embedding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' While prior work on local graph clustering  mainly focuses on graphs without node attributes, modern real-world graph datasets typically come with  node attributes that provide valuable additional information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' We present a simple local graph clustering  algorithm for graphs with node attributes, based on the idea of diffusing mass locally in the graph while  accounting for both structural and attribute proximities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Using high-dimensional concentration results,  we provide statistical guarantees on the performance of the algorithm for the recovery of a target cluster  with a single seed node.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' We give conditions under which a target cluster generated from a fairly general  contextual random graph model, which includes both the stochastic block model and the planted cluster  model as special cases, can be fully recovered with bounded false positives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Empirically, we validate all  theoretical claims using synthetic data, and we show that incorporating node attributes leads to superior  local clustering performances using real-world graph datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  1  Introduction  Given a graph G and a seed node in that graph, a local graph clustering algorithm finds a good small cluster  that contains the seed node without looking at the whole graph [3, 25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Because the graphs arising from  modern applications are massive in size and yet are rich in small-scale local structures [18, 16], local graph  clustering has become an important scalable tool for probing large-scale graph datasets with a wide range of  applications in machine learning and data analytics [14, 13, 20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  Traditional local graph clustering algorithms primarily focus on the structural properties of a graph dataset, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  nodes and edges, and consequently the analyses of these algorithms are often concerned with the combinatorial  properties of the output cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' For example, in most previous studies one is interested in the conductance  of a cluster and define a good cluster as one that has low conductance [25, 3, 22, 2, 4, 24, 28, 13, 19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' In  this case, the objective of local graph clustering is thus detecting a low conductance cluster around the  seed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' With the increasing availability of multi-modal datasets, it is now very common for a graph dataset to  contain additional sources of information such as node attributes, which may prove to be crucial for correctly  identifying clusters with rather noisy edge connections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' However, nearly all existing local graph clustering  algorithms do not work with attributed graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Moreover, in the presence of node attributes, the objective  and analysis of a local graph clustering algorithm should also adjust to take into account both sources of  information (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' graph structure and attributes) as opposed to focus solely on the combinatorial notion of  conductance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  David R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Cheriton School of Computer Science, University of Waterloo, Waterloo, Canada.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  Emails: shenghao.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='yang@uwaterloo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='ca, kimon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='fountoulakis@uwaterloo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='ca  1  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='13187v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='SI]  30 Jan 2023  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='1  Our contributions  We propose a simple local graph clustering algorithm that simultaneously considers both graph structural  and node attribute information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' We analyze the performance of the proposed algorithm from a statistical  perspective where we assume that the target cluster and the node attributes have been generated from a  random data model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' We provide conditions under which the algorithm is guaranteed to fully recover the  target cluster with bounded false positives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  Our local graph clustering algorithm uses the recently proposed flow diffusion model on graphs [13, 8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' The  original flow diffusion is proposed to solve the local graph clustering problem on unweighted graphs without  node attributes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' In this work we consider flow diffusion on weighted graphs where the edge weights are  designed to reflect the proximity between node attributes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' A distinct characteristic of the proposed algorithm  is its simplicity and flexibility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' On one hand, the algorithm has few hyperparameters and thus it does  not require much tuning;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' while on the other hand, it allows flexible initialization of source mass and sink  capacities, which enables us to obtain different types of recovery guarantees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  Our main contribution is the analyses of the algorithm for the recovery of a target cluster with a single seed  node.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' We provide high probability guarantees on the performance of the algorithm under a certain type of  contextual random graph model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' The data model we consider is fairly general.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' On the structural side, it only  concerns the connectivity of nodes within the target cluster and its adjacent nodes, and hence it encompasses  the stochastic block model (SBM) and the planted cluster model as special cases;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' on the node attribute  side, it allows an attribute be modelled by a sub-Gaussian random variable, and this includes Gaussian,  uniform, Bernoulli, and any discrete or continuous random variables over a finite domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Depending on a  signal-to-noise ratio of the node attributes, we present two recovery results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Informally, if we have very good  node attributes, then with overwhelming probability the algorithm fully recovers the target cluster with nearly  zero false positives, irrespective of the interval connectivity of the target cluster (as long as it is connected);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  on the other hand, if we have good, but not too good, node attributes, then with overwhelming probability  the algorithm fully recovers the target cluster, with the size of the false positives jointly controlled by both  the combinatorial conductance of the target cluster and the signal-to-noise ratio of the node attributes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  Finally, we carry out experiments on synthetic data to verify all theoretical claims and on real-world data to  demonstrate the advantage of incorporating node attributes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='2  Previous work  The local graph clustering problem is first introduced by [25] where the authors proposed a random-walk  based algorithm with early termination.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Later [3] studied the same problem using approximate personalized  PageRank vectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' There is a long line of work on local graph clustering where the analysis of the algorithm  concerns the conductance of the output cluster [3, 22, 25, 2, 4, 24, 28, 13, 19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' The first statistical analysis  of local graph clustering is considered in [15] where the authors analyze the average-case performance of  the ℓ1-regularized PageRank [12] over a random data model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' None of these work studies local clustering in  attributed graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  The idea to utilize both structural and node attribute information has been applied in the context of  community detection, where the goal is to detect all clusters in a graph [30, 17, 31, 26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' These methods  require processing the whole graph and hence are not suitable for local graph clustering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  Recently, contextual random graph models are been used in the literature for analyzing the performance  of certain algorithms for attributed graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' [10, 29, 7, 1] study algorithms for community detection in the  contextual stochastic block model (CSBM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' [5, 11, 6] analyze the separability of nodes in CSBM by functions  that are representable by graph neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' The random model we consider in this work is more general  and we are the first to consider statistical performance of a local graph clustering algorithm in contextual  2  random models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  2  Weighted flow diffusion and local graph clustering with node  attributes  In this section, we start by providing an overview of flow diffusion on graphs, describing its physical  interpretation as spreading mass in a graph along edges, and disucssing some important algorithmic properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  Then, we present an algorithm that uses edge-weighted flow diffusion for local graph clustering with node  attributes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='1  Notations and basic properties of flow diffusion  We consider undirected, weighted and connected graph G = (A, W) which consists of n nodes and m edges,  where A ∈ {0, 1}n×n is the combinatorial adjacency matrix, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=', Aij = 1 if node i is adjacent to node j and  0 otherwise, W ∈ Rm×m is a diagonal matrix of edge weights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' We write wij = W(i,j),(i,j) as the weight of  an edge (i, j).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' If W = I then G reduces to an unweighted graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' We denote V = {1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' , n} as the set of  nodes and E as the set of edges, i ∼ j if (i, j) ∈ E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' The combinatorial degree degG(i) of a node i ∈ V is the  number of edges incident to it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' For a subset C ⊆ V , the volume of C is given by volG(C) = �  i∈C degG(i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  We use subscripts to indicate the graph we are working with, and we omit them when the graph is clear from  context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' We denote B ∈ Rm×n as the combinatorial signed incidence matrix under an arbitrary orientation  of the graph, where the row that corresponds to the oriented edge (i, j) has two nonzero entries, with −1 at  column i and 1 at column j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' The support of a vector x is supp(x) = {i : xi ̸= 0}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' We use standard notations  On, Ωn, Θn, on, ωn for asymptotic behaviors of a function with respect to n, and we omit the subscript when  it is clear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  Given a source vector ∆ ∈ Rn and a sink capacity vector T ∈ Rn, a flow diffusion on G is formulated as the  following optimization problem:  min  f  1  2f T Wf  s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' ∆ + BT Wf ≤ T,  (1)  where W is restricted to be the identity matrix in the original formulation [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' The flow variables f ∈ Rm  determine the amount of mass that moves between nodes i and j for every edge (i, j) ∈ E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' More precisely,  wijfij specifies the amount of mass that travels along (i, j).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' We abuse the notation and use fij = −fji for  an edge (i, j), so wijfij is the amount of mass that moves from node i to node j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' In a flow diffusion, we  assign ∆i source mass to node i and enforce a constraint that node i can hold up to Ti mass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Because one  may always scale ∆ and T by the same constant, we assume without loss of generality that Ti ≥ 1 for all  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' If Ti > ∆i at some node i, then we need to spread the source mass along edges in the graph to satisfy  the capacity constraint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' The vector ∆ + BT Wf measures the final mass at each node if we spread the mass  according to f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Therefore, the goal of the flow diffusion problem (1) is to find a feasible way to spread the  mass while minimizing the cost of flow f T Wf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' In this work we allow different edge weights as long as they  are positive, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=', W consists of positive diagonal entries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' In the context of flow diffusion, edge weights define  the efficiencies at which mass can spread over edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' To see this, simply note that wijfij determines the  amount of mass that moves along the edge (i, j), and thus for fixed fij, the higher wij is the more mass we  can move along (i, j).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  For local graph clustering, it is usually more convenient to consider the dual problem of (1):  min  x≥0  1  2xT Lx + xT (T − ∆)  (2)  3  Algorithm 1 Flow diffusion (algorithmic form)  Input: graph G, source ∆ and sink T  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Initialize xi = 0 and mi = ∆i for all i ∈ V .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' For t = 1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' do  (a) Pick i ∈ {j : mj > Tj} uniformly at random.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  (b) Apply push(i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Return x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  push(i):  Make the following updates:  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' xi ← xi + (mi − Ti)/wi where wi = �  j∼i wij.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' mi ← Ti.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' For each node j ∼ i: mj ← mj + (mi − Ti)wij/wi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  where L = BT WB is the weighted Laplacian matrix of G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Throughout this work we use f ∗ and x∗ to denote  the optimal solutions of (1) and (2), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' The solution x∗ ∈ Rn  + embeds the nodes on the nonnegative  real line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' In [13] the authors apply a sweep-cut rounding procedure for local graph clustering without node  attributes, and they obtain a combinatorial guarantee in terms of the conductance of a cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' In this work,  with the presence of node attributes which may come from some unknown distributions, we take a natural  statistical perspective and show how supp(x∗) recovers a target cluster generated from a contextual random  graph model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  In order to compute the solution to (2) one may extend the iterative coordinate method in [13] to work with  weighted edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' We layout the algorithmic steps in Algorithm 1, where we describe each coordinate-wise  gradient update (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=', push(i)) using its combinatorial interpretation as spreading mass from a node to its  neighbors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' In Algorithm 1, mi represents the current mass at node i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' At every iteration, we pick a node  i whose current mass mi exceeds its capacity Ti, and we remove the excess amount mi − Ti by sending it  to the neighbors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Algorithm 1 may be viewed as an equivalent algorithmic form of flow diffusion since the  iterates converge to x∗ [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' An important property of Algorithm 1 is that it updates xi only if x∗  i > 0, and  it updates mj only if j ∼ i for some i such that x∗  i > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' This means that the algorithm will not explore the  whole graph if x∗ is sparse, which is usually the case in applications such local clustering and node ranking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  We state this local property in Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='1 and provide a running time bound in Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Both  propositions can be proved by simply including edge weights in the original arguments from [13] and our  assumption that Ti ≥ 1 for all i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='1 ([13]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Let xt for t ≥ 1 be iterates generated by Algorithm 1, then supp(xt) ⊆ supp(x∗).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  Moreover, |supp(x∗)| ≤ ∥∆∥1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='2 ([13]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Assuming |supp(x∗)| < n, then after τ = O(∥∆∥1 α  β log 1  ϵ ) iterations, where α =  maxi∈supp(x∗) wi where wi = �  j∼i wij, and β ≥ min(i,j)∈supp(Bx∗) wij, one has E[F(xτ)] − F(x∗) ≤ ϵ, where  F denotes the objective function of (2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  Let ¯d denote the maximum degree of a node in supp(x∗).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Since each iteration of Algorithm 1 only touches a  node i ∈ supp(x∗) and its neighbors, Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='1 implies that the total number of nodes (except their  neighbors j such that x∗  j = 0) that Algorithm 1 will ever look at is upper bounded by the total amount  of source mass ∥∆∥1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Therefore, if the source mass is small and ¯d does not scale linearly with n, then  Algorithm 1 would only explore locally in the graph, and the size of the subgraph which Algorithm 1 explores  is controlled by ∥∆∥1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='2 implies that the total running time of Algorithm 1 for computing  an ϵ-accurate solution is O( ¯d∥∆∥1 α  β log 1  ϵ ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Therefore, if ¯d, ∥∆∥1, α  β are all sublinear in n, then Algorithm 1  takes sublinear time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  4  Algorithm 2 Local graph clustering with node attributes  Input: unweighted graph G = (A, I), node attributes Xi for all i ∈ V , seed node s ∈ V , hyperparameter  γ ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  Output: a cluster C ⊆ V  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Define weighted graph G′ = (A, W) whose edge weights are given by wij = exp(−γ∥Xi − Xj∥2  2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Set source mass ∆s > 0 and ∆i = 0 for i ̸= s, set sink capacity Ti.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Run flow diffusion (Algorithm 1) with input G′, ∆, T and obtain output xτ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Return supp(xτ)  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='2  Local clustering with node attributes  In local graph clustering, we are given a seed node s ∈ V and the goal is to identify a good cluster that  contains the seed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Existing methods mostly focus on the setting where one only has access to the structural  information, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' nodes and edges of a graph, and they do not take into account node attributes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' However,  it is reasonable to expect that informative node attributes should help improve the performance of a local  clustering algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' For example, the original flow diffusion solves the local graph clustering problem by  spreading source mass from the seed node to nearby nodes, and an output cluster is obtained based on where  in the graph the mass diffuse to [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' In this case, node attributes may be used to guide the spread of mass so  that more mass are trapped inside the ground-truth target cluster, and consequently, improve the accuracy of  the algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  The idea to guide the diffusion by using node attributes can be easily realized by relating edge weights to  node attributes, which we describe in the next.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Given a graph G = (A, W) with a set of node attributes  Xi ∈ Rd for i ∈ V , and given a seed node s from an unknown target cluster K, the goal is to recover  K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' To do so, we construct a new graph G′ = (A, W ′) having the same structure but new edge weights  w′  ij = h(wij, Xi, Xj) where h is some function that should improve diffusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' For example, one may set  h(wij, Xi, Xj) = wijρ(Xi, Xj) where ρ(Xi, Xj) measures the proximity between Xi and Xj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' This means that,  for a flow diffusion in G′, if two adjacent nodes i and j have similar attributes, then it is easier to send a lot  of mass along the edge (i, j).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' In particular, when one removes the excess mass from a node i by sending it  to the neighbors, the amount of mass that a neighbor j receives is proportional to w′  ij (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' push(i)), and  hence more mass will be sent to a neighbor whose attributes also bear close proximity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Therefore, if nodes  within the target cluster K share similar attributes, then a flow diffusion in G′, which starts from a seed  node s ∈ K, would force more mass to spread within K than a flow diffusion in the original graph G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  In this work, we focus on a particular choice of h given by w′  ij = h(wij, Xi, Xj) = wij exp(−γ∥Xi − Xj∥2  2)  where γ ≥ 0 is a hyperparameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' For simplicity we will assume that wij = 1 for all (i, j) ∈ E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' In this case, h  is the Gaussian kernel of node attributes and has proved useful in many applications, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=', spectral clustering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  In the next section we provide rigorous statistical guarantees on the performance of local graph clustering with  node attributes by using the optimal solution of weighted flow diffusion (2), where edge weights are defined  by the Gaussian kernel for an appropriately chosen γ > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' We summarize the local clustering procedure in  Algorithm 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' As we show in the next section, suitable choices for T include Ti = 1 or Ti = degG(i) for all i,  and one may correspondingly set ∆s = α �  i∈K Ti for α > 1 where K is the target cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  3  Statistical guarantees under contextual random graph model  We assume that the node attributes and a target cluster are generated from the following random model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='1 (Contextual local random model).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Given a set of nodes V , let K ⊆ V be a target cluster  with cardinality |K| = k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' For every pair of nodes i and j, if i, j ∈ K then we draw an edge (i, j) with  5  probability p;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' if i ∈ K and j /∈ K then we draw an edge (i, j) with probability q;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' otherwise, we allow  any (deterministic or random) model to draw an edge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' The node attributes Xi for a node i are given as  Xi = µi +Zi, where µi ∈ Rd is a fixed signal vector and Zi ∈ Rd is a random noise vector whose ℓth coordinate  Ziℓ follows independent mean zero sub-Gaussian distribution with variance proxy σℓ, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=', for any t ≥ 0 we  have P(|Ziℓ| ≥ t) ≤ 2 exp(− t2  2σ2  ℓ ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Though not necessary, to simplify the discussion we require µi = µj for  i, j ∈ K .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  This random model is fairly general.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' For example, if the edges that connect nodes in V \\K have been  generated from the SBM, µi = µj for every i, j that belong to the same block, and all Zi’s follow the  same isotropic Gaussian distribution, then we obtain the CSBM which has been extensively used in the  analyses of algorithms for attributed graphs [10, 5, 29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' On the other hand, if the edges that connect nodes  in V \\K have been generated from the Erd˝os-Renyi model with probability q, µi = µj for i, j ∈ K and  µi = 0 for i ̸∈ K, and all Zi’s follow the same isotropic Gaussian distribution, then we obtain a natural  coupling of the planted densest subgraph problem and the submatrix localization problem [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' In terms of  modelling the noise of node attributes, sub-Gaussian distributions include Gaussian, Bernoulli, and any other  continuous or discrete distribution over finite domains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Therefore the random model allows different types of  coordinate-wise noise (and different level of noise controlled by σℓ) which could depend on the nature of the  specific attribute.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' For example, the noise of a continuous attribute may be Gaussian or uniform, whereas the  noise of a binary-encoded categorical attribute may be Bernoulli.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  In order for node attributes to provide useful information, nodes inside K should have distinguishable  attributes compared to nodes not in K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Denote  ˆµ :=  min  i∈K,j̸∈K ∥µi − µj∥2,  ˆσ := max  1≤ℓ≤d σℓ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  We make Assumption 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='2 which states that the relative signal ˆµ dominates the maximum coordinate-wise  noise ˆσ, and that the sum of normalized noises does not grow faster than log n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' The later assumption is  easily satisfied, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=', when the dimension d of node attributes does not scale with the number of nodes n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' In  practice, when the set of available or measurable attributes are fixed a priori, one always has d = On(1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' This  is particularly relevant in the context of local clustering where it is desirable to have sublinear algorithms,  since if d = Ω(n) then even computing a single edge weight wij would take time at least linear in n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  Assumption 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' ˆµ = ω(ˆσ√λ log n) for some λ = Ωn(1);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' �d  ℓ=1 σ2  ℓ/ˆσ2 = O(log n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  Before we move on to discuss how exactly node attributes help to recover K, we need to talk about the signal  and noise from the graph structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' For a node i ∈ K, the expected number of neighbors in K is p(k − 1),  and the expected number of neighbors not in K is q(n − k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Since mass spread along edges, if there are too  many edges connecting K to V \\K, it may become difficult to prevent a lot of mass from spreading out of K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  The consequence of having too much mass which start in K to leak out of K is that supp(x∗) may have little  overlap with K, and consequently Algorithm 2 would have poor performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  Fortunately, node attributes may be very helpful when the structural information is not strong enough, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=',  when q(n − k) > p(k − 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' As discussed earlier, informative node attributes should be able to guide the spread  of mass in the graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' In a flow diffusion, where the mass get spread to from the source node depends on the  edge weights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' The higher weight an edge has, the easier to send mass along that edge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Therefore, in order  to keep as much mass as possible inside the target cluster K, an ideal situation would be that edges inside  K have significantly more weights than an edge that connects K to V \\K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' It turns out that this is exactly  the case when we have good node attributes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' By applying concentration results on the sum of squares of  sub-Gaussian random variables, Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='3 says that, with overwhelming probability, one obtains a desirable  separation of edge weights as a consequence of node attributes having more signal than noise (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' when  Assumption 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='2 holds).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  6  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Under Assumption 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='2, one may pick γ such that γˆσ2 = o(log−1 n) and γˆµ2 = ωn(λ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  Consequently, with probability at least 1 − on(1), the edge weight wij = exp(−γ∥Xi − Xj∥2  2) satisfies wij ≥  1 − on(1) for all i, j ∈ K, and wij ≤ exp(−ωn(λ)) for all i ∈ K, j ̸∈ K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  Not surprisingly, Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='3 implies that the gap between edge weights is controlled by λ which, according  to Assumption 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='2, measures how strong the attribute signal is.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' If λ is sufficiently large, then naturally  one would expect an algorithm that uses the node attributes to nearly perfectly recover K, irrespective  of how noisy the graph is.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Otherwise, the performance to recover K would depend on a combination of  both structural and attribute information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' In what follows we present two recovery results which precisely  correspond to these two scenarios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' In all probability bounds, we keep explicit dependence on the cluster size  k because, for local graph clustering, k may be a large constant and does not necessarily scale with n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='4 (Recovery with very good node attributes).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Under Assumption 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='2, for any γ satisfying  γˆσ2 = o(log−1 n) and γˆµ2 = ωn(λ), with source mass ∆s = (1 + β) �  i∈K Ti for any β > 0, we have that for  large enough n,  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' if K is connected and λ = Ωn(log k+log(q(n−k))+log(1/β)), then with probability at least 1−on(1)−k−1/3,  for every seed node s ∈ K we have K ⊆ supp(x∗) and �  i∈supp(x∗)\\K Ti ≤ β �  i∈K Ti;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' if p ≥ (4+ϵ)  δ2  log k  k−1 for some 0 < δ < 1 and ϵ > 0, and λ = Ωn(log k + log( q(n−k)  p(k−1) ) + log(1/β) + log(1 − δ)),  then with probability at least 1 − on(1) − k−1/3 − ek−ϵ/2, for every seed node s ∈ K we have K ⊆ supp(x∗)  and �  i∈supp(x∗)\\K Ti ≤ β �  i∈K Ti.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  In particular, we obtain the following bounds on false positives: if Ti = 1 for all i ∈ V then  |supp(x∗)\\K| ≤ β|K|;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  if Ti = degG(i) for all i ∈ V then  volG(supp(x∗)\\K) ≤ βvolG(K).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  Some discussions are in order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' The first part of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='4 does not assume anything about the internal  connectivity of K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' It applies as long as K is connected, and this includes the extreme case when the induced  subgraph on K is a tree but each node in K is also connected to many other nodes not in K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' The second  part of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='4 requires a weaker condition on the strength of attribute signal ˆµ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' The additive term  log(q(n − k)) from part 1 is weakened to log( q(n−k)  p(k−1) ) due to the improved connectivity of K, under the  additional assumption that p ≥ Ω(log k/k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' We consider two specific choices of T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' The first choice gives the  exact bound on the number of false positives, and the second choice bounds the size of false positives in terms  of volume [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Note that even in the case where the node attributes alone provide sufficient signal, the graph  structure still plays a very important role as it allows the possibility that an algorithm would return a good  output without having to explore all data points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' For example, during the execution of Algorithm 2, one only  needs to query the attributes of a node whenever they are required for subsequent computations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  Let us introduce one more notion before presenting the recovery guarantee with good, but not too good,  node attributes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Given the contextual random model described in Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='1, consider a “population”  graph ¯G = ( ¯A, ¯W) where ¯Aij = 1 for every pair i, j such that i ̸= j, and the edge weight ¯wij satisfies  ¯wij = p exp(−γ∥E[Xi] − E[Xj]∥2  2) = p if i, j ∈ K, ¯wij = q exp(−γ∥E[Xi] − E[Xj]∥2  2) ≤ qe−γ ˆµ2 if i ∈ K, j /∈ K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  A frequently used measure of cluster quality is conductance which quantifies the ratio between external and  internal connectivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' For a set of nodes C in ¯G, its conductance is defined as �  i∈C,j /∈C ¯wij/ �  i∈C  �  j∼i ¯wij.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  For 0 ≤ c ≤ 1 denote  η(c) :=  p(k − 1)  p(k − 1) + q(n − k)e−cγ ˆµ2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  One may easily verify that the conductance of K in ¯G is upper bounded by 1 − η(1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Therefore, the higher  η(1) is the lower conductance K may have in ¯G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' On the other hand, in the absence of node attributes,  7  or if all nodes share identical attributes, then the conductance of K in ¯G is exactly 1 − η(0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Note that  1 − η(c) ≥ 1 − η(0) for any c ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Intuitively, a low conductance cluster is better connected internally than  externally, and thus it should be easier to detect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Therefore, the advantage of having node attributes is  that they help reduce the conductance of the target cluster, making it easier to recover from the population  graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' While in practice one never works with the population graph, our next theorem indicates that, with  overwhelming probability, the recoverability of K in the population graph transfers to an realization of the  random model in Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' More specifically, Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='5 says that when the node attributes are good,  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Assumption 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='2 holds, but not too good, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' conditions required in Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='4 may not hold, then  Algorithm 2 still fully recovers K as long as there is sufficient internal connection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Moreover, the relative size  of false positives (compared to the size of K) is upper bounded by O(1/η(c)2) − 1 for any c < 1 and large  enough n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Denote  m(δ1, δ2) =  (1 + 3δ1 +  1  p(k−1))2  (1 − δ1)(1 − δ2)  ,  Tmax = max  i∈K Ti.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='5 (Recovery with good node attributes).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Under Assumption 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='2, if p ≥ max( (3+ϵ1)  δ2  1  log k  k−1 ,  (2+ϵ2)  δ2  √1−δ1  √log k  √k−1 )  where 0 < δ1, δ2 ≤ 1 and ϵ1, ϵ2 > 0, then with probability at least 1 − on(1) − 4k−ϵ1/3 − k−2ϵ2, for every seed  node s ∈ K with source mass  ∆s = c1Tmax  m(δ1, δ2)k  η(c2)2  for any constants c1 > 1 and c2 < 1, it holds that for all large enough n, K ⊆ supp(x∗).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Moreover, if Ti = 1  for all i ∈ V then  |supp(x∗)\\K| ≤  �c1m(δ1, δ2)  η(c2)2  − 1  �  |K|;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  if Ti = degG(i) for all i ∈ V  volG(supp(x∗)\\K) ≤  �c1m(δ1, δ2)  η(c2)2  (1 + δ1)  (1 − δ1) − 1  �  volG(K).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  In the special case where there is no node attribute, we may simply take ˆµ = 0 and Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='5 still holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  For this specific setting we obtain a nearly identical recovery guarantee (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' same assumption and same  result) that has been previously obtained for local graph clustering using PageRank vectors without node  attributes [15], where the relative size of false positives is O(1/η(0)2 − 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' This comparison quantifies the  advantage of having good node attributes as they reduce the bound to O(1/η(c)2 − 1) for any c < 1, which  can be substantially smaller.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Note that the expression 1/η(c)2 is jointly controlled by the combinatorial  conductance of K and the attribute signal ˆµ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  4  Experiments  We evaluate the performance of Algorithm 2 for local graph clustering with node attributes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' First, we  investigate empirically our theoretical results over synthetic data generated from a specification of the random  model described in Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' We use the synthetic experiments to demonstrate (i) the distinction  between having weak and strong graph structural information, and (ii) the distinction between having very  good and moderately good node attributes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' In addition, the synthetic experiments indicates the necessity of  Assumption 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='2 in order for Algorithm 2 to have notable performance improvement against method that does  not use node attributes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Second, we carry out experiments using real-world data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' We show that incorporating  node attributes improves the F1 scores by an average of 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='3% over 20 clusters from two academic co-authorship  networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  8  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='1  Simulated data and results  The generative model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' We generate random graphs using the stochastic block model with block size  k = 500 and the total number of clusters r = 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' The total number of nodes is n = kr = 10, 000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Two nodes  within the same cluster are connected with probability p, and two nodes from different clusters are connected  with probability q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' We fix q = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='002 and vary p to control the strength of the structural signal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' We randomly  pick one of the clusters as the target cluster K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' The dimension of the node attributes is set to d = 100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' For  node attributes Xi = µi + Zi, we sample Zi from Gaussian distribution with mean 0 and identity covariance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  Therefore σℓ = 1 for all ℓ = 1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' , d, and hence ˆσ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' We set µiℓ = aˆσ√log n/2  √  d for all ℓ if i ∈ K, and  µiℓ = −aˆσ√log n/2  √  d for all ℓ if i ̸∈ K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' In this way, we get that ˆµ = maxi∈K,j̸∈K ∥µi − µj∥2 = aˆσ√log n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  We vary a to control the strength of node attribute signal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  Setup and evaluation metric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' We set the sink capacity Ti = 1 for all i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' We set the source mass ∆s = αk  and we allow α to vary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' We set γ = (log−3/2 n)/4ˆσ2 so that γˆσ2 = o(log−1 n) as required by Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='4 and  Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' To measure the quality of an output cluster C := supp(xτ), we use precision and recall which  are defined as |C ∩ K|/|C| and |C ∩ K|/|K|, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' The F1 score is the harmonic mean of precision and  recall given by 2/(Precision−1 + Recall−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' For comparison we also consider the performance of unweighted  flow diffusion which does not use node attributes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' There are other methods for local graph clustering without  node attributes, such as the ℓ1-regularized PageRank [3, 15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' We did not consider other methods because the  unweighted flow diffusion is shown to achieve state-of-the-art performance [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Moreover, the comparison  between weighted and unweighted flow diffusions, which either use or does not use node attributes, allows us  to obtain a fair estimate on the benefits of node attributes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  Results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Figure 1 shows detailed views of the performance of Algorithm 2 as we vary α between [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='1, 5]  with 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='1 increments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  It is used to demonstrate the two claims of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  In Figure 1a, we set  p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='01 < log k/k, so the target cluster K is very sparse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' On average, each node i ∈ K only has 5 neighbors  inside K while it has 19 neighbors outside of K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' This means that the graph structural information alone is not  very helpful for recovering K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' On the other hand, we set a = 3√log n so ˆµ = 3ˆσ log n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' This means that the  node attributes contain very strong signal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' In this case, observe that as soon as α becomes strictly larger than  1, the output cluster C fully recovers K, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Recall = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' This demonstrates the first claim of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  As a comparison, the unweighted flow diffusion which does not use node attributes has very poor performance  for every choice of α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' This is expected because edge connectivity reveals very little clustering information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  In Figure 1b, we keep the same graph structure but slightly weaken the node attributes to ˆµ = 5  2 ˆσ log n by  reducing a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' This stops the output cluster C from fully recovering K for small α larger than 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' The algorithm  still has a good performance if one chooses α properly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' This scenario is covered by Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='5 and we will  discuss more about it later.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' In Figure 1c, we keep the same node attributes as in Figure 1b but increase p  from 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='01 to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='03 which is slightly larger than 2 log k/k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' In this case, the output cluster C again fully recovers  K as soon as α is strictly larger than 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' The distinction between Figure 1b and Figure 1c means that the  required threshold for ˆµ to fully recover K at any α > 1 decreases as p increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' This demonstrates the  second claim of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  In Figure 2 we consider a more realistic setting where one may not know the size of the target cluster K  and the node attributes may be noisy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' We keep the same graph connectivity (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='03 and q = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='002)  and vary a between [0, 8] with 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='5 increments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Recall that the node attributes are set in a way such that  ˆµ = aˆσ√log n, therefore the strength of node attributes increases as a increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' For each choice of a, given a  seed node s, we run Algorithm 2 multiple times with source mass αk for α ∈ {1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='1, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='6, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' , 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='1}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' This gives  multiple output clusters, one from each choice of α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' We consider two cases for selecting a final cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' The  first case is a best-case scenario where we pick the cluster that achieves the best F1 score, the second case is  a more realistic case where we pick the cluster that has the minimum conductance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='1 Figure 2 illustrates the  performance of Algorithm 2 in these two cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' The x-axis of Figure 2 is the value of a where ˆµ = aˆσ√log n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  Overall, the performance improves as ˆµ increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' When the node attributes are reasonably strong, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  1Given edge weights wij and a cluster C, we consider weighted conductance which is the ratio �  i∈C,j̸∈C wij/ �  i∈C  �  j∼i wij.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  9  0  1  2  3  4  5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='0  Recall  Precision  = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='1  Recall (no attributes)  Precision (no attributes)  (a) p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='01, q = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='002, ˆµ = 3ˆσ log n  0  1  2  3  4  5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='0  (b) p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='01, q = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='002, ˆµ = 5  2 ˆσ log n  0  1  2  3  4  5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='0  (c) p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='03, q = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='002, ˆµ = 5  2 ˆσ log n  Figure 1: Demonstration of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' The lines show average performance over 100 trails.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' In each trial  we randomly pick a seed node s from the target cluster K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' The error bars show standard deviation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Figure 1a  and Figure 1c show full recovery of K as soon as α > 1 (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' as soon as β > 0, see first part of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  The distinction between Figure 1b and Figure 1c demonstrate that the required threshold for ˆµ depends on p  (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' second part of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' With very good node attributes, the performance of flow diffusion that  uses node attributes is significantly better than the performance of flow diffusion that does not use node  attributes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  a ≥ 4, the scenario where we select a cluster based on minimum conductance matches with the best-case  performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Note that, the higher ˆµ is, the lower η(c) is for any 0 < c ≤ 1, and according to Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='5,  there should be less false positives and hence a higher F1 score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' This is exactly what Figure 2 shows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' In  Figure 2 we also plot the best-case performance of unweighted flow diffusion without node attributes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' When  the node attributes are very noisy, and in particular, when ˆµ ≤ ˆσ√log n where Assumption 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='2 clearly fails,  we see that using node attributes can be harmful as it can lead to worse performance than not using node  attributes at all.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' On the other hand, once the node attributes become strong enough, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=', a ≥ 4, using node  attributes start to yield much better outcome.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  10  0  1  2  3  4  5  6  7  8  Strength of node attributes  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='9  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='0  F1 score  Best performance  Perf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' for min conductance  Best perf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' without attributes  =  logn  Figure 2: Performance of Algorithm 2 as ˆµ increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' ˆµ needs to be larger than ˆσ√log n in order for node  attributes to be useful.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' The x-axis shows the value of a where ˆµ = aˆσ√log n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' We average over 100 trials,  each trial uses a randomly selected seed node.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='2  Real-world graphs and results  We evaluate the performance of Algorithm 2 on two co-authorship graphs based on the Microsoft Academic  Graph from the KDD Cup 2016 challenge [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='2 In these graphs, nodes are authors, and two nodes are  connected by an edge if they have coauthored a paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' The clusters are defined according to the most  active research field of each author.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' The node attributes represent paper keywords for each author’s papers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  The first graph consists of 18,333 computer science researchers and 81,894 connections among them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Each  computer science researcher belongs to one of the 15 ground-truth clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' The second graph consists of  34,493 physics researchers and 247,962 connections among them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Each physics researcher belongs to one of  the 5 ground-truth clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Details of node attributes and cluster sizes are found in Appendix D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  We consider two choices for the sink capacities T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' The first is Ti = degG(i) for all i and the second is Ti = 1  for all i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' For each cluster K in a graph, given a seed node s ∈ K, we run Algorithm 2 with source mass  ∆s = α �  i∈K Ti for α ∈ {1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='5, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='75, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' , 5}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' We select the output cluster that has the minimum conductance  and measure the recovery quality using the F1 score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' For each of the 20 target clusters we run 100 trials and  each trial uses a different seed node.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' We report the average F1 scores using the first choice for T in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  Additional results using the second choice for T, along with more details on parameter choices, are found in  Appendix D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' In most cases, incorporating node attributes improves recovery accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Over the total 20  clusters in the two co-authorship networks, using node attributes increases the F1 score by 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='3% on average.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  5  Conclusion and future work  In this work we propose and analyze a simple algorithm for local graph clustering with node attributes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' We  provide conditions under which the algorithm is guaranteed to work well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' We empirically demonstrate the  advantage of incorporating node attributes over both synthetic and real-world datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' To the best of our  knowledge, this is the first local graph clustering algorithm for attributed graphs that also have provable  guarantees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' The current work is the first step towards building principled tools for local learning on graphs  2In Appendix D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='1 we include additional experiments using Amazon co-purchase graph [21] and demonstrate the performance  of Algorithm 2 when the node attributes are not strong enough.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' (F1 only increases by 1% on average.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=')  11  Table 1: F1 scores for local clustering in co-authorship networks  Network  Cluster  No attr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  Use attr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  Improv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  Computer Science  Bioinformatics  32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='1  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='3  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='2  Machine Learning  30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='9  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='3  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='4  Computer Vision  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='6  35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='1  NLP  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='2  52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='3  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='1  Graphics  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='6  49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='2  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='6  Networks  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='1  47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='9  Security  29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='9  35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='7  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='8  Databases  48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='5  58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='1  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='6  Data Mining  27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='5  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='3  Game Theory  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='6  66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='0  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='4  HCI  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='0  77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='6  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='6  Information Theory  47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='4  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='9  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='5  Medical Informatics  65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='7  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='3  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='6  Robotics  59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='9  59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='9  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='0  Theoretical CS  66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='3  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='7  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='4  Physics  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' A  69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='4  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='9  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='5  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' B  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='4  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='9  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' C  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='3  82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='1  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='8  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' D  62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='3  68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='9  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='6  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' E  49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='5  53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='7  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='2  AVERAGE  50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='3  54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='6  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='3  using both structural and attribute information without processing the whole graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' An interesting future  direction is to incorporate node embedding and parameter learning into local diffusion, where the attributes  and their relative importance may be optimized simultaneously alongside the local diffusion process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  12  References  [1] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Abbe, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Fan, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Wang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' An ℓp theory of pca and spectral clustering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' The Annals of Statistics,  50(4):2359–2385, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  [2] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Allen-Zhu, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Silvio, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Vahab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' A local algorithm for finding well-connected clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' In  Proceedings of the 30th International Conference on Machine Learning (ICML), pages 396–404, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  [3] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Andersen, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Chung, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Lang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Local graph partitioning using pagerank vectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Proceedings of  the 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS), pages 475–486, 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  [4] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Andersen, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Gharan, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Peres, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Trevisan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Almost optimal local graph clustering using  evolving sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Journal of the ACM, 63(2), 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  [5] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Baranwal, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Fountoulakis, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Jagannath.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Graph convolution for semi-supervised classifica-  tion: Improved linear separability and out-of-distribution generalization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' In Proceedings of the 38th  International Conference on Machine Learning (ICML), volume 139, pages 684–693, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  [6] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Baranwal, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Fountoulakis, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Jagannath.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Effects of graph convolutions in multi-layer networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  In International Conference on Learning Representations (ICLR), 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  [7] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Braun, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Tyagi, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Biernacki.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' An iterative clustering algorithm for the contextual stochastic  block model with optimality guarantees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' In Proceedings of the 39th International Conference on Machine  Learning (ICML), pages 2257–2291.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' PMLR, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  [8] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Chen, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Peng, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Wang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' 2-norm flow diffusion in near-linear time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' In IEEE 62nd Annual  Symposium on Foundations of Computer Science (FOCS), pages 540–549, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  [9] Yudong Chen and Jiaming Xu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Statistical-computational tradeoffs in planted problems and submatrix  localization with a growing number of clusters and submatrices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' The Journal of Machine Learning  Research, 17(1):882–938, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  [10] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Deshpande, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Sen, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Montanari, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Mossel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Contextual stochastic block models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Advances in  Neural Information Processing Systems (NeurIPS), 31, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  [11] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Fountoulakis, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Levi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Yang, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Baranwal, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Jagannath.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Graph attention retrospective, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  [12] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Fountoulakis, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Roosta-Khorasani, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Shun, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Cheng, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Mahoney.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Variational perspective  on local graph clustering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Mathematical Programming, 174:553–573, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  [13] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Fountoulakis, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Wang, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Yang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' p-norm flow diffusion for local graph clustering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Proceedings of  the 37th International Conference on Machine Learning (ICML), 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  [14] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Gleich.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Pagerank beyond the web.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' SIAM Review, 57(3):321–363, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  [15] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Ha, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Fountoulakis, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Mahoney.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Statistical guarantees for local graph clustering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' The  Journal of Machine Learning Research, 22(1):6538–6591, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  [16] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Jeub, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Balachandran, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Porter, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Mucha, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Mahoney.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Think locally, act  locally: Detection of small, medium-sized, and large communities in large networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Physical Review E,  91:012821, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  [17] Caiyan Jia, Yafang Li, Matthew B Carson, Xiaoyang Wang, and Jian Yu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Node attribute-enhanced  community detection in complex networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Scientific reports, 7(1):1–15, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  [18] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Leskovec, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Lang, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Dasgupta, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Mahoney.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Community structure in large networks:  Natural cluster sizes and the absence of large well-defined clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Internet Mathematics, 6(1):29–123,  2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  13  [19] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Liu and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Gleich.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Strongly local p-norm-cut algorithms for semi-supervised learning and local  graph clustering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' In Advances in Neural Information Processing Systems (NeurIPS), volume 33, pages  5023–5035, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  [20] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Macgregor and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Sun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Local algorithms for finding densely connected clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' In Proceedings of the  38th International Conference on Machine Learning (ICML), pages 7268–7278.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' PMLR, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  [21] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' McAuley, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Targett, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Shi, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Van Den Hengel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Image-based recommendations on styles  and substitutes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' In Proceedings of the 38th ACM SIGIR International Conference on Research and  Development in Information Retrieval, pages 43–52, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  [22] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Reid and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Yuval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Finding sparse cuts locally using evolving sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' In Proceedings of the 41st ACM  Symposium on Theory of Computing (STOC), pages 235–244, 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  [23] O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Shchur, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Mumme, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Bojchevski, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' G¨unnemann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Pitfalls of graph neural network evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  Relational Representation Learning Workshop, NeurIPS 2018, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  [24] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Shi, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' He, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Bindel, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Hopcroft.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Local Lanczos spectral approximation for community  detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' In Proceedings of the European Conference on Machine Learning and Principles and Practice  of Knowledge Discovery in Databases (ECML-PKDD), September 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  [25] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Spielman and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Teng.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' A local clustering algorithm for massive graphs and its application to  nearly linear time graph partitioning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' SIAM Journal on computing, 42(1):1–26, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  [26] Heli Sun, Fang He, Jianbin Huang, Yizhou Sun, Yang Li, Chenyu Wang, Liang He, Zhongbin Sun, and  Xiaolin Jia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Network embedding for community detection in attributed networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' ACM Transactions on  Knowledge Discovery from Data (TKDD), 14(3):1–25, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  [27] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Vershynin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' High-dimensional probability: An introduction with applications in data science, volume 47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  Cambridge university press, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  [28] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Wang, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Fountoulakis, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Henzinger, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Mahoney, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Rao.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Capacity releasing diffusion  for speed and locality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Proceedings of the 34th International Conference on Machine Learning (ICML),  70:3607–2017, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  [29] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Yan and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Sarkar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Covariate regularized community detection in sparse graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Journal of the  American Statistical Association, 116(534):734–745, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  [30] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Yang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' McAuley, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Leskovec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Community detection in networks with node attributes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' In IEEE  13th International Conference on Data Mining (ICDM), pages 1151–1156.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' IEEE, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  [31] Chen Zhe, Aixin Sun, and Xiaokui Xiao.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Community detection on large complex attribute network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' In  Proceedings of the 25th ACM SIGKDD international conference on knowledge discovery & data mining,  pages 2041–2049, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  14  A  Primal-dual solutions of flow diffusion  Recall that we denote f ∗ and x∗ as the optimal solutions of the primal and dual flow diffusion problem (1)  and (2), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' We derive two useful properties of x∗ based on the primal-dual relationships between  f ∗ and x∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' In Appendix B when we analyze the support of x∗, we will repeatedly use these properties to  characterize the nodes covered by supp(x∗).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Note that  min  f  1  2f T Wf  s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' ∆ + BT Wf ≤ T  = min  f  max  x≥0  1  2f T Wf + xT (∆ + BT Wf − T)  = max  x≥0 min  f  1  2f T Wf + xT (∆ + BT Wf − T)  = max  x≥0 −1  2xT BT WBx + xT (∆ − T),  therefore the optimal solutions f ∗ and x∗ are related by f ∗ = −Bx∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' According to the physical interpretation  of the flow variables f, this means that, in an optimal flow diffusion, the amount of mass that moves from  node i to node j is precisely wij(x∗  i − x∗  j) where wij is the weight for the edge (i, j).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Moreover, we have  x∗  i > 0 only if ∆i + [BT Wf ∗]i = Ti.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Recall that the quantity ∆i + [BT Wf ∗]i represents the amount of mass  at node i after spreading mass according to f ∗, therefore, we get that x∗  i > 0 only if the final mass at node i  equals exactly to its sink capacity Ti.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' In this case, we say that node i is saturated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  B  Proofs  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='1  Proof of Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='3  We have that  ∥Xi − Xj∥2  2 =  � ∥Zi − Zj∥2  2,  if i, j ∈ K,  ∥Zi − Zj∥2  2 + ∥µi − µj∥2  2 + (µi − µj)T (Zi − Zj),  if i ∈ K, j ̸∈ K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  (3)  Consider the random variable  ∥Zi − Zj∥2  2 − E[∥Zi − Zj∥2  2] =  d  �  ℓ=1  �  (Ziℓ − Zjℓ)2 − E[(Ziℓ − Zjℓ)2]  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  Each term in the summation is sub-exponential and satisfies  ∥(Ziℓ − Zjℓ)2 − E[(Ziℓ − Zjℓ)2]∥ψ1 ≤ C∥(Ziℓ − Zjℓ)2∥ψ1 = C∥Ziℓ − Zjℓ∥2  ψ2 ≤ 2C∥Ziℓ∥2  ψ2 ≤ C′σ2  ℓ  for some absolute constants C, C′, where ∥ · ∥ψ1 and ∥ · ∥ψ2 denote the sub-exponential norm and the  sub-Gaussian norm, respectively [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' The first inequality follows from standard centering inequality for the  sub-exponential norm (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' see Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='8 and Exercise 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='10 in [27]), and the second equality follows from  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='6 in [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Therefore, we may apply a Bernstein-type inequality for the sum of sub-exponential  15  random variables (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' see Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='1 in [27]) and get  P  ����∥Zi − Zj∥2  2 − E∥Zi − Zj∥2  2  ��� > t  �  ≤ exp  �  − min  �  t2  c �d  ℓ=1 ∥(Ziℓ − Zjℓ)2 − E[(Ziℓ − Zjℓ)2]∥2  ψ1  ,  t  c′ maxℓ ∥(Ziℓ − Zjℓ)2 − E[(Ziℓ − Zjℓ)2]∥ψ1  ��  = exp  �  − min  �  t2  c′ �d  ℓ=1 σ4  ℓ  ,  t  c′′ˆσ2  ��  for some absolute constants c, c′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Set t = c′′ˆσ2 log n for a large enough constant c′′, use �d  ℓ=1(σℓ/ˆσ)4 ≤  �d  ℓ=1(σℓ/ˆσ)2 = O(log n) which follows from Assumption 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='2, and take a union bound over all i, j ∈ V , we  get that with probability at least 1 − on(1), for all i, j ∈ V it holds that  ∥Zi − Zj∥2  2 ≤ E∥Zi − Zj∥2  2 + O(ˆσ2 log n)  ≤ ˜c  d  �  ℓ=1  ∥Ziℓ − Zjℓ∥2  ψ2 + O(ˆσ2 log n)  ≤ ˜c′  d  �  ℓ=1  σ2  ℓ + O(ˆσ2 log n)  = O(ˆσ2 log n),  (4)  where ˜c, ˜c′ are absolute constants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  For i ∈ K and j /∈ K, the term (µi − µj)T (Zi − Zj) = �d  ℓ=1(µiℓ − µjℓ)(Ziℓ − Zjℓ) is a sum of independent  and mean zero sub-Gaussian random variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' We may apply a general Hoeffding’s inequality (see Lemma  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='3 in [27]) and get that  P(|(µi − µj)T (Zi − Zj)| ≥ t) ≤ 2 exp  �  ct2  maxℓ ∥Ziℓ − Zjℓ∥2  ψ2∥µi − µj∥2  2  �  ≤ 2 exp  �  −  c′t2  ˆσ2∥µi − µj∥2  2  �  ,  and hence by setting t = c′′ˆσ√log n∥µi − µj∥2 for a large enough constant c′′ we get that with probability at  least 1 − on(1),  (µi − µj)T (Zi − Zj) ≥ −O(ˆσ  �  log n∥µi − µj∥2), ∀i ∈ K, j /∈ K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  (5)  Combining (3), (4), (5), and using ∥µi − µj∥2 ≥ ˆµ = ω(ˆσ√log n), we get that with probability at least  1 − on(1),  ∥Xi − Xj∥2  2 ≤ O(ˆσ2 log n), ∀i ∈ K, ∀j ∈ K,  ∥Xi − Xj∥2  2 ≥ ∥µi − µj∥2  2 − O(ˆσ  �  log n∥µi − µj∥2)  = ∥µi − µj∥2  2(1 − on(1)) ≥ ˆµ2(1 − on(1)), ∀i ∈ K, ∀j ̸∈ K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  By Assumption 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='2, we may pick γ that satisfies γˆσ2 = o(log−1 n) and γˆµ2 = ωn(λ), and for any such γ we  have  exp(−γ∥Xi − Xj∥2  2) ≥ exp(−on(1)), ∀i ∈ K, ∀j ∈ K,  exp(−γ∥Xi − Xj∥2  2) ≤ exp(−γˆµ2(1 − on(1))), ∀i ∈ K, ∀j ̸∈ K,  as required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  16  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='2  Proof of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='4  We start with part 1 of the theorem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Without loss of generality let us assume that the node indices are  such that K = {1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' , k} and that x∗  1 ≥ x∗  2 ≥ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' ≥ x∗  k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' In order to show that K ⊆ supp(x∗), it suffices  to show that x∗  k > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Assume for the sake of contradiction that x∗  k = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Note that since the initial mass is  (1 + β) �  i∈K Ti, in an optimal flow routing, the amount of mass that flows over an edge cannot be greater  than (1 + β) �  i∈K Ti.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' This means that wij|x∗  i − x∗  j| ≤ (1 + β) �  i′∈K Ti′ for all i, j ∈ V (recall the basic  properties of x∗ provided in Section A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Therefore we have that  x∗  1 ≤  k−1  �  i=1  (1 + β) �  i′∈K Ti′  wi(i+1)  + x∗  k =  k−1  �  i=1  (1 + β) �  i′∈K Ti′  wi(i+1)  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  It then follows from Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='3 that with probability at least 1 − on(1),  x∗  1 ≤ (1 + β)k(1 + on(1))  �  i∈K  Ti.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  On the other hand, the total amount of mass that leaves K is  k  �  i=1  �  j≥k+1  j∼i  wij(x∗  i − x∗  j) ≤  k  �  i=1  x∗  i  �  j≥k+1  j∼i  wij ≤ x∗  1  �  (i,j)∈cutG(K)  wij.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  Apply Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='3, Lemma C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='2 and pick ϵ = δ = 1 there, and use the above bound on x∗  1, we get that, with  probability at least 1 − on(1) − k−1/3,  k  �  i=1  �  j≥k+1  j∼i  wij(x∗  i − x∗  j) ≤ (1 + β)k2(1 + on(1))(2q(n − k) + 4 log k/k) exp(−γˆµ2(1 − on(1)))  �  i∈K  Ti.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  Since we started with (1 + β) �  i∈K Ti initial mass inside K, nodes in K can settle at most �  i∈K Ti units  of mass, we know that at least β �  i∈K Ti amount of mass must leave K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' In what follows we show that  this cannot be the case for appropriately chosen γ, and hence arriving at the desired contradiction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Since  ˆµ = ω(ˆσ  �  log n(1 + λ)), we may pick γ such that γˆσ2 = o(log−1 n) to satisfy the assumption required for  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='3, and at the same time γˆµ2 = ω(1 + λ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Since λ = Ω(log k + log(q(n − k)) + log(1/β)), we know  that for any terms an = on(1) and bn = on(1) and for sufficiently large n,  γˆµ2(1 − an) > 2 log k + log(2q(n − k) + 4 log k/k) + log(1/β + 1) + log(1 + bn),  which implies that, for sufficiently large n,  (1 + β)k2(1 + on(1))(2q(n − k) + 4 log k/k) exp(−γˆµ2(1 − on(1))) < β,  and hence  k  �  i=1  �  j≥k+1  j∼i  wij(x∗  i − x∗  j) < β  �  i∈K  Ti,  which is the desired contradiction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Therefore we must have that x∗  k > 0 and consequently K ⊆ supp(x∗).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  Now, since x∗  i > 0 for all i ∈ K, this means that nodes inside K settles exactly �  i∈K Ti units mass, and  hence exactly β �  i∈K Ti mass leaves K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Because x∗  i > 0 only if node j is saturated with Ti unit mass, we  get that �  i∈supp(x∗  i )\\K Ti ≤ β �  i∈K Ti.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  Part 2 of the theorem is prove by following the same reasoning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Assume for the sake of contradiction  that x∗  k = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Since p ≥ (4+ϵ)  δ2  log k  k−1 , we apply Lemma C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='1 and get that with probability at least 1 − ek−ϵ/2,  17  cutK(C) ≥ (1 − δ)p(k − 1) for every C ⊆ K such that 1 ≤ |C| ≤ k − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' We will assume that this event holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  Moreover, for any 1 ≤ i ≤ k − 1, the total amount of mass that moves from {1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' , i} to {i + 1, i + 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' , k}  cannot be greater than (1 + β) �  i∈K Ti.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Since there are at least (1 − δ)p(k − 1) edges between {1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' , i}  and {i + 1, i + 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' , k}, we must have that  x∗  i − x∗  i+1 ≤  (1 + β) �  i′∈K Ti′  (1 − δ)p(k − 1) minj,j′∈K,j∼j′ wjj′ , ∀i = 1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' , k − 1,  because, otherwise, there would be more than (1 + β) �  i∈K Ti mass that moves from {1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' , i} to  {i + 1, i + 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' , k}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Apply Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='3 we have that, with probability at least 1 − on(1) − ek−ϵ/2,  x∗  1 ≤  k−1  �  i=1  (1 + β) �  i′∈K Ti′  (1 − δ)p(k − 1) minj,j′∈K,j∼j′ wjj′ ≤ (1 + β)k(1 + on(1)) �  i′∈K Ti′  (1 − δ)p(k − 1)  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  The rest of the proof proceeds as the proof of part 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='3  Proof of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='5  To see that K ⊆ supp(x∗), let us assume for the sake of contradiction that x∗  i = 0 for some i ∈ K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' This  means that node i receives at most Ti ≤ Tmax mass, because otherwise we would have x∗  i > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' We also know  that i ̸= s because Tmax < ∆s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Denote F := {j ∈ K : j ∼ s}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' We will consider two cases depending on if  i ∈ F or not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' If i ∈ F, then we must have that, with probability at least 1 − on(1),  wis(x∗  s − x∗  i ) ≤ Tmax ⇐⇒ x∗  s ≤ Tmax/wis + x∗  i = Tmax(1 + an)  for some an = on(1), where the last equality follows Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Moreover, since c2 < 1 we have that  p(k − 1)  η(c2)  = p(k − 1) + q(n − k)e−c2γ ˆµ2 > p(k − 1) + q(n − k)e−γ ˆµ2(1−bn)  (6)  for any bn = on(1) and for all sufficiently large n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Therefore,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' with probability at least 1 − on(1) − 4k−ϵ1/3  and for all sufficiently large n,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' the total amount of mass that is sent out from node s is  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='ℓ∼s  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='wis(x∗  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='s − x∗  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='ℓ) =  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='ℓ∼s  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='ℓ∈K  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='wis(x∗  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='s − x∗  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='ℓ) +  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='ℓ∼s  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='ℓ/∈K  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='wis(x∗  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='s − x∗  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='ℓ)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='(i)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='≤  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='ℓ∼s  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='ℓ∈K  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='x∗  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='s +  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='ℓ∼s  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='ℓ/∈K  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='e−γ ˆµ2(1−bn)x∗  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='s  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='for some bn = on(1)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='(ii)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='≤ (1 + δ1)p(k − 1)x∗  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='s + ((1 + δ1)q(n − k) + 2δ1p(k − 1))e−γ ˆµ2(1−bn)x∗  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='s  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='≤ (1 + 3δ1)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='p(k − 1) + q(n − k)e−γ ˆµ2(1−bn)�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='x∗  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='s  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='(iii)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='< (1 + 3δ1)p(k − 1)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='η(c2)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='x∗  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='s  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='≤ (1 + 3δ1)p(k − 1)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='η(c2)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='Tmax(1 + an)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='(iv)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='< c1(1 + 3δ1)p(k − 1)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='η(c2)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='Tmax,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  where (i) follows from Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='3 and x∗ ≥ 0, (ii) follows from Lemma C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='3, (iii) follows from (6), (iv) follows  from the assumption that c1 > 1 and hence for all sufficiently large n we have c1 ≥ (1 + an) where an = on(1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  18  Since the initial mass equals the sum of Ts and the total amount of mass that is sent out from s, we get that  the total amount of initial mass is  ∆s < c1(1 + 3δ1)p(k − 1)  η(c2)  Tmax + Tmax < c1Tmax  �  (1 + 3δ1)(1 +  1  k−1)k  η(c2)  �  < c1Tmax  m(δ1, δ2)k  η(c2)2  = ∆s,  which is a contradiction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Therefore, we must have i ̸∈ F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  Suppose now that i ̸∈ F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Then we know that node i receives at most Ti ≤ Tmax mass from its neighbors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' In  particular, node i receives at most Tmax mass from nodes in F, that is, �  j∈F  j∼i  wijx∗  j ≤ Tmax.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' By Lemma C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='4,  we know that with probability at least 1 − 2k−ϵ1/3 − k−2ϵ2, node i has at least (1 − δ1)(1 − δ2)p2(k − 1)  neighbors in F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Apply Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='3 we get that, with probability at least 1 − on(1) − 2k−ϵ1/3 − k−2ϵ2,  �  j∈F  j∼i  wijx∗  j ≤ Ti =⇒ (1 − δ1)(1 − δ2)p2(k − 1) · min  j∈F  j∼i  x∗  j ≤ Tmax · max  j∈F  j∼i  1  wij  =⇒ min  j∈F  j∼i  ≤  Tmax(1 + an)  (1 − δ1)(1 − δ2)p2(k − 1)  =⇒ min  j∈F ≤  Tmax(1 + an)  (1 − δ1)(1 − δ2)p2(k − 1)  for some an = on(1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Let j ∈ F a node such that x∗  j ≤ x∗  ℓ for all ℓ ∈ F, then  x∗  j ≤  Tmax(1 + an)  (1 − δ1)(1 − δ2)p2(k − 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  (7)  By Lemma C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='4, with probability at least 1 − 2k−ϵ1/3 − k−2ϵ2, node j has at least (1 − δ1)(1 − δ2)p2(k − 1) − 1  neighbors in F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Since x∗  j ≤ x∗  ℓ for all ℓ ∈ F and x∗  j ≤ x∗  s,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' we know that  |{ℓ ∈ K : x∗  ℓ ≥ x∗  j}| ≥ (1 − δ1)(1 − δ2)p2(k − 1)  (8)  Therefore,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' for all sufficiently large n,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' with probability at least 1 − on(1) − 4k−ϵ1/3 − k−2ϵ2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' the maximum  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='amount of mass that node j can send out is  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='ℓ∼j  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='wjℓ(x∗  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='j − x∗  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='ℓ) =  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='ℓ∼j  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='ℓ∈K  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='wjℓ(x∗  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='j − x∗  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='ℓ) +  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='ℓ∼j  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='ℓ̸∈K  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='wjℓ(x∗  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='j − x∗  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='ℓ)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='(i)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='≤  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='ℓ∼j  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='ℓ∈K  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='wjℓ(x∗  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='j − x∗  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='ℓ) +  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='ℓ∼j  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='ℓ̸∈K  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='e−γ ˆµ2(1−bn)(x∗  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='j − x∗  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='ℓ)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='for some bn = on(1)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='(ii)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='≤  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='(1 + δ1)p(k − 1) − (1 − δ1)(1 − δ2)p2(k − 1)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='x∗  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='j  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='+  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='(1 + δ1)q(n − k) + 2δ1p(k − 1)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='e−γ ˆµ2(1−bn)x∗  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='j  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='≤  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='(1 + 3δ1)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='p(k − 1) + q(n − k)e−γ ˆµ2(1−bn)�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='− (1 − δ1)(1 − δ2)p2(k − 1)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='x∗  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='j  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='(iii)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='≤  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='(1 + 3δ1)p(k − 1)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='η(c2)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='− (1 − δ1)(1 − δ2)p2(k − 1)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='x∗  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='j  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='(iv)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='≤  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='(1 + 3δ1)p(k − 1)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='η(c2)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='− (1 − δ1)(1 − δ2)p2(k − 1)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='Tmax(1 + an)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='(1 − δ1)(1 − δ2)p2(k − 1)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='≤ Tmax(1 + an)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='(1 + 3δ1)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='(1 − δ1)(1 − δ2)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='pη(c2) − Tmax,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  19  where (i) follows from Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='3, (ii) follows from Lemma C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='3 and (8), (iii) follows from (6) and (iv) follows  from (7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Now, since node j settles at most Tj ≤ Tmax mass, the maximum amount of mass that node j  receives is  Tmax(1 + an)  (1 + 3δ1)  (1 − δ1)(1 − δ2)  1  pη(c2) − Tmax + Tmax = Tmax(1 + an)  (1 + 3δ1)  (1 − δ1)(1 − δ2)  1  pη(c2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  This means that  wjs(x∗  s − x∗  j) ≤ Tmax(1 + an)  (1 + 3δ1)  (1 − δ1)(1 − δ2)  1  pη(c2)  =⇒ x∗  s ≤  Tmax(1 + a′  n)  (1 − δ1)(1 − δ2)  �  1  p2(k − 1) + (1 + 3δ1)  pη(c2)  �  for some a′  n = on(1), where we have applied Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='3 for wjs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Apply the same reasoning as before,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' we get  that with probability at least 1 − on(1) − 4k−ϵ1/3 − k−2ϵ2 for all sufficiently large n,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' the total amount of mass  that is sent out from node s is  �  ℓ∼s  wis(x∗  s − x∗  ℓ) < (1 + 3δ1)p(k − 1)  η(c2)  x∗  s  ≤  Tmax(1 + a′  n)  (1 − δ1)(1 − δ2)  �(1 + 3δ1)  pη(c2)  + (1 + 3δ1)2(k − 1)  η(c2)2  �  ≤ c1Tmax  (1 + 3δ1)  (1 − δ1)(1 − δ2)  (1 + 3δ2 +  1  p(k−1))  η(c2)2  (k − 1)  ≤ c1Tmax  m(δ1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' δ2)(k − 1)  η(c2)2  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  but then this means that the total amount of initial mass is  ∆s < c1Tmax  m(δ1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' δ2)(k − 1)  η(c2)2  + Tmax < c1Tmax  m(δ1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' δ2)k  η(c2)2  = ∆s  which is a contradiction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Therefore we must have i ̸∈ K, but then this contradicts our assumption that i ∈ K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  Since our choice of i, s ∈ K were arbitrary, this means that x∗  i > 0 for all i ∈ K and for all s ∈ K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  Finally, the upper bound on the false positives follows directly from the fact that x∗  i > 0 only if node i is  saturated with exactly Ti mass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' When Ti = 1 for all i the result follows directly from ∆s = c1m(δ1, δ2)k/η(c2)2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  When Ti = deg(i) for all i, we may apply Lemma C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='3 and get that  ∆s ≤ c1m(δ1, δ2)  η(c2)2  (1 + δ1)k(p(k − 1) + q(n − k)) ≤ c1m(δ1, δ2)  η(c2)2  (1 + δ1)  (1 − δ1)vol(K)  from which the result follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  C  Technical lemmas  Lemma C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='1 (Lower bound of internal cut).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' For any 0 < δ ≤ 1 and ϵ > 0, if p ≥ (4+ϵ)  δ2  log k  k−1 and k ≥ 20, then  with probability at least 1 − ek−ϵ/2 we have that cutK(C) ≥ (1 − δ)p(k − 1) for all proper subsets C ⊂ K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Consider integers j such that 1 ≤ j ≤ k/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' First fix some j and let C ⊂ K be such that |C| = j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Note  that cut(C) is the sum of j(k − j) independent Bernoulli random variables with expectation E(cut(C)) =  20  pj(k − j).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Therefore we may apply the Chernoff bound and get  P(cutK(C) ≤ (1 − δ)p(k − 1)) ≤ e−pj(k−j)  �  ej(k − j)  (1 − δ)(k − 1)  �(1−δ)p(k−1)  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  By a union bound over all subsets C ⊂ K such that |C| = j we get that  P (cutK(C) ≤ (1 − δ)p(k − 1), ∀C ⊂ K s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' |C| = j)  ≤  �k  j  �  e−pj(k−j)  �  ej(k − j)  (1 − δ)(k − 1)  �(1−δ)p(k−1)  ≤  �ek  j  �j  exp  �  −pj(k − j) + (1 − δ)p(k − 1) + (1 − δ)p(k − 1) log  �  j(k − j)  (1 − δ)(k − 1)  ��  = exp  �  −pj(k − j) + (1 − δ)p(k − 1) + (1 − δ)p(k − 1) log  �  j(k − j)  (1 − δ)(k − 1)  �  + j + j log  �k  j  ��  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  (9)  Now consider the exponent in (9),  f(j) = −pj(k − j) + (1 − δ)p(k − 1) + (1 − δ)p(k − 1) log  �  j(k − j)  (1 − δ)(k − 1)  �  + j + j log  �k  j  �  ,  we will show that f(j) ≤ −(1 + ϵ/2) log k + 1 for all 1 ≤ j ≤ k/2 and k ≥ 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Let us first consider the interval  [1, 3k/8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' The derivative of f(j) with respect to j is  f ′(j) = −p(k − 2j) + (1 − δ)p(k − 1)(k − 2j)  j(k − j) + log  �k  j  �  ,  and we have that f ′(j) ≤ 0 for all 1 ≤ j ≤ 3k/8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' To see this, for 1 ≤ j ≤ k/2 we have  (k − 1)  j(k − j) ≤ 1 ⇐⇒ (1 − δ)p(k − 1)(k − 2j)  j(k − j)  ≤ (1 − δ)p(k − 2j)  ⇐⇒ −p(k − 2j) + (1 − δ)p(k − 1)(k − 2j)  j(k − j) ≤ −δp(k − 2j),  (10)  moreover, since p ≥ (4+ϵ)  δ2  log k  k−1 , for 1 ≤ j ≤ 3k/8 and k ≥ 2 we have  − δp(k − 2j) ≤ −δpk  4  ≤ − (4 + ϵ)k  4δ(k − 1) log k ≤ − log k ≤ − log(k/j),  (11)  and thus by combining (10) and (11) we get f ′(j) ≤ −δp(k − 2j) + log(k/j) ≤ 0 for all 1 ≤ j ≤ 3k/8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' This  implies that f(j) achieves maximum at j = 1 over the interval [1, 3k/8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Therefore, for all 1 ≤ j ≤ 3k/8,  f(j) ≤ f(1) = −p(k − 1) + (1 − δ)p(k − 1) − (1 − δ)p(k − 1) log(1 − δ) + 1 + log k  = −p(k − 1)(δ + (1 − δ) log(1 − δ)) + 1 + log k  ≤ −p(k − 1)δ2/2 + 1 + log k  ≤ −(2 + ϵ/2) log k + 1 + log k  = −(1 + ϵ/2) log k + 1  where the second inequality follows from the numeric inequality δ + (1 − δ) log(1 − δ) ≥ δ2/2 for δ ∈ (0, 1),  and the third inequality follows from the assumption that p ≥ (4+ϵ)  δ2  log k  k−1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  21  Next, consider the value of f(j) over the interval [3k/8, k/2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' We have that for 3k/8 ≤ j ≤ k/2 and k ≥ 20,  f(j) ≤ −p  �3k  8  � �5k  8  �  + (1 − δ)p(k − 1)  �  1 + log  �  k2/4  (1 − δ)(k − 1)  ��  + k  2 + 3k  8 log  �8  3  �  ≤ −15  64pk2 + p(k − 1)  �  1 + (1 − δ) log  � k2/4  k − 1  ��  + 22  25k  ≤ −pk  � 41  256k − 1 − log  � k2/4  k − 1  ��  − k  � 19  256pk − 22  25  �  ≤ −1  2pk  ≤ −(2 + ϵ/2) log k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  In the above, the first inequality follows from the fact that the term j log(k/j) is decreasing over the interval  [3k/8, k/2], the second inequality follows from the numeric inequality (1 − δ) − (1 − δ) log(1 − δ) ≤ 1 for  δ ∈ (0, 1) which follows from the fact that log x ≥ 1 − 1/x for x > 0, the forth inequality follows from k ≥ 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  Therefore, the exponent in (9) satisfies f(j) ≤ −(1 + ϵ/2) log k + 1 for all 1 ≤ j ≤ k/2 and k ≥ 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Finally,  apply a union bound we get that  P(cutK(C) ≤ (1 − δ)p(k − 1), ∀C ⊂ K s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' 1 ≤ |C| ≤ k − 1)  =  ⌊k/2⌋  �  j=1  P(cutK(C) ≤ (1 − δ)p(k − 1), ∀C ⊂ K s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' |C| = j)  ≤ exp(f(j) + log k) ≤ exp  �  − ϵ  2 log k + 1  �  = ek−ϵ/2  which proves the required result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  Lemma C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='2 (Upper bound of external cut).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' For any 0 < δ ≤ 1 and ϵ > 0 with probability at least 1 − k−ϵ/3  we have that cutG(K) ≤ (1 + δ)qk(n − k) + (eϵ/δ2 + ϵ/3) log k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Note that cutG(K) is the sum of k(n − k) independent Bernoulli random variables with mean  E[cutG(K)] = qk(n−k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' We consider two cases depending on the value of qk(n−k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' If qk(n−k) ≥ ϵ log k/δ2,  then by the multiplicative Chernoff bound we have that,  P(cutG(K) ≥ (1 + δ)qk(n − k)) ≤ exp  �  −δ2  3 qk(n − k)  �  ≤ exp (−ϵ log k/3) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  (12)  Next consider the case qk(n − k) ≤ ϵ log k/δ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Denote c(ϵ, δ) := eϵ/δ2 + ϵ/3 and observe that  ϵ  δ2 = c(ϵ, δ) − ϵ/3  e  =  �  1 −  ϵ/3  c(ϵ, δ)  � c(ϵ, δ)  e  ≤ exp  �  − ϵ/3  c(ϵ, δ)  � c(ϵ, δ)  e  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  This means that  qk(n − k) ≤ ϵ  δ2 log k ≤ exp  �  − ϵ/3  c(ϵ, δ) − 1  �  c(ϵ, δ) log k,  and thus  qk(n − k)  c(ϵ, δ) log k ≤ exp  �  − ϵ/3  c(ϵ, δ) − 1  �  ⇐⇒  c(ϵ, δ) + c(ϵ, δ) log  � qk(n − k)  c(ϵ, δ) log k  �  ≤ −ϵ/3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  22  Therefore the Chernoff bound yields  P (cutG(K) ≥ c(ϵ, δ) log k) ≤ e−qk(n−k)  � eqk(n − k)  c(ϵ, δ) log k  �c(ϵ,δ) log k  = exp  �  −qk(n − k) + c(ϵ, δ) log k  �  1 + log  � qk(n − k)  c(ϵ, δ) log k  ���  ≤ exp  �  log k  �  c(ϵ, δ) + c(ϵ, δ) log  � qk(n − k)  c(ϵ, δ) log k  ���  ≤ exp(−ϵ log k/3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  (13)  Combining (12) and (13) gives the required result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  Lemma C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='3 (Concentration of degrees).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' If p ≥ (3+ϵ)  δ2  log k  k−1 for some ϵ > 0 and 0 < δ ≤ 1, then with probability  at least 1 − 2k−ϵ/3 we have that  (1 − δ)p(k − 1) ≤ degK(i) ≤ (1 + δ)p(k − 1), ∀i ∈ K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  Similarly, with probability at least 1 − 2k−ϵ/3 we have that  (1 − δ)(p(k − 1) + q(n − k)) ≤ degG(i) ≤ (1 + δ)(p(k − 1) + q(n − k)), ∀i ∈ K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' For each node i ∈ K, degK(i) is the sum of independent Bernoulli random variables with mean  E[degK(i)] = p(k − 1), therefore, apply the multiplicative Chernoff bound we have  P(| degK(i) − p(k − 1)| ≥ δp(k − 1)) ≤ 2 exp(−δ2p(k − 1)/3) ≤ 2 exp(−(1 + ϵ) log k/3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  By taking a union bound over all i ∈ K we obtain the required concentration result for degK(i) for all i ∈ K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  The result for degG(i) for all i ∈ K is obtained similarly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  Lemma C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='4 (Well-connected cluster).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' If p ≥ max( (3+ϵ1)  δ2  1  log k  k−1 ,  (2+ϵ2)  δ2  √1−δ1  √log k  √k−1 ), then with probability at least  1 − 2k−ϵ1/3 − k−2ϵ2 we have that for all s ∈ K, for all i ∈ K\\{s}, there are at least (1 − δ1)(1 − δ2)p2(k − 1)  paths connecting node i to node s such that, the path lengths are at most 2 and the paths are mutually  non-overlapping, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=', an edge appears in at most one of the paths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Let s ∈ K and denote F the set of neighbors of s in K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' By Lemma C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='3 and our assumption on p we  know that |F| ≥ (1 − δ1)p(k − 1) with probability at least 1 − 2k−ϵ1/3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Let us denote E(A, B) the set of edges  between A ⊆ K and B ⊆ K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Let i ∈ K\\{s}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' If i ̸∈ F, then |E({i}, F)| is the sum of independent Bernoulli  random variables with mean E[|E({i}, F)|] = |F|p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Apply the multiplicative Chernoff bound we get that  P(|E({i}, F)| ≤ (1 − δ2)|F|p) ≤ exp  �  −δ2  2  2 |F|p  �  ≤ exp  �  −δ2  2(1 − δ1)  2  p2(k − 1)  �  ≤ exp(−(2 + 2ϵ2) log k)  where the last inequality is due to our assumption that p ≥  (2+ϵ2)  δ2  √1−δ1  √log k  √k−1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' If i ∈ F, then the edge (i, s) is a  path of length 1 between node i and node s, moreover,  P(|E({i}, F\\{i})| + 1 ≤ (1 − δ2)|F|p) ≤ P(|E(i′, F)| ≤ (1 − δ2)|F|p)  for any node i′ ∈ K\\F and i′ ̸= s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Note that, for i ∈ K\\{s}, each edge (i, j) in E({i}, F\\{i}) identifies a  unique path (i, j, s) and all these paths do not have overlapping edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Therefore, denote P(i, s) the set  of mutually non-overlapping paths of length at most 2 between i and s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' and take union bounds over all  i ∈ K\\{s} and then over all s ∈ K, we get that  P(P(i, s) ≤ (1 − δ2)|F|p, ∀s ∈ K, ∀i ∈ K\\{s}) ≤ k−2ϵ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  Finally, a union bound over the above event and the event that |F| ≤ (1 − δ1)p(k − 1) gives the required  result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  23  D  Dataset details, empirical setup and additional results  The co-authorship graphs are based on the Microsoft Academic Graph from the KDD Cup 2016 challenge [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  In these graphs, nodes are authors, and two nodes are connected by an edge if they have coauthored a paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  The clusters are defined according to the most active research field of each author.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' The node attributes  represent paper keywords for each author’s papers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' The first graph consists of 18,333 computer science  researchers and 81,894 connections among them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Each computer science researcher belongs to one of the 15  ground-truth clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' The node attributes consists of 6,805 key words.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' The second graph consists of 34,493  physics researchers and 247,962 connections among them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Each physics researcher belongs to one of the 5  ground-truth clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' The node attributes consists of 8,415 key words.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' The cluster sizes are given in Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='Table 2: Cluster statistics in co-authorship graphs  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='Network Cluster  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='Number of nodes Volume  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='Computer Science  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='Bioinformatics  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='708  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='3767  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='Machine Learning  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='462  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='4387  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='Computer Vision  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='2050  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='20384  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='NLP  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='429  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='2476  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='Graphics  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='1394  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='15429  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='Networks  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='2193  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='18364  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='Security  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='371  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='2493  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='Databases  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='924  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='9954  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='Data Mining  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='775  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='7573  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='Game Theory  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='118  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='362  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='HCI  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='1444  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='15145  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='Information Theory  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='2033  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='16007  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='Medical Informatics  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='420  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='3838  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='Robotics  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='4136  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='33708  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='Theoretical CS  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='876  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='9901  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='TOTAL  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='18333 163788  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='Physics  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' A  5750  52151  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' B  5045  54853  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' C  17426 325475  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' D  2753  40451  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' E  3519  22994  TOTAL  34493 495924  For both datasets, we preprocess the node attributes by applying PCA to reduce the dimension to 128.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' In  addition, for each node we enhance its attributes by taking a uniform average over its own attributes and  the neighbors’ attributes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Uniform averaging of neighborhood attributes has been shown to improve the  signal-to-noise ratio in CSBM [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' This operation does not break the local nature of Algorithm 2 because  it only needs to be done whenever it becomes necessary for subsequent computations, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=', when a node is  looked at by Algorithm 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  We consider two ways for setting the sink capacities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' The first is Ti = degG(i) for all i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' The corresponding  local clustering results are reported in Table 1 in the main text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' The second is Ti = 1 for all i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' The additional  results are presented in Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' For each cluster K in a graph, given a seed node s ∈ K, we run Algorithm 2  with source mass ∆s = α �  i∈K Ti for α ∈ {1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='5, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='75, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' , 5}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' We select the cluster that has the minimum  edge-weighted conductance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Given edge weights wij for (i, j) ∈ E and a cluster C ⊆ V , the edge-weighted  24  conductance of C is the ratio  �  i∈C,j̸∈C wij  �  i∈C  �  j∼i wij  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  We measure recovery quality using the F1 score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' For each cluster we run 100 trials, for each trial we randomly  select a seed node from the target cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' We report average F1 scores over 100 trials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' We set γ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='02 so  that the edge weights are reasonably distributed between 0 and 1, that is, not all edges weights are arbitrarily  close to 1, and not all edge weights are arbitrarily close 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' We find that the results do not change much when  we use other choices for γ within a reasonable range, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' γ ∈ [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='005, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' For both choices of T, using node  attributes generally improves the recovery accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Overall, setting the sink capacities to Ti = degG(i) leads  to higher F1 scores than setting Ti = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  Table 3: F1 scores for local clustering in co-authorship networks under different settings of flow diffusion  Ti = degG(i) for all i  Ti = 1 for all i  Network  Cluster  No attr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  Ues attr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  Improv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  No attr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  Ues attr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  Improv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  Computer Science  Bioinformatics  32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='1  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='3  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='2  23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='5  31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='7  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='2  Machine Learning  30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='9  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='3  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='4  27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='5  34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='4  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='9  Computer Vision  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='6  35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='1  40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='4  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='8  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='6  NLP  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='2  52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='3  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='1  34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='3  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='9  Graphics  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='6  49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='2  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='6  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='1  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='3  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='2  Networks  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='1  47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='9  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='0  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='1  Security  29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='9  35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='7  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='8  23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='0  26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='2  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='2  Databases  48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='5  58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='1  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='6  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='9  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='7  Data Mining  27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='5  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='3  26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='2  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='6  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='4  Game Theory  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='6  66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='0  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='4  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='9  62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='6  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='7  HCI  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='0  77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='6  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='6  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='0  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='1  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='1  Information Theory  47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='4  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='9  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='5  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='6  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='2  Medical Informatics  65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='7  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='3  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='6  62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='7  68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='1  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='4  Robotics  59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='9  59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='9  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='0  58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='8  55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='9  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='9  Theoretical CS  66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='3  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='7  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='4  54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='9  59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='1  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='2  Physics  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' A  69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='4  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='9  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='5  53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='5  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='9  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='4  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' B  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='4  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='9  40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='4  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='7  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' C  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='3  82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='1  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='8  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='9  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='9  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='0  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' D  62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='3  68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='9  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='6  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='6  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='0  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='4  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' E  49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='5  53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='7  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='2  30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='1  34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='9  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='8  AVERAGE  50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='3  54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='6  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='3  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='5  48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='3  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='8  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='1  Additional experiments with Amazon co-purchase graph  We carry out additional experiments using a segment of the Amazon co-purchase graph [21, 23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' In this  graph, nodes represent products, and two products are connected by an edge if they are frequently bought  together.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' The clusters are defined according to the product category.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' The node attributes are bag-of-words  encoded product reviews.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' The cluster sizes are given in Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' We use exactly the same empirical settings  as before.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' The local clustering results are reported in Table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  We estimate an average signal-to-noise ratio in each dataset as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Let K1, K2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' KC denote a partition  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='Table 4: Cluster statistics in the Amazon co-purchase graph  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='Cluster  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='Number of nodes Volume  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='Film Photography  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='365  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='13383  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='Digital Cameras  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='1634  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='32208  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='Binoculars & Scopes  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='686  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='21611  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='Lenses  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='901  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='26479  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='Tripods & Monopods  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='872  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='26133  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='Video Surveillance  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='798  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='17959  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='Lighting & Studio  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='1900  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='86989  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='Flashes  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='331  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='13324  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='TOTAL  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='18333 163788  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='Table 5: F1 scores for local clustering in a segment of the Amazon co-purchase graph  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='Ti = degG(i) for all i  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='Ti = 1 for all i  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='Cluster  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='No attr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  Ues attr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  Improv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  No attr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  Ues attr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  Improv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  Film Photography  69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='0  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='9  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='9  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='4  74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='6  Digital Cameras  54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='4  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='6  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='7  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='4  Binoculars  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='3  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='8  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='8  82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='9  Lenses  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='0  40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='4  32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='2  32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='9  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='7  Tripods & Monopods  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='3  47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='5  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='9  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='2  Video Surveillance  94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='7  94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='9  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='2  94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='0  93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='2  Lighting & Studio  49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='6  49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='1  53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='7  53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='2  Flashes  33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='3  32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='6  27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='0  25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='2  AVERAGE  58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='7  59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='1  55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='0  55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='5  of nodes into distinct clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Let Xi be the node attributes of node i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' For 1 ≤ r ≤ C let  ¯µr :=  1  |Kr|  �  i∈Kr  Xi  be the empirical mean of node attributes in the cluster Kr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Denote  ¯λr :=  min  1≤s≤C,s̸=r ∥¯µr − ¯µs∥2  the empirical minimum pairwise mean distance between cluster Kr and other clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Let ¯σℓ denote the  empirical standard deviation for the ℓth attribute and let ¯σ = 1  d  �d  ℓ=1 ¯σℓ, where d is the dimension of node  attributes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Then we compute an average relative signal strength for the entire dataset as  ratio :=  1  |C|  C  �  r=1  ¯λr/¯σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  The computed results are shown in Table 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' Observe that the ratio is much smaller for the Amazon co-purchase  graph than the two co-authorships graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content=' This means that the relative strength of attribute signal is much  smaller for the Amazon co-purchase graph, and it explains why there is only a very small improvement when  using node attributes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  The results we observe in the experiments with real-world datasets indicate that, an very interesting future  work is to incorporate node embedding and parameter learning into the local flow diffusion pipeline (to  26  Table 6: Relative signal strength for each dataset  graph  ratio  Co-authorship (Computer Science)  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='69  Co-authorship (Physics)  77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='09  Amazon co-purchase  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='58  improve signal-to-noise ratio of node attributes), where the attributes and their relative importance may be  optimized simultaneously alongside the local diffusion process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
+page_content='  27' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/k9FPT4oBgHgl3EQf2jWr/content/2301.13187v1.pdf'}
diff --git a/ktE3T4oBgHgl3EQf5wsL/vector_store/index.pkl b/ktE3T4oBgHgl3EQf5wsL/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..fa7cbda681f4ab1d223e6466dd9ab0b048bc92cd
--- /dev/null
+++ b/ktE3T4oBgHgl3EQf5wsL/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:847f53e6e376e18066795db363425de6d4a488ec411ff62b49050d2015ed596c
+size 195290
diff --git a/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf b/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..3c1bbe810762afc056d6a5a7bc68c516a7c9bf37
--- /dev/null
+++ b/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:c5459883e4e07f55ff04e149612abd44f28ad284c994ef72c0eccfde0ecdc910
+size 2629124
diff --git a/m9E5T4oBgHgl3EQfHw6d/vector_store/index.faiss b/m9E5T4oBgHgl3EQfHw6d/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..21721bb4fe1672033a56cb2787d7f822098e4467
--- /dev/null
+++ b/m9E5T4oBgHgl3EQfHw6d/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:d8e845f65efd25e5353258d09457606ac3e81af0e7ccc930a407177228c4a5ed
+size 2359341
diff --git a/m9E5T4oBgHgl3EQfHw6d/vector_store/index.pkl b/m9E5T4oBgHgl3EQfHw6d/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..ddcc4f2c942a3a14aee175ab571ff593cf22dd9c
--- /dev/null
+++ b/m9E5T4oBgHgl3EQfHw6d/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:6f3c98339cf44405d6f12e6d97718aa686a9454b7eaaeeda7328ffac1670b45a
+size 104986
diff --git a/mNFQT4oBgHgl3EQfojZZ/content/tmp_files/2301.13373v1.pdf.txt b/mNFQT4oBgHgl3EQfojZZ/content/tmp_files/2301.13373v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e6fcd80b1d04cb2cce7174a9d37c5686317ac196
--- /dev/null
+++ b/mNFQT4oBgHgl3EQfojZZ/content/tmp_files/2301.13373v1.pdf.txt
@@ -0,0 +1,1920 @@
+Force moment partitioning and scaling analysis of vortices shed by a
+2D pitching wing in quiescent fluid
+Yuanhang Zhu1*†, Howon Lee1‡, Sushrut Kumar2, Karthik Menon3, Rajat Mittal2 and Kenneth Breuer1
+1Center for Fluid Mechanics, School of Engineering, Brown University, Providence, RI, 02912, USA.
+2Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD, 21218, USA.
+3Department of Pediatrics (Cardiology) and Institute for Computational and Mathematical
+Engineering, Stanford University, Stanford, CA, 94305, USA.
+*Corresponding author. E-mail: yuanhang zhu@brown.edu;
+†Present Address: Department of Mechanical and Aerospace Engineering, University of Virginia,
+Charlottesville, VA 22904, USA
+‡Present Address: School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA
+30332, USA
+Abstract
+We experimentally study the dynamics and strength of vortices shed from a NACA 0012 wing
+undergoing sinusoidal pitching in quiescent water. We characterize the temporal evolution of
+the vortex trajectory and circulation over a range of pitching frequencies, amplitudes and pivot
+locations. By employing a physics-based force and moment partitioning method (FMPM), we
+estimate the vortex-induced aerodynamic moment from the velocity fields measured using par-
+ticle image velocimetry. The vortex circulation, formation time and vorticity-induced moment
+are shown to follow scaling laws based on the feeding shear-layer velocity. The vortex dynamics,
+together with the spatial distribution of the vorticity-induced moment, provide quantitative
+explanations for the nonlinear behaviors observed in the fluid damping (Zhu et al., J. Fluid
+Mech., vol. 923, 2021, R2).
+1 Introduction
+The unsteady flow and vortex dynamics associated
+with flapping wings/foils have been extensively
+studied for understanding the complex lift/thrust
+generation mechanism of animal flight and swim-
+ming (Ellington et al, 1996; Lentink and Dick-
+inson, 2009; Anderson et al, 1998; Triantafyllou
+et al, 2000), as well as developing bio-inspired
+flapping-wing micro air vehicles (MAVs, Ho et al,
+2003; Shyy et al, 2010; Jafferis et al, 2019),
+oscillating-foil autonomous underwater vehicles
+(AUVs, Barrett, 1996; Zhu et al, 2019; Zhong
+et al, 2021) and energy-harvesting devices (Xiao
+and Zhu, 2014; Young et al, 2014). Flapping
+wings/foils were commonly studied in the presence
+of an ambient flow to match real flying/swim-
+ming settings. Numerous studies have focused on
+1
+arXiv:2301.13373v1  [physics.flu-dyn]  31 Jan 2023
+
+Article Title
+2
+identifying scaling laws that characterize the for-
+mation and development of the shed vortices,
+along with the corresponding aerodynamic loads
+(Buchholz and Smits, 2008; Buchholz et al, 2011;
+Baik et al, 2012; Onoue and Breuer, 2016). In
+the absence of a freestream flow, the problem
+is associated with the hovering flight of insects
+(Wang, 2005; Bergou et al, 2007; Kang and Shyy,
+2014) and the starting motion of fish (Heath-
+cote et al, 2004; Epps and Techet, 2007; DeVoria
+and Ringuette, 2012, 2013; Shinde and Arakeri,
+2013; Jimreeves David et al, 2018). In these stud-
+ies, the pitching panel was usually hinged at the
+leading-edge to mimic the corresponding biologi-
+cal appendage, and more emphasis was placed on
+the vorticity-induced lift and thrust. On the other
+hand, the vorticity-induced aerodynamic moment
+has attracted less attention, despite its close con-
+nections with maneuvering and its importance in
+regulating aerodynamic damping.
+In aeroelastic systems, the formation and shed-
+ding of vortices from elastically mounted bluff
+bodies is the main source of aerodynamic damp-
+ing (Williamson and Govardhan, 2004; Morse and
+Williamson, 2009; Menon and Mittal, 2019; Zhu
+et al, 2020). Menon and Mittal (2019) and Zhu
+et al (2020) have analyzed the energy trans-
+fer between an elastically mounted pitching wing
+and the unsteady ambient flow, and found that
+the total damping in an aeroelastic system has
+to equal to zero for flow-induced oscillations to
+sustain. This means that the positive structural
+damping has to balance the negative aerodynamic
+damping. With a free-stream flow, the negative
+aerodynamic damping mainly comes from the
+dynamic stall vortex (McCroskey, 1982; Corke and
+Thomas, 2015). Without a free-stream flow, how-
+ever, the aerodynamic damping becomes purely
+positive, as the pitch-induced vortices act as a
+source of drag (Morison et al, 1950). Zhu et al
+(2021) have adopted a dynamical system approach
+to study the nonlinear fluid damping associ-
+ated with vortices shed from a cyber-physically
+mounted pitching wing in the absence of a free-
+stream flow. They extracted the fluid damping
+coefficient using “ring-down” experiments and
+were able to identify a universal non-dimensional
+fluid damping coefficient that depends on the
+pitching frequency, amplitude, pivot location and
+sweep angle. They also explained the nonlinear
+behavior of the fluid damping using the corre-
+sponding vortex dynamics. However, their analysis
+of the complex vortex dynamics was purely qual-
+itative, and no quantitative evaluations of the
+vortex trajectory and strength were performed.
+Another limitation of Zhu et al (2021)’s work was
+that the dynamical system framework was only
+capable of resolving cycle-averaged vortex-induced
+damping. No direct measurements of the instan-
+taneous force and moment associated with the
+shed vortices were available, although correlating
+this information with the corresponding vortex
+dynamics could provide useful insights toward a
+more complete understanding of the underlying
+flow physics.
+The recent development of the Force and
+Moment Partitioning Method (FMPM, Quar-
+tapelle and Napolitano, 1983; Zhang et al, 2015;
+Moriche et al, 2017; Menon and Mittal, 2021a,b,c)
+(a variant is also known as the vortex force/mo-
+ment map method, Li and Wu, 2018; Li et al,
+2020) provides us with a framework to deter-
+mine the instantaneous flow-induced forces and
+moments from the corresponding velocity fields.
+In the FMPM, the Navier-Stokes equation is pro-
+jected onto the gradient of an auxiliary potential
+which satisfies the Laplace equation and certain
+boundary conditions. The individual contribu-
+tions of the added-mass, vorticity-induced, and
+viscous terms to the fluid force/moment exerted
+on the immersed body can be separated ana-
+lytically, enabling independent dissection of each
+term. Moreover, the FMPM is able to visual-
+ize the spatial distribution of the flow-induced
+force/moment, which is valuable for associating
+the vortex dynamics with the resultant aerody-
+namic loads. Zhang et al (2015) have applied
+FMPM to a numerical simulation of the flight of
+a hawkmoth and a fruit fly and found that, in
+addition to the leading-edge vortex, which con-
+tributes to the majority of the lift, the centripetal
+acceleration reaction, which is analogous to the
+added-mass effect, also plays an important role
+in the overall lift generation. Menon and Mit-
+tal (2021a) have revisited the classical problem
+of vortex-induced vibrations associated with flow
+over a cylinder and found using FMPM that the
+self-sustained oscillations are driven by the vortic-
+ity in the shear layer instead of the shed vortices
+in the wake. Moreover, using FMPM, Menon and
+
+Article Title
+3
+Mittal (2021c) discovered that, in addition to the
+rotation-dominated region (i.e. regions defined as
+vortices), the strain-dominated region surround-
+ing the vortices also has a significant effect on the
+aerodynamic load generation of pitching airfoils.
+Seo and Mittal (2022) have used FMPM in con-
+junction with direct numerical simulations to show
+that most of the thrust generated by a carangi-
+form swimmer is due to the leading-edge vortex
+on the caudal fin.
+The above examples have demonstrated the
+powerful capability of FMPM to provide new
+physical insights for vortex-dominated flows. How-
+ever, in these examples, the FMPM was only
+tested and validated on results obtained from
+numerical simulations, where data was usually
+considered to be clean and ideal. Applying FMPM
+to experimental data will open up numerous new
+possibilities for flow measurement techniques such
+as particle image velocimetry (PIV). However,
+there are many foreseeable challenges. First, in
+many experiments, the measured velocity fields
+are usually ensemble- or phase-averaged so as to
+reduce measurement noise and incoherent flow
+structures, but it is not clear how ensemble- or
+phase-averaging will affect the accuracy of the
+FMPM due to the nonlinear operations involved.
+Second, it is well-acknowledged that the accuracy
+of PIV measurements suffers close to the bound-
+ary of immersed bodies, which brings challenges
+to PIV-based load estimation methods (Rival and
+van Oudheusden, 2017). Third, for nominally two-
+dimensional flows measured using planar PIV, the
+existence of out-of-plane flows might introduce
+errors into the FMPM, depending on the strength
+of the three-dimensionality of the flow.
+The present work extends the study of Zhu
+et al (2021) on cycle-averaged vortex-induced
+damping and examines the instantaneous vor-
+tex trajectory, strength, structure, and vorticity-
+induced moment of sinusoidally pitching wings in
+a quiescent fluid. We also aim to use the present
+problem as an example to address the aforemen-
+tioned potential challenges of applying FMPM
+to experimental data. Since the current experi-
+ment focuses on a pitching wing, we confine our
+analysis to moment partitioning, but the results
+are equally applicable to force partitioning. For
+simplicity, we continue to refer to the analysis
+technique by its full name (or acronym) – FMPM.
+In the following sections, we introduce the
+experimental
+setup,
+the
+vortex
+identification
+method, and the FMPM (Section 2), including
+the relative benefits of applying FMPM to instan-
+taneous (noisy) velocity fields as compared with
+ensemble-averaged (less noisy) fields. In Section
+3, we analyze and scale the effect of pitching
+frequency, amplitude and pivot location on the
+temporal evolution of the vortex trajectory, cir-
+culation and the FMPM-based vorticity-induced
+moment. Finally, we summarize all the key find-
+ings and reiterate the significance of the present
+study in Section 4.
+2 Methods
+2.1 Experimental setup
+A schematic of the experimental setup is shown in
+Fig. 1(a). The setup is very similar to that used in
+Zhu et al (2021), but without the cyber-physical
+control loop. We conduct all the experiments in
+the Brown University free-surface water tunnel
+(test section width × depth × length = 0.8 m ×
+0.6 m × 4.0 m), with a zero flow speed (U∞ = 0
+m/s) to create a quiescent environment. We use a
+servo motor (Parker SM233AE) with a 5:1 gearbox
+to pitch a transparent acrylic NACA 0012 wing
+(span s = 0.3 m, chord c = 0.1 m, aspect ratio
+AR = 3). The wing has an endplate on the top end
+to reduce three-dimensional effects and skim sur-
+face waves at the root; the wing tip (bottom end)
+is left free. The wing is mounted above the end-
+plate (not shown) using an adjustable bracket that
+allows the pitching axis location x/c to be varied
+between 0 and 1. In between the servo motor and
+the wing, an optical encoder (US Digital E3-2500)
+is used to measure the pitching position θ, and a
+six-axis force/torque transducer (ATI 9105-TIF-
+Delta-IP65) is used to measure the fluid forces
+and torques exerted on the wing. In the experi-
+ments, we pitch the wing using a sinusoidal profile
+θ = A sin (2πft), where A is the pitching ampli-
+tude, f is the pitching frequency and t is time.
+In this study, we focus on four pitching ampli-
+tudes: A = 30◦ (0.52 rad), 60◦ (1.05 rad), 90◦
+(1.57 rad) and 120◦ (2.09 rad), four pitching fre-
+quencies: f = 0.25, 0.5, 0.75 and 1.0 Hz, and three
+pitching axis locations: x/c = 0.5 (mid-chord),
+x/c = 0.25 (quarter-chord) and x/c = 0 (leading-
+edge). Because we pitch the wing sinusoidally, we
+
+Article Title
+4
+Servo motor
+& gearbox
+Force
+transducer
+Laser sheet
+@ mid-span
+Endplate
+2×sCMOS
+with 35mm lens
+Mirror
+Optical encoder
+U   = 0 m/s
+NACA 0012
+(transparent)
+c
+s
+∞
+-1
+0 
+1 
+-1
+0 
+1 
+-50
+0
+50
+(a)
+(b)
+(c)
+θ
+LEV
+TEV
+-1
+0 
+1 
+-1
+0 
+1 
+0
+-200
+0
+200
+TEV
+LEV
+(d)
+(e)
+-1
+0
+1
+-1
+0
+1
+-1e-3
+0
+1e-3
+-1
+0 
+1 
+-1
+0 
+1 
+-0.05
+0
+0.05
+Fig. 1 (a) A schematic of the experimental setup. (b) A sample phase-averaged spanwise vorticity field, ωz, for the case
+A = 30◦, f = 0.5 Hz and x/c = 0.5 during the pitch-up motion (t/T = 0.13, where T = 1/f is the pitching period). The
+original frame (i.e. the gray box) is rotated by θ to keep the wing at zero angle-of-attack. (c) The corresponding Q field.
+Insets are zoom-in views of the LEV and TEV, with the identified vortex positions and boundaries. (d) The influence field,
+φ (i.e. the auxiliary potential). (e) The vortex-induced moment density distribution, −2Qφ.
+can approximate the averaged angular velocity as
+˙θ = 4Af (i.e. the wing rotates four times the pitch-
+ing amplitude A over one cycle 1/f) and define
+the Reynolds number as Re ≡ 4ρAfc2
+m/µ, where
+cm is the effective chord length, ρ and µ are water
+density and dynamic viscosity, respectively. Re is
+of O(104) for the wing kinematics considered in
+the present study.
+To study the vortex dynamics associated with
+the pitching wing, we use a two-dimensional PIV
+system to measure the flow field around the wing.
+We seed the water with 50 µm diameter neutrally
+buoyant hollow ceramic spheres and illuminate
+the mid-span plane using a double-pulse Nd:YAG
+laser (532 nm, Quantel EverGreen) with LaVi-
+sion sheet optics. Two co-planar sCMOS cameras
+(LaVision, 2560 × 2160 pixels) with a 45◦ mirror
+are used to record PIV image pairs at a frame rate
+of 15 Hz. The recorded PIV images are processed
+using the DaVis software (v10, LaVision, two
+passes at 64×64 pixels, two passes at 32×32 pixels,
+both with 50% overlap) to calculate the velocity
+vectors. Finally, the velocity fields obtained from
+the two cameras are stitched together to form a
+3.2c×3.2c field of view. A sample spanwise vortic-
+ity field, ωz, for the case A = 30◦, f = 0.5 Hz and
+x/c = 0.5 during the pitch-up motion is shown in
+Fig. 1(b). For visualization purposes, we rotate the
+original frame (i.e. the gray box) by the pitching
+angle, θ, to keep the wing at zero angle-of-attack.
+We see that as the wing pitches up, two patches
+of positive spanwise vorticity are generated at the
+leading edge and the trailing edge, corresponding
+to the leading-edge vortex (LEV) and the trailing-
+edge vortex (TEV), respectively. The LEV/TEV
+shear layers are also visible, although they start to
+break into smaller secondary vortices (Francescan-
+geli and Mulleners, 2021). Two patches of negative
+vorticity are seen near the positive vortices, corre-
+sponding to the negative LEV and TEV left over
+from the previous pitch-down cycle.
+2.2 Vortex identification and
+trajectory tracking
+We identify the vortex cores and boundaries using
+the Q-criterion (Hunt et al, 1988; Jeong and
+Hussain, 1995),
+Q = 1
+2(∥Ω∥2 − ∥S∥2),
+(1)
+where Q is the second invariant of the velocity gra-
+dient tensor, Ω is the vorticity tensor and S is the
+strain-rate tensor. Connected regions with Q > 0,
+where rotation is higher than strain, are identi-
+fied as a vortex (Lee et al, 2022). The position
+of the vortex core is calculated as the centroid of
+the top ten Q values within the vortex boundary.
+The Q field corresponding to Fig. 1(b) is plot-
+ted in Fig. 1(c). The insets are zoom-in views
+
+Article Title
+5
+of the LEV and TEV, with the identified vortex
+positions and boundaries. We see that the vortex
+boundaries (Q = 0, green curves) faithfully cap-
+ture the LEV and TEV domains. There are regions
+with negative Q values surrounding the vortices,
+corresponding to strain-dominated regions. These
+strain-dominated regions have been shown to con-
+tribute to the generation of opposite-signed aero-
+dynamic loads (Menon and Mittal, 2021c). The
+spanwise circulation of the vortex, Γ, is evaluated
+by integrating the spanwise vorticity, ωz, within
+the vortex boundary using Stokes’ theorem. All
+velocity fields are phase-averaged over 20 cycles
+before being fed into the vortex identification and
+circulation calculation pipelines. Note that cal-
+culating the circulation from the phase-averaged
+velocity field is equivalent to taking the phase
+average of individual circulations, as calculating
+the vortex circulation is a linear operation.
+2.3 Force and moment partitioning
+method (FMPM)
+For convenience and completeness, we first review
+the FMPM approach. Following this, we will
+consider the extension of the method to ensemble-
+averaged velocity fields. Following Menon and
+Mittal (2021b), we first construct an auxiliary
+potential, φ, with
+∇2φ = 0, ∂φ
+∂n =
+�
+[(x − xp) × n] · ez on airfoil
+0 on outer boundary
+,
+(2)
+where n is the outward-facing unit vector normal
+to the boundary, x − xp is the location vector
+pointing from the pitching axis xp towards the
+location x on the surface of the airfoil, and ez
+is the spanwise unit vector. Note that this aux-
+iliary potential φ is specifically constructed for
+moment partitioning. A different potential can be
+constructed to determine lift forces or drag forces,
+etc (Menon and Mittal, 2021b). In addition, the
+FMPM potential, which we refer to as the “influ-
+ence field”, should not be confused with the more
+familiar velocity potential from the classical irro-
+tational flow theory. The influence field quantifies
+the spatial influence of the Q-field on the resultant
+moment acting on the submerged body.
+The influence field, φ, satisfies the Laplace
+equation,
+subject
+to
+two
+different
+Neumann
+boundary conditions on the airfoil and the outer
+boundary. It is only a function of the airfoil shape,
+its orientation, and the location of the pitching
+axis. We solve Eqn. 2 numerically using the MAT-
+LAB Partial Differential Equation Toolbox (Finite
+Element Method). Fig. 1(d) shows the calculated
+influence field, φ, for a NACA 0012 airfoil pitching
+at the mid-chord. For this choice of the pitching
+axis, we see that the φ field can be divided into
+four quadrants, with the upper surface of the fore
+wing and the lower surface of the aft wing being
+positive, and the upper surface of the aft wing and
+the lower surface of the fore wing being negative.
+The magnitude of φ is the highest near the wing
+surface and decreases with distance. The φ field is
+not exactly symmetric about the mid-chord due to
+the airfoil shape, with the zero-φ boundary slightly
+shifted towards the trailing edge.
+The vortex-induced force/moment density is
+expressed in terms of Q (Menon and Mittal,
+2021b) as follows:
+fQ = −2ρQφ,
+(3)
+where ρ is the fluid density. The vortex-induced
+force/moment is then given by the integral of fQ:
+τ = −2ρ
+�
+V
+Qφ dV,
+(4)
+where
+�
+V represents volume integral over the field
+of interest. As mentioned above, we focus on the
+torque, τ, in this paper. However, as shown in
+Menon and Mittal (2021a,c), with the appropriate
+influence field, any force can be computed in this
+manner.
+The
+spatial
+distribution
+of
+the
+vorticity-
+induced torque (moment) near the pitching wing
+can thus be visualized by plotting contours of
+−2Qφ (i.e. the vorticity-induced moment density
+distribution). Fig. 1(e) shows the moment den-
+sity distribution corresponding to Fig. 1(b). As
+expected, in this small-amplitude pitching case
+(A = 30◦), the LEV and TEV both contribute
+to positive (counterclockwise) moments. However,
+as we will show later, the vortex-induced moment
+can switch signs during the pitch-up/down cycle
+for large pitching amplitudes.
+The Force and Moment Partitioning Method
+can also be used to obtain the added-mass torque
+
+Article Title
+6
+(Menon and Mittal, 2021a,b,c)
+τa = −ρ
+�
+S
+n ·
+�dU
+dt φ
+�
+dS,
+(5)
+where U is the velocity of the moving wing bound-
+ary, φ is the same influence field calculated using
+Eqn. 2, and
+�
+S is the integral along the wing sur-
+face. We see from Eqn. 5 that the added-mass
+torque is only a function of the wing geometry and
+kinematics, flow field data is not required for cal-
+culating τa. The torque due to viscous diffusion
+can also be calculated using FMPM (Menon and
+Mittal, 2021b). However, it is negligible for the
+present study due to the relatively high Reynolds
+number Re ∼ O(104).
+2.4 Application of FMPM to
+ensemble- and phase-averaged data
+In many experiments, including those discussed
+in this paper, measured velocity data may be
+ensemble-, or phase-averaged so as to remove noise
+or turbulence-related flow structures. In what fol-
+lows, we consider ensemble- and phase-averaged
+data as interchangeable, both representing time-
+dependent averages of a more complex and noisy
+flow. Application of FMPM to phase-averaged
+data introduces some subtleties because Q is a
+nonlinear function of velocity (Eqn. 1). Any quan-
+tity, for example the velocity u that is measured
+in an experiment can be expressed as a sum of the
+time-averaged value, ¯u, the phase-averaged value,
+⟨u⟩, and the instantaneous fluctuations, u′:
+u(x, y, z, t) = ¯u(x, y, z)+⟨u⟩(x, y, z, t)+u′(x, y, z, t).
+(6)
+The quantity Q can be expressed as
+Q = −0.5 ∂
+∂xi
+(uj
+∂ui
+∂xj
+) ≡ −0.5ui,juj,i,
+(7)
+where indicial notation, with implied summation,
+has been used. As with the velocity, Q can be
+expressed as
+Q(x, y, z, t) = ¯Q(x, y, z)+⟨Q⟩(x, y, z, t)+Q′(x, y, z, t).
+(8)
+We can obtain the expression for the above Q
+components in terms of velocity as follows
+Q = Q¯u¯u+Q⟨u⟩⟨u⟩+Qu′u′+2Q¯u⟨u⟩+2Q¯uu′+2Q⟨u⟩u′,
+(9)
+where Q¯u⟨u⟩ = −0.5¯ui,j⟨uj,i⟩, etc. Taking a time
+average of the above expression, we can get ¯Q ≡
+Q¯u¯u. Taking a phase average of the above expres-
+sion gives
+⟨Q⟩ = 
+⟨Q¯u¯u⟩ + ⟨Q⟨u⟩⟨u⟩⟩ + ⟨Qu′u′⟩
++ 2⟨Q¯u⟨u⟩⟩ +
+2⟨Q¯uu′⟩ + 2⟨Q⟨u⟩u′⟩
+≡ Q⟨u⟩⟨u⟩ + 2Q¯u⟨u⟩ + 2⟨Q⟨u⟩u′⟩ + ⟨Qu′u′⟩.
+(10)
+The phase-averaged vortex-induced force/moment
+density is given by
+⟨fQ⟩(x, y, z, t) = −2ρ⟨Q⟩φ
+= −2ρ[Q⟨u⟩⟨u⟩ + 2Q¯u⟨u⟩ + 2⟨Q⟨u⟩u′⟩ + ⟨Qu′u′⟩]φ.
+(11)
+If the flow is highly turbulent and the time-
+dependent fluctuations are large, the last two
+terms in the above equation should not be ignored.
+However, for laminar flows, where we can assume
+|u′| << |⟨u⟩|, we have
+⟨fQ⟩(x, y, z, t) ≈ −2ρ⟨Q⟩φ
+= −2ρ[Q⟨u⟩⟨u⟩ + 2Q¯u⟨u⟩]φ.
+(12)
+This assumption will be tested for the present data
+in the next section. Thus, to obtain an accurate
+estimation of ⟨fQ⟩ from velocity data, we should
+either compute ⟨Q⟩ from the instantaneous Q field
+directly (i.e. calculate Q from the instantaneous
+velocity field and then phase average), or esti-
+mate the sum of Q⟨u⟩⟨u⟩ + 2Q¯u⟨u⟩. Note that the
+2Q¯u⟨u⟩ term might not be negligible when there
+is a free-stream flow. The estimation of ¯u is not
+straightforward in a flow with moving boundaries
+such as oscillating foils, since it is not clear how
+to obtain time-averaged data in regions through
+which the foil passes over time. The resolution of
+this issue is left to a future study and, as we will
+show later, for the present study, where there is
+no free-stream flow, the 2Q¯u⟨u⟩ term can be safely
+neglected.
+
+Article Title
+7
+3 Results and Discussion
+3.1 Scaling of vortex circulation and
+trajectory
+To characterize the vortex dynamics associated
+with the pitching wing in quiescent water, we first
+analyze the vortex trajectories and circulation.
+Because we pitch the wing sinusoidally, the wing
+moves symmetrically during pitch-up and pitch-
+down motions. Moreover, Zhu et al (2021) have
+shown that the fluid damping induced by LEVs
+and TEVs are comparable, although there are sub-
+tle differences caused by the rounded leading edge
+and the sharp trailing edge of the NACA 0012 air-
+foil. Therefore, in this study, we choose to focus
+on analyzing the TEV dynamics during the pitch-
+down motion. The LEV dynamics will only be
+analyzed for some cases for comparison.
+Fig. 2(a) shows the TEV circulation, Γ, during
+pitch-down for a wing pitching at the mid-chord,
+x/c = 0.5, with a pitching amplitude of A = 30◦,
+and a pitching frequency varied from f = 0.25 to
+1.0 Hz. Because the wing undergoes a pitch-down
+motion, the TEV has negative circulation. We see
+that for a fixed pitching frequency, the TEV circu-
+lation starts from zero (t/T = 0.25) and decreases
+as the wing pitches downward, as more negative
+vorticity is fed into the TEV through the shear
+layer. This process continues until t/T = 0.75,
+when the pitch-up motion starts and the connec-
+tion between the TEV and the shear layer is cut
+off. A bump in Γ for f = 0.75 and f = 1.0
+Hz shows up right before t/T = 0.75 when the
+TEV starts to separate from the shear layer. After
+t/T ≈ 0.75, the TEV begins to decline as there
+is no new vorticity input and the existing vortex
+starts to dissipate. The magnitude of the TEV cir-
+culation increases with the pitching frequency, as
+the vortex feeding shear-layer velocity increases
+linearly with the pitching frequency (Onoue and
+Breuer, 2016, 2017).
+The inset of Fig. 2(a) shows the TEV trajec-
+tories for the corresponding four pitching frequen-
+cies. The figure frame is rotated so as to keep the
+wing at zero pitching angle. It is observed that
+for a fixed pitching amplitude, TEV trajectories
+collapse well for different pitching frequencies. A
+circle centered at the mid-chord with a diameter
+c is plotted in gray dots to illustrate the trailing
+edge trajectory. The initial part of the TEV tra-
+jectory is almost perpendicular to the wing chord,
+confirming the validity of the linear assumptions
+used in the fluid damping scaling proposed in Zhu
+et al (2021) for small pitching amplitudes. As the
+pitch reversal starts, the TEV trajectories turn
+abruptly upwards. We see that the TEV trajectory
+deviates from the trailing edge trajectory. This is
+in contrast to the results of Francescangeli and
+Mulleners (2021), who observed that the shed vor-
+tex closely follows the trajectory of the edge of a
+flat plate pitching with a trapezoidal velocity pro-
+file. In our sinusoidal pitching case, the deviation
+between the TEV trajectory and the trailing edge
+trajectory presumably comes from two effects: the
+interaction between the TEV and the opposite-
+signed residual vortex from the previous pitch-up
+motion, and the weak ambient flow induced by the
+sinusoidal pitching motion (Shinde and Arakeri,
+2013).
+Onoue and Breuer (2016) showed that for a
+pitching plate undergoing large-amplitude limit-
+cycle oscillations in a freestream flow, the LEV
+circulation scales with the feeding shear-layer
+velocity multiplied by a characteristic length scale.
+Following a similar approach, we propose an LEV-
+/TEV circulation scaling for pitching wings in
+quiescent flow. Because the freestream velocity is
+zero, the feeding shear-layer velocity equals the
+leading-edge/trailing-edge velocity, which is given
+by USL = 4Afcm, where cm represents the dis-
+tance between the leading/trailing edge and the
+pivot point (i.e. the effective chord length). There-
+fore, we can write the non-dimensional circulation
+as
+Γ∗ =
+Γ
+4Afc2m
+.
+(13)
+We note that the definition of Γ∗ is analogous to
+the vortex formation number, ˆT, which quantifies
+the growth of a vortex, and the maximum value
+(i.e. the optimal vortex formation number) repre-
+sents when the vortex stops entraining additional
+vorticities from the feeding shear layer. We can
+also non-dimensionalize the vortex formation time
+as
+t∗ = 4Acm
+c
+(t/T − 0.25),
+(14)
+where T = 1/f is the pitching period; we use
+the t/T − 0.25 term to offset the starting time
+to coincide with the start of LEV/TEV forma-
+tion. In Γ∗ and t∗, cm = cLE for LEVs and
+
+Article Title
+8
+0
+0.25
+0.5
+0.75
+1
+1.25
+1.5
+-0.02
+-0.015
+-0.01
+-0.005
+0
+-1
+0
+1
+0
+0.2
+0.4
+0.6
+0.8
+1
+0
+1
+2
+3
+(a)
+(b)
+Fig. 2 (a) Trailing-edge vortex (TEV) circulation, Γ, during pitch-down for A = 30◦, x/c = 0.5 and f = 0.25 to 1.0 Hz.
+The gray dotted curve represents the non-dimensional pitching position, θ/A, on the right axis. Inset: TEV trajectories for
+the corresponding cases. (b) Magnitudes of the non-dimensional circulations, |Γ∗| (Eqn. 13), for both LEVs (plus signs)
+and TEVs (circles), with the marker colors corresponding to the frequencies in (a). The black dotted line shows the linear
+trend for data points within the initial linear growth regime, 0 ≤ t∗ ≤ 0.3.
+cm = cT E for TEVs, where cLE and cT E repre-
+sent the leading-edge chord and the trailing-edge
+chord, respectively, and c = cLE + cT E is the full
+chord length of the wing.
+Fig. 2(b) shows the evolution of the magni-
+tude of the TEV circulation, |Γ∗| (circles), as a
+function of the vortex formation time, t∗, for four
+different pitching frequencies (f = 0.25, 0.5, 0.75
+and 1.0 Hz), corresponding to the cases plotted
+in Fig. 2(a). The scaled LEV circulations at these
+frequencies are also plotted using plus signs for
+comparison. We see that the data points collapse
+well under the proposed scaling, showing the fre-
+quency dependence of the circulation. An initial
+linear growth regime (0 ≤ t∗ ≤ 0.3) is observed for
+both the LEV and the TEV circulations. In this
+linear regime, LEV and TEV circulations over-
+lap and no significant difference in their slopes is
+observed. After the linear regime, the TEV cir-
+culation (circles) keeps on increasing and reaches
+its maximum |Γ∗| ≈ 3 at t∗ ≈ 0.6. On the other
+hand, the LEV circulation (plus signs) decreases
+right after the linear regime despite that the pitch
+reversal starts around t∗ ≈ 0.5. This difference
+is believed to result from the fact that the TEVs
+generated by the sharp trailing edge are more
+coherent so that they can sustain longer than the
+LEVs generated by the rounded leading edge. This
+difference is clearly captured by the vorticity field
+shown in Fig. 1(b). We see that at this time instant
+(t∗ ≈ 0.9), the negative vorticities from the pitch-
+down motion (i.e. the blue regions) still retain a
+circular shape for the TEV, but become unidentifi-
+able for the LEV. The difference in the circulation
+also echoes the observations of Zhu et al (2021)
+that the fluid damping associated with a sharp
+trailing edge is higher than that resulted from a
+rounded leading edge.
+Next, we look into the effect of pitching ampli-
+tude on the TEV circulation and trajectory. Fig.
+3(a) shows the TEV circulation, Γ, during pitch-
+down for a wing pitching around the mid-chord
+x/c = 0.5 and at a frequency of f = 0.5 Hz,
+with the pitching amplitude varied from A = 30◦
+to 120◦. We see that, again, the TEV circulation
+decreases from zero when the pitch-down motion
+starts at t/T = 0.25. The magnitude of Γ increases
+with A due to the higher feeding shear-layer veloc-
+ity induced at higher pitching amplitudes. There
+exists a linear growth regime for |Γ| at all four
+pitching amplitudes, and this regime shrinks as
+A increases. Following this regime, we observe
+an abrupt drop of the TEV circulation magni-
+tude for A = 60◦ to 120◦, which we attribute to
+vortex splitting. This vortex splitting behavior is
+depicted in Fig. 3(b) inset, where we plot a sample
+spanwise vorticity field for A = 60◦ at t/T ≈ 0.75.
+At this time instant, the TEV (as well as the LEV)
+split into two smaller vortices, V1 and V2, with
+V1 persisting and V2 quickly dissipating away. As
+such, the circulation for V1 is tracked after this
+split. The opposite-signed vortex V3 is the resid-
+ual TEV from the previous pitch-up motion. No
+
+Article Title
+9
+0
+0.25
+0.5
+0.75
+1
+1.25
+1.5
+-0.04
+-0.03
+-0.02
+-0.01
+0
+-1
+0
+1
+0
+0.5
+1
+1.5
+2
+2.5
+3
+0
+1
+2
+3
+4
+(a)
+(b)
+V3
+V2
+V1
+Vortex
+splitting
+Fig. 3 (a) TEV circulation, Γ, during pitch-down for f = 0.5 Hz, x/c = 0.5 and A = 30◦ to 120◦, with the non-dimensional
+pitching position, θ/A, plotted on the right axis. Inset: TEV trajectories for the corresponding cases. (b) Magnitudes of the
+non-dimensional TEV circulation, |Γ∗|. The black dotted line shows the linear trend for data points within the initial linear
+growth regime, 0 ≤ t∗ ≤ 0.6. The inset is a sample spanwise vorticity field for A = 60◦ at t/T ≈ 0.75. At this time instant,
+the TEV (as well as the LEV) split into two smaller vortices, V1 and V2, with V1 persisting and V2 quickly dissipating
+away. The opposite-signed vortex V3 is the residual TEV from the previous pitch-up motion.
+TEV splitting is observed for the smallest pitching
+amplitude A = 30◦.
+Fig. 3(a) inset shows the TEV trajectories for
+different pitching amplitudes. We see that as the
+pitching amplitude increases, the TEV trajectory
+no longer follows the perpendicular path observed
+for the lowest pitching amplitude case (i.e. A =
+30◦, the blue curve, see also Fig. 2a inset). Instead,
+the TEV starts to loosely follow the trailing edge
+trajectory (i.e. the gray dotted circle) at the begin-
+ning of the pitch-down motion. As the pitching
+amplitude further increases (A = 90◦ and 120◦),
+the TEV trajectory sees the emergence of a turn-
+over loop – the TEV moves to the front of the pivot
+axis, turns closer to the wing surface, intersects
+with its initial path and eventually dissipates to
+the other side of the wing. The vortex trajectories
+cannot be simply scaled by the pitching amplitude
+because of their complex geometries. The vortex
+splitting and the complex vortex trajectories both
+add complexities to the problem, causing the non-
+linear behaviors of the fluid damping at higher
+pitching amplitudes observed in Zhu et al (2021).
+A more quantitative analysis of this issue and the
+connections between vortex dynamics and fluid
+damping will be discussed later in 3.2.
+We scale the TEV circulations as well as the
+vortex formation time for different pitching ampli-
+tudes using Eqns. 13 and 14, respectively, and
+show the results in Fig. 3(b). Once again, the
+TEV circulation collapses well under the proposed
+Γ∗ scaling, revealing the amplitude dependence of
+the vortex strength. The A term in the t∗ scal-
+ing (Eqn. 14) aligns the location of the maximum
+Γ for different pitching amplitudes. The initial
+linear growth regime for moderate to large pitch-
+ing amplitudes (A = 60◦ to 120◦) extends to
+t∗ > 0.6 as compared to A = 30◦ (see also Fig.
+2b), with the maximum |Γ∗| elevated to |Γ∗| > 3.
+After the linear regime and the abrupt amplitude
+drop caused by vortex splitting, the scaled vor-
+tex circulation for A = 60◦ to 120◦ decays slowly
+with a relatively constant slope at t∗ > 1.2 (i.e.
+vortex saturation, DeVoria and Ringuette, 2012).
+The |Γ∗| for A = 30◦ does not reach this slow-
+decay regime before the vortex boundary becomes
+unidentifiable.
+Another important parameter governing the
+LEV/TEV dynamics is the location of the pitching
+axis. Fig. 4(a) shows the temporal evolution of the
+TEV circulation, Γ, during the pitch-down motion
+for a wing pitching at a frequency of f = 0.5 Hz
+and an amplitude of A = 30◦, with the pitching
+axis located at the mid-chord (x/c = 0.5), the
+quarter-chord (x/c = 0.25) and the leading-edge
+(x/c = 0). Similar to previous results for different
+pitching frequencies and amplitudes, the TEV cir-
+culation starts from zero and decreases as the wing
+pitches down. The circulation magnitude increases
+as the pitching axis moves farther from the mid-
+chord, due to the higher feeding shear-layer veloc-
+ity USL = 4Afcm. Again, Γ decreases linearly in
+
+Article Title
+10
+0
+0.25
+0.5
+0.75
+1
+1.25
+1.5
+-0.04
+-0.03
+-0.02
+-0.01
+0
+-1
+0
+1
+0
+0.5
+1
+1.5
+2
+0
+1
+2
+3
+4
+(a)
+(b)
+Vortex
+splitting
+Fig. 4 (a) TEV circulation, Γ, during pitch-down for A = 30◦, f = 0.5 Hz, x/c = 0.5 (mid-chord pitching), x/c = 0.25
+(quarter-chord pitching) and x/c = 0 (leading-edge pitching), with the pitching position, θ/A, on the right axis. Inset: TEV
+trajectories for the corresponding cases. (b) Magnitudes of the non-dimensional TEV circulation, |Γ∗|, with a black dotted
+line showing the linear trend for data points within the initial linear growth regime, 0 ≤ t∗ ≤ 0.6. Inset: TEV trajectory
+scaling.
+the early stage of the pitch-down motion, and this
+linear regime shortens in time as the pitching axis
+moves towards the leading edge. After the linear
+regime, the TEV circulation drops near-linearly
+first and then abruptly for x/c = 0.25 and x/c = 0
+as the TEV splits into two. The TEV circula-
+tion and formation time are scaled using Eqn. 13
+and 14, and replotted in Fig. 4(b). We continue
+to see a very nice collapse of all the data points
+under the Γ∗ scaling, confirming the pitching axis
+dependence of the vortex strength. The |Γ∗| peaks
+around t∗ = 0.6, similar to the results observed in
+Fig. 2(b) and Fig. 3(b).
+Fig. 4(a) inset shows the pitching axis loca-
+tions and the corresponding trailing edge (dotted
+circles) and trailing-edge vortex (solid curves) tra-
+jectories. We see that the three TEV trajectories
+overlap initially. As the pitching axis moves away
+from the mid-chord while the angular pitching
+amplitude is maintained, the curvature of the TE
+trajectory decreases but its arc length increases.
+In the meantime, the TEV trajectory scales up in
+both x- and y-directions. We then scale both the
+TE and the TEV trajectories using the trailing-
+edge chord (i.e. cT E, the chord length between the
+pitching axis and the trailing edge) and the results
+are shown in the inset of Fig. 4(b). The three
+vortex trajectories collapse well under this scal-
+ing despite some discrepancies for x/c = 0 (green
+curve). This indicates that, unlike the pitching
+amplitude, which has a nonlinear effect on the vor-
+tex trajectory, the location of the pitching axis
+changes the vortex trajectory in a linear manner.
+We believe this linear dependence comes from the
+fact that the trailing edge trajectory (curvature
+and arc length) is linearly scalable by cT E in the
+(x, y)-coordinate. On the other hand, the trailing
+edge trajectories under different pitching ampli-
+tudes cannot be simply scaled by A in the (x,
+y)-coordinate, resulting in the nonlinear unscal-
+able trajectories of the vortex (see Fig. 3a inset).
+This argument is also supported by the frequency
+independence of the TEV trajectories observed in
+Fig. 2(a) inset, where the trailing edge trajectories
+remain the same at different pitching frequencies.
+These results also imply that the vortex trajectory
+is largely determined by the trailing (or leading)
+edge trajectory, instead of the edge velocity.
+It is also worth noting that in Figs. 2(b), 3(b)
+and 4(b), the maximum |Γ∗| corresponds to the
+optimal vortex formation number (Gharib et al,
+1998; Dabiri, 2009). However, |Γ∗|max observed
+in the present study is within a range of 2.5 -
+3.5, which is smaller than that observed in previ-
+ous studies (Milano and Gharib, 2005; Ringuette
+et al, 2007; Rival et al, 2009; Onoue and Breuer,
+2016), where ˆT ≈ 4. Because there is no convective
+free-stream flow in the present study, the vortex
+formation is dominated by the pitching kinemat-
+ics (Eqn. 13). Therefore, the vortex is forced to
+pinch off from the feeding shear layer by the wing
+kinematics before the universal optimal vortex
+formation number ˆT ≈ 4 can be achieved.
+
+Article Title
+11
+Summarizing these results: the vortex trajec-
+tory tracking and scaling analysis performed in
+this section provides us with many useful insights
+on the vortex dynamics of pitching wings in a
+quiescent flow. However, these traditional analysis
+methods have several limitations. Firstly, vortex
+tracking and circulation calculation become diffi-
+cult when the vortex dissipates to an extent that
+the vortex boundary becomes unidentifiable, and
+when multiple vortices are in close proximity (e.g.
+Fig. 3b inset). In these situations, although the
+vortices may still contribute to the moment gener-
+ation, we are not always able to accurately quan-
+tify their positions and strengths. Secondly and
+more importantly, the traditional analysis meth-
+ods are not capable of directly correlating the spa-
+tial position and strength of shed vortices with the
+resultant vorticity-induced force/moment, which
+is critical for studying these vortex-dominated
+flows. Therefore, in the following section, we apply
+the Force and Moment Partitioning Method to
+gain more physical insights.
+3.2 Vorticity-induced moment
+obtained from FMPM
+The complex behaviors of vortex trajectories and
+circulations discussed in the above section fur-
+ther affect the corresponding vorticity-induced
+moment and thus the fluid damping. In this
+section, we use FMPM to quantify this vorticity-
+induced torque. The detailed implementation of
+the FMPM has been introduced in Section 2.3,
+and a sample case demonstrating the vorticity
+field, the Q field, the influence field and the
+moment density distribution has been shown in
+Fig. 1(b-e). The FMPM is not only capable of
+identifying the total vorticity-induced force/mo-
+ment, it is also able to separate the force/moment
+contributions from individual vortices by choosing
+different integration windows for the expression
+in Eqn. 4. Fig. 5(a) shows the time trace of the
+leading-edge torque, τLE, the trailing-edge torque,
+τT E, and the total vorticity-induced torque, τ =
+τLE +τT E, calculated using the PIV-based FMPM
+for the case A = 30◦, f = 0.5 Hz and x/c = 0.5.
+The inset shows the integration windows for calcu-
+lating τLE and τT E. We see that the leading-edge
+torque and trailing-edge torque behave differently
+over time, and to analyze, we divide the pitch-
+ing cycle into four regimes (Fig. 5). In regimes 1
+and 3, τT E has a higher magnitude than τLE, pre-
+sumably, as mentioned earlier due to the increased
+coherence of the TEV as compared to that of the
+LEV (Fig. 2b). In regimes 2 and 4, where the
+pitch-down/up motions first start, τLE overtakes
+τT E in magnitude because the newly generated
+LEV stays closer to the wing surface than the
+TEV. The change of sign in τLE and τT E aligns
+with that of the angular pitching velocity, ˙θ.
+The total vorticity-induced torque, τ = τLE +
+τT E, directly correlates with the fluid damping
+discussed in Zhu et al (2021), as τ = bf ˙θ, where bf
+is the fluid damping coefficient and ˙θ is the angu-
+lar velocity. Approximating ˙θ with 4Af, we modify
+the fluid damping scaling proposed in Zhu et al
+(2021) to get a vorticity-induced torque scaling for
+sinusoidally pitching wings in quiescent water
+τ ∗ =
+τ
+8ρf 2A2s(KLEc4
+LE + KT Ec4
+T E),
+(15)
+where cLE and cT E are the leading-edge chord and
+trailing-edge chord, respectively. KLE = 0.95 and
+KT E = 1.05 are empirical factors that account for
+the rounded leading edge and sharp trailing edge,
+which agree well with experimental observations,
+as we will show next.
+The
+frequency-squared
+dependence
+of
+the
+vorticity-induced torque (Eqn. 15) is verified in
+Fig. 5(b), where we plot the non-dimensional
+vorticity-induced torque, τ ∗, for four different
+pitching frequencies f = 0.25, 0.5, 0.75 and 1.0
+Hz at a pitching amplitude of A = 30◦ and a
+pitching axis of x/c = 0.5. We see that τ ∗ col-
+lapses nicely under the proposed scaling. Recalling
+that the vortex trajectory remains unchanged for
+a wing pitching at a fixed amplitude and different
+frequencies (Fig. 2a), we know that the weighting
+by the influence field, φ, also remains unchanged
+for different pitching frequencies, and we thus con-
+clude that the τ ∼ f 2 scaling must come from
+Q ∼ f 2 (Eqn. 4). By definition, Q scales with the
+vorticity squared, which further scales with circu-
+lation (according to Stokes’ theorem). Eqn. 13 and
+Fig. 2(b) confirm that Γ ∼ f, and therefore, we
+infer that Q ∼ f 2, which again leads to the τ ∼ f 2
+scaling. These two independent scaling analyses
+show the self-consistency of our data.
+The inset of Fig. 5(b) shows the ratio between
+the cycle-averaged absolute trailing-edge torque
+and leading-edge torque (i.e. |τT E|/|τLE|) for the
+
+Article Title
+12
+0
+0.25
+0.5
+0.75
+1
+-5
+0
+5
+10-3
+-1
+-0.5
+0
+0.5
+1
+0
+0.25
+0.5
+0.75
+1
+-4
+-2
+0
+2
+4
+-1
+-0.5
+0
+0.5
+1
+0
+0.5
+1
+1
+1.5
+(a)
+(b)
+Fig. 5 (a) Time trace of the leading-edge torque (τLE), trailing-edge torque (τT E) and total vorticity-induced torque
+(τLE +τT E) calculated using the PIV-based FMPM for the case A = 30◦, f = 0.5 Hz and x/c = 0.5. Inset: Moment density
+distribution (−2Qφ) at t/T = 0 and integration windows for the leading-edge and trailing-edge torque. (b) Non-dimensional
+vorticity-induced torque (τ ∗) for A = 30◦, x/c = 0.5 and f = 0.25 to 1.0 Hz. Inset: Ratio between the cycle-averaged
+absolute trailing-edge torque and leading-edge torque (|τT E|/|τLE|) for the corresponding frequencies. The black dashed
+line represents the empirical ratio (1.05/0.95 = 1.105) used in Zhu et al (2021). The red solid line represents a ratio of one.
+corresponding four frequencies, with the black
+dashed line representing the empirical factors
+KT E/KLE = 1.05/0.95 = 1.105 used in Eqn. 15,
+and the red solid line representing a ratio of one.
+We find that the measured ratios (colored circles)
+are all above one, and match well with the empir-
+ical ratio 1.05/0.95. This shows that the empirical
+ratio faithfully captures the subtle differences in
+the cycle-averaged magnitude of the trailing-edge
+torque and leading-edge torque, agreeing with the
+trend observed in Zhu et al (2021) that the cycle-
+averaged trailing-edge fluid damping is slightly
+higher than that of the leading edge.
+The scaled torque, Eqn. 15, suggests that the
+vorticity-induced torque scales with the fourth
+power of the effective chord length. To validate
+this, we change the axis of a wing pitching at
+A = 30◦, f = 0.5 Hz from x/c = 0.5 (mid-
+chord) to x/c = 0.25 (quarter-chord) and x/c =
+0 (leading-edge) and plot the non-dimensional
+vorticity-induced torque, τ ∗, in Fig. 6(a). We see
+that τ ∗ collapse reasonably well under the pitch-
+ing axis scaling, despite some small discrepancies.
+The spanwise vorticity field, ωz, the Q field, the
+influence field, φ, and the moment density distri-
+bution, −2Qφ, at t/T = 0 are plotted in Fig. 6(b)
+for further analysis of the pitching axis effect. The
+ωz field shows that as the pitching axis moves from
+the mid-chord (x/c = 0.5) to the quarter-chord
+(x/c = 0.25), the leading-edge vortex becomes
+significantly weaker and less coherent, whereas
+the trailing-edge vortex becomes stronger and
+more coherent, due to a higher feeding shear-layer
+velocity (see Fig. 4). The φ field also changes sig-
+nificantly from x/c = 0.5 to 0.25. The quadrant
+pattern disappears and φ becomes entirely nega-
+tive on the upper surface of the wing and positive
+on the lower surface. This change in φ also alters
+the moment density distribution. We see that
+the weak LEV, despite its positive vorticity, now
+induces a negative torque, which is opposite to
+that induced by its counterpart at x/c = 0.5. The
+TEV-induced torque becomes a lot higher because
+both Q and φ increase. As the pitching axis further
+moves to the leading edge (x/c = 0), a negative
+LEV is generated due to the strong pitch-induced
+flow around the leading edge. The influence field,
+φ, stays similar to that of x/c = 0.25 with an
+increase in magnitude. The negative LEV induces
+a positive torque, because it is on the upper sur-
+face of the wing. These complex behaviors of the
+pitch-induced vortices as the pitching axis shifts
+might account for the discrepancies observed in τ ∗
+in Fig. 6(a).
+In Eqn. 15, we see that the vorticity-induced
+torque, τ, scales with the pitching amplitude
+squared. However, this scaling is based on the
+linear assumption that trajectories of shed vor-
+tices stay perpendicular to the wing chord (Zhu
+et al, 2021), so it is presumably only valid for
+small-amplitude pitching. As the vortex trajecto-
+ries vary nonlinearly for high pitching amplitudes
+
+Article Title
+13
+0
+0.25
+0.5
+0.75
+1
+-4
+-2
+0
+2
+4
+-1
+-0.5
+0
+0.5
+1
+-50
+0
+50
+-400
+0
+400
+-2e-3
+0
+2e-3
+-1
+0
+1
+-1
+0
+1
+-0.2
+0
+0.2
+(a)
+(b)
+Fig. 6 (a) Non-dimensional vorticity-induced torque (τ ∗) for A = 30◦, f = 0.5 Hz, x/c = 0.5 (mid-chord pitching),
+x/c = 0.25 (quarter-chord pitching) and x/c = 0 (leading-edge pitching). (b) Spanwise vorticity field (ωz, first column),
+Q field (second column), influence field (φ, third column) and moment density distribution (−2Qφ, fourth column) for
+A = 30◦, f = 0.5 Hz, x/c = 0.5 (first row), 0.25 (second row) and 0 (third row) at t/T = 0.
+(see Fig. 3a inset), the scaling breaks down. This
+is confirmed by Fig. 7(a), where we show that
+the non-dimensional vorticity-induced torque, τ ∗,
+does not collapse satisfactorily under the A2 scal-
+ing, although the general trend of τ ∗ roughly
+matches for different pitching amplitudes. To fur-
+ther characterize the effect of pitching amplitudes
+on the vorticity-induced torque, in addition to
+the time trace data shown in Fig. 7(a), we also
+look at the cycle-averaged τ ∗ and associate it
+with the non-dimensional fluid damping coeffi-
+cient, B∗
+f = 4Afτ ∗/ ˙θ. In Fig. 7(b), we compare
+B∗
+f obtained from the PIV-based FMPM (hol-
+low markers) to those extracted by “ring-down”
+(direct torque) measurements of Zhu et al (2021)
+(solid curves) as a function of the pitching ampli-
+tude. Two pitching axes are considered, as B∗
+f
+has been shown to behave differently when the
+wing pitches at the mid-chord (x/c = 0.5) and
+the quarter-chord (x/c = 0.25). The first thing
+we notice is that the PIV-based FMPM under-
+estimates the vorticity-induced torque and hence
+the corresponding fluid damping. The potential
+cause for this underestimation will be discussed
+
+Article Title
+14
+0
+0.5
+1
+1.5
+2
+2.5
+0
+1
+2
+3
+0
+0.25
+0.5
+0.75
+1
+-4
+-2
+0
+2
+4
+-1
+-0.5
+0
+0.5
+1
+-1
+0
+1
+-1
+0
+1
+-50
+0
+50
+-0.1
+0
+0.1
+-100
+0
+100
+-1
+0
+1
+-1
+0
+1
+-0.4
+0
+0.4
+Quarter-chord:
+(a)
+(b)
+TEV
+TEV
+TEV
+TEV
+TEV
+TEV
+(c)
+f
+e
+c
+d
+Mid-chord:
+TEV
+TEV
+TEV
+TEV
+TEV
+TEV
+(e)
+(f)
+(d)
+Fig. 7 (a) Non-dimensional vorticity-induced torque (τ ∗) for a wing pitching at x/c = 0.5, f = 0.5 Hz and A = 30◦
+to 120◦ (solid lines). Purple dashed line: A = 120◦, f = 0.5 Hz, x/c = 0.25. (b) Cycle-averaged non-dimensional fluid
+damping coefficient (B∗
+f) extracted by ring-down experiments (solid curves, Zhu et al, 2021) and by PIV-based FMPM
+(hollow markers) for mid-chord pitching (x/c = 0.5, purple) and quarter-chord pitching (x/c = 0.25, green). Note the factor
+1.5 applied to the FMPM data. The labeled data points correspond to (c–f ) temporal snapshots of the spanwise vorticity
+field (ωz, first row) and the moment density distribution (−2Qφ, second row) during the pitch-down motion. (c) A = 30◦,
+x/c = 0.5. (d) A = 30◦, x/c = 0.25. (e) A = 120◦, x/c = 0.5. (f ) A = 120◦, x/c = 0.25. The pitching frequency maintains
+at f = 0.5 Hz for all the cases.
+later. To better compare the trend between the
+FMPM-based B∗
+f and the ring-down-based B∗
+f, we
+multiply a factor of 1.5 to the former. We see that
+the FMPM-based B∗
+f agrees very well in trend
+with those extracted by ring-down experiments.
+For x/c = 0.5, B∗
+f increases non-monotonically
+with the pitching amplitude, whereas for x/c =
+0.25, B∗
+f increases monotonically with the pitching
+amplitude with a decreasing slope.
+To explain the differences in B∗
+f for different
+pitching amplitudes and axes, we choose four rep-
+resentative cases (data points c–f on Fig. 7b) and
+plot the corresponding spanwise vorticity field, ωz,
+and the moment density distribution, −2Qφ, in
+Fig. 7(c–f ). For each case, three temporal snap-
+shots, t/T = 0.33, 0.5 and 0.67, are plotted to
+capture the initial, middle and late stages of the
+
+Article Title
+15
+pitch-down motion. Fig. 7(c) depicts a conven-
+tional scenario where the wing pitches at A = 30◦
+and x/c = 0.5. In this case, two negative vor-
+tices are generated at the leading edge and the
+trailing edge. These two vortices are of compara-
+ble size and strength (see also Fig. 5a), and both
+contribute to negative moments. When the pitch-
+ing axis moves to x/c = 0.25 (Fig. 7d), the LEV
+becomes weaker and the TEV becomes stronger,
+due to the change in the feeding shear-layer veloci-
+ties. While the LEV is still negative, it generates a
+small positive moment due to the negative φ field
+(see Fig. 6b).
+Comparing Fig. 7(e) to (c), we see that when
+the pitching amplitude is very high (A = 120◦),
+the LEV and TEV both move towards the pitch-
+ing axis from t/T = 0.33 to 0.5. At the same time,
+they also become less coherent. These two effects
+combined lead to the near-zero τ ∗ observed in Fig.
+7(a) at t/T = 0.5. As the pitch-down motion con-
+tinues, the LEV moves to the aft wing, and the
+TEV moves to the fore wing, resulting in a sign
+switch of the induced torque – the LEV and TEV
+both generate positive moments at the late stage
+of the motion (t/T = 0.67). However, the total
+vorticity-induced torque, τ ∗ remains slightly nega-
+tive because of the positive surface vortices, which
+are closer to the wing surface and thus generate
+more negative moments. The fact that the LEV
+and TEV move across the pitching axis brings τ ∗
+close to zero earlier than that of smaller pitching
+amplitudes. This further results in the decreas-
+ing B∗
+f observed for mid-chord pitching wings at
+large pitching amplitudes. At this same pitching
+amplitude (A = 120◦), as the pitching axis moves
+to x/c = 0.25 (Fig. 7f ), we see that the TEV
+again moves across the pitching axis at the late
+stage (t/T = 0.67). However, because the φ field
+is entirely positive under the wing (see Fig. 6b),
+the TEV continues to generate negative moments.
+In addition, a positive LEV emerges due to the
+pitch-induced flow and also generates a negative
+moment. These effects result in a higher τ ∗ mag-
+nitude at t/T > 0.5 for x/c = 0.25 (Fig. 7a,
+purple dashed line) as compared to the x/c =
+0.5 case (purple solid line), explaining the differ-
+ence we see in B∗
+f at A = 120◦ (Fig. 7b, data
+points f and e). We want to note that, although
+the LEVs and TEVs move across the pitching
+axis for large-amplitude pitching, the vorticity-
+induced moment always stays negative during the
+pitch-down motion (0.25 < t/T < 0.75), where
+the angular velocity is also negative ( ˙θ < 0).
+This assures that the instantaneous aerodynamic
+damping is always positive (i.e. bf = τ/ ˙θ > 0)
+during the entire pitching cycle, which holds valid
+for all the cases considered in the present study
+(see Fig. 5a, Fig. 6a and Fig. 7a).
+3.3 Error analysis of FMPM results
+To further explain the underestimation of the fluid
+damping coefficient by the FMPM (Fig. 7b), we
+compare the vorticity-induced torque calculated
+by the PIV-based FMPM to that measured by the
+force transducer (see Fig. 1a). According to the
+Morison equation (Morison et al, 1950), the total
+fluid force experienced by a moving body can be
+divided into the vorticity-induced force and the
+added-mass force. Therefore, to get the vorticity-
+induced torque, τ, from the force transducer, we
+have to first estimate the added-mass torque, τa,
+using Eqn. 5. Then, this torque as well as the
+physical wing inertia, τI, are subtracted from the
+measured torque, τF T .
+The torque measured by the force transducer,
+τF T , the sum of the inertial torque and the added-
+mass torque, τI + τa, the true vorticity-induced
+torque, τF T − (τI + τa), and the vorticity-induced
+torque calculated using PIV-based FMPM, τ,
+for A = 30◦, f
+= 0.5 Hz, x/c = 0.25 are
+plotted in Fig. 8(a). We assume that the vis-
+cous torque is negligible in comparison to the
+vortex-induced torque, due to the relatively high
+Reynolds number - Re ∼ O(104). We find that the
+PIV-based FMPM underestimates the vorticity-
+induced torque, τ, roughly by a factor of 1.5,
+which explains the 1.5 factor used for the non-
+dimensional fluid damping coefficient, B∗
+f, in Fig.
+7(b). After applying a factor of 1.5 to τ, we see
+that it agrees well with the true vorticity-induced
+torque, τF T − (τI + τa).
+However, the question remains why the PIV-
+based FMPM significantly underestimates the
+vorticity-induced torque. One conjecture, as dis-
+cussed earlier, is that because we are using phase-
+averaged PIV velocity fields (⟨u⟩, ⟨v⟩) to calculate
+the Q fields, some small instantaneous flow struc-
+tures, which also contribute to the moment gener-
+ation, might have been averaged out, as discussed
+in Section 2.4. To assess this effect, we compare
+τ based on Q calculated using phase-averaged
+
+Article Title
+16
+0
+0.25
+0.5
+0.75
+1
+-5
+0
+5
+10-3
+-1
+-0.5
+0
+0.5
+1
+0
+0.25
+0.5
+0.75
+1
+-0.02
+-0.01
+0
+0.01
+0.02
+(a)
+(b)
+Fig. 8 (a) Time trace of the torque measured by the force transducer (τF T ), the sum of the inertial torque and the
+added-mass torque calculated using FMPM (τI + τa), the true vorticity-induced torque (τF T − (τI + τa)) and 1.5 times
+the vorticity-induced torque calculated using PIV-based FMPM (1.5τ) for A = 30◦, f = 0.5 Hz, x/c = 0.25. (b) vorticity-
+induced torque, τ, based on Q calculated using phase-averaged velocity fields (⟨u⟩, ⟨v⟩), phase-averaged ⟨Q⟩ calculated using
+instantaneous velocity fields (u, v), and phase-averaged ⟨Qφ⟩ calculated using instantaneous velocity fields (u, v). Error bars
+denote standard deviations over 20 cycles.
+velocity fields (⟨u⟩, ⟨v⟩), phase-averaged ⟨Q⟩ calcu-
+lated using instantaneous velocity fields (u, v), and
+phase-averaged ⟨Qφ⟩ calculated using instanta-
+neous velocity fields (u, v) in Fig. 8(b). We see that
+the vorticity-induced torque calculated using these
+three different methods matches closely, indicat-
+ing that phase-averaging is not the main cause for
+the FMPM to underestimate τ. The good agree-
+ments between −2ρ
+�
+Q(⟨u⟩, ⟨v⟩)φdV (blue solid
+curve) and −2ρ
+�
+⟨Q(u, v)⟩φdV (orange dashed
+curve) also indicates that the 2Q¯u⟨u⟩ term in Eqn.
+12 might be dropped for the cases considered in
+the present study.
+Another potential error source comes from the
+PIV measurements, and in particular, the diffi-
+culty in obtaining accurate velocity vectors near
+the solid boundary (Rival and van Oudheusden,
+2017). Because the vorticity-induced torque is
+calculated by integrating the −2Qφ field (Eqn.
+4), any missing velocity vectors near the solid
+boundary will result in a significant decrease of
+the overall vorticity-induced torque, as φ reaches
+its maximum near the boundary. This conjecture
+could be tested by comparing the PIV-measured
+near-boundary velocity fields with those obtained
+by from a high-accuracy numerical simulation.
+Alternatively, a physics-informed neural network,
+PINN (Raissi et al, 2019; Cai et al, 2021; Arzani
+et al, 2021), could potentially be used to recon-
+struct and resolve near-boundary velocity fields
+so as to improve the accuracy of the PIV-based
+FMPM. These tasks, unfortunately, lie beyond the
+scope of the current paper but are well worthy of
+investigation.
+Lastly, all FMPM calculations in this study
+are based on two-component, two-dimensional
+(2C2D) PIV measurements taken at the mid span,
+but without considering three-dimensional effects.
+This means the contributions from the spanwise
+velocity (w) and the spanwise gradient (∂/∂z) of
+(u, v) to Q have not been considered, but might
+play an important role in causing the differences
+between the PIV-based FMPM results and the
+force sensor results. The recent paper of Menon
+et al (2022) has employed FMPM to quantify the
+role of cross-span vorticity on the force generation
+over a finite-aspect ratio wing and these effects
+were shown to be quite significant. In addition, the
+pitching wing in this experiment has a free wingtip
+(Fig. 1a) and the tip vortex presumably plays a
+non-negligible role in the generation of the total
+torque. As with the boundary-related errors, one
+could assess the three-dimensional flow effects by
+comparing our results with 2D and 3D CFD sim-
+ulations or by conducting 3D PIV measurements,
+both of which, unfortunately, are beyond the scope
+of the present study.
+4 Conclusion
+In this study, we have characterized the vortex
+dynamics associated with a NACA 0012 wing
+
+Article Title
+17
+undergoing prescribed sinusoidal pitching in quies-
+cent water. We employed two-dimensional particle
+image velocimetry (PIV) to measure the velocity
+field around the wing, and used the Q criterion
+to identify positions and boundaries of pitch-
+generated vortices to study the evolution of their
+trajectories and strengths. We found that the
+vortex trajectory is insensitive to the pitching fre-
+quency, but varies nonlinearly with the pitching
+amplitude and scales linearly with the pitching
+axis. The vortex circulation was shown to scale
+with the pitching frequency, amplitude, and effec-
+tive chord length squared for sinusoidal pitch
+oscillations. A vortex splitting behavior causing
+the vortex circulation to drop abruptly after a lin-
+ear growth regime was observed for all the pitching
+cases, except for those at the mid-chord and the
+lowest pitching amplitude.
+In the second part of this study, the Force
+and Moment Partitioning Method (FMPM) was
+adopted to quantify and visualize the aerodynamic
+moment generated by the pitch-induced vortices.
+The moment contributions from leading-edge vor-
+tices and trailing-edge vortices were separated by
+the FMPM, and the ratio between the two was
+shown to match the empirical factor used in Zhu
+et al (2021). A scaling for the vorticity-induced
+torque was proposed, revealing its dependence
+on the squared pitching frequency, the squared
+pitching amplitude, and the fourth power of the
+effective chord length. The pitching amplitude
+was shown to have a nonlinear effect on the
+vorticity-induced moment due to the complex vor-
+tex dynamics. The vorticity-induced moment was
+further connected with the fluid damping reported
+by Zhu et al (2021), and the results obtained
+using PIV-based FMPM were found to match well
+with that measured using ring-down experiments,
+despite a lower magnitude. Finally, the FMPM
+was found to underestimate the moment compared
+to the force transducer data, potentially due to the
+missing velocity vectors near the wing boundary
+and three-dimensional effects.
+Together with our previous study on cycle-
+averaged vorticity-induced damping (Zhu et al,
+2021), the present work, which focuses on the
+instantaneous evolution of vortex dynamics and
+moments, provides a comprehensive understand-
+ing of the frequency, amplitude and pivot axis
+effects on the trajectory, strength, and associ-
+ated aerodynamic moment of vortices shed from
+a sinusoidally pitching wing in quiescent water,
+a configuration that is of tremendous engineer-
+ing and biological relevance. Moreover, this work
+is among the first to apply FMPM for analyzing
+experimental data (see also Kumar et al, 2021).
+The good agreements we see between the FMPM-
+based results and the ring-down experiments/force
+transducer measurements further demonstrate the
+effectiveness and robustness of this method. The
+discussions on applying FMPM to phase-averaged
+data and the possible error source for caus-
+ing the underestimation of the vorticity-induced
+moment can potentially benefit future applica-
+tions of FMPM to experimental data.
+Acknowledgments
+This work was funded by the Air Force Office
+of Scientific Research, Grant FA9550-21-1-0462,
+managed by Dr. Gregg Abate. RM acknowledges
+support from NSF grant CBET-2011619 and ONR
+Grants N00014-22-1-2655 and N00014-22-1-2770
+monitored by Dr. Bob Brizzolara.
+References
+Anderson JM, Streitlien K, Barrett DS, et al
+(1998) Oscillating foils of high propulsive effi-
+ciency. J Fluid Mech 360:41–72
+Arzani A, Wang JX, D’Souza RM (2021) Uncover-
+ing near-wall blood flow from sparse data with
+physics-informed neural networks. Phys Fluids
+33(7):071,905
+Baik YS, Bernal LP, Granlund K, et al (2012)
+Unsteady force generation and vortex dynamics
+of pitching and plunging aerofoils. J Fluid Mech
+709:37–68
+Barrett DS (1996) Propulsive efficiency of a flex-
+ible hull underwater vehicle. PhD thesis, Mas-
+sachusetts Institute of Technology
+Bergou AJ, Xu S, Wang ZJ (2007) Passive wing
+pitch reversal in insect flight. J Fluid Mech
+591:321–337
+Buchholz JHJ, Smits AJ (2008) The wake struc-
+ture and thrust performance of a rigid low-
+aspect-ratio
+pitching
+panel.
+J
+Fluid
+Mech
+603:331–365
+
+Article Title
+18
+Buchholz JHJ, Green MA, Smits AJ (2011) Scal-
+ing the circulation shed by a pitching panel. J
+Fluid Mech 688:591–601
+Cai S, Wang Z, Fuest F, et al (2021) Flow over an
+espresso cup: inferring 3-d velocity and pressure
+fields from tomographic background oriented
+schlieren via physics-informed neural networks.
+J Fluid Mech 915:A102
+Corke TC, Thomas FO (2015) Dynamic stall
+in pitching airfoils: aerodynamic damping and
+compressibility effects. Annu Rev Fluid Mech
+47:479–505
+Dabiri JO (2009) Optimal vortex formation as a
+unifying principle in biological propulsion. Annu
+Rev Fluid Mech 41:17–33
+DeVoria AC, Ringuette MJ (2012) Vortex forma-
+tion and saturation for low-aspect-ratio rotating
+flat-plate fins. Exp Fluids 52(2):441–462
+DeVoria AC, Ringuette MJ (2013) The force and
+impulse of a flapping plate performing advanc-
+ing and returning strokes in a quiescent fluid.
+Exp Fluids 54(5):1–15
+Ellington CP, van den Berg C, Willmott AP, et al
+(1996) Leading-edge vortices in insect flight.
+Nature 384(6610):626
+Epps BP, Techet AH (2007) Impulse generated
+during unsteady maneuvering of swimming fish.
+Exp Fluids 43(5):691–700
+Francescangeli D, Mulleners K (2021) Discrete
+shedding of secondary vortices along a modified
+kaden spiral. J Fluid Mech 917:A44
+Gharib M, Rambod E, Shariff K (1998) A univer-
+sal time scale for vortex ring formation. J Fluid
+Mech 360:121–140
+Heathcote S, Martin D, Gursul I (2004) Flexi-
+ble flapping airfoil propulsion at zero freestream
+velocity. AIAA J 42(11):2196–2204
+Ho S, Nassef H, Pornsinsirirak N, et al (2003)
+Unsteady aerodynamics and flow control for
+flapping wing flyers. Prog Aerosp Sci 39(8):635–
+681
+Hunt JCR, Wray AA, Moin P (1988) Eddies,
+streams, and convergence zones in turbulent
+flows. Center for Turbulence Research Report
+CTR-S88 pp 193–208
+Jafferis NT, Helbling EF, Karpelson M, et al
+(2019) Untethered flight of an insect-sized
+flapping-wing microscale aerial vehicle. Nature
+570(7762):491–495
+Jeong J, Hussain F (1995) On the identification of
+a vortex. J Fluid Mech 285:69–94
+Jimreeves David M, Mathur M, Govardhan RN,
+et al (2018) The kinematic genesis of vortex for-
+mation due to finite rotation of a plate in still
+fluid. J Fluid Mech 839:489–524
+Kang CK, Shyy W (2014) Analytical model for
+instantaneous lift and shape deformation of an
+insect-scale flapping wing in hover. J R Soc
+Interface 11(101):20140,933
+Kumar S, Brooks S, Green M, et al (2021) A
+data-driven method for determining the hydro-
+dynamic force induced by vortices-force parti-
+tioning applied to piv data for a caudal fin
+model. In: APS DFD Meeting Abstracts, pp
+M13–003
+Lee H, Simone N, Su Y, et al (2022) Leading
+edge vortex formation and wake trajectory: Syn-
+thesizing measurements, analysis, and machine
+learning. Phys Rev Fluids 7:074,704
+Lentink D, Dickinson MH (2009) Rotational
+accelerations stabilize leading edge vortices on
+revolving fly wings. J Exp Biol 212(16):2705–
+2719
+Li J, Wu ZN (2018) Vortex force map method for
+viscous flows of general airfoils. J Fluid Mech
+836:145–166
+Li J, Wang Y, Graham M, et al (2020) Vor-
+tex moment map for unsteady incompressible
+viscous flows. J Fluid Mech 891:A13
+McCroskey WJ (1982) Unsteady airfoils. Annu
+Rev Fluid Mech 14(1):285–311
+
+Article Title
+19
+Menon K, Mittal R (2019) Flow physics and
+dynamics of flow-induced pitch oscillations of an
+airfoil. J Fluid Mech 877:582–613
+Menon K, Mittal R (2021a) On the initiation and
+sustenance of flow-induced vibration of cylin-
+ders: insights from force partitioning. J Fluid
+Mech 907
+Menon K, Mittal R (2021b) Quantitative anal-
+ysis of the kinematics and induced aerody-
+namic loading of individual vortices in vortex-
+dominated flows: a computation and data-
+driven approach. J Comput Phys 443:110,515
+Menon K, Mittal R (2021c) Significance of the
+strain-dominated region around a vortex on
+induced
+aerodynamic
+loads.
+J
+Fluid
+Mech
+918:R3
+Menon K, Kumar S, Mittal R (2022) Contri-
+bution of spanwise and cross-span vortices to
+the lift generation of low-aspect-ratio wings:
+Insights from force partitioning. Phys Rev Flu-
+ids 7(11):114,102
+Milano M, Gharib M (2005) Uncovering the
+physics of flapping flat plates with artificial
+evolution. J Fluid Mech 534:403–409
+Moriche M, Flores O, Garc´ıa-Villalba M (2017)
+On the aerodynamic forces on heaving and
+pitching airfoils at low reynolds number. J Fluid
+Mech 828:395–423
+Morison JR, Johnson JW, Schaaf SA (1950) The
+force exerted by surface waves on piles. J Pet
+Technol 2(05):149–154
+Morse TL, Williamson CHK (2009) Prediction of
+vortex-induced vibration response by employing
+controlled motion. J Fluid Mech 634:5–39
+Onoue K, Breuer K (2016) Vortex formation and
+shedding from a cyber-physical pitching plate.
+J Fluid Mech 793:229–247
+Onoue K, Breuer K (2017) A scaling for vortex
+formation on swept and unswept pitching wings.
+J Fluid Mech 832:697–720
+Quartapelle L, Napolitano M (1983) Force and
+moment
+in
+incompressible
+flows.
+AIAA
+J
+21(6):911–913
+Raissi M, Perdikaris P, Karniadakis GE (2019)
+Physics-informed
+neural
+networks:
+A
+deep
+learning framework for solving forward and
+inverse problems involving nonlinear partial dif-
+ferential equations. J Comput Phys 378:686–707
+Ringuette MJ, Milano M, Gharib M (2007) Role
+of the tip vortex in the force generation of low-
+aspect-ratio normal flat plates. J Fluid Mech
+581:453–468
+Rival D, Prangemeier T, Tropea C (2009) The
+influence of airfoil kinematics on the formation
+of leading-edge vortices in bio-inspired flight.
+Exp Fluids 46:823–833
+Rival DE, van Oudheusden B (2017) Load-
+estimation techniques for unsteady incompress-
+ible flows. Exp Fluids 58(3):1–11
+Seo JH, Mittal R (2022) Improved swimming
+performance
+in
+schooling
+fish
+via
+leading-
+edge vortex enhancement. Bioinspir Biomim
+17(6):066,020
+Shinde SY, Arakeri JH (2013) Jet meandering by
+a foil pitching in quiescent fluid. Phys Fluids
+25(4):041,701
+Shyy W, Aono H, Chimakurthi SK, et al (2010)
+Recent progress in flapping wing aerodynamics
+and aeroelasticity. Prog Aerosp Sci 46(7):284–
+327
+Triantafyllou MS, Triantafyllou GS, Yue DKP
+(2000) Hydrodynamics of fishlike swimming.
+Annu Rev Fluid Mech 32(1):33–53
+Wang ZJ (2005) Dissecting insect flight. Annu Rev
+Fluid Mech 37:183–210
+Williamson CHK, Govardhan R (2004) Vortex-
+induced vibrations. Annu Rev Fluid Mech
+36:413–455
+Xiao Q, Zhu Q (2014) A review on flow energy har-
+vesters based on flapping foils. J Fluids Struct
+46:174–191
+
+Article Title
+20
+Young J, Lai JCS, Platzer MF (2014) A review
+of progress and challenges in flapping foil power
+generation. Prog Aerosp Sci 67:2–28
+Zhang C, Hedrick TL, Mittal R (2015) Centripetal
+acceleration reaction: an effective and robust
+mechanism for flapping flight in insects. PloS
+One 10(8):e0132,093
+Zhong Q, Zhu J, Fish FE, et al (2021) Tunable
+stiffness enables fast and efficient swimming in
+fish-like robots. Sci Robot 6(57):eabe4088
+Zhu J, White C, Wainwright DK, et al (2019)
+Tuna robotics: A high-frequency experimental
+platform exploring the performance space of
+swimming fishes. Sci Robot 4(34):eaax4615
+Zhu Y, Su Y, Breuer K (2020) Nonlinear flow-
+induced instability of an elastically mounted
+pitching wing. J Fluid Mech 899:A35
+Zhu Y, Mathai V, Breuer K (2021) Nonlinear fluid
+damping of elastically mounted pitching wings
+in quiescent water. J Fluid Mech 923:R2
+
diff --git a/mNFQT4oBgHgl3EQfojZZ/content/tmp_files/load_file.txt b/mNFQT4oBgHgl3EQfojZZ/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d40ec1a7fe728388019283736804e0864140b024
--- /dev/null
+++ b/mNFQT4oBgHgl3EQfojZZ/content/tmp_files/load_file.txt
@@ -0,0 +1,845 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf,len=844
+page_content='Force moment partitioning and scaling analysis of vortices shed by a  2D pitching wing in quiescent fluid  Yuanhang Zhu1*†, Howon Lee1‡, Sushrut Kumar2, Karthik Menon3, Rajat Mittal2 and Kenneth Breuer1  1Center for Fluid Mechanics, School of Engineering, Brown University, Providence, RI, 02912, USA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  2Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD, 21218, USA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  3Department of Pediatrics (Cardiology) and Institute for Computational and Mathematical  Engineering, Stanford University, Stanford, CA, 94305, USA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  Corresponding author.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' E-mail: yuanhang zhu@brown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='edu;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  †Present Address: Department of Mechanical and Aerospace Engineering, University of Virginia,  Charlottesville, VA 22904, USA  ‡Present Address: School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA  30332, USA  Abstract  We experimentally study the dynamics and strength of vortices shed from a NACA 0012 wing  undergoing sinusoidal pitching in quiescent water.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' We characterize the temporal evolution of  the vortex trajectory and circulation over a range of pitching frequencies, amplitudes and pivot  locations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' By employing a physics-based force and moment partitioning method (FMPM), we  estimate the vortex-induced aerodynamic moment from the velocity fields measured using par-  ticle image velocimetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' The vortex circulation, formation time and vorticity-induced moment  are shown to follow scaling laws based on the feeding shear-layer velocity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' The vortex dynamics,  together with the spatial distribution of the vorticity-induced moment, provide quantitative  explanations for the nonlinear behaviors observed in the fluid damping (Zhu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=', J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Fluid  Mech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 923, 2021, R2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  1 Introduction  The unsteady flow and vortex dynamics associated  with flapping wings/foils have been extensively  studied for understanding the complex lift/thrust  generation mechanism of animal flight and swim-  ming (Ellington et al, 1996;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Lentink and Dick-  inson, 2009;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Anderson et al, 1998;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Triantafyllou  et al, 2000), as well as developing bio-inspired  flapping-wing micro air vehicles (MAVs, Ho et al,  2003;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Shyy et al, 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Jafferis et al, 2019),  oscillating-foil autonomous underwater vehicles  (AUVs, Barrett, 1996;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Zhu et al, 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Zhong  et al, 2021) and energy-harvesting devices (Xiao  and Zhu, 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Young et al, 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Flapping  wings/foils were commonly studied in the presence  of an ambient flow to match real flying/swim-  ming settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Numerous studies have focused on  1  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='13373v1  [physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='flu-dyn]  31 Jan 2023  Article Title  2  identifying scaling laws that characterize the for-  mation and development of the shed vortices,  along with the corresponding aerodynamic loads  (Buchholz and Smits, 2008;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Buchholz et al, 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  Baik et al, 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Onoue and Breuer, 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' In  the absence of a freestream flow, the problem  is associated with the hovering flight of insects  (Wang, 2005;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Bergou et al, 2007;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Kang and Shyy,  2014) and the starting motion of fish (Heath-  cote et al, 2004;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Epps and Techet, 2007;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' DeVoria  and Ringuette, 2012, 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Shinde and Arakeri,  2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Jimreeves David et al, 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' In these stud-  ies, the pitching panel was usually hinged at the  leading-edge to mimic the corresponding biologi-  cal appendage, and more emphasis was placed on  the vorticity-induced lift and thrust.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' On the other  hand, the vorticity-induced aerodynamic moment  has attracted less attention, despite its close con-  nections with maneuvering and its importance in  regulating aerodynamic damping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  In aeroelastic systems, the formation and shed-  ding of vortices from elastically mounted bluff  bodies is the main source of aerodynamic damp-  ing (Williamson and Govardhan, 2004;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Morse and  Williamson, 2009;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Menon and Mittal, 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Zhu  et al, 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Menon and Mittal (2019) and Zhu  et al (2020) have analyzed the energy trans-  fer between an elastically mounted pitching wing  and the unsteady ambient flow, and found that  the total damping in an aeroelastic system has  to equal to zero for flow-induced oscillations to  sustain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' This means that the positive structural  damping has to balance the negative aerodynamic  damping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' With a free-stream flow, the negative  aerodynamic damping mainly comes from the  dynamic stall vortex (McCroskey, 1982;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Corke and  Thomas, 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Without a free-stream flow, how-  ever, the aerodynamic damping becomes purely  positive, as the pitch-induced vortices act as a  source of drag (Morison et al, 1950).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Zhu et al  (2021) have adopted a dynamical system approach  to study the nonlinear fluid damping associ-  ated with vortices shed from a cyber-physically  mounted pitching wing in the absence of a free-  stream flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' They extracted the fluid damping  coefficient using “ring-down” experiments and  were able to identify a universal non-dimensional  fluid damping coefficient that depends on the  pitching frequency, amplitude, pivot location and  sweep angle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' They also explained the nonlinear  behavior of the fluid damping using the corre-  sponding vortex dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' However, their analysis  of the complex vortex dynamics was purely qual-  itative, and no quantitative evaluations of the  vortex trajectory and strength were performed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  Another limitation of Zhu et al (2021)’s work was  that the dynamical system framework was only  capable of resolving cycle-averaged vortex-induced  damping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' No direct measurements of the instan-  taneous force and moment associated with the  shed vortices were available, although correlating  this information with the corresponding vortex  dynamics could provide useful insights toward a  more complete understanding of the underlying  flow physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  The recent development of the Force and  Moment Partitioning Method (FMPM, Quar-  tapelle and Napolitano, 1983;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Zhang et al, 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  Moriche et al, 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Menon and Mittal, 2021a,b,c)  (a variant is also known as the vortex force/mo-  ment map method, Li and Wu, 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Li et al,  2020) provides us with a framework to deter-  mine the instantaneous flow-induced forces and  moments from the corresponding velocity fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  In the FMPM, the Navier-Stokes equation is pro-  jected onto the gradient of an auxiliary potential  which satisfies the Laplace equation and certain  boundary conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' The individual contribu-  tions of the added-mass, vorticity-induced, and  viscous terms to the fluid force/moment exerted  on the immersed body can be separated ana-  lytically, enabling independent dissection of each  term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Moreover, the FMPM is able to visual-  ize the spatial distribution of the flow-induced  force/moment, which is valuable for associating  the vortex dynamics with the resultant aerody-  namic loads.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Zhang et al (2015) have applied  FMPM to a numerical simulation of the flight of  a hawkmoth and a fruit fly and found that, in  addition to the leading-edge vortex, which con-  tributes to the majority of the lift, the centripetal  acceleration reaction, which is analogous to the  added-mass effect, also plays an important role  in the overall lift generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Menon and Mit-  tal (2021a) have revisited the classical problem  of vortex-induced vibrations associated with flow  over a cylinder and found using FMPM that the  self-sustained oscillations are driven by the vortic-  ity in the shear layer instead of the shed vortices  in the wake.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Moreover, using FMPM, Menon and  Article Title  3  Mittal (2021c) discovered that, in addition to the  rotation-dominated region (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' regions defined as  vortices), the strain-dominated region surround-  ing the vortices also has a significant effect on the  aerodynamic load generation of pitching airfoils.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  Seo and Mittal (2022) have used FMPM in con-  junction with direct numerical simulations to show  that most of the thrust generated by a carangi-  form swimmer is due to the leading-edge vortex  on the caudal fin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  The above examples have demonstrated the  powerful capability of FMPM to provide new  physical insights for vortex-dominated flows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' How-  ever, in these examples, the FMPM was only  tested and validated on results obtained from  numerical simulations, where data was usually  considered to be clean and ideal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Applying FMPM  to experimental data will open up numerous new  possibilities for flow measurement techniques such  as particle image velocimetry (PIV).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' However,  there are many foreseeable challenges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' First, in  many experiments, the measured velocity fields  are usually ensemble- or phase-averaged so as to  reduce measurement noise and incoherent flow  structures, but it is not clear how ensemble- or  phase-averaging will affect the accuracy of the  FMPM due to the nonlinear operations involved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  Second, it is well-acknowledged that the accuracy  of PIV measurements suffers close to the bound-  ary of immersed bodies, which brings challenges  to PIV-based load estimation methods (Rival and  van Oudheusden, 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Third, for nominally two-  dimensional flows measured using planar PIV, the  existence of out-of-plane flows might introduce  errors into the FMPM, depending on the strength  of the three-dimensionality of the flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  The present work extends the study of Zhu  et al (2021) on cycle-averaged vortex-induced  damping and examines the instantaneous vor-  tex trajectory, strength, structure, and vorticity-  induced moment of sinusoidally pitching wings in  a quiescent fluid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' We also aim to use the present  problem as an example to address the aforemen-  tioned potential challenges of applying FMPM  to experimental data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Since the current experi-  ment focuses on a pitching wing, we confine our  analysis to moment partitioning, but the results  are equally applicable to force partitioning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' For  simplicity, we continue to refer to the analysis  technique by its full name (or acronym) – FMPM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  In the following sections, we introduce the  experimental  setup,  the  vortex  identification  method, and the FMPM (Section 2), including  the relative benefits of applying FMPM to instan-  taneous (noisy) velocity fields as compared with  ensemble-averaged (less noisy) fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' In Section  3, we analyze and scale the effect of pitching  frequency, amplitude and pivot location on the  temporal evolution of the vortex trajectory, cir-  culation and the FMPM-based vorticity-induced  moment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Finally, we summarize all the key find-  ings and reiterate the significance of the present  study in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  2 Methods  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='1 Experimental setup  A schematic of the experimental setup is shown in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 1(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' The setup is very similar to that used in  Zhu et al (2021), but without the cyber-physical  control loop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' We conduct all the experiments in  the Brown University free-surface water tunnel  (test section width × depth × length = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='8 m ×  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='6 m × 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='0 m), with a zero flow speed (U∞ = 0  m/s) to create a quiescent environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' We use a  servo motor (Parker SM233AE) with a 5:1 gearbox  to pitch a transparent acrylic NACA 0012 wing  (span s = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='3 m, chord c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='1 m, aspect ratio  AR = 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' The wing has an endplate on the top end  to reduce three-dimensional effects and skim sur-  face waves at the root;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' the wing tip (bottom end)  is left free.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' The wing is mounted above the end-  plate (not shown) using an adjustable bracket that  allows the pitching axis location x/c to be varied  between 0 and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' In between the servo motor and  the wing, an optical encoder (US Digital E3-2500)  is used to measure the pitching position θ, and a  six-axis force/torque transducer (ATI 9105-TIF-  Delta-IP65) is used to measure the fluid forces  and torques exerted on the wing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' In the experi-  ments, we pitch the wing using a sinusoidal profile  θ = A sin (2πft), where A is the pitching ampli-  tude, f is the pitching frequency and t is time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  In this study, we focus on four pitching ampli-  tudes: A = 30◦ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='52 rad), 60◦ (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='05 rad), 90◦  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='57 rad) and 120◦ (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='09 rad), four pitching fre-  quencies: f = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='25, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='75 and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='0 Hz, and three  pitching axis locations: x/c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5 (mid-chord),  x/c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='25 (quarter-chord) and x/c = 0 (leading-  edge).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Because we pitch the wing sinusoidally, we  Article Title  4  Servo motor  & gearbox  Force  transducer  Laser sheet  @ mid-span  Endplate  2×sCMOS  with 35mm lens  Mirror  Optical encoder  U   = 0 m/s  NACA 0012  (transparent)  c  s  ∞  1  0  1  1  0  1  50  0  50  (a)  (b)  (c)  θ  LEV  TEV  1  0  1  1  0  1  0  200  0  200  TEV  LEV  (d)  (e)  1  0  1  1  0  1  1e-3  0  1e-3  1  0  1  1  0  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='05  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='05  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 1 (a) A schematic of the experimental setup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' (b) A sample phase-averaged spanwise vorticity field, ωz, for the case  A = 30◦, f = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5 Hz and x/c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5 during the pitch-up motion (t/T = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='13, where T = 1/f is the pitching period).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' The  original frame (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' the gray box) is rotated by θ to keep the wing at zero angle-of-attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' (c) The corresponding Q field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  Insets are zoom-in views of the LEV and TEV, with the identified vortex positions and boundaries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' (d) The influence field,  φ (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' the auxiliary potential).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' (e) The vortex-induced moment density distribution, −2Qφ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  can approximate the averaged angular velocity as  ˙θ = 4Af (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' the wing rotates four times the pitch-  ing amplitude A over one cycle 1/f) and define  the Reynolds number as Re ≡ 4ρAfc2  m/µ, where  cm is the effective chord length, ρ and µ are water  density and dynamic viscosity, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Re is  of O(104) for the wing kinematics considered in  the present study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  To study the vortex dynamics associated with  the pitching wing, we use a two-dimensional PIV  system to measure the flow field around the wing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  We seed the water with 50 µm diameter neutrally  buoyant hollow ceramic spheres and illuminate  the mid-span plane using a double-pulse Nd:YAG  laser (532 nm, Quantel EverGreen) with LaVi-  sion sheet optics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Two co-planar sCMOS cameras  (LaVision, 2560 × 2160 pixels) with a 45◦ mirror  are used to record PIV image pairs at a frame rate  of 15 Hz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' The recorded PIV images are processed  using the DaVis software (v10, LaVision, two  passes at 64×64 pixels, two passes at 32×32 pixels,  both with 50% overlap) to calculate the velocity  vectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Finally, the velocity fields obtained from  the two cameras are stitched together to form a  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='2c×3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='2c field of view.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' A sample spanwise vortic-  ity field, ωz, for the case A = 30◦, f = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5 Hz and  x/c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5 during the pitch-up motion is shown in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 1(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' For visualization purposes, we rotate the  original frame (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' the gray box) by the pitching  angle, θ, to keep the wing at zero angle-of-attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  We see that as the wing pitches up, two patches  of positive spanwise vorticity are generated at the  leading edge and the trailing edge, corresponding  to the leading-edge vortex (LEV) and the trailing-  edge vortex (TEV), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' The LEV/TEV  shear layers are also visible, although they start to  break into smaller secondary vortices (Francescan-  geli and Mulleners, 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Two patches of negative  vorticity are seen near the positive vortices, corre-  sponding to the negative LEV and TEV left over  from the previous pitch-down cycle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='2 Vortex identification and  trajectory tracking  We identify the vortex cores and boundaries using  the Q-criterion (Hunt et al, 1988;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Jeong and  Hussain, 1995),  Q = 1  2(∥Ω∥2 − ∥S∥2),  (1)  where Q is the second invariant of the velocity gra-  dient tensor, Ω is the vorticity tensor and S is the  strain-rate tensor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Connected regions with Q > 0,  where rotation is higher than strain, are identi-  fied as a vortex (Lee et al, 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' The position  of the vortex core is calculated as the centroid of  the top ten Q values within the vortex boundary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  The Q field corresponding to Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 1(b) is plot-  ted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 1(c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' The insets are zoom-in views  Article Title  5  of the LEV and TEV, with the identified vortex  positions and boundaries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' We see that the vortex  boundaries (Q = 0, green curves) faithfully cap-  ture the LEV and TEV domains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' There are regions  with negative Q values surrounding the vortices,  corresponding to strain-dominated regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' These  strain-dominated regions have been shown to con-  tribute to the generation of opposite-signed aero-  dynamic loads (Menon and Mittal, 2021c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' The  spanwise circulation of the vortex, Γ, is evaluated  by integrating the spanwise vorticity, ωz, within  the vortex boundary using Stokes’ theorem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' All  velocity fields are phase-averaged over 20 cycles  before being fed into the vortex identification and  circulation calculation pipelines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Note that cal-  culating the circulation from the phase-averaged  velocity field is equivalent to taking the phase  average of individual circulations, as calculating  the vortex circulation is a linear operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='3 Force and moment partitioning  method (FMPM)  For convenience and completeness, we first review  the FMPM approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Following this, we will  consider the extension of the method to ensemble-  averaged velocity fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Following Menon and  Mittal (2021b), we first construct an auxiliary  potential, φ, with  ∇2φ = 0, ∂φ  ∂n =  �  [(x − xp) × n] · ez on airfoil  0 on outer boundary  ,  (2)  where n is the outward-facing unit vector normal  to the boundary, x − xp is the location vector  pointing from the pitching axis xp towards the  location x on the surface of the airfoil, and ez  is the spanwise unit vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Note that this aux-  iliary potential φ is specifically constructed for  moment partitioning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' A different potential can be  constructed to determine lift forces or drag forces,  etc (Menon and Mittal, 2021b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' In addition, the  FMPM potential, which we refer to as the “influ-  ence field”, should not be confused with the more  familiar velocity potential from the classical irro-  tational flow theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' The influence field quantifies  the spatial influence of the Q-field on the resultant  moment acting on the submerged body.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  The influence field, φ, satisfies the Laplace  equation,  subject  to  two  different  Neumann  boundary conditions on the airfoil and the outer  boundary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' It is only a function of the airfoil shape,  its orientation, and the location of the pitching  axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' We solve Eqn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 2 numerically using the MAT-  LAB Partial Differential Equation Toolbox (Finite  Element Method).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 1(d) shows the calculated  influence field, φ, for a NACA 0012 airfoil pitching  at the mid-chord.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' For this choice of the pitching  axis, we see that the φ field can be divided into  four quadrants, with the upper surface of the fore  wing and the lower surface of the aft wing being  positive, and the upper surface of the aft wing and  the lower surface of the fore wing being negative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  The magnitude of φ is the highest near the wing  surface and decreases with distance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' The φ field is  not exactly symmetric about the mid-chord due to  the airfoil shape, with the zero-φ boundary slightly  shifted towards the trailing edge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  The vortex-induced force/moment density is  expressed in terms of Q (Menon and Mittal,  2021b) as follows:  fQ = −2ρQφ,  (3)  where ρ is the fluid density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' The vortex-induced  force/moment is then given by the integral of fQ:  τ = −2ρ  �  V  Qφ dV,  (4)  where  �  V represents volume integral over the field  of interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' As mentioned above, we focus on the  torque, τ, in this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' However, as shown in  Menon and Mittal (2021a,c), with the appropriate  influence field, any force can be computed in this  manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  The  spatial  distribution  of  the  vorticity-  induced torque (moment) near the pitching wing  can thus be visualized by plotting contours of  −2Qφ (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' the vorticity-induced moment density  distribution).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 1(e) shows the moment den-  sity distribution corresponding to Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 1(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' As  expected, in this small-amplitude pitching case  (A = 30◦), the LEV and TEV both contribute  to positive (counterclockwise) moments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' However,  as we will show later, the vortex-induced moment  can switch signs during the pitch-up/down cycle  for large pitching amplitudes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  The Force and Moment Partitioning Method  can also be used to obtain the added-mass torque  Article Title  6  (Menon and Mittal, 2021a,b,c)  τa = −ρ  �  S  n ·  �dU  dt φ  �  dS,  (5)  where U is the velocity of the moving wing bound-  ary, φ is the same influence field calculated using  Eqn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 2, and  �  S is the integral along the wing sur-  face.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' We see from Eqn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 5 that the added-mass  torque is only a function of the wing geometry and  kinematics, flow field data is not required for cal-  culating τa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' The torque due to viscous diffusion  can also be calculated using FMPM (Menon and  Mittal, 2021b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' However, it is negligible for the  present study due to the relatively high Reynolds  number Re ∼ O(104).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='4 Application of FMPM to  ensemble- and phase-averaged data  In many experiments, including those discussed  in this paper, measured velocity data may be  ensemble-, or phase-averaged so as to remove noise  or turbulence-related flow structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' In what fol-  lows, we consider ensemble- and phase-averaged  data as interchangeable, both representing time-  dependent averages of a more complex and noisy  flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Application of FMPM to phase-averaged  data introduces some subtleties because Q is a  nonlinear function of velocity (Eqn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Any quan-  tity, for example the velocity u that is measured  in an experiment can be expressed as a sum of the  time-averaged value, ¯u, the phase-averaged value,  ⟨u⟩, and the instantaneous fluctuations, u′:  u(x, y, z, t) = ¯u(x, y, z)+⟨u⟩(x, y, z, t)+u′(x, y, z, t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  (6)  The quantity Q can be expressed as  Q = −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5 ∂  ∂xi  (uj  ∂ui  ∂xj  ) ≡ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5ui,juj,i,  (7)  where indicial notation, with implied summation,  has been used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' As with the velocity, Q can be  expressed as  Q(x, y, z, t) = ¯Q(x, y, z)+⟨Q⟩(x, y, z, t)+Q′(x, y, z, t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  (8)  We can obtain the expression for the above Q  components in terms of velocity as follows  Q = Q¯u¯u+Q⟨u⟩⟨u⟩+Qu′u′+2Q¯u⟨u⟩+2Q¯uu′+2Q⟨u⟩u′,  (9)  where Q¯u⟨u⟩ = −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5¯ui,j⟨uj,i⟩, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Taking a time  average of the above expression, we can get ¯Q ≡  Q¯u¯u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Taking a phase average of the above expres-  sion gives  ⟨Q⟩ = \x18\x18\x18  ⟨Q¯u¯u⟩ + ⟨Q⟨u⟩⟨u⟩⟩ + ⟨Qu′u′⟩  + 2⟨Q¯u⟨u⟩⟩ +\x18\x18\x18\x18  2⟨Q¯uu′⟩ + 2⟨Q⟨u⟩u′⟩  ≡ Q⟨u⟩⟨u⟩ + 2Q¯u⟨u⟩ + 2⟨Q⟨u⟩u′⟩ + ⟨Qu′u′⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  (10)  The phase-averaged vortex-induced force/moment  density is given by  ⟨fQ⟩(x, y, z, t) = −2ρ⟨Q⟩φ  = −2ρ[Q⟨u⟩⟨u⟩ + 2Q¯u⟨u⟩ + 2⟨Q⟨u⟩u′⟩ + ⟨Qu′u′⟩]φ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  (11)  If the flow is highly turbulent and the time-  dependent fluctuations are large, the last two  terms in the above equation should not be ignored.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  However, for laminar flows, where we can assume  |u′| << |⟨u⟩|, we have  ⟨fQ⟩(x, y, z, t) ≈ −2ρ⟨Q⟩φ  = −2ρ[Q⟨u⟩⟨u⟩ + 2Q¯u⟨u⟩]φ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  (12)  This assumption will be tested for the present data  in the next section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Thus, to obtain an accurate  estimation of ⟨fQ⟩ from velocity data, we should  either compute ⟨Q⟩ from the instantaneous Q field  directly (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' calculate Q from the instantaneous  velocity field and then phase average), or esti-  mate the sum of Q⟨u⟩⟨u⟩ + 2Q¯u⟨u⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Note that the  2Q¯u⟨u⟩ term might not be negligible when there  is a free-stream flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' The estimation of ¯u is not  straightforward in a flow with moving boundaries  such as oscillating foils, since it is not clear how  to obtain time-averaged data in regions through  which the foil passes over time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' The resolution of  this issue is left to a future study and, as we will  show later, for the present study, where there is  no free-stream flow, the 2Q¯u⟨u⟩ term can be safely  neglected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  Article Title  7  3 Results and Discussion  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='1 Scaling of vortex circulation and  trajectory  To characterize the vortex dynamics associated  with the pitching wing in quiescent water, we first  analyze the vortex trajectories and circulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  Because we pitch the wing sinusoidally, the wing  moves symmetrically during pitch-up and pitch-  down motions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Moreover, Zhu et al (2021) have  shown that the fluid damping induced by LEVs  and TEVs are comparable, although there are sub-  tle differences caused by the rounded leading edge  and the sharp trailing edge of the NACA 0012 air-  foil.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Therefore, in this study, we choose to focus  on analyzing the TEV dynamics during the pitch-  down motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' The LEV dynamics will only be  analyzed for some cases for comparison.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 2(a) shows the TEV circulation, Γ, during  pitch-down for a wing pitching at the mid-chord,  x/c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5, with a pitching amplitude of A = 30◦,  and a pitching frequency varied from f = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='25 to  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='0 Hz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Because the wing undergoes a pitch-down  motion, the TEV has negative circulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' We see  that for a fixed pitching frequency, the TEV circu-  lation starts from zero (t/T = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='25) and decreases  as the wing pitches downward, as more negative  vorticity is fed into the TEV through the shear  layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' This process continues until t/T = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='75,  when the pitch-up motion starts and the connec-  tion between the TEV and the shear layer is cut  off.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' A bump in Γ for f = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='75 and f = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='0  Hz shows up right before t/T = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='75 when the  TEV starts to separate from the shear layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' After  t/T ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='75, the TEV begins to decline as there  is no new vorticity input and the existing vortex  starts to dissipate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' The magnitude of the TEV cir-  culation increases with the pitching frequency, as  the vortex feeding shear-layer velocity increases  linearly with the pitching frequency (Onoue and  Breuer, 2016, 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  The inset of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 2(a) shows the TEV trajec-  tories for the corresponding four pitching frequen-  cies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' The figure frame is rotated so as to keep the  wing at zero pitching angle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' It is observed that  for a fixed pitching amplitude, TEV trajectories  collapse well for different pitching frequencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' A  circle centered at the mid-chord with a diameter  c is plotted in gray dots to illustrate the trailing  edge trajectory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' The initial part of the TEV tra-  jectory is almost perpendicular to the wing chord,  confirming the validity of the linear assumptions  used in the fluid damping scaling proposed in Zhu  et al (2021) for small pitching amplitudes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' As the  pitch reversal starts, the TEV trajectories turn  abruptly upwards.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' We see that the TEV trajectory  deviates from the trailing edge trajectory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' This is  in contrast to the results of Francescangeli and  Mulleners (2021), who observed that the shed vor-  tex closely follows the trajectory of the edge of a  flat plate pitching with a trapezoidal velocity pro-  file.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' In our sinusoidal pitching case, the deviation  between the TEV trajectory and the trailing edge  trajectory presumably comes from two effects: the  interaction between the TEV and the opposite-  signed residual vortex from the previous pitch-up  motion, and the weak ambient flow induced by the  sinusoidal pitching motion (Shinde and Arakeri,  2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  Onoue and Breuer (2016) showed that for a  pitching plate undergoing large-amplitude limit-  cycle oscillations in a freestream flow, the LEV  circulation scales with the feeding shear-layer  velocity multiplied by a characteristic length scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  Following a similar approach, we propose an LEV-  /TEV circulation scaling for pitching wings in  quiescent flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Because the freestream velocity is  zero, the feeding shear-layer velocity equals the  leading-edge/trailing-edge velocity, which is given  by USL = 4Afcm, where cm represents the dis-  tance between the leading/trailing edge and the  pivot point (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' the effective chord length).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' There-  fore, we can write the non-dimensional circulation  as  Γ∗ =  Γ  4Afc2m  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  (13)  We note that the definition of Γ∗ is analogous to  the vortex formation number, ˆT, which quantifies  the growth of a vortex, and the maximum value  (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' the optimal vortex formation number) repre-  sents when the vortex stops entraining additional  vorticities from the feeding shear layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' We can  also non-dimensionalize the vortex formation time  as  t∗ = 4Acm  c  (t/T − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='25),  (14)  where T = 1/f is the pitching period;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' we use  the t/T − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='25 term to offset the starting time  to coincide with the start of LEV/TEV forma-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' In Γ∗ and t∗, cm = cLE for LEVs and  Article Title  8  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='75  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='25  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='015  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='005  0  1  0  1  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='8  1  0  1  2  3  (a)  (b)  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 2 (a) Trailing-edge vortex (TEV) circulation, Γ, during pitch-down for A = 30◦, x/c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5 and f = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='25 to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='0 Hz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  The gray dotted curve represents the non-dimensional pitching position, θ/A, on the right axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Inset: TEV trajectories for  the corresponding cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' (b) Magnitudes of the non-dimensional circulations, |Γ∗| (Eqn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 13), for both LEVs (plus signs)  and TEVs (circles), with the marker colors corresponding to the frequencies in (a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' The black dotted line shows the linear  trend for data points within the initial linear growth regime, 0 ≤ t∗ ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  cm = cT E for TEVs, where cLE and cT E repre-  sent the leading-edge chord and the trailing-edge  chord, respectively, and c = cLE + cT E is the full  chord length of the wing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 2(b) shows the evolution of the magni-  tude of the TEV circulation, |Γ∗| (circles), as a  function of the vortex formation time, t∗, for four  different pitching frequencies (f = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='25, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='75  and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='0 Hz), corresponding to the cases plotted  in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 2(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' The scaled LEV circulations at these  frequencies are also plotted using plus signs for  comparison.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' We see that the data points collapse  well under the proposed scaling, showing the fre-  quency dependence of the circulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' An initial  linear growth regime (0 ≤ t∗ ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='3) is observed for  both the LEV and the TEV circulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' In this  linear regime, LEV and TEV circulations over-  lap and no significant difference in their slopes is  observed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' After the linear regime, the TEV cir-  culation (circles) keeps on increasing and reaches  its maximum |Γ∗| ≈ 3 at t∗ ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' On the other  hand, the LEV circulation (plus signs) decreases  right after the linear regime despite that the pitch  reversal starts around t∗ ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' This difference  is believed to result from the fact that the TEVs  generated by the sharp trailing edge are more  coherent so that they can sustain longer than the  LEVs generated by the rounded leading edge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' This  difference is clearly captured by the vorticity field  shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 1(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' We see that at this time instant  (t∗ ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='9), the negative vorticities from the pitch-  down motion (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' the blue regions) still retain a  circular shape for the TEV, but become unidentifi-  able for the LEV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' The difference in the circulation  also echoes the observations of Zhu et al (2021)  that the fluid damping associated with a sharp  trailing edge is higher than that resulted from a  rounded leading edge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  Next, we look into the effect of pitching ampli-  tude on the TEV circulation and trajectory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  3(a) shows the TEV circulation, Γ, during pitch-  down for a wing pitching around the mid-chord  x/c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5 and at a frequency of f = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5 Hz,  with the pitching amplitude varied from A = 30◦  to 120◦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' We see that, again, the TEV circulation  decreases from zero when the pitch-down motion  starts at t/T = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' The magnitude of Γ increases  with A due to the higher feeding shear-layer veloc-  ity induced at higher pitching amplitudes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' There  exists a linear growth regime for |Γ| at all four  pitching amplitudes, and this regime shrinks as  A increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Following this regime, we observe  an abrupt drop of the TEV circulation magni-  tude for A = 60◦ to 120◦, which we attribute to  vortex splitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' This vortex splitting behavior is  depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 3(b) inset, where we plot a sample  spanwise vorticity field for A = 60◦ at t/T ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  At this time instant, the TEV (as well as the LEV)  split into two smaller vortices, V1 and V2, with  V1 persisting and V2 quickly dissipating away.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' As  such, the circulation for V1 is tracked after this  split.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' The opposite-signed vortex V3 is the resid-  ual TEV from the previous pitch-up motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' No  Article Title  9  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='75  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='25  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='03  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='01  0  1  0  1  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5  2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5  3  0  1  2  3  4  (a)  (b)  V3  V2  V1  Vortex  splitting  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 3 (a) TEV circulation, Γ, during pitch-down for f = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5 Hz, x/c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5 and A = 30◦ to 120◦, with the non-dimensional  pitching position, θ/A, plotted on the right axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Inset: TEV trajectories for the corresponding cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' (b) Magnitudes of the  non-dimensional TEV circulation, |Γ∗|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' The black dotted line shows the linear trend for data points within the initial linear  growth regime, 0 ≤ t∗ ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' The inset is a sample spanwise vorticity field for A = 60◦ at t/T ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' At this time instant,  the TEV (as well as the LEV) split into two smaller vortices, V1 and V2, with V1 persisting and V2 quickly dissipating  away.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' The opposite-signed vortex V3 is the residual TEV from the previous pitch-up motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  TEV splitting is observed for the smallest pitching  amplitude A = 30◦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 3(a) inset shows the TEV trajectories for  different pitching amplitudes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' We see that as the  pitching amplitude increases, the TEV trajectory  no longer follows the perpendicular path observed  for the lowest pitching amplitude case (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' A =  30◦, the blue curve, see also Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 2a inset).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Instead,  the TEV starts to loosely follow the trailing edge  trajectory (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' the gray dotted circle) at the begin-  ning of the pitch-down motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' As the pitching  amplitude further increases (A = 90◦ and 120◦),  the TEV trajectory sees the emergence of a turn-  over loop – the TEV moves to the front of the pivot  axis, turns closer to the wing surface, intersects  with its initial path and eventually dissipates to  the other side of the wing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' The vortex trajectories  cannot be simply scaled by the pitching amplitude  because of their complex geometries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' The vortex  splitting and the complex vortex trajectories both  add complexities to the problem, causing the non-  linear behaviors of the fluid damping at higher  pitching amplitudes observed in Zhu et al (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  A more quantitative analysis of this issue and the  connections between vortex dynamics and fluid  damping will be discussed later in 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  We scale the TEV circulations as well as the  vortex formation time for different pitching ampli-  tudes using Eqns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 13 and 14, respectively, and  show the results in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 3(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Once again, the  TEV circulation collapses well under the proposed  Γ∗ scaling, revealing the amplitude dependence of  the vortex strength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' The A term in the t∗ scal-  ing (Eqn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 14) aligns the location of the maximum  Γ for different pitching amplitudes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' The initial  linear growth regime for moderate to large pitch-  ing amplitudes (A = 60◦ to 120◦) extends to  t∗ > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='6 as compared to A = 30◦ (see also Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  2b), with the maximum |Γ∗| elevated to |Γ∗| > 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  After the linear regime and the abrupt amplitude  drop caused by vortex splitting, the scaled vor-  tex circulation for A = 60◦ to 120◦ decays slowly  with a relatively constant slope at t∗ > 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='2 (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  vortex saturation, DeVoria and Ringuette, 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  The |Γ∗| for A = 30◦ does not reach this slow-  decay regime before the vortex boundary becomes  unidentifiable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  Another important parameter governing the  LEV/TEV dynamics is the location of the pitching  axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 4(a) shows the temporal evolution of the  TEV circulation, Γ, during the pitch-down motion  for a wing pitching at a frequency of f = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5 Hz  and an amplitude of A = 30◦, with the pitching  axis located at the mid-chord (x/c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5), the  quarter-chord (x/c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='25) and the leading-edge  (x/c = 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Similar to previous results for different  pitching frequencies and amplitudes, the TEV cir-  culation starts from zero and decreases as the wing  pitches down.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' The circulation magnitude increases  as the pitching axis moves farther from the mid-  chord, due to the higher feeding shear-layer veloc-  ity USL = 4Afcm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Again, Γ decreases linearly in  Article Title  10  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='75  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='25  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='03  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='01  0  1  0  1  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5  2  0  1  2  3  4  (a)  (b)  Vortex  splitting  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 4 (a) TEV circulation, Γ, during pitch-down for A = 30◦, f = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5 Hz, x/c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5 (mid-chord pitching), x/c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='25  (quarter-chord pitching) and x/c = 0 (leading-edge pitching), with the pitching position, θ/A, on the right axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Inset: TEV  trajectories for the corresponding cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' (b) Magnitudes of the non-dimensional TEV circulation, |Γ∗|, with a black dotted  line showing the linear trend for data points within the initial linear growth regime, 0 ≤ t∗ ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Inset: TEV trajectory  scaling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  the early stage of the pitch-down motion, and this  linear regime shortens in time as the pitching axis  moves towards the leading edge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' After the linear  regime, the TEV circulation drops near-linearly  first and then abruptly for x/c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='25 and x/c = 0  as the TEV splits into two.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' The TEV circula-  tion and formation time are scaled using Eqn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 13  and 14, and replotted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 4(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' We continue  to see a very nice collapse of all the data points  under the Γ∗ scaling, confirming the pitching axis  dependence of the vortex strength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' The |Γ∗| peaks  around t∗ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='6, similar to the results observed in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 2(b) and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 3(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 4(a) inset shows the pitching axis loca-  tions and the corresponding trailing edge (dotted  circles) and trailing-edge vortex (solid curves) tra-  jectories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' We see that the three TEV trajectories  overlap initially.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' As the pitching axis moves away  from the mid-chord while the angular pitching  amplitude is maintained, the curvature of the TE  trajectory decreases but its arc length increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  In the meantime, the TEV trajectory scales up in  both x- and y-directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' We then scale both the  TE and the TEV trajectories using the trailing-  edge chord (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' cT E, the chord length between the  pitching axis and the trailing edge) and the results  are shown in the inset of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 4(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' The three  vortex trajectories collapse well under this scal-  ing despite some discrepancies for x/c = 0 (green  curve).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' This indicates that, unlike the pitching  amplitude, which has a nonlinear effect on the vor-  tex trajectory, the location of the pitching axis  changes the vortex trajectory in a linear manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  We believe this linear dependence comes from the  fact that the trailing edge trajectory (curvature  and arc length) is linearly scalable by cT E in the  (x, y)-coordinate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' On the other hand, the trailing  edge trajectories under different pitching ampli-  tudes cannot be simply scaled by A in the (x,  y)-coordinate, resulting in the nonlinear unscal-  able trajectories of the vortex (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 3a inset).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  This argument is also supported by the frequency  independence of the TEV trajectories observed in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 2(a) inset, where the trailing edge trajectories  remain the same at different pitching frequencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  These results also imply that the vortex trajectory  is largely determined by the trailing (or leading)  edge trajectory, instead of the edge velocity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  It is also worth noting that in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 2(b), 3(b)  and 4(b), the maximum |Γ∗| corresponds to the  optimal vortex formation number (Gharib et al,  1998;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Dabiri, 2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' However, |Γ∗|max observed  in the present study is within a range of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5 -  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5, which is smaller than that observed in previ-  ous studies (Milano and Gharib, 2005;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Ringuette  et al, 2007;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Rival et al, 2009;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Onoue and Breuer,  2016), where ˆT ≈ 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Because there is no convective  free-stream flow in the present study, the vortex  formation is dominated by the pitching kinemat-  ics (Eqn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 13).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Therefore, the vortex is forced to  pinch off from the feeding shear layer by the wing  kinematics before the universal optimal vortex  formation number ˆT ≈ 4 can be achieved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  Article Title  11  Summarizing these results: the vortex trajec-  tory tracking and scaling analysis performed in  this section provides us with many useful insights  on the vortex dynamics of pitching wings in a  quiescent flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' However, these traditional analysis  methods have several limitations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Firstly, vortex  tracking and circulation calculation become diffi-  cult when the vortex dissipates to an extent that  the vortex boundary becomes unidentifiable, and  when multiple vortices are in close proximity (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 3b inset).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' In these situations, although the  vortices may still contribute to the moment gener-  ation, we are not always able to accurately quan-  tify their positions and strengths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Secondly and  more importantly, the traditional analysis meth-  ods are not capable of directly correlating the spa-  tial position and strength of shed vortices with the  resultant vorticity-induced force/moment, which  is critical for studying these vortex-dominated  flows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Therefore, in the following section, we apply  the Force and Moment Partitioning Method to  gain more physical insights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='2 Vorticity-induced moment  obtained from FMPM  The complex behaviors of vortex trajectories and  circulations discussed in the above section fur-  ther affect the corresponding vorticity-induced  moment and thus the fluid damping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' In this  section, we use FMPM to quantify this vorticity-  induced torque.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' The detailed implementation of  the FMPM has been introduced in Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='3,  and a sample case demonstrating the vorticity  field, the Q field, the influence field and the  moment density distribution has been shown in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 1(b-e).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' The FMPM is not only capable of  identifying the total vorticity-induced force/mo-  ment, it is also able to separate the force/moment  contributions from individual vortices by choosing  different integration windows for the expression  in Eqn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 5(a) shows the time trace of the  leading-edge torque, τLE, the trailing-edge torque,  τT E, and the total vorticity-induced torque, τ =  τLE +τT E, calculated using the PIV-based FMPM  for the case A = 30◦, f = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5 Hz and x/c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  The inset shows the integration windows for calcu-  lating τLE and τT E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' We see that the leading-edge  torque and trailing-edge torque behave differently  over time, and to analyze, we divide the pitch-  ing cycle into four regimes (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' In regimes 1  and 3, τT E has a higher magnitude than τLE, pre-  sumably, as mentioned earlier due to the increased  coherence of the TEV as compared to that of the  LEV (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 2b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' In regimes 2 and 4, where the  pitch-down/up motions first start, τLE overtakes  τT E in magnitude because the newly generated  LEV stays closer to the wing surface than the  TEV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' The change of sign in τLE and τT E aligns  with that of the angular pitching velocity, ˙θ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  The total vorticity-induced torque, τ = τLE +  τT E, directly correlates with the fluid damping  discussed in Zhu et al (2021), as τ = bf ˙θ, where bf  is the fluid damping coefficient and ˙θ is the angu-  lar velocity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Approximating ˙θ with 4Af, we modify  the fluid damping scaling proposed in Zhu et al  (2021) to get a vorticity-induced torque scaling for  sinusoidally pitching wings in quiescent water  τ ∗ =  τ  8ρf 2A2s(KLEc4  LE + KT Ec4  T E),  (15)  where cLE and cT E are the leading-edge chord and  trailing-edge chord, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' KLE = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='95 and  KT E = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='05 are empirical factors that account for  the rounded leading edge and sharp trailing edge,  which agree well with experimental observations,  as we will show next.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  The  frequency-squared  dependence  of  the  vorticity-induced torque (Eqn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 15) is verified in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 5(b), where we plot the non-dimensional  vorticity-induced torque, τ ∗, for four different  pitching frequencies f = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='25, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='75 and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='0  Hz at a pitching amplitude of A = 30◦ and a  pitching axis of x/c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' We see that τ ∗ col-  lapses nicely under the proposed scaling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Recalling  that the vortex trajectory remains unchanged for  a wing pitching at a fixed amplitude and different  frequencies (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 2a), we know that the weighting  by the influence field, φ, also remains unchanged  for different pitching frequencies, and we thus con-  clude that the τ ∼ f 2 scaling must come from  Q ∼ f 2 (Eqn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' By definition, Q scales with the  vorticity squared, which further scales with circu-  lation (according to Stokes’ theorem).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Eqn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 13 and  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 2(b) confirm that Γ ∼ f, and therefore, we  infer that Q ∼ f 2, which again leads to the τ ∼ f 2  scaling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' These two independent scaling analyses  show the self-consistency of our data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  The inset of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 5(b) shows the ratio between  the cycle-averaged absolute trailing-edge torque  and leading-edge torque (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' |τT E|/|τLE|) for the  Article Title  12  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='75  1  5  0  5  10-3  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5  1  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='75  1  4  2  0  2  4  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5  1  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5  1  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5  (a)  (b)  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 5 (a) Time trace of the leading-edge torque (τLE), trailing-edge torque (τT E) and total vorticity-induced torque  (τLE +τT E) calculated using the PIV-based FMPM for the case A = 30◦, f = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5 Hz and x/c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Inset: Moment density  distribution (−2Qφ) at t/T = 0 and integration windows for the leading-edge and trailing-edge torque.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' (b) Non-dimensional  vorticity-induced torque (τ ∗) for A = 30◦, x/c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5 and f = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='25 to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='0 Hz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Inset: Ratio between the cycle-averaged  absolute trailing-edge torque and leading-edge torque (|τT E|/|τLE|) for the corresponding frequencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' The black dashed  line represents the empirical ratio (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='05/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='95 = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='105) used in Zhu et al (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' The red solid line represents a ratio of one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  corresponding four frequencies, with the black  dashed line representing the empirical factors  KT E/KLE = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='05/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='95 = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='105 used in Eqn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 15,  and the red solid line representing a ratio of one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  We find that the measured ratios (colored circles)  are all above one, and match well with the empir-  ical ratio 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='05/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' This shows that the empirical  ratio faithfully captures the subtle differences in  the cycle-averaged magnitude of the trailing-edge  torque and leading-edge torque, agreeing with the  trend observed in Zhu et al (2021) that the cycle-  averaged trailing-edge fluid damping is slightly  higher than that of the leading edge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  The scaled torque, Eqn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 15, suggests that the  vorticity-induced torque scales with the fourth  power of the effective chord length.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' To validate  this, we change the axis of a wing pitching at  A = 30◦, f = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5 Hz from x/c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5 (mid-  chord) to x/c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='25 (quarter-chord) and x/c =  0 (leading-edge) and plot the non-dimensional  vorticity-induced torque, τ ∗, in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 6(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' We see  that τ ∗ collapse reasonably well under the pitch-  ing axis scaling, despite some small discrepancies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  The spanwise vorticity field, ωz, the Q field, the  influence field, φ, and the moment density distri-  bution, −2Qφ, at t/T = 0 are plotted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 6(b)  for further analysis of the pitching axis effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' The  ωz field shows that as the pitching axis moves from  the mid-chord (x/c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5) to the quarter-chord  (x/c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='25), the leading-edge vortex becomes  significantly weaker and less coherent, whereas  the trailing-edge vortex becomes stronger and  more coherent, due to a higher feeding shear-layer  velocity (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' The φ field also changes sig-  nificantly from x/c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5 to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' The quadrant  pattern disappears and φ becomes entirely nega-  tive on the upper surface of the wing and positive  on the lower surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' This change in φ also alters  the moment density distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' We see that  the weak LEV, despite its positive vorticity, now  induces a negative torque, which is opposite to  that induced by its counterpart at x/c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' The  TEV-induced torque becomes a lot higher because  both Q and φ increase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' As the pitching axis further  moves to the leading edge (x/c = 0), a negative  LEV is generated due to the strong pitch-induced  flow around the leading edge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' The influence field,  φ, stays similar to that of x/c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='25 with an  increase in magnitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' The negative LEV induces  a positive torque, because it is on the upper sur-  face of the wing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' These complex behaviors of the  pitch-induced vortices as the pitching axis shifts  might account for the discrepancies observed in τ ∗  in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 6(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  In Eqn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 15, we see that the vorticity-induced  torque, τ, scales with the pitching amplitude  squared.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' However, this scaling is based on the  linear assumption that trajectories of shed vor-  tices stay perpendicular to the wing chord (Zhu  et al, 2021), so it is presumably only valid for  small-amplitude pitching.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' As the vortex trajecto-  ries vary nonlinearly for high pitching amplitudes  Article Title  13  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='75  1  4  2  0  2  4  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5  1  50  0  50  400  0  400  2e-3  0  2e-3  1  0  1  1  0  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='2  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='2  (a)  (b)  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 6 (a) Non-dimensional vorticity-induced torque (τ ∗) for A = 30◦, f = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5 Hz, x/c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5 (mid-chord pitching),  x/c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='25 (quarter-chord pitching) and x/c = 0 (leading-edge pitching).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' (b) Spanwise vorticity field (ωz, first column),  Q field (second column), influence field (φ, third column) and moment density distribution (−2Qφ, fourth column) for  A = 30◦, f = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5 Hz, x/c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5 (first row), 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='25 (second row) and 0 (third row) at t/T = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 3a inset), the scaling breaks down.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' This  is confirmed by Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 7(a), where we show that  the non-dimensional vorticity-induced torque, τ ∗,  does not collapse satisfactorily under the A2 scal-  ing, although the general trend of τ ∗ roughly  matches for different pitching amplitudes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' To fur-  ther characterize the effect of pitching amplitudes  on the vorticity-induced torque, in addition to  the time trace data shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 7(a), we also  look at the cycle-averaged τ ∗ and associate it  with the non-dimensional fluid damping coeffi-  cient, B∗  f = 4Afτ ∗/ ˙θ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 7(b), we compare  B∗  f obtained from the PIV-based FMPM (hol-  low markers) to those extracted by “ring-down”  (direct torque) measurements of Zhu et al (2021)  (solid curves) as a function of the pitching ampli-  tude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Two pitching axes are considered, as B∗  f  has been shown to behave differently when the  wing pitches at the mid-chord (x/c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5) and  the quarter-chord (x/c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='25).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' The first thing  we notice is that the PIV-based FMPM under-  estimates the vorticity-induced torque and hence  the corresponding fluid damping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' The potential  cause for this underestimation will be discussed  Article Title  14  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5  2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5  0  1  2  3  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='75  1  4  2  0  2  4  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5  1  1  0  1  1  0  1  50  0  50  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='1  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='1  100  0  100  1  0  1  1  0  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='4  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='4  Quarter-chord:  (a)  (b)  TEV  TEV  TEV  TEV  TEV  TEV  (c)  f  e  c  d  Mid-chord:  TEV  TEV  TEV  TEV  TEV  TEV  (e)  (f)  (d)  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 7 (a) Non-dimensional vorticity-induced torque (τ ∗) for a wing pitching at x/c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5, f = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5 Hz and A = 30◦  to 120◦ (solid lines).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Purple dashed line: A = 120◦, f = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5 Hz, x/c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' (b) Cycle-averaged non-dimensional fluid  damping coefficient (B∗  f) extracted by ring-down experiments (solid curves, Zhu et al, 2021) and by PIV-based FMPM  (hollow markers) for mid-chord pitching (x/c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5, purple) and quarter-chord pitching (x/c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='25, green).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Note the factor  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5 applied to the FMPM data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' The labeled data points correspond to (c–f ) temporal snapshots of the spanwise vorticity  field (ωz, first row) and the moment density distribution (−2Qφ, second row) during the pitch-down motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' (c) A = 30◦,  x/c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' (d) A = 30◦, x/c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' (e) A = 120◦, x/c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' (f ) A = 120◦, x/c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' The pitching frequency maintains  at f = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5 Hz for all the cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  later.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' To better compare the trend between the  FMPM-based B∗  f and the ring-down-based B∗  f, we  multiply a factor of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5 to the former.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' We see that  the FMPM-based B∗  f agrees very well in trend  with those extracted by ring-down experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  For x/c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5, B∗  f increases non-monotonically  with the pitching amplitude, whereas for x/c =  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='25, B∗  f increases monotonically with the pitching  amplitude with a decreasing slope.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  To explain the differences in B∗  f for different  pitching amplitudes and axes, we choose four rep-  resentative cases (data points c–f on Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 7b) and  plot the corresponding spanwise vorticity field, ωz,  and the moment density distribution, −2Qφ, in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 7(c–f ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' For each case, three temporal snap-  shots, t/T = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='33, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='67, are plotted to  capture the initial, middle and late stages of the  Article Title  15  pitch-down motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 7(c) depicts a conven-  tional scenario where the wing pitches at A = 30◦  and x/c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' In this case, two negative vor-  tices are generated at the leading edge and the  trailing edge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' These two vortices are of compara-  ble size and strength (see also Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 5a), and both  contribute to negative moments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' When the pitch-  ing axis moves to x/c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='25 (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 7d), the LEV  becomes weaker and the TEV becomes stronger,  due to the change in the feeding shear-layer veloci-  ties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' While the LEV is still negative, it generates a  small positive moment due to the negative φ field  (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 6b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  Comparing Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 7(e) to (c), we see that when  the pitching amplitude is very high (A = 120◦),  the LEV and TEV both move towards the pitch-  ing axis from t/T = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='33 to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' At the same time,  they also become less coherent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' These two effects  combined lead to the near-zero τ ∗ observed in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  7(a) at t/T = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' As the pitch-down motion con-  tinues, the LEV moves to the aft wing, and the  TEV moves to the fore wing, resulting in a sign  switch of the induced torque – the LEV and TEV  both generate positive moments at the late stage  of the motion (t/T = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='67).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' However, the total  vorticity-induced torque, τ ∗ remains slightly nega-  tive because of the positive surface vortices, which  are closer to the wing surface and thus generate  more negative moments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' The fact that the LEV  and TEV move across the pitching axis brings τ ∗  close to zero earlier than that of smaller pitching  amplitudes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' This further results in the decreas-  ing B∗  f observed for mid-chord pitching wings at  large pitching amplitudes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' At this same pitching  amplitude (A = 120◦), as the pitching axis moves  to x/c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='25 (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 7f ), we see that the TEV  again moves across the pitching axis at the late  stage (t/T = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='67).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' However, because the φ field  is entirely positive under the wing (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 6b),  the TEV continues to generate negative moments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  In addition, a positive LEV emerges due to the  pitch-induced flow and also generates a negative  moment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' These effects result in a higher τ ∗ mag-  nitude at t/T > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5 for x/c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='25 (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 7a,  purple dashed line) as compared to the x/c =  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5 case (purple solid line), explaining the differ-  ence we see in B∗  f at A = 120◦ (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 7b, data  points f and e).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' We want to note that, although  the LEVs and TEVs move across the pitching  axis for large-amplitude pitching, the vorticity-  induced moment always stays negative during the  pitch-down motion (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='25 < t/T < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='75), where  the angular velocity is also negative ( ˙θ < 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  This assures that the instantaneous aerodynamic  damping is always positive (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' bf = τ/ ˙θ > 0)  during the entire pitching cycle, which holds valid  for all the cases considered in the present study  (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 5a, Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 6a and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 7a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='3 Error analysis of FMPM results  To further explain the underestimation of the fluid  damping coefficient by the FMPM (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 7b), we  compare the vorticity-induced torque calculated  by the PIV-based FMPM to that measured by the  force transducer (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 1a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' According to the  Morison equation (Morison et al, 1950), the total  fluid force experienced by a moving body can be  divided into the vorticity-induced force and the  added-mass force.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Therefore, to get the vorticity-  induced torque, τ, from the force transducer, we  have to first estimate the added-mass torque, τa,  using Eqn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Then, this torque as well as the  physical wing inertia, τI, are subtracted from the  measured torque, τF T .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  The torque measured by the force transducer,  τF T , the sum of the inertial torque and the added-  mass torque, τI + τa, the true vorticity-induced  torque, τF T − (τI + τa), and the vorticity-induced  torque calculated using PIV-based FMPM, τ,  for A = 30◦, f  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5 Hz, x/c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='25 are  plotted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 8(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' We assume that the vis-  cous torque is negligible in comparison to the  vortex-induced torque, due to the relatively high  Reynolds number - Re ∼ O(104).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' We find that the  PIV-based FMPM underestimates the vorticity-  induced torque, τ, roughly by a factor of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5,  which explains the 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5 factor used for the non-  dimensional fluid damping coefficient, B∗  f, in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  7(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' After applying a factor of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5 to τ, we see  that it agrees well with the true vorticity-induced  torque, τF T − (τI + τa).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  However, the question remains why the PIV-  based FMPM significantly underestimates the  vorticity-induced torque.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' One conjecture, as dis-  cussed earlier, is that because we are using phase-  averaged PIV velocity fields (⟨u⟩, ⟨v⟩) to calculate  the Q fields, some small instantaneous flow struc-  tures, which also contribute to the moment gener-  ation, might have been averaged out, as discussed  in Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' To assess this effect, we compare  τ based on Q calculated using phase-averaged  Article Title  16  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='75  1  5  0  5  10-3  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5  1  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='75  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='01  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='02  (a)  (b)  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 8 (a) Time trace of the torque measured by the force transducer (τF T ), the sum of the inertial torque and the  added-mass torque calculated using FMPM (τI + τa), the true vorticity-induced torque (τF T − (τI + τa)) and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5 times  the vorticity-induced torque calculated using PIV-based FMPM (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5τ) for A = 30◦, f = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='5 Hz, x/c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' (b) vorticity-  induced torque, τ, based on Q calculated using phase-averaged velocity fields (⟨u⟩, ⟨v⟩), phase-averaged ⟨Q⟩ calculated using  instantaneous velocity fields (u, v), and phase-averaged ⟨Qφ⟩ calculated using instantaneous velocity fields (u, v).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Error bars  denote standard deviations over 20 cycles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  velocity fields (⟨u⟩, ⟨v⟩), phase-averaged ⟨Q⟩ calcu-  lated using instantaneous velocity fields (u, v), and  phase-averaged ⟨Qφ⟩ calculated using instanta-  neous velocity fields (u, v) in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 8(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' We see that  the vorticity-induced torque calculated using these  three different methods matches closely, indicat-  ing that phase-averaging is not the main cause for  the FMPM to underestimate τ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' The good agree-  ments between −2ρ  �  Q(⟨u⟩, ⟨v⟩)φdV (blue solid  curve) and −2ρ  �  ⟨Q(u, v)⟩φdV (orange dashed  curve) also indicates that the 2Q¯u⟨u⟩ term in Eqn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  12 might be dropped for the cases considered in  the present study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  Another potential error source comes from the  PIV measurements, and in particular, the diffi-  culty in obtaining accurate velocity vectors near  the solid boundary (Rival and van Oudheusden,  2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Because the vorticity-induced torque is  calculated by integrating the −2Qφ field (Eqn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  4), any missing velocity vectors near the solid  boundary will result in a significant decrease of  the overall vorticity-induced torque, as φ reaches  its maximum near the boundary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' This conjecture  could be tested by comparing the PIV-measured  near-boundary velocity fields with those obtained  by from a high-accuracy numerical simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  Alternatively, a physics-informed neural network,  PINN (Raissi et al, 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Cai et al, 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Arzani  et al, 2021), could potentially be used to recon-  struct and resolve near-boundary velocity fields  so as to improve the accuracy of the PIV-based  FMPM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' These tasks, unfortunately, lie beyond the  scope of the current paper but are well worthy of  investigation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  Lastly, all FMPM calculations in this study  are based on two-component, two-dimensional  (2C2D) PIV measurements taken at the mid span,  but without considering three-dimensional effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  This means the contributions from the spanwise  velocity (w) and the spanwise gradient (∂/∂z) of  (u, v) to Q have not been considered, but might  play an important role in causing the differences  between the PIV-based FMPM results and the  force sensor results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' The recent paper of Menon  et al (2022) has employed FMPM to quantify the  role of cross-span vorticity on the force generation  over a finite-aspect ratio wing and these effects  were shown to be quite significant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' In addition, the  pitching wing in this experiment has a free wingtip  (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' 1a) and the tip vortex presumably plays a  non-negligible role in the generation of the total  torque.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' As with the boundary-related errors, one  could assess the three-dimensional flow effects by  comparing our results with 2D and 3D CFD sim-  ulations or by conducting 3D PIV measurements,  both of which, unfortunately, are beyond the scope  of the present study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  4 Conclusion  In this study, we have characterized the vortex  dynamics associated with a NACA 0012 wing  Article Title  17  undergoing prescribed sinusoidal pitching in quies-  cent water.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' We employed two-dimensional particle  image velocimetry (PIV) to measure the velocity  field around the wing, and used the Q criterion  to identify positions and boundaries of pitch-  generated vortices to study the evolution of their  trajectories and strengths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' We found that the  vortex trajectory is insensitive to the pitching fre-  quency, but varies nonlinearly with the pitching  amplitude and scales linearly with the pitching  axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' The vortex circulation was shown to scale  with the pitching frequency, amplitude, and effec-  tive chord length squared for sinusoidal pitch  oscillations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' A vortex splitting behavior causing  the vortex circulation to drop abruptly after a lin-  ear growth regime was observed for all the pitching  cases, except for those at the mid-chord and the  lowest pitching amplitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  In the second part of this study, the Force  and Moment Partitioning Method (FMPM) was  adopted to quantify and visualize the aerodynamic  moment generated by the pitch-induced vortices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  The moment contributions from leading-edge vor-  tices and trailing-edge vortices were separated by  the FMPM, and the ratio between the two was  shown to match the empirical factor used in Zhu  et al (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' A scaling for the vorticity-induced  torque was proposed, revealing its dependence  on the squared pitching frequency, the squared  pitching amplitude, and the fourth power of the  effective chord length.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' The pitching amplitude  was shown to have a nonlinear effect on the  vorticity-induced moment due to the complex vor-  tex dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' The vorticity-induced moment was  further connected with the fluid damping reported  by Zhu et al (2021), and the results obtained  using PIV-based FMPM were found to match well  with that measured using ring-down experiments,  despite a lower magnitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Finally, the FMPM  was found to underestimate the moment compared  to the force transducer data, potentially due to the  missing velocity vectors near the wing boundary  and three-dimensional effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  Together with our previous study on cycle-  averaged vorticity-induced damping (Zhu et al,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  2021),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' the present work,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' which focuses on the  instantaneous evolution of vortex dynamics and  moments,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' provides a comprehensive understand-  ing of the frequency,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' amplitude and pivot axis  effects on the trajectory,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' strength,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' and associ-  ated aerodynamic moment of vortices shed from  a sinusoidally pitching wing in quiescent water,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  a configuration that is of tremendous engineer-  ing and biological relevance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Moreover, this work  is among the first to apply FMPM for analyzing  experimental data (see also Kumar et al, 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  The good agreements we see between the FMPM-  based results and the ring-down experiments/force  transducer measurements further demonstrate the  effectiveness and robustness of this method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' The  discussions on applying FMPM to phase-averaged  data and the possible error source for caus-  ing the underestimation of the vorticity-induced  moment can potentially benefit future applica-  tions of FMPM to experimental data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  Acknowledgments  This work was funded by the Air Force Office  of Scientific Research, Grant FA9550-21-1-0462,  managed by Dr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Gregg Abate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' RM acknowledges  support from NSF grant CBET-2011619 and ONR  Grants N00014-22-1-2655 and N00014-22-1-2770  monitored by Dr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Bob Brizzolara.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  References  Anderson JM, Streitlien K, Barrett DS, et al  (1998) Oscillating foils of high propulsive effi-  ciency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' J Fluid Mech 360:41–72  Arzani A, Wang JX, D’Souza RM (2021) Uncover-  ing near-wall blood flow from sparse data with  physics-informed neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Phys Fluids  33(7):071,905  Baik YS, Bernal LP, Granlund K, et al (2012)  Unsteady force generation and vortex dynamics  of pitching and plunging aerofoils.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' J Fluid Mech  709:37–68  Barrett DS (1996) Propulsive efficiency of a flex-  ible hull underwater vehicle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' PhD thesis, Mas-  sachusetts Institute of Technology  Bergou AJ, Xu S, Wang ZJ (2007) Passive wing  pitch reversal in insect flight.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' J Fluid Mech  591:321–337  Buchholz JHJ, Smits AJ (2008) The wake struc-  ture and thrust performance of a rigid low-  aspect-ratio  pitching  panel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  J  Fluid  Mech  603:331–365  Article Title  18  Buchholz JHJ, Green MA, Smits AJ (2011) Scal-  ing the circulation shed by a pitching panel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' J  Fluid Mech 688:591–601  Cai S, Wang Z, Fuest F, et al (2021) Flow over an  espresso cup: inferring 3-d velocity and pressure  fields from tomographic background oriented  schlieren via physics-informed neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  J Fluid Mech 915:A102  Corke TC, Thomas FO (2015) Dynamic stall  in pitching airfoils: aerodynamic damping and  compressibility effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Annu Rev Fluid Mech  47:479–505  Dabiri JO (2009) Optimal vortex formation as a  unifying principle in biological propulsion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Annu  Rev Fluid Mech 41:17–33  DeVoria AC, Ringuette MJ (2012) Vortex forma-  tion and saturation for low-aspect-ratio rotating  flat-plate fins.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Exp Fluids 52(2):441–462  DeVoria AC, Ringuette MJ (2013) The force and  impulse of a flapping plate performing advanc-  ing and returning strokes in a quiescent fluid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  Exp Fluids 54(5):1–15  Ellington CP, van den Berg C, Willmott AP, et al  (1996) Leading-edge vortices in insect flight.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  Nature 384(6610):626  Epps BP, Techet AH (2007) Impulse generated  during unsteady maneuvering of swimming fish.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  Exp Fluids 43(5):691–700  Francescangeli D, Mulleners K (2021) Discrete  shedding of secondary vortices along a modified  kaden spiral.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' J Fluid Mech 917:A44  Gharib M, Rambod E, Shariff K (1998) A univer-  sal time scale for vortex ring formation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' J Fluid  Mech 360:121–140  Heathcote S, Martin D, Gursul I (2004) Flexi-  ble flapping airfoil propulsion at zero freestream  velocity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' AIAA J 42(11):2196–2204  Ho S, Nassef H, Pornsinsirirak N, et al (2003)  Unsteady aerodynamics and flow control for  flapping wing flyers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Prog Aerosp Sci 39(8):635–  681  Hunt JCR, Wray AA, Moin P (1988) Eddies,  streams, and convergence zones in turbulent  flows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Center for Turbulence Research Report  CTR-S88 pp 193–208  Jafferis NT, Helbling EF, Karpelson M, et al  (2019) Untethered flight of an insect-sized  flapping-wing microscale aerial vehicle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Nature  570(7762):491–495  Jeong J, Hussain F (1995) On the identification of  a vortex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' J Fluid Mech 285:69–94  Jimreeves David M, Mathur M, Govardhan RN,  et al (2018) The kinematic genesis of vortex for-  mation due to finite rotation of a plate in still  fluid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' J Fluid Mech 839:489–524  Kang CK, Shyy W (2014) Analytical model for  instantaneous lift and shape deformation of an  insect-scale flapping wing in hover.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' J R Soc  Interface 11(101):20140,933  Kumar S, Brooks S, Green M, et al (2021) A  data-driven method for determining the hydro-  dynamic force induced by vortices-force parti-  tioning applied to piv data for a caudal fin  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' In: APS DFD Meeting Abstracts, pp  M13–003  Lee H, Simone N, Su Y, et al (2022) Leading  edge vortex formation and wake trajectory: Syn-  thesizing measurements, analysis, and machine  learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Phys Rev Fluids 7:074,704  Lentink D, Dickinson MH (2009) Rotational  accelerations stabilize leading edge vortices on  revolving fly wings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' J Exp Biol 212(16):2705–  2719  Li J, Wu ZN (2018) Vortex force map method for  viscous flows of general airfoils.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' J Fluid Mech  836:145–166  Li J, Wang Y, Graham M, et al (2020) Vor-  tex moment map for unsteady incompressible  viscous flows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' J Fluid Mech 891:A13  McCroskey WJ (1982) Unsteady airfoils.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Annu  Rev Fluid Mech 14(1):285–311  Article Title  19  Menon K, Mittal R (2019) Flow physics and  dynamics of flow-induced pitch oscillations of an  airfoil.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' J Fluid Mech 877:582–613  Menon K, Mittal R (2021a) On the initiation and  sustenance of flow-induced vibration of cylin-  ders: insights from force partitioning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' J Fluid  Mech 907  Menon K, Mittal R (2021b) Quantitative anal-  ysis of the kinematics and induced aerody-  namic loading of individual vortices in vortex-  dominated flows: a computation and data-  driven approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' J Comput Phys 443:110,515  Menon K, Mittal R (2021c) Significance of the  strain-dominated region around a vortex on  induced  aerodynamic  loads.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  J  Fluid  Mech  918:R3  Menon K, Kumar S, Mittal R (2022) Contri-  bution of spanwise and cross-span vortices to  the lift generation of low-aspect-ratio wings:  Insights from force partitioning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Phys Rev Flu-  ids 7(11):114,102  Milano M, Gharib M (2005) Uncovering the  physics of flapping flat plates with artificial  evolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' J Fluid Mech 534:403–409  Moriche M, Flores O, Garc´ıa-Villalba M (2017)  On the aerodynamic forces on heaving and  pitching airfoils at low reynolds number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' J Fluid  Mech 828:395–423  Morison JR, Johnson JW, Schaaf SA (1950) The  force exerted by surface waves on piles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' J Pet  Technol 2(05):149–154  Morse TL, Williamson CHK (2009) Prediction of  vortex-induced vibration response by employing  controlled motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' J Fluid Mech 634:5–39  Onoue K, Breuer K (2016) Vortex formation and  shedding from a cyber-physical pitching plate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  J Fluid Mech 793:229–247  Onoue K, Breuer K (2017) A scaling for vortex  formation on swept and unswept pitching wings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  J Fluid Mech 832:697–720  Quartapelle L, Napolitano M (1983) Force and  moment  in  incompressible  flows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  AIAA  J  21(6):911–913  Raissi M, Perdikaris P, Karniadakis GE (2019)  Physics-informed  neural  networks:  A  deep  learning framework for solving forward and  inverse problems involving nonlinear partial dif-  ferential equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' J Comput Phys 378:686–707  Ringuette MJ, Milano M, Gharib M (2007) Role  of the tip vortex in the force generation of low-  aspect-ratio normal flat plates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' J Fluid Mech  581:453–468  Rival D, Prangemeier T, Tropea C (2009) The  influence of airfoil kinematics on the formation  of leading-edge vortices in bio-inspired flight.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  Exp Fluids 46:823–833  Rival DE, van Oudheusden B (2017) Load-  estimation techniques for unsteady incompress-  ible flows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Exp Fluids 58(3):1–11  Seo JH, Mittal R (2022) Improved swimming  performance  in  schooling  fish  via  leading-  edge vortex enhancement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Bioinspir Biomim  17(6):066,020  Shinde SY, Arakeri JH (2013) Jet meandering by  a foil pitching in quiescent fluid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Phys Fluids  25(4):041,701  Shyy W, Aono H, Chimakurthi SK, et al (2010)  Recent progress in flapping wing aerodynamics  and aeroelasticity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Prog Aerosp Sci 46(7):284–  327  Triantafyllou MS, Triantafyllou GS, Yue DKP  (2000) Hydrodynamics of fishlike swimming.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content='  Annu Rev Fluid Mech 32(1):33–53  Wang ZJ (2005) Dissecting insect flight.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Annu Rev  Fluid Mech 37:183–210  Williamson CHK, Govardhan R (2004) Vortex-  induced vibrations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Annu Rev Fluid Mech  36:413–455  Xiao Q, Zhu Q (2014) A review on flow energy har-  vesters based on flapping foils.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' J Fluids Struct  46:174–191  Article Title  20  Young J, Lai JCS, Platzer MF (2014) A review  of progress and challenges in flapping foil power  generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Prog Aerosp Sci 67:2–28  Zhang C, Hedrick TL, Mittal R (2015) Centripetal  acceleration reaction: an effective and robust  mechanism for flapping flight in insects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' PloS  One 10(8):e0132,093  Zhong Q, Zhu J, Fish FE, et al (2021) Tunable  stiffness enables fast and efficient swimming in  fish-like robots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Sci Robot 6(57):eabe4088  Zhu J, White C, Wainwright DK, et al (2019)  Tuna robotics: A high-frequency experimental  platform exploring the performance space of  swimming fishes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' Sci Robot 4(34):eaax4615  Zhu Y, Su Y, Breuer K (2020) Nonlinear flow-  induced instability of an elastically mounted  pitching wing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' J Fluid Mech 899:A35  Zhu Y, Mathai V, Breuer K (2021) Nonlinear fluid  damping of elastically mounted pitching wings  in quiescent water.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
+page_content=' J Fluid Mech 923:R2' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNFQT4oBgHgl3EQfojZZ/content/2301.13373v1.pdf'}
diff --git a/mtE3T4oBgHgl3EQfigpW/content/tmp_files/2301.04580v1.pdf.txt b/mtE3T4oBgHgl3EQfigpW/content/tmp_files/2301.04580v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4af36e45d202df138f81f581a31ef38d1d6c9b61
--- /dev/null
+++ b/mtE3T4oBgHgl3EQfigpW/content/tmp_files/2301.04580v1.pdf.txt
@@ -0,0 +1,1375 @@
+Superconductivity in Ce-based cage compounds
+Suman Raj Panday1 and Maxim Dzero1
+1Department of Physics, Kent State University, Kent, Ohio 44242, USA
+Cerium-based ternary compounds CeNi2Cd20 and CePd2Cd20 do not exhibit long-range order
+down to millikelvin temperature range. Given the large separation between Ce ions which signif-
+icantly reduces the super-exchange interactions and vanishingly small RKKY interaction, here we
+show that nodal superconductivity mediated by the valence fluctuations must be a ground state in
+these materials. We propose that the critical temperature for the superconducting transition can be
+significantly increased by applying hydrostatic pressure. We employ an extended periodic Anderson
+lattice model which includes the long-range Coulomb interactions between the itinerant electrons
+as well as the local Coulomb interaction between the predominantly localized and itinerant elec-
+trons to compute a critical temperature of the superconducting transition. Using the slave-boson
+approach we show that fluctuations mediated by the repulsive electron-electron interactions lead to
+the emergence of d-wave superconductivity.
+I.
+INTRODUCTION
+Ternary compounds CeNi2Cd20 and CePd2Cd20 are
+members of a family of compounds with chemical formula
+RT2X20 (R= rare-earth element, T=transition-metal ele-
+ment and X=Al,Zn,Cd) and cubic lattice structure.1–7 It
+was reported recently that no long-range order has been
+observed in CeNi2Cd20 and CePd2Cd20 down to tem-
+peratures in the millikelvin range even though the well
+formed cerium magnetic moments were observed in mag-
+netization measurements.8 This surprising experimental
+fact may be understood by taking into account that (i)
+there is a fairly large separation between the neighboring
+cerium ions ∼ 6.8˚A, so that super-exchange interactions9
+are vanishingly small and (ii) the RKKY10–12 interaction
+between the cerium local moments is essentially zero due
+to the symmetry of the lowest lying f-orbital multiplet.13
+Furthermore, transport measurements indicate the weak
+hybridization between the conduction and predominantly
+localized f-electrons.
+Vanishingly small RKKY interaction in CeNi2Cd20
+and CePd2Cd20 makes these compounds analogous to
+CeAl2.
+The latter, however, develops long-range an-
+tiferromagnetic order driven by the super-exchange
+interactions.14 Therefore, in the absence of interactions
+which would promote magnetic long-range order, these
+materials should be expected to develop superconduc-
+tivity upon further cooling. Superconductivity may be
+driven either by electron-phonon interactions15 or by
+purely electron-electron interactions.16 It is indeed very
+well known by now that valence fluctuations originating
+from the hybridization between the conduction and f-
+electrons may lead to a superconducting instability.17–19
+As it follows from the results of the transport and ther-
+modynamic measurements, hybridization between the
+itinerant and f-electrons remains weak down to low tem-
+peratures as manifested by the absence of the coherence
+peak in resistivity as well as low values of the Sommerfeld
+coefficient γ.20 On the other hand, it is known that ap-
+plying pressure will promote the valence fluctuations and,
+as a result, will lead to an increase in the hybridization
+amplitude in the f 0 ↔ f 1 channel. As a consequence,
+average occupation on the f-site may become lower than
+one and electron-electron correlations may produce su-
+perconducting instability in the d-wave channel.
+In this paper we propose that upon further cooling
+CeNi2Cd20 and CePd2Cd20 will develop superconduct-
+ing instability with the d-wave of the order parameter. In
+the limit of the weak coupling, the energy scale which de-
+termines the critical temperature is given by the Kondo
+coherence temperature, Tcoh. One of the consequences
+is that applying external pressure, which promotes the
+fluctuations between the cerium f 0 and f 1 valence con-
+figurations, will boost Tcoh and superconducting transi-
+tion temperature will also increase. In this regard, these
+compounds may be similar to another Ce-based ternary
+compound CeCu2Si2 where similar mechanism for super-
+conductivity was proposed awhile ago.19 Although con-
+ceptually similar to the previous works17–19, our work is
+different from the previous ones in two aspects: (i) we
+use the large-N approach based on the generators of the
+SP(2N) group, which preserves the time-reversal symme-
+try and allows us to consider spin-triplet superconduct-
+ing instability and (ii) we take into account long-range
+Coulomb interactions between the conduction electrons.
+In this context, we are interested to check how the fluc-
+tuations associated with the plasmon field would affect
+the Cooper pairing in the nodal superconductor with re-
+pulsive interactions.21
+In what follows, we will analyze the superconducting
+instability induced by the fluctuations of the bosonic
+fields associated with the long-rangle electron-electron
+correlations. Our results show that the presence of the
+fluctuations associated with the plasmon field leads to a
+significant (factor of ∼ 2) suppression of the critical tem-
+perature, when the local f − c Coulomb interactions are
+relatively weak. We find that the maximum of the critical
+temperature is attained in a mixed-valent regime when
+the average occupation number for the f-electrons ∼ 0.8.
+In this regard, these systems may provide a clearest ex-
+ample of superconductivity induced by strong electron-
+electron correlations without requiring system’s proxim-
+ity to a quantum critical phase transition. Unless pointed
+arXiv:2301.04580v1  [cond-mat.supr-con]  11 Jan 2023
+
+2
+out otherwise, throughout this paper we will adopt the
+energy units e = ℏ = c = kB = 1.
+II.
+MODEL AND BASIC EQUATIONS
+We consider a system of itinerant (c) and flat-band (f)
+electrons described by the following Hamiltonian:
+H = Hc + Hf + HV + Hfc + HC.
+(1)
+Here the first two terms on the right hand side are
+Hc =
+1
+√NL
+�
+kσ
+ϵkc†
+kσckσ,
+Hf = εf0
+�
+jσ
+f †
+jσfjσ + Uff
+�
+j
+nf
+j↑nf
+j↓,
+(2)
+where the summation is performed over the f-sites, NL
+is a number of lattice sites, ϵk is the single-particle dis-
+persion for the itinerant electrons (to be specified below),
+εf0 is the single particle energy for the f-electrons and
+nf
+jσ = f †
+jσfjσ. The third term (1) accounts for the hy-
+bridization between the itinerant and f-electrons:
+HV =
+1
+√NL
+�
+kσ
+�
+Vkf †
+kσckσ + V ∗
+k c†
+kσfkσ
+�
+,
+(3)
+where Vij = (1/
+√
+N L) �
+k Vkeik(Ri−Rj) is the hybridiza-
+tion amplitude. Although Vk is anisotropic due to the dif-
+ference in symmetry of the conduction and f-orbitals,22
+in what follows without loss of generality we ignore its
+momentum dependence Vk → V . Due to the fact that
+number of the conduction and f-electrons are not sepa-
+rately conserved, both εk and εf0 are taken relative to
+the chemical potential µ, which will be computed self-
+consistently.
+Lastly, the remaining last two terms in (1) describe the
+Coulomb interactions between the electrons:
+Hfc = Ufc
+�
+jσσ′
+�
+drψ†
+σ(r)ψσ(r)nf
+jσ′δ(r − Rj),
+HC = 1
+2
+�
+dr
+�
+dr′ρc(r)U(r − r′)ρc(r′).
+(4)
+Here ρc(r) = �
+σ ψ†
+σ(r)ψσ(r) is the density operator,
+U(r) = e2/|r| is the bare Coulomb potential and
+ψσ(r) =
+1
+√NL
+�
+q
+cqσeiqr.
+(5)
+To generate the large-N expansion, we first extend the
+number of spin and orbital degrees of freedom for both
+conduction and f-electrons from 2 to N using the gen-
+erators of the SP(N) (N = 2k, k = 1, 2, ...) subgroup
+of SU(N) to preserve the invariance with respect to the
+time-reversal symmetry.23 Since the interaction between
+the localized f-electrons is assumed to be the largest en-
+ergy scale of the problem, we are going to adopt the limit
+Uff = ∞,
+(6)
+which means that we are projecting out the doubly oc-
+cupied states and therefore we need to introduce slave-
+boson projection operators according to fjα → fjαb†
+j,
+f †
+jα → f †
+jαbj (α = ±1, ..., ±k) along with the constraint
+condition
+Qj =
+�
+α
+f †
+jαfjα + b†
+jbj = 1.
+(7)
+We can now follow the avenue of Ref.
+[19].
+The
+large-N expansion is generated by rescaling Qj → qN,
+bj → bj
+√
+N, V → V/
+√
+N, Ufc → Ufc/
+√
+N and U(r) →
+U(r)/N. First, we use the path integral approach within
+the Matsubara formalism, so that the partition function
+is given by
+Z =
+�
+D[cc†ff †ρλ]e−S,
+(8)
+where ρ is a real bosonic field which appears as a result
+of the gauge transformation bj(τ) = ρj(τ)eiθj(τ), fjα →
+fjαeiθj(τ) and λj(τ) → λj(τ) + θj(τ) is the slave field
+which is used to enforce the constraint (7).
+We employ the Hubbard-Stratonovich transformation
+�
+D [σ, σ] exp
+�
+�− 1
+J
+β
+�
+0
+dτ
+�����σ(τ) + J
+�
+kα
+f †
+kαckα
+�����
+2�
+�
+= const.
+(9)
+to decouple the interaction terms (4) in the action (8) by
+using the bosonic fields ϕc(r, τ), ϕf(r, τ) and φ(r, τ). Af-
+ter this step, one can formally integrate out the fermionic
+fields which yields the purely bosonic action
+S = −NTr log ˆG + N
+�
+kk′
+ρ(−k)(iλ(k − k′))ρ(k′)
+− NUfc
+4
+�
+k
+ϕf(k)ϕc(−k) + N
+2
+�
+k
+φ(−k)φ(k)
+U(k)
+− qN
+�
+NL
+β
+�
+0
+dτ (iλ(k = 0, τ)) .
+(10)
+Here q
+=
+1/N,
+U(k)
+=
+4πe2/k2 and �
+k
+{...}
+=
+T �
+iνl
+(1/√NL) �
+k
+{...}. The first term in (10) is a matrix
+representing a single-particle fermionic propagator:
+
+3
+ˆG(k, k′) =
+�
+(−iωn + ϵk)δkk′ + Ufc
+2 ϕf(k − k′) + iφ(k − k′)
+V ρ(k − k′)
+V ρ(k′ − k)
+(−iωn + εf0)δkk′ + Ufc
+2 ϕc(k − k′) + iλ(k − k′)
+�
+,
+(11)
+-1
+-0.8
+-0.6
+-0.4
+-0.2
+0
+εf0 / D
+0.1
+0.2
+0.3
+0.4
+0.5
+f-level occupation number, nf
+Ufc = 0
+Ufc = 0.1D
+Ufc = 0.2D
+Ufc = 0.3D
+Ufc = 0.5D
+Ufc = 0.9D
+n=0.875
+V=0.5D
+FIG. 1: Dependence of the f-level occupation number (per
+spin) on the position of the ’bare’ f-level energy εf0 computed
+using the saddle-point approximation. All energies are given
+in the units of the band width D of the conduction band.
+The values of the parameters used to obtain this plot are:
+T = 10−4D, N = 2, V = 0.5D, n = 0.875.
+where k = (iωn, k), iωn = iπT(2n + 1) are the fermionic
+Matsubara frequencies.
+Note that the constraint field
+iλ(k) plays the same role for the f-electron part of the
+propagator as a plasmon field iφ(k) for the c-electron
+part of the propagator.
+A.
+Saddle-point approximation
+In the saddle-point approximation the bosonic fields
+are chosen in the following form:
+ρ(k, τ) = ρδk,0,
+λ(k, τ) = λδk,0,
+ϕc,f(k, τ) = ϕc,fδk,0,
+φ(k, τ) = 0.
+(12)
+The zero value of the plasmon field φ(k, τ) in (12) means
+that its effect at the saddle-point level has already been
+included into the definition of the chemical potential.
+The stationary point equations in the saddle-point ap-
+proximation are found by minimizing the action with
+respect to the bosonic fields (12), which results in the
+0.001
+0.01
+0.1
+(εf−µ)/D
+10
+1
+10
+2
+10
+3
+10
+4
+γ/γ0
+Ufc = 0.0
+Ufc = 0.1D
+Ufc = 0.3D
+Ufc = 0.5D
+0
+0.1
+0.2
+(εf−µ)/D
+0.1
+0.2
+0.3
+0.4
+0.5
+nf
+FIG. 2: Plot of the Sommerfeld coefficient γ = (π2/3)DνF
+in the units of the Sommerfeld coefficient γ0 in the absence
+of hybridization (νF is the single-particle density of states
+at the Fermi level) as a function of the Kondo lattice co-
+herence temperature Tcoh = εf − µ for various values of the
+coupling Ufc. The inset shows the dependence of the f-level
+occupation numbers as a function of Tcoh. These results are
+found from the solution of the saddle-point equations assum-
+ing T = 10−4D, N = 2, V = 0.5D and the total particle
+number n = 0.875.
+system of the following equations:19
+iλ = −T
+�
+iωn
+�
+k
+V 2
+(iωn − εk)(iωn − εf) − (V ρ)2 ,
+q − ρ2 = T
+�
+iωn
+�
+k
+(iωn − εk)eiωn0+
+(iωn − εk)(iωn − εf) − (V ρ)2 ,
+ϕf = 2T
+�
+iωn
+�
+k
+(iωn − εk)eiωn0+
+(iωn − εk)(iωn − εf) − (V ρ)2 ,
+ϕc = 2T
+�
+iωn
+�
+k
+(iωn − εf)eiωn0+
+(iωn − εk)(iωn − εf) − (V ρ)2 .
+(13)
+In these equations
+�
+k =
+�
+d3k
+(2π)3 , εk = ϵk + Ufcϕf/2 and
+εf = εf0 + Ufcϕc/2 + iλ. From the last two equations
+(13) it follows that ϕc,f = 2nc,f, where nα are the average
+occupation numbers per spin. In what follows we assume
+that the total number of particles is fixed
+n = nc + nf = const.
+(14)
+
+4
+The Matsubara summations can be easily performed us-
+ing the Poisson summation formula
+T
+�
+iωn
+1
+(iωn + iν − a)(iωn − b) = nF (b) − nF (a)
+iν + b − a
+,
+(15)
+where nF (ε) = 1/ (exp[(ε − µ)/T] + 1) is the Fermi dis-
+tribution function and µ is a chemical potential. As a
+result, we obtain the following three equations which self-
+consistently determine the values of εf, ρ and the chem-
+ical potential µ:
+εf − εf0 − Ufcnc =
+�
+k
+nF (E2k) − nF (E1k)
+�
+(εf − εk)2 + (2V ρ)2 ,
+nf + nc =
+�
+k
+[nF (E1k) + nF (E2k)] ,
+nf − nc =
+�
+k
+(εk − εf)[nF (E2k) − nF (E1k)]
+�
+(εf − εk)2 + (2V ρ)2
+,
+(16)
+where we introduced
+E1(2)k = 1
+2
+�
+εk + εf ±
+�
+(εf − εk)2 + 4(V ρ)2
+�
+.
+(17)
+To perform the integration over momentum, we will
+assume that the particle density in the conduction band
+is low enough. Thus, we consider the Galilean-invariant
+spectrum
+ϵk = k2
+2m − D,
+(18)
+where D is set as a unit of energy. The effective mass m =
+(3π2/
+√
+2)2/3/2D of the conduction electrons is obtained
+from the condition that the total number of particles (per
+spin) equals one:
+D
+�
+−D
+ν0(ϵk)dϵk = 1.
+(19)
+In this formula ν0(ϵ) = (3/4
+√
+2D)
+�
+ϵ/D + 1 is the single-
+particle density of states for the non-interacting system.
+In what follows we will limit out calculations to the case
+when the particle occupation number of the conduction
+band (per spin) equals to 0.375, which means that the
+total particle occupation number per spin must be n =
+0.875.
+The results of the numerical solution of these equations
+are presented in Fig. 1 and Fig. 2. In Fig. 1 we show
+the dependence of the f-level occupation numbers as a
+function of the bare f-level energy.
+Notice, that with
+an increase in the values of Ufc the system approaches
+the first order phase transition when the value of nf
+changes abruptly from n(interm.)
+f
+∼ 0.1 to n(local)
+f
+∼ 0.5.
+In Fig. 2 we plot the dependence of the Sommerfeld co-
+efficient γ = lim
+T →0 C(T)/T as a function of the parameter
+-2
+-1.5
+-1
+-0.5
+0
+0.5
+εf0 / D
+0
+0.05
+0.1
+0.15
+0.2
+critical temperature, Tc / D  x 10
+-3
+δφ = 0
+δφ = 0
+Ufc = 0.9D
+(a)
+-2
+-1.5
+-1
+-0.5
+0
+εf0 / D
+0
+0.05
+0.1
+0.15
+0.2
+0.25
+0.3
+critical temperature, Tc / D  x 10
+-3
+δφ = 0
+δφ = 0
+Ufc = 0.5D
+(b)
+-2
+-1.5
+-1
+-0.5
+0
+0.5
+εf0 / D
+0
+0.1
+0.2
+0.3
+0.4
+0.5
+critical temperature, Tc / D  x 10
+-3
+δφ = 0
+δφ = 0
+Ufc = 0.1D
+(c)
+FIG. 3: Superconducting critical temperature computed for
+three different values of the Hubbard Ufc interaction and
+for the two separate cases of zero and non-zero plasmonic
+field fluctuations. We find that the fluctuations of the plas-
+monic field has significant effect on critical temperature when
+Ufc ≪ D.
+Contrary to the earlier studies, we found that
+the maximum value of the critical temperature is decreasing
+with the increase in the strength of Ufc.
+These results are
+found from the solution of the saddle-point equations with
+pF = (2mEF /D)1/2 ≈ 3.73, T = 10−5D, N = 2, V = 0.5D
+and the total particle number n = 0.875.
+εf − µ (the latter is usually associated with the coher-
+ence temperature of the Kondo lattice, Tcoh). The value
+of γ is significantly enhanced in the local moment regime
+nf ∼ 0.5. It is worth pointing out that at least in the
+local moment regime the fluctuations associated with the
+plasmon field φ(k, τ) will not affect the value of γ signif-
+icantly, since their contribution is proportional to 1/N.
+Since Tcoh ∼ ν−1
+F
+and both of these parameters will ulti-
+mately determine the value of the superconducting tran-
+
+5
+sition temperature, it is clear that the effects associated
+with the plasmon field will be encoded into the magni-
+tude of the pairing strength.
+Furthermore, the Fermi
+energy is given by
+EF = µ + (V ρ)2
+Tcoh
+− Ufcnf
+(20)
+and so the Fermi energy increases with an increase in ef-
+fective hybridization, V ρ. Overall, our results presented
+in Figs 1 and Fig. 2 agree with those reported earlier.19
+B.
+Fluctuation propagator
+Having determined the values of the bosonic fields at
+the stationary point, we can determine the propagators
+of the bosonic fields at the gaussian level. We represent
+the bosonic fields as
+ρ(k, τ) = ρδk,0 + δρ(k, τ), iφ(k, τ) = δ(iφ(k, τ)),
+iλ(k, τ) = iλδk,0 + δ(iλ(k, τ)),
+ϕc,f(k, τ) = ϕc,fδk,0 + δϕc,f(k, τ),
+(21)
+and expand each term in the action (10) in powers of the
+components of
+δˆΦ = (δρ, δ(iλ), δϕc, δϕf, δ(iφ))t
+(22)
+up to the second order (t means transpose).
+For the
+details on the derivation we refer the reader to Appendix
+A. As a result, an inverse of the fluctuation propagator
+can be represented in terms of a 5 × 5 matrix given by
+ˆSq =
+�
+�������
+iλ + V 2Πvv(q) + V 2Π3(q)
+ρ + V Π2(q)
+� V Ufc
+2
+�
+Π2(q)
+� V Ufc
+2
+�
+Π1(q)
+V Π1(q)
+ρ + V Π2(−q)
+1
+2Πff(q)
+� Ufc
+4
+�
+Πff(q)
+� Ufc
+4
+�
+Πvv(q)
+1
+2Πvv(q)
+� V Ufc
+2
+�
+Π2(−q)
+� Ufc
+4
+�
+Πff(−q)
+�
+U 2
+fc
+8
+�
+Πff(q)
+− Ufc
+8 +
+�
+U 2
+fc
+8
+�
+Πvv(q)
+� Ufc
+4
+�
+Πvv(q)
+� V Ufc
+2
+�
+Π1(−q)
+� Ufc
+4
+�
+Πvv(−q) − Ufc
+8 +
+�
+U 2
+fc
+8
+�
+Πvv(−q)
+�
+U 2
+fc
+8
+�
+Πcc(q)
+� Ufc
+4
+�
+Πcc(q)
+� V Ufc
+2
+�
+Π1(−q)
+1
+2Πvv(−q)
+� Ufc
+4
+�
+Πvv(−q)
+� Ufc
+4
+�
+Πcc(−q)
+−
+1
+2U(q) + 1
+2Πcc(q)
+�
+�������
+.
+(23)
+The corresponding expressions for the polarization oper-
+ators entering into this expression can be found in the
+Appendix B. It is worth noting here that not all of the
+polarization operators are independent. For example, a
+simple calculation shows that
+V 2Π3(q) = −iλ + V 2Πvv(q) − iν V
+ρ Π2(q),
+(24)
+where q = (q, iν). Finally, a quantity which will be cen-
+tral to our discussion below - bosonic propagator - is
+given by the inverse of (23):
+ˆD(q) = −ˆS−1
+q .
+(25)
+In what follows we will use equations (23,25) to investi-
+gate the superconducting instability mediated by the in-
+teractions between the fermions and fluctuating bosonic
+fields.
+III.
+SUPERCONDUCTIVITY FROM
+REPULSIVE ELECTRON-ELECTRON
+INTERACTIONS
+The problem of superconductivity emerging as a
+ground state in the Anderson lattice model has been
+extensively discussed in the literature starting with the
+pioneering papers by Lavagna, Millis and Lee [17] and
+by Houghton, Read and Won [18].
+In the context of
+the extended Anderson model the problem of supercon-
+ducting pairing mediated by the bosonic fluctuations has
+been studied by Onishi and Miyake [19].
+Specifically,
+they found that with an increase in the strength of the
+Hubbard interaction Ufc between the conduction and f-
+electrons, the critical temperature of the superconducting
+transition also increases, i.e. increasing the strength of
+the local repulsive interaction boosts superconductivity.
+Since there are no retardation effects and all interactions
+are repulsive, it is expected that the superconducting or-
+der parameter has nodes and the highest transition tem-
+perature was found to be for the d-wave symmetry. In
+this regard, it will be interesting to check whether the
+long-range Coulomb interactions may produce the same
+effect here.
+By the nature of the interaction which induces the
+Cooper pairing, in the weak coupling theory the Kondo
+lattice coherence temperature Tcoh plays a role of the
+characteristic energy scale analogous to the Debye fre-
+quency in the conventional theory of superconductivity.
+The critical temperature describing the superconducting
+instability in the l-orbital channel is given by
+T (l)
+c
+= Tcohe−1/λl,
+(26)
+where λl = νF Γl is the dimensionless coupling constant,
+νF is the density of states at the Fermi level and Γl > 0
+
+6
+is given by
+Γl =
+�2l + 1
+2
+�
+π
+�
+0
+Γ(0)(θ)Pl(cos θ) sin θdθ.
+(27)
+Here Pl(cos θ) is the Legendre polynomial and Γ(0)(θ) the
+bare interaction in the Cooper channel.24
+Interaction function Γ(0)(θ) is determined by the ma-
+trix elements of the fluctuation propagator ˆD(q, iν) eval-
+uated at |q| = 2kF sin(θ/2) and iν → 0.17–19 The specific
+form of Γ(0)(θ) depends on whether the chemical poten-
+tial is in the first E1k or the second E2k band. Since
+we have chosen the fairly low occupation number for the
+conduction band, we find that the chemical potential lies
+close to the top of the second band, E2k. The fermionic
+operators akσ, a†
+kσ, which describe the quasiparticles in
+this band are related to the original fermionic operators
+ckσ and fkσ by the following relation:
+ckσ = −vkakσ,
+fkσ = ukakσ.
+(28)
+Here uk and vk are the coherence factors defined in the
+Appendix B. We introduce the two-particle correlation
+function
+Γαβγδ(12; 34) = −
+�
+ˆTτ
+�
+aα(1)aβ(2)a†
+γ(3)a†
+δ(4)
+��
+, (29)
+where averaging is performed over the action (10) and
+aσ(1) = aσ(k1, τ1) etc. Expanding the action up to the
+second order in δΦ (22), we have found the following
+expression for the interaction function:
+Γ(0)(θ) = v4
+kF
+��Ufc
+2
+�2
+Dϕfϕf(θ) + Ufc
+2 Dϕfφ(θ) + Ufc
+2 Dφϕf(θ) + Dφφ(θ)
+�
++ u4
+kF
+�
+Dλλ(θ) + Ufc
+2 Dλϕc(θ)
++Ufc
+2 Dϕcλ(θ) +
+�Ufc
+2
+�2
+Dϕcϕc(θ)
+�
++ 2u2
+kF v2
+kF
+�
+Ufc
+2 Dλϕf(θ) +
+�Ufc
+2
+�2
+Dϕcϕf(θ) + Ufc
+2 Dϕcφ(θ) + Dλφ(θ)
++2V 2Dρρ(θ)
+�
+− 4ukF v3
+kF
+�
+V Dφρ(θ) + V Ufc
+2
+Dϕfρ(θ)
+�
+− 4vkF u3
+kF
+�
+V Dλρ(θ) + V Ufc
+2
+Dϕcρ(θ)
+�
+≡ Γcccc(θ) + Γffff(θ) + Γffcc(θ) + Γcccf(θ) + Γfffc(θ)
+(30)
+and the coherence factors ukF , vkF are evaluated at the
+Fermi energy:
+ukF =
+V ρ
+�
+T 2
+coh + (V ρ)2 , vkF =
+Tcoh
+�
+T 2
+coh + (V ρ)2 .
+(31)
+The subscripts in D refer to its matrix elements, i.e. Dϕcλ
+corresponds to the matrix element D32 etc. in accordance
+with the definition (22).
+The relations (31) imply that in the vicinity of the
+local moment regime nf ∼ 1/2, when Tcoh ≪ D we find
+that ukF ∼ 1. Therefore, we can expect that the largest
+contribution to the pairing interaction is provided by the
+last term in (30), which is confirmed by the numerical
+calculations. This means that the long-range Coulomb
+interactions should not significantly affect the value of
+the transition temperature in the local moment regime:
+in comparison to the contribution from the itinerant c-
+states, the f-states provide significantly larger spectral
+weight contribution to the pairing quasiparticles.
+Our results of the numerical calculation of the super-
+conducting critical temperature are shown in Fig.
+3.
+First, we found that the largest critical temperature is
+realized in the d-wave (l = 2) channel. In agreement with
+the previous studies, we have found that the maximum
+of the critical temperature remains weakly dependent on
+the value of εf0. At the same time we find that the crit-
+ical temperature is decreasing with both an inclusion of
+the plasmon field fluctuations as well as with an increase
+in the values of Ufc, which is strike contrast with the
+earlier results.19
+In order to get insight into the origin of this effect, we
+fix the values of εf, ρ and µ to their corresponding values
+at the maximum of Tc and consider how the interaction
+(30) changes with the changes in Ufc.
+First of all, we
+recall that νF remains independent on the value of Ufc,
+Fig. 2. This result implies that Tcoh must also remain
+essentially independent of Ufc.
+Indeed, for the results
+shown in Fig. 3 we found that Tcoh/D ≈ 2.3 × 10−3 and
+νF /ν0 ≈ 770 when Tc approaches its maximum value.
+At the same time two largest contributions to the inter-
+action kernel, Γfffc(θ) and Γffff(θ), do change with Ufc,
+Fig.
+4.
+As it turns, however, their respective contri-
+butions to the νF Γ(0)(θ) yield similar results and, as a
+consequence, we find that νF Γ(0)(θ) is slightly increased
+while the value of the maximum Tc is somewhat reduced
+with an increase of Ufc. In other words, valence fluctua-
+tions produce superconductivity even in the case of when
+Ufc can be neglected and the increasing the value of Ufc
+reduced the value of the superconducting critical tem-
+perature to an intermediate valence regime. The same
+
+7
+0
+0.5
+1
+1.5
+2
+q/kF
+-10
+0
+10
+20
+30
+40
+Interaction kernel, νF Γ
+(0)(θ)
+νFΓfffc(θ), Ufc = 0.5D
+νFΓfffc(θ), Ufc = 0.9D
+νFΓffff(θ), Ufc = 0.5D
+νFΓffff(θ), Ufc = 0.9D
+νFΓ
+(0)(θ), Ufc = 0.5D
+νFΓ
+(0)(θ), Ufc = 0.9D
+FIG. 4: Interaction kernel as a function of momentum com-
+puted without the effects of the plasmon fluctuations. This re-
+sult shows that although separate contributions to Γ(0), such
+as the leading ones Γfffc and Γffff, do depend on the value of
+Ufc, Γ(0) shows much weaker dependence on Ufc. Notably, as
+the value of Ufc increases, the effective interaction becomes
+more repulsive rendering the lower Tc in the d-wave channel.
+These results are found from the solution of the saddle-point
+equations with kF = (2mEF /D)1/2 ≈ 3.73, T = 10−5D,
+N = 2, V = 0.5D and the total particle number n = 0.875.
+The values of the remaining parameters are as follows: for
+Ufc = 0.5D: εf0 = −0.40487D, εf = 0.3461D, ρ = 0.2304
+and µ = 0.3279D and for Ufc = 0.9D and εf0 = −0.46915D
+we found εf = 0.50685D, ρ = 0.17148 and µ = 0.49712D.
+argument can be implied to the effects of the long-range
+Coulomb interactions, which also lead to the reduction
+in the value of Tc as soon as the system in tuned away
+from the local moment regime.
+IV.
+CONCLUSIONS
+In this paper we have presented the results of the calcu-
+lations for the critical temperature of the superconduct-
+ing transition in the extended Anderson lattice model,
+which also included the long-range Coulomb repulsion
+between the conduction electrons. Our work has been
+motivated by recent discovery of the Ce-based cage com-
+pounds CeNi2Cd20 and CePd2Cd20. These compounds
+have vanishing RKKY interactions and do not exhibit a
+long-range order down to very low temperatures in the
+millikelvin range. We propose that d-wave superconduc-
+tivity may develop in these compounds under an appli-
+cation of the hydrostatic pressure.
+We have also found that the long-range Coulomb repul-
+sion leads to a decrease in the values of superconducting
+critical temperature: in the local moment regime it has
+small effect on the value of Tc due to the fact the most of
+the spectral weight carried by the quasiparticles, which
+form the Cooper pairs, is provided by the f-electrons. In
+the mixed-valent regime and for the low enough values
+of Ufc the fluctuations of the plasmon field significantly
+reduces the value of the superconducting critical temper-
+ature.
+V.
+ACKNOWLEDGMENTS
+The authors would like to thank C. C. Almasan and M.
+B. Maple for bringing their attention to this problem. We
+acknowledge useful discussions with B. Fregoso and Y.
+Li related to this project. This work was financially sup-
+ported by the National Science Foundation grant NSF-
+DMR-2002795.
+Appendix A: Effective action in the gaussian
+approximation
+We define the single-particle fermionic propagator in
+the stationary point, which is obtained from (11) using
+(12)
+ˆG−1(k) =
+�
+iωn − ϵk − Ufcnf
+−V ρ
+−V ρ
+iωn − εf
+�
+.
+(A1)
+Then the action at the stationary point is given by
+S0 = −NTr log
+�
+−ˆG−1�
++ iNλ
+�
+ρ2 − q0
+�
+− NUfc
+4
+ϕfϕc.
+(A2)
+Minimizing S0 with respect to the slave-boson fields
+yields the equations (13).
+We can now expand action (10) up to the second order
+in powers of δΦ (see (21) in main text). It follows
+S = S0 + δS,
+(A3)
+where the fluctuation correction to the action δS is of the
+form
+δS = −NTr log
+�
+1 − ˆG ˆ
+M
+�
++ N
+�
+k
+�
+(iλ)δρ(−k)δρ(k) + 2ρiδλ(−k)δρ(k)
+�
+−N
+�
+k
+�Ufc
+4 δϕf(−k)δϕc(k) + δ(iφ(−k))δ(iφ(k))
+U(k)
+�
+.
+(A4)
+
+8
+Here matrix ˆ
+M is defined by
+ˆ
+Mkk′ =
+� Ufc
+2 δϕf(k − k′) + δ(iφ(k − k′))
+V δρ(k − k′)
+V δρ(k − k′)
+Ufc
+2 δϕc(k − k′) + δ(iλ(k − k′))
+�
+.
+(A5)
+In the gaussian approximation we formally expand the
+expression under the logarithm (A4)
+− Tr log
+�
+1 − ˆG ˆ
+M
+�
+=
+∞
+�
+n=1
+1
+nTr
+�
+ˆG ˆ
+M
+�n
+(A6)
+and retain only the term with n = 2. As a result we find
+the following expression for (A4):
+δS = N
+�
+k
+δˆΦ(−k)ˆSk ˆΦ(k),
+(A7)
+with ˆSk given by Eq. (23) in the main text. Upon in-
+tegrating out the bosonic fields, it is straightforward to
+check that the fluctuations give the correction of the or-
+der of O(1/N) to the free energy.
+Appendix B: Polarization operators
+The polarization operators which enter into equation
+(23) are defined according to
+Πcc(q) = T
+�
+iωn
+�
+k
+Gcc(k + q)Gcc(k),
+Πff(q) = T
+�
+iωn
+�
+k
+Gff(k + q)Gff(k),
+Πvv(q) = T
+�
+iωn
+�
+k
+Gfc(k + q)Gcf(k),
+Πcv(q) = T
+�
+iωn
+�
+k
+Gcc(k + q)Gcf(k) = Πvc(−q),
+Πfv(q) = T
+�
+iωn
+�
+k
+Gff(k + q)Gfc(k) = Πvf(−q),
+Πfc(q) = T
+�
+iωn
+�
+k
+Gff(k + q)Gcc(k) = Πcf(−q).
+(B1)
+Here q = (q, iνm), iνm = 2iπTm is the bosonic Matsub-
+ara frequency, k = (k, iωn) and iωn = iπT(2n + 1) is the
+fermionic Matsubara frequency. Functions Gaa(k) which
+appear in this expressions are defined according to
+Gcc(k + q) =
+iωn − εf
+(iωn − εk)(iωn − εf) − (V ρ)2
+=
+u2
+k
+iωn − E1k
++
+v2
+k
+iωn − E2k
+,
+Gff(k + q) =
+iωn − εk
+(iωn − εk)(iωn − εf) − (V ρ)2
+=
+v2
+k
+iωn − E1k
++
+u2
+k
+iωn − E2k
+,
+(B2)
+The remaining correlator Gfc = Gcf is given by
+Gfc(k + q) =
+V 2
+(iωn − εk)(iωn − εf) − (V ρ)2
+=
+V ρ
+E1k − E2k
+�
+1
+iωn − E1k
+−
+1
+iωn − E2k
+�
+.
+(B3)
+In the expressions above we introduced the coherence
+factors
+u2
+k = 1
+2
+�
+1 + εk − εf
+Rk
+�
+, v2
+k = 1
+2
+�
+1 − εk − εf
+Rk
+�
+(B4)
+and Rk = E1k−E2k. For convenience, instead of the last
+three polarization functions, we will consider
+Π1(q, iνl) = 1
+2 [Πcv(q, iνl) + Πvc(q, iνl)] ,
+Π2(q, iνl) = 1
+2 [Πfv(q, iνl) + Πvf(q, iνl)] ,
+Π3(q, iνl) = 1
+2 [Πcf(q, iνl) + Πfc(q, iνl)] .
+(B5)
+The summations over the Matsubara frequencies can be
+easily performed using (15). For example
+T
+�
+iωn
+(iωn+l − εk+q)
+(iωn+l − E1k+q + µ)(iωn+l − E2k+q + µ)
+(iωn − εf)
+(iωn − E1k + µ)(iωn − E2k + µ)
+= v2
+k+qu2
+k
+[nF (E1k) − nF (E1k+q)]
+iνl + E1k − E1k+q
++ v2
+k+qv2
+k
+[nF (E2k) − nF (E1k+q)]
+iνl + E2k − E1k+q
++ u2
+k+qu2
+k
+[nF (E1k) − nF (E2k+q)]
+iνl + E1k − E2k+q
++ u2
+k+qv2
+k
+[nF (E2k) − nF (E2k+q)]
+iνl + E2k − E2k+q
+.
+(B6)
+
+9
+We also would like to remind the reader that all the ener-
+gies entering into these expressions are taken relative to
+the chemical potential µ. Formally, this is accomplished
+by including the chemical potential into the definition of
+the Fermi distribution function, Eq. (15).
+1 V. Burnett, D. Yazici, B. White, N. Dilley, A. Friedman,
+B. Brandom, and M. Maple, “Structure and physical prop-
+erties of RT2Cd20 (R=rare earth, T=Ni, Pd) compounds
+with the CeCr2al20-type structure,” Journal of Solid State
+Chemistry, vol. 215, pp. 114–121, jul 2014.
+2 D. Yazici, T. Yanagisawa, B. D. White, and M. B.
+Maple, “Nonmagnetic ground state in the cubic com-
+pounds PrNi2Cd20 and PrPd2Cd20,” Physical Review B,
+vol. 91, p. 115136, mar 2015.
+3 T. Onimaru, K. T. Matsumoto, Y. F. Inoue, K. Umeo,
+Y. Saiga, Y. Matsushita, R. Tamura, K. Nishimoto, I. Ishii,
+T. Suzuki, and T. Takabatake, “Superconductivity and
+structural phase transitions in caged compounds RT2Zn20
+(r = La, Pr, t = Ru, Ir),” Journal of the Physical Society
+of Japan, vol. 79, p. 033704, Mar 2010.
+4 S. Niemann and W. Jeitschko,
+“Ternary aluminides
+AT2Al20 (A = rare earth elements and uranium:
+T =
+Ti, Nb, Ta, Mo, and W) with CeCr2Al20-type structure,”
+Journal of Solid State Chemistry, vol. 114, pp. 337–341,
+Feb 1995.
+5 M. J. Kangas, D. C. Schmitt, A. Sakai, S. Nakatsuji, and
+J. Y. Chan, “Structure and physical properties of single
+crystal PrCr2Al20 and CeM2Al20 (M=V, Cr): A compari-
+son of compounds adopting the CeCr2al20 structure type,”
+Journal of Solid State Chemistry, vol. 196, pp. 274–281,
+Dec 2012.
+6 Y. Isikawa, T. Mizushima, K. Kumagai, and T. Kuwai,
+“Dense Kondo effect in caged compound CeRu2Zn20,”
+Journal of the Physical Society of Japan, vol. 82, p. 083711,
+Aug 2013.
+7 P. Swatek and D. Kaczorowski, “Intermediate valence be-
+havior in the novel cage compound CeIr2Zn20,” Journal of
+Physics: Condensed Matter, vol. 25, p. 055602, Jan 2013.
+8 B. D. White, D. Yazici, P.-C. Ho, N. Kanchanavatee,
+N. Pouse, Y. Fang, A. J. Breindel, A. J. Friedman, and
+M. B. Maple, “Weak hybridization and isolated localized
+magnetic moments in the compounds CeT2Cd20(T = Ni,
+Pd),” Journal of Physics:
+Condensed Matter, vol. 27,
+p. 315602, Jul 2015.
+9 P. W. Anderson, “Antiferromagnetism. theory of superex-
+change interaction,” Phys. Rev., vol. 79, pp. 350–356, Jul
+1950.
+10 M. A. Ruderman and C. Kittel, “Indirect exchange cou-
+pling of nuclear magnetic moments by conduction elec-
+trons,” Physical Review, vol. 96, pp. 99–102, oct 1954.
+11 T. Kasuya, “A theory of metallic ferro- and antiferromag-
+netism on zener's model,” Progress of Theoretical Physics,
+vol. 16, pp. 45–57, jul 1956.
+12 K. Yosida, “Magnetic properties of Cu-Mn alloys,” Physi-
+cal Review, vol. 106, pp. 893–898, jun 1957.
+13 A. M. Konic, Y. Zhu, A. J. Breindel, Y. Deng, C. C. Moir,
+M. B. Maple, C. C. Almasan, and M. Dzero, “Vanishing
+rkky interactions in ce-based cage compounds,” pre-print
+arXiv:, December 2022.
+14 M. B. Maple, “Dependence of s − f exchange on atomic
+number in rare-earth dialuminades,” Solid State Comm.,
+vol. 8, pp. 1915–1917, May 1970.
+15 V. Barzykin and L. P. Gor’kov, “Competition between
+phonon superconductivity and Kondo screening in mixed
+valence and heavy fermion compounds,” Phys. Rev. B,
+vol. 71, p. 214521, Jun 2005.
+16 S.
+Maiti
+and
+A.
+V.
+Chubukov,
+“Superconductivity
+from repulsive interaction,” AIP Conference Proceedings,
+vol. 1550, no. 1, pp. 3–73, 2013.
+17 M. Lavagna, A. J. Millis, and P. A. Lee, ”d -wave super-
+conductivity in the large-degeneracy limit of the Anderson
+lattice,” Phys. Rev. Lett., vol. 58, pp. 266–269, Jan 1987.
+18 A. Houghton, N. Read, and H. Won, “Charge fluctuations,
+spin fluctuations, and superconductivity in the anderson
+lattice model of heavy-fermion systems,” Phys. Rev. B,
+vol. 37, pp. 3782–3785, Mar 1988.
+19 Y. Onishi and K. Miyake, “Enhanced valence fluctuations
+caused by f-c Coulomb interaction in Ce-based heavy elec-
+trons: Possible origin of pressure-induced enhancement of
+superconducting transition temperature in CeCu2Ge2 and
+related compounds,” Journal of the Physical Society of
+Japan, vol. 69, no. 12, pp. 3955–3964, 2000.
+20 P. Coleman, Heavy Fermions: Electrons at the Edge of
+Magnetism. John Wiley & Sons, Ltd, 2007.
+21 S. Fischer, M. Hecker, M. Hoyer, and J. Schmalian, “Short-
+distance breakdown of the Higgs mechanism and the ro-
+bustness of the BCS theory for charged superconductors,”
+Phys. Rev. B, vol. 97, p. 054510, Feb 2018.
+22 M. Dzero, J. Xia, V. Galitski, and P. Coleman, “Topo-
+logical Kondo insulators,” Annual Review of Condensed
+Matter Physics, vol. 7, no. 1, pp. 249–280, 2016.
+23 R. Flint, M. Dzero, and P. Coleman, “Heavy electrons
+and the symplectic symmetry of spin,” Nat Phys, vol. 4,
+pp. 643–648, 08 2008.
+24 A. A. Abrikosov, L. P. Gorkov, and I. E. Dzyaloshinski,
+Methods of Quantum Field Theory in Statistical Physics.
+Dover, 1977.
+
diff --git a/mtE3T4oBgHgl3EQfigpW/content/tmp_files/load_file.txt b/mtE3T4oBgHgl3EQfigpW/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..3577c0186e90fdbc1c6811994291a29c6a231518
--- /dev/null
+++ b/mtE3T4oBgHgl3EQfigpW/content/tmp_files/load_file.txt
@@ -0,0 +1,641 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf,len=640
+page_content='Superconductivity in Ce-based cage compounds  Suman Raj Panday1 and Maxim Dzero1  1Department of Physics, Kent State University, Kent, Ohio 44242, USA  Cerium-based ternary compounds CeNi2Cd20 and CePd2Cd20 do not exhibit long-range order  down to millikelvin temperature range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Given the large separation between Ce ions which signif-  icantly reduces the super-exchange interactions and vanishingly small RKKY interaction, here we  show that nodal superconductivity mediated by the valence fluctuations must be a ground state in  these materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' We propose that the critical temperature for the superconducting transition can be  significantly increased by applying hydrostatic pressure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' We employ an extended periodic Anderson  lattice model which includes the long-range Coulomb interactions between the itinerant electrons  as well as the local Coulomb interaction between the predominantly localized and itinerant elec-  trons to compute a critical temperature of the superconducting transition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Using the slave-boson  approach we show that fluctuations mediated by the repulsive electron-electron interactions lead to  the emergence of d-wave superconductivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  INTRODUCTION  Ternary compounds CeNi2Cd20 and CePd2Cd20 are  members of a family of compounds with chemical formula  RT2X20 (R= rare-earth element, T=transition-metal ele-  ment and X=Al,Zn,Cd) and cubic lattice structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='1–7 It  was reported recently that no long-range order has been  observed in CeNi2Cd20 and CePd2Cd20 down to tem-  peratures in the millikelvin range even though the well  formed cerium magnetic moments were observed in mag-  netization measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='8 This surprising experimental  fact may be understood by taking into account that (i)  there is a fairly large separation between the neighboring  cerium ions ∼ 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='8˚A, so that super-exchange interactions9  are vanishingly small and (ii) the RKKY10–12 interaction  between the cerium local moments is essentially zero due  to the symmetry of the lowest lying f-orbital multiplet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='13  Furthermore, transport measurements indicate the weak  hybridization between the conduction and predominantly  localized f-electrons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  Vanishingly small RKKY interaction in CeNi2Cd20  and CePd2Cd20 makes these compounds analogous to  CeAl2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  The latter, however, develops long-range an-  tiferromagnetic order driven by the super-exchange  interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='14 Therefore, in the absence of interactions  which would promote magnetic long-range order, these  materials should be expected to develop superconduc-  tivity upon further cooling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Superconductivity may be  driven either by electron-phonon interactions15 or by  purely electron-electron interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='16 It is indeed very  well known by now that valence fluctuations originating  from the hybridization between the conduction and f-  electrons may lead to a superconducting instability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='17–19  As it follows from the results of the transport and ther-  modynamic measurements, hybridization between the  itinerant and f-electrons remains weak down to low tem-  peratures as manifested by the absence of the coherence  peak in resistivity as well as low values of the Sommerfeld  coefficient γ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='20 On the other hand, it is known that ap-  plying pressure will promote the valence fluctuations and,  as a result, will lead to an increase in the hybridization  amplitude in the f 0 ↔ f 1 channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' As a consequence,  average occupation on the f-site may become lower than  one and electron-electron correlations may produce su-  perconducting instability in the d-wave channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  In this paper we propose that upon further cooling  CeNi2Cd20 and CePd2Cd20 will develop superconduct-  ing instability with the d-wave of the order parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' In  the limit of the weak coupling, the energy scale which de-  termines the critical temperature is given by the Kondo  coherence temperature, Tcoh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' One of the consequences  is that applying external pressure, which promotes the  fluctuations between the cerium f 0 and f 1 valence con-  figurations, will boost Tcoh and superconducting transi-  tion temperature will also increase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' In this regard, these  compounds may be similar to another Ce-based ternary  compound CeCu2Si2 where similar mechanism for super-  conductivity was proposed awhile ago.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='19 Although con-  ceptually similar to the previous works17–19, our work is  different from the previous ones in two aspects: (i) we  use the large-N approach based on the generators of the  SP(2N) group, which preserves the time-reversal symme-  try and allows us to consider spin-triplet superconduct-  ing instability and (ii) we take into account long-range  Coulomb interactions between the conduction electrons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  In this context, we are interested to check how the fluc-  tuations associated with the plasmon field would affect  the Cooper pairing in the nodal superconductor with re-  pulsive interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='21  In what follows, we will analyze the superconducting  instability induced by the fluctuations of the bosonic  fields associated with the long-rangle electron-electron  correlations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Our results show that the presence of the  fluctuations associated with the plasmon field leads to a  significant (factor of ∼ 2) suppression of the critical tem-  perature, when the local f − c Coulomb interactions are  relatively weak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' We find that the maximum of the critical  temperature is attained in a mixed-valent regime when  the average occupation number for the f-electrons ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  In this regard, these systems may provide a clearest ex-  ample of superconductivity induced by strong electron-  electron correlations without requiring system’s proxim-  ity to a quantum critical phase transition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Unless pointed  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='04580v1  [cond-mat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='supr-con]  11 Jan 2023  2  out otherwise, throughout this paper we will adopt the  energy units e = ℏ = c = kB = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  MODEL AND BASIC EQUATIONS  We consider a system of itinerant (c) and flat-band (f)  electrons described by the following Hamiltonian:  H = Hc + Hf + HV + Hfc + HC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  (1)  Here the first two terms on the right hand side are  Hc =  1  √NL  �  kσ  ϵkc†  kσckσ,  Hf = εf0  �  jσ  f †  jσfjσ + Uff  �  j  nf  j↑nf  j↓,  (2)  where the summation is performed over the f-sites, NL  is a number of lattice sites, ϵk is the single-particle dis-  persion for the itinerant electrons (to be specified below),  εf0 is the single particle energy for the f-electrons and  nf  jσ = f †  jσfjσ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' The third term (1) accounts for the hy-  bridization between the itinerant and f-electrons:  HV =  1  √NL  �  kσ  �  Vkf †  kσckσ + V ∗  k c†  kσfkσ  �  ,  (3)  where Vij = (1/  √  N L) �  k Vkeik(Ri−Rj) is the hybridiza-  tion amplitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Although Vk is anisotropic due to the dif-  ference in symmetry of the conduction and f-orbitals,22  in what follows without loss of generality we ignore its  momentum dependence Vk → V .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Due to the fact that  number of the conduction and f-electrons are not sepa-  rately conserved, both εk and εf0 are taken relative to  the chemical potential µ, which will be computed self-  consistently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  Lastly, the remaining last two terms in (1) describe the  Coulomb interactions between the electrons:  Hfc = Ufc  �  jσσ′  �  drψ†  σ(r)ψσ(r)nf  jσ′δ(r − Rj),  HC = 1  2  �  dr  �  dr′ρc(r)U(r − r′)ρc(r′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  (4)  Here ρc(r) = �  σ ψ†  σ(r)ψσ(r) is the density operator,  U(r) = e2/|r| is the bare Coulomb potential and  ψσ(r) =  1  √NL  �  q  cqσeiqr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  (5)  To generate the large-N expansion, we first extend the  number of spin and orbital degrees of freedom for both  conduction and f-electrons from 2 to N using the gen-  erators of the SP(N) (N = 2k, k = 1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=') subgroup  of SU(N) to preserve the invariance with respect to the  time-reversal symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='23 Since the interaction between  the localized f-electrons is assumed to be the largest en-  ergy scale of the problem, we are going to adopt the limit  Uff = ∞,  (6)  which means that we are projecting out the doubly oc-  cupied states and therefore we need to introduce slave-  boson projection operators according to fjα → fjαb†  j,  f †  jα → f †  jαbj (α = ±1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=', ±k) along with the constraint  condition  Qj =  �  α  f †  jαfjα + b†  jbj = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  (7)  We can now follow the avenue of Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  The  large-N expansion is generated by rescaling Qj → qN,  bj → bj  √  N, V → V/  √  N, Ufc → Ufc/  √  N and U(r) →  U(r)/N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' First, we use the path integral approach within  the Matsubara formalism, so that the partition function  is given by  Z =  �  D[cc†ff †ρλ]e−S,  (8)  where ρ is a real bosonic field which appears as a result  of the gauge transformation bj(τ) = ρj(τ)eiθj(τ), fjα →  fjαeiθj(τ) and λj(τ) → λj(τ) + θj(τ) is the slave field  which is used to enforce the constraint (7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  We employ the Hubbard-Stratonovich transformation  �  D [σ, σ] exp  �  �− 1  J  β  �  0  dτ  �����σ(τ) + J  �  kα  f †  kαckα  �����  2�  �  = const.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  (9)  to decouple the interaction terms (4) in the action (8) by  using the bosonic fields ϕc(r, τ), ϕf(r, τ) and φ(r, τ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Af-  ter this step, one can formally integrate out the fermionic  fields which yields the purely bosonic action  S = −NTr log ˆG + N  �  kk′  ρ(−k)(iλ(k − k′))ρ(k′)  − NUfc  4  �  k  ϕf(k)ϕc(−k) + N  2  �  k  φ(−k)φ(k)  U(k)  − qN  �  NL  β  �  0  dτ (iλ(k = 0, τ)) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  (10)  Here q  =  1/N,  U(k)  =  4πe2/k2 and �  k  {.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='}  =  T �  iνl  (1/√NL) �  k  {.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' The first term in (10) is a matrix  representing a single-particle fermionic propagator:  3  ˆG(k, k′) =  �  (−iωn + ϵk)δkk′ + Ufc  2 ϕf(k − k′) + iφ(k − k′)  V ρ(k − k′)  V ρ(k′ − k)  (−iωn + εf0)δkk′ + Ufc  2 ϕc(k − k′) + iλ(k − k′)  �  ,  (11)  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='2  0  εf0 / D  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='5  f-level occupation number, nf  Ufc = 0  Ufc = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='1D  Ufc = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='2D  Ufc = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='3D  Ufc = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='5D  Ufc = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='9D  n=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='875  V=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='5D  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' 1: Dependence of the f-level occupation number (per  spin) on the position of the ’bare’ f-level energy εf0 computed  using the saddle-point approximation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' All energies are given  in the units of the band width D of the conduction band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  The values of the parameters used to obtain this plot are:  T = 10−4D, N = 2, V = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='5D, n = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='875.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  where k = (iωn, k), iωn = iπT(2n + 1) are the fermionic  Matsubara frequencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  Note that the constraint field  iλ(k) plays the same role for the f-electron part of the  propagator as a plasmon field iφ(k) for the c-electron  part of the propagator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  Saddle-point approximation  In the saddle-point approximation the bosonic fields  are chosen in the following form:  ρ(k, τ) = ρδk,0,  λ(k, τ) = λδk,0,  ϕc,f(k, τ) = ϕc,fδk,0,  φ(k, τ) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  (12)  The zero value of the plasmon field φ(k, τ) in (12) means  that its effect at the saddle-point level has already been  included into the definition of the chemical potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  The stationary point equations in the saddle-point ap-  proximation are found by minimizing the action with  respect to the bosonic fields (12), which results in the  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='001  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='1  (εf−µ)/D  10  1  10  2  10  3  10  4  γ/γ0  Ufc = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='0  Ufc = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='1D  Ufc = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='3D  Ufc = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='5D  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='2  (εf−µ)/D  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='5  nf  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' 2: Plot of the Sommerfeld coefficient γ = (π2/3)DνF  in the units of the Sommerfeld coefficient γ0 in the absence  of hybridization (νF is the single-particle density of states  at the Fermi level) as a function of the Kondo lattice co-  herence temperature Tcoh = εf − µ for various values of the  coupling Ufc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' The inset shows the dependence of the f-level  occupation numbers as a function of Tcoh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' These results are  found from the solution of the saddle-point equations assum-  ing T = 10−4D, N = 2, V = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='5D and the total particle  number n = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='875.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  system of the following equations:19  iλ = −T  �  iωn  �  k  V 2  (iωn − εk)(iωn − εf) − (V ρ)2 ,  q − ρ2 = T  �  iωn  �  k  (iωn − εk)eiωn0+  (iωn − εk)(iωn − εf) − (V ρ)2 ,  ϕf = 2T  �  iωn  �  k  (iωn − εk)eiωn0+  (iωn − εk)(iωn − εf) − (V ρ)2 ,  ϕc = 2T  �  iωn  �  k  (iωn − εf)eiωn0+  (iωn − εk)(iωn − εf) − (V ρ)2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  (13)  In these equations  �  k =  �  d3k  (2π)3 , εk = ϵk + Ufcϕf/2 and  εf = εf0 + Ufcϕc/2 + iλ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' From the last two equations  (13) it follows that ϕc,f = 2nc,f, where nα are the average  occupation numbers per spin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' In what follows we assume  that the total number of particles is fixed  n = nc + nf = const.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  (14)  4  The Matsubara summations can be easily performed us-  ing the Poisson summation formula  T  �  iωn  1  (iωn + iν − a)(iωn − b) = nF (b) − nF (a)  iν + b − a  ,  (15)  where nF (ε) = 1/ (exp[(ε − µ)/T] + 1) is the Fermi dis-  tribution function and µ is a chemical potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' As a  result, we obtain the following three equations which self-  consistently determine the values of εf, ρ and the chem-  ical potential µ:  εf − εf0 − Ufcnc =  �  k  nF (E2k) − nF (E1k)  �  (εf − εk)2 + (2V ρ)2 ,  nf + nc =  �  k  [nF (E1k) + nF (E2k)] ,  nf − nc =  �  k  (εk − εf)[nF (E2k) − nF (E1k)]  �  (εf − εk)2 + (2V ρ)2  ,  (16)  where we introduced  E1(2)k = 1  2  �  εk + εf ±  �  (εf − εk)2 + 4(V ρ)2  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  (17)  To perform the integration over momentum, we will  assume that the particle density in the conduction band  is low enough.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Thus, we consider the Galilean-invariant  spectrum  ϵk = k2  2m − D,  (18)  where D is set as a unit of energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' The effective mass m =  (3π2/  √  2)2/3/2D of the conduction electrons is obtained  from the condition that the total number of particles (per  spin) equals one:  D  �  −D  ν0(ϵk)dϵk = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  (19)  In this formula ν0(ϵ) = (3/4  √  2D)  �  ϵ/D + 1 is the single-  particle density of states for the non-interacting system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  In what follows we will limit out calculations to the case  when the particle occupation number of the conduction  band (per spin) equals to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='375, which means that the  total particle occupation number per spin must be n =  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='875.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  The results of the numerical solution of these equations  are presented in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' 1 and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' 1 we show  the dependence of the f-level occupation numbers as a  function of the bare f-level energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  Notice, that with  an increase in the values of Ufc the system approaches  the first order phase transition when the value of nf  changes abruptly from n(interm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=')  f  ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='1 to n(local)  f  ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' 2 we plot the dependence of the Sommerfeld co-  efficient γ = lim  T →0 C(T)/T as a function of the parameter  2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='5  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='5  εf0 / D  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='2  critical temperature, Tc / D  x 10  3  δφ = 0  δφ = 0  Ufc = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='9D  (a)  2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='5  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='5  0  εf0 / D  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='3  critical temperature, Tc / D  x 10  3  δφ = 0  δφ = 0  Ufc = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='5D  (b)  2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='5  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='5  εf0 / D  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='5  critical temperature, Tc / D  x 10  3  δφ = 0  δφ = 0  Ufc = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='1D  (c)  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' 3: Superconducting critical temperature computed for  three different values of the Hubbard Ufc interaction and  for the two separate cases of zero and non-zero plasmonic  field fluctuations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' We find that the fluctuations of the plas-  monic field has significant effect on critical temperature when  Ufc ≪ D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  Contrary to the earlier studies, we found that  the maximum value of the critical temperature is decreasing  with the increase in the strength of Ufc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  These results are  found from the solution of the saddle-point equations with  pF = (2mEF /D)1/2 ≈ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='73, T = 10−5D, N = 2, V = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='5D  and the total particle number n = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='875.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  εf − µ (the latter is usually associated with the coher-  ence temperature of the Kondo lattice, Tcoh).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' The value  of γ is significantly enhanced in the local moment regime  nf ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' It is worth pointing out that at least in the  local moment regime the fluctuations associated with the  plasmon field φ(k, τ) will not affect the value of γ signif-  icantly, since their contribution is proportional to 1/N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  Since Tcoh ∼ ν−1  F  and both of these parameters will ulti-  mately determine the value of the superconducting tran-  5  sition temperature, it is clear that the effects associated  with the plasmon field will be encoded into the magni-  tude of the pairing strength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  Furthermore, the Fermi  energy is given by  EF = µ + (V ρ)2  Tcoh  − Ufcnf  (20)  and so the Fermi energy increases with an increase in ef-  fective hybridization, V ρ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Overall, our results presented  in Figs 1 and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' 2 agree with those reported earlier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='19  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  Fluctuation propagator  Having determined the values of the bosonic fields at  the stationary point, we can determine the propagators  of the bosonic fields at the gaussian level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' We represent  the bosonic fields as  ρ(k, τ) = ρδk,0 + δρ(k, τ), iφ(k, τ) = δ(iφ(k, τ)),  iλ(k, τ) = iλδk,0 + δ(iλ(k, τ)),  ϕc,f(k, τ) = ϕc,fδk,0 + δϕc,f(k, τ),  (21)  and expand each term in the action (10) in powers of the  components of  δˆΦ = (δρ, δ(iλ), δϕc, δϕf, δ(iφ))t  (22)  up to the second order (t means transpose).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  For the  details on the derivation we refer the reader to Appendix  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' As a result,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' an inverse of the fluctuation propagator  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='can be represented in terms of a 5 × 5 matrix given by  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='ˆSq =  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='�������  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='iλ + V 2Πvv(q) + V 2Π3(q)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='ρ + V Π2(q)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='� V Ufc  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='Π2(q)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='� V Ufc  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='Π1(q)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='V Π1(q)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='ρ + V Π2(−q)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='2Πff(q)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='� Ufc  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='Πff(q)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='� Ufc  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='Πvv(q)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='2Πvv(q)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='� V Ufc  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='Π2(−q)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='� Ufc  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='Πff(−q)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='U 2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='fc  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='Πff(q)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='− Ufc  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='8 +  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='U 2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='fc  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='Πvv(q)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='� Ufc  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='Πvv(q)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='� V Ufc  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='Π1(−q)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='� Ufc  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='Πvv(−q) − Ufc  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='8 +  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='U 2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='fc  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='Πvv(−q)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='U 2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='fc  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='Πcc(q)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='� Ufc  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='Πcc(q)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='� V Ufc  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='Π1(−q)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='2Πvv(−q)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='� Ufc  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='Πvv(−q)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='� Ufc  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='Πcc(−q)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='−  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='2U(q) + 1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='2Πcc(q)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='�������  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  (23)  The corresponding expressions for the polarization oper-  ators entering into this expression can be found in the  Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' It is worth noting here that not all of the  polarization operators are independent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' For example, a  simple calculation shows that  V 2Π3(q) = −iλ + V 2Πvv(q) − iν V  ρ Π2(q),  (24)  where q = (q, iν).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Finally, a quantity which will be cen-  tral to our discussion below - bosonic propagator - is  given by the inverse of (23):  ˆD(q) = −ˆS−1  q .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  (25)  In what follows we will use equations (23,25) to investi-  gate the superconducting instability mediated by the in-  teractions between the fermions and fluctuating bosonic  fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  SUPERCONDUCTIVITY FROM  REPULSIVE ELECTRON-ELECTRON  INTERACTIONS  The problem of superconductivity emerging as a  ground state in the Anderson lattice model has been  extensively discussed in the literature starting with the  pioneering papers by Lavagna, Millis and Lee [17] and  by Houghton, Read and Won [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  In the context of  the extended Anderson model the problem of supercon-  ducting pairing mediated by the bosonic fluctuations has  been studied by Onishi and Miyake [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  Specifically,  they found that with an increase in the strength of the  Hubbard interaction Ufc between the conduction and f-  electrons, the critical temperature of the superconducting  transition also increases, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' increasing the strength of  the local repulsive interaction boosts superconductivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  Since there are no retardation effects and all interactions  are repulsive, it is expected that the superconducting or-  der parameter has nodes and the highest transition tem-  perature was found to be for the d-wave symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' In  this regard, it will be interesting to check whether the  long-range Coulomb interactions may produce the same  effect here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  By the nature of the interaction which induces the  Cooper pairing, in the weak coupling theory the Kondo  lattice coherence temperature Tcoh plays a role of the  characteristic energy scale analogous to the Debye fre-  quency in the conventional theory of superconductivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  The critical temperature describing the superconducting  instability in the l-orbital channel is given by  T (l)  c  = Tcohe−1/λl,  (26)  where λl = νF Γl is the dimensionless coupling constant,  νF is the density of states at the Fermi level and Γl > 0  6  is given by  Γl =  �2l + 1  2  �  π  �  0  Γ(0)(θ)Pl(cos θ) sin θdθ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  (27)  Here Pl(cos θ) is the Legendre polynomial and Γ(0)(θ) the  bare interaction in the Cooper channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='24  Interaction function Γ(0)(θ) is determined by the ma-  trix elements of the fluctuation propagator ˆD(q, iν) eval-  uated at |q| = 2kF sin(θ/2) and iν → 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='17–19 The specific  form of Γ(0)(θ) depends on whether the chemical poten-  tial is in the first E1k or the second E2k band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Since  we have chosen the fairly low occupation number for the  conduction band, we find that the chemical potential lies  close to the top of the second band, E2k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' The fermionic  operators akσ, a†  kσ, which describe the quasiparticles in  this band are related to the original fermionic operators  ckσ and fkσ by the following relation:  ckσ = −vkakσ,  fkσ = ukakσ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  (28)  Here uk and vk are the coherence factors defined in the  Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' We introduce the two-particle correlation  function  Γαβγδ(12;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' 34) = −  �  ˆTτ  �  aα(1)aβ(2)a†  γ(3)a†  δ(4)  ��  , (29)  where averaging is performed over the action (10) and  aσ(1) = aσ(k1, τ1) etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Expanding the action up to the  second order in δΦ (22),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' we have found the following  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='expression for the interaction function:  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='Γ(0)(θ) = v4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='kF  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='��Ufc  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='�2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='Dϕfϕf(θ) + Ufc  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='2 Dϕfφ(θ) + Ufc  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='2 Dφϕf(θ) + Dφφ(θ)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='+ u4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='kF  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='Dλλ(θ) + Ufc  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='2 Dλϕc(θ)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='+Ufc  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='2 Dϕcλ(θ) +  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='�Ufc  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='�2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='Dϕcϕc(θ)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='+ 2u2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='kF v2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='kF  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='Ufc  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='2 Dλϕf(θ) +  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='�Ufc  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='�2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='Dϕcϕf(θ) + Ufc  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='2 Dϕcφ(θ) + Dλφ(θ)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='+2V 2Dρρ(θ)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='− 4ukF v3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='kF  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='V Dφρ(θ) + V Ufc  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='Dϕfρ(θ)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='− 4vkF u3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='kF  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='V Dλρ(θ) + V Ufc  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='Dϕcρ(θ)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='≡ Γcccc(θ) + Γffff(θ) + Γffcc(θ) + Γcccf(θ) + Γfffc(θ)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='(30)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='and the coherence factors ukF ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' vkF are evaluated at the  Fermi energy:  ukF =  V ρ  �  T 2  coh + (V ρ)2 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' vkF =  Tcoh  �  T 2  coh + (V ρ)2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  (31)  The subscripts in D refer to its matrix elements, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Dϕcλ  corresponds to the matrix element D32 etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' in accordance  with the definition (22).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  The relations (31) imply that in the vicinity of the  local moment regime nf ∼ 1/2, when Tcoh ≪ D we find  that ukF ∼ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Therefore, we can expect that the largest  contribution to the pairing interaction is provided by the  last term in (30), which is confirmed by the numerical  calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' This means that the long-range Coulomb  interactions should not significantly affect the value of  the transition temperature in the local moment regime:  in comparison to the contribution from the itinerant c-  states, the f-states provide significantly larger spectral  weight contribution to the pairing quasiparticles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  Our results of the numerical calculation of the super-  conducting critical temperature are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  First, we found that the largest critical temperature is  realized in the d-wave (l = 2) channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' In agreement with  the previous studies, we have found that the maximum  of the critical temperature remains weakly dependent on  the value of εf0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' At the same time we find that the crit-  ical temperature is decreasing with both an inclusion of  the plasmon field fluctuations as well as with an increase  in the values of Ufc, which is strike contrast with the  earlier results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='19  In order to get insight into the origin of this effect, we  fix the values of εf, ρ and µ to their corresponding values  at the maximum of Tc and consider how the interaction  (30) changes with the changes in Ufc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  First of all, we  recall that νF remains independent on the value of Ufc,  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' This result implies that Tcoh must also remain  essentially independent of Ufc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  Indeed, for the results  shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' 3 we found that Tcoh/D ≈ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='3 × 10−3 and  νF /ν0 ≈ 770 when Tc approaches its maximum value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  At the same time two largest contributions to the inter-  action kernel, Γfffc(θ) and Γffff(θ), do change with Ufc,  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  As it turns, however, their respective contri-  butions to the νF Γ(0)(θ) yield similar results and, as a  consequence, we find that νF Γ(0)(θ) is slightly increased  while the value of the maximum Tc is somewhat reduced  with an increase of Ufc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' In other words, valence fluctua-  tions produce superconductivity even in the case of when  Ufc can be neglected and the increasing the value of Ufc  reduced the value of the superconducting critical tem-  perature to an intermediate valence regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' The same  7  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='5  2  q/kF  10  0  10  20  30  40  Interaction kernel, νF Γ  (0)(θ)  νFΓfffc(θ), Ufc = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='5D  νFΓfffc(θ), Ufc = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='9D  νFΓffff(θ), Ufc = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='5D  νFΓffff(θ), Ufc = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='9D  νFΓ  (0)(θ), Ufc = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='5D  νFΓ  (0)(θ), Ufc = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='9D  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' 4: Interaction kernel as a function of momentum com-  puted without the effects of the plasmon fluctuations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' This re-  sult shows that although separate contributions to Γ(0), such  as the leading ones Γfffc and Γffff, do depend on the value of  Ufc, Γ(0) shows much weaker dependence on Ufc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Notably, as  the value of Ufc increases, the effective interaction becomes  more repulsive rendering the lower Tc in the d-wave channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  These results are found from the solution of the saddle-point  equations with kF = (2mEF /D)1/2 ≈ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='73, T = 10−5D,  N = 2, V = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='5D and the total particle number n = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='875.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  The values of the remaining parameters are as follows: for  Ufc = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='5D: εf0 = −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='40487D, εf = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='3461D, ρ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='2304  and µ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='3279D and for Ufc = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='9D and εf0 = −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='46915D  we found εf = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='50685D, ρ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='17148 and µ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='49712D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  argument can be implied to the effects of the long-range  Coulomb interactions, which also lead to the reduction  in the value of Tc as soon as the system in tuned away  from the local moment regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  CONCLUSIONS  In this paper we have presented the results of the calcu-  lations for the critical temperature of the superconduct-  ing transition in the extended Anderson lattice model,  which also included the long-range Coulomb repulsion  between the conduction electrons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Our work has been  motivated by recent discovery of the Ce-based cage com-  pounds CeNi2Cd20 and CePd2Cd20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' These compounds  have vanishing RKKY interactions and do not exhibit a  long-range order down to very low temperatures in the  millikelvin range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' We propose that d-wave superconduc-  tivity may develop in these compounds under an appli-  cation of the hydrostatic pressure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  We have also found that the long-range Coulomb repul-  sion leads to a decrease in the values of superconducting  critical temperature: in the local moment regime it has  small effect on the value of Tc due to the fact the most of  the spectral weight carried by the quasiparticles, which  form the Cooper pairs, is provided by the f-electrons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' In  the mixed-valent regime and for the low enough values  of Ufc the fluctuations of the plasmon field significantly  reduces the value of the superconducting critical temper-  ature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  ACKNOWLEDGMENTS  The authors would like to thank C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Almasan and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Maple for bringing their attention to this problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' We  acknowledge useful discussions with B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Fregoso and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  Li related to this project.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' This work was financially sup-  ported by the National Science Foundation grant NSF-  DMR-2002795.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  Appendix A: Effective action in the gaussian  approximation  We define the single-particle fermionic propagator in  the stationary point, which is obtained from (11) using  (12)  ˆG−1(k) =  �  iωn − ϵk − Ufcnf  −V ρ  −V ρ  iωn − εf  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  (A1)  Then the action at the stationary point is given by  S0 = −NTr log  �  −ˆG−1�  + iNλ  �  ρ2 − q0  �  − NUfc  4  ϕfϕc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  (A2)  Minimizing S0 with respect to the slave-boson fields  yields the equations (13).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  We can now expand action (10) up to the second order  in powers of δΦ (see (21) in main text).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' It follows  S = S0 + δS,  (A3)  where the fluctuation correction to the action δS is of the  form  δS = −NTr log  �  1 − ˆG ˆ  M  �  + N  �  k  �  (iλ)δρ(−k)δρ(k) + 2ρiδλ(−k)δρ(k)  �  −N  �  k  �Ufc  4 δϕf(−k)δϕc(k) + δ(iφ(−k))δ(iφ(k))  U(k)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  (A4)  8  Here matrix ˆ  M is defined by  ˆ  Mkk′ =  � Ufc  2 δϕf(k − k′) + δ(iφ(k − k′))  V δρ(k − k′)  V δρ(k − k′)  Ufc  2 δϕc(k − k′) + δ(iλ(k − k′))  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  (A5)  In the gaussian approximation we formally expand the  expression under the logarithm (A4)  − Tr log  �  1 − ˆG ˆ  M  �  =  ∞  �  n=1  1  nTr  �  ˆG ˆ  M  �n  (A6)  and retain only the term with n = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' As a result we find  the following expression for (A4):  δS = N  �  k  δˆΦ(−k)ˆSk ˆΦ(k),  (A7)  with ˆSk given by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' (23) in the main text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Upon in-  tegrating out the bosonic fields, it is straightforward to  check that the fluctuations give the correction of the or-  der of O(1/N) to the free energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  Appendix B: Polarization operators  The polarization operators which enter into equation  (23) are defined according to  Πcc(q) = T  �  iωn  �  k  Gcc(k + q)Gcc(k),  Πff(q) = T  �  iωn  �  k  Gff(k + q)Gff(k),  Πvv(q) = T  �  iωn  �  k  Gfc(k + q)Gcf(k),  Πcv(q) = T  �  iωn  �  k  Gcc(k + q)Gcf(k) = Πvc(−q),  Πfv(q) = T  �  iωn  �  k  Gff(k + q)Gfc(k) = Πvf(−q),  Πfc(q) = T  �  iωn  �  k  Gff(k + q)Gcc(k) = Πcf(−q).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  (B1)  Here q = (q, iνm), iνm = 2iπTm is the bosonic Matsub-  ara frequency, k = (k, iωn) and iωn = iπT(2n + 1) is the  fermionic Matsubara frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Functions Gaa(k) which  appear in this expressions are defined according to  Gcc(k + q) =  iωn − εf  (iωn − εk)(iωn − εf) − (V ρ)2  =  u2  k  iωn − E1k  +  v2  k  iωn − E2k  ,  Gff(k + q) =  iωn − εk  (iωn − εk)(iωn − εf) − (V ρ)2  =  v2  k  iωn − E1k  +  u2  k  iωn − E2k  ,  (B2)  The remaining correlator Gfc = Gcf is given by  Gfc(k + q) =  V 2  (iωn − εk)(iωn − εf) − (V ρ)2  =  V ρ  E1k − E2k  �  1  iωn − E1k  −  1  iωn − E2k  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  (B3)  In the expressions above we introduced the coherence  factors  u2  k = 1  2  �  1 + εk − εf  Rk  �  , v2  k = 1  2  �  1 − εk − εf  Rk  �  (B4)  and Rk = E1k−E2k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' For convenience, instead of the last  three polarization functions, we will consider  Π1(q, iνl) = 1  2 [Πcv(q, iνl) + Πvc(q, iνl)] ,  Π2(q, iνl) = 1  2 [Πfv(q, iνl) + Πvf(q, iνl)] ,  Π3(q, iνl) = 1  2 [Πcf(q, iνl) + Πfc(q, iνl)] .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  (B5)  The summations over the Matsubara frequencies can be  easily performed using (15).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' For example  T  �  iωn  (iωn+l − εk+q)  (iωn+l − E1k+q + µ)(iωn+l − E2k+q + µ)  (iωn − εf)  (iωn − E1k + µ)(iωn − E2k + µ)  = v2  k+qu2  k  [nF (E1k) − nF (E1k+q)]  iνl + E1k − E1k+q  + v2  k+qv2  k  [nF (E2k) − nF (E1k+q)]  iνl + E2k − E1k+q  + u2  k+qu2  k  [nF (E1k) − nF (E2k+q)]  iνl + E1k − E2k+q  + u2  k+qv2  k  [nF (E2k) − nF (E2k+q)]  iνl + E2k − E2k+q  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  (B6)  9  We also would like to remind the reader that all the ener-  gies entering into these expressions are taken relative to  the chemical potential µ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Formally, this is accomplished  by including the chemical potential into the definition of  the Fermi distribution function, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' (15).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  1 V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Burnett, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Yazici, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' White, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Dilley, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Friedman,  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Brandom, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Maple, “Structure and physical prop-  erties of RT2Cd20 (R=rare earth, T=Ni, Pd) compounds  with the CeCr2al20-type structure,” Journal of Solid State  Chemistry, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' 215, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' 114–121, jul 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  2 D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Yazici, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Yanagisawa, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' White, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  Maple, “Nonmagnetic ground state in the cubic com-  pounds PrNi2Cd20 and PrPd2Cd20,” Physical Review B,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' 91, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' 115136, mar 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  3 T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Onimaru, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Matsumoto, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Inoue, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Umeo,  Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Saiga, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Matsushita, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Tamura, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Nishimoto, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Ishii,  T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Suzuki, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Takabatake, “Superconductivity and  structural phase transitions in caged compounds RT2Zn20  (r = La, Pr, t = Ru, Ir),” Journal of the Physical Society  of Japan, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' 79, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' 033704, Mar 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  4 S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Niemann and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Jeitschko,  “Ternary aluminides  AT2Al20 (A = rare earth elements and uranium:  T =  Ti, Nb, Ta, Mo, and W) with CeCr2Al20-type structure,”  Journal of Solid State Chemistry, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' 114, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' 337–341,  Feb 1995.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  5 M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Kangas, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Schmitt, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Sakai, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Nakatsuji, and  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Chan, “Structure and physical properties of single  crystal PrCr2Al20 and CeM2Al20 (M=V, Cr): A compari-  son of compounds adopting the CeCr2al20 structure type,”  Journal of Solid State Chemistry, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' 196, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' 274–281,  Dec 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  6 Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Isikawa, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Mizushima, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Kumagai, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Kuwai,  “Dense Kondo effect in caged compound CeRu2Zn20,”  Journal of the Physical Society of Japan, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' 82, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' 083711,  Aug 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  7 P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Swatek and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Kaczorowski, “Intermediate valence be-  havior in the novel cage compound CeIr2Zn20,” Journal of  Physics: Condensed Matter, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' 25, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' 055602, Jan 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  8 B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' White, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Yazici, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Ho, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Kanchanavatee,  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Pouse, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Fang, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Breindel, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Friedman, and  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Maple, “Weak hybridization and isolated localized  magnetic moments in the compounds CeT2Cd20(T = Ni,  Pd),” Journal of Physics:  Condensed Matter, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' 27,  p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' 315602, Jul 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  9 P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Anderson, “Antiferromagnetism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' theory of superex-  change interaction,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' 79, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' 350–356, Jul  1950.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  10 M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Ruderman and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Kittel, “Indirect exchange cou-  pling of nuclear magnetic moments by conduction elec-  trons,” Physical Review, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' 96, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' 99–102, oct 1954.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  11 T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=" Kasuya, “A theory of metallic ferro- and antiferromag-  netism on zener's model,” Progress of Theoretical Physics,  vol." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' 16, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' 45–57, jul 1956.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  12 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Yosida, “Magnetic properties of Cu-Mn alloys,” Physi-  cal Review, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' 106, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' 893–898, jun 1957.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  13 A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Konic, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Zhu, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Breindel, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Deng, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Moir,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Maple, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Almasan, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Dzero, “Vanishing  rkky interactions in ce-based cage compounds,” pre-print  arXiv:, December 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  14 M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Maple, “Dependence of s − f exchange on atomic  number in rare-earth dialuminades,” Solid State Comm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=',  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' 8, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' 1915–1917, May 1970.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  15 V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Barzykin and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Gor’kov, “Competition between  phonon superconductivity and Kondo screening in mixed  valence and heavy fermion compounds,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' B,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' 71, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' 214521, Jun 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  16 S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  Maiti  and  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  Chubukov,  “Superconductivity  from repulsive interaction,” AIP Conference Proceedings,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' 1550, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' 3–73, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  17 M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Lavagna, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Millis, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Lee, ”d -wave super-  conductivity in the large-degeneracy limit of the Anderson  lattice,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' 58, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' 266–269, Jan 1987.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  18 A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Houghton, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Read, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Won, “Charge fluctuations,  spin fluctuations, and superconductivity in the anderson  lattice model of heavy-fermion systems,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' B,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' 37, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' 3782–3785, Mar 1988.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  19 Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Onishi and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Miyake, “Enhanced valence fluctuations  caused by f-c Coulomb interaction in Ce-based heavy elec-  trons: Possible origin of pressure-induced enhancement of  superconducting transition temperature in CeCu2Ge2 and  related compounds,” Journal of the Physical Society of  Japan, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' 69, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' 12, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' 3955–3964, 2000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  20 P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Coleman, Heavy Fermions: Electrons at the Edge of  Magnetism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' John Wiley & Sons, Ltd, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  21 S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Fischer, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Hecker, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Hoyer, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Schmalian, “Short-  distance breakdown of the Higgs mechanism and the ro-  bustness of the BCS theory for charged superconductors,”  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' B, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' 97, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' 054510, Feb 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  22 M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Dzero, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Xia, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Galitski, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Coleman, “Topo-  logical Kondo insulators,” Annual Review of Condensed  Matter Physics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' 7, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' 249–280, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  23 R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Flint, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Dzero, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Coleman, “Heavy electrons  and the symplectic symmetry of spin,” Nat Phys, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' 4,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' 643–648, 08 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  24 A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Abrikosov, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Gorkov, and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content=' Dzyaloshinski,  Methods of Quantum Field Theory in Statistical Physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
+page_content='  Dover, 1977.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mtE3T4oBgHgl3EQfigpW/content/2301.04580v1.pdf'}
diff --git a/n9E_T4oBgHgl3EQf8Byb/vector_store/index.faiss b/n9E_T4oBgHgl3EQf8Byb/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..be1ebe0242cf9d711f06956194bfa5f06ed01088
--- /dev/null
+++ b/n9E_T4oBgHgl3EQf8Byb/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:a57337235427c07500dd17283c0370746efb2362e38a23952962ea871d3a1f38
+size 3407917
diff --git a/nNFIT4oBgHgl3EQfuCsf/content/2301.11341v1.pdf b/nNFIT4oBgHgl3EQfuCsf/content/2301.11341v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..fe8cf4d0da5989f4609dc07ac10f016c3e231d21
--- /dev/null
+++ b/nNFIT4oBgHgl3EQfuCsf/content/2301.11341v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:e6c8f54bf9ce2efe547975f203a3f92225ebde799b593f1a235e3fa9222c95f1
+size 766960
diff --git a/nNFIT4oBgHgl3EQfuCsf/vector_store/index.faiss b/nNFIT4oBgHgl3EQfuCsf/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..8790e445b66bcd0d5be3c02bdda4c1a3969a76c1
--- /dev/null
+++ b/nNFIT4oBgHgl3EQfuCsf/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:c67d893a6e0c1daa9e6e9ca8160c8d713f7fdbb8cd4f1165a194ddf08641d73f
+size 2490413
diff --git a/nNFIT4oBgHgl3EQfuCsf/vector_store/index.pkl b/nNFIT4oBgHgl3EQfuCsf/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..82b9e6138d3e5d03e6092ef404a2e48ce25b8fd3
--- /dev/null
+++ b/nNFIT4oBgHgl3EQfuCsf/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:539e700b93c45c535520917ca6d03fd78290995c37c194355d44a6e8f15a0258
+size 93980
diff --git a/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf b/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..a7ae3018ff1d39bc4b0eef51582cec897e1aca46
--- /dev/null
+++ b/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:dce70d16d55d24ce439aac7a5c9a895aee464de155cd35b6ac4762b50d8eb3cd
+size 1103839
diff --git a/ndE1T4oBgHgl3EQfhgRQ/vector_store/index.faiss b/ndE1T4oBgHgl3EQfhgRQ/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..870a6c1f526e8014468a998c864548c136139148
--- /dev/null
+++ b/ndE1T4oBgHgl3EQfhgRQ/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:4b18ff7399fd1832517bf407420fcebc52ed6c2692fbdc1e4f7c09494ed8a8db
+size 3276845
diff --git a/ndE1T4oBgHgl3EQfhgRQ/vector_store/index.pkl b/ndE1T4oBgHgl3EQfhgRQ/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..030bd8e292be319aaabd4babd895113cb9814b7b
--- /dev/null
+++ b/ndE1T4oBgHgl3EQfhgRQ/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:0a16cf819a6a293200269eb2486328939b72d124a1996b5c81d7ecb3074a2cc5
+size 109934
diff --git a/ndE3T4oBgHgl3EQf7Asa/vector_store/index.faiss b/ndE3T4oBgHgl3EQf7Asa/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..65fa1dfea1849bad48b365d3e19d074556fd31a5
--- /dev/null
+++ b/ndE3T4oBgHgl3EQf7Asa/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:3c06673c594e31798c07d6a9652c0d30cadcb88b6f974c1dc069bf7c2c30a0ad
+size 3407917
diff --git a/oNAyT4oBgHgl3EQfY_dp/content/tmp_files/2301.00214v1.pdf.txt b/oNAyT4oBgHgl3EQfY_dp/content/tmp_files/2301.00214v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..81e7daf1b5b0ed02a7006153e8b67e727987ad5a
--- /dev/null
+++ b/oNAyT4oBgHgl3EQfY_dp/content/tmp_files/2301.00214v1.pdf.txt
@@ -0,0 +1,4244 @@
+ 
+ 
+ 
+ 
+Understanding the Role of Non-Fullerene Acceptors Crystallinity 
+on the Charge Transport Properties and Performance of Organic 
+Solar Cells 
+Pierluigi Mondelli,a,d,†,* Pascal Kaienburg,a Francesco Silvestri,b Rebecca Scatena,a Claire 
+Weltonc, Martine Grandjean,d Vincent Lemaur,e Eduardo Solano,f Mathias Nyman,g Peter N. 
+Horton,h Simon J. Coles,h Esther Barrena,b Moritz Riede,a Paolo Radaelli,a David Beljonne,e G. 
+N. Manjunatha Reddyc and Graham Morsed,† 
+The acceptor crystallinity has long been associated with favourable organic solar cells (OSCs) properties such as high mobility 
+and Fill Factor. In particular, this applies to acceptor materials such as fullerene-derivatives and the most recent Non-
+Fullerene Acceptors (NFAs), which are now surpassing 19% of Power Conversion Efficiency. Despite these advantages are 
+commonly attributed to their 3-dimensional crystal packing motif in the single crystal, the bridge that links the acceptor 
+crystal packing from single crystals to solar cells has not clearly been shown yet. In this work, we investigate the molecular 
+organisation of seven NFAs (o-IDTBR, IDIC, ITIC, m-ITIC, 4TIC, 4TICO, m-4TICO), following the evolution of their packing motif 
+in single-crystals, powder, and thin films made with pure NFAs and donor:NFA blends. We observed a good correlation 
+between the NFA single crystal packing motif and their molecular arrangement in the bulk heterojunction. The NFA packing 
+motif affects the material’s propensity to form highly crystalline domain in the blend. We specifically found that 3D reticular 
+packing motifs show stronger ordering than 0D herringbone ones. However, the NFA packing motif is not directly correlating 
+with device performance parameters: Although higher NFA crystallinity yields higher mobility, we found the domain purity 
+to be more important for obtaining high efficiency organic solar cells by governing bimolecular recombination.
+Introduction 
+The recent surge in Organic Solar Cells (OSCs) performance, now 
+exceeding 19%,1, 2 results from the development of Non-
+Fullerene Acceptors (NFAs).3-8 Previous work centred around 
+fullerene based acceptors has drawn a connection between 
+molecular 
+design/shape 
+to 
+the 
+formation 
+of 
+highly-
+interconnected acceptor domains and charge percolation 
+pathways towards the electrodes, resulting in superior charge 
+transport properties and high Fill Factors (FF) in OSC.9-12 
+Moreover, recent works are attributing the improved 
+performance and charge transport of state of the art NFAs to 
+their 3D-interconnected crystal packing motif (Figure 1).5, 7-9, 13-
+17 It is thus important to construct a clear understanding based 
+on concrete evidence of the relationship between the NFA 
+molecular packing and crystallinity in the bulk heterojunction 
+and the charge transport properties and performance of 
+organic solar cells. 
+A growing variety of NFA single-crystals is now being reported,8, 
+14, 15, 18-31 from which useful information on the molecular 
+packing can be derived. Still, bridging the molecular scale from 
+molecular packing in single-crystals to the one found in Bulk 
+Heterojuction (BHJ) needs more detailed investigations.10, 31, 32 
+The identification of the packing motif of the NFA within a 
+donor:acceptor blend is a challanging task, yet the structural 
+analysis is commonly based on Grazing Incidence Wide Angle X-
+Ray Scattering (GIWAXS) patterns that lack of enough 
+diffraction features for the structural determination. The 
+analysis of the main Bragg peaks of the NFA, often referred as 
+the lamellar (100) and the π-π stacking (010) distances,33-35 is 
+routinely considered enough to draw conclusions. Misleading 
+results can, however, arise from the similar (if not overlapping) 
+spectral features of the donor and acceptor components in the 
+q-space, the typical peak broadening of organic compounds 
+reflecting a high degree of flexibility, the presence of rotational 
+isomers, polymorphism,36, 37 and a general lack of long-range 
+crystalline order.34  
+In this work, we used an extensive set of both experimental and 
+theoretical approaches to study the molecular packing and 
+morphology of a specific set of common NFAs (o-IDTBR, IDIC, 
+ITIC, m-ITIC, 4TIC, 4TICO, m-4TICO, whose structures are shown 
+in Figure 2), by means of single-crystal X-Ray Diffraction (XRD), 
+powder XRD and Le Bail refinement, GIWAXS, Atomic Force 
+Microscopy (AFM), crystal lattice simulations, ss-NMR, and 
+Gauge Including Projected Augmented Wave (GIPAW) DFT 
+calculations. Our aim was to analyse the NFA molecular packing, 
+a. Clarendon Laboratory, Department of Physics, University of Oxford, Parks Road, 
+Oxford, OX1 3PU, United Kingdom. E-mail: pierluigi.mondelli@physics.ox.ac.uk 
+b. Institut de Ciència de Materials de Barcelona, ICMAB-CSIC, Campus UAB, 08193 
+Bellaterra, Spain 
+c. University of Lille, CNRS, Centrale Lille, Univ. Artois, UMR 8181- UCCS - Unité de 
+Catalyse et Chimie du Solide, F-59000 Lille, France 
+d. Merck Chemicals Ltd, Chilworth Technical Centre, University Parkway, 
+Southampton, SO16 7QD, United Kingdom 
+e. Laboratory for Chemistry of Novel Materials, University of Mons, Place du Parc, 
+20, 7000 Mons (Belgium) 
+f. NCD‐SWEET beamline, ALBA Synchrotron Light Source, Cerdanyola del Vallès, 
+08290 Spain 
+g. Physics, Faculty of Science and Engineering, Åbo Akademi University, 20500 
+Turku, Finland 
+h. EPSRC Crystallographic Service, Department of Chemistry, University of 
+Southampton, Highfield, SO17 1BJ, UK 
+*Current address: Italian Institute of Technology, Printed and Molecular 
+Electronics, Via Pascoli 70/3, 20133 Milan, Italy 
+† Email: pierluigi.mondelli@gmail.com, graham.morse@gmail.com 
+
+ 
+ 
+with a special focus on the structural evolution from single 
+crystals to solar cells. We studied the molecular arrangement 
+from single crystals, to powders, then thin films and finally 
+morphology in the bulk heterojunction (BHJ) to bring important 
+insights into the NFA arrangement in the BHJs. We analysed the 
+most relevant NFA packing motifs and polymorphs, discussing 
+their role in the solar cell morphology, current-voltage 
+performance, and charge transport properties, such as electron 
+mobility and bimolecular recombination, by means of photo-
+CELIV (Charge Extraction Linear Increasing Voltage) and MIS-
+CELIV (Metal-Insulator-Semiconductor-Charge Extraction Linear 
+Increasing Voltage). 
+Experimental 
+General Characterisation 
+UV-Vis absorption spectra were recorded on an OceanOptics QE 
+PRO spectrometer using a tungsten halogen light source (HL-
+2000-FHSA from OceanOptics). The HOMO levels of the 
+compounds in thin films were obtained by measuring the film 
+photoemission current onset with the Air Photoemission 
+Spectroscopy module (APS02) of the Kelvin Probe from KP 
+Technology Ltd. The Kelvin Probe was equipped with a 2.0 mm 
+diameter tip coated with gold alloy, a UV deuterium lamp, and 
+a monochromator (range 3.44-3.88 eV). LUMO levels were 
+estimated by adding the optical bandgap (determined from the 
+onset of the UV-Vis absorption) to the measured HOMO. 
+Single-crystal X-ray diffraction data were collected on a Rigaku 
+Oxford Diffraction Supernova diffractometer equipped with 
+micro-focus sealed (Mo-Kα) X-ray Source, CCD plate detector 
+and Oxford Cryostream N2 flow cryostat. The samples were 
+mounted on Kapton loops from the solution and shock-cooled 
+to 173.0(2) K or 100.0(2) K. Cell indexing and peak integration 
+were performed with CrysAlisPro. Structural solution and 
+refinement were carried out with ShelxT and ShelxL, 
+respectively. 
+Powder X-ray diffraction was performed using a PANalytical X'Pert 
+PRO diffractometer with Cu -Kα radiation. During the measurement, 
+the sample was kept at room temperature and under ambient 
+conditions. 
+ 
+GIWAXS 
+The GIWAXS experiments were carried out at NCD-SWEET beamline 
+at ALBA synchrotron (Beamtime ID: 2019093873). A monochromatic 
+X-ray beam with a photon energy of 12.4 keV was set using a Si (1 1 
+1) channel cut monochromator, further collimated with an array of 
+beryllium lenses. The GIWAXS maps were recorded with a Rayonix LX 
+255-HS detector, consisting of a pixel array of 960 × 2880 pixels of 
+88.54 × 88.54 μm2 (H × V) for the binning employed. The samples 
+were thermally annealed before the measurements at the optimised 
+temperature for the solar cell performance (see below) using a 
+hotplate in air. GIWAXS frames were acquired near the critical angle 
+of the glass substrate (ca. 0.15° for the X-ray wavelength employed), 
+penetrating a depth of 11 nm for the layer of interest38 while 
+minimizing the contribution of the substrate.‡ The recorded 2D 
+scattering patterns were analysed using a home-made python 
+routine based on pyFAI (the Fast Azimuthal Integration Python 
+library).39 GIWAXS images are in logarithmic scale, ranging from dark 
+blue (low intensity) to yellow (high intensity). The in-plane and out-
+of-plane profiles were obtained by integrating the diffraction 
+intensity in rectangular areas centred at 𝜒=0° and 𝜒=90° from 𝜒-q 
+images (scattering intensity as a function of the azimuthal angle). The 
+scattering peaks of the bulk structure were compared to the 
+experimental data using SimDiffraction, a MatLab code for simulating 
+the film diffraction pattern for a given crystal structure and 
+orientation.40 For each NFA, The simulations were performed by 
+choosing a specific NFA orientation with respect to the substrate 
+(typically in-plane and out-of-plane). The Miller indices (h k l) 
+associated with the NFA packing direction were determined by 
+Mercury41 and used as input parameters for the simulations. A better 
+fit between simulated and experimental GIWAXS was obtained when 
+Figure 1. Sketch of the different molecular packing motifs observed in Acceptor-Donor-Acceptor (A-D-A) type NFAs crystal structures and labelled according to the dimensionality 
+of the π-π stacking. 
+R
+D
+A-D-A Structure
+ID
+IT
+4T
+IC
+BR
+PhC6
+m-PhC6
+PhOC6
+m-PhOC6
+R group
+D unit
+A unit
+NFA
+D unit
+A unit
+R group
+ITIC
+IT
+IC
+PhC6
+m-ITIC
+IT
+IC
+m-ITIC
+4TIC
+4T
+IC
+PhC6
+4TICO
+4T
+IC
+PhOC8
+m-4TICO
+4T
+IC
+m-PhC8
+IDIC
+ID
+IC
+C6
+o-IDTBR
+ID
+BR
+C8
+Molecular Packing
+0D - Herringbone
+2D - Brickwork
+3D - Reticular
+A
+A
+R
+C6 = C6H13
+C8 = C8H17
+
+ 
+ 
+using the unit cell parameters obtained by Le Bail refinement (see 
+below) as input for the simulations. 
+ 
+Solid-state NMR spectroscopy  
+For ssNMR experiments, O-IDTBR powder was packed into a 1.3 
+mm (outer diameter) rotor. All 1D 1H and 13C20, and 2D 1H-1H 
+and 1H-13C correlation NMR experiments were carried out on a 
+Bruker Avance Neo (18.8 T) spectrometer using a 1.3 mm 
+double resonance H-X probehead tuned to 
+1H (Larmor 
+frequency, 800.13 MHz) and 13C (Larmor frequency, 201.2 MHz) 
+nuclei. Unless otherwise states, the Magic Angle Spinning (MAS) 
+frequency was 50 kHz in all cases. The nutation frequencies for 
+1H and 13C were 100 kHz and 90 kHz, corresponding to 90o pulse 
+durations of 2.5 and 2.75 s, respectively. The longitudinal 
+relaxation time (T1) of 1H was determined to be 3 s based on 
+inversion recovery measurements and analyses. 1D 1H MAS 
+NMR spectrum was acquired using 16 co-added transients. A 2D 
+1H-1H 
+double-quantum 
+(DQ)-single-quantum 
+(SQ) 
+NMR 
+spectrum was acquired using Back-to-Back (BaBa) sequence at 
+fast MAS,42 using a rotor-synchronized t1 increment of 20 µs 
+corresponding to one rotor period (r). The indirect 1H DQ 
+dimension was acquired using 256 t1 increments, each with 16 
+co-added transients, corresponding to a total experimental 
+time of ~4 h. 1H detected 2D 1H-13C heteronuclear correlation 
+(HETCOR) spectra were acquired with 0.1 ms and 3 ms of CP 
+contact time and the indirect 13C dimension was acquired using 
+140 t1 increments, each with 32 co-added transients, 
+corresponding to a total experimental time of 8 h each.  
+ 
+Atomic Force Microscopy 
+The thin films were investigated by AFM both in contact and 
+dynamic modes using a commercial head and control unit from 
+Nanotec Electronica. The used thermal annealing protocol was 
+the one optimized for the devices (see Table S10). For each 
+sample, after each annealing step, different spots of the surface 
+were imaged (at several image sizes) to have a statistical validity 
+of the measurements. The images presented in the article are 
+chosen as high-resolution representative images of the surface. 
+The estimation of the root mean square (RMS) roughness was 
+done selecting about 6 contact mode images (30x30 and 50x50 
+µm²) for each temperature. Si3N4 V-shaped cantilevers (Veeco) 
+with the nominal force constant ranging between 0.03 and 0.5 
+N/m were employed for the contact mode, while Cr/Pt-coated 
+silicon tips on rectangular cantilevers (BudgetSensors) with a 
+nominal resonance frequency of 75 kHz and a force constant of 
+3 N/m were used for the dynamic mode. The open-source 
+Gwyddion software was used to analyse all the presented AFM 
+images,43 including the domain size calculation which were 
+done using the watershed algorithm.44 The input parameters 
+used for the watershed analysis can be found in the Supporting 
+Information (pages S20-S25). 
+ 
+Solar Cells Fabrication and Characterisation 
+Inverted-architecture organic solar cells were fabricated by 
+blade coating of the organic layers on Indium Tin 
+Oxide(ITO)/glass pre-patterned 5x5 cm2 substrates (Zencatec 
+Limited). A detailed description of the interlayers and 
+electrodes fabrication, along with the experimental description 
+of the current-voltage (I-V) measurements can be found in the 
+experimental section of a recent work from our group.36 
+Aluminium-doped zinc oxide from Avantama (N-21X-Slot) was 
+Figure 2. Structure of an Acceptor-Donor-Acceptor (A-D-A) NFA with its building blocks on the top left. The NFAs studied 
+in this work (table on the top right) are identified with their chemical subunits (A, D and R groups) whose chemical 
+structures are also shown. 
+R
+D
+A-D-A Structure
+ID
+IT
+4T
+IC
+BR
+PhC6
+m-PhC6
+PhOC6
+m-PhOC6
+R group
+D unit
+A unit
+NFA
+D unit
+A unit
+R group
+ITIC
+IT
+IC
+PhC6
+m-ITIC
+IT
+IC
+m-ITIC
+4TIC
+4T
+IC
+PhC6
+4TICO
+4T
+IC
+PhOC8
+m-4TICO
+4T
+IC
+m-PhC8
+IDIC
+ID
+IC
+C6
+o-IDTBR
+ID
+BR
+C8
+Molecular Packing
+0D - Herringbone
+2D - Brickwork
+3D - Reticular
+A
+A
+R
+C6 = C6H13
+C8 = C8H17
+
+ 
+ 
+used for the electron transporting layer, while PEDOT:PSS 
+(Clevios Al 4083 from Heraeus) for the hole transporting layer. 
+All the NFAs were supplied by 1-Material Inc., with the only 
+exception of 4TICO (Merck KGaA). For the active layer, PBTZT-
+stat-BDTT-8 (Merck KGaA) was used as the donor material45 in 
+combination with the NFAs listed in Figure 2. Each blend was 
+dissolved in a 1:1.3 ratio (by weight) and 80 nm thick layers‡‡ 
+were processed from a 23 mg/ml solid content o-xylene 
+solution, without the use of additional additives. The blade 
+speed was adjusted between 7 to 13 mm s-1 to reach the desired 
+thickness with a 100 µm blade gap and 70 µL cast volume. 
+Casting plate temperature was varied between 60°C and 80°C 
+and the as-cast devices were further annealed at temperatures 
+ranging from 100°C to 140°C on a hot plate in air following the 
+optimisation protocol. A 100 nm silver back electrode was 
+thermally evaporated on top of the hole transporting layer, 
+under a pressure of 2x10-6 mbar at a rate of 1 Å/s. Solar cells 
+have a device area of ∼ 8.5 mm2, as determined from the 
+geometrical overlap between cathode and anode. 
+  
+Photo-CELIV 
+Photo-CELIV was performed using the Transient Measurement 
+Unit by Automatic Research. A 655 nm laser pulse (5 µs long) 
+was used to photo-generate charges into ∼ 8.5 mm2 area solar 
+cells. The linear increasing voltage ramp range was 0 - 1.5 V and 
+10 µs long. The delay time between the laser pulse and the 
+voltage ramp was varied between 0.1 to 100 µs, during which a 
+constant pre-bias voltage (close to VOC) was applied to limit the 
+charge injection. The charge mobility was determined by using 
+eq.(1) of ref.46 on the 30 µs long delay time data collection. The 
+bimolecular recombination coefficient was calculated using 
+eq.(2) of ref.47  
+ 
+MIS-CELIV 
+MIS-CELIV48 was performed with a PAIOS system from Fluxim 
+AG, Switzerland. The layer stack was 
+ITO/AZO/active 
+layer/MgF2/Ag with an insulating 50 nm MgF2 layer that blocks 
+injection of holes so that the electron mobility is obtained. The 
+chosen thickness balances the layer's insulating properties with 
+its capacitance in relation to the absorber’s capacitance. The 
+other layers are processed as for the solar cell devices with 
+some deviations in the annealing protocol discussed in the 
+Support Information. A small device area of ~1mm2 was chosen 
+to minimize RC effects. The offset voltage was typically varied 
+between 0V and 8V and the ramp rate between 50 V/ms and 
+1600 V/ms. The latter allowed to account for injection barrier 
+effects49. The analysis was carried out following the diffusion-
+corrected eq.(11) of ref.49 with saturation and geometric 
+displacement current densities extracted from the CELIV curves.  
+ 
+Density Functional Theory calculations 
+Periodic DFT calculations on the o-IDTBR crystalline structure 
+have been performed using the CASTEP module with the 
+Materials Studio software. All calculations have been carried 
+out with the PBE GGA functional, a plane-wave energy cutoff of 
+50 Rydbergs (680 eV) and a k-point spacing of 0.05Å-1.50 The 
+crystalline structure of o-IDTBR has first been full relaxed using 
+the Tkatchenko-Scheffler dispersion correction method, 
+optimizing both all atomic positions within the cell and unit cell 
+parameters. The resulting DFT-optimized cell parameters (a = 
+13.8706Å, b = 15.5913Å, c = 32.6925Å,  = 90°,  = 96.0529,  = 
+90°) are in excellent agreement with the measured 
+crystallographic data in Table 1. NMR calculations have then 
+been performed on the optimized crystal structure using the 
+Gauge-Including Projector Augmented-Wave method (GIPAW); 
+reference shieldings of 31.09 and 179.02 ppm were used for 1H 
+and 13C, respectively. 
+Results and Discussion 
+Structural Analysis 
+A common way of classifying the organic semiconductor packing 
+motif is by observing their π-π stacking dimensionality.18, 51-54 A-D-A 
+molecules (Figure 2) in particular, can form highly interconnected 
+domains through intermolecular interactions between the acceptor 
+units (A units) of adjacent molecules.18, 55 The percolation pathway 
+that forms through π-π stacking can develop along multiple 
+directions of the crystalline domain. Molecules can arrange through 
+brickwork pattern with 2D percolation pathways, or through the so-
+called "reticular" packing motif which is characterised by 3D-
+interconnected domains. For herringbone crystal structures the 
+molecular backbones of adjacent units are orthogonal, therefore lack 
+π-π stacking (Figure 1).  
+To reveal the NFA packing within the BHJ we started our 
+investigations from single crystals, which represent the perfect 
+platform to explore the influence of the solid-state arrangement on 
+the charge transport. Most of the crystal structures analysed in this 
+work were previously resolved by our group,18 while others were 
+found in literature. As indicated in Table 1, some NFAs showed 
+polymorphism. For instance, ITIC single crystals can be found to be 
+either 0D herringbone or 2D brickwork motifs and m-4TICO also 
+presents two different unit cells.  
+Single crystals represent the NFA molecular ordering of high purity 
+and large millimetre sized crystal grown from controlled conditions 
+(solvent vapour diffusion, see reference18) and measured by XRD in 
+a low-temperature (100 K) environment. Thus, it is possible to 
+observe substantial differences in the molecular arrangement as we 
+deviate from such ideal systems towards the BHJ. Therefore, we 
+wanted to understand how the crystal packing changes by raising the 
+temperature to ambient conditions (200 K shift between single 
+crystal and powder XRD) and by disrupting the ideal growth 
+conditions and long-range crystallinity of NFA single crystals. As an 
+intermediate step, ss-NMR and XRD of purified NFA powders were 
+performed. In the main text, we limit our observations on o-IDTBR, 
+extending the analysis and discussion to the other materials in the 
+Supplementary Information (pages S6-S9). 
+ 
+
+ 
+ 
+Table 1. Crystallographic information of the NFA crystal structures available for the materials analysed in this work. 
+From Single Crystals to Powder 
+o-IDTBR has a 3D reticular packing motif in the single crystal,56 
+characterised by close-contacts between the electron accepting 
+units (A units) of tilted adjacent molecules (Figure 1). To 
+understand if this packing geometry is retained in powder 
+samples, we performed X-Ray Diffraction and ss-NMR 
+measurements. The powder diffractogram showed a long-range 
+crystallinity with well-defined Bragg peaks in the low-angle 
+region (Figure 3a). A partial agreement exists between the 
+experimental data and the simulated 1D pattern of the single 
+crystal structure, yet a certain mismatch between the positions 
+for most of the reflections suggests that a slightly different unit 
+cell is formed in powder. This can occur because of the 
+CCDC 
+Identifier 
+Molecul
+e 
+Motif 
+π-π 
+a (Å) 
+b (Å) 
+c (Å) 
+𝛼 (deg) 
+𝛽 (deg) 
+𝛾 (deg) 
+Volume 
+(Å3) 
+FOSPOV56 
+o-IDTBR 
+reticular 
+3D 
+13.7663(2) 
+15.8103(17) 
+32.7146(3) 
+90 
+96.2928(12) 
+90 
+7077.43(15) 
+YEBKEY19 
+4TIC 
+reticular 
+3D 
+13.969(7) 
+17.144(9) 
+17.970(10) 
+104.668(16) 
+109.998(17) 
+96.169(14) 
+3822.08 
+VUBJIO18 
+m-4TICO 
+brickwork 
+2D 
+8.6526(3) 
+16.4878(8) 
+18.0435(8) 
+114.697(5) 
+103.822(4) 
+90.890(4) 
+2251.45(19) 
+This work 
+m-4TICO 
+brickwork 
+2D 
+8.7845(7) 
+15.3726(13) 
+16.7896(13) 
+67.136(7) 
+85.678(7) 
+79.630(7) 
+2054.98 
+VUBJOU18 
+m-ITIC 
+brickwork 
+2D 
+8.7454(13) 
+18.872(2) 
+25.2647(18) 
+87.770(8) 
+88.724(9) 
+78.001(12) 
+4075.1(9) 
+VUBKAH18 
+IDIC 
+brickwork 
+2D 
+8.6679(4) 
+12.5073(7) 
+13.5784(6) 
+72.096(4) 
+75.545(4) 
+88.839(4) 
+1353.88(12) 
+VUBJEK18 
+4TICO 
+herringbone 
+0D 
+15.2836(2) 
+20.0101(5) 
+29.3242(6) 
+90 
+89.997(2) 
+90 
+8968.1(3) 
+KIZSUK20 
+ITIC 
+brickwork 
+2D 
+8.420(6) 
+23.019(17) 
+23.126(17) 
+101.780(10) 
+95.319(10) 
+91.105(14) 
+4366(5) 
+HEHQUJ01
+18 
+ITIC 
+herringbone 
+0D 
+14.9009(7) 
+15.5043(4) 
+18.1199(5) 
+99.309(2) 
+101.541(3) 
+108.366(3) 
+3777.2(2) 
+Figure 3 a) Powder XRD diffractogram overlaid to the simulated powder pattern of the single crystal structure. The inset is showing the progressive improvement of the fitting 
+from the original fit to manual and Le Bail refinement. c) Periodic DFT optimised crystal structure and highlighted backbone-backbone (red boxes) and backbone-sidechains 
+interaction (blue boxes). b-d) DFT calculated 2D plots of the 1H-1H and 1H-13C chemical shifts (red circles) overlaid on the experimental 1H-1H double-quantum-single-quantum 
+(DQ-SQ) correlation and 1H-13C heteronuclear correlation spectra (contours), respectively. The dashed blue rectangles indicate the minor changes in the backbone-sidechain 
+interactions when comparing the crystalline to powder form, meaning that the π-π interactions (along with the packing motif) remains substantially unvaried.  
+
+a)
+b)
+Data
+Initial Fit
+Manual Fit
+Le Bail
+10
+(01 1)
+28
+Gaf
+HDQ chemical shift(ppm)
+0
+8
+824
+6
+20
+4
+4
+(110)
+Inisal FaManuat Fit
+LeBa
+8
+2
+(0.1.2)
+0
+12
+-2
+16
+6
+8
+10
+12
+14
+20 (°)
+10
+8
+6
+2
+0
+"HSQchemicalshift(ppm)
+c)
+(p
+0
+sideview
+20
+40
+chemicalshift (ppm)
+60
+80
+100
+backbone-sidechaininteractions
+120
+140
+topview
+160
+180
+200
+10
+8
+1
+6
+1
+4
+2
+1
+0
+1
+backbone-backboneinteractions
+Hchemicalshift(ppm) 
+ 
+temperature shift (200 K) between the single crystal and 
+powder XRD measurements,§ which can impact the long-range 
+order, the local structures and packing interactions. In a first 
+approximation,§§ we manually solved the reciprocal-space 
+metric tensor equation for monoclinic structures57 to derive the 
+lattice parameters from the experimental data (Table S1). The 
+spectral agreement between the “manually-refined” simulated 
+diffractogram and the experimental data improves (Figure 3a), 
+as the Goodness of Fit (GOF), Chi2 and residuals (wR) parameters are 
+now reduced. This means that a better fit is obtained after the 
+manual refinement, and therefore it is reasonable to assume a 
+structural agreement between the two phases. A further 
+confirmation is obtained when the lattice parameters and unit 
+cell angles are derived through Le Bail refinement, suggesting that 
+the structure undergoes a volumetric expansion from single 
+crystal to powder phase (Table S1), possibly resulting from the 
+different temperatures of the measurements (see Supporting 
+Information, Figure S5 and Table S2) causing subtle changes in 
+the local interactions. 
+To further confirm this behaviour, we performed NMR 
+crystallography 
+analysis, which combines 
+XRD, ssNMR 
+spectroscopy and modelling (here first principles calculations 
+and GIPAW-DFT based NMR chemical shielding calculations) 
+techniques to resolve atomic-scale interactions.58 Solid-state 
+NMR is particularly sensitive to local structures of polymeric 
+organic semiconductors, NFAs and polymer:NFA blends.59-61 
+Here, we carried out ssNMR crystallography analysis with the 
+aim of identifying the changes in local structures in crystals and 
+powder compositions (Figure 3b-d). This is achieved by 
+analysing and comparing 1H and 13C chemical shifts of crystal 
+structures as calculated by GIPAW-DFT approach with the 
+experimentally measured 13C and 1H chemical shifts for the o-
+IDTBR powder. A detailed analysis of experimental 1D 1H, 13C 
+and 2D 1H-1H and 1H-13C correlation ssNMR spectra is presented 
+in Supporting Information (Figures S1-S4). Periodic DFT 
+optimised crystal structures are shown in Figure 3c, whereby 
+the backbone-backbone and backbone-sidechain interactions 
+are indicated in soft-rectangles (in red) and circles (in blue), 
+respectively. Figure 3b,d compares the 2D plots of DFT-
+calculated chemical shifts generated by MagresView and 
+MagresPython software tool62 for 1H-1H and 1H-13C spin pairs 
+within a 3 Å distance, overlaid on the experimental 1H-1H 
+double-quantum-single-quantum (DQ-SQ) correlation and 1H-
+13C nuclear correlation spectra. In 2D NMR measurements of 
+this type, 2D peaks corresponding to 1H-1H and 1H-13C 
+proximities within sub-nanometre distances in powder solids 
+are detected. It is noteworthy that a good correlation between 
+the GIPAW-DFT calculated chemical shifts and the experimental 
+chemical shifts () are observed for both aliphatic and aromatic 
+moieties. In the DQ-SQ spectrum (Figure 3b, the broad DQ peak 
+at 0-8 ppm in the vertical axis is due to the 1H-1H proximities in 
+alkyl sidechains and the DQ peaks in 12-16 ppm range are due 
+to the through-space 1H-1H proximities between aromatic 
+groups within the chain and in between the − stacked o-
+IDTBR molecules, both of which exhibit good agreement with 
+the DFT-calculated chemical shifts. However, subtle differences 
+between the DFT calculated and experimental chemical shifts 
+(1HDQ) in the 8-12 ppm range (dashed blue boxes), which 
+originate from through-space dipolar interactions between 
+aromatic groups and sidechains, indicate the minor changes in 
+the backbone-sidechain interactions in the vicinity of CH2 
+moieties when compared the crystalline and powder forms.63 
+Similarly, a good agreement is obtained when comparing the 
+DFT-calculated chemical shifts of 
+1H-13C pairs with the 
+experimental 1H-13C 2D peaks in the HETCOR spectrum, which 
+shows 2D peaks associated with the sidechains at (13C) = 10-40 
+ppm and  (1H) = 1-4 ppm, and the backbone moieties  (13C) = 
+110-170 ppm and  (1H) = 5-9 ppm (Figure 3d). However, 
+deviations between the DFT-calculated versus experimental 
+chemical shifts are observed for the 2D peaks corresponding to 
+the through-space aromatic-sidechain dipolar interactions as 
+depicted in the blue dashed boxes. Similar trends are observed 
+for Y-series NFAs that showed changes in the local structures 
+with respect to the backbone-sidechain interactions between 
+the crystalline and powder forms.58 The most important take 
+away from the ssNMR crystallography study is that it allowed us 
+to leverage the Le Bail refinement as a tool to verify the 
+structural compatibility between single crystal and powder in 
+terms of packing motif. This is possible as it allows for shift in 
+the lattice parameters caused by side chains relaxation at 
+elevated temperatures and demonstrated by changes in the 
+backbone-sidechain interactions, while preserving the π-π 
+interactions. By extending the Le Bail analysis to the other NFAs 
+of interest (Figures S5-S8 and Table S3), we obtained useful 
+information about the materials crystallinity: 
+1. 
+ITIC herringbone polymorph is predominant over the 
+brickwork (Figure S7). 
+2. 
+m-4TICO presents two brickwork structures but only 
+the un-solvated one is represented in powder (Figure 
+S8). 
+3. 
+o-IDTBR, IDIC, m-ITIC and 4TICO single crystal packing 
+is preserved in powder (Figure 3a and S6). 
+4. 
+With the only exception of 4TIC,¶ all the NFAs show 
+several Bragg peaks in the low angle region. 
+5. 
+All the non-solvated structures undergo a volumetric 
+expansion due to the temperature difference between 
+single crystal and powder experiments. However, we 
+do not exclude that the volumetric reduction observed 
+for the solvated crystals is only apparent, given that a 
+significant volume portion in the single crystal 
+structure is occupied by the solvent, which is not 
+expected to be found in the powder structure. 
+A summary of the results obtained by Le Bail refinement 
+performed for the different NFAs can be found in Table S3.  
+ 
+From Powder to NFA Films 
+A further intermediate step to approach the NFA packing in the BHJ 
+was to study the molecular organisation in thin films. Here, we 
+expected to see a more compatible unit cell to the one observed in 
+powder rather than in single crystal as we were going towards 
+
+ 
+ 
+systems that are presumably composed of many little crystallites 
+with reduced long-range order, cumulative disorder and multiple 
+orientations.34 Moreover, the temperature held during GIWAXS 
+measurements on film was 300 K as for the powder experiments 
+(XRD and ss-NMR). For convenience, we here report the analysis 
+performed on o-IDTBR, while the complete dataset including the 
+other materials can be found in the Supporting Information (pages 
+S10-S19). 
+GIWAXS data of o-IDTBR film with related 1D integration profiles 
+along the in-plane and out-of-plane directions are shown in Figure 
+4a-b and Table 2. From the q-map two main contributions are visible: 
+a low-angle component, located at q ≈ 3.8 nm-1, which is generally 
+recognised as lamellar peak and is indicative of the separation of the 
+conjugated and aliphatic moieties,35 and a higher angle feature (q ≈ 
+18.3 nm-1) which is commonly attributed to π-π stacking.64 Given the 
+anisotropic nature of these two main diffraction components, we 
+expected a π-π stacking with a preferential face-on crystalline 
+orientation of the o-IDTBR domains. To validate our hypothesis, we 
+simulated the GIWAXS pattern of the o-IDTBR single crystal structure 
+(Le-Bail refined) oriented along the (4 1 1) direction (Figure 4c), which 
+is nearly parallel to the π-π stacking (4 0 2) and perpendicular to 
+the lamellar (0 1 -1) peak (Figure 4e). The good agreement 
+between the simulated and experimental diffraction data suggests 
+that the o-IDTBR packing motif is preserved in film, where the 
+domains adopt a face-on orientation with an in-plane lamellar 
+ordering (0 -1 1) and out-of-plane π-π stacking (4 0 2). The good 
+agreement between our findings with literature65, 66 clarifies the 
+crystal packing motif and orientation of o-IDTBR films.  
+Some more considerations on the o-IDTBR film crystallinity can be 
+done by focussing on the spectral shape of the main diffraction peak 
+(lamellar peak). According to the paracrystalline g parameter found 
+for the lamellar peak (Table 2),34 the film can be classified on the 
+boundary between semi-paracrystalline and amorphous, showing a 
+Crystal Coherence Length (CCL) of ∼ 20 nm. For this class of materials, 
+a direct quantification of the crystalline domain size from the CCL is 
+often not possible. According to the nomenclature used in ref.34, we 
+will refer to the CCL as the spatial extent of the coherently diffracting 
+regions included in the paracrystallites, i.e. column lengths.34  
+To access the NFA domain size (which can be composed of multiple 
+paracrystallites), we investigated the surface morphology by AFM. 
+Figure 4d shows well-defined domain boundaries and a root mean 
+square (RMS) roughness of 6.9 nm. We performed the AFM image 
+segmentation (see pages S20-S25) through watershed algorithm to 
+derive the average domain size and its distribution.44 From the 
+calculations, we observed an average domain size of 36 nm from the 
+maximum of the peak distribution (inset of Figure 4d and Table 2). 
+This value is higher than the CCL, which confirmed that o-IDTBR 
+domains (visible from the AFM) are composed of multiple 
+paracrystallites, whose column length is determined by XRD (CCL). To 
+get an indication of the domain structural purity, we introduced a 
+parameter (ϕ) defined as the ratio (in percent) between the CCL and 
+the domain size obtained by AFM (Table 2). 
+Figure 4. o-IDTBR GIWAXS pattern (a) with in-plane and out-of-plane integration profiles along qz ∼ 0 and qxy ∼ 0, respectively. (b). Simulated GIWAXS pattern of the o-IDTBR unit cell 
+oriented along the (4 1 1) direction. The good agreement with the experimental GIWAXS confirmed a face-on 3D reticular packing motif of o-IDTBR in the blend. (c). 5x5 µm AFM 
+image of o-IDTBR film with domain size distribution and average value (inset). Side (e) and top (f) views of the o-IDTBR crystal packing with π-π stacking (4 0 2) and lamellar (0 1-1) 
+peaks.  
+
+30
+25
+20
+(t-_wu)b
+15
+10
+5
+0
+0
+5
+10
+15
+20
+25
+qr(nm-1) 
+ 
+Analogue characterisation and analysis were performed on the other 
+NFAs of interest for this work (Figure S9-S14 and Tables S4-S9) and 
+some key considerations and results can be summarised as follows: 
+1. most of the NFAs films showed a well-defined GIWAXS 
+scattering, especially in the lamellar and π-π stacking regions 
+(Figure S9-S12 and Tables S4-S7). These two main features are 
+characterised by a low angular distribution and therefore are 
+indicative of a preferential orientation of the crystalline domains 
+with respect to the substrate. 
+2. o-IDTBR, m-4TICO, 4TIC, m-ITIC and IDIC crystal lattice 
+simulations yielded a good structural agreement with the 
+powder unit cell obtained by Le Bail refinement (Figures S9-
+S12a). This proved that a structural continuity in terms of packing 
+motif occurs between powder and films. 
+3. NFAs with a 3D reticular (4TIC and o-IDTBR, see Figures S9b and 
+5e,f) and 2D brickwork (m-ITIC and IDIC, see Figures S11-S12b) 
+crystal packing motifs are involved in a face-on domain 
+orientation, with the m-4TICO as only exception ("quasi" edge-
+on crystal packing, see Figure S10b). 
+4. ITIC and 4TICO were found to have a 0D-herringbone packing 
+motif in powder. However, due to the lack of multiple Bragg 
+peaks, texturing, and long-range crystallinity (Figures S13, S14 
+and Tables S8-S9) we could not perform any crystal lattice 
+simulation. However, we do not exclude the presence of small 
+and randomly oriented herringbone column lengths within the 
+domains.  
+5. The high g parameter found for all the NFAs (> 9.5), prevented us 
+from directly quantifying the crystallite domain size from the 
+lamellar peak shape (FWHM) as the CCL represents the spatial 
+extent of the coherently diffracting regions (Table S4-S9). We 
+therefore estimated the domain size from AFM image 
+segmentation along with an indication for the domain purity (ϕ). 
+6. In general, NFAs that form π-π stacking structures (through 2D 
+brickwork or 3D reticular motifs) in single crystals and powder 
+showed the highest crystallinity in films (lowest g parameters 
+and highest CCL, see Tables S4-S9). Conversely, 0D herringbone 
+NFAs (ITIC and 4TICO) provided the highest paracrystalline 
+parameter g, highest CCL, and surprisingly among the highest 
+domain purity ϕ. 
+NFAs blended with PBTZT-stat-BDTT-8 
+After having characterised the NFA film crystallinity, we extended 
+our investigation on NFA:PBTZT-stat-BDTT-8 blend films, which were 
+used as active layers for the solar cells fabrication (see below). As for 
+the rest of the structural characterisation, we here limit the 
+discussion on PBTZT-stat-BDTT-8:o-IDTBR blend while the analysis 
+for the other systems can be found in the Supporting Information. 
+Figure 5. PBTZT-stat-BDTT-8 (a) and PBTZT-stat-BDTT-8:o-IDTBR (b) GIWAXS patterns with in-plane (c) and out-of-plane (f) integration profiles. The NFA features are clearly 
+visible from the blend GIWAXS, which confirmed that o-IDTBR maintain the packing motif in blend. 5x5 µm AFM images of PBTZT-stat-BDTT-8 (d) and PBTZT-stat-BDTT-8 :o-
+IDTBR (e) with domain size distribution and average value (inset). 
+PBTZT-stat-BDTT-8:o-IDTBR
+PBTZT-stat-BDTT-8
+x20
+(0 1 0)
+(1 0 0)
+a)
+0
+5
+10
+15
+20
+25
+30
+0
+5
+10
+15
+20
+25
+30
+qz (nm-1)
+qz (nm-1)
+-5
+0
+5
+10
+15
+20
+25
+-5
+0
+5
+10
+15
+20
+25
+qxy (nm-1)
+qxy (nm-1)
+In-plane
+Out-of-plane
+(0 1 0) + (4 0 2)
+(1 0 0)
+(0 1 -1)
+(0 1 -1)
+(0 1 -1)
+(1 0 0)
+x5
+b)
+c)
+d)
+e)
+f)
+(4 0 2)
+(4 0 2) + (0 1 0)
+(0 1 0)
+RMS: 1.7 nm
+RMS: 9.3 nm
+
+30
+25
+20
+qz(nm-1)
+15
+10
+5
+0
+0
+5
+15
+20
+25
+qr(nm-1)30
+25
+20
+qz(nm-1)
+15
+10
+5
+0
+-5
+0
+5
+15
+20
+25
+qr(nm-1) 
+ 
+ 
+The PBTZT-stat-BDTT-8 polymer GIWAXS pattern is shown in Figure 
+5a, where a (1 0 0) lamellar reflection is located at q ≈ 2.7 nm-1 and 
+the (0 1 0) π-π stacking feature at q ≈ 18.0 nm-1. The integration 
+profiles suggest a prevalent in-plane orientation of the (1 0 0) feature 
+and an out-of-plane direction of the (0 1 0) (Figure 5c, f). A slight face-
+on crystalline orientation of the PBTZT-stat-BDTT-8 was previously 
+reported, along with its smooth surface morphology with low RMS 
+(Figure 5d).36  
+GIWAXS data and 1D profiles of PBTZT-stat-BDTT-8:o-IDTBR blend 
+are shown in Figure 5b. A broad π-π stacking feature is located at q ≈ 
+18.1 nm-1 along the out-of-plane (Figure 5d), which can arise from 
+both the NFA and the polymer due to the spectral overlap in the q 
+range. Therefore, we focus on the lamellar features of o-IDTBR and 
+PBTZT-stat-BDTT-8 as indicative of the distinct material ordering in 
+the blend given that they can be distinguished from the in-plane 
+profiles (Figure 5c). The o-IDTBR (0 1 -1) lamellar peak is located here 
+at q ≈ 3.8 nm-1, meaning that the NFA crystalline ordering in the blend 
+is preserved with a similar lattice spacing and crystal packing. 
+A remarkable difference is reported for the spectral shape of the NFA 
+lamellar peak as it is characterised by an increased FWHM, indicating 
+a reduced long-range ordering (lower CCL) of the o-IDTBR domains in 
+the blend when compared to pure o-IDTBR film, resulting in higher g. 
+In addition to this, the increased domain size calculated from the 
+AFM image (Figure 5e), which implies a lower degree of domain 
+purity (φ) of the NFA in the blend (Table 2).  
+The analysis for the other NFAs can be found in the Supporting 
+Information (Figures S9-S14 and Tables S4-S9). However, the main 
+conclusions can be outlined as follows: 
+1. 
+The NFA crystallinity in PBTZT-stat-BDTT-8:NFA blends 
+presented broader and slightly shifted (towards lower q) 
+lamellar peaks. As a result, the NFA domains in the blend 
+are characterised by reduced crystallinity (lower CCL, 
+higher g) and relaxed lamellar packing with respect to the 
+bare NFA film. Furthermore, the presence of the polymer 
+is also affecting the domain purity (ϕ), which is reduced for 
+most of the blends with respect to the films made of NFAs. 
+2. 
+NFAs with 3D-reticular (o-IDTBR and 4TIC) and 2D-
+brickwork (m-4TICO, IDIC and m-ITIC) arrangements in 
+pure NFA films, preserved their packing motif and texturing 
+in NFA:PBTZT-stat-BDTT-8 blends (Figure 5 and pages S10-
+S17). 
+3. 
+NFAs that formed 0D herringbone structures in single 
+crystal and powder phases (ITIC and 4TICO), showed the 
+lowest crystallinity (highest g parameter and lowest CCL 
+calculated on the NFA lamellar peak) and poor texturing 
+among the series of NFA:PBTZT-stat-BDTT-8 blends (pages 
+S18-S19). Our results are in good agreement with a recent 
+report, where the importance of the π-π stacking 
+interaction energy to preserve the NFA packing motif in the 
+blend films is highlighted.67 
+Solar Cells Characteristics 
+To investigate the role of the NFA packing motif and crystallinity 
+on the charge transport properties and performance of OSCs, 
+we fabricated inverted architecture devices (Figure 6a). The 
+NFAs of interest were tested with PBTZT-stat-BDTT-8 active layers 
+and optimised with respect to the choice of the solvent, casting 
+temperature, and post-annealing treatment (Table S10). The 
+energy levels of the different NFAs with respect to the donor 
+polymer are shown in Figure 6b, along with the UV-Vis spectra 
+of each active layer used (figure 6c). The JV curves delivering the 
+highest PCE are shown in Figure 6d, and the JV characteristics 
+are listed in Table 3 (dark JV curves in Figure S24). Surprisingly, 
+4TICO and ITIC were among the best performing NFAs in terms 
+of maximum and average PCE obtained, despite having the 
+lowest crystallinity as indicated by the highest g parameter and 
+lowest CCL (Table 3). Moreover, the NFA crystal packing motif 
+does not seem to have a direct impact on performance (Table 
+3): 3D reticular packing NFAs such as o-IDTBR and 4TIC reached 
+a maximum PCE of 6.6 and 5.9 while m-4TICO (2D brickwork 
+packing motif) was the least performing NFA (5.3% PCE). 
+Interestingly, NFAs with a 0D herringbone packing motif in 
+single crystal (4TICO and ITIC) delivered the highest 
+performance (8.1 % and 7.2 %, respectively). Nevertheless, we 
+still expected a strong interplay between the active layer 
+crystallinity, NFA packing, and charge transport properties, 
+which may have an impact on the solar cells performance and 
+in particular the FF.68, 69 Thus, we performed photo-CELIV 
+experiments to determine the charge mobility and the 
+Component 
+Peak 
+Orientation 
+q (nm-1) 
+d (nm) 
+FWHM 
+(nm-1) 
+CCL 
+(nm) 
+g 
+Domain 
+Size (nm) 
+ϕ (%) 
+NFA film 
+o-IDTBR 
+(0 1 -1) 
+In-plane 
+3.79 
+1.66 
+0.27 
+20.9 
+10.6 
+36 ± 7 
+58.1 
+o-IDTBR 
+(4 0 2) 
+Out-of-plane 
+18.35 
+0.34 
+2.22 
+2.5 
+13.9 
+- 
+- 
+Polymer film  
+PBTZT-stat-BDTT-8 
+(1 0 0) 
+In-plane 
+2.71 
+2.32 
+0.78 
+7.2 
+21.4 
+24 ± 5 
+30.2 
+PBTZT-stat-BDTT-8 
+(0 1 0) 
+Out-of-plane 
+18.05 
+0.35 
+0.75 
+7.5 
+25.7 
+- 
+- 
+Blend film 
+o-IDTBR 
+(0 1 -1) 
+In-plane 
+3.77 
+1.67 
+0.33 
+17.1 
+11.8 
+50 ± 10 
+34.3 
+PBTZT-stat-BDTT-8 
+(1 0 0) 
+In-plane 
+2.80 
+2.24 
+1.58 
+3.6 
+30.0 
+- 
+- 
+PBTZT-stat-BDTT-8, o-IDTBR 
+(0 1 0) + (4 0 2) 
+Out-of-plane 
+18.14 
+0.35 
+2.80 
+2.0 
+15.7 
+- 
+- 
+Table 2 Crystallographic information of the main peaks observed by GIWAXS on o-IDTBR, PBTZT-stat-BDTT-8 and PBTZT-stat-BDTT-8:o-IDTBR films. AFM domain size and purity are 
+also shown. The domain purity parameter (ϕ) is defined as the ratio (in percent) between the CCL and the domain size obtained by AFM. 
+
+ 
+ 
+bimolecular recombination coefficient for each NFA:PBTZT-stat-
+BDTT-8 blend (Figure 6e,f and Table 3)¶ ¶.46, 47, 70-75 
+With regards to the mobility, we observed a remarkable 
+correlation between the NFA lamellar CCL in the blend and the 
+charge mobility (Figure 7a). The lowest mobility for ITIC and 
+4TICO blends is related to their poor crystallinity (low CCL and 
+high g parameter) detected in the pure NFA (Tables S4-S9) and 
+blend films (Table 3). The 0D packing nature might be another 
+disadvantage 
+for 
+efficient 
+long-range 
+transport. 
+The 
+relationship between charge mobility and NFA crystallinity was 
+further investigated by MIS-CELIV measurements, performed 
+on electron-injecting devices. The electron mobility determined 
+by MIS-CELIV matched the values obtained via photo-CELIV 
+(Figure S23). Since the photo-CELIV current is dominated by the 
+species with higher mobility,76 we could attribute the photo-
+CELIV mobility to electrons. This lead to the conclusion that the 
+electron mobility is clearly dependent on the NFA crystallinity, 
+as expressed by the CCL and g parameter. However, the 
+mobility determined from both photo-CELIV and MIS-CELIV did 
+not dominate the solar cell performance, as seen from FF and 
+PCE (Table 3). This result encouraged us to investigate the 
+bimolecular recombination and its possible implications in the 
+device performance.  
+We derived the bimolecular recombination coefficient by 
+photo-CELIV, exploring a purely quadratic dependence between 
+recombination and charge carrier density (Figure 6f).47 The 
+model provided a good fit with the sweep-out of free charges at 
+different time delays, (Figure 6f) and the bimolecular 
+recombination coefficient (𝛽exp) was derived according to the 
+equation (2) used in ref.,47 and is shown in Table 3. Interestingly, 
+we find the lowest recombination coefficients for the solar cells 
+made of ITIC and 4TICO blends, which delivered the highest 
+performance and among the highest FF, highlighting the 
+importance of the bimolecular recombination on the device 
+parameters.36, 77 Despite their lower crystallinity, active layers 
+made of ITIC and 4TICO resulted in higher domain purity (ϕ). 
+Conversely, NFAs characterised by higher CCL and lower g, such 
+as IDIC and m-4TICO, provided among the lowest domain purity 
+and highest bimolecular recombination coefficient. Overall, a 
+correlation is found between the NFA domain purity and the 
+bimolecular recombination coefficient (Figure 7b). 
+As mentioned above, the ϕ-parameter compares the spatial 
+extent of the NFA ordered regions in the domain (i.e., column 
+lengths, derived from the CCL), with the domain size obtained 
+from AFM images and can be calculated as follows: 𝜙 =
+ 𝐶𝐶𝐿 (𝑛𝑚) 𝐷𝑜𝑚𝑎𝑖𝑛 𝑠𝑖𝑧𝑒 (𝑛𝑚)
+⁄
+ ×  100). A blend film with low 
+domain purity (ϕ) can be understood as formed by domains 
+with a larger relative fraction of regions with an amorphous or 
+mixed nature that prompt recombination.78 Assessing domain 
+purity via the ϕ-parameter is easy-to-access compared to more 
+sophisticated methods such as resonant soft X-ray scattering 
+(RSoXS).79, 80 
+ 
+Figure 6. Device architecture with 80 ± 5 nm thick active layers (a) and energy levels determined by Air Photoemission Spectroscopy (see experimental section) (b) of PBTZT-stat-
+BDTT-8 and the different NFAs used for the solar cells' fabrication. UV-Vis of the different active layers (c). Characterisation of solar cells: J-V characteristics under illumination 
+(dark curves are plotted in Figure S17) (d), photo-CELIV curves (e) and bimolecular recombination coefficients (f). Legends of panels c-f) are shared and shown in d). 
+e)
+f)
+b)
+c)
+a)
+d)
+
+OnybogobATd
+HITBEDOLB22
+Lob EJGcLOgG:ye 
+ 
+Table 3 Solar cells characteristics for the different NFAs combined with PBTZT-stat-BDTT-8. Results for the best solar cell in terms of PCE (average and standard deviation over a minimum of 10 devices) are shown for each active layer. Device mobility 
+and bimolecular recombination coefficients are also listed along the other parameters related to the film crystallinity (g, CCL, packing), morphology (RMS, domain size) and domain purity (ϕ). The energy bandgap of the blend is also shown (Eg).  
+Active layer 
+PCE (%) 
+FF (%) 
+VOC (mV) 
+JSC  (mA･cm-2) 
+µ (cm2 V-1 s-1) 
+𝛽exp  (m3 s-1) 
+g 
+CCL 
+(nm) 
+Dom. size 
+(nm) 
+φ 
+(%) 
+RMS 
+(nm) 
+Pack
+ing 
+Eg 
+(meV) 
+PBTZT-stat-BDTT-8:4TICO 
+8.1 (7.5 ± 0.3) 
+70.9 (68.5 ± 1.2) 
+725 (717 ± 4) 
+16.8 (15.3 ± 0.7) 
+5.2 ± 0.5 x10-5  
+4.6 ± 2.3 x 10-18 
+22.4 
+5.8 
+12.1 ± 2 
+47.7 
+1.4 
+0D 
+870 
+PBTZT-stat-BDTT-8:ITIC 
+7.2 (6.8 ± 0.2) 
+69.3 (67.5 ± 1.1) 
+820 (816 ± 3) 
+12.9 (12.4 ± 0.4) 
+5.7 ± 0.6 x10-5 
+4.2 ± 2.1 x 10-18 
+21.0 
+5.7 
+9.6 ± 2 
+59.4 
+1.2 
+0D 
+920 
+PBTZT-stat-BDTT-8:IDIC 
+7.0 (6.8 ± 0.2) 
+73.0 (71.2 ± 1.7) 
+750 (745 ± 2) 
+13.4 (12.8 ± 0.4) 
+1.4 ± 0.1 x10-4 
+1.3 ± 0.6 x 10-17 
+15.4 
+10.5 
+41.1 ± 8 
+25.5 
+5.1 
+2D 
+750 
+PBTZT-stat-BDTT-8:m-ITIC 
+6.9 (6.6 ± 0.3) 
+69.7 (67.7 ± 1.6) 
+850 (837 ± 7) 
+12.2 (11.7 ± 0.5) 
+8.7 ± 0.9 x10-5 
+2.6 ± 1.3 x 10-17 
+16.3 
+8.4 
+51.5 ± 10 
+16.3 
+6.7 
+2D 
+910 
+PBTZT-stat-BDTT-8:4TIC 
+6.6 (6.4 ± 0.2) 
+67.5 (65.6 ± 1.1) 
+685 (685 ± 5) 
+14.3 (14.2 ± 0.3) 
+1.1 ± 0.1 x10-4 
+2.1 ± 1.0 x 10-17 
+14.1 
+9.0 
+29.6 ± 6 
+30.3 
+2.7 
+3D 
+830 
+PBTZT-stat-BDTT-8:o-IDTBR 
+5.9 (5.6 ± 0.2) 
+58.7 (57.6 ± 0.6) 
+950 (944 ± 3) 
+10.8 (10.3 ± 0.4) 
+N/A 
+N/A 
+11.8 
+17.1 
+50.0 ± 10 
+34.3 
+10.1 
+3D 
+1090 
+PBTZT-stat-BDTT-8:m-4TICO 
+5.3 (4.6 ± 0.6) 
+63.7 (61.5 ± 1.6) 
+765 (755 ± 6) 
+11.2 (9.9 ± 1.1) 
+1.4 ± 0.1 x10-4 
+1.2 ± 0.6 x 10-16 
+14.9 
+9.6 
+68.5 ± 14 
+14.0 
+11.7 
+2D 
+800 
+
+ 
+ 
+To summarise the influence of the NFA crystallinity (g, CCL), 
+packing motif and morphology (domain size, RMS and ϕ) on the 
+solar cell parameters (PCE,# FF, VOC and JSC) and charge transport 
+properties (𝜇 and 𝛽exp), we built a multivariable cross-
+correlation map with the most relevant parameters## (Figure 8). 
+While, strictly speaking, the cross-correlation map tests for 
+linear correlation, data that is correlated in a non-linear fashion 
+will still result in high (absolute) values. As such the map may 
+serve as semi-quantitative tool to assess correlations in complex 
+multivariable systems, where not all dependencies are fully 
+understood physically. 
+With regards to the initial motivation of our study on the role of 
+the NFA crystal packing, we didn't observe a clear correlation 
+with the device performance parameters. However, an 
+enhanced propensity for NFAs with increasing directionality of 
+π-π stacking to form crystalline domains in the blend is evident 
+by the high Pearson correlation coefficient (r) between the 
+packing motif with g and CCL, 0.97 and 0.76, respectively. Thus, 
+the directionality of the π-π stacking directly promotes the NFA 
+crystallinity in blends (g and CCL), which is, in turn, favouring the 
+electron mobility (r coefficient of µ is 0.97 and -0.88 with CCL 
+and g. It is worth to mention a recent work, in which a long 
+exciton diffusion lifetime was observed in systems with 
+enhanced π-π stacking systems and crystallinity.67 The tendence 
+to obtain higher mobilities in organic solar cells by increasing 
+the materials crystallinity is generally acknowledged.34, 81-83 In 
+addition to this, a lack of a direct correlation between packing 
+motif and performance was also recently reported, although 
+the identification of the NFA packing motif in the blend was 
+based on a visual examination of the GIWAXS pattern and 0D 
+herringbone systems were not included in the study .67 
+Interestingly, we found that the bulk heterojunction 
+morphology is having a bigger impact on performance. In 
+particular, active layers forming big domains at the surface have 
+low domain purity (r = -0.9), which is a good correlator for the 
+bimolecular recombination coefficient (Figure 7b-8 and S25). 
+𝛽exp is, in turn, a first-tier correlator to JSC and FF (r is -0.79 and -
+0.81, respectively) and the best correlating factor for the solar 
+cell performance (r = 0.94). The primary importance of the 
+bimolecular recombination on the device performance and its 
+relation with the domain purity was also observed in 
+literature.84 
+According the cross-correlation analysis, VOC is generally not 
+dependent on the film crystallinity and morphology. The energy 
+bandgap of the blend EG, determined with the difference 
+between HOMO of the polymer and the LUMO of the NFA 
+(Figure 6b), is the only significant correlator to VOC. The last 
+result agrees with the general knowledge about the relation 
+between VOC and the energetics of the donor and the acceptor 
+used in the blend.85-87 
+Conclusions 
+We have studied how NFAs crystal packing evolves from single 
+crystals to the bulk heterojunction of a solar cell. Given the 
+complexity of unambiguously determine the NFA packing motif 
+in an active layer, arising when moving from ideal systems, i.e., 
+millimetre-size single crystals, to the most complex BHJ 
+morphology, we employed a step-by-step structural analysis. 
+The first step involved ss-NMR crystallography and powder XRD, 
+which helped us to leverage the Le Bail refinement as a quick 
+and effective tool to verify the structural compatibility between 
+single crystal and powder samples. Then, we combined 
+GIWAXS, crystal lattice simulations and AFM to systematically 
+identify the NFA packing motif in the bare NFA films and blends 
+with the PBTZT-stat-BDTT-8 polymer, and to derive key 
+parameters to describe the material crystallinity (CCL and g 
+parameter) and morphology (RMS, domain size and domain 
+purity, ϕ). Finally, we investigated the influence of those key 
+Figure 7 a) Mobility is plotted versus the NFA crystal coherence length in the blend films. A linear fit of the data is represented with a 
+dashed grey line and indicates a correlation between CCL and electron mobility. b) Bimolecular recombination coefficient determined by 
+photo-CELIV in relation to the NFA domain structural coherency in the blend. A linear fit is represented with a dashed grey line and 
+indicates a correlation between the bimolecular recombination coefficient and the domain purity. 
+
+(e
+(q
+10-16.
+m-4TICO
+m-4TICO
+1.5
+S
+IDIC
+4TIC
+4TIC
+m-ITIC
+m-ITIC
+IDIC
+ITIC
+4TICO
+ITIC
+4TICO
+0.5
+5
+10
+25
+50
+75
+Crystal Coherence Length, CCL (nm)
+Domain Purity, @ (%) 
+ 
+structural parameters on the solar cell performance and charge 
+transport properties. 
+Our main findings are:  
+1. 
+NFA packing motifs largely track from single crystals to 
+the thin-film blend.  
+2. 
+Compounds that crystallise easily as single crystal also 
+show high crystallinity in the blend films. For instance, 
+we found that the poor propensity of ITIC to form 
+single 
+crystals (as 
+indicated 
+by the multiple 
+unsuccessful trials to grow single crystals)18 also 
+translates into a low blend crystallinity (high g and low 
+CCL).  
+3. 
+NFAs with higher π-π stacking dimensionality showed 
+an increased propensity to form crystalline films (low 
+g and high CCL) in both NFA films and blends. 
+4. 
+Despite our initial expectations, the NFA packing motif 
+does not directly correlate with the solar cell 
+performance parameters. 
+5. 
+NFAs with high film crystallinity (low g, high CCL) 
+provided higher electron mobility. However, the 
+mobility is not the dominating factor for device 
+performance. At the same time, we found no 
+correlation between the NFA crystallinity in the blend 
+and the bimolecular recombination coefficient (𝛽exp). 
+6. 
+The bimolecular recombination coefficient (𝛽exp) is 
+found to be the main factor influencing FF and JSC. 
+Systems with 
+low 
+𝛽exp reported the 
+highest 
+performance. For instance, blend with lower NFA 
+crystallinity (4TICO and ITIC) delivered the highest 
+performance and lowest bimolecular recombination 
+despite the lowest electron mobility. 
+7. 
+Domain purity stood out as an interesting design 
+target, to limit the bimolecular recombination and 
+obtain high efficiencies in organic solar cells. A better 
+understanding 
+of 
+the 
+influence 
+of 
+molecular 
+properties on domain purity is needed. 
+A high domain purity could be targeted through chemical design 
+that aims at limiting void space within the unit cell while also 
+managing the solubility/miscibility of the donor-acceptor 
+pairing to 
+control 
+BHJ formation 
+and 
+intermolecular 
+interactions.36, 88 This could in theory be targeted by the design 
+of space filling yet flexible sidechains to increase the NFA 
+rotational freedom and prevent NFA crystallisation that might 
+induce an excessive phase segregation.37 Alternatively, thermal 
+annealing can also be used as a handle to tune the morphology 
+of kinetically trapped systems,89, 90 allowing the formation of a 
+controlled BHJ morphology characterised by domain with high 
+structural purity.36, 89, 91 This was observed for NFAs that can 
+rearrange their structures undergoing an endothermic 
+transition (glass or liquid crystalline) during post-annealing 
+process (ITIC and 4TICO). Conversely, systems with shorter or 
+sterically locked sidechains may promote the formation of 
+crystalline domains even before any thermal treatment (4TIC, 
+m-4TICO, m-ITIC).36 These domains tend to excessively phase 
+segregate upon annealing without improving their domain 
+purity. 
+Figure 8. Multivariable cross-correlation map between solar cell characteristics and crystallinity/morphology parameters. 
+
+ 
+ 
+Conflicts of interest 
+Merck KGaA provided the PBTZT-stat-BDTT-8 polymer and the 
+4TICO NFA. 
+Acknowledgements 
+P. Mondelli and M. Riede acknowledge the European Union's 
+Horizon 2020 research and innovation programme under Marie 
+Skłodowska Curie Grant agreement no. 722651 (SEPOMO) for 
+the support in the realization of this work. P. Kaienburg 
+acknowledges funding from the Global Challenges Research 
+Fund (GCRF) through STFC, START project ST/R002754/1; and 
+from EPSRC for a Postdoctoral Fellowship EP/V035770/1.  
+GIWAXS experiments were performed at NCD-SWEET beamline 
+at ALBA synchrotron with the collaboration of ALBA staff 
+(proposal 2019093873).  
+Footnotes 
+‡Cu-K𝛼 X-Ray penetration depth on our films is ∼ 11 nm for 
+incident angles 𝛼 = 0.11° (assuming the same critical angle of 𝜃c 
+= 0.17°). 
+‡‡The active layer thickness was determined by using a Veeco 
+DEKTAK 150 surface profilometer. 
+§Single crystal structures are measured under a continuous flow 
+produced by liquid nitrogen at 100 K, while powder diffraction 
+is measured at 300 K. 
+§§We assume in this first step that the unit cells angles (𝛼, 𝛽 and 
+𝛾) are not varying from the single crystal unit cell. 
+¶4TIC powder XRD data quality didn't allow to perform Le Bail 
+analysis due to poor scattering (Figure S6). 
+¶¶We did not detect a meaningful signal from o-IDTBR:PBTZT-
+stat-BDTT-8 to extract the mobility and recombination 
+coefficient. We believe this is due to a combination of factors, 
+among which the lowest shunt resistance leading to the lowest 
+FF observed among all the different devices. 
+#Although the PCE is a linear combination of FF, VOC and JSC, we 
+included it in the cross-correlation analysis for convenience. 
+##We assigned a constant value for each motif which is 
+representative of the dimensionality of the π-π stacking: "0" for 
+0D herringbone, "2" for 2D brickwork and "3" for 3D reticular. 
+References 
+1. 
+L. Zhu, M. Zhang, J. Xu, C. Li, J. Yan, G. Zhou, W. Zhong, T. 
+Hao, J. Song and X. Xue, Nature Materials, 2022, 21, 656-
+663. 
+2. 
+Y. Cui, Y. Xu, H. Yao, P. Bi, L. Hong, J. Zhang, Y. Zu, T. Zhang, 
+J. Qin and J. Ren, Advanced Materials, 2021, 33, 2102420. 
+3. 
+S. Li, C.-Z. Li, M. Shi and H. Chen, ACS Energy Letters, 2020, 
+5, 1554-1567. 
+4. 
+Q. Wei, W. Liu, M. Leclerc, J. Yuan, H. Chen and Y. Zou, 
+Science China Chemistry, 2020, 1-15. 
+5. 
+J. Yuan, Y. Zhang, L. Zhou, G. Zhang, H.-L. Yip, T.-K. Lau, X. 
+Lu, C. Zhu, H. Peng, P. A. Johnson, M. Leclerc, Y. Cao, J. 
+Ulanski, Y. Li and Y. Zou, Joule, 2019, 3, 1-12. 
+6. 
+H. Lai, Q. Zhao, Z. Chen, H. Chen, P. Chao, Y. Zhu, Y. Lang, 
+N. Zhen, D. Mo and Y. Zhang, Joule, 2020, 4, 688-700. 
+7. 
+G. Li, X. Zhang, L. O. Jones, J. M. Alzola, S. Mukherjee, L.-w. 
+Feng, W. Zhu, C. L. Stern, W. Huang and J. Yu, Journal of the 
+American Chemical Society, 2021, 143, 6123-6139. 
+8. 
+L. Wang, Q. An, L. Yan, H.-R. Bai, M. Jiang, A. Mahmood, C. 
+Yang, H. Zhi and J.-L. Wang, Energy & Environmental 
+Science, 2022. 
+9. 
+L. Zhu, M. Zhang, G. Zhou, T. Hao, J. Xu, J. Wang, C. Qiu, N. 
+Prine, J. Ali and W. Feng, Advanced Energy Materials, 2020, 
+10, 1904234. 
+10. 
+L. Zhu, M. Zhang, W. Zhong, S. Leng, G. Zhou, Y. Zou, X. Su, 
+H. Ding, P. Gu, F. Liu and Y. Zhang, Energy & Environmental 
+Science, 2021, 14, 4341-4357. 
+11. 
+S. S. Babu, H. Möhwald and T. Nakanishi, Chemical Society 
+Reviews, 2010, 39, 4021-4035. 
+12. 
+F. Steiner, S. Foster, A. Losquin, J. Labram, T. D. 
+Anthopoulos, J. M. Frost and J. Nelson, Materials Horizons, 
+2015, 2, 113-119. 
+13. 
+F. Lin, K. Jiang, W. Kaminsky, Z. Zhu and A. K.-Y. Jen, Journal 
+of the American Chemical Society, 2020, 142, 15246-15251. 
+14. 
+W. Zhu, A. P. Spencer, S. Mukherjee, J. M. Alzola, V. K. 
+Sangwan, S. H. Amsterdam, S. M. Swick, L. O. Jones, M. C. 
+Heiber and A. A. Herzing, Journal of the American Chemical 
+Society, 2020, 142, 14532-14547. 
+15. 
+G. Zhang, X.-K. Chen, J. Xiao, P. C. Chow, M. Ren, G. Kupgan, 
+X. Jiao, C. C. Chan, X. Du and R. Xia, Nature 
+communications, 2020, 11, 1-10. 
+16. 
+S. Dai, M. Li, J. Xin, G. Lu, P. Xue, Y. Zhao, Y. Liu, M. Sun, L. 
+Yu and Z. Tang, Journal of Materials Chemistry A, 2022. 
+17. 
+X. Wang, H. Lu, Y. Liu, A. Zhang, N. Yu, H. Wang, S. Li, Y. 
+Zhou, X. Xu and Z. Tang, Advanced Energy Materials, 2021, 
+11, 2102591. 
+18. 
+P. Mondelli, G. Boschetto, P. N. Horton, P. Tiwana, C.-K. 
+Skylaris, S. J. Coles, M. Krompiec and G. Morse, Materials 
+Horizons, 2020, 7, 1062-1072. 
+19. 
+X. Shi, L. Zuo, S. B. Jo, K. Gao, F. Lin, F. Liu and A. K. Y. Jen, 
+Chemistry of Materials, 2017, 29, 8369-8376. 
+20. 
+T. J. Aldrich, M. Matta, W. Zhu, S. M. Swick, C. L. Stern, G. 
+C. Schatz, A. Facchetti, F. S. Melkonyan and T. J. Marks, J 
+Am Chem Soc, 2019, DOI: 10.1021/jacs.8b13653. 
+21. 
+J. Qu, H. Chen, J. Zhou, H. Lai, T. Liu, P. Chao, D. Li, Z. Xie, F. 
+He and Y. Ma, ACS Appl Mater Interfaces, 2018, 10, 39992-
+40000. 
+22. 
+S. M. Swick, W. Zhu, M. Matta, T. J. Aldrich, A. Harbuzaru, 
+J. T. Lopez Navarrete, R. Ponce Ortiz, K. L. Kohlstedt, G. C. 
+Schatz, A. Facchetti, F. S. Melkonyan and T. J. Marks, Proc 
+Natl Acad Sci U S A, 2018, DOI: 10.1073/pnas.1807535115. 
+23. 
+M. Wu, J. Zhou, Y. Luo, N. Zheng, C. Wang, L. Liu, Z. Xie and 
+Y. Ma, 
+Organic 
+Chemistry Frontiers, 
+2018, 
+DOI: 
+10.1039/c8qo00934a. 
+24. 
+D. Yan, W. Liu, J. Yao and C. Zhan, Advanced Energy 
+Materials, 
+2018, 
+DOI: 
+10.1002/aenm.201800204, 
+1800204. 
+25. 
+S. Li, L. Zhan, W. Zhao, S. Zhang, B. Ali, Z. Fu, T.-K. Lau, X. 
+Lu, M. Shi, C.-Z. Li, J. Hou and H. Chen, Journal of Materials 
+Chemistry A, 2018, 6, 12132-12141. 
+26. 
+H. Lai, H. Chen, J. Zhou, J. Qu, P. Chao, T. Liu, X. Chang, N. 
+Zheng, Z. Xie and F. He, iScience, 2019, 17, 302-314. 
+27. 
+Y. Zhang, Z. Liu, T. Shan, Y. Wang, L. Zhu, T. Li, F. Liu and H. 
+Zhong, Materials Chemistry Frontiers, 2020. 
+
+ 
+ 
+28. 
+D. Mo, H. Chen, J. Zhou, N. Tang, L. Han, Y. Zhu, P. Chao, H. 
+Lai, Z. Xie and F. He, Journal of Materials Chemistry A, 2020, 
+8, 8903-8912. 
+29. 
+X. Li, H. Huang, I. Angunawela, J. Zhou, J. Du, A. Liebman‐
+Pelaez, C. Zhu, Z. Zhang, L. Meng and Z. Xie, Advanced 
+Functional Materials, 2020, 30, 1906855. 
+30. 
+S. Feng, M. Li, N. Tang, X. Wang, H. Huang, G. Ran, Y. Liu, Z. 
+Xie, W. Zhang and Z. Bo, ACS applied materials & interfaces, 
+2020, 12, 4638-4648. 
+31. 
+L. Ma, S. Zhang and J. Hou, Journal of Materials Chemistry 
+A, 2022. 
+32. 
+H. Lai and F. He, Advanced Energy Materials, 2020, 10, 
+2002678. 
+33. 
+Y. Xiao and X. Lu, Materials Today Nano, 2019, 100030. 
+34. 
+Z. Peng, L. Ye and H. Ade, Materials Horizons, 2022. 
+35. 
+Y.-Y. Lai, V.-H. Huang, H.-T. Lee and H.-R. Yang, ACS omega, 
+2018, 3, 18656-18662. 
+36. 
+P. Mondelli, F. Silvestri, L. Ciammaruchi, E. Solano, E. 
+Beltrán-Gracia, E. Barrena, M. Riede and G. Morse, Journal 
+of Materials Chemistry A, 2021, 9, 26917-26928. 
+37. 
+S. Marina, A. D. Scaccabarozzi, E. Gutierrez‐Fernandez, E. 
+Solano, A. Khirbat, L. Ciammaruchi, A. Iturrospe, A. Balzer, 
+L. Yu and E. Gabirondo, Advanced Functional Materials, 
+2021, 2103784. 
+38. 
+H. Yoshida and N. Sato, Applied physics letters, 2006, 89, 
+101919. 
+39. 
+G. Ashiotis, A. Deschildre, Z. Nawaz, J. P. Wright, D. 
+Karkoulis, F. E. Picca and J. Kieffer, Journal of applied 
+crystallography, 2015, 48, 510-519. 
+40. 
+D. W. Breiby, O. Bunk, J. W. Andreasen, H. T. Lemke and M. 
+M. Nielsen, Journal of Applied Crystallography, 2008, 41, 
+262-271. 
+41. 
+C. F. Macrae, I. Sovago, S. J. Cottrell, P. T. Galek, P. McCabe, 
+E. Pidcock, M. Platings, G. P. Shields, J. S. Stevens and M. 
+Towler, Journal of applied crystallography, 2020, 53, 226-
+235. 
+42. 
+G. M. Reddy, M. Malon, A. Marsh, Y. Nishiyama and S. P. 
+Brown, Analytical chemistry, 2016, 88, 11412-11419. 
+43. 
+D. Nečas and P. Klapetek, Open Physics, 2012, 10, 181-188. 
+44. 
+A. S. Kornilov and I. V. Safonov, Journal of Imaging, 2018, 
+4, 123. 
+45. 
+S. Berny, N. Blouin, A. Distler, H. J. Egelhaaf, M. Krompiec, 
+A. Lohr, O. R. Lozman, G. E. Morse, L. Nanson, A. Pron, T. 
+Sauermann, N. Seidler, S. Tierney, P. Tiwana, M. Wagner 
+and H. Wilson, Adv Sci (Weinh), 2016, 3, 1500342. 
+46. 
+A. Baumann, J. Lorrmann, D. Rauh, C. Deibel and V. 
+Dyakonov, Advanced Materials, 2012, 24, 4381-4386. 
+47. 
+T. M. Clarke, C. Lungenschmied, J. Peet, N. Drolet and A. J. 
+Mozer, Advanced Energy Materials, 2015, 5, 1401345. 
+48. 
+G. Juška, N. Nekrašas and K. Genevičius, Journal of non-
+crystalline solids, 2012, 358, 748-750. 
+49. 
+O. J. Sandberg, M. Nyman, S. Dahlström, S. Sandén, B. 
+Törngren, J.-H. Smått and R. Österbacka, Applied Physics 
+Letters, 2017, 110, 153504. 
+50. 
+S. R. Chaudhari, J. M. Griffin, K. Broch, A. Lesage, V. Lemaur, 
+D. Dudenko, Y. Olivier, H. Sirringhaus, L. Emsley and C. P. 
+Grey, Chemical science, 2017, 8, 3126-3136. 
+51. 
+C. Wang, H. Dong, L. Jiang and W. Hu, Chem Soc Rev, 2018, 
+47, 422-500. 
+52. 
+M. Mas-Torrent and C. Rovira, Chem Rev, 2011, 111, 4833-
+4856. 
+53. 
+C. Wang, H. Dong, W. Hu, Y. Liu and D. Zhu, Chemical 
+Reviews, 2011, 112, 2208-2267. 
+54. 
+C. Wang, H. Dong, H. Li, H. Zhao, Q. Meng and W. Hu, 
+Crystal Growth & Design, 2010, 10, 4155-4160. 
+55. 
+J. Hou, O. Inganäs, R. H. Friend and F. Gao, Nature 
+Materials, 2018, 17, 119-128. 
+56. 
+H. Bristow, K. J. Thorley, A. J. P. White, A. Wadsworth, M. 
+Babics, Z. Hamid, W. Zhang, A. F. Paterson, J. Kosco, J. 
+Panidi, T. D. Anthopoulos and I. McCulloch, Advanced 
+Electronic Materials, 2019, 5, 1900344. 
+57. 
+C. Hammond, The basics of crystallography and diffraction, 
+International Union of Crystal, 2015. 
+58. 
+R. L. B, P. Raval, T. Pawlak, Z. Du, T. Wang, G. Kupgan, N. 
+Schopp, S. Chae, S. Yoon, A. Yi, H. Jung Kim, V. Coropceanu, 
+J. L. Bredas, T. Q. Nguyen and G. N. M. Reddy, Advanced 
+Materials, 2022, 34, e2105943. 
+59. 
+M. Seifrid, G. Reddy, B. F. Chmelka and G. C. Bazan, Nature 
+Reviews Materials, 2020, 5, 910-930. 
+60. 
+A. Karki, J. Vollbrecht, A. J. Gillett, S. S. Xiao, Y. L. Yang, Z. X. 
+Peng, N. Schopp, A. L. Dixon, S. Yoon, M. Schrock, H. Ade, 
+G. N. M. Reddy, R. H. Friend and T. Q. Nguyen, Energy & 
+Environmental Science, 2020, 13, 3679-3692. 
+61. 
+A. Karki, J. Vollbrecht, A. L. Dixon, N. Schopp, M. Schrock, 
+G. M. Reddy and T. Q. Nguyen, Advanced Materials, 2019, 
+31, 1903868. 
+62. 
+S. Sturniolo, T. F. Green, R. M. Hanson, M. Zilka, K. Refson, 
+P. Hodgkinson, S. P. Brown and J. R. Yates, Solid state 
+nuclear magnetic resonance, 2016, 78, 64-70. 
+63. 
+P. Hodgkinson, Progress in Nuclear Magnetic Resonance 
+Spectroscopy, 2020, 118, 10-53. 
+64. 
+S. C. B. M. Jonathan Rivnay, Chad E. Miller, Alberto Salleo, 
+and Michael F. Toney, chemical Reviews, 2012, 112. 
+65. 
+Q. Liang, X. Jiao, Y. Yan, Z. Xie, G. Lu, J. Liu and Y. Han, 
+Advanced Functional Materials, 2019, 29, 1807591. 
+66. 
+J. Hong, M. J. Sung, H. Cha, C. E. Park, J. R. Durrant, T. K. An, 
+Y.-H. Kim and S.-K. Kwon, ACS applied materials & 
+interfaces, 2018, 10, 36037-36046. 
+67. 
+J. Xu, F. Lin, L. Zhu, M. Zhang, T. Hao, G. Zhou, K. Gao, Y. 
+Zou, G. Wei and Y. Yi, Advanced Energy Materials, 2022, 
+2201338. 
+68. 
+D. Bartesaghi, I. D. C. Pérez, J. Kniepert, S. Roland, M. 
+Turbiez, D. Neher and L. Koster, Nature communications, 
+2015, 6, 1-10. 
+69. 
+P. Kaienburg, U. Rau and T. Kirchartz, Physical review 
+applied, 2016, 6, 024001. 
+70. 
+J. Gorenflot, M. C. Heiber, A. Baumann, J. Lorrmann, M. 
+Gunz, A. Kämpgen, V. Dyakonov and C. Deibel, Journal of 
+Applied Physics, 2014, 115, 144502. 
+71. 
+D. Murthy, A. Melianas, Z. Tang, G. Juška, K. Arlauskas, F. 
+Zhang, L. D. Siebbeles, O. Inganäs and T. J. Savenije, 
+Advanced Functional Materials, 2013, 23, 4262-4268. 
+72. 
+S. Chen, K. R. Choudhury, J. Subbiah, C. M. Amb, J. R. 
+Reynolds and F. So, Advanced Energy Materials, 2011, 1, 
+963-969. 
+73. 
+A. Baumann, T. J. Savenije, D. H. K. Murthy, M. Heeney, V. 
+Dyakonov and C. Deibel, Advanced Functional Materials, 
+2011, 21, 1687-1692. 
+74. 
+G. Dennler, A. J. Mozer, G. Juška, A. Pivrikas, R. Österbacka, 
+A. Fuchsbauer and N. S. Sariciftci, Organic Electronics, 
+2006, 7, 229-234. 
+
+ 
+ 
+75. 
+A. J. Mozer, N. S. Sariciftci, L. Lutsen, D. Vanderzande, R. 
+Österbacka, M. Westerling and G. Juška, Applied Physics 
+Letters, 2005, 86, 112104. 
+76. 
+O. J. Sandberg and M. Nyman, Organic Electronics, 2019, 
+64, 97-103. 
+77. 
+G. Lakhwani, A. Rao and R. H. Friend, Annual review of 
+physical chemistry, 2014, 65, 557-581. 
+78. 
+T. P. Chaney, A. J. Levin, S. A. Schneider and M. F. Toney, 
+Materials Horizons, 2022, 9, 43-60. 
+79. 
+B. A. Collins and E. Gann, Journal of Polymer Science, 2022, 
+60, 1199-1243. 
+80. 
+B. A. Collins, Z. Li, J. R. Tumbleston, E. Gann, C. R. McNeill 
+and H. Ade, Advanced Energy Materials, 2013, 3, 1-1. 
+81. 
+J. S. Park, G. U. Kim, D. Lee, S. Lee, B. Ma, S. Cho and B. J. 
+Kim, Advanced Functional Materials, 2020, 30, 2005787. 
+82. 
+A. T. Yiu, P. M. Beaujuge, O. P. Lee, C. H. Woo, M. F. Toney 
+and J. M. Frechet, Journal of the American Chemical 
+Society, 2012, 134, 2180-2185. 
+83. 
+W. Li, S. Albrecht, L. Yang, S. Roland, J. R. Tumbleston, T. 
+McAfee, L. Yan, M. A. Kelly, H. Ade and D. Neher, Journal of 
+the American Chemical Society, 2014, 136, 15566-15576. 
+84. 
+S. Wilken, D. Scheunemann, S. Dahlström, M. Nyman, J. 
+Parisi and R. Österbacka, Advanced Electronic Materials, 
+2021, 7, 2001056. 
+85. 
+M. Azzouzi, T. Kirchartz and J. Nelson, Trends in Chemistry, 
+2019, 1, 49-62. 
+86. 
+K. D. Rosenthal, M. P. Hughes, B. R. Luginbuhl, N. A. Ran, A. 
+Karki, S. J. Ko, H. Hu, M. Wang, H. Ade and T. Q. Nguyen, 
+Advanced Energy Materials, 2019, 9, 1901077. 
+87. 
+K. Vandewal and K. T. , Abay Gadisa, Olle Inganäs and Jean 
+V. 
+Manca, 
+nature 
+materials, 
+2009, 
+DOI: 
+10.1038/nmat2548. 
+88. 
+L. Ye, H. Hu, M. Ghasemi, T. Wang, B. A. Collins, J.-H. Kim, 
+K. Jiang, J. H. Carpenter, H. Li and Z. Li, Nature materials, 
+2018, 17, 253-260. 
+89. 
+Y. Qin, Y. Xu, Z. Peng, J. Hou and H. Ade, Advanced 
+Functional Materials, 2020, 30, 2005011. 
+90. 
+L. Ye, S. Li, X. Liu, S. Zhang, M. Ghasemi, Y. Xiong, J. Hou and 
+H. Ade, Joule, 2019, 3, 443-458. 
+91. 
+W. Köntges, P. Perkhun, J. Kammerer, R. Alkarsifi, U. 
+Würfel, O. Margeat, C. Videlot-Ackermann, J.-J. Simon, R. 
+R. Schröder and J. Ackermann, Energy & Environmental 
+Science, 2020, 13, 1259-1268. 
+ 
+
+ 
+ 
+Supporting Information: 
+Understanding the Role of Non-Fullerene Acceptors Crystallinity on the Charge 
+Transport Properties and Performance of Organic Solar Cells 
+ 
+Pierluigi Mondelli,*a,d Pascal Kaienburg,a Francesco Silvestri,b Rebecca Scatena,a Claire Welton,c Martine Grandjean,d 
+Vincent Lemaur,e Eduardo Solano,f Mathias Nyman,g Peter N. Horton,h Simon J. Coles,h Esther Barrena,b Moritz Riede,a 
+Paolo Radaelli,a David Beljonne,e G. N. Manjunatha Reddyc and Graham Morsed (Authors are listed in an arbitrary order 
+and list is temporary) 
+a Clarendon Laboratory, University of Oxford, Parks Road, Oxford, OX1 3PU, United Kingdom. E-mail: 
+pierluigi.mondelli@gmail.com 
+b Institut de Ciència de Materials de Barcelona, ICMAB-CSIC, Campus UAB, 08193 Bellaterra, Spain 
+c University of Lille, CNRS, Centrale Lille, Univ. Artois, UMR 8181- UCCS - Unité de Catalyse et Chimie du Solide, F-59000 
+Lille, France 
+d Merck Chemicals Ltd, Chilworth Technical Centre, University Parkway, Southampton, SO16 7QD, United Kingdom 
+e Laboratory for Chemistry of Novel Materials, University of Mons, Place du Parc, 20, 7000 Mons (Belgium) 
+f ALBA Synchrotron Light Source, NCD-SWEET beamline, Cerdanyola del Vallès, 08290 Spain 
+g Physics, Faculty of Science and Engineering, Åbo Akademi University, 20500 Turku, Finland 
+h EPSRC Crystallographic Service, Department of Chemistry, University of Southampton, Highfield, SO17 1BJ, UK 
+ 
+Table of Contents 
+ 
+1. Solid-state NMR analysis of o-IDTBR powder  
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+2-5 
+2. Powder and Single Crystal X-Ray Diffraction  
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+6-9 
+3. Film Morphology by 2D-GIWAXS and AFM 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+10-19 
+4. AFM Watershed Analysis  
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+20-25 
+5. Electron Mobility by MIS-CELIV 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+26-27 
+6. Annealing Temperature, Dark J-V and !exp 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+28 
+7. References  
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+29 
+ 
+ 
+ 
+ 
+
+ 
+ 
+ 
+ 
+1. Solid-state NMR analysis of o-IDTBR powder 
+ 
+Figure S1. 1D solid-state 1H NMR spectrum of o-IDTBR powder acquired at 18.8 T (1H = 800 MHz) with 50 kHz MAS. Peak assignments are 
+colour coded as depicted in the crystal structure shown in the inset.  
+Figure S1 presents 1H MAS NMR spectra of O-IDTBR powder, whereby the 1H peaks are color coded as depicted in 
+the schematic structure figure of O-IDTBR shown on top and the isotropic chemical shifts calculated by GIPAW-DFT 
+approach are overlaid. The broad 1H peak centered at ~1.7 ppm is due to the branched alkyls sidechains attached 
+to the aromatic core. The different distributions of 1H peaks in the 3-5 ppm range are due to the -NCH2CH3 moieties 
+attached to the terminal 3-ethyl-2-thioxothiazolidin-4-one groups. In the aromatic region, the peak at ~6 ppm is 
+due to the protons in the benzothiadiazole (BDT) groups (green dots), and the low ppm chemical shift value of these 
+BDT protons can be ascribed to the ring current effects caused by the partial overlap of the aromatic rings. The peak 
+at ~7 ppm can be attributed to the -CH moieties bridging the BDT and 3-ethyl-2-thioxothiazolidin-4-one groups as 
+depicted in the magenta dot. The overlapped peaks in the range between 7.5 to 8.5 ppm are due to the protons in 
+the BDT groups facing towards thiophene (T) groups (blue dot) and the protons in the central benzene ring (purple 
+dots). The weak intensity peak at ~8.8 ppm is due to thiophene protons (red dot). 
+ 
+ 
+ 
+ 
+
+8.26
+8.55
+7.89 5.94
+8.208.79
+7.79
+10
+8
+6
+4
+2
+0
+1H chemical shift (ppm) 
+ 
+ 
+Figure S2. 1D solid-state 13C1 CP-MAS NMR spectra of o-IDTBR powder acquired with 0.1 (bottom) and 3 ms (top) CP contact time. All 
+spectra were acquired at 18.8 T and 50 kHz MAS. Peak assignments are colour coded as depicted in the crystal structure shown in the inset. 
+For O-IDTBR powder, the 1H→13C cross-polarization (CP)-MAS NMR spectra of o-IDTBR were acquired with 0.1 ms 
+and 3 ms of CP contact time and compared. CP-MAS based experiments exploit the enhancement of the 13C signal 
+intensities that are increased by transfer of 1H spin-polarization by the adjacent protons, according to the strengths 
+of the 1H-13C dipole-dipole couplings. The isotropic 13C chemical shifts are color coded as presented in the spectrum, 
+the CH3 peaks are well resolved in 10-20 ppm range and the CH2 moieties produce peaks in 20-37 ppm range. The 
+peaks around 40 ppm are due to the -NCH2CH3 groups of 3-ethyl-2-thioxothiazolidin-4-one, and the peak centered 
+at ~55 ppm can be assigned to the quaternary carbon atom bearing the branched alkyl sidechains. In the aromatic 
+region, the one-bond CH moieties produce peaks in the 110-130 ppm; the broad peak in the 110-115 range 
+originates from the protonated carbon atoms in the benzene ring that produces a peak at ~112 ppm (purple dot) 
+and the protonated thiophene carbon atoms that give rise to a peak at ~ 115 ppm (red dot). Partially resolved peaks 
+in the 118-122 ppm range are due to the protonated carbon atom (facing towards the T group as depicted by the 
+blue dot) and the -CH moieties (purple dots) bridging the BDT and 3-ethyl-2-thioxothiazolidin-4-one groups. By 
+comparison, a CP-MAS NMR spectrum of o-IDTBR was acquired with 3 ms CP contact time which displayed 
+additional peaks corresponding to the quaternary carbon atoms (top spectrum), signals of which are enhanced by 
+the CP transfer via through-space 13C-1H dipolar interactions. Specifically, the 13C peak of the quaternary carbon 
+atom bearing the sidechains (gray dot) is enhanced as shown by the peak at ~55 ppm. In addition, the 13C signals 
+associated with the quaternary aromatic carbon atoms at 135-160 ppm are enhanced by the CP transfer from the 
+adjacent protons via 13C-1H dipolar couplings. The 13C peak at ~168 is due to the carbonyl group of the O-IDTBR 
+molecules. 
+
+Branched sidechains
+CH2
+8.26
+7.89 5.94
+CH
+7.79
+quaternary
+carbonatoms
+CC
+1H →13C CP 4 ms
+(through-space C...H)
+m
+1H →13C CP 0.1 ms
+(one-bond CH)
+180
+160
+140
+120
+100
+80
+60
+40
+20
+0
+13C chemical shift (ppm) 
+ 
+ 
+Figure S3. 2D solid-state 1H-1H NMR spectrum of o-IDTBR powder acquired at 18.8 T (1H = 800 MHz) with 50 kHz MAS. Peak assignments 
+are colour coded as depicted in the crystal structure shown in the inset. 1H chemical shift values associated with the aromatic protons are 
+depicted in the GIPAW-DFT geometry optimized structure as shown by the coloured dots. 
+ 
+     2D 1H-1H double-quantum single-quantum (DQ-SQ) correlation spectrum presented in Figure S3 displays 
+the DQ peaks in the vertical axis that correspond to 1H-1H proximities in less than 5 Å distance. The 1H 
+SQ signals are color coded as depicted in the schematic structure figure of O-IDTBR shown on top. In 
+particular, the different aromatic chemical shifts of thiophene (T) and benzothiadiazole (BDT) are due 
+to the different aromatic ring current effects. The inter- and intramolecular 1H-1H proximities in the alkyl 
+and aromatic regions (i, ii, iii, and iv) that contribute to the 1H DQ peaks are marked by ovals in the 
+crystal structure in the left. The broad DQ peak at ~3.6 ppm (i) is due to the inter-and intramolecular 1H-
+1H proximities in branched sidechains. The DQ peaks at ~7.7 and ~9.4 ppm (ii) are due to the dipolar 
+coupled 1H-1H pairs between branched sidechains and aromatic groups (T and BDT). The DQ peaks in 
+the aromatic region (iii and iv) are due to the intramolecular 1H-1H proximities between the aromatic 
+moieties, whereby the DQ peak 12.1 ppm is attributable to intramolecular 1H-1H  dipolar interactions 
+between the BDT proton and C-H protons in the bridged position (green and magenta dots).The DQ 
+peak at 13.1 ppm is due to the intramolecular 1H-1H dipolar interactions between the BDT protons (blue 
+and green dots), and the peak at 15.2 ppm is ascribed to the intramolecular 1H-1H dipolar interactions 
+between the BDT and T protons (blue and red dots) of O-IDTBR molecules. The different packing 
+interactions that contribute to the DQ peaks are marked by ovals in the crystal structure depicted in the 
+left. 
+ 
+ 
+
+8.26
+7.79
+ chemical shift (ppm)
+0
+(0)
+4
+8
+(i)
+ii
+1H DQ 
+12
+(iii)
+16
+(ii), (iv)
+(iii), (iv)
+(iv)
+10
+8
+6
+4
+2
+0
+1HSQchemicalshift(ppm) 
+ 
+ 
+Figure S4. 2D solid-state 1H-13C heteronuclear correlation (HETCOR) spectrum of o-IDTBR powder acquired with (a) 0.1 ms and (b) 3 ms CP 
+contact time. Peak assignments are color coded as depicted in the crystal structure shown in (c). All spectra were acquired at 18.8 T (1H = 
+800 MHz) with 50 kHz MAS.  
+ 
+Figure S4 presents 2D HETCOR spectra acquired with 0.1 ms and 3 ms CP contact times in order to detect 
+2D peaks that originate from directly bonded C-H as well as through-space dipolar coupled C…H moieties in 
+o-IDTBR molecules. Inter- and intramolecular C-H proximities corresponding to the 2D peaks are shown in 
+the crystal structure (c). In the spectrum acquired with 0.1 ms CP contact time, the isotropic 13C chemical 
+shifts at d(13C) = 10-45 ppm are due to the directly bonded C-H moieties in alkyl groups (yellow dots), and 
+the isotropic 13C chemical shifts at d(13C) = 110-122 ppm are due to the directly bonded C-H moieties in BDT 
+(blue and green dots), T (red dot), CH moiety at the bridged position (magenta) and benzene ring (purple 
+dots) at the aromatic core. In addition to these, the 2D HETCOR spectrum acquired with 3 ms CP contact 
+time exhibits the 2D peaks corresponds to the through-space inter and intramolecular 1H-13C dipolar 
+interactions between aliphatic and aromatic groups, as depicted in the boxes and ovals. Specifically, the 
+2D 13C-1H correlation peaks associated with the quaternary carbon atoms that are in close proximities to 
+aromatic protons in the core are emerged as depicted in the red color box. The 2D peaks shown in the blue 
+boxes are due to the inter- and intramolecular 13C-1H dipolar interactions between the alkyl chains and the 
+aromatic moieties. The carbonyl carbon atom is in close proximity to the CH protons (magenta) and 
+intermolecularly with the BDT protons (green dots) that lead to the 2D peaks as depicted in the red oval. 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+
+(a)
+(b)
+(c)
+0
+CP = 0.1 ms
+CF
+3ms
+(iii) (iv)
+20
+40
+chemical shift (ppm)
+60
+(iii),
+80
+(iv)
+100
+(iii)
+120
+140
+iv
+160
+CO-CH
+180
+CO-BDT
+200
+10
+8
+6
+4
+2
+0
+10
+8
+6
+4
+2
+0
+1Hchemicalshift (ppm)
+1H chemical shift (ppm) 
+ 
+2. Powder and Single Crystal X-Ray Diffraction 
+Manual calculation of the lattice parameters 
+The o-IDTBR lattice parameters (a, b and c) for powder sample were initially obtained by solving the reciprocal-space metric tensor 
+for monoclinic structures: 
+1
+#! 	=	
+1
+&'(!! )ℎ!
++! + -!&'(!!
+.!
++ /!
+0! −	2ℎ/03&!
++0
+4 
+where the positions of the (0 1 1), (0 1 2) and (110) were derived from the experimental pattern. The unit cell angles (5, ! and 6) were 
+assumed to be the same as in single crystal. The results are shown in (Table S1) and compared to the single crystal unit cell and the 
+ones obtained by Le Bail refinement of powder data. 
+ 
+Table S1. Evolution of the o-IDTBR unit cell parameters from the known single crystal data to the manual and Le Bail refinements. 
+Unit Cell 
+a (Å) 
+b (Å) 
+c (Å) 
+5	(°) 
+!	(°) 
+6	(°) 
+Volume	(Å3) 
+Single crystal 
+13.7663(2) 
+15.81032(17) 
+32.7146(3) 
+90 
+96.2928(12) 
+90 
+7077.43(15) 
+Manual 
+14.0646 
+16.0432 
+32.7057 
+90 
+96.293 
+90 
+7335.288 
+Le Bail 
+14.03086 
+16.06125 
+32.68444 
+90 
+96.716 
+90 
+7314.994 
+ 
+Temperature effect on the single crystal unit cell 
+The effect of the temperature on the NFA unit cell parameters was explored by performing temperature-dependent single-crystal 
+XRD on IDIC‡1(Figure S5, Table S2). The experiments have shown how temperature can influence both lattice parameters and 
+angles of IDIC.  
+Figure S5 a) IDIC powder XRD datapoints with Le Bail refinement compared to the simulated powder pattern from the single crystals 
+measured at 100 and 173 K. b) Fitting parameters evolution towards lower values 
+ 
+ 
+ 
+ 
+ 
+ 
+‡ The IDIC single crystal structures are accessible from the CCDC Database: Deposition Number 2226731 for the measurement 
+taken at 173 K and Deposition Number 2040188 for the dataset taken at 100 K. 
+b)
+a)
+
+ 
+ 
+ 
+Table S2 IDIC unit cell parameters evolution with temperature 
+Structure 
+Crystal 
+System 
+Space 
+Group 
+a (Å) 
+b (Å) 
+c (Å) 
+5	(°) 
+!	(°) 
+6	(°) 
+Volume	
+(Å3) 
+100 K 
+triclinic 
+P1" 
+8.6679(4) 
+12.5073(7) 
+13.5784(6) 
+72.096(4) 
+75.545(4) 
+88.839(4) 
+1353.88(12) 
+173 K 
+triclinic 
+P1" 
+8.6379(4) 
+12.6391(6) 
+13.9041(5) 
+70.650(4) 
+75.044(4) 
+88.148(4) 
+1381.35(11) 
+Le Bail 
+triclinic 
+P1" 
+8.63994 
+12.80154 
+14.39796 
+69.913 
+74.405 
+88.479 
+1436.737 
+ 
+ 
+Le Bail analysis 
+ 
+ 
+Figure S6. Powder XRD datapoints with Le Bail refinement compared to the simulated powder pattern from the single crystal. 
+4TIC
+4TICO
+IDIC
+m-ITIC
+
+ 
+ 
+ 
+ 
+Herringbone
+Brickwork
+ITIC
+Un-solvated
+Solvated
+m-4TICO
+Figure S7. Powder XRD datapoints with Le Bail refinement compared to the simulated powder pattern from the single crystal. 
+Figure S8. Powder XRD datapoints with Le Bail refinement compared to the simulated powder pattern from the single crystal. 
+
+ 
+ 
+Table S3 NFA unit cell parameters for the known crystal structures in comparison with the parameters obtained from Le Bail refinement.  
+CCDC 
+Molecule 
+Solvates 
+a (Å) 
+b (Å) 
+c (Å) 
+5	(°) 
+!	(°) 
+6	(°) 
+Volume	
+(Å3) 
+GOF 
+Chi2 
+wR 
+Before Le Bail Refinement 
+HEHQUJ01 
+ITIC 
+none 
+14.9009(7) 
+15.5043(4) 
+18.1199(5) 
+99.309(2) 
+101.541(3) 
+108.366(3) 
+3777.2(2) 
+10.43 
+91145.1 
+24.046 
+KIZSUK 
+ITIC 
+CH2Br2 
+8.420(6) 
+23.019(17) 
+23.126(17) 
+101.780(10) 
+95.319(10) 
+91.105(14) 
+4366(5) 
+18.24 
+278780.8 
+42.055 
+VUBJOU 
+m-ITIC 
+CHCl3 
+8.7454(13) 
+18.872(2) 
+25.2647(18) 
+87.770(8) 
+88.724(9) 
+78.001(12) 
+4075.1(9) 
+20.51 
+352372 
+38.001 
+VUBJEK 
+4TICO 
+C3H6O 
+15.2836(2) 
+20.0101(5) 
+29.3242(6) 
+90 
+29.3242(6) 
+90 
+8968.1(3) 
+18.95 
+300794.4 
+37.892 
+FOSPOV 
+o-IDTBR 
+none 
+13.7663(2) 
+15.81032(17) 
+32.7146(3) 
+90 
+96.2928(12) 
+90 
+7077.43(15) 
+9.10 
+63293.5 
+31.079 
+VUBKAH 
+IDIC 
+none 
+8.6679(4) 
+12.5073(7) 
+13.5784(6) 
+72.096(4) 
+75.545(4) 
+88.839(4) 
+1353.88(12) 
+20.93 
+367143.8 
+69.427 
+N/A 
+m-4TICO 
+none 
+8.7845(7) 
+15.3726(13) 
+16.7896(13) 
+67.136(7) 
+85.678(7) 
+79.630(7) 
+2054.98 
+35.82 
+1075472.2 
+62.264 
+VUBJIO 
+m-4TICO 
+CHCl3 
+8.6526(3) 
+16.4878(8) 
+18.0435(8) 
+114.697(5) 
+103.822(4) 
+90.890(4) 
+2251.45(19) 
+40.43 
+1369716.7 
+70.267 
+YEBKEY 
+4TIC 
+C7H8, 
+CH3OH 
+13.969(7) 
+17.144(9) 
+17.970(10) 
+104.668(16) 
+109.998(17) 
+96.169(14) 
+3822.08 
+24.62 
+507853 
+44.652 
+After Le Bail Refinement 
+HEHQUJ01 
+ITIC 
+none 
+15.06724 
+15.46733 
+17.89986 
+100.067 
+100.804 
+107.462 
+3788.083 
+7.87 
+51968.4 
+18.157 
+KIZSUK 
+ITIC 
+CH2Br2 
+8.57001 
+23.49976 
+22.22479 
+100.617 
+92.928 
+93.867 
+4380.067 
+18.16 
+274453.9 
+41.727 
+VUBJOU 
+m-ITIC 
+CHCl3 
+8.74588 
+17.77874 
+25.48191 
+88.391 
+89.072 
+78.262 
+3877.599 
+10.96 
+1000667.7 
+20.331 
+VUBJEK 
+4TICO 
+C3H6O 
+15.66764 
+19.60675 
+29.04299 
+90 
+90.799 
+90 
+8920.893 
+5.65 
+26766 
+11.303 
+FOSPOV 
+o-IDTBR 
+none 
+14.03086 
+16.06125 
+32.78444 
+90 
+96.716 
+90 
+7337.375 
+5.02 
+19267.4 
+17.148 
+VUBKAH 
+IDIC 
+none 
+8.67925 
+12.79671 
+14.4997 
+70.019 
+74.42 
+88.239 
+1454.553 
+7.43 
+46096.4 
+24.6 
+N/A 
+m-4TICO 
+none 
+9.0868 
+15.7656 
+16.6819 
+67.74 
+85.699 
+79.53 
+2167.014 
+16.70 
+233612.4 
+29.019 
+VUBJIO 
+m-4TICO 
+CHCl3 
+8.74656 
+16.15453 
+17.81585 
+114.163 
+104.908 
+89.942 
+2203.878 
+40.27 
+1348979.8 
+69.733 
+
+ 
+ 
+3. Film Morphology by 2D-GIWAXS and AFM 
+4TIC 
+4TIC 2D-GIWAXS pattern (Figure S6c) is in good agreement with the one obtained in our previous report.2 We have simulated the 
+2D-GIWAXS map by using the single crystal unit cell available from literature3 (Figure S9a) and oriented along the (1 0 0) direction. 
+Such direction is parallel to the π-π stacking (4 -1 -1) and the lamellar (1 0 0) peak, which is representative of a face-on orientation 
+of 4TIC domains with respect to the substrate (Figure S9b). Although the (1 0 0) lamellar contribution is not visible from the 
+simulated data (all crystallites are assumed to be perfectly oriented along the (1 0 0) and therefore are not accessible4), 
+experimental and simulated GIWAXS are in good agreement confirming a face-on 3D reticular packing with respect to the 
+substrate. As the 4TIC lamellar feature is still evident from the PBTZT-stat-BDTT-8:4TIC GIWAXS (Figure S9d) and out-of-plane 
+Figure S9. Simulated 2D-GIWAXS pattern of the 4TIC unit cell oriented along the (1 0 0) direction (a). Graphical representation of the π-π 
+stacking (4 -1 -1) and lamellar (1 0 0) peaks orientation with respect to the (1 0 0) vector (b). 4TIC (c) and PBTZT-stat-BDTT-8:4TIC (d) 
+GIWAXS pattern with in-plane (e) and out-of-plane (g) integration profiles. 5x5 µm AFM images of 4TIC (f) and PBTZT-stat-BDTT-8:4TIC (g) 
+films with domain size distribution and average value (inset). 
+Out-of-plane
+4TIC
+(1 0 0)
+PBTZT-stat-BDTT-8:4TIC
+c)
+In-plane
+ (1 0 0)
+ (0 1 0)
+(0 1 1)
+(1 0 0)
+(1 0 0)
+(4 -1 -1)
+(4 -1 -1) + (0 1 0)
+(1 0 0)
+(1 0 0)
+(4 -1 -1)
+(4 -1 -1) + (0 1 0)
+(1 0 0)
+(1 0 0)
+�-�
+(4 -1 -1)
+a)
+b)
+e)
+d)
+f)
+h)
+g)
+lamellar
+(1 0 0)
+RMS: 1.5 nm
+RMS: 3.7 nm
+qxy (nm-1)
+qxy (nm-1)
+qxy (nm-1)
+qz (nm-1)
+
+30
+25
+20
+(t-wu)b
+15
+10
+5
+0
+-5
+0
+5
+10
+15
+20
+25
+qr(nm-1)30
+25
+20
+qz(nm-1)
+15
+10
+5
+0
+-5
+0
+5
+10
+15
+20
+25
+qr(nm-1)30
+25
+20
+(t-wu)b
+15
+10
+5
+0
+-5
+0
+5
+10
+15
+20
+25
+qr(nm-1) 
+ 
+integration profile (Figure S6h), we assume that the NFA is maintaining its crystalline order in blend with a slightly relaxed (1 0 0) 
+periodicity (Table S5) compared to the pure NFA film. 
+ 
+Table S4. Crystallographic information of the main peaks observed by 2D-GIWAXS on 4TIC and PBTZT-stat-BDTT-8:4TIC films. AFM domain 
+size and domain purity are also shown. 
+Component 
+Peak 
+Orientation 
+q (nm-1) 
+d (nm) 
+FWHM 
+(nm-1) 
+CCL (nm) 
+g 
+Domain 
+Size (nm) 
+ϕ (%) 
+NFA film 
+4TIC 
+(1 0 0) 
+Out-of-plane 
+5.09 
+1.23 
+0.29 
+19.5 
+9.5 
+N/A 
+N/A 
+4TIC 
+ (4 -1 -1) 
+Out-of-plane 
+17.34 
+0.36 
+1.16 
+4.9 
+10.3 
+- 
+- 
+Blend film 
+4TIC 
+ (1 0 0) 
+Out-of-Plane 
+5.02 
+1.25 
+0.58 
+9.0 
+14.1 
+29.6 
+30.3 
+PBTZT-stat-BDTT-8 
+ (1 0 0) 
+In-plane 
+2.75 
+2.28 
+0.87 
+6.5 
+22.4 
+- 
+- 
+PBTZT-stat-BDTT-8, 4TIC 
+(0 1 0) + (4 -1 -1) 
+Out-of-plane 
+17.81 
+0.35 
+3.00 
+1.9 
+16.4 
+- 
+- 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+
+ 
+ 
+m-4TICO 
+m-4TICO 2D-GIWAXS pattern (Figure S10c) shows a strong Bragg peak along qz and other less intense features in the q map. To 
+verify whether the NFA arrangement in film is compatible to the phase existing in powder and single crystal, we have simulated 
+the 2D-GIWAXS of the single crystal unit cell (Le Bail refined) and oriented along the (0 1 1) direction (Figure S10a). Such direction 
+is parallel to the lamellar (1 0 0) peak and diagonal with respect to π-π stacking (2 3 2). This is representative of a quasi-edge-on 
+orientation of the m-4TICO domains with respect to the substrate (Figure S10b). The good agreement between experimental and 
+simulated GIWAXS confirms a quasi-edge-on 2D brickwork packing with respect to the substrate. As the m-4TICO lamellar feature 
+is still evident from the PBTZT-stat-BDTT-8:m-4TICO GIWAXS (Figure S10d) and out-of-plane integration profile (Figure S10h), we 
+assume that the NFA is maintaining its crystalline order in blend with a slightly relaxed (0 1 1) periodicity (Table S5) compared to 
+the pure NFA film. 
+Figure S10. Simulated 2D-GIWAXS pattern of the m-4TICO unit cell oriented along the (0 1 1) direction (a). Graphical representation of the 
+π-π stacking (2 3 2) and lamellar (0 1 1) peaks orientation with respect to the (0 1 1) vector (b). m-4TICO (c) and PBTZT-stat-BDTT-8:m-
+4TICO (d) GIWAXS pattern with in-plane (e) and out-of-plane (f) integration profiles. 5x5 µm AFM images of m-4TICO (f) and PBTZT-stat-
+BDTT-8:m-4TICO (g) films with domain size distribution and average value (inset). 
+  
+nm
+nm
+(2 3 2)
+c)
+a)
+b)
+e)
+d)
+f)
+h)
+�-�
+(2 3 2)
+qz (nm-1)
+RMS: 11.7 nm
+RMS: 7.4 nm
+qxy (nm-1)
+g)
+(0 1 1)
+lamellar
+(0 1 1)
+qxy (nm-1)
+qxy (nm-1)
+
+30
+25
+20
+(t-uu)b
+15
+10
+5
+0
+0
+5
+10
+15
+20
+25
+qr(nm-1)30
+25
+20
+(t-wu)b
+15
+10
+5
+0
+0
+5
+10
+15
+20
+25
+qr(nm-1) 
+ 
+Table S5. Crystallographic information of the main peaks observed by 2D-GIWAXS on m-4TICO and PBTZT-stat-BDTT-8:m-4TICO films. AFM 
+domain size and domain purity are also shown. 
+Component 
+Peak 
+Orientation 
+q (nm-1) 
+d (nm) 
+FWHM 
+(nm-1) 
+CCL (nm) 
+g 
+Domain 
+Size (nm) 
+ϕ (%) 
+NFA film 
+m-4TICO 
+(0 1 1) 
+Out-of-plane 
+4.52 
+1.39 
+0.33 
+17.1 
+10.8 
+62.1 
+27.6 
+Blend film 
+m-4TICO 
+ (0 1 1) 
+Out-of-Plane 
+4.25 
+1.48 
+0.59 
+9.6 
+14.9 
+68.5 
+14.0 
+PBTZT-stat-BDTT-8 
+ (1 0 0) 
+In-plane 
+2.60 
+2.42 
+1.42 
+4.0 
+29.5 
+- 
+- 
+PBTZT-stat-BDTT-8 
+(0 1 0) 
+Out-of-plane 
+17.85 
+0.35 
+5.00 
+1.1 
+21.1 
+- 
+- 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+
+ 
+ 
+m-ITIC 
+m-ITIC 2D-GIWAXS pattern (Figure S11c) shows a couple of features in the π-π stacking region along qz and other less intense peaks 
+in the low angle region, both in-plane and out-of-plane. To verify whether the NFA arrangement in film is compatible to the phase 
+existing in powder and single crystal, we have simulated the 2D-GIWAXS of the single crystal unit cell5 (Le Bail refined) and oriented 
+along the (1 1 1) direction (Figure S11a). Such direction is perpendicular to the lamellar (0 -1 1) peak and parallel with respect to 
+π-π stacking features, (2 3 3) and (2 2 5). This is representative of a face-on orientation of the m-ITIC domains with respect to the 
+substrate (Figure S11b). The good agreement between experimental and simulated GIWAXS confirms a face-on 2D brickwork 
+packing with respect to the substrate. The feature located qz ∼ 5 nm-1 represents the (1 1 1) reflections but is not evident from the 
+simulation because of its purely perpendicular orientation with respect to the substrate (region not accessible). As the m-ITIC 
+lamellar (0 1 -1) feature is still evident from the PBTZT-stat-BDTT-8:m-ITIC GIWAXS (Figure S11d) and in-plane integration profile 
+(Figure S11h), we assume that the NFA is maintaining its crystalline order in blend with a slightly relaxed lamellar (0 1 -1) and (2 2 
+5) π-π stacking periodicity (Table S6) compared to the pure NFA film. 
+Figure S11. Simulated 2D-GIWAXS pattern of the m-ITIC unit cell oriented along the (1 1 1) direction (a). Graphical representation of the π-
+π stacking, (2 3 3) and (2 2 5), and lamellar (0 1 1) peaks orientation with respect to the (1 1 1) vector (b). m-ITIC (c) and PBTZT-stat-BDTT-
+8:m-ITIC (d) GIWAXS pattern with in-plane (e) and out-of-plane (h) integration profiles. 5x5 µm AFM images of m-ITIC (f) and PBTZT-stat-
+BDTT-8:m-ITIC (g) films with domain size distribution and average value (inset). 
+c)
+a)
+d)
+h)
+(2 2 5)
+(2 3 3)
+(2 2 5)
+(2 2 5)
+(2 3 3)
+(2 2 5)
+RMS: 8.7 nm
+RMS: 4.6 nm
+qxy (nm-1)
+qxy (nm-1)
+(2 2 5)
+e)
+b)
+�-�
+(2 2 5), (2 3 3)
+(1 1 2)
+lamellar
+(0 -1 1)
+f)
+g)
+qz (nm-1)
+qxy (nm-1)
+
+30
+25
+20
+(t-wu)b
+15
+10
+5
+0
+-5
+0
+5
+10
+15
+20
+25
+qr(nm-1)30
+25
+20
+(t-wu)b
+15
+10
+5
+0
+-5
+0
+5
+10
+15
+20
+25
+qr(nm-1) 
+ 
+ 
+Table S6. Crystallographic information of the main peaks observed by 2D-GIWAXS on m-ITIC and PBTZT-stat-BDTT-8:m-ITIC films. AFM 
+domain size and domain purity are also shown. 
+Component 
+Peak 
+Orientation 
+q (nm-1) 
+d (nm) 
+FWHM 
+(nm-1) 
+CCL (nm) 
+g 
+Domain 
+Size (nm) 
+ϕ (%) 
+NFA film 
+m-ITIC 
+(0 1 -1) 
+In-Plane 
+4.09 
+1.54 
+0.43 
+13.1 
+8.6 
+59.3 
+22.2 
+m-ITIC 
+(2 2 5) 
+Out-of-plane 
+17.75 
+0.35 
+2.41 
+2.3 
+14.7 
+- 
+- 
+Blend film 
+m-ITIC 
+ (0 1 -1) 
+In-Plane 
+4.03 
+1.56 
+0.67 
+8.4 
+16.3 
+51.5 
+16.3 
+PBTZT-stat-BDTT-8 
+ (1 0 0) 
+In-plane 
+2.67 
+2.35 
+0.55 
+10.2 
+18.1 
+- 
+- 
+PBTZT-stat-BDTT-8:m-ITIC 
+(0 1 0) + (2 2 5) 
+Out-of-plane 
+17.54 
+0.36 
+2.30 
+2.5 
+14.4 
+- 
+- 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+
+ 
+ 
+IDIC 
+IDIC 2D-GIWAXS pattern (Figure S12c) shows a couple of features in the π-π stacking region along qz and multiple peaks in the low 
+angle region among multiple directions. To verify whether the NFA arrangement in film is compatible to the phase existing in 
+powder and single crystal, we have simulated the 2D-GIWAXS of the single crystal unit cell5 (Le Bail refined) and oriented along the 
+(2 2 3) direction (Figure S12a). Such direction is nearly perpendicular to the lamellar (0 1 0) peak and parallel with respect to the 
+(2 1 3) π-π stacking feature, which is representative of a face-on orientation of the m-ITIC domains with respect to the substrate 
+(Figure S12b). The partial agreement between experimental and simulated GIWAXS suggests a possible competition between two 
+different polymorphs. The first one represented by the (0 1 0) and (2 1 3) features with a face-on 2D brickwork packing with respect 
+to the substrate, while a second one identified by the (0 1 0)' and (2 1 3)' peaks. We hypothesise for the second polymorph to be 
+still characterised by a face-on packing motif (2D or 3D) because of the presence of an intense out-of-plane (2 1 3)' π-π stacking 
+feature and a (0 1 0)' lamellar peak developing along the in-plane direction. This second polymorph is becoming predominant in 
+PBTZT-stat-BDTT-8:IDIC blend as visible from the GIWAXS data (Figure S12d), integration profiles (Figure S12e,h) and Table S7. As 
+Figure S12. Simulated 2D-GIWAXS pattern of the IDIC unit cell (Le Bail refined) oriented along the (2 2 3) direction (a). Graphical 
+representation of the (2 1 3) π-π stacking and (0 1 0) lamellar peaks orientation with respect to the (2 2 3) vector (b). IDIC (c) and PBTZT-
+stat-BDTT-8:IDIC (d) GIWAXS pattern with in-plane (e) and out-of-plane (h) integration profiles. 5x5 µm AFM images of IDIC (f) and PBTZT-
+stat-BDTT-8:IDIC (g) films with domain size distribution and average value (inset). 
+ 
+c)
+1.5 nm
+3.7 nm
+
+a)
+b)
+30
+×106
+(2.2.3)
+lamellar
+2.5
+(0 1 0)
+lamellar
+25
+(2 2 3)
+(0 1 0)
+20
+2
+(2.1 3)
+(rwu)
+元-元
+15
+1.5
+(2 1 3)
+10
+1
+5
+0.5
+0
+(0 1 0)
+(2 2 3)
+- 5
+0
+5
+10
+15
+20
+25
+qxy (nm-1)
+c)
+IDIC
+d)
+PBTZT-stat-BDTT-8:IDIC
+e)
+In-plane
+30
+30
+(010)
+25
+25
+2
+Intensity (x105)
+(0 10)
+20
+(2 13)'
+20
+(2 13)+ (0 1 0)
+(2 1 3)
+15
+IDIC
+PBTZT-stat-BDTT-8:IDIC
+(1 0 0)
+10
+10
+(010)
+5
+(010)
+(1 0 0)
+10)
+0
+5
+10
+15
+20
+-5 
+0
+5
+10
+15
+20
+25
+0
+5
+10
+15
+20
+25
+q (nm-1)
+f)
+qxy (nm=1)
+qxy (nm)
+g)
+h)
+Out-of-plane
+6
+RMS: 8.9 nm
+41.1nm
+RMS:
+:4.8 nm
+IDIC
+5
+PBTZT-stat-BDTT-8:IDIC
+(2 1 3)
+(x105)
+4
+20
+50
+Intensity (
+Domain Size (nm)
+Domain Size (nm)
+3
+(2 13)
+(2 1 3) + (0 1 0)
+0
+μm
+5
+10
+15
+20
+q (nm1) 
+ 
+the IDIC lamellar (0 1 0)' feature is still evident and distinguishable from the polymer, we assume that the NFA is still crystalline in 
+the blend with a face-on 2D/3D crystal packing motif. 
+ 
+Table S7. Crystallographic information of the main peaks observed by 2D-GIWAXS on IDIC and PBTZT-stat-BDTT-8:IDIC films. AFM domain 
+size and domain purity are also shown. 
+Component 
+Peak 
+Orientation 
+q (nm-1) 
+d (nm) 
+FWHM 
+(nm-1) 
+CCL (nm) 
+g 
+Domain 
+Size (nm) 
+ϕ (%) 
+NFA film 
+IDIC 
+(0 1 0) 
+In-Plane 
+4.32 
+1.45 
+0.26 
+21.7 
+9.8 
+52.7 
+41.2 
+IDIC 
+(2 1 3) 
+Out-of-plane 
+18.46 
+0.34 
+1.44 
+3.9 
+11.1 
+- 
+- 
+Blend film 
+IDIC 
+ (0 1 0)' 
+In-Plane 
+3.60 
+1.74 
+0.54 
+10.5 
+15.4 
+41.1 
+25.5 
+PBTZT-stat-BDTT-8 
+ (1 0 0) 
+In-plane 
+2.62 
+2.40 
+0.59 
+9.6 
+18.9 
+- 
+- 
+PBTZT-stat-BDTT-8:m-ITIC 
+(0 1 0) + (2 1 3)' 
+Out-of-plane 
+18.05 
+0.35 
+1.79 
+3.1 
+12.6 
+- 
+- 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+
+ 
+ 
+4TICO 
+4TICO 2D-GIWAXS pattern (Figure S13a) is characterised by a weak crystallinity as it only presents two main features, both featuring 
+a lack of domain ordering along any specific direction. For this reason, it is not convenient to perform a side-by-side comparison 
+with the single crystal structure.5 However, a low angle (1 0 0) and a high angle (0 1 0) diffraction rings can still be distinguished 
+(Figure S13a,b) and used for the evaluation of the NFA crystallinity in films (Table S8). As regards the PBTZT-stat-BDTT-8:4TICO 
+blend, we could differentiate between the 4TICO and PBTZT-stat-BDTT-8 lamellar reflections since the latter is typically 
+characterised by in-plane scattering in the low angle region (Figure 5). We therefore conclude that the NFA is weakly crystalline in 
+the blend given the higher FWHM of the observed reflections with lack of texturing. 
+ 
+Table S8. Crystallographic information of the main peaks observed by 2D-GIWAXS on 4TICO and PBTZT-stat-BDTT-8:4TICO films. AFM 
+domain size and domain purity are also shown. 
+Component 
+Peak 
+Orientation 
+q (nm-1) 
+d (nm) 
+FWHM 
+(nm-1) 
+CCL (nm) 
+g 
+Domain 
+Size (nm) 
+ϕ (%) 
+NFA film 
+4TICO 
+(1 0 0) 
+In-Plane 
+3.20 
+1.96 
+0.89 
+6.3 
+21.0 
+11.3 
+56.2 
+4TICO 
+(0 1 0) 
+Out-of-plane 
+17.55 
+0.36 
+3.09 
+1.8 
+16.7 
+- 
+- 
+Blend film 
+4TICO 
+ (1 0 0) 
+In-Plane 
+3.12 
+2.01 
+0.98 
+5.8 
+22.4 
+12.1 
+47.7 
+PBTZT-stat-BDTT-8 
+ (1 0 0) 
+In-plane 
+2.77 
+2.27 
+0.64 
+8.8 
+19.2 
+- 
+- 
+PBTZT-stat-BDTT-8:4TICO 
+(0 1 0) 
+Out-of-plane 
+17.67 
+0.36 
+3.14 
+1.8 
+16.8 
+- 
+- 
+ 
+ 
+ 
+ 
+ 
+Figure S13. 4TICO and PBTZT-stat-BDTT-8:4TICO (a) GIWAXS patterns with in-plane and out-of-plane (b) integration profiles. 5x5 µm AFM 
+images (c) of IDIC and PBTZT-stat-BDTT-8:IDIC films with domain size distribution and average value (inset). 
+Out-of-plane
+4TICO
+(1 0 0)
+PBTZT-stat-BDTT-8:4TICO
+a)
+b)
+c)
+In-plane
+RMS: 1.9 nm
+RMS: 1.7 nm
+(1 0 0)
+(1 0 0) + 
+(0 1 0)
+(1 0 0)
+(1 0 0)
+(1 0 0)
+(1 0 0)
+(1 0 0)
+(0 1 0)
++ (0 1 0)
+(0 1 0)
+(0 1 0) + (0 1 0)
+(0 1 0) + (0 1 0)
+(0 1 0)
+qxy (nm-1)
+qxy (nm-1)
+
+30
+25
+20
+(t-wu)b
+15
+10
+5
+0
+-5
+0
+5
+10
+15
+20
+25
+qr(nm-1)30
+25
+20
+(t-wu)b
+15
+10
+5
+0
+-5
+0
+5
+10
+15
+20
+25
+qr(nm-1) 
+ 
+ITIC 
+ITIC 2D-GIWAXS pattern (Figure S14a) is characterised by a weak crystallinity as it only presents one main feature with a lack of 
+domain ordering along any specific direction. For this reason, it is not convenient to perform a side-by-side comparison with the 
+single crystal structure.5 However, a low angle (1 0 0) diffraction ring can still be distinguished (Figure S14a,b) and used for the 
+evaluation of the NFA crystallinity in films (Table S9). As regards the PBTZT-stat-BDTT-8:ITIC blend, we could differentiate between 
+the ITIC and PBTZT-stat-BDTT-8 lamellar reflections since the two are characterised by a different in-plane lattice spacing (Table S9 
+and Figure S14). We therefore conclude that the NFA is poorly crystalline in the blend given the high FWHM of the observed 
+reflections with lack of directionality. 
+ 
+Table S9. Crystallographic information of the main peaks observed by 2D-GIWAXS on ITIC and PBTZT-stat-BDTT-8:ITIC films. AFM domain 
+size and domain purity are also shown. 
+Component 
+Peak 
+Orientation 
+q (nm-1) 
+d (nm) 
+FWHM 
+(nm-1) 
+CCL (nm) 
+g 
+Domain 
+Size (nm) 
+ϕ (%) 
+NFA film 
+ITIC 
+(1 0 0) 
+In-Plane 
+3.66 
+1.72 
+1.65 
+3.43 
+26.8 
+7.4 
+46.3 
+Blend film 
+ITIC 
+ (1 0 0) 
+In-Plane 
+3.57 
+1.76 
+0.99 
+5.7 
+21.0 
+9.6 
+59.4 
+PBTZT-stat-BDTT-8 
+ (1 0 0) 
+In-plane 
+2.76 
+2.28 
+0.79 
+7.1 
+21.3 
+- 
+- 
+PBTZT-stat-BDTT-8:4TICO 
+(0 1 0) 
+Out-of-plane 
+18.09 
+0.35 
+2.44 
+2.3 
+14.7 
+- 
+- 
+ 
+ 
+Figure S14. ITIC and PBTZT-stat-BDTT-8:ITIC (a) GIWAXS patterns with in-plane and out-of-plane (b) integration profiles. 5x5 µm AFM 
+images (c) of ITIC and PBTZT-stat-BDTT-8:ITIC films with domain size distribution and average value (inset). 
+Out-of-plane
+ITIC
+(1 0 0)
+PBTZT-stat-BDTT-8:ITIC
+a)
+b)
+c)
+In-plane
+RMS: 0.7 nm
+RMS: 1.1 nm
+(1 0 0)
+(1 0 0) 
+(0 1 0)
+(1 0 0)
+(0 1 0)
+(1 0 0)
+(1 0 0)
+qxy (nm-1)
+qxy (nm-1)
+
+30
+25
+20
+(t-wu)b
+15
+10
+5
+0
+-5
+0
+5
+10
+15
+20
+25
+qr(nm-1)30
+25
+20
+(t-wu)b
+15
+10
+5
+0
+-5
+0
+5
+10
+15
+20
+25
+qr(nm-1) 
+ 
+ 
+4. AFM Watershed Analysis 
+ 
+ 
+ 
+ 
+ 
+IDIC
+PBTZT-stat-BDTT-8:IDIC
+Avg. Domain Size: 52.7 nm
+Avg. Domain Size: 41.1 nm
+Figure S15. AFM images (1 µm x 1 µm) of IDIC and PBTZT-stat-BDTT-8:IDIC films with and without the mask used for the 
+calculation of the average domain size by watershed algorithm. The input parameters and the result of the simulation are also 
+shown. 
+
+200 nm200 nm200 nm200 nmGrainLocation
+Numberof steps:
+20周
+Drop size:
+1.500周
+%
+Threshold:
+80周px2
+Segmentation
+Numberofsteps:
+199周
+D rop size:
+0.600周%
+Options
+Mask color:
+Invert height
+Combine with existing maskGrainLocation
+Numberofsteps:
+20日
+Drop size:
+0.500周%
+Threshold:
+40合px2
+Segmentation
+Number of steps:
+140周
+Drop size:
+0.500周%
+Options
+Mask color:
+ Invert height
+Combinewithexistingmask 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+m-ITIC
+PBTZT-stat-BDTT-8:m-ITIC
+Avg. Domain Size: 59.3 nm
+Avg. Domain Size: 51.5 nm
+Figure S16. AFM images (1 µm x 1 µm) of m-ITIC and PBTZT-stat-BDTT-8:m-ITIC films with and without the mask used for the 
+calculation of the average domain size by watershed algorithm. The input parameters and the result of the simulation are also 
+shown. 
+
+200 nm200 nm200 nm200 nmGrainLocation
+Numberof steps:
+10
+Drop size:
+1.500周%
+Threshold:
+40周px2
+Segmentation
+Numberofsteps:
+200周
+Drop size:
+1.000周%
+Options
+Mask color:
+ Invert height
+ Combine with existing maskGrain Location
+Number of steps:
+10周
+Drop size:
+0.500周
+%
+Threshold:
+40周px
+Segmentation
+Numberof steps:
+200周
+Drop size:
+0.600周%
+Options
+Mask color:
+8
+ Invert height
+ Combine with existing mask 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+o-IDTBR
+PBTZT-stat-BDTT-8:o-IDTBR
+Avg. Domain Size: 36.0 nm
+Avg. Domain Size: 50.0 nm
+Figure S17. AFM images of o-IDTBR (0.6 µm x 0.6 µm) and PBTZT-stat-BDTT-8:o-IDTBR (1 µm x 1 µm) films with and without 
+the mask used for the calculation of the average domain size by watershed algorithm. The input parameters and the result of 
+the simulation are also shown. 
+
+200 nm200 nmGrain Location
+Number of steps:
+5周
+Drop size:
+1.500周
+%
+Threshold:
+20周
+px
+Segmentation
+Nurmber of steps:
+图09
+Drop size:
+1.600周%
+Options
+Mask color:
+ Invert height
+ Combine with existing maskGrain Location
+Number of steps:
+4周
+Drop size:
+0.751周
+%
+Threshold:
+5周
+px
+Segmentation
+Number of steps:
+49周
+Drop size:
+0.831周%
+Options
+Mask color:
+ Invert height
+Combine with existing mask200 nm200 nm 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+m-4TICO
+PBTZT-stat-BDTT-8:m-4TICO
+Avg. Domain Size: 62.1 nm
+Avg. Domain Size: 68.5 nm
+Figure S18. AFM images (2 µm x 2 µm) of m-4TICO and PBTZT-stat-BDTT-8:m-4TICO films with and without the mask used for 
+the calculation of the average domain size by watershed algorithm. The input parameters and the result of the simulation are 
+also shown. 
+
+500 nm500nmGrainLocation
+Numberof steps:
+5周
+Drop size:
+0.566
+%
+Threshold:
+5日px2
+Segmentation
+Numberofsteps:
+129 周
+Drop size:
+0.341周%
+Options
+Mask color:
+ Invert height
+Combine with existing maskGrainLocation
+Numberofsteps:
+20日
+Drop size:
+0.500周%
+Threshold:
+40合px2
+Segmentation
+Number of steps:
+140周
+Drop size:
+0.500周%
+Options
+Mask color:
+ Invert height
+Combinewithexistingmask500 nm500nm 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ITIC
+PBTZT-stat-BDTT-8:ITIC
+Avg. Domain Size: 7.4 nm
+Avg. Domain Size: 9.6 nm
+Figure S19. AFM images (0.5 µm x 0.5 µm) of ITIC and PBTZT-stat-BDTT-8:ITIC films with and without the mask used for the 
+calculation of the average domain size by watershed algorithm. The input parameters and the result of the simulation are also 
+shown. 
+
+100nmGrain Location
+Number of steps:
+10日
+Drop size:
+1.000周
+%
+Threshold:
+10合
+px
+Segmentation
+Numberofstepis:
+563合
+Drop size:
+0.100周
+%
+Options
+Mask color:
+ Invert height
+ Combine with existing maskGrain Location
+Numberofsteps:
+44日
+Drop size:
+0.435周%
+Threshold:
+15日 px2
+Segmentation
+Numberofsteps:
+517周
+Drop size:
+0.044周%
+Options
+Mask color:
+ Invert height
+Combine with existing mask100 nm100 nmGrain Location
+Number of steps:
+10 周
+Drop size:
+1.000周
+Threshold:
+10周
+px
+Segmentation
+Numberofsteps:
+563
+Drop size:
+0.100周
+%100 nm 
+ 
+ 
+4TICO
+PBTZT-stat-BDTT-8:4TICO
+Avg. Domain Size: 11.3 nm
+Avg. Domain Size: 12.1 nm
+Figure S20. AFM images of 4TICO (0.3 µm x 0.3 µm) and PBTZT-stat-BDTT-8:4TICO (0.5 µm x 0.5 µm)  films with and without the mask used 
+for the calculation of the average domain size by watershed algorithm. The input parameters and the result of the simulation are also 
+shown. 
+PBTZT-stat-BDTT-8:4TIC
+Avg. Domain Size: 29.6 nm
+Figure S21. AFM images of PBTZT-stat-BDTT-8:4TIC (0.5 µm x 0.5 µm)  films with and without the mask used for the calculation of 
+the average domain size by watershed algorithm. The input parameters and the result of the simulation are also shown. 
+ 
+
+100nmGrain Location
+Number of steps:
+22周
+Drop size:
+0.595日%
+Threshold:
+7周px2
+Segmentation
+Number of steps:
+258
+Drop size:
+0.204日%
+Options
+Mask color:
+ Invert height
+ Combine with existing maskGrain Location
+Numberofsteps:
+44日
+Drop size:
+0.435周%
+Threshold:
+15日 px2
+Segmentation
+Numberofsteps:
+517周
+Drop size:
+0.044周%
+Options
+Mask color:
+ Invert height
+Combine with existing mask50nm50nm100 nm100 nmGrain Location
+Number of steps:
+24周
+D2rop size:
+0.435周
+Threshold:
+3周
+P
+Segmentation
+Numberof steps
+478周
+Drop size:
+0.180周
+Options
+Mask color:
+ Invert height
+ Combine with existing mask100 nm 
+ 
+5. Electron Mobility by MIS-CELIV 
+ 
+Figure S22 Typical MIS CELIV dataset taken for the 4TIC blend. The ramp rate A was varied between (a) 50 V/ms, (b) 200V/ms, (c) 400V/ms, 
+(d) 800V/ms, and (e) 1600V/ms. (f) Extracted electron mobilities for the different blends in dependence of the ramp rate. Dashed lines 
+indicated the estimated saturated mobility used in the main part. See text for further explanations. 
+ 
+Figure S15 shows representative example MIS-CELIV traces for PBTZT-stat-BDTT-8:4TIC. Different panels show measurements at 
+different ramp rates and for each ramp rate the offset voltage is varied. The solid black lines indicate the displacement current 
+density j0 resulting from the geometric capacitance, and 2×j0 used to determine time t1 (red dot) in MIS-CELIV measurements. 
+Finally, the saturated current density jsat is estimated by the top dashed line. Measurements at higher offset voltage suffered from 
+increased current injection so that jsat had to be roughly estimated from the depicted traces. Note that the extracted mobility 
+values change little with the exact value of jsat. With t1, the mobility is calculated for all ramp rates and blends and plotted in fig. 
+S15 (bottom right panel). In the presence of some injection barrier, the measured apparent mobility depends on the product of 
+ramp rate A and t1. The measured mobility saturates and reaches its true value for large A×t1.6 The estimated saturated mobility 
+is indicated with dashed lines in fig. S15 (bottom right panel).  
+With increasing annealing temperature, the blocking properties of MgF2 diminished and for some samples leakage currents 
+prevented data analysis. Hence, the m-4TICO blend at 100°C, rather than 120°C, and the unannealed m-ITIC were analysed. 
+!0	
+2!0	
+!sat	
+$1	
+0.0
+0.5
+1.0
+1.5
+0.01
+0.1
+1
+IDIC
+4TIC
+mITIC
+4TICO
+µe (10-8 m2/Vs)
+At1 (V)
+m4TICO
+(a) 
+(b) 
+(c) 
+(d) 
+(e) 
+(f) 
+
+50 V/ms
+oV
+4
+1 V
+2 V
+3 V
+2
+0
+25
+50
+75
+100
+125
+150
+175
+time (us)200 V/ms
+25
+oV
+1v
+2 V
+current density (mA/cm^2)
+20
+3 V
+4 V
+15 
+10 
+5
+0
+10
+20
+30
+40
+time (us)400 V/ms
+oV
+40
+1 V
+2 V
+current density (mA/cm^2)
+3 V
+OE
+20
+10
+0
+0
+5
+T
+10
+T
+15
+20
+time (us)800 V/ms
+80
+oV
+1 V
+70
+2 V
+3 V
+60
+4 V
+5 V
+50
+40
+30
+20
+10
+0
+0
+2
+T
+4
+6
+T
+8
+10
+12
+time (us)1600 V/ms
+ov
+140
+1V
+2 V
+current density (mA/cm^2)
+120
+3 V
+4 V
+100
+5 V
+6 V
+80
+60
+40
+20
+0
+0
+1
+2
+3
+4
+5
+6
+7
+time (us) 
+ 
+However, we did not observe a notable change for other samples with annealing temperature. Hence, we can assume that the 
+measured values are representative. 
+Figure S23. Photo-CELIV mobility compared to MIS-CELIV. A bisecting line is 
+also plotted.  
+
+ 
+ 
+.  
+ 
+6. Active Layer Annealing Temperature and Dark J-V 
+Table	S10.	Thermal	annealing	protocol	used	for	each	active	layer.	
+Active	Layer	
+Annealing Protocol 
+PBTZT-stat-BDTT-8:o-IDTBR	
+5' at 100 °C 
+PBTZT-stat-BDTT-8:m-ITIC	
+5' at 100 °C + 5' at 120 °C + 3' at 140 °C 
+PBTZT-stat-BDTT-8:ITIC	
+5' at 100 °C + 5' at 120 °C + 3' at 140 °C 
+PBTZT-stat-BDTT-8:IDIC	
+5' at 100 °C + 5' at 120 °C 
+PBTZT-stat-BDTT-8:4TICO	
+5' at 100 °C + 5' at 120 °C + 3' at 140 °C 
+PBTZT-stat-BDTT-8:4TIC	
+5' at 100 °C + 5' at 120 °C + 3' at 140 °C 
+PBTZT-stat-BDTT-8:m-4TICO	
+5' at 100 °C + 5' at 120 °C 
+Figure S24. J-V characteristics measured in dark conditions. 
+
+ 
+ 
+ 
+7. References 
+1. 
+T. F. Schulze and T. W. Schmidt, Energy & Environmental Science, 2015, 8, 103-125. 
+2. 
+P. Mondelli, F. Silvestri, L. Ciammaruchi, E. Solano, E. Beltrán-Gracia, E. Barrena, M. Riede and G. Morse, Journal of Materials 
+Chemistry A, 2021, 9, 26917-26928. 
+3. 
+X. Shi, L. Zuo, S. B. Jo, K. Gao, F. Lin, F. Liu and A. K. Y. Jen, Chemistry of Materials, 2017, 29, 8369-8376. 
+4. 
+J. B. Sherman, B. Purushothaman, S. R. Parkin, C. Kim, S. Collins, J. Anthony, T.-Q. Nguyen and M. L. Chabinyc, Journal of Materials 
+Chemistry A, 2015, 3, 9989-9998. 
+5. 
+P. Mondelli, G. Boschetto, P. N. Horton, P. Tiwana, C.-K. Skylaris, S. J. Coles, M. Krompiec and G. Morse, Materials Horizons, 2020, 
+7, 1062-1072. 
+6. 
+O. J. Sandberg, M. Nyman, S. Dahlström, S. Sandén, B. Törngren, J.-H. Smått and R. Österbacka, Applied Physics Letters, 2017, 110, 
+153504. 
+ 
+m-4TICO
+IDIC
+m-ITIC
+4TIC
+4TICO
+ITIC
+Figure S25. Plot showing the trend between the bimolecular recombination coefficient and 
+the average domain size determined from AFM.. 
+
+1E-16
+p
+1E-17
+6
+7
+8
+9
+10
+11
+12
+CCL (nm)1E-16
+1E-17
+10
+20
+30
+40 50 607080
+Domain Size (nm)1E-16
+1E-17
+0
+2
+4
+6
+8
+RMS (nm)
\ No newline at end of file
diff --git a/oNAyT4oBgHgl3EQfY_dp/content/tmp_files/load_file.txt b/oNAyT4oBgHgl3EQfY_dp/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4cfcafe0fafa1118df77e9585e088099abbb6ed9
--- /dev/null
+++ b/oNAyT4oBgHgl3EQfY_dp/content/tmp_files/load_file.txt
@@ -0,0 +1,2590 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf,len=2589
+page_content='Understanding the Role of Non-Fullerene Acceptors Crystallinity  on the Charge Transport Properties and Performance of Organic  Solar Cells  Pierluigi Mondelli,a,d,†,* Pascal Kaienburg,a Francesco Silvestri,b Rebecca Scatena,a Claire  Weltonc, Martine Grandjean,d Vincent Lemaur,e Eduardo Solano,f Mathias Nyman,g Peter N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Horton,h Simon J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Coles,h Esther Barrena,b Moritz Riede,a Paolo Radaelli,a David Beljonne,e G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Manjunatha Reddyc and Graham Morsed,†  The acceptor crystallinity has long been associated with favourable organic solar cells (OSCs) properties such as high mobility  and Fill Factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' In particular, this applies to acceptor materials such as fullerene-derivatives and the most recent Non-  Fullerene Acceptors (NFAs), which are now surpassing 19% of Power Conversion Efficiency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Despite these advantages are  commonly attributed to their 3-dimensional crystal packing motif in the single crystal, the bridge that links the acceptor  crystal packing from single crystals to solar cells has not clearly been shown yet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' In this work, we investigate the molecular  organisation of seven NFAs (o-IDTBR, IDIC, ITIC, m-ITIC, 4TIC, 4TICO, m-4TICO), following the evolution of their packing motif  in single-crystals, powder, and thin films made with pure NFAs and donor:NFA blends.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' We observed a good correlation  between the NFA single crystal packing motif and their molecular arrangement in the bulk heterojunction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The NFA packing  motif affects the material’s propensity to form highly crystalline domain in the blend.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' We specifically found that 3D reticular  packing motifs show stronger ordering than 0D herringbone ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' However, the NFA packing motif is not directly correlating  with device performance parameters: Although higher NFA crystallinity yields higher mobility, we found the domain purity  to be more important for obtaining high efficiency organic solar cells by governing bimolecular recombination.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Introduction  The recent surge in Organic Solar Cells (OSCs) performance, now  exceeding 19%,1, 2 results from the development of Non-  Fullerene Acceptors (NFAs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='3-8 Previous work centred around  fullerene based acceptors has drawn a connection between  molecular  design/shape  to  the  formation  of  highly-  interconnected acceptor domains and charge percolation  pathways towards the electrodes, resulting in superior charge  transport properties and high Fill Factors (FF) in OSC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='9-12  Moreover, recent works are attributing the improved  performance and charge transport of state of the art NFAs to  their 3D-interconnected crystal packing motif (Figure 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='5, 7-9, 13-  17 It is thus important to construct a clear understanding based  on concrete evidence of the relationship between the NFA  molecular packing and crystallinity in the bulk heterojunction  and the charge transport properties and performance of  organic solar cells.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  A growing variety of NFA single-crystals is now being reported,8,  14, 15, 18-31 from which useful information on the molecular  packing can be derived.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Still, bridging the molecular scale from  molecular packing in single-crystals to the one found in Bulk  Heterojuction (BHJ) needs more detailed investigations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='10, 31, 32  The identification of the packing motif of the NFA within a  donor:acceptor blend is a challanging task, yet the structural  analysis is commonly based on Grazing Incidence Wide Angle X-  Ray Scattering (GIWAXS) patterns that lack of enough  diffraction features for the structural determination.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The  analysis of the main Bragg peaks of the NFA, often referred as  the lamellar (100) and the π-π stacking (010) distances,33-35 is  routinely considered enough to draw conclusions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Misleading  results can, however, arise from the similar (if not overlapping)  spectral features of the donor and acceptor components in the  q-space, the typical peak broadening of organic compounds  reflecting a high degree of flexibility, the presence of rotational  isomers, polymorphism,36, 37 and a general lack of long-range  crystalline order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='34  In this work,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' we used an extensive set of both experimental and  theoretical approaches to study the molecular packing and  morphology of a specific set of common NFAs (o-IDTBR,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' IDIC,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  ITIC,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' m-ITIC,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' 4TIC,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' 4TICO,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' m-4TICO,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' whose structures are shown  in Figure 2),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' by means of single-crystal X-Ray Diffraction (XRD),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  powder XRD and Le Bail refinement,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' GIWAXS,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Atomic Force  Microscopy (AFM),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' crystal lattice simulations,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' ss-NMR,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' and  Gauge Including Projected Augmented Wave (GIPAW) DFT  calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Our aim was to analyse the NFA molecular packing,  a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Clarendon Laboratory, Department of Physics, University of Oxford, Parks Road,  Oxford, OX1 3PU, United Kingdom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' E-mail: pierluigi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='mondelli@physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='ox.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='uk  b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Institut de Ciència de Materials de Barcelona, ICMAB-CSIC, Campus UAB, 08193  Bellaterra, Spain  c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' University of Lille, CNRS, Centrale Lille, Univ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Artois, UMR 8181- UCCS - Unité de  Catalyse et Chimie du Solide, F-59000 Lille, France  d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Merck Chemicals Ltd, Chilworth Technical Centre, University Parkway,  Southampton, SO16 7QD, United Kingdom  e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Laboratory for Chemistry of Novel Materials, University of Mons, Place du Parc,  20, 7000 Mons (Belgium)  f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' NCD‐SWEET beamline, ALBA Synchrotron Light Source, Cerdanyola del Vallès,  08290 Spain  g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Physics, Faculty of Science and Engineering, Åbo Akademi University, 20500  Turku, Finland  h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' EPSRC Crystallographic Service, Department of Chemistry, University of  Southampton, Highfield, SO17 1BJ, UK  Current address: Italian Institute of Technology, Printed and Molecular  Electronics, Via Pascoli 70/3, 20133 Milan, Italy  † Email: pierluigi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='mondelli@gmail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='com, graham.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='morse@gmail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='com  with a special focus on the structural evolution from single  crystals to solar cells.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' We studied the molecular arrangement  from single crystals, to powders, then thin films and finally  morphology in the bulk heterojunction (BHJ) to bring important  insights into the NFA arrangement in the BHJs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' We analysed the  most relevant NFA packing motifs and polymorphs, discussing  their role in the solar cell morphology, current-voltage  performance, and charge transport properties, such as electron  mobility and bimolecular recombination, by means of photo-  CELIV (Charge Extraction Linear Increasing Voltage) and MIS-  CELIV (Metal-Insulator-Semiconductor-Charge Extraction Linear  Increasing Voltage).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Experimental  General Characterisation  UV-Vis absorption spectra were recorded on an OceanOptics QE  PRO spectrometer using a tungsten halogen light source (HL-  2000-FHSA from OceanOptics).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The HOMO levels of the  compounds in thin films were obtained by measuring the film  photoemission current onset with the Air Photoemission  Spectroscopy module (APS02) of the Kelvin Probe from KP  Technology Ltd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The Kelvin Probe was equipped with a 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='0 mm  diameter tip coated with gold alloy, a UV deuterium lamp, and  a monochromator (range 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='44-3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='88 eV).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' LUMO levels were  estimated by adding the optical bandgap (determined from the  onset of the UV-Vis absorption) to the measured HOMO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Single-crystal X-ray diffraction data were collected on a Rigaku  Oxford Diffraction Supernova diffractometer equipped with  micro-focus sealed (Mo-Kα) X-ray Source, CCD plate detector  and Oxford Cryostream N2 flow cryostat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The samples were  mounted on Kapton loops from the solution and shock-cooled  to 173.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='0(2) K or 100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='0(2) K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Cell indexing and peak integration  were performed with CrysAlisPro.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Structural solution and  refinement were carried out with ShelxT and ShelxL,  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content="  Powder X-ray diffraction was performed using a PANalytical X'Pert  PRO diffractometer with Cu -Kα radiation." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' During the measurement,  the sample was kept at room temperature and under ambient  conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  GIWAXS  The GIWAXS experiments were carried out at NCD-SWEET beamline  at ALBA synchrotron (Beamtime ID: 2019093873).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' A monochromatic  X-ray beam with a photon energy of 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='4 keV was set using a Si (1 1  1) channel cut monochromator, further collimated with an array of  beryllium lenses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The GIWAXS maps were recorded with a Rayonix LX  255-HS detector, consisting of a pixel array of 960 × 2880 pixels of  88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='54 × 88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='54 μm2 (H × V) for the binning employed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The samples  were thermally annealed before the measurements at the optimised  temperature for the solar cell performance (see below) using a  hotplate in air.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' GIWAXS frames were acquired near the critical angle  of the glass substrate (ca.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='15° for the X-ray wavelength employed),  penetrating a depth of 11 nm for the layer of interest38 while  minimizing the contribution of the substrate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='‡ The recorded 2D  scattering patterns were analysed using a home-made python  routine based on pyFAI (the Fast Azimuthal Integration Python  library).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='39 GIWAXS images are in logarithmic scale, ranging from dark  blue (low intensity) to yellow (high intensity).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The in-plane and out-  of-plane profiles were obtained by integrating the diffraction  intensity in rectangular areas centred at 𝜒=0° and 𝜒=90° from 𝜒-q  images (scattering intensity as a function of the azimuthal angle).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The  scattering peaks of the bulk structure were compared to the  experimental data using SimDiffraction, a MatLab code for simulating  the film diffraction pattern for a given crystal structure and  orientation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='40 For each NFA, The simulations were performed by  choosing a specific NFA orientation with respect to the substrate  (typically in-plane and out-of-plane).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The Miller indices (h k l)  associated with the NFA packing direction were determined by  Mercury41 and used as input parameters for the simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' A better  fit between simulated and experimental GIWAXS was obtained when  Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Sketch of the different molecular packing motifs observed in Acceptor-Donor-Acceptor (A-D-A) type NFAs crystal structures and labelled according to the dimensionality  of the π-π stacking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  R  D  A-D-A Structure  ID  IT  4T  IC  BR  PhC6  m-PhC6  PhOC6  m-PhOC6  R group  D unit  A unit  NFA  D unit  A unit  R group  ITIC  IT  IC  PhC6  m-ITIC  IT  IC  m-ITIC  4TIC  4T  IC  PhC6  4TICO  4T  IC  PhOC8  m-4TICO  4T  IC  m-PhC8  IDIC  ID  IC  C6  o-IDTBR  ID  BR  C8  Molecular Packing  0D - Herringbone  2D - Brickwork  3D - Reticular  A  A  R  C6 = C6H13  C8 = C8H17  using the unit cell parameters obtained by Le Bail refinement (see  below) as input for the simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Solid-state NMR spectroscopy  For ssNMR experiments, O-IDTBR powder was packed into a 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='3  mm (outer diameter) rotor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' All 1D 1H and 13C20, and 2D 1H-1H  and 1H-13C correlation NMR experiments were carried out on a  Bruker Avance Neo (18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='8 T) spectrometer using a 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='3 mm  double resonance H-X probehead tuned to  1H (Larmor  frequency, 800.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='13 MHz) and 13C (Larmor frequency, 201.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='2 MHz)  nuclei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Unless otherwise states, the Magic Angle Spinning (MAS)  frequency was 50 kHz in all cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The nutation frequencies for  1H and 13C were 100 kHz and 90 kHz, corresponding to 90o pulse  durations of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='5 and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='75 \uf06ds, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The longitudinal  relaxation time (T1) of 1H was determined to be 3 s based on  inversion recovery measurements and analyses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' 1D 1H MAS  NMR spectrum was acquired using 16 co-added transients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' A 2D  1H-1H  double-quantum  (DQ)-single-quantum  (SQ)  NMR  spectrum was acquired using Back-to-Back (BaBa) sequence at  fast MAS,42 using a rotor-synchronized t1 increment of 20 µs  corresponding to one rotor period (\uf074r).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The indirect 1H DQ  dimension was acquired using 256 t1 increments, each with 16  co-added transients, corresponding to a total experimental  time of ~4 h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' 1H detected 2D 1H-13C heteronuclear correlation  (HETCOR) spectra were acquired with 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1 ms and 3 ms of CP  contact time and the indirect 13C dimension was acquired using  140 t1 increments, each with 32 co-added transients,  corresponding to a total experimental time of 8 h each.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Atomic Force Microscopy  The thin films were investigated by AFM both in contact and  dynamic modes using a commercial head and control unit from  Nanotec Electronica.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The used thermal annealing protocol was  the one optimized for the devices (see Table S10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' For each  sample, after each annealing step, different spots of the surface  were imaged (at several image sizes) to have a statistical validity  of the measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The images presented in the article are  chosen as high-resolution representative images of the surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  The estimation of the root mean square (RMS) roughness was  done selecting about 6 contact mode images (30x30 and 50x50  µm²) for each temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Si3N4 V-shaped cantilevers (Veeco)  with the nominal force constant ranging between 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='03 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='5  N/m were employed for the contact mode, while Cr/Pt-coated  silicon tips on rectangular cantilevers (BudgetSensors) with a  nominal resonance frequency of 75 kHz and a force constant of  3 N/m were used for the dynamic mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The open-source  Gwyddion software was used to analyse all the presented AFM  images,43 including the domain size calculation which were  done using the watershed algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='44 The input parameters  used for the watershed analysis can be found in the Supporting  Information (pages S20-S25).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Solar Cells Fabrication and Characterisation  Inverted-architecture organic solar cells were fabricated by  blade coating of the organic layers on Indium Tin  Oxide(ITO)/glass pre-patterned 5x5 cm2 substrates (Zencatec  Limited).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' A detailed description of the interlayers and  electrodes fabrication, along with the experimental description  of the current-voltage (I-V) measurements can be found in the  experimental section of a recent work from our group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='36  Aluminium-doped zinc oxide from Avantama (N-21X-Slot) was  Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Structure of an Acceptor-Donor-Acceptor (A-D-A) NFA with its building blocks on the top left.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The NFAs studied  in this work (table on the top right) are identified with their chemical subunits (A, D and R groups) whose chemical  structures are also shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  R  D  A-D-A Structure  ID  IT  4T  IC  BR  PhC6  m-PhC6  PhOC6  m-PhOC6  R group  D unit  A unit  NFA  D unit  A unit  R group  ITIC  IT  IC  PhC6  m-ITIC  IT  IC  m-ITIC  4TIC  4T  IC  PhC6  4TICO  4T  IC  PhOC8  m-4TICO  4T  IC  m-PhC8  IDIC  ID  IC  C6  o-IDTBR  ID  BR  C8  Molecular Packing  0D - Herringbone  2D - Brickwork  3D - Reticular  A  A  R  C6 = C6H13  C8 = C8H17  used for the electron transporting layer,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' while PEDOT:PSS  (Clevios Al 4083 from Heraeus) for the hole transporting layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  All the NFAs were supplied by 1-Material Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=', with the only  exception of 4TICO (Merck KGaA).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' For the active layer, PBTZT-  stat-BDTT-8 (Merck KGaA) was used as the donor material45 in  combination with the NFAs listed in Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Each blend was  dissolved in a 1:1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='3 ratio (by weight) and 80 nm thick layers‡‡  were processed from a 23 mg/ml solid content o-xylene  solution, without the use of additional additives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The blade  speed was adjusted between 7 to 13 mm s-1 to reach the desired  thickness with a 100 µm blade gap and 70 µL cast volume.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Casting plate temperature was varied between 60°C and 80°C  and the as-cast devices were further annealed at temperatures  ranging from 100°C to 140°C on a hot plate in air following the  optimisation protocol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' A 100 nm silver back electrode was  thermally evaporated on top of the hole transporting layer,  under a pressure of 2x10-6 mbar at a rate of 1 Å/s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Solar cells  have a device area of ∼ 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='5 mm2, as determined from the  geometrical overlap between cathode and anode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Photo-CELIV  Photo-CELIV was performed using the Transient Measurement  Unit by Automatic Research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' A 655 nm laser pulse (5 µs long)  was used to photo-generate charges into ∼ 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='5 mm2 area solar  cells.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The linear increasing voltage ramp range was 0 - 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='5 V and  10 µs long.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The delay time between the laser pulse and the  voltage ramp was varied between 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1 to 100 µs, during which a  constant pre-bias voltage (close to VOC) was applied to limit the  charge injection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The charge mobility was determined by using  eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' (1) of ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='46 on the 30 µs long delay time data collection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The  bimolecular recombination coefficient was calculated using  eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' (2) of ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='47  MIS-CELIV  MIS-CELIV48 was performed with a PAIOS system from Fluxim  AG, Switzerland.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The layer stack was  ITO/AZO/active  layer/MgF2/Ag with an insulating 50 nm MgF2 layer that blocks  injection of holes so that the electron mobility is obtained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=" The  chosen thickness balances the layer's insulating properties with  its capacitance in relation to the absorber’s capacitance." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The  other layers are processed as for the solar cell devices with  some deviations in the annealing protocol discussed in the  Support Information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' A small device area of ~1mm2 was chosen  to minimize RC effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The offset voltage was typically varied  between 0V and 8V and the ramp rate between 50 V/ms and  1600 V/ms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The latter allowed to account for injection barrier  effects49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The analysis was carried out following the diffusion-  corrected eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' (11) of ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='49 with saturation and geometric  displacement current densities extracted from the CELIV curves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Density Functional Theory calculations  Periodic DFT calculations on the o-IDTBR crystalline structure  have been performed using the CASTEP module with the  Materials Studio software.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' All calculations have been carried  out with the PBE GGA functional, a plane-wave energy cutoff of  50 Rydbergs (680 eV) and a k-point spacing of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='05Å-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='50 The  crystalline structure of o-IDTBR has first been full relaxed using  the Tkatchenko-Scheffler dispersion correction method,  optimizing both all atomic positions within the cell and unit cell  parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The resulting DFT-optimized cell parameters (a =  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='8706Å, b = 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='5913Å, c = 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='6925Å, \uf061 = 90°, \uf062 = 96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='0529, \uf067 =  90°) are in excellent agreement with the measured  crystallographic data in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' NMR calculations have then  been performed on the optimized crystal structure using the  Gauge-Including Projector Augmented-Wave method (GIPAW);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  reference shieldings of 31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='09 and 179.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='02 ppm were used for 1H  and 13C, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Results and Discussion  Structural Analysis  A common way of classifying the organic semiconductor packing  motif is by observing their π-π stacking dimensionality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='18, 51-54 A-D-A  molecules (Figure 2) in particular, can form highly interconnected  domains through intermolecular interactions between the acceptor  units (A units) of adjacent molecules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='18, 55 The percolation pathway  that forms through π-π stacking can develop along multiple  directions of the crystalline domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Molecules can arrange through  brickwork pattern with 2D percolation pathways, or through the so-  called "reticular" packing motif which is characterised by 3D-  interconnected domains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' For herringbone crystal structures the  molecular backbones of adjacent units are orthogonal, therefore lack  π-π stacking (Figure 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  To reveal the NFA packing within the BHJ we started our  investigations from single crystals, which represent the perfect  platform to explore the influence of the solid-state arrangement on  the charge transport.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Most of the crystal structures analysed in this  work were previously resolved by our group,18 while others were  found in literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' As indicated in Table 1, some NFAs showed  polymorphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' For instance, ITIC single crystals can be found to be  either 0D herringbone or 2D brickwork motifs and m-4TICO also  presents two different unit cells.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Single crystals represent the NFA molecular ordering of high purity  and large millimetre sized crystal grown from controlled conditions  (solvent vapour diffusion, see reference18) and measured by XRD in  a low-temperature (100 K) environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Thus, it is possible to  observe substantial differences in the molecular arrangement as we  deviate from such ideal systems towards the BHJ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Therefore, we  wanted to understand how the crystal packing changes by raising the  temperature to ambient conditions (200 K shift between single  crystal and powder XRD) and by disrupting the ideal growth  conditions and long-range crystallinity of NFA single crystals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' As an  intermediate step, ss-NMR and XRD of purified NFA powders were  performed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' In the main text, we limit our observations on o-IDTBR,  extending the analysis and discussion to the other materials in the  Supplementary Information (pages S6-S9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Crystallographic information of the NFA crystal structures available for the materials analysed in this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  From Single Crystals to Powder  o-IDTBR has a 3D reticular packing motif in the single crystal,56  characterised by close-contacts between the electron accepting  units (A units) of tilted adjacent molecules (Figure 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' To  understand if this packing geometry is retained in powder  samples, we performed X-Ray Diffraction and ss-NMR  measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The powder diffractogram showed a long-range  crystallinity with well-defined Bragg peaks in the low-angle  region (Figure 3a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' A partial agreement exists between the  experimental data and the simulated 1D pattern of the single  crystal structure, yet a certain mismatch between the positions  for most of the reflections suggests that a slightly different unit  cell is formed in powder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' This can occur because of the  CCDC  Identifier  Molecul  e  Motif  π-π  a (Å)  b (Å)  c (Å)  𝛼 (deg)  𝛽 (deg)  𝛾 (deg)  Volume  (Å3)  FOSPOV56  o-IDTBR  reticular  3D  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='7663(2)  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='8103(17)  32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='7146(3)  90  96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='2928(12)  90  7077.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='43(15)  YEBKEY19  4TIC  reticular  3D  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='969(7)  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='144(9)  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='970(10)  104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='668(16)  109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='998(17)  96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='169(14)  3822.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='08  VUBJIO18  m-4TICO  brickwork  2D  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='6526(3)  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='4878(8)  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='0435(8)  114.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='697(5)  103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='822(4)  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='890(4)  2251.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='45(19)  This work  m-4TICO  brickwork  2D  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='7845(7)  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='3726(13)  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='7896(13)  67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='136(7)  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='678(7)  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='630(7)  2054.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='98  VUBJOU18  m-ITIC  brickwork  2D  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='7454(13)  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='872(2)  25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='2647(18)  87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='770(8)  88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='724(9)  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='001(12)  4075.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1(9)  VUBKAH18  IDIC  brickwork  2D  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='6679(4)  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='5073(7)  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='5784(6)  72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='096(4)  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='545(4)  88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='839(4)  1353.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='88(12)  VUBJEK18  4TICO  herringbone  0D  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='2836(2)  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='0101(5)  29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='3242(6)  90  89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='997(2)  90  8968.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1(3)  KIZSUK20  ITIC  brickwork  2D  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='420(6)  23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='019(17)  23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='126(17)  101.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='780(10)  95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='319(10)  91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='105(14)  4366(5)  HEHQUJ01  18  ITIC  herringbone  0D  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='9009(7)  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='5043(4)  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1199(5)  99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='309(2)  101.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='541(3)  108.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='366(3)  3777.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='2(2)  Figure 3 a) Powder XRD diffractogram overlaid to the simulated powder pattern of the single crystal structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The inset is showing the progressive improvement of the fitting  from the original fit to manual and Le Bail refinement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' c) Periodic DFT optimised crystal structure and highlighted backbone-backbone (red boxes) and backbone-sidechains  interaction (blue boxes).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' b-d) DFT calculated 2D plots of the 1H-1H and 1H-13C chemical shifts (red circles) overlaid on the experimental 1H-1H double-quantum-single-quantum  (DQ-SQ) correlation and 1H-13C heteronuclear correlation spectra (contours), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The dashed blue rectangles indicate the minor changes in the backbone-sidechain  interactions when comparing the crystalline to powder form, meaning that the π-π interactions (along with the packing motif) remains substantially unvaried.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  a)  b)  Data  Initial Fit  Manual Fit  Le Bail  10  (01 1)  28  Gaf  HDQ chemical shift(ppm)  0  8  824  6  20  4  4  (110)  Inisal FaManuat Fit  LeBa  8  2  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='2)  0  12  2  16  6  8  10  12  14  20 (°)  10  8  6  2  0  "HSQchemicalshift(ppm)  c)  (p  0  sideview  20  40  chemicalshift (ppm)  60  80  100  backbone-sidechaininteractions  120  140  topview  160  180  200  10  8  1  6  1  4  2  1  0  1  backbone-backboneinteractions  Hchemicalshift(ppm)  temperature shift (200 K) between the single crystal and  powder XRD measurements,§ which can impact the long-range  order, the local structures and packing interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' In a first  approximation,§§ we manually solved the reciprocal-space  metric tensor equation for monoclinic structures57 to derive the  lattice parameters from the experimental data (Table S1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The  spectral agreement between the “manually-refined” simulated  diffractogram and the experimental data improves (Figure 3a),  as the Goodness of Fit (GOF), Chi2 and residuals (wR) parameters are  now reduced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' This means that a better fit is obtained after the  manual refinement, and therefore it is reasonable to assume a  structural agreement between the two phases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' A further  confirmation is obtained when the lattice parameters and unit  cell angles are derived through Le Bail refinement, suggesting that  the structure undergoes a volumetric expansion from single  crystal to powder phase (Table S1), possibly resulting from the  different temperatures of the measurements (see Supporting  Information, Figure S5 and Table S2) causing subtle changes in  the local interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  To further confirm this behaviour, we performed NMR  crystallography  analysis, which combines  XRD, ssNMR  spectroscopy and modelling (here first principles calculations  and GIPAW-DFT based NMR chemical shielding calculations)  techniques to resolve atomic-scale interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='58 Solid-state  NMR is particularly sensitive to local structures of polymeric  organic semiconductors, NFAs and polymer:NFA blends.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='59-61  Here, we carried out ssNMR crystallography analysis with the  aim of identifying the changes in local structures in crystals and  powder compositions (Figure 3b-d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' This is achieved by  analysing and comparing 1H and 13C chemical shifts of crystal  structures as calculated by GIPAW-DFT approach with the  experimentally measured 13C and 1H chemical shifts for the o-  IDTBR powder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' A detailed analysis of experimental 1D 1H, 13C  and 2D 1H-1H and 1H-13C correlation ssNMR spectra is presented  in Supporting Information (Figures S1-S4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Periodic DFT  optimised crystal structures are shown in Figure 3c, whereby  the backbone-backbone and backbone-sidechain interactions  are indicated in soft-rectangles (in red) and circles (in blue),  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Figure 3b,d compares the 2D plots of DFT-  calculated chemical shifts generated by MagresView and  MagresPython software tool62 for 1H-1H and 1H-13C spin pairs  within a 3 Å distance, overlaid on the experimental 1H-1H  double-quantum-single-quantum (DQ-SQ) correlation and 1H-  13C nuclear correlation spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' In 2D NMR measurements of  this type, 2D peaks corresponding to 1H-1H and 1H-13C  proximities within sub-nanometre distances in powder solids  are detected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' It is noteworthy that a good correlation between  the GIPAW-DFT calculated chemical shifts and the experimental  chemical shifts (\uf064) are observed for both aliphatic and aromatic  moieties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' In the DQ-SQ spectrum (Figure 3b, the broad DQ peak  at 0-8 ppm in the vertical axis is due to the 1H-1H proximities in  alkyl sidechains and the DQ peaks in 12-16 ppm range are due  to the through-space 1H-1H proximities between aromatic  groups within the chain and in between the \uf070−\uf070 stacked o-  IDTBR molecules, both of which exhibit good agreement with  the DFT-calculated chemical shifts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' However, subtle differences  between the DFT calculated and experimental chemical shifts  \uf064(1HDQ) in the 8-12 ppm range (dashed blue boxes), which  originate from through-space dipolar interactions between  aromatic groups and sidechains, indicate the minor changes in  the backbone-sidechain interactions in the vicinity of CH2  moieties when compared the crystalline and powder forms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='63  Similarly, a good agreement is obtained when comparing the  DFT-calculated chemical shifts of  1H-13C pairs with the  experimental 1H-13C 2D peaks in the HETCOR spectrum, which  shows 2D peaks associated with the sidechains at \uf064(13C) = 10-40  ppm and \uf064 (1H) = 1-4 ppm, and the backbone moieties \uf064 (13C) =  110-170 ppm and \uf064 (1H) = 5-9 ppm (Figure 3d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' However,  deviations between the DFT-calculated versus experimental  chemical shifts are observed for the 2D peaks corresponding to  the through-space aromatic-sidechain dipolar interactions as  depicted in the blue dashed boxes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Similar trends are observed  for Y-series NFAs that showed changes in the local structures  with respect to the backbone-sidechain interactions between  the crystalline and powder forms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='58 The most important take  away from the ssNMR crystallography study is that it allowed us  to leverage the Le Bail refinement as a tool to verify the  structural compatibility between single crystal and powder in  terms of packing motif.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' This is possible as it allows for shift in  the lattice parameters caused by side chains relaxation at  elevated temperatures and demonstrated by changes in the  backbone-sidechain interactions, while preserving the π-π  interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' By extending the Le Bail analysis to the other NFAs  of interest (Figures S5-S8 and Table S3), we obtained useful  information about the materials crystallinity:  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  ITIC herringbone polymorph is predominant over the  brickwork (Figure S7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  m-4TICO presents two brickwork structures but only  the un-solvated one is represented in powder (Figure  S8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  o-IDTBR, IDIC, m-ITIC and 4TICO single crystal packing  is preserved in powder (Figure 3a and S6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  With the only exception of 4TIC,¶ all the NFAs show  several Bragg peaks in the low angle region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  All the non-solvated structures undergo a volumetric  expansion due to the temperature difference between  single crystal and powder experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' However, we  do not exclude that the volumetric reduction observed  for the solvated crystals is only apparent, given that a  significant volume portion in the single crystal  structure is occupied by the solvent, which is not  expected to be found in the powder structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  A summary of the results obtained by Le Bail refinement  performed for the different NFAs can be found in Table S3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  From Powder to NFA Films  A further intermediate step to approach the NFA packing in the BHJ  was to study the molecular organisation in thin films.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Here, we  expected to see a more compatible unit cell to the one observed in  powder rather than in single crystal as we were going towards  systems that are presumably composed of many little crystallites  with reduced long-range order, cumulative disorder and multiple  orientations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='34 Moreover, the temperature held during GIWAXS  measurements on film was 300 K as for the powder experiments  (XRD and ss-NMR).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' For convenience, we here report the analysis  performed on o-IDTBR, while the complete dataset including the  other materials can be found in the Supporting Information (pages  S10-S19).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  GIWAXS data of o-IDTBR film with related 1D integration profiles  along the in-plane and out-of-plane directions are shown in Figure  4a-b and Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' From the q-map two main contributions are visible:  a low-angle component, located at q ≈ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='8 nm-1, which is generally  recognised as lamellar peak and is indicative of the separation of the  conjugated and aliphatic moieties,35 and a higher angle feature (q ≈  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='3 nm-1) which is commonly attributed to π-π stacking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='64 Given the  anisotropic nature of these two main diffraction components, we  expected a π-π stacking with a preferential face-on crystalline  orientation of the o-IDTBR domains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' To validate our hypothesis, we  simulated the GIWAXS pattern of the o-IDTBR single crystal structure  (Le-Bail refined) oriented along the (4 1 1) direction (Figure 4c), which  is nearly parallel to the π-π stacking (4 0 2) and perpendicular to  the lamellar (0 1 -1) peak (Figure 4e).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The good agreement  between the simulated and experimental diffraction data suggests  that the o-IDTBR packing motif is preserved in film, where the  domains adopt a face-on orientation with an in-plane lamellar  ordering (0 -1 1) and out-of-plane π-π stacking (4 0 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The good  agreement between our findings with literature65, 66 clarifies the  crystal packing motif and orientation of o-IDTBR films.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Some more considerations on the o-IDTBR film crystallinity can be  done by focussing on the spectral shape of the main diffraction peak  (lamellar peak).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' According to the paracrystalline g parameter found  for the lamellar peak (Table 2),34 the film can be classified on the  boundary between semi-paracrystalline and amorphous, showing a  Crystal Coherence Length (CCL) of ∼ 20 nm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' For this class of materials,  a direct quantification of the crystalline domain size from the CCL is  often not possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' According to the nomenclature used in ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='34, we  will refer to the CCL as the spatial extent of the coherently diffracting  regions included in the paracrystallites, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' column lengths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='34  To access the NFA domain size (which can be composed of multiple  paracrystallites), we investigated the surface morphology by AFM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Figure 4d shows well-defined domain boundaries and a root mean  square (RMS) roughness of 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='9 nm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' We performed the AFM image  segmentation (see pages S20-S25) through watershed algorithm to  derive the average domain size and its distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='44 From the  calculations, we observed an average domain size of 36 nm from the  maximum of the peak distribution (inset of Figure 4d and Table 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  This value is higher than the CCL, which confirmed that o-IDTBR  domains (visible from the AFM) are composed of multiple  paracrystallites, whose column length is determined by XRD (CCL).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' To  get an indication of the domain structural purity, we introduced a  parameter (ϕ) defined as the ratio (in percent) between the CCL and  the domain size obtained by AFM (Table 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' o-IDTBR GIWAXS pattern (a) with in-plane and out-of-plane integration profiles along qz ∼ 0 and qxy ∼ 0, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Simulated GIWAXS pattern of the o-IDTBR unit cell  oriented along the (4 1 1) direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The good agreement with the experimental GIWAXS confirmed a face-on 3D reticular packing motif of o-IDTBR in the blend.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' (c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' 5x5 µm AFM  image of o-IDTBR film with domain size distribution and average value (inset).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Side (e) and top (f) views of the o-IDTBR crystal packing with π-π stacking (4 0 2) and lamellar (0 1-1)  peaks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  30  25  20  (t-_wu)b  15  10  5  0  0  5  10  15  20  25  qr(nm-1)  Analogue characterisation and analysis were performed on the other  NFAs of interest for this work (Figure S9-S14 and Tables S4-S9) and  some key considerations and results can be summarised as follows:  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' most of the NFAs films showed a well-defined GIWAXS  scattering, especially in the lamellar and π-π stacking regions  (Figure S9-S12 and Tables S4-S7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' These two main features are  characterised by a low angular distribution and therefore are  indicative of a preferential orientation of the crystalline domains  with respect to the substrate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' o-IDTBR, m-4TICO, 4TIC, m-ITIC and IDIC crystal lattice  simulations yielded a good structural agreement with the  powder unit cell obtained by Le Bail refinement (Figures S9-  S12a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' This proved that a structural continuity in terms of packing  motif occurs between powder and films.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' NFAs with a 3D reticular (4TIC and o-IDTBR, see Figures S9b and  5e,f) and 2D brickwork (m-ITIC and IDIC, see Figures S11-S12b)  crystal packing motifs are involved in a face-on domain  orientation, with the m-4TICO as only exception ("quasi" edge-  on crystal packing, see Figure S10b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' ITIC and 4TICO were found to have a 0D-herringbone packing  motif in powder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' However, due to the lack of multiple Bragg  peaks, texturing, and long-range crystallinity (Figures S13, S14  and Tables S8-S9) we could not perform any crystal lattice  simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' However, we do not exclude the presence of small  and randomly oriented herringbone column lengths within the  domains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The high g parameter found for all the NFAs (> 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='5), prevented us  from directly quantifying the crystallite domain size from the  lamellar peak shape (FWHM) as the CCL represents the spatial  extent of the coherently diffracting regions (Table S4-S9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' We  therefore estimated the domain size from AFM image  segmentation along with an indication for the domain purity (ϕ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' In general, NFAs that form π-π stacking structures (through 2D  brickwork or 3D reticular motifs) in single crystals and powder  showed the highest crystallinity in films (lowest g parameters  and highest CCL, see Tables S4-S9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Conversely, 0D herringbone  NFAs (ITIC and 4TICO) provided the highest paracrystalline  parameter g, highest CCL, and surprisingly among the highest  domain purity ϕ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  NFAs blended with PBTZT-stat-BDTT-8  After having characterised the NFA film crystallinity, we extended  our investigation on NFA:PBTZT-stat-BDTT-8 blend films, which were  used as active layers for the solar cells fabrication (see below).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' As for  the rest of the structural characterisation, we here limit the  discussion on PBTZT-stat-BDTT-8:o-IDTBR blend while the analysis  for the other systems can be found in the Supporting Information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' PBTZT-stat-BDTT-8 (a) and PBTZT-stat-BDTT-8:o-IDTBR (b) GIWAXS patterns with in-plane (c) and out-of-plane (f) integration profiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The NFA features are clearly  visible from the blend GIWAXS, which confirmed that o-IDTBR maintain the packing motif in blend.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' 5x5 µm AFM images of PBTZT-stat-BDTT-8 (d) and PBTZT-stat-BDTT-8 :o-  IDTBR (e) with domain size distribution and average value (inset).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  PBTZT-stat-BDTT-8:o-IDTBR  PBTZT-stat-BDTT-8  x20  (0 1 0)  (1 0 0)  a)  0  5  10  15  20  25  30  0  5  10  15  20  25  30  qz (nm-1)  qz (nm-1)  5  0  5  10  15  20  25  5  0  5  10  15  20  25  qxy (nm-1)  qxy (nm-1)  In-plane  Out-of-plane  (0 1 0) + (4 0 2)  (1 0 0)  (0 1 -1)  (0 1 -1)  (0 1 -1)  (1 0 0)  x5  b)  c)  d)  e)  f)  (4 0 2)  (4 0 2) + (0 1 0)  (0 1 0)  RMS: 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='7 nm  RMS: 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='3 nm  30  25  20  qz(nm-1)  15  10  5  0  0  5  15  20  25  qr(nm-1)30  25  20  qz(nm-1)  15  10  5  0  5  0  5  15  20  25  qr(nm-1)  The PBTZT-stat-BDTT-8 polymer GIWAXS pattern is shown in Figure  5a, where a (1 0 0) lamellar reflection is located at q ≈ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='7 nm-1 and  the (0 1 0) π-π stacking feature at q ≈ 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='0 nm-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The integration  profiles suggest a prevalent in-plane orientation of the (1 0 0) feature  and an out-of-plane direction of the (0 1 0) (Figure 5c, f).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' A slight face-  on crystalline orientation of the PBTZT-stat-BDTT-8 was previously  reported, along with its smooth surface morphology with low RMS  (Figure 5d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='36  GIWAXS data and 1D profiles of PBTZT-stat-BDTT-8:o-IDTBR blend  are shown in Figure 5b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' A broad π-π stacking feature is located at q ≈  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1 nm-1 along the out-of-plane (Figure 5d), which can arise from  both the NFA and the polymer due to the spectral overlap in the q  range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Therefore, we focus on the lamellar features of o-IDTBR and  PBTZT-stat-BDTT-8 as indicative of the distinct material ordering in  the blend given that they can be distinguished from the in-plane  profiles (Figure 5c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The o-IDTBR (0 1 -1) lamellar peak is located here  at q ≈ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='8 nm-1, meaning that the NFA crystalline ordering in the blend  is preserved with a similar lattice spacing and crystal packing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  A remarkable difference is reported for the spectral shape of the NFA  lamellar peak as it is characterised by an increased FWHM, indicating  a reduced long-range ordering (lower CCL) of the o-IDTBR domains in  the blend when compared to pure o-IDTBR film, resulting in higher g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  In addition to this, the increased domain size calculated from the  AFM image (Figure 5e), which implies a lower degree of domain  purity (φ) of the NFA in the blend (Table 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  The analysis for the other NFAs can be found in the Supporting  Information (Figures S9-S14 and Tables S4-S9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' However, the main  conclusions can be outlined as follows:  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  The NFA crystallinity in PBTZT-stat-BDTT-8:NFA blends  presented broader and slightly shifted (towards lower q)  lamellar peaks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' As a result, the NFA domains in the blend  are characterised by reduced crystallinity (lower CCL,  higher g) and relaxed lamellar packing with respect to the  bare NFA film.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Furthermore, the presence of the polymer  is also affecting the domain purity (ϕ), which is reduced for  most of the blends with respect to the films made of NFAs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  NFAs with 3D-reticular (o-IDTBR and 4TIC) and 2D-  brickwork (m-4TICO, IDIC and m-ITIC) arrangements in  pure NFA films, preserved their packing motif and texturing  in NFA:PBTZT-stat-BDTT-8 blends (Figure 5 and pages S10-  S17).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  NFAs that formed 0D herringbone structures in single  crystal and powder phases (ITIC and 4TICO), showed the  lowest crystallinity (highest g parameter and lowest CCL  calculated on the NFA lamellar peak) and poor texturing  among the series of NFA:PBTZT-stat-BDTT-8 blends (pages  S18-S19).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Our results are in good agreement with a recent  report, where the importance of the π-π stacking  interaction energy to preserve the NFA packing motif in the  blend films is highlighted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='67  Solar Cells Characteristics  To investigate the role of the NFA packing motif and crystallinity  on the charge transport properties and performance of OSCs,  we fabricated inverted architecture devices (Figure 6a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The  NFAs of interest were tested with PBTZT-stat-BDTT-8 active layers  and optimised with respect to the choice of the solvent, casting  temperature, and post-annealing treatment (Table S10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The  energy levels of the different NFAs with respect to the donor  polymer are shown in Figure 6b, along with the UV-Vis spectra  of each active layer used (figure 6c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The JV curves delivering the  highest PCE are shown in Figure 6d, and the JV characteristics  are listed in Table 3 (dark JV curves in Figure S24).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Surprisingly,  4TICO and ITIC were among the best performing NFAs in terms  of maximum and average PCE obtained, despite having the  lowest crystallinity as indicated by the highest g parameter and  lowest CCL (Table 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Moreover, the NFA crystal packing motif  does not seem to have a direct impact on performance (Table  3): 3D reticular packing NFAs such as o-IDTBR and 4TIC reached  a maximum PCE of 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='6 and 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='9 while m-4TICO (2D brickwork  packing motif) was the least performing NFA (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='3% PCE).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Interestingly, NFAs with a 0D herringbone packing motif in  single crystal (4TICO and ITIC) delivered the highest  performance (8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1 % and 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='2 %, respectively).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Nevertheless, we  still expected a strong interplay between the active layer  crystallinity, NFA packing, and charge transport properties,  which may have an impact on the solar cells performance and  in particular the FF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='68, 69 Thus, we performed photo-CELIV  experiments to determine the charge mobility and the  Component  Peak  Orientation  q (nm-1)  d (nm)  FWHM  (nm-1)  CCL  (nm)  g  Domain  Size (nm)  ϕ (%)  NFA film  o-IDTBR  (0 1 -1)  In-plane  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='79  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='66  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='27  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='9  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='6  36 ± 7  58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1  o-IDTBR  (4 0 2)  Out-of-plane  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='35  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='34  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='22  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='5  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='9 Polymer film  PBTZT-stat-BDTT-8  (1 0 0)  In-plane  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='71  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='32  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='78  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='2  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='4  24 ± 5  30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='2  PBTZT-stat-BDTT-8  (0 1 0)  Out-of-plane  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='35  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='75  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='5  25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='7 Blend film  o-IDTBR  (0 1 -1)  In-plane  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='77  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='67  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='33  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='8  50 ± 10  34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='3  PBTZT-stat-BDTT-8  (1 0 0)  In-plane  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='80  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='24  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='58  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='6  30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='0 PBTZT-stat-BDTT-8, o-IDTBR  (0 1 0) + (4 0 2)  Out-of-plane  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='14  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='35  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='80  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='0  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='7 Table 2 Crystallographic information of the main peaks observed by GIWAXS on o-IDTBR, PBTZT-stat-BDTT-8 and PBTZT-stat-BDTT-8:o-IDTBR films.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' AFM domain size and purity are  also shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The domain purity parameter (ϕ) is defined as the ratio (in percent) between the CCL and the domain size obtained by AFM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  bimolecular recombination coefficient for each NFA:PBTZT-stat-  BDTT-8 blend (Figure 6e,f and Table 3)¶ ¶.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='46, 47, 70-75  With regards to the mobility, we observed a remarkable  correlation between the NFA lamellar CCL in the blend and the  charge mobility (Figure 7a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The lowest mobility for ITIC and  4TICO blends is related to their poor crystallinity (low CCL and  high g parameter) detected in the pure NFA (Tables S4-S9) and  blend films (Table 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The 0D packing nature might be another  disadvantage  for  efficient  long-range  transport.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  The  relationship between charge mobility and NFA crystallinity was  further investigated by MIS-CELIV measurements, performed  on electron-injecting devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The electron mobility determined  by MIS-CELIV matched the values obtained via photo-CELIV  (Figure S23).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Since the photo-CELIV current is dominated by the  species with higher mobility,76 we could attribute the photo-  CELIV mobility to electrons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' This lead to the conclusion that the  electron mobility is clearly dependent on the NFA crystallinity,  as expressed by the CCL and g parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' However, the  mobility determined from both photo-CELIV and MIS-CELIV did  not dominate the solar cell performance, as seen from FF and  PCE (Table 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' This result encouraged us to investigate the  bimolecular recombination and its possible implications in the  device performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  We derived the bimolecular recombination coefficient by  photo-CELIV, exploring a purely quadratic dependence between  recombination and charge carrier density (Figure 6f).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='47 The  model provided a good fit with the sweep-out of free charges at  different time delays, (Figure 6f) and the bimolecular  recombination coefficient (𝛽exp) was derived according to the  equation (2) used in ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=',47 and is shown in Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Interestingly,  we find the lowest recombination coefficients for the solar cells  made of ITIC and 4TICO blends, which delivered the highest  performance and among the highest FF, highlighting the  importance of the bimolecular recombination on the device  parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='36, 77 Despite their lower crystallinity, active layers  made of ITIC and 4TICO resulted in higher domain purity (ϕ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Conversely, NFAs characterised by higher CCL and lower g, such  as IDIC and m-4TICO, provided among the lowest domain purity  and highest bimolecular recombination coefficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Overall, a  correlation is found between the NFA domain purity and the  bimolecular recombination coefficient (Figure 7b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  As mentioned above, the ϕ-parameter compares the spatial  extent of the NFA ordered regions in the domain (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=', column  lengths, derived from the CCL), with the domain size obtained  from AFM images and can be calculated as follows: 𝜙 =  𝐶𝐶𝐿 (𝑛𝑚) 𝐷𝑜𝑚𝑎𝑖𝑛 𝑠𝑖𝑧𝑒 (𝑛𝑚)  ⁄  ×  100).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' A blend film with low  domain purity (ϕ) can be understood as formed by domains  with a larger relative fraction of regions with an amorphous or  mixed nature that prompt recombination.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='78 Assessing domain  purity via the ϕ-parameter is easy-to-access compared to more  sophisticated methods such as resonant soft X-ray scattering  (RSoXS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='79, 80  Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=" Device architecture with 80 ± 5 nm thick active layers (a) and energy levels determined by Air Photoemission Spectroscopy (see experimental section) (b) of PBTZT-stat-  BDTT-8 and the different NFAs used for the solar cells' fabrication." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' UV-Vis of the different active layers (c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Characterisation of solar cells: J-V characteristics under illumination  (dark curves are plotted in Figure S17) (d), photo-CELIV curves (e) and bimolecular recombination coefficients (f).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Legends of panels c-f) are shared and shown in d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  e)  f)  b)  c)  a)  d)  OnybogobATd  HITBEDOLB22  Lob EJGcLOgG:ye  Table 3 Solar cells characteristics for the different NFAs combined with PBTZT-stat-BDTT-8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Results for the best solar cell in terms of PCE (average and standard deviation over a minimum of 10 devices) are shown for each active layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Device mobility  and bimolecular recombination coefficients are also listed along the other parameters related to the film crystallinity (g, CCL, packing), morphology (RMS, domain size) and domain purity (ϕ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The energy bandgap of the blend is also shown (Eg).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Active layer  PCE (%)  FF (%)  VOC (mV)  JSC  (mA･cm-2)  µ (cm2 V-1 s-1)  𝛽exp  (m3 s-1)  g  CCL  (nm)  Dom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' size  (nm)  φ  (%)  RMS  (nm)  Pack  ing  Eg  (meV)  PBTZT-stat-BDTT-8:4TICO  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1 (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='5 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='3)  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='9 (68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='5 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='2)  725 (717 ± 4)  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='8 (15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='3 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='7)  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='2 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='5 x10-5  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='6 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='3 x 10-18  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='4  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='8  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1 ± 2  47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='7  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='4  0D  870  PBTZT-stat-BDTT-8:ITIC  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='2 (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='8 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='2)  69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='3 (67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='5 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1)  820 (816 ± 3)  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='9 (12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='4 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='4)  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='7 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='6 x10-5  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='2 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1 x 10-18  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='0  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='7  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='6 ± 2  59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='2  0D  920  PBTZT-stat-BDTT-8:IDIC  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='0 (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='8 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='2)  73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='0 (71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='2 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='7)  750 (745 ± 2)  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='4 (12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='8 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='4)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='4 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1 x10-4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='3 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='6 x 10-17  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='4  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='5  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1 ± 8  25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='5  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1  2D  750  PBTZT-stat-BDTT-8:m-ITIC  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='9 (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='6 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='3)  69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='7 (67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='7 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='6)  850 (837 ± 7)  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='2 (11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='7 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='5)  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='7 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='9 x10-5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='6 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='3 x 10-17  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='3  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='4  51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='5 ± 10  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='3  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='7  2D  910  PBTZT-stat-BDTT-8:4TIC  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='6 (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='4 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='2)  67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='5 (65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='6 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1)  685 (685 ± 5)  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='3 (14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='2 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='3)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1 x10-4  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='0 x 10-17  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='0  29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='6 ± 6  30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='3  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='7  3D  830  PBTZT-stat-BDTT-8:o-IDTBR  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='9 (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='6 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='2)  58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='7 (57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='6 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='6)  950 (944 ± 3)  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='8 (10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='3 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='4)  N/A  N/A  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='8  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1  50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='0 ± 10  34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='3  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1  3D  1090  PBTZT-stat-BDTT-8:m-4TICO  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='3 (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='6 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='6)  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='7 (61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='5 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='6)  765 (755 ± 6)  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='2 (9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='9 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='4 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1 x10-4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='2 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='6 x 10-16  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='9  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='6  68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='5 ± 14  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='0  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='7  2D  800  To summarise the influence of the NFA crystallinity (g, CCL),  packing motif and morphology (domain size, RMS and ϕ) on the  solar cell parameters (PCE,# FF, VOC and JSC) and charge transport  properties (𝜇 and 𝛽exp), we built a multivariable cross-  correlation map with the most relevant parameters## (Figure 8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  While, strictly speaking, the cross-correlation map tests for  linear correlation, data that is correlated in a non-linear fashion  will still result in high (absolute) values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' As such the map may  serve as semi-quantitative tool to assess correlations in complex  multivariable systems, where not all dependencies are fully  understood physically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content="  With regards to the initial motivation of our study on the role of  the NFA crystal packing, we didn't observe a clear correlation  with the device performance parameters." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' However, an  enhanced propensity for NFAs with increasing directionality of  π-π stacking to form crystalline domains in the blend is evident  by the high Pearson correlation coefficient (r) between the  packing motif with g and CCL, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='97 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='76, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Thus,  the directionality of the π-π stacking directly promotes the NFA  crystallinity in blends (g and CCL), which is, in turn, favouring the  electron mobility (r coefficient of µ is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='97 and -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='88 with CCL  and g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' It is worth to mention a recent work, in which a long  exciton diffusion lifetime was observed in systems with  enhanced π-π stacking systems and crystallinity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='67 The tendence  to obtain higher mobilities in organic solar cells by increasing  the materials crystallinity is generally acknowledged.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='34, 81-83 In  addition to this, a lack of a direct correlation between packing  motif and performance was also recently reported, although  the identification of the NFA packing motif in the blend was  based on a visual examination of the GIWAXS pattern and 0D  herringbone systems were not included in the study .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='67  Interestingly, we found that the bulk heterojunction  morphology is having a bigger impact on performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' In  particular, active layers forming big domains at the surface have  low domain purity (r = -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='9), which is a good correlator for the  bimolecular recombination coefficient (Figure 7b-8 and S25).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  𝛽exp is, in turn, a first-tier correlator to JSC and FF (r is -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='79 and -  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='81, respectively) and the best correlating factor for the solar  cell performance (r = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='94).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The primary importance of the  bimolecular recombination on the device performance and its  relation with the domain purity was also observed in  literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='84  According the cross-correlation analysis, VOC is generally not  dependent on the film crystallinity and morphology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The energy  bandgap of the blend EG, determined with the difference  between HOMO of the polymer and the LUMO of the NFA  (Figure 6b), is the only significant correlator to VOC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The last  result agrees with the general knowledge about the relation  between VOC and the energetics of the donor and the acceptor  used in the blend.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='85-87  Conclusions  We have studied how NFAs crystal packing evolves from single  crystals to the bulk heterojunction of a solar cell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Given the  complexity of unambiguously determine the NFA packing motif  in an active layer, arising when moving from ideal systems, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=',  millimetre-size single crystals, to the most complex BHJ  morphology, we employed a step-by-step structural analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  The first step involved ss-NMR crystallography and powder XRD,  which helped us to leverage the Le Bail refinement as a quick  and effective tool to verify the structural compatibility between  single crystal and powder samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Then, we combined  GIWAXS, crystal lattice simulations and AFM to systematically  identify the NFA packing motif in the bare NFA films and blends  with the PBTZT-stat-BDTT-8 polymer, and to derive key  parameters to describe the material crystallinity (CCL and g  parameter) and morphology (RMS, domain size and domain  purity, ϕ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Finally, we investigated the influence of those key  Figure 7 a) Mobility is plotted versus the NFA crystal coherence length in the blend films.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' A linear fit of the data is represented with a  dashed grey line and indicates a correlation between CCL and electron mobility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' b) Bimolecular recombination coefficient determined by  photo-CELIV in relation to the NFA domain structural coherency in the blend.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' A linear fit is represented with a dashed grey line and  indicates a correlation between the bimolecular recombination coefficient and the domain purity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  (e  (q  10-16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  m-4TICO  m-4TICO  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='5  S  IDIC  4TIC  4TIC  m-ITIC  m-ITIC  IDIC  ITIC  4TICO  ITIC  4TICO  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='5  5  10  25  50  75  Crystal Coherence Length, CCL (nm)  Domain Purity, @ (%)  structural parameters on the solar cell performance and charge  transport properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Our main findings are:  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  NFA packing motifs largely track from single crystals to  the thin-film blend.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Compounds that crystallise easily as single crystal also  show high crystallinity in the blend films.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' For instance,  we found that the poor propensity of ITIC to form  single  crystals (as  indicated  by the multiple  unsuccessful trials to grow single crystals)18 also  translates into a low blend crystallinity (high g and low  CCL).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  NFAs with higher π-π stacking dimensionality showed  an increased propensity to form crystalline films (low  g and high CCL) in both NFA films and blends.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Despite our initial expectations, the NFA packing motif  does not directly correlate with the solar cell  performance parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  NFAs with high film crystallinity (low g, high CCL)  provided higher electron mobility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' However, the  mobility is not the dominating factor for device  performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' At the same time, we found no  correlation between the NFA crystallinity in the blend  and the bimolecular recombination coefficient (𝛽exp).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  The bimolecular recombination coefficient (𝛽exp) is  found to be the main factor influencing FF and JSC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Systems with  low  𝛽exp reported the  highest  performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' For instance, blend with lower NFA  crystallinity (4TICO and ITIC) delivered the highest  performance and lowest bimolecular recombination  despite the lowest electron mobility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Domain purity stood out as an interesting design  target, to limit the bimolecular recombination and  obtain high efficiencies in organic solar cells.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' A better  understanding  of  the  influence  of  molecular  properties on domain purity is needed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  A high domain purity could be targeted through chemical design  that aims at limiting void space within the unit cell while also  managing the solubility/miscibility of the donor-acceptor  pairing to  control  BHJ formation  and  intermolecular  interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='36, 88 This could in theory be targeted by the design  of space filling yet flexible sidechains to increase the NFA  rotational freedom and prevent NFA crystallisation that might  induce an excessive phase segregation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='37 Alternatively, thermal  annealing can also be used as a handle to tune the morphology  of kinetically trapped systems,89, 90 allowing the formation of a  controlled BHJ morphology characterised by domain with high  structural purity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='36, 89, 91 This was observed for NFAs that can  rearrange their structures undergoing an endothermic  transition (glass or liquid crystalline) during post-annealing  process (ITIC and 4TICO).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Conversely, systems with shorter or  sterically locked sidechains may promote the formation of  crystalline domains even before any thermal treatment (4TIC,  m-4TICO, m-ITIC).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='36 These domains tend to excessively phase  segregate upon annealing without improving their domain  purity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Multivariable cross-correlation map between solar cell characteristics and crystallinity/morphology parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Conflicts of interest  Merck KGaA provided the PBTZT-stat-BDTT-8 polymer and the  4TICO NFA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Acknowledgements  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Mondelli and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=" Riede acknowledge the European Union's  Horizon 2020 research and innovation programme under Marie  Skłodowska Curie Grant agreement no." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' 722651 (SEPOMO) for  the support in the realization of this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Kaienburg  acknowledges funding from the Global Challenges Research  Fund (GCRF) through STFC, START project ST/R002754/1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' and  from EPSRC for a Postdoctoral Fellowship EP/V035770/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  GIWAXS experiments were performed at NCD-SWEET beamline  at ALBA synchrotron with the collaboration of ALBA staff  (proposal 2019093873).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Footnotes  ‡Cu-K𝛼 X-Ray penetration depth on our films is ∼ 11 nm for  incident angles 𝛼 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='11° (assuming the same critical angle of 𝜃c  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='17°).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  ‡‡The active layer thickness was determined by using a Veeco  DEKTAK 150 surface profilometer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  §Single crystal structures are measured under a continuous flow  produced by liquid nitrogen at 100 K, while powder diffraction  is measured at 300 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  §§We assume in this first step that the unit cells angles (𝛼, 𝛽 and  𝛾) are not varying from the single crystal unit cell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content="  ¶4TIC powder XRD data quality didn't allow to perform Le Bail  analysis due to poor scattering (Figure S6)." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  ¶¶We did not detect a meaningful signal from o-IDTBR:PBTZT-  stat-BDTT-8 to extract the mobility and recombination  coefficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' We believe this is due to a combination of factors,  among which the lowest shunt resistance leading to the lowest  FF observed among all the different devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  #Although the PCE is a linear combination of FF, VOC and JSC, we  included it in the cross-correlation analysis for convenience.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  ##We assigned a constant value for each motif which is  representative of the dimensionality of the π-π stacking: "0" for  0D herringbone, "2" for 2D brickwork and "3" for 3D reticular.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  References  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Zhu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Zhang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Xu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Li, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Yan, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Zhou, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Zhong, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Hao, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Song and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Xue, Nature Materials, 2022, 21, 656-  663.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Cui, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Xu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Yao, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Bi, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Hong, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Zhang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Zu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Zhang,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Qin and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Ren, Advanced Materials, 2021, 33, 2102420.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Li, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='-Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Li, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Shi and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Chen, ACS Energy Letters, 2020,  5, 1554-1567.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Wei, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Liu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Leclerc, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Yuan, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Chen and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Zou,  Science China Chemistry, 2020, 1-15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Yuan, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Zhang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Zhou, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Zhang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Yip, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='-K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Lau, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Lu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Zhu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Peng, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Johnson, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Leclerc, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Cao, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Ulanski, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Li and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Zou, Joule, 2019, 3, 1-12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Lai, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Zhao, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Chen, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Chen, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Chao, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Zhu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Lang,  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Zhen, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Mo and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Zhang, Joule, 2020, 4, 688-700.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Li, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Zhang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Jones, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Alzola, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Mukherjee, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='-w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Feng, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Zhu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Stern, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Huang and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Yu, Journal of the  American Chemical Society, 2021, 143, 6123-6139.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Wang, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' An, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Yan, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='-R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Bai, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Jiang, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Mahmood, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Yang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Zhi and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Wang, Energy & Environmental  Science, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Zhu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Zhang, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Zhou, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Hao, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Xu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Wang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Qiu, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Prine, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Ali and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Feng, Advanced Energy Materials, 2020,  10, 1904234.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Zhu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Zhang, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Zhong, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Leng, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Zhou, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Zou, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Su,  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Ding, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Gu, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Liu and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Zhang, Energy & Environmental  Science, 2021, 14, 4341-4357.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Babu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Möhwald and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Nakanishi, Chemical Society  Reviews, 2010, 39, 4021-4035.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Steiner, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Foster, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Losquin, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Labram, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Anthopoulos, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Frost and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Nelson, Materials Horizons,  2015, 2, 113-119.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Lin, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Jiang, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Kaminsky, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Zhu and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Jen, Journal  of the American Chemical Society, 2020, 142, 15246-15251.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Zhu, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Spencer, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Mukherjee, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Alzola, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Sangwan, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Amsterdam, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Swick, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Jones, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Heiber and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Herzing, Journal of the American Chemical  Society, 2020, 142, 14532-14547.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Zhang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='-K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Chen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Xiao, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Chow, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Ren, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Kupgan,  X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Jiao, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Chan, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Du and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Xia, Nature  communications, 2020, 11, 1-10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Dai, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Li, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Xin, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Lu, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Xue, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Zhao, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Liu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Sun, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Yu and Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Tang, Journal of Materials Chemistry A, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Wang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Lu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Liu, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Zhang, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Yu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Wang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Li, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Zhou, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Xu and Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Tang, Advanced Energy Materials, 2021,  11, 2102591.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Mondelli, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Boschetto, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Horton, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Tiwana, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='-K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Skylaris, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Coles, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Krompiec and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Morse, Materials  Horizons, 2020, 7, 1062-1072.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Shi, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Zuo, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Jo, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Gao, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Lin, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Liu and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Jen,  Chemistry of Materials, 2017, 29, 8369-8376.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Aldrich, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Matta, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Zhu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Swick, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Stern, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Schatz, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Facchetti, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Melkonyan and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Marks, J  Am Chem Soc, 2019, DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1021/jacs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='8b13653.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Qu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Chen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Zhou, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Lai, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Liu, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Chao, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Li, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Xie, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  He and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Ma, ACS Appl Mater Interfaces, 2018, 10, 39992-  40000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Swick, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Zhu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Matta, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Aldrich, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Harbuzaru,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Lopez Navarrete, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Ponce Ortiz, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Kohlstedt, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Schatz, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Facchetti, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Melkonyan and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Marks, Proc  Natl Acad Sci U S A, 2018, DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1073/pnas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1807535115.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Wu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Zhou, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Luo, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Zheng, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Wang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Liu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Xie and  Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Ma,  Organic  Chemistry Frontiers,  2018,  DOI:  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1039/c8qo00934a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Yan, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Liu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Yao and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Zhan, Advanced Energy  Materials,  2018,  DOI:  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1002/aenm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='201800204,  1800204.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Li, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Zhan, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Zhao, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Zhang, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Ali, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Fu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='-K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Lau, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Lu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Shi, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='-Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Li, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Hou and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Chen, Journal of Materials  Chemistry A, 2018, 6, 12132-12141.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Lai, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Chen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Zhou, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Qu, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Chao, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Liu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Chang, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Zheng, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Xie and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' He, iScience, 2019, 17, 302-314.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Zhang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Liu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Shan, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Wang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Zhu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Li, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Liu and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Zhong, Materials Chemistry Frontiers, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Mo, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Chen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Zhou, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Tang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Han, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Zhu, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Chao, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Lai, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Xie and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' He, Journal of Materials Chemistry A, 2020,  8, 8903-8912.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Li, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Huang, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Angunawela, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Zhou, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Du, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Liebman‐  Pelaez, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Zhu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Zhang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Meng and Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Xie, Advanced  Functional Materials, 2020, 30, 1906855.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Feng, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Li, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Tang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Wang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Huang, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Ran, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Liu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Xie, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Zhang and Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Bo, ACS applied materials & interfaces,  2020, 12, 4638-4648.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Ma, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Zhang and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Hou, Journal of Materials Chemistry  A, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Lai and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' He, Advanced Energy Materials, 2020, 10,  2002678.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Xiao and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Lu, Materials Today Nano, 2019, 100030.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Peng, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Ye and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Ade, Materials Horizons, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Lai, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Huang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='-T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Lee and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='-R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Yang, ACS omega,  2018, 3, 18656-18662.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Mondelli, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Silvestri, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Ciammaruchi, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Solano, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Beltrán-Gracia, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Barrena, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Riede and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Morse, Journal  of Materials Chemistry A, 2021, 9, 26917-26928.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Marina, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Scaccabarozzi, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Gutierrez‐Fernandez, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Solano, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Khirbat, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Ciammaruchi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Iturrospe, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Balzer,  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Yu and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Gabirondo, Advanced Functional Materials,  2021, 2103784.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Yoshida and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Sato, Applied physics letters, 2006, 89,  101919.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Ashiotis, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Deschildre, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Nawaz, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Wright, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Karkoulis, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Picca and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Kieffer, Journal of applied  crystallography, 2015, 48, 510-519.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Breiby, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Bunk, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Andreasen, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Lemke and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Nielsen, Journal of Applied Crystallography, 2008, 41,  262-271.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Macrae, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Sovago, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Cottrell, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Galek, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' McCabe,  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Pidcock, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Platings, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Shields, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Stevens and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Towler, Journal of applied crystallography, 2020, 53, 226-  235.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Reddy, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Malon, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Marsh, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Nishiyama and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Brown, Analytical chemistry, 2016, 88, 11412-11419.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Nečas and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Klapetek, Open Physics, 2012, 10, 181-188.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Kornilov and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Safonov, Journal of Imaging, 2018,  4, 123.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Berny, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Blouin, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Distler, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Egelhaaf, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Krompiec,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Lohr, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Lozman, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Morse, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Nanson, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Pron, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Sauermann, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Seidler, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Tierney, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Tiwana, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Wagner  and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Wilson, Adv Sci (Weinh), 2016, 3, 1500342.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Baumann, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Lorrmann, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Rauh, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Deibel and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Dyakonov, Advanced Materials, 2012, 24, 4381-4386.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Clarke, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Lungenschmied, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Peet, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Drolet and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Mozer, Advanced Energy Materials, 2015, 5, 1401345.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Juška, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Nekrašas and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Genevičius, Journal of non-  crystalline solids, 2012, 358, 748-750.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Sandberg, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Nyman, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Dahlström, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Sandén, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Törngren, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Smått and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Österbacka, Applied Physics  Letters, 2017, 110, 153504.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Chaudhari, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Griffin, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Broch, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Lesage, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Lemaur,  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Dudenko, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Olivier, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Sirringhaus, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Emsley and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Grey, Chemical science, 2017, 8, 3126-3136.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Wang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Dong, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Jiang and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Hu, Chem Soc Rev, 2018,  47, 422-500.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Mas-Torrent and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Rovira, Chem Rev, 2011, 111, 4833-  4856.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Wang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Dong, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Hu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Liu and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Zhu, Chemical  Reviews, 2011, 112, 2208-2267.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Wang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Dong, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Li, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Zhao, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Meng and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Hu,  Crystal Growth & Design, 2010, 10, 4155-4160.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Hou, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Inganäs, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Friend and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Gao, Nature  Materials, 2018, 17, 119-128.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Bristow, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Thorley, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' White, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Wadsworth, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Babics, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Hamid, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Zhang, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Paterson, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Kosco, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Panidi, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Anthopoulos and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' McCulloch, Advanced  Electronic Materials, 2019, 5, 1900344.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Hammond, The basics of crystallography and diffraction,  International Union of Crystal, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' B, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Raval, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Pawlak, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Du, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Wang, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Kupgan, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Schopp, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Chae, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Yoon, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Yi, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Jung Kim, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Coropceanu,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Bredas, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Nguyen and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Reddy, Advanced  Materials, 2022, 34, e2105943.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Seifrid, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Reddy, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Chmelka and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Bazan, Nature  Reviews Materials, 2020, 5, 910-930.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Karki, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Vollbrecht, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Gillett, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Xiao, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Yang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Peng, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Schopp, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Dixon, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Yoon, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Schrock, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Ade,  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Reddy, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Friend and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Nguyen, Energy &  Environmental Science, 2020, 13, 3679-3692.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Karki, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Vollbrecht, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Dixon, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Schopp, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Schrock,  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Reddy and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Nguyen, Advanced Materials, 2019,  31, 1903868.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Sturniolo, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Green, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Hanson, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Zilka, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Refson,  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Hodgkinson, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Brown and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Yates, Solid state  nuclear magnetic resonance, 2016, 78, 64-70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Hodgkinson, Progress in Nuclear Magnetic Resonance  Spectroscopy, 2020, 118, 10-53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Jonathan Rivnay, Chad E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Miller, Alberto Salleo,  and Michael F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Toney, chemical Reviews, 2012, 112.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Liang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Jiao, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Yan, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Xie, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Lu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Liu and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Han,  Advanced Functional Materials, 2019, 29, 1807591.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Hong, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Sung, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Cha, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Park, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Durrant, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' An,  Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Kim and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='-K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Kwon, ACS applied materials &  interfaces, 2018, 10, 36037-36046.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Xu, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Lin, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Zhu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Zhang, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Hao, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Zhou, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Gao, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Zou, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Wei and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Yi, Advanced Energy Materials, 2022,  2201338.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Bartesaghi, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Pérez, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Kniepert, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Roland, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Turbiez, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Neher and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Koster, Nature communications,  2015, 6, 1-10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Kaienburg, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Rau and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Kirchartz, Physical review  applied, 2016, 6, 024001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Gorenflot, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Heiber, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Baumann, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Lorrmann, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Gunz, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Kämpgen, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Dyakonov and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Deibel, Journal of  Applied Physics, 2014, 115, 144502.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Murthy, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Melianas, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Tang, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Juška, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Arlauskas, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Zhang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Siebbeles, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Inganäs and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Savenije,  Advanced Functional Materials, 2013, 23, 4262-4268.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Chen, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Choudhury, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Subbiah, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Amb, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Reynolds and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' So, Advanced Energy Materials, 2011, 1,  963-969.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Baumann, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Savenije, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Murthy, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Heeney, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Dyakonov and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Deibel, Advanced Functional Materials,  2011, 21, 1687-1692.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Dennler, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Mozer, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Juška, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Pivrikas, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Österbacka,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Fuchsbauer and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Sariciftci, Organic Electronics,  2006, 7, 229-234.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Mozer, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Sariciftci, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Lutsen, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Vanderzande, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Österbacka, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Westerling and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Juška, Applied Physics  Letters, 2005, 86, 112104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Sandberg and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Nyman, Organic Electronics, 2019,  64, 97-103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Lakhwani, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Rao and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Friend, Annual review of  physical chemistry, 2014, 65, 557-581.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Chaney, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Levin, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Schneider and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Toney,  Materials Horizons, 2022, 9, 43-60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Collins and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Gann, Journal of Polymer Science, 2022,  60, 1199-1243.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Collins, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Li, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Tumbleston, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Gann, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' McNeill  and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Ade, Advanced Energy Materials, 2013, 3, 1-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Park, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Kim, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Lee, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Lee, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Ma, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Cho and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Kim, Advanced Functional Materials, 2020, 30, 2005787.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Yiu, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Beaujuge, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Lee, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Woo, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Toney  and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Frechet, Journal of the American Chemical  Society, 2012, 134, 2180-2185.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Li, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Albrecht, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Yang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Roland, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Tumbleston, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  McAfee, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Yan, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Kelly, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Ade and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Neher, Journal of  the American Chemical Society, 2014, 136, 15566-15576.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Wilken, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Scheunemann, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Dahlström, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Nyman, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Parisi and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Österbacka, Advanced Electronic Materials,  2021, 7, 2001056.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Azzouzi, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Kirchartz and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Nelson, Trends in Chemistry,  2019, 1, 49-62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Rosenthal, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Hughes, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Luginbuhl, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Ran, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Karki, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Ko, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Hu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Wang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Ade and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Nguyen,  Advanced Energy Materials, 2019, 9, 1901077.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Vandewal and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' , Abay Gadisa, Olle Inganäs and Jean  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Manca,  nature  materials,  2009,  DOI:  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1038/nmat2548.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Ye, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Hu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Ghasemi, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Wang, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Collins, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Kim,  K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Jiang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Carpenter, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Li and Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Li, Nature materials,  2018, 17, 253-260.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Qin, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Xu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Peng, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Hou and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Ade, Advanced  Functional Materials, 2020, 30, 2005011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Ye, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Li, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Liu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Zhang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Ghasemi, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Xiong, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Hou and  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Ade, Joule, 2019, 3, 443-458.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Köntges, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Perkhun, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Kammerer, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Alkarsifi, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Würfel, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Margeat, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Videlot-Ackermann, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Simon, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Schröder and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Ackermann, Energy & Environmental  Science, 2020, 13, 1259-1268.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Supporting Information:  Understanding the Role of Non-Fullerene Acceptors Crystallinity on the Charge  Transport Properties and Performance of Organic Solar Cells  Pierluigi Mondelli,*a,d Pascal Kaienburg,a Francesco Silvestri,b Rebecca Scatena,a Claire Welton,c Martine Grandjean,d  Vincent Lemaur,e Eduardo Solano,f Mathias Nyman,g Peter N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Horton,h Simon J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Coles,h Esther Barrena,b Moritz Riede,a  Paolo Radaelli,a David Beljonne,e G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Manjunatha Reddyc and Graham Morsed (Authors are listed in an arbitrary order  and list is temporary)  a Clarendon Laboratory, University of Oxford, Parks Road, Oxford, OX1 3PU, United Kingdom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' E-mail:  pierluigi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='mondelli@gmail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='com  b Institut de Ciència de Materials de Barcelona, ICMAB-CSIC, Campus UAB, 08193 Bellaterra, Spain  c University of Lille, CNRS, Centrale Lille, Univ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Artois,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' UMR 8181- UCCS - Unité de Catalyse et Chimie du Solide,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' F-59000  Lille,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' France  d Merck Chemicals Ltd,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Chilworth Technical Centre,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' University Parkway,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Southampton,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' SO16 7QD,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' United Kingdom  e Laboratory for Chemistry of Novel Materials,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' University of Mons,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Place du Parc,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' 20,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' 7000 Mons (Belgium)  f ALBA Synchrotron Light Source,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' NCD-SWEET beamline,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Cerdanyola del Vallès,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' 08290 Spain  g Physics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Faculty of Science and Engineering,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Åbo Akademi University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' 20500 Turku,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Finland  h EPSRC Crystallographic Service,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Department of Chemistry,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' University of Southampton,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Highfield,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' SO17 1BJ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' UK  Table of Contents  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Solid-state NMR analysis of o-IDTBR powder  2-5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Powder and Single Crystal X-Ray Diffraction  6-9  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Film Morphology by 2D-GIWAXS and AFM  10-19  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' AFM Watershed Analysis  20-25  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Electron Mobility by MIS-CELIV  26-27  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Annealing Temperature, Dark J-V and !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='exp  28  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' References  29  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Solid-state NMR analysis of o-IDTBR powder  Figure S1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' 1D solid-state 1H NMR spectrum of o-IDTBR powder acquired at 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='8 T (1H = 800 MHz) with 50 kHz MAS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Peak assignments are  colour coded as depicted in the crystal structure shown in the inset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Figure S1 presents 1H MAS NMR spectra of O-IDTBR powder, whereby the 1H peaks are color coded as depicted in  the schematic structure figure of O-IDTBR shown on top and the isotropic chemical shifts calculated by GIPAW-DFT  approach are overlaid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The broad 1H peak centered at ~1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='7 ppm is due to the branched alkyls sidechains attached  to the aromatic core.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The different distributions of 1H peaks in the 3-5 ppm range are due to the -NCH2CH3 moieties  attached to the terminal 3-ethyl-2-thioxothiazolidin-4-one groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' In the aromatic region, the peak at ~6 ppm is  due to the protons in the benzothiadiazole (BDT) groups (green dots), and the low ppm chemical shift value of these  BDT protons can be ascribed to the ring current effects caused by the partial overlap of the aromatic rings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The peak  at ~7 ppm can be attributed to the -CH moieties bridging the BDT and 3-ethyl-2-thioxothiazolidin-4-one groups as  depicted in the magenta dot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The overlapped peaks in the range between 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='5 to 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='5 ppm are due to the protons in  the BDT groups facing towards thiophene (T) groups (blue dot) and the protons in the central benzene ring (purple  dots).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The weak intensity peak at ~8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='8 ppm is due to thiophene protons (red dot).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='26  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='55  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='89 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='94  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='208.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='79  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='79  10  8  6  4  2  0  1H chemical shift (ppm)  Figure S2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' 1D solid-state 13C1 CP-MAS NMR spectra of o-IDTBR powder acquired with 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1 (bottom) and 3 ms (top) CP contact time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' All  spectra were acquired at 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='8 T and 50 kHz MAS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Peak assignments are colour coded as depicted in the crystal structure shown in the inset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  For O-IDTBR powder, the 1H→13C cross-polarization (CP)-MAS NMR spectra of o-IDTBR were acquired with 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1 ms  and 3 ms of CP contact time and compared.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' CP-MAS based experiments exploit the enhancement of the 13C signal  intensities that are increased by transfer of 1H spin-polarization by the adjacent protons, according to the strengths  of the 1H-13C dipole-dipole couplings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The isotropic 13C chemical shifts are color coded as presented in the spectrum,  the CH3 peaks are well resolved in 10-20 ppm range and the CH2 moieties produce peaks in 20-37 ppm range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The  peaks around 40 ppm are due to the -NCH2CH3 groups of 3-ethyl-2-thioxothiazolidin-4-one, and the peak centered  at ~55 ppm can be assigned to the quaternary carbon atom bearing the branched alkyl sidechains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' In the aromatic  region, the one-bond CH moieties produce peaks in the 110-130 ppm;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' the broad peak in the 110-115 range  originates from the protonated carbon atoms in the benzene ring that produces a peak at ~112 ppm (purple dot)  and the protonated thiophene carbon atoms that give rise to a peak at ~ 115 ppm (red dot).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Partially resolved peaks  in the 118-122 ppm range are due to the protonated carbon atom (facing towards the T group as depicted by the  blue dot) and the -CH moieties (purple dots) bridging the BDT and 3-ethyl-2-thioxothiazolidin-4-one groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' By  comparison, a CP-MAS NMR spectrum of o-IDTBR was acquired with 3 ms CP contact time which displayed  additional peaks corresponding to the quaternary carbon atoms (top spectrum), signals of which are enhanced by  the CP transfer via through-space 13C-1H dipolar interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Specifically, the 13C peak of the quaternary carbon  atom bearing the sidechains (gray dot) is enhanced as shown by the peak at ~55 ppm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' In addition, the 13C signals  associated with the quaternary aromatic carbon atoms at 135-160 ppm are enhanced by the CP transfer from the  adjacent protons via 13C-1H dipolar couplings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The 13C peak at ~168 is due to the carbonyl group of the O-IDTBR  molecules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Branched sidechains  CH2  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='26  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='89 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='94  CH  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='79  quaternary  carbonatoms  CC  1H →13C CP 4 ms  (through-space C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='H)  m  1H →13C CP 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1 ms  (one-bond CH)  180  160  140  120  100  80  60  40  20  0  13C chemical shift (ppm)  Figure S3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' 2D solid-state 1H-1H NMR spectrum of o-IDTBR powder acquired at 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='8 T (1H = 800 MHz) with 50 kHz MAS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Peak assignments  are colour coded as depicted in the crystal structure shown in the inset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' 1H chemical shift values associated with the aromatic protons are  depicted in the GIPAW-DFT geometry optimized structure as shown by the coloured dots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  2D 1H-1H double-quantum single-quantum (DQ-SQ) correlation spectrum presented in Figure S3 displays  the DQ peaks in the vertical axis that correspond to 1H-1H proximities in less than 5 Å distance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The 1H  SQ signals are color coded as depicted in the schematic structure figure of O-IDTBR shown on top.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' In  particular, the different aromatic chemical shifts of thiophene (T) and benzothiadiazole (BDT) are due  to the different aromatic ring current effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The inter- and intramolecular 1H-1H proximities in the alkyl  and aromatic regions (i, ii, iii, and iv) that contribute to the 1H DQ peaks are marked by ovals in the  crystal structure in the left.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The broad DQ peak at ~3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='6 ppm (i) is due to the inter-and intramolecular 1H-  1H proximities in branched sidechains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The DQ peaks at ~7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='7 and ~9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='4 ppm (ii) are due to the dipolar  coupled 1H-1H pairs between branched sidechains and aromatic groups (T and BDT).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The DQ peaks in  the aromatic region (iii and iv) are due to the intramolecular 1H-1H proximities between the aromatic  moieties, whereby the DQ peak 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1 ppm is attributable to intramolecular 1H-1H  dipolar interactions  between the BDT proton and C-H protons in the bridged position (green and magenta dots).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='The DQ  peak at 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1 ppm is due to the intramolecular 1H-1H dipolar interactions between the BDT protons (blue  and green dots), and the peak at 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='2 ppm is ascribed to the intramolecular 1H-1H dipolar interactions  between the BDT and T protons (blue and red dots) of O-IDTBR molecules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The different packing  interactions that contribute to the DQ peaks are marked by ovals in the crystal structure depicted in the  left.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='26  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='79  chemical shift (ppm)  0  (0)  4  8  (i)  ii  1H DQ  12  (iii)  16  (ii), (iv)  (iii), (iv)  (iv)  10  8  6  4  2  0  1HSQchemicalshift(ppm)  Figure S4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' 2D solid-state 1H-13C heteronuclear correlation (HETCOR) spectrum of o-IDTBR powder acquired with (a) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1 ms and (b) 3 ms CP  contact time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Peak assignments are color coded as depicted in the crystal structure shown in (c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' All spectra were acquired at 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='8 T (1H =  800 MHz) with 50 kHz MAS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Figure S4 presents 2D HETCOR spectra acquired with 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1 ms and 3 ms CP contact times in order to detect  2D peaks that originate from directly bonded C-H as well as through-space dipolar coupled C…H moieties in  o-IDTBR molecules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Inter- and intramolecular C-H proximities corresponding to the 2D peaks are shown in  the crystal structure (c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' In the spectrum acquired with 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1 ms CP contact time, the isotropic 13C chemical  shifts at d(13C) = 10-45 ppm are due to the directly bonded C-H moieties in alkyl groups (yellow dots), and  the isotropic 13C chemical shifts at d(13C) = 110-122 ppm are due to the directly bonded C-H moieties in BDT  (blue and green dots), T (red dot), CH moiety at the bridged position (magenta) and benzene ring (purple  dots) at the aromatic core.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' In addition to these, the 2D HETCOR spectrum acquired with 3 ms CP contact  time exhibits the 2D peaks corresponds to the through-space inter and intramolecular 1H-13C dipolar  interactions between aliphatic and aromatic groups, as depicted in the boxes and ovals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Specifically, the  2D 13C-1H correlation peaks associated with the quaternary carbon atoms that are in close proximities to  aromatic protons in the core are emerged as depicted in the red color box.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The 2D peaks shown in the blue  boxes are due to the inter- and intramolecular 13C-1H dipolar interactions between the alkyl chains and the  aromatic moieties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The carbonyl carbon atom is in close proximity to the CH protons (magenta) and  intermolecularly with the BDT protons (green dots) that lead to the 2D peaks as depicted in the red oval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  (a)  (b)  (c)  0  CP = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1 ms  CF  3ms  (iii) (iv)  20  40  chemical shift (ppm)  60  (iii),  80  (iv)  100  (iii)  120  140  iv  160  CO-CH  180  CO-BDT  200  10  8  6  4  2  0  10  8  6  4  2  0  1Hchemicalshift (ppm)  1H chemical shift (ppm)  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Powder and Single Crystal X-Ray Diffraction  Manual calculation of the lattice parameters  The o-IDTBR lattice parameters (a, b and c) for powder sample were initially obtained by solving the reciprocal-space metric tensor  for monoclinic structures:  1  #!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=" =  1  &'(!" metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' )ℎ!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  +!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' + -!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content="&'(!" metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  + /!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  0!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' − 2ℎ/03&!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  +0  4  where the positions of the (0 1 1), (0 1 2) and (110) were derived from the experimental pattern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The unit cell angles (5, !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' and 6) were  assumed to be the same as in single crystal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The results are shown in (Table S1) and compared to the single crystal unit cell and the  ones obtained by Le Bail refinement of powder data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Table S1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Evolution of the o-IDTBR unit cell parameters from the known single crystal data to the manual and Le Bail refinements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Unit Cell  a (Å)  b (Å)  c (Å)  5 (°)  !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' (°)  6 (°)  Volume (Å3)  Single crystal  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='7663(2)  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='81032(17)  32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='7146(3)  90  96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='2928(12)  90  7077.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='43(15)  Manual  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='0646  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='0432  32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='7057  90  96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='293  90  7335.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='288  Le Bail  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='03086  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='06125  32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='68444  90  96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='716  90  7314.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='994  Temperature effect on the single crystal unit cell  The effect of the temperature on the NFA unit cell parameters was explored by performing temperature-dependent single-crystal  XRD on IDIC‡1(Figure S5, Table S2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The experiments have shown how temperature can influence both lattice parameters and  angles of IDIC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Figure S5 a) IDIC powder XRD datapoints with Le Bail refinement compared to the simulated powder pattern from the single crystals  measured at 100 and 173 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' b) Fitting parameters evolution towards lower values  ‡ The IDIC single crystal structures are accessible from the CCDC Database: Deposition Number 2226731 for the measurement  taken at 173 K and Deposition Number 2040188 for the dataset taken at 100 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  b)  a)  Table S2 IDIC unit cell parameters evolution with temperature  Structure  Crystal  System  Space  Group  a (Å)  b (Å)  c (Å)  5 (°)  !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' (°)  6 (°)  Volume  (Å3)  100 K  triclinic  P1"  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='6679(4)  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='5073(7)  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='5784(6)  72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='096(4)  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='545(4)  88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='839(4)  1353.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='88(12)  173 K  triclinic  P1"  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='6379(4)  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='6391(6)  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='9041(5)  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='650(4)  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='044(4)  88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='148(4)  1381.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='35(11)  Le Bail  triclinic  P1"  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='63994  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='80154  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='39796  69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='913  74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='405  88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='479  1436.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='737  Le Bail analysis  Figure S6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Powder XRD datapoints with Le Bail refinement compared to the simulated powder pattern from the single crystal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  4TIC  4TICO  IDIC  m-ITIC  Herringbone  Brickwork  ITIC  Un-solvated  Solvated  m-4TICO  Figure S7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Powder XRD datapoints with Le Bail refinement compared to the simulated powder pattern from the single crystal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Figure S8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Powder XRD datapoints with Le Bail refinement compared to the simulated powder pattern from the single crystal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Table S3 NFA unit cell parameters for the known crystal structures in comparison with the parameters obtained from Le Bail refinement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  CCDC  Molecule  Solvates  a (Å)  b (Å)  c (Å)  5 (°)  !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' (°)  6 (°)  Volume  (Å3)  GOF  Chi2  wR  Before Le Bail Refinement  HEHQUJ01  ITIC  none  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='9009(7)  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='5043(4)  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1199(5)  99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='309(2)  101.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='541(3)  108.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='366(3)  3777.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='2(2)  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='43  91145.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='046  KIZSUK  ITIC  CH2Br2  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='420(6)  23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='019(17)  23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='126(17)  101.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='780(10)  95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='319(10)  91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='105(14)  4366(5)  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='24  278780.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='8  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='055  VUBJOU  m-ITIC  CHCl3  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='7454(13)  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='872(2)  25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='2647(18)  87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='770(8)  88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='724(9)  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='001(12)  4075.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1(9)  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='51  352372  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='001  VUBJEK  4TICO  C3H6O  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='2836(2)  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='0101(5)  29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='3242(6)  90  29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='3242(6)  90  8968.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1(3)  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='95  300794.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='4  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='892  FOSPOV  o-IDTBR  none  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='7663(2)  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='81032(17)  32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='7146(3)  90  96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='2928(12)  90  7077.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='43(15)  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='10  63293.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='5  31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='079  VUBKAH  IDIC  none  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='6679(4)  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='5073(7)  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='5784(6)  72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='096(4)  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='545(4)  88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='839(4)  1353.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='88(12)  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='93  367143.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='8  69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='427  N/A  m-4TICO  none  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='7845(7)  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='3726(13)  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='7896(13)  67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='136(7)  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='678(7)  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='630(7)  2054.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='98  35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='82  1075472.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='2  62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='264  VUBJIO  m-4TICO  CHCl3  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='6526(3)  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='4878(8)  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='0435(8)  114.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='697(5)  103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='822(4)  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='890(4)  2251.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='45(19)  40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='43  1369716.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='7  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='267  YEBKEY  4TIC  C7H8,  CH3OH  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='969(7)  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='144(9)  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='970(10)  104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='668(16)  109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='998(17)  96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='169(14)  3822.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='08  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='62  507853  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='652  After Le Bail Refinement  HEHQUJ01  ITIC  none  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='06724  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='46733  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='89986  100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='067  100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='804  107.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='462  3788.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='083  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='87  51968.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='4  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='157  KIZSUK  ITIC  CH2Br2  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='57001  23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='49976  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='22479  100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='617  92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='928  93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='867  4380.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='067  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='16  274453.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='9  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='727  VUBJOU  m-ITIC  CHCl3  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='74588  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='77874  25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='48191  88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='391  89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='072  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='262  3877.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='599  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='96  1000667.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='7  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='331  VUBJEK  4TICO  C3H6O  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='66764  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='60675  29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='04299  90  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='799  90  8920.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='893  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='65  26766  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='303  FOSPOV  o-IDTBR  none  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='03086  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='06125  32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='78444  90  96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='716  90  7337.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='375  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='02  19267.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='4  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='148  VUBKAH  IDIC  none  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='67925  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='79671  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='4997  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='019  74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='42  88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='239  1454.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='553  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='43  46096.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='4  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='6  N/A  m-4TICO  none  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='0868  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='7656  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='6819  67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='74  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='699  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='53  2167.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='014  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='70  233612.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='4  29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='019  VUBJIO  m-4TICO  CHCl3  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='74656  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='15453  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='81585  114.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='163  104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='908  89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='942  2203.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='878  40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='27  1348979.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='8  69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='733  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Film Morphology by 2D-GIWAXS and AFM  4TIC  4TIC 2D-GIWAXS pattern (Figure S6c) is in good agreement with the one obtained in our previous report.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='2 We have simulated the  2D-GIWAXS map by using the single crystal unit cell available from literature3 (Figure S9a) and oriented along the (1 0 0) direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Such direction is parallel to the π-π stacking (4 -1 -1) and the lamellar (1 0 0) peak, which is representative of a face-on orientation  of 4TIC domains with respect to the substrate (Figure S9b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Although the (1 0 0) lamellar contribution is not visible from the  simulated data (all crystallites are assumed to be perfectly oriented along the (1 0 0) and therefore are not accessible4),  experimental and simulated GIWAXS are in good agreement confirming a face-on 3D reticular packing with respect to the  substrate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' As the 4TIC lamellar feature is still evident from the PBTZT-stat-BDTT-8:4TIC GIWAXS (Figure S9d) and out-of-plane  Figure S9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Simulated 2D-GIWAXS pattern of the 4TIC unit cell oriented along the (1 0 0) direction (a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Graphical representation of the π-π  stacking (4 -1 -1) and lamellar (1 0 0) peaks orientation with respect to the (1 0 0) vector (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' 4TIC (c) and PBTZT-stat-BDTT-8:4TIC (d)  GIWAXS pattern with in-plane (e) and out-of-plane (g) integration profiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' 5x5 µm AFM images of 4TIC (f) and PBTZT-stat-BDTT-8:4TIC (g)  films with domain size distribution and average value (inset).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Out-of-plane  4TIC  (1 0 0)  PBTZT-stat-BDTT-8:4TIC  c)  In-plane  (1 0 0)  (0 1 0)  (0 1 1)  (1 0 0)  (1 0 0)  (4 -1 -1)  (4 -1 -1) + (0 1 0)  (1 0 0)  (1 0 0)  (4 -1 -1)  (4 -1 -1) + (0 1 0)  (1 0 0)  (1 0 0)  �-�  (4 -1 -1)  a)  b)  e)  d)  f)  h)  g)  lamellar  (1 0 0)  RMS: 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='5 nm  RMS: 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='7 nm  qxy (nm-1)  qxy (nm-1)  qxy (nm-1)  qz (nm-1)  30  25  20  (t-wu)b  15  10  5  0  5  0  5  10  15  20  25  qr(nm-1)30  25  20  qz(nm-1)  15  10  5  0  5  0  5  10  15  20  25  qr(nm-1)30  25  20  (t-wu)b  15  10  5  0  5  0  5  10  15  20  25  qr(nm-1)  integration profile (Figure S6h), we assume that the NFA is maintaining its crystalline order in blend with a slightly relaxed (1 0 0)  periodicity (Table S5) compared to the pure NFA film.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Table S4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Crystallographic information of the main peaks observed by 2D-GIWAXS on 4TIC and PBTZT-stat-BDTT-8:4TIC films.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' AFM domain  size and domain purity are also shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Component  Peak  Orientation  q (nm-1)  d (nm)  FWHM  (nm-1)  CCL (nm)  g  Domain  Size (nm)  ϕ (%)  NFA film  4TIC  (1 0 0)  Out-of-plane  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='09  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='23  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='29  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='5  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='5  N/A  N/A  4TIC  (4 -1 -1)  Out-of-plane  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='34  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='36  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='16  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='9  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='3 Blend film  4TIC  (1 0 0)  Out-of-Plane  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='02  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='58  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='0  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1  29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='6  30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='3  PBTZT-stat-BDTT-8  (1 0 0)  In-plane  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='75  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='28  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='87  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='5  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='4 PBTZT-stat-BDTT-8, 4TIC  (0 1 0) + (4 -1 -1)  Out-of-plane  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='81  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='35  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='00  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='9  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='4 m-4TICO  m-4TICO 2D-GIWAXS pattern (Figure S10c) shows a strong Bragg peak along qz and other less intense features in the q map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' To  verify whether the NFA arrangement in film is compatible to the phase existing in powder and single crystal, we have simulated  the 2D-GIWAXS of the single crystal unit cell (Le Bail refined) and oriented along the (0 1 1) direction (Figure S10a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Such direction  is parallel to the lamellar (1 0 0) peak and diagonal with respect to π-π stacking (2 3 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' This is representative of a quasi-edge-on  orientation of the m-4TICO domains with respect to the substrate (Figure S10b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The good agreement between experimental and  simulated GIWAXS confirms a quasi-edge-on 2D brickwork packing with respect to the substrate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' As the m-4TICO lamellar feature  is still evident from the PBTZT-stat-BDTT-8:m-4TICO GIWAXS (Figure S10d) and out-of-plane integration profile (Figure S10h), we  assume that the NFA is maintaining its crystalline order in blend with a slightly relaxed (0 1 1) periodicity (Table S5) compared to  the pure NFA film.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Figure S10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Simulated 2D-GIWAXS pattern of the m-4TICO unit cell oriented along the (0 1 1) direction (a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Graphical representation of the  π-π stacking (2 3 2) and lamellar (0 1 1) peaks orientation with respect to the (0 1 1) vector (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' m-4TICO (c) and PBTZT-stat-BDTT-8:m-  4TICO (d) GIWAXS pattern with in-plane (e) and out-of-plane (f) integration profiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' 5x5 µm AFM images of m-4TICO (f) and PBTZT-stat-  BDTT-8:m-4TICO (g) films with domain size distribution and average value (inset).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  nm  nm  (2 3 2)  c)  a)  b)  e)  d)  f)  h)  �-�  (2 3 2)  qz (nm-1)  RMS: 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='7 nm  RMS: 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='4 nm  qxy (nm-1)  g)  (0 1 1)  lamellar  (0 1 1)  qxy (nm-1)  qxy (nm-1)  30  25  20  (t-uu)b  15  10  5  0  0  5  10  15  20  25  qr(nm-1)30  25  20  (t-wu)b  15  10  5  0  0  5  10  15  20  25  qr(nm-1)  Table S5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Crystallographic information of the main peaks observed by 2D-GIWAXS on m-4TICO and PBTZT-stat-BDTT-8:m-4TICO films.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' AFM  domain size and domain purity are also shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Component  Peak  Orientation  q (nm-1)  d (nm)  FWHM  (nm-1)  CCL (nm)  g  Domain  Size (nm)  ϕ (%)  NFA film  m-4TICO  (0 1 1)  Out-of-plane  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='52  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='39  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='33  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='8  62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1  27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='6  Blend film  m-4TICO  (0 1 1)  Out-of-Plane  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='25  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='48  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='59  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='6  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='9  68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='5  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='0  PBTZT-stat-BDTT-8  (1 0 0)  In-plane  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='60  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='42  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='42  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='0  29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='5 PBTZT-stat-BDTT-8  (0 1 0)  Out-of-plane  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='85  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='35  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='00  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1 m-ITIC  m-ITIC 2D-GIWAXS pattern (Figure S11c) shows a couple of features in the π-π stacking region along qz and other less intense peaks  in the low angle region, both in-plane and out-of-plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' To verify whether the NFA arrangement in film is compatible to the phase  existing in powder and single crystal, we have simulated the 2D-GIWAXS of the single crystal unit cell5 (Le Bail refined) and oriented  along the (1 1 1) direction (Figure S11a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Such direction is perpendicular to the lamellar (0 -1 1) peak and parallel with respect to  π-π stacking features, (2 3 3) and (2 2 5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' This is representative of a face-on orientation of the m-ITIC domains with respect to the  substrate (Figure S11b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The good agreement between experimental and simulated GIWAXS confirms a face-on 2D brickwork  packing with respect to the substrate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The feature located qz ∼ 5 nm-1 represents the (1 1 1) reflections but is not evident from the  simulation because of its purely perpendicular orientation with respect to the substrate (region not accessible).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' As the m-ITIC  lamellar (0 1 -1) feature is still evident from the PBTZT-stat-BDTT-8:m-ITIC GIWAXS (Figure S11d) and in-plane integration profile  (Figure S11h), we assume that the NFA is maintaining its crystalline order in blend with a slightly relaxed lamellar (0 1 -1) and (2 2  5) π-π stacking periodicity (Table S6) compared to the pure NFA film.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Figure S11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Simulated 2D-GIWAXS pattern of the m-ITIC unit cell oriented along the (1 1 1) direction (a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Graphical representation of the π-  π stacking, (2 3 3) and (2 2 5), and lamellar (0 1 1) peaks orientation with respect to the (1 1 1) vector (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' m-ITIC (c) and PBTZT-stat-BDTT-  8:m-ITIC (d) GIWAXS pattern with in-plane (e) and out-of-plane (h) integration profiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' 5x5 µm AFM images of m-ITIC (f) and PBTZT-stat-  BDTT-8:m-ITIC (g) films with domain size distribution and average value (inset).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  c)  a)  d)  h)  (2 2 5)  (2 3 3)  (2 2 5)  (2 2 5)  (2 3 3)  (2 2 5)  RMS: 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='7 nm  RMS: 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='6 nm  qxy (nm-1)  qxy (nm-1)  (2 2 5)  e)  b)  �-�  (2 2 5), (2 3 3)  (1 1 2)  lamellar  (0 -1 1)  f)  g)  qz (nm-1)  qxy (nm-1)  30  25  20  (t-wu)b  15  10  5  0  5  0  5  10  15  20  25  qr(nm-1)30  25  20  (t-wu)b  15  10  5  0  5  0  5  10  15  20  25  qr(nm-1)  Table S6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Crystallographic information of the main peaks observed by 2D-GIWAXS on m-ITIC and PBTZT-stat-BDTT-8:m-ITIC films.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' AFM  domain size and domain purity are also shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Component  Peak  Orientation  q (nm-1)  d (nm)  FWHM  (nm-1)  CCL (nm)  g  Domain  Size (nm)  ϕ (%)  NFA film  m-ITIC  (0 1 -1)  In-Plane  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='09  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='54  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='43  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='6  59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='3  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='2  m-ITIC  (2 2 5)  Out-of-plane  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='75  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='35  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='41  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='3  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='7 Blend film  m-ITIC  (0 1 -1)  In-Plane  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='03  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='56  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='67  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='4  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='3  51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='5  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='3  PBTZT-stat-BDTT-8  (1 0 0)  In-plane  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='67  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='35  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='55  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='2  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1 PBTZT-stat-BDTT-8:m-ITIC  (0 1 0) + (2 2 5)  Out-of-plane  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='54  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='36  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='30  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='5  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='4 IDIC  IDIC 2D-GIWAXS pattern (Figure S12c) shows a couple of features in the π-π stacking region along qz and multiple peaks in the low  angle region among multiple directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' To verify whether the NFA arrangement in film is compatible to the phase existing in  powder and single crystal, we have simulated the 2D-GIWAXS of the single crystal unit cell5 (Le Bail refined) and oriented along the  (2 2 3) direction (Figure S12a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Such direction is nearly perpendicular to the lamellar (0 1 0) peak and parallel with respect to the  (2 1 3) π-π stacking feature, which is representative of a face-on orientation of the m-ITIC domains with respect to the substrate  (Figure S12b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The partial agreement between experimental and simulated GIWAXS suggests a possible competition between two  different polymorphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=" The first one represented by the (0 1 0) and (2 1 3) features with a face-on 2D brickwork packing with respect  to the substrate, while a second one identified by the (0 1 0)' and (2 1 3)' peaks." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=" We hypothesise for the second polymorph to be  still characterised by a face-on packing motif (2D or 3D) because of the presence of an intense out-of-plane (2 1 3)' π-π stacking  feature and a (0 1 0)' lamellar peak developing along the in-plane direction." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' This second polymorph is becoming predominant in  PBTZT-stat-BDTT-8:IDIC blend as visible from the GIWAXS data (Figure S12d), integration profiles (Figure S12e,h) and Table S7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' As  Figure S12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Simulated 2D-GIWAXS pattern of the IDIC unit cell (Le Bail refined) oriented along the (2 2 3) direction (a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Graphical  representation of the (2 1 3) π-π stacking and (0 1 0) lamellar peaks orientation with respect to the (2 2 3) vector (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' IDIC (c) and PBTZT-  stat-BDTT-8:IDIC (d) GIWAXS pattern with in-plane (e) and out-of-plane (h) integration profiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' 5x5 µm AFM images of IDIC (f) and PBTZT-  stat-BDTT-8:IDIC (g) films with domain size distribution and average value (inset).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  c)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='5 nm  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='7 nm  a)  b)  30  ×106  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='3)  lamellar  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='5  (0 1 0)  lamellar  25  (2 2 3)  (0 1 0)  20  2  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1 3)  (rwu)  元-元  15  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='5  (2 1 3)  10  1  5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content="5  0  (0 1 0)  (2 2 3)  5  0  5  10  15  20  25  qxy (nm-1)  c)  IDIC  d)  PBTZT-stat-BDTT-8:IDIC  e)  In-plane  30  30  (010)  25  25  2  Intensity (x105)  (0 10)  20  (2 13)'  20  (2 13)+ (0 1 0)  (2 1 3)  15  IDIC  PBTZT-stat-BDTT-8:IDIC  (1 0 0)  10  10  (010)  5  (010)  (1 0 0)  10)  0  5  10  15  20  5  0  5  10  15  20  25  0  5  10  15  20  25  q (nm-1)  f)  qxy (nm=1)  qxy (nm)  g)  h)  Out-of-plane  6  RMS: 8." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='9 nm  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1nm  RMS:  :4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content="8 nm  IDIC  5  PBTZT-stat-BDTT-8:IDIC  (2 1 3)  (x105)  4  20  50  Intensity (  Domain Size (nm)  Domain Size (nm)  3  (2 13)  (2 1 3) + (0 1 0)  0  μm  5  10  15  20  q (nm1)  the IDIC lamellar (0 1 0)' feature is still evident and distinguishable from the polymer, we assume that the NFA is still crystalline in  the blend with a face-on 2D/3D crystal packing motif." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Table S7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Crystallographic information of the main peaks observed by 2D-GIWAXS on IDIC and PBTZT-stat-BDTT-8:IDIC films.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' AFM domain  size and domain purity are also shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Component  Peak  Orientation  q (nm-1)  d (nm)  FWHM  (nm-1)  CCL (nm)  g  Domain  Size (nm)  ϕ (%)  NFA film  IDIC  (0 1 0)  In-Plane  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='32  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='45  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='26  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='7  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='8  52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='7  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='2  IDIC  (2 1 3)  Out-of-plane  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='46  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='34  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='44  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='9  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content="1 Blend film  IDIC  (0 1 0)'  In-Plane  3." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='60  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='74  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='54  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='5  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='4  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1  25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='5  PBTZT-stat-BDTT-8  (1 0 0)  In-plane  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='62  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='40  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='59  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='6  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content="9 PBTZT-stat-BDTT-8:m-ITIC  (0 1 0) + (2 1 3)'  Out-of-plane  18." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='35  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='79  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='6 4TICO  4TICO 2D-GIWAXS pattern (Figure S13a) is characterised by a weak crystallinity as it only presents two main features, both featuring  a lack of domain ordering along any specific direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' For this reason, it is not convenient to perform a side-by-side comparison  with the single crystal structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='5 However, a low angle (1 0 0) and a high angle (0 1 0) diffraction rings can still be distinguished  (Figure S13a,b) and used for the evaluation of the NFA crystallinity in films (Table S8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' As regards the PBTZT-stat-BDTT-8:4TICO  blend, we could differentiate between the 4TICO and PBTZT-stat-BDTT-8 lamellar reflections since the latter is typically  characterised by in-plane scattering in the low angle region (Figure 5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' We therefore conclude that the NFA is weakly crystalline in  the blend given the higher FWHM of the observed reflections with lack of texturing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Table S8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Crystallographic information of the main peaks observed by 2D-GIWAXS on 4TICO and PBTZT-stat-BDTT-8:4TICO films.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' AFM  domain size and domain purity are also shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Component  Peak  Orientation  q (nm-1)  d (nm)  FWHM  (nm-1)  CCL (nm)  g  Domain  Size (nm)  ϕ (%)  NFA film  4TICO  (1 0 0)  In-Plane  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='20  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='96  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='89  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='3  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='0  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='3  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='2  4TICO  (0 1 0)  Out-of-plane  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='55  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='36  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='09  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='8  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='7 Blend film  4TICO  (1 0 0)  In-Plane  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='12  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='98  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='8  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='4  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1  47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='7  PBTZT-stat-BDTT-8  (1 0 0)  In-plane  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='77  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='27  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='64  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='8  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='2 PBTZT-stat-BDTT-8:4TICO  (0 1 0)  Out-of-plane  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='67  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='36  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='14  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='8  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='8 Figure S13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' 4TICO and PBTZT-stat-BDTT-8:4TICO (a) GIWAXS patterns with in-plane and out-of-plane (b) integration profiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' 5x5 µm AFM  images (c) of IDIC and PBTZT-stat-BDTT-8:IDIC films with domain size distribution and average value (inset).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Out-of-plane  4TICO  (1 0 0)  PBTZT-stat-BDTT-8:4TICO  a)  b)  c)  In-plane  RMS: 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='9 nm  RMS: 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='7 nm  (1 0 0)  (1 0 0) +  (0 1 0)  (1 0 0)  (1 0 0)  (1 0 0)  (1 0 0)  (1 0 0)  (0 1 0)  + (0 1 0)  (0 1 0)  (0 1 0) + (0 1 0)  (0 1 0) + (0 1 0)  (0 1 0)  qxy (nm-1)  qxy (nm-1)  30  25  20  (t-wu)b  15  10  5  0  5  0  5  10  15  20  25  qr(nm-1)30  25  20  (t-wu)b  15  10  5  0  5  0  5  10  15  20  25  qr(nm-1)  ITIC  ITIC 2D-GIWAXS pattern (Figure S14a) is characterised by a weak crystallinity as it only presents one main feature with a lack of  domain ordering along any specific direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' For this reason, it is not convenient to perform a side-by-side comparison with the  single crystal structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='5 However, a low angle (1 0 0) diffraction ring can still be distinguished (Figure S14a,b) and used for the  evaluation of the NFA crystallinity in films (Table S9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' As regards the PBTZT-stat-BDTT-8:ITIC blend, we could differentiate between  the ITIC and PBTZT-stat-BDTT-8 lamellar reflections since the two are characterised by a different in-plane lattice spacing (Table S9  and Figure S14).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' We therefore conclude that the NFA is poorly crystalline in the blend given the high FWHM of the observed  reflections with lack of directionality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Table S9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Crystallographic information of the main peaks observed by 2D-GIWAXS on ITIC and PBTZT-stat-BDTT-8:ITIC films.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' AFM domain  size and domain purity are also shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Component  Peak  Orientation  q (nm-1)  d (nm)  FWHM  (nm-1)  CCL (nm)  g  Domain  Size (nm)  ϕ (%)  NFA film  ITIC  (1 0 0)  In-Plane  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='66  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='72  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='65  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='43  26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='8  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='4  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='3  Blend film  ITIC  (1 0 0)  In-Plane  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='57  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='76  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='99  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='7  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='0  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='6  59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='4  PBTZT-stat-BDTT-8  (1 0 0)  In-plane  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='76  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='28  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='79  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='3 PBTZT-stat-BDTT-8:4TICO  (0 1 0)  Out-of-plane  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='09  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='35  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='44  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='3  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='7 Figure S14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' ITIC and PBTZT-stat-BDTT-8:ITIC (a) GIWAXS patterns with in-plane and out-of-plane (b) integration profiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' 5x5 µm AFM  images (c) of ITIC and PBTZT-stat-BDTT-8:ITIC films with domain size distribution and average value (inset).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Out-of-plane  ITIC  (1 0 0)  PBTZT-stat-BDTT-8:ITIC  a)  b)  c)  In-plane  RMS: 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='7 nm  RMS: 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1 nm  (1 0 0)  (1 0 0)  (0 1 0)  (1 0 0)  (0 1 0)  (1 0 0)  (1 0 0)  qxy (nm-1)  qxy (nm-1)  30  25  20  (t-wu)b  15  10  5  0  5  0  5  10  15  20  25  qr(nm-1)30  25  20  (t-wu)b  15  10  5  0  5  0  5  10  15  20  25  qr(nm-1)  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' AFM Watershed Analysis  IDIC  PBTZT-stat-BDTT-8:IDIC  Avg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Domain Size: 52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='7 nm  Avg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Domain Size: 41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1 nm  Figure S15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' AFM images (1 µm x 1 µm) of IDIC and PBTZT-stat-BDTT-8:IDIC films with and without the mask used for the  calculation of the average domain size by watershed algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The input parameters and the result of the simulation are also  shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  200 nm200 nm200 nm200 nmGrainLocation  Numberof steps:  20周  Drop size:  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='500周  %  Threshold:  80周px2  Segmentation  Numberofsteps:  199周  D rop size:  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='600周%  Options  Mask color:  Invert height  Combine with existing maskGrainLocation  Numberofsteps:  20日  Drop size:  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='500周%  Threshold:  40合px2  Segmentation  Number of steps:  140周  Drop size:  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='500周%  Options  Mask color:  Invert height  Combinewithexistingmask  m-ITIC  PBTZT-stat-BDTT-8:m-ITIC  Avg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Domain Size: 59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='3 nm  Avg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Domain Size: 51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='5 nm  Figure S16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' AFM images (1 µm x 1 µm) of m-ITIC and PBTZT-stat-BDTT-8:m-ITIC films with and without the mask used for the  calculation of the average domain size by watershed algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The input parameters and the result of the simulation are also  shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  200 nm200 nm200 nm200 nmGrainLocation  Numberof steps:  10  Drop size:  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='500周%  Threshold:  40周px2  Segmentation  Numberofsteps:  200周  Drop size:  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='000周%  Options  Mask color:  Invert height  Combine with existing maskGrain Location  Number of steps:  10周  Drop size:  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='500周  %  Threshold:  40周px  Segmentation  Numberof steps:  200周  Drop size:  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='600周%  Options  Mask color:  8  Invert height  Combine with existing mask  o-IDTBR  PBTZT-stat-BDTT-8:o-IDTBR  Avg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Domain Size: 36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='0 nm  Avg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Domain Size: 50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='0 nm  Figure S17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' AFM images of o-IDTBR (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='6 µm x 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='6 µm) and PBTZT-stat-BDTT-8:o-IDTBR (1 µm x 1 µm) films with and without  the mask used for the calculation of the average domain size by watershed algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The input parameters and the result of  the simulation are also shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  200 nm200 nmGrain Location  Number of steps:  5周  Drop size:  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='500周  %  Threshold:  20周  px  Segmentation  Nurmber of steps:  图09  Drop size:  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='600周%  Options  Mask color:  Invert height  Combine with existing maskGrain Location  Number of steps:  4周  Drop size:  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='751周  %  Threshold:  5周  px  Segmentation  Number of steps:  49周  Drop size:  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='831周%  Options  Mask color:  Invert height  Combine with existing mask200 nm200 nm  m-4TICO  PBTZT-stat-BDTT-8:m-4TICO  Avg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Domain Size: 62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1 nm  Avg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Domain Size: 68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='5 nm  Figure S18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' AFM images (2 µm x 2 µm) of m-4TICO and PBTZT-stat-BDTT-8:m-4TICO films with and without the mask used for  the calculation of the average domain size by watershed algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The input parameters and the result of the simulation are  also shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  500 nm500nmGrainLocation  Numberof steps:  5周  Drop size:  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='566  %  Threshold:  5日px2  Segmentation  Numberofsteps:  129 周  Drop size:  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='341周%  Options  Mask color:  Invert height  Combine with existing maskGrainLocation  Numberofsteps:  20日  Drop size:  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='500周%  Threshold:  40合px2  Segmentation  Number of steps:  140周  Drop size:  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='500周%  Options  Mask color:  Invert height  Combinewithexistingmask500 nm500nm  ITIC  PBTZT-stat-BDTT-8:ITIC  Avg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Domain Size: 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='4 nm  Avg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Domain Size: 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='6 nm  Figure S19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' AFM images (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='5 µm x 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='5 µm) of ITIC and PBTZT-stat-BDTT-8:ITIC films with and without the mask used for the  calculation of the average domain size by watershed algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The input parameters and the result of the simulation are also  shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  100nmGrain Location  Number of steps:  10日  Drop size:  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='000周  %  Threshold:  10合  px  Segmentation  Numberofstepis:  563合  Drop size:  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='100周  %  Options  Mask color:  Invert height  Combine with existing maskGrain Location  Numberofsteps:  44日  Drop size:  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='435周%  Threshold:  15日 px2  Segmentation  Numberofsteps:  517周  Drop size:  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='044周%  Options  Mask color:  Invert height  Combine with existing mask100 nm100 nmGrain Location  Number of steps:  10 周  Drop size:  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='000周  Threshold:  10周  px  Segmentation  Numberofsteps:  563  Drop size:  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='100周  %100 nm  4TICO  PBTZT-stat-BDTT-8:4TICO  Avg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Domain Size: 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='3 nm  Avg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Domain Size: 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1 nm  Figure S20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' AFM images of 4TICO (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='3 µm x 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='3 µm) and PBTZT-stat-BDTT-8:4TICO (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='5 µm x 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='5 µm)  films with and without the mask used  for the calculation of the average domain size by watershed algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The input parameters and the result of the simulation are also  shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  PBTZT-stat-BDTT-8:4TIC  Avg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Domain Size: 29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='6 nm  Figure S21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' AFM images of PBTZT-stat-BDTT-8:4TIC (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='5 µm x 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='5 µm)  films with and without the mask used for the calculation of  the average domain size by watershed algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The input parameters and the result of the simulation are also shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  100nmGrain Location  Number of steps:  22周  Drop size:  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='595日%  Threshold:  7周px2  Segmentation  Number of steps:  258  Drop size:  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='204日%  Options  Mask color:  Invert height  Combine with existing maskGrain Location  Numberofsteps:  44日  Drop size:  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='435周%  Threshold:  15日 px2  Segmentation  Numberofsteps:  517周  Drop size:  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='044周%  Options  Mask color:  Invert height  Combine with existing mask50nm50nm100 nm100 nmGrain Location  Number of steps:  24周  D2rop size:  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='435周  Threshold:  3周  P  Segmentation  Numberof steps  478周  Drop size:  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='180周  Options  Mask color:  Invert height  Combine with existing mask100 nm  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Electron Mobility by MIS-CELIV  Figure S22 Typical MIS CELIV dataset taken for the 4TIC blend.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The ramp rate A was varied between (a) 50 V/ms, (b) 200V/ms, (c) 400V/ms,  (d) 800V/ms, and (e) 1600V/ms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' (f) Extracted electron mobilities for the different blends in dependence of the ramp rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Dashed lines  indicated the estimated saturated mobility used in the main part.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' See text for further explanations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Figure S15 shows representative example MIS-CELIV traces for PBTZT-stat-BDTT-8:4TIC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Different panels show measurements at  different ramp rates and for each ramp rate the offset voltage is varied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The solid black lines indicate the displacement current  density j0 resulting from the geometric capacitance, and 2×j0 used to determine time t1 (red dot) in MIS-CELIV measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Finally, the saturated current density jsat is estimated by the top dashed line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Measurements at higher offset voltage suffered from  increased current injection so that jsat had to be roughly estimated from the depicted traces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Note that the extracted mobility  values change little with the exact value of jsat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' With t1, the mobility is calculated for all ramp rates and blends and plotted in fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  S15 (bottom right panel).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' In the presence of some injection barrier, the measured apparent mobility depends on the product of  ramp rate A and t1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' The measured mobility saturates and reaches its true value for large A×t1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='6 The estimated saturated mobility  is indicated with dashed lines in fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' S15 (bottom right panel).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  With increasing annealing temperature, the blocking properties of MgF2 diminished and for some samples leakage currents  prevented data analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Hence, the m-4TICO blend at 100°C, rather than 120°C, and the unannealed m-ITIC were analysed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='0  2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='0  !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='sat  $1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='IDIC  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='4TIC  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='mITIC  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='4TICO  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='µe (10-8 m2/Vs)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='At1 (V)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='m4TICO  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='(a)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='(b)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='(c)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='(d)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='(e)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='(f)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='50 V/ms  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='oV  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1 V  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='2 V  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='3 V  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='50  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='75  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='100  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='125  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='150  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='175  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='time (us)200 V/ms  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='oV  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1v  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='2 V  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='current density (mA/cm^2)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='3 V  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='4 V  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='40  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='time (us)400 V/ms  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='oV  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='40  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1 V  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='2 V  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='current density (mA/cm^2)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='3 V  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='OE  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='T  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='T  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='time (us)800 V/ms  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='80  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='oV  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1 V  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='70  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='2 V  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='3 V  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='60  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='4 V  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='5 V  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='50  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='40  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='T  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='T  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='time (us)1600 V/ms  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='ov  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='140  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1V  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='2 V  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='current density (mA/cm^2)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='120  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='3 V  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='4 V  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='100  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='5 V  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='6 V  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='80  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='60  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='40  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='time (us)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='However,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' we did not observe a notable change for other samples with annealing temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Hence, we can assume that the  measured values are representative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  Figure S23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Photo-CELIV mobility compared to MIS-CELIV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' A bisecting line is  also plotted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Active Layer Annealing Temperature and Dark J-V  Table S10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Thermal annealing protocol used for each active layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content="  Active Layer  Annealing Protocol  PBTZT-stat-BDTT-8:o-IDTBR  5' at 100 °C  PBTZT-stat-BDTT-8:m-ITIC  5' at 100 °C + 5' at 120 °C + 3' at 140 °C  PBTZT-stat-BDTT-8:ITIC  5' at 100 °C + 5' at 120 °C + 3' at 140 °C  PBTZT-stat-BDTT-8:IDIC  5' at 100 °C + 5' at 120 °C  PBTZT-stat-BDTT-8:4TICO  5' at 100 °C + 5' at 120 °C + 3' at 140 °C  PBTZT-stat-BDTT-8:4TIC  5' at 100 °C + 5' at 120 °C + 3' at 140 °C  PBTZT-stat-BDTT-8:m-4TICO  5' at 100 °C + 5' at 120 °C  Figure S24." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' J-V characteristics measured in dark conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' References  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Schulze and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Schmidt, Energy & Environmental Science, 2015, 8, 103-125.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Mondelli, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Silvestri, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Ciammaruchi, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Solano, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Beltrán-Gracia, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Barrena, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Riede and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Morse, Journal of Materials  Chemistry A, 2021, 9, 26917-26928.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Shi, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Zuo, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Jo, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Gao, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Lin, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Liu and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Jen, Chemistry of Materials, 2017, 29, 8369-8376.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Sherman, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Purushothaman, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Parkin, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Kim, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Collins, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Anthony, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='-Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Nguyen and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Chabinyc, Journal of Materials  Chemistry A, 2015, 3, 9989-9998.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Mondelli, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Boschetto, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Horton, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Tiwana, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='-K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Skylaris, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Coles, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Krompiec and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Morse, Materials Horizons, 2020,  7, 1062-1072.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Sandberg, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Nyman, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Dahlström, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Sandén, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Törngren, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Smått and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Österbacka, Applied Physics Letters, 2017, 110,  153504.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='  m-4TICO  IDIC  m-ITIC  4TIC  4TICO  ITIC  Figure S25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content=' Plot showing the trend between the bimolecular recombination coefficient and  the average domain size determined from AFM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
+page_content='.  1E-16  p  1E-17  6  7  8  9  10  11  12  CCL (nm)1E-16  1E-17  10  20  30  40 50 607080  Domain Size (nm)1E-16  1E-17  0  2  4  6  8  RMS (nm)' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNAyT4oBgHgl3EQfY_dp/content/2301.00214v1.pdf'}
diff --git a/p9AzT4oBgHgl3EQfAvo4/vector_store/index.faiss b/p9AzT4oBgHgl3EQfAvo4/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..667ee53417fadd14e467a9b55b31453215bde89e
--- /dev/null
+++ b/p9AzT4oBgHgl3EQfAvo4/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:882890e3fbffc10d282f8ff6a535959006cfefb2ce4918695b6209846f0d36fd
+size 4980781
diff --git a/p9AzT4oBgHgl3EQfAvo4/vector_store/index.pkl b/p9AzT4oBgHgl3EQfAvo4/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..6111951fe973d7a0219605d049d6adf465f22015
--- /dev/null
+++ b/p9AzT4oBgHgl3EQfAvo4/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:63fefd9e365dfc34a882d1a7786bc443bd99758dc11fac85e338d0f4b96eb726
+size 204690
diff --git a/p9FPT4oBgHgl3EQfMjQS/content/tmp_files/2301.13026v1.pdf.txt b/p9FPT4oBgHgl3EQfMjQS/content/tmp_files/2301.13026v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b92ce552717395411978e8d38708b9f39e9ec6f5
--- /dev/null
+++ b/p9FPT4oBgHgl3EQfMjQS/content/tmp_files/2301.13026v1.pdf.txt
@@ -0,0 +1,3976 @@
+SOBOLEV EMBEDDINGS AND DISTANCE FUNCTIONS
+LORENZO BRASCO, FRANCESCA PRINARI, AND ANNA CHIARA ZAGATI
+Abstract. On a general open set of the euclidean space, we study the relation between the
+embedding of the homogeneous Sobolev space D1,p
+0
+into Lq and the summability properties of
+the distance function. We prove that in the superconformal case (i.e. when p is larger than the
+dimension) these two facts are equivalent, while in the subconformal and conformal cases (i.e.
+when p is less than or equal to the dimension) we construct counterexamples to this equivalence. In
+turn, our analysis permits to study the asymptotic behaviour of the positive solution of the Lane-
+Emden equation for the p−Laplacian with sub-homogeneous right-hand side, as the exponent
+p diverges to ∞. The case of first eigenfunctions of the p−Laplacian is included, as well. As
+particular cases of our analysis, we retrieve some well-known convergence results, under optimal
+assumptions on the open sets. We also give some new geometric estimates for generalized principal
+frequencies.
+Contents
+1.
+Introduction
+2
+1.1.
+Homogeneous Sobolev spaces
+2
+1.2.
+Main results
+3
+1.3.
+Plan of the paper
+6
+2.
+Preliminaries
+7
+2.1.
+Notation
+7
+2.2.
+Sobolev embeddings
+9
+2.3.
+The Lane-Emden equation
+11
+3.
+The distance function
+15
+4.
+A Morrey–type inequality and its consequences
+18
+5.
+Embedding theorems
+24
+5.1.
+The case q < p
+24
+5.2.
+The case p = q: continuity
+28
+5.3.
+The case p = q: compactness
+29
+5.4.
+The super-homogeneous case q > p and beyond
+31
+6.
+Asymptotics
+33
+6.1.
+Asymptotics for λp,q(Ω)
+33
+6.2.
+Asymptotics for the solution of the Lane-Emden equation
+35
+6.3.
+Asymptotics for λp(Ω)
+37
+6.4.
+Asymptotics for the first p−eigenfunction
+37
+Appendix A.
+An infinite strip with slowly shrinking ends
+40
+References
+41
+Date: January 31, 2023.
+2010 Mathematics Subject Classification. 46E35, 35J92, 35P30.
+Key words and phrases. Sobolev embeddings, p−Laplacian, Lane-Emden equation, inradius, distance function,
+capacity.
+1
+arXiv:2301.13026v1  [math.AP]  30 Jan 2023
+
+2
+BRASCO, PRINARI, AND ZAGATI
+1. Introduction
+1.1. Homogeneous Sobolev spaces. Let 1 < p < ∞ and let Ω ⊆ RN be an open set. We indicate
+by D1,p
+0 (Ω) the homogeneous Sobolev space defined by the completion of C∞
+0 (Ω), with respect to
+the norm
+ψ �→ ∥∇ψ∥Lp(Ω),
+for every ψ ∈ C∞
+0 (Ω).
+Our primary goal is to deepen the study of conditions on Ω assuring the validity of the continuous
+embedding
+(1.1)
+D1,p
+0 (Ω) �→ Lq(Ω),
+in the range 1 ≤ q ≤ p. Equivalently, if we introduce the generalized principal frequencies
+(1.2)
+λp,q(Ω) :=
+inf
+ψ∈C∞
+0 (Ω)
+�ˆ
+Ω
+|∇ψ|p dx : ∥ψ∥Lq(Ω) = 1
+�
+,
+we seek for necessary and sufficient conditions on Ω assuring that λp,q(Ω) > 0. Indeed, λp,q(Ω) is
+nothing but the sharp constant in the following Poincar´e-type inequality
+c
+�ˆ
+Ω
+|ψ|q dx
+� p
+q
+≤
+ˆ
+Ω
+|∇ψ|p dx,
+for every ψ ∈ C∞
+0 (Ω).
+This is a classical subject, we refer to [32, Chapter 15] for a thorough treatment of the problem. In
+particular, before proceeding further, it is important to recall some important facts.
+The first one is the following remarkable equivalence
+D1,p
+0 (Ω) �→ Lq(Ω) is continuous
+⇐⇒
+D1,p
+0 (Ω) �→ Lq(Ω) is compact,
+which holds in the sub-homogeneous case 1 ≤ q < p < ∞. We refer to [32, Theorem 15.6.2] for this
+result (see also [11, Theorem 1.2], for a different proof). Such an equivalence ceases to be true at
+the threshold q = p, as shown by the simple example of
+Ω = RN−1 × (−1, 1).
+A second important fact is that, for the super-homogeneous case p < q, we have
+D1,p
+0 (Ω) �→ Lp(Ω) is continuous
+⇐⇒
+D1,p
+0 (Ω) �→ Lq(Ω) is continuous,
+and
+D1,p
+0 (Ω) �→ Lp(Ω) is compact
+⇐⇒
+D1,p
+0 (Ω) �→ Lq(Ω) is compact.
+More precisely, here q is such that
+p < q
+�
+�
+�
+�
+�
+<
+N p
+N − p,
+if 1 < p < N,
+< ∞,
+if p = N,
+≤ ∞,
+if p ≥ N.
+We refer to [32, Theorem 15.4.1] and [32, Theorem 15.6.1] for these equivalences. This second fact
+explains why we will essentially limit ourselves to treat the case q ≤ p and only briefly discuss the
+case q > p.
+In particular, in this paper we want to discuss the link between the continuous (and compact)
+embedding (1.1) and the summability of the distance function
+dΩ(x) := min
+y∈∂Ω |x − y|,
+for every x ∈ Ω.
+
+SOBOLEV EMBEDDINGS AND DISTANCE FUNCTIONS
+3
+At this aim, it is useful to recall that in [11] (see also [13]), a similar study has been done, with the
+so-called p−torsion function of Ω in place of dΩ. The former, denoted by wΩ
+p,1, is formally defined
+as the positive solution of
+−∆pu = 1,
+in Ω,
+u = 0,
+on ∂Ω,
+where ∆pu = div(|∇u|p−2∇u) is the p−Laplace operator, see [11, Definitions 2.1 and 2.2] for the
+precise definition. Then, for the case q < p, in [11, Theorem 1.2] the first author and Ruffini proved
+that
+D1,p
+0 (Ω) �→ Lq(Ω) is continuous
+⇐⇒
+wΩ
+p,1 ∈ L
+p−1
+p−q q(Ω).
+As for the limit case q = p, by [11, Theorem 1.3] we have
+D1,p
+0 (Ω) �→ Lp(Ω) is continuous
+⇐⇒
+wΩ
+p,1 ∈ L∞(Ω),
+and
+D1,p
+0 (Ω) �→ Lp(Ω) is compact
+⇐⇒
+lim
+R→+∞ ∥wΩ
+p,1∥L∞(RN\BR) = 0,
+where BR is the N−dimensional ball of center 0 and radius R > 0.
+These characterizations are quite useful: we give an example in Appendix A of an open planar set
+with infinite volume, for which one can get the compactness of the embedding D1,2
+0 (Ω) �→ L2(Ω) by
+appealing to the torsion function. Nevertheless, dealing with the p−torsion function is not always
+practical, thus the previous characterizations are a bit implicit. It would be desirable to have some
+characterizations which are more intrinsically geometric.
+Roughly speaking, in this paper we will study to which extent we can replace wΩ
+p,1 with dΩ in
+the aforementioned results. For capacitary reasons, we will see that this is possible only in the
+superconformal case p > N. In the case p ≤ N, we will find that some summability conditions on
+dΩ are necessary for the embeddings to hold, but not sufficient.
+1.2. Main results. In this paper, we will show at first that for 1 ≤ q < p
+D1,p
+0 (Ω) �→ Lq(Ω) is continuous
+=⇒
+dΩ ∈ L
+p q
+p−q (Ω).
+In the case q = p, we will prove that
+D1,p
+0 (Ω) �→ Lp(Ω) is continuous
+=⇒
+dΩ ∈ L∞(Ω),
+and
+D1,p
+0 (Ω) �→ Lp(Ω) is compact
+=⇒
+lim
+R→+∞ ∥dΩ∥L∞(RN\BR) = 0.
+Moreover, when p > N we will show that all these implications actually become equivalences. We
+will also construct suitable counterexamples to show that for 1 < p ≤ N, on the contrary, none of
+the converse implications hold true.
+We recall that the condition
+lim
+R→+∞ ∥dΩ∥L∞(RN\BR) = 0,
+is somehow classical in the theory of Sobolev spaces, when it holds Ω is said to be quasibounded
+(see for example [1, 14]).
+Remark 1.1 (Comparison with previous results, q < p). The fact that the continuity of the
+embedding implies the stated summability of dΩ can be found in [7, Theorem 3], at least for the
+case p = 2. However, apart for the generalization to p ̸= 2, our proof is different and exploits a
+
+4
+BRASCO, PRINARI, AND ZAGATI
+comparison principle for the sub-homogeneous Lane-Emden equation, that we recently proved in
+[10]. This in turn permits to obtain a geometric estimate on λp,q of the type
+λp,q(Ω)
+�ˆ
+Ω
+d
+p q
+p−q
+Ω
+dx
+� p−q
+q
+≤ C,
+with a constant C which does not blow-up as q ↗ p, differently from [7] (see Remark 5.2 below).
+The converse implication exploits the same idea of [7], i.e. it is based on Hardy’s inequality
+CΩ
+ˆ
+Ω
+|u|p
+dp
+Ω
+dx ≤
+ˆ
+Ω
+|∇u|p dx,
+for every u ∈ C∞
+0 (Ω).
+There is however a difference here: while the result in [7] is proved conditionally on the validity of
+such an inequality, we use here the important fact that such an inequality holds for every open set
+Ω ⊊ RN, provided p > N. This is a major result proved independently by Lewis [30] and Wannebo
+[38].
+Remark 1.2 (Comparison with previous results, q = p). Here our embedding results were already
+known and due to Adams. However, to prove that on a quasibounded open set the embedding
+D1,p
+0 (Ω) �→ Lp(Ω) is compact for p > N, we use a different argument.
+As before, the crucial
+ingredient is the Hardy inequality recalled above, which permits to give a simpler proof. We believe
+this fact to be of independent interest.
+With these embedding results at hand, we then proceed to study the asymptotic behaviour of
+both λp,q(Ω) and their relevant extremals (provided they exist), in the limit as p goes to ∞. Here
+we are going to unify and extend previous results, scattered in the literature. For example, for the
+generalized principal frequencies, we will prove that
+lim
+p→∞
+�
+λp,q(Ω)
+� 1
+p =
+1
+∥dΩ∥Lq(Ω)
+and
+lim
+p→∞
+�
+λp(Ω)
+� 1
+p = 1
+rΩ
+,
+for every open set Ω ⊊ RN. Here we used the simplified notation λp(Ω) = λp,p(Ω). The quantity
+rΩ is the inradius of Ω, which coincides with the supremum of the distance function.
+As for the relevant extremals, we will prove at first that under the assumption dΩ ∈ Lq(Ω) for
+some 1 ≤ q < ∞ and Ω connected, we have
+lim
+p→∞ ∥wΩ
+p,q − dΩ∥Lq(Ω) = 0,
+where for q < p the function wΩ
+p,q is the unique positive solution of the Lane-Emden equation
+−∆pu = uq−1,
+in Ω,
+with Dirichlet homogeneous boundary conditions. By observing that (see equation (2.14) below)
+∥wΩ
+p,q∥Lq(Ω) =
+�
+λp,q(Ω)
+�
+1
+q−p ,
+we get that
+wΩ
+p,q :=
+�
+λp,q(Ω)
+�
+1
+p−q wΩ
+p,q,
+is the unique positive extremal in D1,p
+0 (Ω) for λp,q(Ω) and we have
+lim
+p→∞
+����wΩ
+p,q −
+dΩ
+∥dΩ∥Lq(Ω)
+����
+Lq(Ω)
+= 0.
+
+SOBOLEV EMBEDDINGS AND DISTANCE FUNCTIONS
+5
+We remark that this convergence is obtained under the optimal assumption dΩ ∈ Lq(Ω), thus Ω is
+not supposed either bounded or with finite volume. Moreover, by an interpolation argument, we
+can upgrade these convergences and infer convergence in Lr(Ω) and C0,β(Ω), for every q < r ≤ ∞
+and 0 < β < 1.
+In the case of λp(Ω), extremals in D1,p
+0 (Ω) are usually called first eigenfunctions of the p−Laplacian
+with Dirichlet conditions. In this case, we will prove that if Ω is connected and quasibounded, then
+the family {up} is precompact in L∞(Ω) and every accumulation point u∞ is a solution of
+min
+u∈W 1,∞(Ω)
+�
+∥∇u∥L∞(Ω) : ∥u∥L∞(Ω) = 1, u ≡ 0 on ∂Ω
+�
+= 1
+rΩ
+.
+Here each up is the first positive eigenfunction on Ω, normalized by the requirement to have unit
+Lp(Ω) norm.
+Finally, we will also consider the variational problem associated to the endpoint Poincar´e-Sobolev
+constant λp,∞(Ω) for p > N, recently studied in [17] and [22] when Ω is a bounded open set. More
+precisely, we will generalize [17, Theorems 2.1 and 2.3], by showing that for every open set Ω ⊊ RN,
+it holds
+lim
+q→∞ λp,q(Ω) = λp,∞(Ω),
+and by proving that the variational problem defining λp,∞(Ω) has a minimizer under the sole
+assumption of quasiboundedness on Ω. Moreover, inspired by [17, Theorem 3.3], we will also study
+the asymptotic behaviour of both λp,∞ and its extremals, as p goes to ∞.
+At the level of generalized principal frequencies, we can summarize the previous convergence
+results with the following diagram, which holds for every N < p < ∞, every 1 ≤ q ≤ p and every
+open set Ω ⊊ RN (see Corollary 6.1, Corollary 6.2 and Corollary 6.4).
+�
+λp,q(Ω)
+� 1
+p
+�
+λp,∞(Ω)
+� 1
+p
+1
+∥dΩ∥Lq(Ω)
+1
+rΩ
+q→∞
+p→∞
+p=q→∞
+p→∞
+The elements in the bottom line have to be considered as 0, whenever dΩ ̸∈ Lq(Ω) or rΩ = +∞.
+Moreover, when Ω is such that dΩ ∈ Lq0(Ω) for some q0 < ∞, then we can close the diagram by
+1
+∥dΩ∥Lq(Ω)
+q→∞
+−→
+1
+rΩ
+,
+thus making it commutative.
+Remark 1.3 (Comparison with previous results). These convergence results are not a complete
+novelty, of course. However, our treatment extends, improves and generalizes some known results
+previously obtained by various authors in some particular cases (i.e. q = 1 or q = p) and under
+more restrictive assumptions on Ω. The asymptotics for λp(Ω) generalize [26, Lemma 1.5] and [18,
+Theorem 3.1], shown under the restrictive assumption that Ω is a bounded open set (see also [16,
+Theorem 5.1]).
+
+6
+BRASCO, PRINARI, AND ZAGATI
+The behaviour of λp,1(Ω) is due to [5, Proposition 2.1] and [28, Theorem 1], in the case of an
+open bounded set, after getting the uniform convergence of the relevant extremals wΩ
+p,1 to dΩ. This
+result is extended to sets with finite volume in [12, Corollary A.4]. As for the constant λp,∞, the
+case of open bounded sets is considered in [17].
+We point out that the extension of these convergence results to open sets which are unbounded or
+with infinite volume is not trivial: we crucially rely on the comparison principle for the Lane-Emden
+equation recalled above, as well as on the asymptotic behaviour as p goes to ∞ of the following
+Morrey-type constant
+µp(B1) :=
+inf
+u∈W 1,p(B1)
+�ˆ
+B1
+|∇u|p dx : u(0) = 1 and u(z) = 0
+�
+,
+with z ∈ ∂B1.
+The study of this constant is contained in Section 4 below. The study of the asymptotics for µp(B1)
+permits in turn to obtain a couple of collateral results, which are interesting in themselves: the
+behaviour for large p of the two sharp Hardy constants
+hp(Ω) =
+inf
+u∈C∞
+0 (Ω)
+�ˆ
+Ω
+|∇u|p dx :
+����
+u
+dΩ
+����
+Lp(Ω)
+= 1
+�
+,
+and
+hp,∞(Ω) =
+inf
+u∈C∞
+0 (Ω)
+�
+�
+�
+�
+�
+ˆ
+Ω
+|∇u|p dx :
+������
+u
+d
+1− N
+p
+Ω
+������
+L∞(Ω)
+= 1
+�
+�
+�
+�
+�
+,
+as well as the asymptotic behaviour of the sharp Morrey constant
+mp(Ω) :=
+inf
+u∈C∞
+0 (Ω)
+�ˆ
+Ω
+|∇u|p dx : [u]C0,αp(Ω) = 1
+�
+,
+where αp := 1 − N
+p .
+We observe that the latter is actually independent of the open set Ω, i.e. it coincides with that of
+the whole space (see Corollary 4.3 below, for example). Some studies on such a constant and its
+extremals have been done recently by Hynd and Seuffert in a series of papers (see [23, 24] and [25]),
+but the exact value of the sharp constant is still unknown. We show in Corollary 4.3 that
+lim
+p→∞
+�
+mp(Ω)
+� 1
+p = lim
+p→∞
+�
+mp(RN)
+� 1
+p = 1.
+1.3. Plan of the paper. In Section 2 we present the functional analytic setting, give some pre-
+liminary embedding results and recall some important properties of the Lane-Emden equation.
+Then in Section 3 we discuss the role of summability assumptions on the distance function
+dΩ. This section also contains a generalized version of the classical Ascoli-Arzel`a Theorem, for
+continuous functions on quasibounded open sets.
+In the subsequent Section 4 we present one of the key ingredients of this work, i.e. an Hardy’s
+inequality which holds for every open set Ω ⊊ RN and p > N (see Theorem 4.4). In particular, we
+focus on the asymptotics of the relevant sharp constant, when p goes to ∞. For this reason, we
+first need to study the asymptotics of a particular sharp Morrey-type constant (see Lemma 4.1).
+Section 5 contains the main embedding theorems for D1,p
+0 (Ω) and their relations with the summa-
+bility of the distance function. Finally, in Section 6 we investigate the asymptotic behaviour for the
+generalized principal frequencies and the positive solutions of Lane-Emden equation when p goes
+to ∞.
+
+SOBOLEV EMBEDDINGS AND DISTANCE FUNCTIONS
+7
+Acknowledgments. We thank Ryan Hynd and Erik Lindgren for some discussions on Hardy’s
+inequality and the constant λp,∞. This paper has been finalized during the meeting “PDEs in
+Cogne: a friendly meeting in the snow ”, held in Cogne in January 2023. We wish to thank the
+organizers for the kind invitation and the nice working atmosphere provided during the staying.
+F. P. and A. C. Z. are members of the Gruppo Nazionale per l’Analisi Matematica, la Probabilit`a
+e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM).
+2. Preliminaries
+2.1. Notation. For x0 ∈ RN and R > 0, we will denote by BR(x0) the N−dimensional open
+ball with radius R, centered at x0. In particular, when the center coincides with the origin, we
+will simply write BR. For an open set Ω ⊊ RN, we denote by dΩ the distance function from the
+boundary ∂Ω, defined by
+dΩ(x) := min
+y∈∂Ω |x − y|,
+for every x ∈ Ω.
+We extend dΩ by 0 in RN \Ω. We define the inradius rΩ of Ω as the radius of a largest ball contained
+in Ω. More precisely, this quantity is given by
+(2.1)
+rΩ = sup
+�
+r > 0 : there exists x0 ∈ Ω such that Br(x0) ⊂ Ω
+�
+.
+It is well-known that this coincides with the supremum over Ω of dΩ.
+The following simple result will be quite useful.
+Lemma 2.1. Let Ω ⊊ RN be an open set, we denote by C0(Ω) the completion of C∞
+0 (Ω) with
+respect to the sup norm. Then we get
+C0(Ω) ⊂
+�
+u ∈ Cbound(Ω) : u = 0 on ∂Ω
+�
+.
+Here Cbound(Ω) is the set of continuous and bounded functions on Ω.
+Proof. Let {un}n∈N ⊂ C∞
+0 (Ω) be a Cauchy sequence, with respect to the sup norm. In particular,
+it is Cauchy sequence in Cbound(Ω), which is a Banach space (see for example [21, Theorem 7.9]).
+Thus, there exists u ∈ Cbound(Ω) such that un converges to u uniformly on Ω. Moreover, such a
+function must vanish at the boundary ∂Ω, as a uniform limit of functions with compact support in
+Ω.
+□
+For every open set Ω ⊆ RN, 0 < α ≤ 1 and u a continuous function on Ω, we set
+[u]C0,α(Ω) =
+sup
+x̸=y; x,y∈Ω
+|u(x) − u(y)|
+|x − y|α
+.
+We have the following interpolation–type estimate.
+Lemma 2.2. Let 0 < β < α ≤ 1, let 1 ≤ γ ≤ ∞ and let Ω ⊊ RN be an open set. For every
+u ∈ C0(Ω) ∩ Lγ(Ω) such that
+[u]C0,α(Ω) < +∞,
+we have
+[u]C0,β(Ω) ≤ C1 ∥u∥θ
+Lγ(Ω) [u]1−θ
+C0,α(Ω),
+with θ = α − β
+α + N
+γ
+,
+
+8
+BRASCO, PRINARI, AND ZAGATI
+for some C1 = C1(N, α, β, γ) > 0. Moreover, if 1 ≤ γ < ∞ we also have
+∥u∥L∞(Ω) ≤ C2 ∥u∥χ
+Lγ(Ω) [u]1−χ
+C0,α(Ω),
+with χ =
+α
+α + N
+γ
+,
+for some C2 = C2(N, α, γ) > 0.
+Proof. By Lemma 2.1, we can extend u to a continuous function on the whole RN, by setting it to
+be 0 on RN \ Ω. We first observe that for such an extension it holds
+(2.2)
+[u]C0,α(Ω) = [u]C0,α(RN).
+Indeed, we may write
+[u]C0,α(RN) = max
+�
+[u]C0,α(Ω),
+sup
+x∈Ω,y /∈Ω
+|u(x)|
+|x − y|α
+�
+= max
+�
+[u]C0,α(Ω),
+sup
+x∈Ω,y /∈Ω
+|u(x)|
+|x − y|α
+�
+.
+If x ∈ Ω and y /∈ Ω then the segment x y connecting x and y is such that x y ∩ Ω ̸= ∅ and
+x y ∩ (RN \ Ω) ̸= ∅. Hence, there exists y0 ∈ x y ∩ ∂Ω satisfying
+|x − y| ≥ |x − y0|.
+This implies
+|u(x)|
+|x − y|α ≤ |u(x) − u(y0)|
+|x − y0|α
+≤ [u]C0,α(Ω),
+that gives
+sup
+x∈Ω,y /∈Ω
+|u(x)|
+|x − y|α ≤ [u]C0,α(Ω).
+This concludes the proof of (2.2).
+We now come to the proof of the claimed interpolation inequality. For every x, y ∈ RN such that
+x ̸= y, we write
+|u(x) − u(y)|
+|x − y|β
+=
+�|u(x) − u(y)|
+|x − y|α
+� β
+α
+|u(x) − u(y)|
+α−β
+α
+≤ [u]
+β
+α
+C0,α(Ω)
+�
+|u(x)|
+α−β
+α
++ |u(y)|
+α−β
+α
+�
+.
+(2.3)
+Observe that we used the triangle inequality and the sub-additivity of concave powers. In order to
+estimate the last term, we use that for every z ∈ BR(x) we have
+|u(x)| ≤ |u(x) − u(z)| + |u(z)| ≤ [u]C0,α(Ω) |x − z|α + |u(z)|
+≤ Rα [u]C0,α(Ω) + |u(z)|,
+where we also used (2.2). We now take the integral average of this estimate on BR(x). This gives
+|u(x)| ≤ Rα [u]C0,α(Ω) +
+1
+ωN RN
+ˆ
+BR(x)
+|u(z)| dz
+≤ Rα [u]C0,α(Ω) + (ωN RN)− 1
+γ
+�ˆ
+Ω
+|u(z)|γ dz
+� 1
+γ
+.
+(2.4)
+
+SOBOLEV EMBEDDINGS AND DISTANCE FUNCTIONS
+9
+With the same argument, we have also
+|u(y)| ≤ Rα [u]C0,α(Ω) + (ωN RN)− 1
+γ
+�ˆ
+Ω
+|u(z)|γ dz
+� 1
+γ
+.
+We insert these estimates in (2.3) and use again the subadditivity of concave powers. We get
+|u(x) − u(y)|
+|x − y|β
+≤ 2 [u]
+β
+α
+C0,α(Ω)
+�
+Rα−β [u]
+α−β
+α
+C0,α(Ω) +
+�
+1
+ωN RN
+� α−β
+α γ
+∥u∥
+α−β
+α
+Lγ(Ω)
+�
+,
+which is valid for every x ̸= y and every R > 0. If we not optimize in R > 0, we finally get the
+desired estimate for the C0,β seminorm. The sup norm can be estimated with a similar optimization
+argument, by using (2.4).
+□
+Remark 2.3. We remark that the constants C1 and C2 in the previous result are given by
+C1 = 2 ω
+−
+α−β
+γ α+N
+N
+�α γ
+N
+�
+N
+α γ+N 1
+χ,
+and
+C2 = ω
+− χ
+γ
+N
+�α γ
+N
+�
+N
+α γ+N 1
+χ.
+In particular, we notice that C1 stays uniformly bounded, as α varies in (β, 1]. Similary, the constant
+C2 stays bounded, as α varies in (0, 1]. This observation will be useful in the sequel.
+2.2. Sobolev embeddings. We recall the following family of Gagliardo-Nirenberg interpolation
+inequalities
+(2.5)
+∥ψ∥Lr(Ω) ≤ GN,p,q,r ∥∇ψ∥ϑ
+Lp(Ω) ∥ψ∥1−ϑ
+Lq(Ω),
+for every ψ ∈ C∞
+0 (Ω),
+which hold for every 1 < p < ∞, 1 ≤ q ≤ p and r satisfying
+�
+�
+�
+�
+�
+�
+�
+q < r ≤
+Np
+N − p,
+if 1 < p < N,
+q < r < ∞,
+if p = N,
+q < r ≤ ∞,
+if p > N,
+with GN,p,q,r > 0 only depending on N, p, q, r and
+ϑ =
+N (r − q)
+N r (p − q) + p q r,
+(for a proof, see for example [11, Proposition 2.6]).
+For 1 < p < ∞ and Ω ⊂ RN open set, we will indicate by W 1,p
+0
+(Ω) the closure of C∞
+0 (Ω) in the
+usual Sobolev space W 1,p(Ω). We will say that Ω is (p, q)−admissible if λp,q(Ω) > 0, the latter
+being defined in (1.2).
+By using (2.5), one can prove the following result:
+Proposition 2.4. Let 1 ≤ q < p < ∞ and let Ω ⊆ RN be an open set. Then
+D1,p
+0 (Ω) �→ Lq(Ω)
+⇐⇒
+W 1,p
+0
+(Ω) �→ Lq(Ω).
+In particular, if Ω ⊆ RN is a (p, q)−admissible open set, then
+W 1,p
+0
+(Ω) = D1,p
+0 (Ω).
+
+10
+BRASCO, PRINARI, AND ZAGATI
+Proof. The implication =⇒ is straightforward. For the converse implication, we suppose that there
+exists C > 0 such that
+∥ψ∥Lq(Ω) ≤ C ∥ψ∥W 1,p(Ω),
+for every ψ ∈ C∞
+0 (Ω).
+By applying the Gagliardo-Nirenberg inequality (2.5) with r = p, it holds in particular
+∥ψ∥Lq(Ω) ≤ C ∥ψ∥W 1,p(Ω) ≤ C
+�
+∥∇ψ∥Lp(Ω) + GN,p,q,p ∥∇ψ∥ϑ
+Lp(Ω)∥ψ∥1−ϑ
+Lq(Ω)
+�
+.
+With a standard application of Young’s inequality with exponents 1/ϑ and 1/(1−ϑ), we can absorb
+the Lq norm on the right-hand side and get
+∥ψ∥Lq(Ω) ≤ �C ∥∇ψ∥Lp(Ω),
+for some �C > 0 independent of ψ. Thus, the embedding D1,p
+0 (Ω) �→ Lq(Ω) holds, as well.
+The last part of the statement follows by [10, Proposition 2.5].
+□
+Remark 2.5. It is easily seen that the following implication holds
+λp(Ω) > 0
+=⇒
+W 1,p
+0
+(Ω) = D1,p
+0 (Ω).
+Indeed, the positivity of λp(Ω) automatically gives that
+∥∇u∥Lp(Ω)
+and
+∥u∥W 1,p(Ω),
+are equivalent norms on C∞
+0 (Ω).
+The following simple result will be useful. Observe that we do not put any restriction either on
+q or on the open set.
+Lemma 2.6. Let 1 < p < ∞, 1 ≤ q ≤ ∞ and let Ω ⊊ RN be an open set. Then
+λp,q(Ω) =
+inf
+ψ∈C∞
+0 (Ω)
+�ˆ
+Ω
+|∇ψ|p dx : ∥ψ∥Lq(Ω) = 1
+�
+=
+inf
+ψ∈W 1,p
+0
+(Ω)
+�ˆ
+Ω
+|∇ψ|p dx : ∥ψ∥Lq(Ω) = 1
+�
+.
+Proof. We first observe that the problem on the right-hand side is actually settled on W 1,p
+0
+(Ω) ∩
+Lq(Ω). Since we have C∞
+0 (Ω) ⊂ W 1,p
+0
+(Ω) ∩ Lq(Ω), we immediately obtain
+inf
+ψ∈C∞
+0 (Ω)
+�ˆ
+Ω
+|∇ψ|p dx : ∥ψ∥Lq(Ω) = 1
+�
+≥
+inf
+ψ∈W 1,p
+0
+(Ω)
+�ˆ
+Ω
+|∇ψ|p dx : ∥ψ∥Lq(Ω) = 1
+�
+.
+In order to prove the reverse inequality, we first observe that if λp,q(Ω) = 0, then from the previous
+inequality we would get
+0 =
+inf
+ψ∈C∞
+0 (Ω)
+�ˆ
+Ω
+|∇ψ|p dx : ∥ψ∥Lq(Ω) = 1
+�
+≥
+inf
+ψ∈W 1,p
+0
+(Ω)
+�ˆ
+Ω
+|∇ψ|p dx : ∥ψ∥Lq(Ω) = 1
+�
+≥ 0,
+and thus the desired identity trivially holds true.
+Let us now suppose that λp,q(Ω) > 0. For every u ∈ W 1,p
+0
+(Ω) ∩ Lq(Ω) not identically vanishing,
+there exists a sequence {un}n∈N ⊂ C∞
+0 (Ω) such that
+lim
+n→∞ ∥∇un − ∇u∥Lp(Ω) = lim
+n→∞ ∥un − u∥Lp(Ω) = 0.
+By using the definition of λp,q(Ω) > 0, we have
+λp,q(Ω) ∥un − um∥p
+Lq(Ω) ≤ ∥∇un − ∇um∥p
+Lp(Ω),
+for every n, m ∈ N,
+
+SOBOLEV EMBEDDINGS AND DISTANCE FUNCTIONS
+11
+thus, in particular, {un}n∈N is a Cauchy sequence in Lq(Ω). This shows that we have
+lim
+n→∞ ∥un − u∥Lq(Ω) = 0,
+as well. Hence, we get
+λp,q(Ω) ≤ lim
+n→∞
+ˆ
+Ω
+|∇un|p dx
+∥un∥p
+Lq(Ω)
+=
+ˆ
+Ω
+|∇u|p dx
+∥u∥p
+Lq(Ω)
+.
+Finally, by taking the infimum on W 1,p
+0
+(Ω) ∩ Lq(Ω) on the right-hand side, we obtain that
+λp,q(Ω) ≤
+inf
+ψ∈W 1,p
+0
+(Ω)
+�ˆ
+Ω
+|∇ψ|p dx : ∥ψ∥Lq(Ω) = 1
+�
+.
+This concludes the proof.
+□
+In the sequel, we will need the following Poincar´e–type inequality, for functions which vanish at
+a point of the boundary. Obviously, this may hold only in the superconformal case p > N, i.e. in
+the case where points have positive p−capacity.
+Proposition 2.7 (A Poincar´e inequality). Let p > N and u ∈ W 1,p(BR(x0)) be such that u(z) = 0,
+with z ∈ ∂BR(x0). Then there exists a constant CN,p > 0 such that
+(2.6)
+ˆ
+BR(x0)
+|u|p dx ≤ CN,p Rp
+ˆ
+BR(x0)
+|∇u|p dx.
+Proof. It is sufficient to consider the case x0 = 0 and R = 1, then the general case follows by scaling
+and translating. For the proof of (2.6), we can use a standard contradiction argument, exploiting
+compact Sobolev embeddings. We assume by contradiction that (2.6) fails to hold with a uniform
+constant. Thus, there exists a sequence {un}n∈N ⊂ W 1,p(B1) such that
+∥un∥Lp(B1) = 1,
+lim
+n→∞ ∥∇un∥Lp(B1) = 0,
+and
+un(z) = 0 with z ∈ ∂B1.
+In particular, {un}n∈N is bounded in W 1,p(B1). Hence, thanks to compact Sobolev embeddings for
+p > N, there exists u ∈ W 1,p(B1) ∩ C(B1) such that un converges to u weakly in W 1,p(B1) and
+uniformly in B1, up to a subsequence. In particular, we get
+∥∇u∥Lp(B1) ≤ lim inf
+n→∞ ∥∇un∥Lp(B1) = 0
+and
+u(z) = lim
+n→∞ un(z) = 0.
+Since B1 is a connected set, the last two facts imply that u ≡ 0 in B1. However, by the uniform
+convergence we also have
+∥u∥Lp(B1) = lim
+n→∞ ∥un∥Lp(B1) = 1.
+This contradicts the fact that u identically vanishes.
+□
+2.3. The Lane-Emden equation.
+Definition 2.8. Let 1 ≤ q < p < ∞ and let Ω ⊂ RN be a (p, q)−admissible open set. We say that
+a function v ∈ W 1,p
+0
+(Ω) is a weak solution of the Lane-Emden equation
+(2.7)
+− ∆pu = |u|q−2 u,
+in Ω,
+if it satisfies
+(2.8)
+ˆ
+Ω
+⟨|∇v|p−2 ∇v, ∇ψ⟩ dx =
+ˆ
+Ω
+|v|q−2 v ψ dx,
+for every ψ ∈ C∞
+0 (Ω).
+
+12
+BRASCO, PRINARI, AND ZAGATI
+In the case q = 1, for a non-negative function v, we follow the convention
+|v|q−2 v = vq−1 = 1.
+By density, in the weak formulation (2.8) we can admit test functions in W 1,p
+0
+(Ω).
+Remark 2.9 (Scalings). Let 1 ≤ q < p < ∞. Given t > 0, it is easily seen that if u ∈ W 1,p
+0
+(Ω) is
+a weak solution of (2.7), then the rescaled function
+ut(x) = t
+p
+p−q u
+�x − x0
+t
+�
+,
+is a weak solution of the same equation, in the new set x0 + t Ω. On the other hand, if u ∈ W 1,p
+0
+(Ω)
+weakly solves (2.7), then the function
+v = α
+1
+p−q u
+is a weak solution of
+(2.9)
+− ∆pu = α |u|q−2 u,
+in Ω,
+with α > 0.
+We recall that if Ω ⊆ RN is a (p, q)−admissible connected open set for some 1 ≤ q < p < ∞,
+then there exists a unique weak positive solution of the following problem
+(2.10)
+�
+�
+�
+�
+�
+−∆pu = |u|q−2u,
+in Ω,
+u ∈ W 1,p
+0
+(Ω),
+u > 0,
+in Ω,
+see [10, Corollary 4.4]. We will denote this solution by wΩ
+p,q. We recall that the latter also coincides
+with the unique positive solution of
+(2.11)
+min
+ψ∈W 1,p
+0
+(Ω)
+Fp,q(ψ),
+where
+(2.12)
+Fp,q(ψ) := 1
+p
+ˆ
+Ω
+|∇ψ|p dx − 1
+q
+ˆ
+Ω
+|ψ|q dx,
+for every ψ ∈ W 1,p
+0
+(Ω),
+see [10, Theorem 4.3]. By optimality and thanks to the relevant normalization condition on the Lq
+norm, when Ω is a connected (p, q)−admissible open set, the positive minimizer of (1.2) coincides
+with the weak positive solution of (2.9) corresponding to the choice α = λp,q(Ω).
+The next proof is standard, we include it for completeness.
+Proposition 2.10. Let 1 < p < ∞, 1 ≤ q < p and let Ω ⊆ RN be a (p, q)-admissible connected
+open set. Then
+(2.13)
+min
+ψ∈W 1,p
+0
+(Ω)
+Fp,q(ψ) = q − p
+p q
+�
+1
+λp,q(Ω)
+�
+q
+p−q
+and
+(2.14)
+ˆ
+Ω
+|∇wΩ
+p,q|p dx =
+ˆ
+Ω
+|wΩ
+p,q|q dx =
+�
+1
+λp,q(Ω)
+�
+q
+p−q
+.
+
+SOBOLEV EMBEDDINGS AND DISTANCE FUNCTIONS
+13
+Proof. Exploiting the different homogeneities of the two integrals and the fact that the minimum
+problem is equivalently settled on W 1,p
+0
+(Ω)\{0} (since a positive minimizer exists, see [10, Theorem
+3.3]), we get that
+min
+ψ∈W 1,p
+0
+(Ω)
+Fp,q(ψ) = −
+max
+ψ∈W 1,p
+0
+(Ω)\{0},t>0
+�tq
+q
+ˆ
+Ω
+|ψ|q dx − tp
+p
+ˆ
+Ω
+|∇ψ|p dx
+�
+.
+It is easily seen that, for every ψ ∈ W 1,p
+0
+(Ω) \ {0}, the function
+t �→ tq
+q
+ˆ
+Ω
+|ψ|q dx − tp
+p
+ˆ
+Ω
+|∇ψ|p dx
+is maximal for
+t0 =
+�
+�
+�
+�
+ˆ
+Ω
+|ψ|q dx
+ˆ
+Ω
+|∇ψ|p dx
+�
+�
+�
+�
+1
+p−q
+.
+With such a choice of t, we get
+tq
+0
+q
+ˆ
+Ω
+|ψ|q dx − tp
+0
+p
+ˆ
+Ω
+|∇ψ|p dx = p − q
+p q
+�ˆ
+Ω
+|ψ|q dx
+�
+p
+p−q
+�ˆ
+Ω
+|∇ψ|p dx
+�
+q
+p−q .
+Then, by recalling the definition of λp,q(Ω), we get (2.13).
+Finally, since wΩ
+p,q satifies the Lane-Emden equation (2.7), by using this solution as a test function
+in (2.8), we get that
+ˆ
+Ω
+|∇wΩ
+p,q|p dx =
+ˆ
+Ω
+|wΩ
+p,q|q dx.
+This implies
+Fp,q(wΩ
+p,q) = q − p
+p q
+ˆ
+Ω
+|wΩ
+p,q|q dx.
+Thanks to (2.13), equality (2.14) easily follows.
+□
+We now discuss the behavior of the L∞ norm of wΩ
+p,q when 1 ≤ q < ∞ is fixed, p goes to ∞ and
+Ω is a bounded convex open set. This result will be useful somewhere in Section 6.
+Proposition 2.11. Let 1 < p < ∞, 1 ≤ q < p and Ω ⊆ RN be a bounded convex open set. Then
+lim
+p→∞ ∥wΩ
+p,q∥L∞(Ω) = rΩ.
+In particular, it holds
+(2.15)
+lim
+p→∞ wB1
+p,q(0) = 1.
+Proof. For every η ∈ C∞
+0 (Ω) and ε > 0, the function
+ψ =
+|η|p
+(wΩ
+p,q + ε)p−1 ∈ W 1,p
+0
+(Ω),
+
+14
+BRASCO, PRINARI, AND ZAGATI
+is a feasible test function in the equation (2.8) for wΩ
+p,q. Hence, by applying Picone’s inequality for
+the p−Laplacian (see [3]), we get that
+ˆ
+Ω
+(wΩ
+p,q) q−1
+|η|p
+(wΩ
+p,q + ε)p−1 dx =
+ˆ
+Ω
+�
+|∇wΩ
+p,q|p−2 ∇wΩ
+p,q, ∇
+�
+|η|p
+(wΩ
+p,q + ε)p−1
+��
+dx
+≤
+ˆ
+Ω
+|∇η|p dx.
+Since wΩ
+p,q ∈ W 1,p
+0
+(Ω) is strictly positive by the minimum principle, by sending ε to 0, we get
+(2.16)
+ˆ
+Ω
+|η|p
+(wΩ
+p,q) p−q dx ≤
+ˆ
+Ω
+|∇η|p dx,
+for every η ∈ C∞
+0 (Ω).
+By recalling the definition of λp(Ω) and that wΩ
+p,q is bounded, the latter estimate implies that
+(2.17)
+1 ≤ ∥wΩ
+p,q∥p−q
+L∞(Ω) λp(Ω).
+By raising to the power 1/p and using that
+lim
+p→∞
+�
+λp(Ω)
+� 1
+p = 1
+rΩ
+,
+(see [26, Lemma 1.5]), from (2.17) we obtain
+rΩ ≤ lim inf
+p→∞ ∥wΩ
+p,q∥L∞(Ω).
+On the other hand, by using [10, Corollary 5.3], we have that
+(2.18)
+∥wΩ
+p,q∥L∞(Ω) ≤
+� 2
+πp,q
+�
+p
+p−q �q p − q + p
+p
+� 1
+q
+r
+p−q
+p
+Ω
+,
+where πp,q is the following one-dimensional Sobolev-Poincar´e constant
+πp,q :=
+�
+λp,q((0, 1))
+� 1
+p .
+We claim that
+(2.19)
+πp,q ≥ 2(1− 1
+p)
+�
+q
+�
+1 − 1
+p
+�
++ 1
+� 1
+q
+,
+for every 1 < p < ∞ and 1 ≤ q < ∞. Postponing the proof of this fact for a moment, we see that
+(2.18) and (2.19) would give
+lim sup
+p→∞ ∥wΩ
+p,q∥L∞(Ω) ≤ rΩ,
+as desired. Then the last part of the statement would follow by using that wB1
+p,q is radially symmetric
+decreasing, so that wB1
+p,q(0) = ∥wB1
+p,q∥L∞(B1).
+We are left with establishing (2.19). Let ϕ ∈ C∞
+0 ((0, 1)), for every t ∈ (0, 1), we have that
+|ϕ(t)| = |ϕ(t) − ϕ(0)| ≤
+ˆ t
+0
+|ϕ′| dt ≤ t1− 1
+p ∥ϕ′∥Lp([0,1]),
+and
+|ϕ(t)| = |ϕ(t) − ϕ(1)| ≤
+ˆ 1
+t
+|ϕ′| dt ≤ (1 − t)1− 1
+p ∥ϕ′∥Lp([0,1]).
+
+SOBOLEV EMBEDDINGS AND DISTANCE FUNCTIONS
+15
+By raising to the power q and integrating the first estimate on (0, 1/2) and the second one on
+(1/2, 1), we get
+ˆ 1/2
+0
+|ϕ(t)|q dt ≤
+1
+q
+�
+1 − 1
+p
+�
++ 1
+�1
+2
+�q(1− 1
+p)+1
+∥ϕ′∥q
+Lp([0,1]),
+and
+ˆ 1
+1/2
+|ϕ(t)|q dt ≤
+1
+q
+�
+1 − 1
+p
+�
++ 1
+�1
+2
+�q(1− 1
+p)+1
+∥ϕ′∥q
+Lp([0,1]).
+Then, by summing up, we obtain
+ˆ 1
+0
+|ϕ(t)|q dt ≤
+1
+q
+�
+1 − 1
+p
+�
++ 1
+�1
+2
+�q(1− 1
+p)
+∥ϕ′∥q
+Lp([0,1]).
+By raising to the power 1/q on both sides and using the arbitrariness of ϕ, we get (2.19).
+□
+Remark 2.12. We point out that inequality (2.16) holds for general open sets: in this case, if the
+open set is not (p, q)−admissible, the function wΩ
+p,q has to be carefully defined. We refer to [11,
+Proposition 4.5] for the case of the p−torsion function, i.e. the case q = 1 and 1 < p < ∞. The
+general case is contained in [9, Lemma 4.1] and [37, Corollary 3.3].
+3. The distance function
+In this section we investigate some consequences of the summability of the distance function.
+First of all, we prove that when d α
+Ω is summable for some 0 < α < ∞, the set Ω has finite inradius.
+This comes with an explicit (sharp) bound.
+Lemma 3.1. Let 0 < α < ∞ and let Ω ⊊ RN be an open set such that dα
+Ω ∈ L1(Ω). Then rΩ < +∞
+and it holds
+(3.1)
+rΩ ≤ CN,α
+�ˆ
+Ω
+dα
+Ω dx
+�
+1
+N+α
+,
+where the constant CN,α is given by
+CN,α =
+�
+N ωN
+ˆ 1
+0
+(1 − ϱ)α ϱN−1 dϱ
+�−
+1
+N+α
+.
+Moreover, inequality (3.1) is sharp, since equality holds for a ball.
+Proof. Let Br(x0) ⊆ Ω, then we have that
+(r − |x − x0|)+ = dBr(x0)(x) ≤ dΩ(x),
+for every x ∈ Br(x0).
+By raising to the power α and integrating, we get
+ˆ
+Br(x0)
+(r − |x − x0|)α
++ dx ≤
+ˆ
+Ω
+dα
+Ω dx.
+
+16
+BRASCO, PRINARI, AND ZAGATI
+By using the change of variable y = (x − x0)/r, from the previous estimate we also get
+rN+α ≤
+ˆ
+Ω
+dα
+Ω dx
+ˆ
+B1
+(1 − |y|)α
++ dy
+.
+If we now take the supremum over the admissible balls, we get the conclusion.
+□
+Lemma 3.2. Let 0 < α < ∞ and let Ω ⊊ RN be an open set such that rΩ < +∞. Then for every
+0 < β < 1 we have
+[dΩ]C0,β(Ω) ≤ (2 rΩ)1−β.
+Proof. We extend dΩ to be 0 outside Ω and consider it as a Lipschitz continuous function defined
+on the whole RN, By recalling (2.2), for every 0 < β < 1 we have
+[dΩ]C0,β(Ω) = [dΩ]C0,β(RN).
+It is now sufficient to write for t > 0
+[dΩ]C0,β(RN) = max
+�
+sup
+x̸=y; |x−y|≤t
+|dΩ(x) − dΩ(y)|
+|x − y|β
+,
+sup
+|x−y|>t
+|dΩ(x) − dΩ(y)|
+|x − y|β
+�
+.
+For the first term on the right-hand side, we can just use the 1−Lipschitz character of dΩ. For the
+second one, it is sufficient to use that dΩ is bounded by rΩ. This gives
+[dΩ]C0,β(RN) = max
+�
+t1−β, 2 rΩ
+tβ
+�
+,
+for every t > 0.
+By choosing t = 2 rΩ, we get the claimed estimate.
+□
+Lemma 3.3. Let Ω ⊊ RN be an open set such that dα
+Ω ∈ L1(RN), for some 0 < α < ∞. Then for
+every R ≥ rΩ/2, we have
+dΩ(x) ≤ 2
+�
+1
+ωN
+ˆ
+RN\BR
+dα
+Ω dy
+�
+1
+N+α
+,
+for every |x| > R + rΩ
+2 .
+In particular, Ω is quasibounded.
+Proof. Let R ≥ rΩ/2 and let x ∈ RN be such that |x| > R + rΩ/2. If x ̸∈ Ω, then dΩ(x) = 0 and
+there is nothing to prove. Let us suppose that x ∈ Ω, so that dΩ(x) > 0. We consider the ball
+B :=
+�
+y ∈ RN : |x − y| < dΩ(x)
+2
+�
+,
+and observe that
+dΩ(y) ≥ 1
+2 dΩ(x),
+for every y ∈ B.
+We raise to the power α and integrate this inequality over B. This gives
+2−α dΩ(x)α |B| ≤
+ˆ
+B
+dΩ(y)α dy,
+that is
+(3.2)
+ωN 2−α−N dΩ(x)α+N ≤
+ˆ
+B
+dΩ(y)α dy.
+
+SOBOLEV EMBEDDINGS AND DISTANCE FUNCTIONS
+17
+We then observe that
+|y| ≥ |x| − |y − x| > |x| − 1
+2 dΩ(x) ≥ |x| − rΩ
+2 > R,
+for every y ∈ B.
+This gives that B ⊆ RN \ BR. By using the previous inclusion in (3.2), we get
+ωN 2−α−N dΩ(x)α+N ≤
+ˆ
+RN\BR
+dΩ(y)α dy.
+This concludes the proof.
+□
+Remark 3.4. The converse implication does not hold true: indeed, there exist quasibounded open
+sets for which d α
+Ω /∈ L1(RN), for any 0 < α < ∞ (see Example A.1).
+We conclude this section with a generalized version of Ascoli-Arzel`a Theorem, which is valid
+when Ω is a quasibounded open set. This is probably well-known, but we have not been able to
+detect it in the literature. Thus, we include its proof.
+Proposition 3.5. Let Ω ⊆ RN be a quasibounded open set. Let
+{un}n∈N ⊂
+�
+u ∈ Cbound(Ω) : u = 0 on ∂Ω
+�
+be a sequence with the following properties:
+(a) there exists M > 0 such that ∥un∥L∞(Ω) ≤ M, for every n ∈ N;
+(b) there exist δ0 > 0 and a function ω : (0, δ0] → (0, +∞) such that
+lim
+δ→0+ ω(δ) = 0,
+and
+ωn(δ) := sup
+�
+|un(x) − un(y)| : x, y ∈ Ω, |x − y| ≤ δ
+�
+≤ ω(δ),
+for every 0 < δ ≤ δ0.
+Then, there exists u ∈ Cbound(Ω) vanishing on ∂Ω such that
+lim
+n→∞ ∥un − u∥L∞(Ω) = 0,
+up to a subsequence.
+Proof. Let us denote by k0 ∈ N the smallest natural number such that Ω∩Bk is not empty. Thanks
+to the assumptions, {un}n∈N is a bounded and equicontinuous sequence on the compact set Ω∩Bk,
+for every k ≥ k0. By applying the classical Ascoli-Arzel´a Theorem for compact sets, together with
+a diagonal argument, we have that there exists a function u ∈ C(Ω) such that, up to a subsequence,
+un converges uniformly to u on Ω ∩ Bk, for every k ≥ k0.
+We will show that un converges to u uniformly on the whole Ω. Let 0 < δ ≤ δ0, since Ω is
+quasibounded, there exists Rδ > 0 such that
+dΩ(x) ≤ δ,
+for x ∈ Ω \ BRδ.
+For every x ∈ Ω \ BRδ, we take y ∈ ∂Ω such that |x − y| = dΩ(x). By using property (b), the
+triangle inequality and the fact that un(y) = 0, we get that for every n ∈ N
+|un(x) − u(x)| = lim
+m→∞ |un(x) − um(x)|
+≤ |un(x) − un(y)| + lim
+m→∞ |um(x) − um(y)| ≤ 2 ω(dΩ(x)) ≤ 2 ω(δ).
+
+18
+BRASCO, PRINARI, AND ZAGATI
+This implies that
+∥un − u∥L∞(Ω) = max
+�
+∥un − u∥L∞(Ω\BRδ ), ∥un − u∥L∞(Ω∩BRδ )
+�
+≤ max
+�
+2 ω(δ), ∥un − u∥L∞(Ω∩BRδ )
+�
+.
+By taking the limit as n goes to ∞ and exploiting the uniform convergence of un to u on Ω ∩ BRδ,
+we obtain that
+lim sup
+n→∞ ∥un − u∥L∞(Ω) ≤ 2 ω(δ),
+for 0 < δ ≤ δ0.
+By arbitrariness of δ and using the properties of ω, we get
+lim
+n→∞ ∥un − u∥L∞(Ω) = 0.
+This also shows that u vanishes on ∂Ω, as a uniform limit of functions with the same property.
+Moreover, using again that Cbound(Ω) is a Banach space, we finally get that u ∈ Cbound(Ω), as well.
+This concludes the proof.
+□
+4. A Morrey–type inequality and its consequences
+We will need the following Morrey–type sharp constant.
+Lemma 4.1. Let x0 ∈ RN and let R > 0. For every p > N and every fixed z ∈ ∂BR(x0), we set
+µp(BR(x0); {z}) :=
+min
+ϕ∈W 1,p(BR(x0))
+�ˆ
+BR(x0)
+|∇ϕ|p dx : ϕ(x0) = 1 and ϕ(z) = 0
+�
+.
+Then:
+(1) the minimum above is independent of the point z ∈ ∂BR(x0);
+(2) we have the scaling
+µp(BR(x0); {z}) = RN−p µp
+�
+B1(x0);
+� z
+R
+��
+;
+(3) the family
+�� 1
+ωN
+µp(BR(x0); {z})
+� 1
+p �
+p>N
+is non-decreasing;
+(4) we have the following asymptotics
+(4.1)
+lim
+p→∞
+�
+µp(BR(x0); {z})
+� 1
+p = 1
+R.
+Proof. We first show that µp (BR(x0); {z}) is actually a minimum. To this aim, we consider a
+minimizing sequence {un}n∈N ⊂ W 1,p(BR(x0)) for the problem defined by µp (BR(x0); {z}), i. e.
+lim
+n→∞
+ˆ
+BR(x0)
+|∇un|p dx = µp (BR(x0); {z}) ,
+un(x0) = 1
+and
+un(z) = 0.
+By Proposition 2.7, we also have that
+ˆ
+BR(x0)
+|un|p dx ≤ CN,p Rp
+ˆ
+BR(x0)
+|∇un|p dx.
+
+SOBOLEV EMBEDDINGS AND DISTANCE FUNCTIONS
+19
+This implies that {un}n∈N is a bounded sequence in W 1,p(BR(x0)). Hence, thanks to compact
+Sobolev embeddings for p > N, there exists u ∈ W 1,p(BR(x0))∩C(BR(x0)) such that un converges
+to u weakly in W 1,p(BR(x0)) and uniformly in BR(x0), up to a subsequence. This implies that
+u(x0) = 1 and u(z) = 0, thus u is an admissible trial function for the problem µp (BR(x0); {z}).
+Moreover, by lower semicontinuity we have
+ˆ
+BR(x0)
+|∇u|p dx ≤ lim
+n→∞
+ˆ
+BR(x0)
+|∇un|p dx = µp (BR(x0); {z}) ,
+i. e. u is a minimizer.
+The proof of part (1) and part (2) easily follow by standard arguments, while part (3) is a
+consequence of H¨older’s inequality.
+It remains to prove part (4). We suppose without loss of generality that x0 = 0 and R = 1.
+Thus, we have to show that
+lim
+p→∞
+�
+µp (B1; {z})
+� 1
+p = 1.
+We observe that dB1 is admissible for the problem µp (B1; {z}), thus we get that
+�
+µp (B1; {z})
+� 1
+p ≤ ω
+1
+p
+N.
+This in turn implies that
+(4.2)
+lim sup
+p→∞
+�
+µp (B1; {z})
+� 1
+p ≤ lim
+p→∞ ω
+1
+p
+N = 1.
+We now prove that
+lim inf
+p→∞
+�
+µp (B1; {z})
+� 1
+p ≥ 1.
+At this aim, we consider Up ∈ W 1,p(B1) a minimizer for µp (B1; {z}), i. e.
+�ˆ
+B1
+|∇Up|p dx
+� 1
+p
+=
+�
+µp (B1; {z})
+� 1
+p ,
+Up(0) = 1,
+and
+Up(z) = 0.
+By applying Holder’s inequality, we have
+�ˆ
+B1
+|∇Up|p0 dx
+� 1
+p0
+≤ ω
+1
+p0 − 1
+p
+N
+�ˆ
+B1
+|∇Up|p dx
+� 1
+p
+,
+for every p > p0 > N. Moreover, thanks again to Proposition 2.7, we have
+ˆ
+B1
+|Up|p0 dx ≤ CN,p
+ˆ
+B1
+|∇Up|p0 dx.
+Taking into account (4.2), the above inequality implies that the sequence {Up}p>N is bounded in
+W 1,p0(B1) for every fixed p0 > N. Then, there exists U∞ ∈ W 1,p0(B1) ∩ C(B1) such that {Up}p>N
+converges to U∞ weakly in W 1,p0(B1) and uniformly in B1, up to taking a sequence.
+Thanks
+to a standard argument, we have that {Up}p>N converges to U∞ weakly in W 1,q(B1) for every
+
+20
+BRASCO, PRINARI, AND ZAGATI
+p0 ≤ q < ∞. Thanks to the claimed convergence, we get that
+�ˆ
+B1
+|∇U∞|q dx
+� 1
+q
+≤ lim inf
+p→∞
+�ˆ
+B1
+|∇Up|q dx
+� 1
+q
+≤ lim inf
+p→∞ ω
+1
+q − 1
+p
+N
+�ˆ
+B1
+|∇Up|p dx
+� 1
+p
+= ω
+1
+q
+N lim inf
+p→∞
+�
+µp(B1; {z})
+� 1
+p ,
+for every q ≥ p0,
+and, by sending q to ∞ and recalling (4.2), it holds that
+(4.3)
+1 ≥ lim inf
+p→∞
+�
+µp(B1; {z})
+� 1
+p ≥ ∥∇U∞∥L∞(B1).
+Hence U∞ is a 1−Lipschitz continuous function. Accordingly, we get
+∥∇U∞∥L∞(B1) ≥ |U∞(0)|
+dB1(0) = 1,
+which, combined with (4.3), gives the conclusion.
+□
+Remark 4.2. Thanks to Lemma 4.1 part (1), fixed a point z ∈ ∂B1, we can define
+(4.4)
+µp(B1) :=
+min
+u∈W 1,p(B1)
+�ˆ
+B1
+|∇u|p dx : u(0) = 1 and u(z) = 0
+�
+.
+Moreover, as an easy consequence of Lemma 4.1, when p > N we get the following estimate
+(4.5)
+|u(x0) − u(z)| ≤
+R1− N
+p
+�
+µp(B1)
+� 1
+p ∥∇u∥Lp(BR(x0)),
+for u ∈ W 1,p(BR(x0)) and z ∈ ∂BR(x0).
+Corollary 4.3 (Sharp Morrey constant). Let N < p < ∞ and let Ω ⊆ RN be an open set. We
+define the sharp Morrey constant
+mp(Ω) :=
+inf
+u∈C∞
+0 (Ω)
+�ˆ
+Ω
+|∇u|p dx : [u]C0,αp(Ω) = 1
+�
+,
+where αp := 1 − N
+p .
+Then the constant mp(Ω) is independent of Ω, i.e. we have
+mp(Ω) = mp(RN).
+Moreover, we have
+(4.6)
+µp(B1) ≤ mp(RN) ≤ N ωN
+�p − N
+p − 1
+�p−1
+,
+and
+lim
+p→∞
+�
+mp(RN)
+� 1
+p = 1.
+Proof. We first show that mp(Ω) is independent of Ω. The fact that mp(RN) ≤ mp(Ω) follows by
+monotonicity with respect to sets inclusion and the fact that
+[u]C0,αp(Ω) = [u]C0,αp(RN),
+for every u ∈ C∞
+0 (Ω),
+see (2.2).
+
+SOBOLEV EMBEDDINGS AND DISTANCE FUNCTIONS
+21
+In order to show that mp(Ω) ≤ mp(RN), let u ∈ C∞
+0 (RN) and let
+ur(x) = u
+�x − x0
+r
+�
+,
+with x0 ∈ RN and r > 0.
+Since u has compact support, we have ur ∈ C∞
+0 (Ω) for some suitable x0 and r small enough. Then,
+by scaling and thanks to (2.2), it holds
+mp(Ω) ≤
+ˆ
+Ω
+|∇ur|p dx
+[ur]p
+C0,αp(Ω)
+=
+ˆ
+RN |∇ur|p dx
+[ur]p
+C0,αp(RN)
+=
+ˆ
+RN |∇u|p dx
+[u]p
+C0,αp(RN)
+.
+By taking the infimum on C∞
+0 (RN) on the right-hand side, we get the claimed inequality.
+We now come to the proof of (4.6). Let u ∈ C∞
+0 (RN), for the lower bound it is sufficient to prove
+that
+(4.7)
+|u(x) − u(y)| ≤
+1
+�
+µp(B1)
+� 1
+p ∥∇u∥Lp(Ω) |x − y|αp,
+for every x, y ∈ RN.
+If x = y, then (4.7) trivially holds, thus let us assume that x ̸= y. Without loss of generality, we
+assume u(x) > u(y) and we define
+v(z) := u(z) − u(y)
+u(x) − u(y),
+for z ∈ RN,
+which satisfies v(x) = 1 and v(y) = 0. Since v ∈ W 1,p(BR(x)) with R = |x − y|, we have from (4.5)
+that
+1 = |v(x)| ≤
+|x − y|αp
+�
+µp(B1)
+� 1
+p ∥∇v∥Lp(BR(x)) =
+|x − y|αp
+�
+µp(B1)
+� 1
+p
+1
+|u(x) − u(y)| ∥∇u∥Lp(BR(x)).
+From this estimate, we get
+|u(x) − u(y)| ≤
+|x − y|αp
+�
+µp(B1)
+� 1
+p ∥∇u∥Lp(BR(x)) ≤
+|x − y|αp
+�
+µp(B1)
+� 1
+p ∥∇u∥Lp(RN),
+which is the claimed inequality (4.7).
+As for the upper bound, for every u ∈ C∞
+0 (B1) \ {0}, by the first part of the proof and the very
+definition of mp, we have
+mp(RN) = mp(B1) ≤
+∥∇u∥p
+Lp(B1)
+[u]p
+C0,αp(B1)
+.
+Moreover, by using that u is compactly supported in B1, we have
+[u]C0,αp(B1) ≥
+sup
+x∈B1,y∈∂B1
+|u(x)|
+|x − y|αp ≥ |u(0)|.
+Thus, for every u ∈ C∞
+0 (B1) such that |u(0)| ̸= 0, we get
+mp(RN) ≤
+∥∇u∥p
+Lp(B1)
+|u(0)|p
+.
+
+22
+BRASCO, PRINARI, AND ZAGATI
+By density, the last estimate is still true for functions u ∈ W 1,p
+0
+(B1). Now we consider the function
+u(x) = (1 − |x|
+p−N
+p−1 ) ∈ W 1,p
+0
+(B1),
+hence there exists un ∈ C∞
+0 (B1) such that un converges to u in W 1,p
+0
+(B1). Since
+[u]C0,αp(B1) =
+sup
+x̸=y,x,y∈B1
+���|x|
+p−N
+p−1 − |y|
+p−N
+p−1
+���
+|x − y|αp
+≥ 1,
+it holds that
+�
+mp(RN)
+� 1
+p ≤ lim inf
+n→∞
+∥∇un∥Lp(RN)
+[un]C0,αp(RN)
+≤ lim sup
+n→∞
+(N ωN)
+1
+p
+�p − N
+p − 1
+� p−1
+p
+[un]C0,αp(B1)
+≤ (N ωN)
+1
+p
+�p − N
+p − 1
+� p−1
+p
+.
+This shows the claimed upper bound.
+Finally, by taking the p−rooth in (4.6) and using (4.1), we get the desired asymptotics for mp.
+□
+The following Hardy inequality for general open sets was originally proved for q = p in [30] (see
+also [20] and [38]), without determination of an explicit constant. The latter can be found in [4, 15].
+We generalize the result to cover the case p ≤ q ≤ ∞. We will pay due attention to the asymptotic
+behaviour of the sharp constant, as p goes to ∞.
+Theorem 4.4 (Hardy’s inequality). Let N < p ≤ q ≤ ∞ and let Ω ⊊ RN be an open set. We set
+hp,q(Ω) =
+inf
+u∈C∞
+0 (Ω)
+�
+�
+�
+�
+�
+ˆ
+Ω
+|∇u|p dx :
+������
+u
+d
+N
+q + p−N
+p
+Ω
+������
+Lq(Ω)
+= 1
+�
+�
+�
+�
+�
+,
+for p < q ≤ ∞,
+and
+hp(Ω) =
+inf
+u∈C∞
+0 (Ω)
+�ˆ
+Ω
+|∇u|p dx :
+����
+u
+dΩ
+����
+Lp(Ω)
+= 1
+�
+.
+We have that
+(4.8)
+hp,q(Ω) ≥
+�
+hp(Ω)
+� p
+q �
+hp,∞(Ω)
+� q−p
+q ,
+for p < q < ∞,
+and
+(4.9)
+hp(Ω) ≥
+�p − N
+p
+�p
+,
+hp,∞(Ω) ≥ µp(B1),
+where µp(B1) is the same constant as in (4.4). Moreover, it holds
+(4.10)
+lim
+p→∞
+�
+hp(Ω)
+� 1
+p = lim
+p→∞
+�
+hp,∞(Ω)
+� 1
+p = 1.
+Proof. We first prove the lower bound in the extremal case, i.e. for q = ∞. Let x ∈ Ω and let
+x ∈ ∂Ω be such that
+|x − x| = dΩ(x).
+For every u ∈ C∞
+0 (Ω) and every p > N, we thus get
+(4.11)
+|u(x)| ≤ dΩ(x)1− N
+p
+(µp(B1))
+1
+p
+�ˆ
+BdΩ(x)(x)
+|∇u|p dx
+� 1
+p
+.
+
+SOBOLEV EMBEDDINGS AND DISTANCE FUNCTIONS
+23
+By taking the supremum over Ω, we get
+������
+u
+d
+1− N
+p
+Ω
+������
+L∞(Ω)
+≤
+1
+(µp(B1))
+1
+p
+�ˆ
+RN |∇u|p dx
+� 1
+p
+,
+for every u ∈ C∞
+0 (Ω).
+This gives the desired Hardy inequality result for q = ∞, together with the claimed lower bound
+in (4.9). In the case p = q, the estimate in (4.9) comes from [4, 15], as already recalled.
+The case p < q < ∞ now simply follows from interpolation of the two endpoints. Indeed, for
+every u ∈ C∞
+0 (Ω), we have
+�ˆ
+Ω
+|u|q
+dγ q
+Ω
+dx
+� p
+q
+≤
+�ˆ
+Ω
+|u|p
+dp
+Ω
+dx
+� p
+q
+������
+u
+d
+γ q−p
+q−p
+Ω
+������
+(q−p) p
+q
+L∞(Ω)
+where we set for simplicity
+γ = N
+q + p − N
+p
+.
+We observe that
+γ q − p
+q − p = 1 − N
+p ,
+thus by using the definitions of hp(Ω) and hp,∞(Ω), we obtain
+�ˆ
+Ω
+|u|q
+dγ q
+Ω
+dx
+� p
+q
+≤
+�
+1
+hp(Ω)
+� p
+q �
+1
+hp,∞(Ω)
+� q−p
+q
+ˆ
+Ω
+|∇u|p dx.
+By taking the infimum over u ∈ C∞
+0 (Ω), we get the lower bound (4.8).
+In order to prove the last statement, for the case q = ∞, from (4.9) and Lemma 4.1 we have
+lim inf
+p→∞
+�
+hp,∞(Ω)
+� 1
+p ≥ lim
+p→∞
+�
+µp(B1)
+� 1
+p = 1.
+In the case p = q, we directly have
+lim inf
+p→∞
+�
+hp(Ω)
+� 1
+p ≥ lim
+p→∞
+p − N
+p
+= 1.
+In order to prove that the lim sup is smaller than or equal to 1, it is sufficient to use a suitable trial
+function: for every x0 ∈ Ω, we have that
+ϕ(x) =
+�
+r − |x − x0|
+�
++ ∈ W 1,p
+0
+(Ω),
+for r = dΩ(x0).
+Since p > N, we can infer existence of a sequence {ϕn}n∈N ⊂ C∞
+0 (Ω) such that
+lim
+n→∞ ∥∇ϕn − ∇ϕ∥Lp(Ω) = lim
+n→∞ ∥ϕn − ϕ∥L∞(Ω) = 0.
+Thus we get
+�
+hp,∞(Ω)
+� 1
+p ≤ lim
+n→∞
+∥∇ϕn∥Lp(Ω)
+������
+ϕn
+d
+p−N
+p
+Ω
+������
+L∞(Ω)
+=
+(ωN rN)
+1
+p
+������
+ϕ
+d
+p−N
+p
+Ω
+������
+L∞(Ω)
+,
+
+24
+BRASCO, PRINARI, AND ZAGATI
+and
+�
+hp(Ω)
+� 1
+p ≤ lim
+n→∞
+∥∇ϕn∥Lp(Ω)
+����
+ϕn
+dΩ
+����
+Lp(Ω)
+= (ωN rN)
+1
+p
+����
+ϕ
+dΩ
+����
+Lp(Ω)
+.
+By using that
+lim
+p→∞
+(ωN rN)
+1
+p
+������
+ϕ
+d
+p−N
+p
+Ω
+������
+L∞(Ω)
+= lim
+p→∞
+(ωN rN)
+1
+p
+����
+ϕ
+dΩ
+����
+Lp(Ω)
+=
+inf
+x∈Br(x0)
+dΩ(x)
+(r − |x − x0|)+
+≤ dΩ(x0)
+r
+= 1,
+we then obtain the desired conclusion.
+□
+Remark 4.5. By a standard density argument, for every p > N and p ≤ q ≤ ∞ the Hardy
+inequality
+hp,q(Ω)
+������
+u
+d
+N
+q + p−N
+p
+Ω
+������
+p
+Lq(Ω)
+≤
+ˆ
+Ω
+|∇u|p dx,
+still holds in both spaces D1,p
+0 (Ω) and W 1,p
+0
+(Ω), for every open set Ω ⊊ RN.
+5. Embedding theorems
+For the ease of presentation of our main embedding results, we distinguish between three cases:
+• the case q < p;
+• the case q = p with Ω having finite inradius;
+• the case q = p with Ω being a quasibounded set.
+Then, in the final subsection, we will briefly discuss the case q > p.
+5.1. The case q < p.
+Theorem 5.1. Let 1 ≤ q < p < ∞ and let Ω ⊊ RN be an open set. The following facts hold:
+(i) we have that
+D1,p
+0 (Ω) �→ Lq(Ω)
+=⇒
+dΩ ∈ L
+p q
+p−q (Ω),
+and the following upper bound holds
+(5.1)
+λp,q(Ω)
+�ˆ
+Ω
+d
+p q
+p−q
+Ω
+dx
+� p−q
+q
+≤ λp(B1);
+(ii) moreover, if N < p < ∞, then we also have
+dΩ ∈ L
+p q
+p−q (Ω)
+=⇒
+D1,p
+0 (Ω) �→ Lq(Ω),
+and the following lower bound holds
+(5.2)
+hp(Ω) ≤ λp,q(Ω)
+�ˆ
+Ω
+d
+p q
+p−q
+Ω
+dx
+� p−q
+q
+,
+where hp(Ω) is the sharp Hardy constant (see Theorem 4.4);
+
+SOBOLEV EMBEDDINGS AND DISTANCE FUNCTIONS
+25
+(iii) finally, if p ≤ N, there exists an open set T ⊊ RN such that
+dT ∈ L1(T ) ∩ L∞(T )
+but
+D1,p
+0 (T ) ̸�→ Lq(T ).
+Proof. We prove each point separately.
+(i) Let x0 ∈ Ω. Since both wB1
+p,q and wΩ
+p,q are continuous functions, evaluating the lower bound
+in [10, Theorem 5.2] at x = x0 and r = dΩ(x0), we get
+(5.3)
+dΩ(x0)
+p
+p−q wB1
+p,q(0) ≤ wΩ
+p,q(x0).
+Then, by raising to the power q both sides of (5.3), integrating on Ω and exploiting (2.14),
+we get
+ˆ
+Ω
+d
+p q
+p−q
+Ω
+dx ≤
+�
+wB1
+p,q(0)
+�−q ˆ
+Ω
+(wΩ
+p,q)q(x) dx =
+�
+wB1
+p,q(0)
+�−q
+�
+1
+λp,q(Ω)
+�
+q
+p−q
+.
+By using (2.17) for the ball B1
+�
+wB1
+p,q(0)
+�−q ≤
+�
+λp(B1)
+�
+q
+p−q ,
+we get the claimed summability of dΩ, together with the upper bound in (5.1).
+(ii) Let us suppose that dΩ ∈ L
+p q
+p−q (Ω) and p > N. For every u ∈ C∞
+0 (Ω), a joint application
+of H¨older’s and Hardy’s inequalities (see Theorem 4.4) leads to
+ˆ
+Ω
+|u|q dx ≤
+�ˆ
+Ω
+|u|p
+d p
+Ω
+dx
+� q
+p �ˆ
+Ω
+d
+p q
+p−q
+Ω
+dx
+� p−q
+p
+≤
+�
+hp(Ω)
+�− q
+p �ˆ
+Ω
+|∇u|p dx
+� q
+p �ˆ
+Ω
+d
+p q
+p−q
+Ω
+dx
+� p−q
+p
+.
+This in turn implies that
+ˆ
+Ω
+|∇u|p dx
+�ˆ
+Ω
+|u|q dx
+� p
+q ≥
+hp(Ω)
+�ˆ
+Ω
+d
+p q
+p−q
+Ω
+dx
+� p−q
+q .
+By taking the infimum on C∞
+0 (Ω) on the left-hand side, we get the lower bound in (5.2).
+This in particular shows that λp,q(Ω) > 0, i.e. we have the embedding
+D1,p
+0 (Ω) �→ Lq(Ω),
+as desired.
+(iii) We construct an open set T ⊆ RN such that, under the assumption 1 < p ≤ N
+• dT ∈ L1(T ) ∩ L∞(T ), hence dT ∈ Lα(T ) for every α ∈ [1, +∞];
+• D1,p
+0 (T ) is not compactly embedded in Lq(T ), for every 1 ≤ q < p.
+We consider the (N − 1)−dimensional open hypercube Q = (0, 1)N−1 ⊆ RN−1 and we
+define
+Ck = Q × (k, k + 1],
+for every k ∈ N.
+
+26
+BRASCO, PRINARI, AND ZAGATI
+Figure 1. The construction of the set T . The horizontal dashed lines denote the
+separation lines between the cubes Ck. The dashed circular line highlights the ball
+with maximal radius rT .
+Then, for every k ∈ N, we take a dyadic partition of Ck, made of 2k N cubes with side
+length 2−k. We indicate by Ck(j) each of these cubes, with j = 1, . . . , 2k N. We also denote
+by xk(j) the center of the cube Ck(j) and by
+Sk :=
+�
+xk(i) : 1 ≤ i ≤ 2k N�
+,
+the collection of all these centers, at a given k ∈ N. Finally, we call infinite fragile tower
+the open set given by
+T =
+�
+k∈N
+(Ck \ Sk) .
+We first show that the condition dT ∈ L1(T ) ∩ L∞(T ) is satisfied. Indeed, we first observe
+that
+rT = 5
+12,
+which implies that dT ∈ L∞(T ). Moreover, we have
+dT (x) ≤ 2−k−1 √
+N,
+for x ∈ Ck(j) \ {xk(j)},
+j = 1, . . . , 2k N and k ∈ N,
+by construction. Then
+ˆ
+T
+dT dx =
+�
+k∈N
+2kN
+�
+j=1
+ˆ
+Ck(j)\{xk(j)}
+dT dx
+≤
+√
+N
+2
+�
+k∈N
+� 1
+2k
+�
+|Ck \ Sk| =
+√
+N
+2
+�
+k∈N
+� 1
+2k
+�
+=
+√
+N.
+
+SOBOLEV EMBEDDINGS AND DISTANCE FUNCTIONS
+27
+We now show that for every 1 ≤ q < p ≤ N, we have
+λp,q(T ) = 0.
+This would imply that D1,p
+0 (T ) is not continuously embedded in Lq(T ). At this aim, for
+every m ∈ N, we introduce the truncated tower
+Tm =
+� m
+�
+k=0
+(Ck \ Sk)
+�
+\ (Q × {m + 1}).
+This is a bounded open set contained in T , thus, by monotonicity with respect to set
+inclusion, we have
+λp,q(T ) ≤ λp,q(Tm).
+Therefore, in order to get the desired conclusion, it is sufficient to show that
+lim
+m→∞ λp,q(Tm) = 0.
+Since p ≤ N, we know that points have zero p−capacity and thus we have (see [36, Chapter
+17])
+λp,q(Tm) = λp,q(Q × (0, m + 1)).
+By appealing to [8, Main Theorem], the last quantity can be estimated from above by
+λp,q(Q × (0, m + 1)) ≤
+�πp,q
+2
+�p
+�
+HN−1(Q × (0, m + 1))
+|Q × (0, m + 1)|1− 1
+p + 1
+q
+�p
+≤
+�πp,q
+2
+�p
+�
+2 (N − 1) (m + 1) + 2
+(m + 1)1− 1
+p + 1
+q
+�p
+.
+By using that q < p, it is easily seen that the last term converges to 0, as m goes to ∞.
+This gives the desired conclusion.
+The proof is now over.
+□
+Before proceeding further, a couple of comments are in order on the geometric estimates obtained
+in the previous result.
+Remark 5.2. For p = 2, the lower bound (5.1) has been obtained in [7, Theorem 3]. The proof
+there is simpler: up to some technical issues, it is simply based on using the trial function dΩ in
+the definition of λ2,q(Ω). However, this produces a poorer estimate: observe that the constant
+appearing in [7, equation (9)] blows-up as q ↗ p = 2. This is not the case for our estimate (5.1).
+Remark 5.3. Let N < p < ∞, 1 ≤ q < p and let Ω ⊆ RN be an open set, such that |Ω| < ∞. If
+dΩ ∈ L
+p q
+p−q (Ω), then, from the lower bound in (5.2), we get
+(5.4)
+λp,q(Ω) |Ω|
+p−q
+q
+≥ hp(Ω)
+rp
+Ω
+.
+This is an extension to general open sets of the geometric estimate contained in [10, Theorem 5.7].
+The constant hp(Ω) is very likely not to be sharp, it would be interesting to determine the sharp
+constant for (5.4).
+
+28
+BRASCO, PRINARI, AND ZAGATI
+5.2. The case p = q: continuity.
+Theorem 5.4. Let 1 < p < ∞ and let Ω ⊊ RN be an open set. The following facts hold:
+(i) we have that
+(5.5)
+D1,p
+0 (Ω) �→ Lp(Ω)
+=⇒
+dΩ ∈ L∞(Ω),
+and the following upper bound holds
+(5.6)
+λp(Ω) rp
+Ω ≤ λp(B1);
+(ii) moreover, if N < p < ∞, then we also have
+dΩ ∈ L∞(Ω)
+=⇒
+D1,p
+0 (Ω) �→ Lp(Ω),
+and the following lower bound holds
+(5.7)
+hp(Ω) ≤ λp(Ω) rp
+Ω;
+(iii) finally, if p ≤ N, then for the open set P := RN \ ZN we have
+dP ∈ L∞(P)
+but
+D1,p
+0 (P) ̸�→ Lp(P).
+Proof.
+(i) Let λp(Ω) > 0 and let {Brn(xn)}n∈N ⊆ Ω be a sequence of balls such that rn
+converges to rΩ as n goes to ∞. Thanks to the monotonicity with respect to sets inclusion
+of λp, we get that
+λp(Ω) ≤ λp(Brn(xn)).
+In particular, using the scaling properties of λp, we obtain that
+r p
+n ≤ λp(B1)
+λp(Ω) ,
+and, by sending n to ∞, we get rΩ < +∞ and the upper bound in (5.6);
+(ii) let us suppose that rΩ < +∞ and N < p < ∞. By applying the Hardy inequality of
+Theorem 4.4, we have that
+ˆ
+Ω
+|u|p dx ≤ r p
+Ω
+ˆ
+Ω
+|u|p
+dp
+Ω
+dx ≤
+1
+hp(Ω) r p
+Ω
+ˆ
+Ω
+|∇u|p dx,
+for every u ∈ C∞
+0 (Ω).
+By taking the infimum on C∞
+0 (Ω), we get the lower bound in (5.7).
+In particular, if
+rΩ < +∞, then λp(Ω) > 0 and thus the continuous embedding D1,p
+0 (Ω) �→ Lp(Ω) holds
+true;
+(iii) it is sufficient to note that
+λp(P) ≤ λp(Bm \ ZN),
+for every m ∈ N.
+Thanks to the assumption p ≤ N, again by [36, Chapter 17] it holds
+λp(Bm \ ZN) = λp(Bm).
+By using the scale property of λp, we get that
+λp(P) ≤ lim
+m→∞ λp(Bm) = lim
+m→∞
+λp(B1)
+mp
+= 0.
+This gives the desired conclusion.
+The proof is concluded.
+□
+
+SOBOLEV EMBEDDINGS AND DISTANCE FUNCTIONS
+29
+Remark 5.5. For p > N, the lower bound (5.7) is an extension to general open sets with finite
+inradius of the Hersch-Protter-Kajikiya inequality
+λp(Ω) ≥
+�πp
+2
+�p 1
+rp
+Ω
+,
+which is valid for every Ω ⊆ RN open convex set and every 1 < p < ∞ (see [19, 33] for the case
+p = 2 and [27] for the general case). Such an extension can be also found in [34, Theorem 1.4.1],
+with a different proof and a poorer constant: the result in [34] is stated for bounded open sets,
+however a closer inspection of the proof reveals that it still works for open sets with finite inradius.
+Here as well, it would be very interesting to determine the sharp constant CN,p such that for
+every Ω ⊆ RN open set with finite inradius, we have
+λp(Ω) ≥ CN,p
+rp
+Ω
+,
+for every N < p < ∞.
+We observe that by (5.7) and (4.9), we have
+CN,p ≥
+�p − N
+p
+�p
+.
+5.3. The case p = q: compactness.
+Theorem 5.6. Let 1 < p < ∞ and let Ω ⊊ RN be an open set. The following facts hold:
+(i) we have that
+D1,p
+0 (Ω) �→ Lp(Ω) is compact
+=⇒
+Ω is quasibounded;
+(ii) moreover, if N < p < ∞, then we also have
+Ω is quasibounded
+=⇒
+D1,p
+0 (Ω) �→ Lp(Ω) is compact;
+(iii) finally, if p ≤ N and T ⊊ RN is the same open set of Theorem 5.1, then T is quasibounded
+and the embedding D1,p
+0 (T ) �→ Lp(T ) is continuous, but not compact.
+Proof.
+(i) This follows from [1, Example 6.11]. For completeness, we sketch the idea of the
+proof: let us suppose that Ω is not quasibounded. Then there exists a sequence of balls
+{Br(xn)}n∈N ⊆ Ω, with r > 0 fixed and
+lim
+n→∞ |xn| = +∞.
+We consider ψ ∈ C∞
+0 (B1) \ {0} and then we simply set
+ψn(x) = ψ
+�x − xn
+r
+�
+,
+for x ∈ Br(xn), n ∈ N.
+It is easily seen that {ψn}n∈N is bounded in D1,p
+0 (Ω), but it can not converge in Lp(Ω);
+(ii) this result can be found in [2, Theorem 2], but here we give an alternative proof, which relies
+on the Hardy inequality of Theorem 4.4. Let p > N and assume that Ω is quasibounded. By
+Theorem 5.4, we already know that D1,p
+0 (Ω) is a functional space, continuously embedded
+in Lp(Ω). Let {un}n∈N ⊆ D1,p
+0 (Ω) be a bounded sequence. We can extend these functions
+by 0 outside Ω and consider them as elements of W 1,p(RN). In order to apply the classical
+Riesz–Fr´echet–Kolmogorov Theorem, we first observe that by Theorem 5.4 we have that
+{un}n∈N is bounded in Lp(RN), as well.
+
+30
+BRASCO, PRINARI, AND ZAGATI
+Moreover, the bound on the Lp norm of the gradients guarantees that translations con-
+verge to 0 in Lp(Ω) uniformly in n, i. e.
+lim
+|h|→0 sup
+n∈N
+ˆ
+RN |un(x + h) − un(x)|p dx = 0.
+The crucial point is to exclude the “loss of mass at infinity”.
+For this, we exploit the
+assumption that Ω is quasibounded. The latter entails that for every ε > 0, there exists
+R > 0 such that
+∥dΩ∥L∞(Ω\BR) < ε.
+Let ηR ∈ C∞(RN) be such that
+0 ≤ ηR ≤ 1,
+ηR = 1 in RN \ BR+1,
+ηR ≡ 0 in BR,
+|∇ηR| ≤ C,
+for some universal constant C > 0. Then
+sup
+n∈N
+∥∇(unηR)∥Lp(Ω) ≤ sup
+n∈N
+∥∇un∥Lp(Ω) + C sup
+n∈N
+∥un∥Lp(Ω) =: M < +∞.
+Since the functions un ηR belong to D1,p
+0 (Ω), by applying H¨older’s and Hardy’s inequalities
+(see Theorem 4.4 and Remark 4.5), for every n ∈ N we have that
+�ˆ
+Ω\BR+1
+|un|p dx
+� 1
+p
+≤ ∥dΩ∥L∞(Ω\BR)
+�ˆ
+Ω
+|un ηR|p
+dp
+Ω
+dx
+� 1
+p
+≤ ε hp(Ω)− 1
+p
+�ˆ
+Ω
+|∇(un ηR)|p dx
+� 1
+p
+≤ ε hp(Ω)− 1
+p M.
+We can thus appeal to the Riesz–Fr´echet–Kolmogorov Theorem and get that, up to a
+subsequence, {un}n∈N strongly converges in Lp(Ω);
+(iii) we consider the set T defined as in the proof of Theorem 5.1 part (iii). Since dT ∈ L1(T ), by
+applying Lemma 3.3, we have that T is quasibounded. Moreover, the embedding D1,p
+0 (T ) �→
+Lp(T ) holds. Indeed, it is sufficient to notice that T is bounded in one direction. Thus, by
+Remark 2.5, we can infer
+W 1,p
+0
+(T ) = D1,p
+0 (T ).
+However, the embedding D1,p
+0 (T ) �→ Lp(T ) can not be compact.
+Indeed, we take v ∈
+C∞
+0 (Q × (0, 1)) not identically zero and we build a bounded sequence {vk}k∈N by simply
+translating v in the vertical direction, i.e. for every k ∈ N we set
+vk(x′, xN) = v(x′, xN − k),
+for every (x′, xN) ∈ Q × (k, k + 1).
+By appealing again to [36, Chapter 17], we have that
+vk ∈ C∞
+0 (Q × (k, k + 1)) ⊆ W 1,p
+0
+(Q × (k, k + 1))
+= W 1,p
+0
+((Q × (k, k + 1)) \ Sk) ⊆ W 1,p
+0
+(T ) = D1,p
+0 (T ),
+for every k ∈ N. Hence, the sequence {vk}k∈N is bounded in D1,p
+0 (T ) and ∥vk∥Lp(T ) > 0 is
+constant. This shows that {vk}k∈N can not admit a converging subsequence in Lp(T ).
+This concludes the proof.
+□
+
+SOBOLEV EMBEDDINGS AND DISTANCE FUNCTIONS
+31
+5.4. The super-homogeneous case q > p and beyond. In what follows, for an open set Ω ⊆ RN
+and for 0 < β ≤ 1, we consider the space
+C0,β(Ω) =
+�
+u ∈ Cbound(Ω) : [u]C0,β(Ω) < +∞
+�
+,
+endowed with the standard norm
+∥u∥C0,β(Ω) = ∥u∥L∞(Ω) + [u]C0,β(Ω),
+for every u ∈ C0,β(Ω).
+As a consequence of the previous embedding results, we can draw the following picture, for the case
+N < p < q. The proof is essentially an exercise.
+Corollary 5.7. Let p > N and let Ω ⊊ RN be an open set. The following facts hold:
+(i) if dΩ ∈ L∞(Ω), then we have
+D1,p
+0 (Ω) �→ Lq(Ω),
+for every p ≤ q ≤ ∞,
+and
+D1,p
+0 (Ω) �→ C0(Ω) ∩ C0,β(Ω),
+for every 0 < β ≤ αp;
+(ii) if Ω is quasibounded, then the above embeddings are compact, for
+p ≤ q ≤ ∞
+and
+0 < β < αp;
+(iii) if dΩ ∈ Lγ(Ω), for some 1 ≤ γ < ∞, then we have
+D1,p
+0 (Ω) �→ Lq(Ω),
+for every
+p γ
+p + γ ≤ q ≤ ∞,
+and such an embedding is compact.
+Proof.
+(i) Let dΩ ∈ L∞(Ω). The existence of the embedding D1,p
+0 (Ω) �→ Lp(Ω) is a consequence
+of Theorem 5.4 part (ii). By using the Gagliardo-Nirenberg interpolation inequality (2.5)
+with q = p, it follows that D1,p
+0 (Ω) is continuously embedded in every Lq(Ω) with p ≤ q ≤ ∞.
+As for the embedding in H¨older spaces: we observe at first that from the embedding
+D1,p
+0 (Ω) �→ L∞(Ω), we obtain that each {un}n∈N ⊂ C∞
+0 (Ω) which is a Cauchy sequence in
+the norm of D1,p
+0 (Ω), is a Cauchy sequence in the sup norm, as well. Thus, by recalling the
+definition of the completion space C0(Ω), we get that D1,p
+0 (Ω) �→ C0(Ω). By using this fact
+and Corollary 4.3, we thus get that D1,p
+0 (Ω) is continuously embedded in C0(Ω)∩C0,αp(Ω).
+Then Lemma 2.2 gives the desired conclusion;
+(ii) we now suppose that Ω is quasibounded. In order to prove the first statement, it is sufficient
+to observe that the embedding D1,p
+0 (Ω) �→ Lq(Ω) is compact for q = p thanks to Theorem
+5.6 part (ii). By applying again the Gagliardo-Nirenberg inequality (2.5) with q = p, we
+conclude.
+The case of C0(Ω) ∩ C0,β(Ω) follows as above, by combining Morrey’s inequality and
+Lemma 2.2;
+(iii) we first recall that the assumption dΩ ∈ Lγ(Ω), for some 1 ≤ γ < ∞, implies that Ω is
+a quasibounded set (see Lemma 3.3). The compact embedding D1,p
+0 (Ω) �→ Lq(Ω) easily
+follows by Theorem 5.1 part (ii), when q = p γ/(p+γ), while the case q = ∞ was just proved
+in the part (ii) above. We conclude, by interpolation, that the embedding is compact for
+every p γ/(p + γ) ≤ q ≤ ∞.
+The proof is now complete
+□
+
+32
+BRASCO, PRINARI, AND ZAGATI
+Remark 5.8. It is not difficult to see that the compact embedding of Corollary 5.7 part (ii) does
+not extend up to the borderline case β = αp = 1 − N/p. This can be seen by means of a standard
+scaling argument: take Ω = B1 and ψ ∈ C∞
+0 (B1) \ {0}. We define the sequence
+ψn(x) = n
+N−p
+p
+ψ(n x),
+for n ∈ N.
+It is easily seen that
+∥∇ψn∥Lp(B1) = ∥∇ψ∥Lp(B1)
+and
+[ψn]C0,αp(B1) = [ψ]C0,αp(B1).
+On the other hand, by construction, we have that ψn converges uniformly to 0 as n goes to ∞,
+since N − p < 0. Thus, for this sequence we can not have convergence in the norm of C0,αp(B1).
+We complete the previous result by giving some geometric estimates for the generalized principal
+frequencies λp,q in the case N < p < q, as well.
+Corollary 5.9. Let N < p < ∞, p ≤ q ≤ ∞ and let Ω ⊊ RN be an open set. We have that
+λp,q(Ω) > 0
+⇐⇒
+rΩ < +∞,
+and
+(5.8)
+hp,q(Ω)
+r
+p−N+N p
+q
+Ω
+≤ λp,q(Ω) ≤ λp,q(B1)
+r
+p−N+N p
+q
+Ω
+,
+with hp,q(Ω) defined in Theorem 4.4.
+Moreover, if Ω is quasibounded, then there exists up,q ∈
+W 1,p
+0
+(Ω) which solves
+(5.9)
+λp,q(Ω) =
+inf
+u∈W 1,p
+0
+(Ω)
+�ˆ
+Ω
+|∇u|p dx : ∥u∥Lq(Ω) = 1
+�
+.
+Proof. Let us assume λp,q(Ω) > 0 and let {Brn(xn)}n∈N ⊆ Ω be a sequence of balls such that rn
+goes to rΩ, as n goes to ∞. As in the proof of Theorem 5.4 part (i), it follows that
+r
+p−N+N p
+q
+n
+≤ λp,q(B1)
+λp,q(Ω) ,
+and, by sending n to ∞, we get rΩ < +∞ and the upper bound in (5.8).
+In order to prove the reverse implication, we first observe that this has already been proved in
+Theorem 5.4 for the case q = p part (ii). For the case p < q ≤ ∞, it is sufficient to use the same
+argument, in conjuction with the general Hardy inequality of Theorem 4.4. This comes with the
+lower bound in (5.8). We leave the details to the reader.
+We now come to the existence part, under the stronger assumption that Ω is quasibounded.
+We first observe that the identity (5.9) follows from Lemma 2.6. Moreover, the assumption on Ω,
+Theorem 5.4 and Remark 2.5 guarantee that we have
+D1,p
+0 (Ω) = W 1,p
+0
+(Ω),
+thanks to Proposition 2.4. The existence of a minimizer is now an easy consequence of the Direct
+Method in the Calculus of Variations, once observed that W 1,p
+0
+(Ω) is weakly closed and that we
+have the compact embeddings of Corollary 5.7 at our disposal.
+□
+Remark 5.10. We notice that the value of λp,∞(B1) can be made explicit: according to [35,
+Theorem 2E] we have
+λp,∞(B1) =
+�p − N
+p − 1
+�p−1
+N ωN,
+for p > N.
+
+SOBOLEV EMBEDDINGS AND DISTANCE FUNCTIONS
+33
+This implies that the upper bound for the sharp Morrey constant in (4.6) can be rewritten as
+mp(RN) ≤ λp,∞(B1).
+Moreover, such a value is uniquely attained by the functions
+u(x) = ±
+�
+1 − |x|
+p−N
+p−1
+�
++ .
+We refer to [17, 22] for a thorough study of the variational problem associated to λp,∞, in the case
+of bounded sets.
+6. Asymptotics
+6.1. Asymptotics for λp,q(Ω).
+Corollary 6.1. Let 1 ≤ q < ∞ and let Ω ⊊ RN be an open set. Then
+lim
+p→∞
+�
+λp,q(Ω)
+� 1
+p =
+1
+∥dΩ∥Lq(Ω)
+,
+and
+lim
+p→∞
+�
+λp,∞(Ω)
+� 1
+p = 1
+rΩ
+.
+In the previous equations, the right-hand sides have to be considered 0, if dΩ ̸∈ Lq(Ω) or rΩ = +∞,
+respectively.
+Proof. We start with the case q = ∞. If rΩ = +∞, thanks to Corollary 5.9, there is nothing to
+prove. Let us assume rΩ < +∞, it is sufficient to take the p−rooth in (5.8) and use that
+lim
+p→∞
+�
+λp,∞(B1)
+� 1
+p = 1,
+(see Remark 5.10) and (4.10). This gives the desired conclusion as p goes to ∞.
+We now consider the case q < ∞. We first suppose that dΩ ∈ Lq(Ω). Observe that for every p > 2 q,
+we have
+dΩ(x)
+p q
+p−q ≤ r
+q2
+p−q
+Ω
+dΩ(x)q ≤
+�
+max{1, rΩ}
+�q
+dΩ(x)q,
+for every x ∈ Ω,
+thus we can apply the Dominated Convergence Theorem to get that
+(6.1)
+lim
+p→∞
+�ˆ
+Ω
+d
+p q
+p−q
+Ω
+dx
+� p−q
+q p
+=
+�ˆ
+Ω
+d q
+Ω dx
+� 1
+q
+.
+Moreover, by Theorem 5.1, for every p > q and p > N, we have the two-sided estimate
+hp(Ω) ≤ λp,q(Ω)
+�ˆ
+Ω
+d
+p q
+p−q
+Ω
+dx
+� p−q
+q
+≤ λp(B1).
+By raising this estimate to the power 1/p, using (4.10), (6.1) and the following fact
+lim
+p→∞
+�
+λp(B1)
+� 1
+p = 1,
+(see [26, Lemma 1.5]), we get the desired conclusion.
+
+34
+BRASCO, PRINARI, AND ZAGATI
+We now suppose that dΩ /∈ Lq(Ω). Let n0 ∈ N such that Ωn := Ω ∩ Bn ̸= ∅ for every n ≥ n0.
+By applying the first part of this proof to the set Ωn with n ≥ n0, we have that
+lim
+p→∞
+�
+λp,q(Ωn)
+� 1
+p =
+1
+∥dΩn∥Lq(Ωn)
+.
+Hence, by using the monotonicity of λp,q with respect to the set inclusion, we get that
+(6.2)
+lim sup
+p→∞
+�
+λp,q(Ω)
+� 1
+p ≤
+1
+∥dΩn∥Lq(Ωn)
+,
+for every n ≥ n0. We extend each distance function dΩn equal to 0 in RN \ Ωn. We note that the
+family {dΩn}n≥n0 is not decreasing with respect to n. Thus, in order to conclude, it is sufficient to
+prove that
+(6.3)
+lim
+n→∞ dΩn(x) = dΩ(x),
+for every x ∈ Ω.
+Indeed, by passing to the limit in (6.2) as n goes to ∞ and by using Monotone Convergence
+Theorem, we get that
+lim sup
+p→∞
+�
+λp,q(Ω)
+� 1
+p = 0.
+In order to show (6.3), we note that, for every x ∈ Ω, there exists nx ≥ n0 such that BdΩ(x)(x) ⊆ Ωn,
+for every n ≥ nx. This implies that
+dΩ(x) = dΩn(x),
+for every n ≥ nx.
+This concludes the proof.
+□
+Corollary 6.2. Let N < p < ∞ and let Ω ⊊ RN be an open set. Then
+lim
+q→∞ λp,q(Ω) = λp,∞(Ω).
+Proof. Let ψ ∈ C∞
+0 (Ω) \ {0}. By definition of λp,q(Ω) we have that, for every q ≥ p, it holds
+λp,q(Ω) ≤
+ˆ
+Ω
+|∇ψ|p dx
+�ˆ
+Ω
+|ψ|q dx
+� p
+q .
+If we now take the limit as q goes to ∞, we get
+lim sup
+q→∞ λp,q(Ω) ≤ lim
+q→∞
+ˆ
+Ω
+|∇ψ|p dx
+�ˆ
+Ω
+|ψ|q dx
+� p
+q =
+ˆ
+Ω
+|∇ψ|p dx
+∥ψ∥ p
+L∞(Ω)
+.
+By arbitrariness of ψ and recalling the definition of λp,∞(Ω), we obtain
+lim sup
+q→∞ λp,q(Ω) ≤ λp,∞(Ω).
+In order to show the converse inequality, we can assume that λp,∞(Ω) > 0, otherwise from the
+previous inequality we already get the desired result. Since p > N, by Corollary 5.9 we have that
+
+SOBOLEV EMBEDDINGS AND DISTANCE FUNCTIONS
+35
+rΩ < +∞ and thus λp(Ω) > 0, as well. Then, for every u ∈ C∞
+0 (Ω) \ {0} and for every p < q < ∞
+it holds
+∥u∥Lq(Ω) ≤ ∥u∥
+p
+q
+Lp(Ω) ∥u∥
+1− p
+q
+L∞(Ω) ≤
+�
+λp(Ω)
+�− 1
+q ∥∇u∥
+p
+q
+Lp(Ω) ∥u∥
+1− p
+q
+L∞(Ω),
+by interpolation in Lebesgue spaces. Hence, we have the following lower bound
+∥∇u∥Lp(Ω)
+∥u∥Lq(Ω)
+≥
+�
+λp(Ω)
+� 1
+q ∥∇u∥
+1− p
+q
+Lp(Ω)
+∥u∥
+1− p
+q
+L∞(Ω)
+≥
+�
+λp(Ω)
+� 1
+q �
+λp,∞(Ω)
+� q−p
+p q .
+By raising to the power p on both sides and taking the infimum on C∞
+0 (Ω) \ {0} on the left-hand
+side, this yields
+λp,q(Ω) ≥
+�
+λp(Ω)
+� p
+q �
+λp,∞(Ω)
+� q−p
+q .
+By sending q to ∞ in this inequality, we get
+lim inf
+q→∞ λp,q(Ω) ≥ λp,∞(Ω),
+as desired.
+□
+6.2. Asymptotics for the solution of the Lane-Emden equation. Let Ω ⊊ RN be an open
+connected set. In this subsection we will assume that 1 ≤ q < ∞ and dΩ ∈ Lq(Ω). By Lemma
+3.1, the last assumption entails that dΩ ∈ L∞(Ω), as well. Thus, by interpolation, we have that
+dΩ ∈ L(p q)/(p−q)(Ω) for every q < p < ∞. Hence, by Theorem 5.1, Ω is (p, q)−admissible for every
+p > max{N, q} and, by [10, Corollary 4.4], there exists a unique positive solution wΩ
+p,q to (2.10) for
+every q < p. In the following theorem, we will study the asymptotic behavior of wΩ
+p,q, as p goes to
+∞.
+Theorem 6.3. Let 1 ≤ q < ∞ and let Ω ⊊ RN be an open connected set such that dΩ ∈ Lq(Ω).
+Then
+(6.4)
+lim
+p→∞ ∥wΩ
+p,q − dΩ∥Lr(Ω) = 0
+and
+lim
+p→∞ ∥wΩ
+p,q − dΩ∥C0,β(Ω) = 0
+for every q ≤ r ≤ ∞ and every 0 < β < 1.
+Proof. We will first show that (6.4) holds to r = q. Then, by interpolation, we will obtain all the
+other claimed convergences.
+Part 1: convergence in Lq(Ω). We extend each function wΩ
+p,q to RN by setting it to be zero in
+RN \ Ω. First of all, we note that, by using (2.14) and Corollary 6.1, we have
+(6.5)
+lim
+p→∞
+ˆ
+Ω
+|∇wΩ
+p,q|p dx = lim
+p→∞
+ˆ
+Ω
+|wΩ
+p,q|q dx = lim
+p→∞
+�
+�
+�
+1
+�
+λp,q(Ω)
+� 1
+p
+�
+�
+�
+p q
+p−q
+=
+ˆ
+Ω
+d q
+Ω dx,
+which implies
+(6.6)
+lim
+p→∞ ∥∇wΩ
+p,q||Lp(Ω) = 1.
+Moreover, by applying (4.5), we find the upper bound
+(6.7)
+0 < wΩ
+p,q(x) ≤
+dΩ(x)αp
+�
+µp(B1)
+� 1
+p ∥∇wΩ
+p,q∥Lp(Ω),
+for every x ∈ Ω,
+
+36
+BRASCO, PRINARI, AND ZAGATI
+where αp = 1 − N/p. On the other hand, thanks to (5.3), we obtain the lower bound
+(6.8)
+(dΩ(x))
+p
+p−q wB1
+p,q(0) ≤ wΩ
+p,q(x),
+for every x ∈ Ω.
+By sending p to ∞ in (6.7) and (6.8) and taking into account (4.1), (6.6) and (2.15), we get that
+lim
+p→∞ wΩ
+p,q(x) = dΩ(x),
+for every x ∈ Ω.
+The pointwise convergence, combined with the convergence of the Lq norm given by (6.5), implies
+that
+lim
+p→∞ ∥wΩ
+p,q − dΩ∥Lq(Ω) = 0.
+Part 2: convergence in L∞(Ω). By Corollary 5.7, we have that wΩ
+p,q ∈ C0(Ω)∩C0,αp(Ω). Moreover,
+by applying the estimate on the sharp Morrey constant of Corollary 4.3, we have that wΩ
+p,q satisfies
+[wΩ
+p,q]C0,αp(Ω) ≤
+�
+1
+mp(Ω)
+� 1
+p
+∥∇wΩ
+p,q∥Lp(Ω).
+By using (6.6) and Corollary 4.3, we have
+lim sup
+p→∞ [wΩ
+p,q]C0,αp(Ω) ≤ 1,
+and thus in particular the seminorms [wΩ
+p,q]C0,αp(Ω) are uniformly bounded, for p large enough. We
+also observe that by Lemma 3.2, we have
+[dΩ]C0,αp(Ω) ≤ (2 rΩ)1−αp.
+We now apply Lemma 2.2 to wΩ
+p,q − dΩ, with α = αp and γ = q. Thus, for every 0 < β < 1 and
+every p such that αp > β, we have
+[wΩ
+p,q − dΩ]C0,β(Ω) ≤ C1 ∥wΩ
+p,q − dΩ∥θp
+Lq(Ω) [wΩ
+p,q − dΩ]1−θp
+C0,αp(Ω),
+with θp = αp − β
+αp + N
+q
+,
+and
+∥wΩ
+p,q − dΩ∥L∞(Ω) ≤ C2 ∥wΩ
+p,q − dΩ∥χp
+Lq(Ω) [wΩ
+p,q − dΩ]1−χp
+C0,αp(Ω),
+with χp =
+αp
+αp + N
+q
+.
+We observe that, for p diverging to ∞, the exponent αp goes to 1. Thus, the constants C1 and C2,
+which depend on p through αp, stay uniformly bounded as p goes to ∞ (see Lemma 2.2 and Remark
+2.3). By using this fact, the bound on the C0,αp seminorms inferred above and the convergence in
+Lq proved in Part 1, the previous interpolation estimates give
+lim
+p→∞
+�
+∥wΩ
+p,q − dΩ∥L∞(Ω) + [wΩ
+p,q − dΩ]C0,β(Ω)
+�
+= 0.
+Finally, the convergence in Lr(Ω) for q < r < ∞ can be obtained by interpolation in Lebesgue
+spaces.
+□
+
+SOBOLEV EMBEDDINGS AND DISTANCE FUNCTIONS
+37
+6.3. Asymptotics for λp(Ω). The following corollary generalizes the result shown, independently,
+in [18, Theorem 3.1] and [26, Lemma 1.2]. While these treat the case of bounded open sets, we
+enlarge the result to cover every open set, without further restrictions.
+Corollary 6.4. Let Ω ⊊ RN be an open set, then
+(6.9)
+lim
+p→∞
+�
+λp(Ω)
+� 1
+p = 1
+rΩ
+,
+where the right-hand side has to be considered 0, if rΩ = +∞.
+Proof. First of all, we note that for every 0 < r < rΩ there exists a ball Br(xr) ⊆ Ω. Hence, by
+applying [26, Lemma 1.5], it holds
+(6.10)
+lim sup
+p→∞
+�
+λp(Ω)
+� 1
+p ≤ lim sup
+p→∞
+�
+λp(Br(xr))
+� 1
+p = 1
+r .
+By sending r → rΩ, we get
+lim sup
+p→∞
+�
+λp(Ω)
+� 1
+p ≤ 1
+rΩ
+,
+where the right-hand side is 0 when rΩ = +∞. In order to obtain the reverse inequality when
+rΩ < +∞, it is sufficient to apply (5.7) and (4.10), to get that
+lim inf
+p→∞
+�
+λp(Ω)
+� 1
+p ≥ 1
+rΩ
+lim
+p→∞
+�
+hp(Ω)
+� 1
+p = 1
+rΩ
+.
+This concludes the proof.
+□
+6.4. Asymptotics for the first p−eigenfunction. We first recall that for every function u ∈
+W 1,∞(Ω) vanishing on the boundary ∂Ω, we have
+|u(x)| ≤ dΩ(x) ∥∇u∥L∞(Ω),
+for every x ∈ Ω.
+This may be seen as a limit case of Hardy’s inequality. In particular ± dΩ/rΩ is a solution of the
+following minimization problem
+(6.11)
+min
+u∈W 1,∞(Ω)
+�
+∥∇u∥L∞(Ω) : ∥u∥L∞(Ω) = 1, u ≡ 0 on ∂Ω
+�
+= 1
+rΩ
+,
+provided Ω has finite inradius.
+Theorem 6.5. Let Ω ⊊ RN be an open connected quasibounded set. Then, for every N < p < ∞,
+there exists a unique positive solution up of the problem
+(6.12)
+λp(Ω) =
+min
+u∈W 1,p
+0
+(Ω)
+�ˆ
+Ω
+|∇u|p dx :
+ˆ
+Ω
+|u|p dx = 1
+�
+.
+Moreover, the family {up}p>N is precompact in C0,β(Ω) for every 0 < β < 1 and every accumu-
+lation point u∞ is a solution of (6.11), possibly different from dΩ/rΩ.
+Proof. We first observe that λp(Ω) > 0, thanks to the assumption on Ω. Thus, by Remark 2.5, we
+have
+W 1,p
+0
+(Ω) = D1,p
+0 (Ω).
+By Theorem 5.6, for every p > N the embedding W 1,p
+0
+(Ω) �→ Lp(Ω) is compact. Hence, by using
+also Lemma 2.6, it follows that, for every p > N, there exists a positive solution up ∈ W 1,p
+0
+(Ω) of
+the minimization problem (6.12). Uniqueness can now be inferred by using the Benguria hidden
+
+38
+BRASCO, PRINARI, AND ZAGATI
+convexity principle of [6, 29], for example, as generalized in [10, Theorem 2.9]. See also [3] and [31]
+for other proofs of the uniqueness.
+Without loss of generality, let {pn}n∈N be an increasing sequence diverging at ∞. In particular,
+there exists n0 ∈ N such that pn > N for every n ≥ n0. We denote by upn the unique positive
+solution of the problem defining λpn(Ω). By applying (4.5) and (4.7), we find that
+(6.13)
+|upn(x)| ≤
+1
+�
+µpn(B1)
+� 1
+pn
+�
+λpn(Ω)
+� 1
+pn dΩ(x)αpn ,
+for every x ∈ Ω,
+and
+(6.14)
+|upn(x) − upn(y)| ≤
+1
+�
+µpn(B1)
+� 1
+pn
+�
+λpn(Ω)
+� 1
+pn |x − y|αpn ,
+for every x, y ∈ Ω.
+Since Ω is quasibounded, the previous estimates assures that we can apply Proposition 3.5. Thus,
+we get that {upn}n≥n0 converges uniformly to a function u∞ ∈ C0(Ω), up to a subsequence. By
+passing to the limit in (6.13) and in (6.14) as n goes to ∞, we obtain that
+|u∞(x)| ≤ 1
+rΩ
+dΩ(x),
+for every x ∈ Ω,
+and
+|u∞(x) − u∞(y)| ≤ 1
+rΩ
+|x − y|,
+for every x, y ∈ Ω.
+Observe that we also used (4.1) and (6.9). In particular u∞ ∈ W 1,∞(Ω) and it satisfies
+∥u∞∥L∞(Ω) ≤ 1
+and
+∥∇u∞∥L∞(Ω) ≤ 1
+rΩ
+.
+If we also prove that ∥u∞∥L∞(Ω) ≥ 1, we can conclude that u∞ is a minimizer for the problem
+(6.11).
+In order to show this, for every R > 0, we take ηR ∈ C∞(RN) such that
+0 ≤ ηR ≤ 1,
+ηR = 1 in RN \ BR+1,
+ηR = 0 in BR,
+|∇ηR| ≤ C,
+for some universal constant C > 0. Then
+sup
+n≥n0
+∥∇(upnηR)∥Lpn(Ω) ≤ sup
+n≥n0
+∥∇upn∥Lpn(Ω) + C sup
+n>N
+∥upn∥Lpn(Ω)
+= sup
+n≥n0
+�
+λpn(Ω)
+� 1
+pn + C
+≤ 1
+rΩ
+sup
+n≥n0
+�
+λpn(B1)
+� 1
+pn + C =: M < +∞.
+We notice that M > 0 only depends on N and rΩ. Now, thanks to (4.10), there exists p > N such
+that
+�
+hp(Ω)
+� 1
+p ≥ 1
+2,
+for every p ≥ p.
+Since Ω is quasibounded, for every 0 < ε ≤ 1/2, there exists Rε > 0 such that
+∥dΩ∥L∞(Ω\BRϵ) <
+ε
+2 M .
+
+SOBOLEV EMBEDDINGS AND DISTANCE FUNCTIONS
+39
+By using the properties of η and applying H¨older’s and Hardy’s inequalities to upnηRε ∈ W 1,p
+0
+(Ω),
+for every pn ≥ max{p, pn0}, we have that
+ˆ
+Ω\BRε+1
+|upn|pn dx =
+ˆ
+Ω\BRε+1
+|upnηRε|pn dx ≤ ∥dΩ∥ pn
+L∞(Ω\BRε)
+ˆ
+Ω
+|upn ηRϵ|pn
+d pn
+Ω
+dx
+≤ ∥dΩ∥ pn
+L∞(Ω\BRε)
+1
+hpn(Ω)
+ˆ
+Ω
+|∇(upn ηRε)|pn dx
+≤ ε pn.
+Hence
+1 =
+ˆ
+Ω\BRε+1
+|upn|pn dx +
+ˆ
+BRε+1
+|upn|pn dx ≤ ε pn +
+ˆ
+BRε+1
+|upn|pn dx,
+that is
+�
+1 − ε pn� 1
+pn ≤
+�
+ωN (Rϵ + 1)N� 1
+pn
+sup
+BRϵ+1
+|upn|,
+for every pn ≥ max{p, pn0}.
+By exploiting the uniform convergence of the family {upn}n≥n0 to u∞ on compact sets, if we take
+the limit as n goes to ∞, we get
+1 ≤ sup
+BRε+1
+|u∞| ≤ sup
+Ω
+|u∞|,
+which proves the claim for every Ω quasibounded set.
+In order to get the convergence in C0,β(Ω) for 0 < β < 1, we can use the same interpolation
+argument as in Part 2 of the proof of Theorem 6.3. It is sufficient to observe that it holds
+[u∞]C0,β(Ω) ≤ 21−β ∥u∞∥1−β
+L∞(Ω) ∥∇u∞∥β
+L∞(Ω),
+an estimate that can be proved by repeating the proof of Lemma 3.2. We leave the details to the
+reader.
+□
+Remark 6.6. We underline that, differently from the case 1 ≤ q < p, when p = q it may happen
+that the accumulation points of the family {up}p>N do not coincide with dΩ (see [18, Corollary
+4.7]). We refer to [17, Theorem 3.14] for a study of the multiplicity of extremals for problem (6.11),
+in the case of open bounded sets.
+With the same arguments as in the previous proof, we can show a similar result for minimizers
+of λp,∞(Ω), whose existence is given by Corollary 5.9 when Ω is quasibounded. This generalizes
+[17, Theorem 3.3]. We omit the proof.
+Theorem 6.7. Let N < p and let Ω ⊊ RN be a quasibounded open set. Let up,∞ ∈ W 1,p
+0
+(Ω) be a
+positive solution of
+λp,∞(Ω) =
+min
+u∈W 1,p
+0
+(Ω)
+�ˆ
+Ω
+|∇u|p dx : ∥u∥L∞(Ω) = 1
+�
+.
+Then the family {up,∞}p>N is precompact in C0,β(Ω) for every 0 < β < 1 and every accumulation
+point u∞ is a solution of (6.11).
+
+40
+BRASCO, PRINARI, AND ZAGATI
+Appendix A. An infinite strip with slowly shrinking ends
+In the next example, we consider a quasibounded open set for which dγ
+Ω /∈ L1(RN), for any
+0 < γ < ∞.
+Example A.1. For every α > 0 and x1 ∈ R, we set
+f1(x1) =
+1
+log (2 + x2
+1)
+and
+fα(x1) = f1
+�x1
+α
+�
+=
+1
+log
+�
+2 +
+�x1
+α
+�2�.
+Then we consider the quasibounded open set
+Ωα =
+�
+x = (x1, x2) ∈ R2 : x1 ∈ R, |x2| < fα(x1)
+�
+,
+with α2 > (log 2)−3.
+Observe that for this set we have dγ
+Ω ̸∈ L1(Ω), for any 0 < γ < ∞. Thus, by Theorem 5.1 part (i),
+we have
+D1,2
+0 (Ωα) ̸�→ Lq(Ωα),
+for every 1 ≤ q < 2.
+On the other hand, since Ωα is bounded in the x2 direction, we easily get that λ2(Ωα) > 0, that is
+D1,2
+0 (Ωα) �→ L2(Ωα).
+As for the compactness of this embedding, we observe that this can not be directly inferred from
+Theorem 5.4, since we are in the critical situation p = 2 = N. Nevertheless, we are going to show
+that actually such an embedding is compact, thanks to the particular geometry of the set Ωα. In
+particular, the Dirichlet-Laplacian on Ωα has a discrete spectrum.
+We define
+Ωα,R := Ωα ∩
+�
+(−R, R) × (−R, R)
+�
+,
+for R ≥ R0 =
+1
+log 2.
+We denote by wΩα the torsion function of Ωα, defined as
+wΩα := lim
+R→∞ wΩα,R,
+where wΩα,R ∈ W 1,2
+0
+(Ωα,R) is the torsion function of Ωα,R, i. e. it solves
+(A.1)
+− ∆u = 1,
+in Ωα,R,
+(see [11, Definition 2.2]). In order to prove the compactness of the embedding of D1,2
+0 (Ωα) �→
+L2(Ωα), it is sufficient to prove that
+(A.2)
+lim
+R→∞ ∥wΩα∥L∞(Ω\BR) = 0,
+thanks to [11, Theorem 1.3]. We will achieve (A.2) by exploiting the geometry of Ωα in order to
+construct a suitable upper barrier. For every α > 0 and x1 ∈ R, we set
+F1(x1) = (f1(x1))2
+and
+Fα(x1) := F1
+�x1
+α
+�
+= (fα(x1))2.
+Observe that
+���F ′′
+1
+�x1
+α
+���� ≤ 2 (log 2)−3,
+thus, if we take α > 0 such that α2 > (log 2)−3, we obtain
+(A.3)
+|F ′′
+α(x1)| = 1
+α2
+���F ′′
+1
+�x1
+α
+���� ≤ 2 (1 − C),
+for x1 ∈ R,
+
+SOBOLEV EMBEDDINGS AND DISTANCE FUNCTIONS
+41
+for some C = C(α) ∈ (0, 1). With such a choice of α, we consider the function
+Uα(x1, x2) = Fα(x1) − x2
+2
+2 C
+,
+for every (x1, x2) ∈ Ωα.
+We claim that this is the desired upper barrier. Indeed, by construction we have Uα ≥ 0 and,
+thanks to (A.3), it holds
+−∆Uα(x1, x2) = 1
+C − F ′′
+α(x1)
+2 C
+≥ 1,
+for every (x1, x2) ∈ Ωα.
+By applying the Comparison Principle in every Ωα,R we get that
+wΩα,R(x) ≤ Uα(x) ≤ Fα(x1)
+2 C
+,
+for every x = (x1, x2) ∈ Ωα,R,
+and such an estimate does not depend on R. Hence, by sending R to ∞, we have that
+wΩα(x) ≤ Fα(x1)
+2 C
+,
+for every x = (x1, x2) ∈ Ωα.
+By using the properties of Fα = (fα)2 and the previous estimate, we eventually get (A.2).
+References
+[1] R. A. Adams, J. J. F. Fournier, Sobolev spaces. Second edition. Pure and Applied Mathematics (Amsterdam),
+140. Elsevier/Academic Press, Amsterdam, 2003. 3, 29
+[2] R. A. Adams, Compact Sobolev imbeddings for unbounded domains with discrete boundaries, J. Math. Anal.
+Appl., 24 (1968), 326–333. 29
+[3] W. Allegretto, Y. X. Huang, A Picone’s identity for the p−Laplacian and applications, Nonlinear Anal., 32
+(1998), 819–830. 14, 38
+[4] F. G. Avkhadiev, Hardy type inequalities in higher dimensions with explicit estimate of constants, Lobachevskii
+J. Math., 21 (2006), 3–31. 22, 23
+[5] T. Bhattacharya, E. Di Benedetto, J. Manfredi, Limits as p → ∞ of ∆pup = f and related extremal problems,
+Some topics in nonlinear PDEs (Turin, 1989). Rend. Sem. Mat. Univ. Politec. Torino 1989, Special Issue, 15–68
+(1991). 6
+[6] M. Belloni, B. Kawohl, A direct uniqueness proof for equations involving the p−Laplace operator, Manuscripta
+Math., 109 (2002), 229–231. 38
+[7] M. van den Berg, Estimates for the torsion function and Sobolev constants, Potential Anal., 36 (2012), 607–616.
+3, 4, 27
+[8] L. Brasco, On principal frequencies and isoperimetric ratios in convex sets, Ann. Fac. Sci. Toulouse Math. (6),
+29 (2020), 977–1005. 27
+[9] L. Brasco, G. Franzina, B. Ruffini, Schr¨odinger operators with negative potentials and Lane-Emden densities,
+J. Funct. Anal., 274 (2018), 1825–1863. 15
+[10] L. Brasco, F. Prinari, A. C. Zagati, A comparison principle for the Lane–Emden equation and applications to
+geometric estimates, Nonlinear Analysis, 220 (2022), 112847 4, 10, 12, 13, 14, 25, 27, 35, 38
+[11] L. Brasco, B. Ruffini, Compact Sobolev embeddings and torsion functions, Ann. Inst. Henri Poincar´e, Anal.
+Non Lin´eaire, 34 (2017), 817–843. 2, 3, 9, 15, 40
+[12] L. Briani, G. Buttazzo, F. Prinari, Some inequalities involving perimeter and torsional rigidity, Appl. Math.
+Optim., 84 (2021), 2727–2741. 6
+[13] D. Bucur, G. Buttazzo, On the characterization of the compact embedding of Sobolev spaces, Calc. Var. Partial
+Differential Equations, 44 (2012), 455–475. 3
+[14] C. Clark, An embedding theorem for function spaces, Pacific J. Math., 19 (1965), 243–251. 3
+[15] B.-Y. Chen, Hardy-type inequalities and principal frequency of the p−Laplacian, preprint (2020), available at
+arXiv:2007.06782v1. 22, 23
+[16] T. Champion, L. De Pascale, C. Jimenez, The ∞-eigenvalue problem and a problem of a optimal transportation.
+Commun. Appl. Anal. 13 4 (2009), 547–565. 5
+[17] G. Ercole, G. Pereira, Asymptotics for the best Sobolev constants and their extremal functions, Math. Nachr.,
+289 (2016), 1433–1449 . 5, 6, 33, 39
+
+42
+BRASCO, PRINARI, AND ZAGATI
+[18] N. Fukagai, M. Ito, K. Narukawa, Limit as p → ∞ of p−Laplace eigenvalue problems and L∞−inequality of
+the Poincar´e type, Differential Integral Equations, 12 (1999), 183 – 206. 5, 37, 39
+[19] J. Hersch, Sur la fr´equence fondamentale d’une membrane vibrante: ´evaluations par d´efaut et principe de
+maximum, Z. Angew. Math. Phys., 11 (1960), 387–413. 29
+[20] P. Hajlasz, Pointwise Hardy inequalities, Proc. Amer. Math. Soc., 127 (1999), 417– 423. 22
+[21] E. Hewitt, K. Stromberg, Real and Abstract Analysis. A modern treatment of the theory of functions of one
+real variable. Springer-Verlag, New York, 1965. 7
+[22] R. Hynd, E. Lindgren, Extremal functions for Morrey’s inequality in convex domains, Math. Ann., 375 (2019),
+1721–1743. 5, 33
+[23] R. Hynd, F. Seuffert, Extremal functions for Morrey’s inequality, Arch. Ration. Mech. Anal., 241 (2021),
+903–945. 6
+[24] R. Hynd, F. Seuffert, Asymptotic flatness of Morrey extremals, Calc. Var. Partial Differential Equations, 59
+(2020), Paper No. 159, 24 pp. 6
+[25] R. Hynd, F. Seuffert, On the symmetry and monotonicity of Morrey extremals, Commun. Pure Appl. Anal.,
+19 (2020), 5285–5303. 6
+[26] P. Juutinen, P. Lindqvist, J. J. Manfredi, The ∞−eigenvalue problem, Arch. Rational Mech. Anal., 148 (1999),
+89–105. 5, 14, 33, 37
+[27] R. Kajikiya, A priori estimate for the first eigenvalue of the p−Laplacian, Differential Integral Equations, 28
+(2015), 1011–1028. 29
+[28] B. Kawohl, On a family of torsional creep problems, J. Reine Angew. Math., 410 (1990), 1–22. 6
+[29] B. Kawohl, M. Lucia, S. Prashanth, Simplicity of the principal eigenvalue for indefinite quasilinear problems,
+Adv. Differential Equations, 12 (2007), 407–434. 38
+[30] J. L. Lewis, Uniformly fat sets, Trans. Amer. Math. Soc., 308 (1988), 177–196. 4, 22
+[31] P. Lindqvist, On the equation div(|∇u|p−2 ∇u)+λ |u|p−2 u = 0, Proc. Amer. Math. Soc., 109 (1990), 157–164.
+38
+[32] V. Maz’ya, Sobolev spaces with applications to elliptic partial differential equations. Second, revised and aug-
+mented edition. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical
+Sciences], 342. Springer, Heidelberg, 2011. 2
+[33] M. H. Protter, A lower bound for the fundamental frequency of a convex region, Proc. Amer. Math. Soc., 81
+(1981), 65–70. 29
+[34] G. Poliquin, Principal frequency of the p−Laplacian and the inradius of Euclidean domains, J. Topol. Anal., 7
+(2015), 505–511. 29
+[35] G. Talenti, Inequalities in rearrangement invariant function spaces, in Nonlinear Analysis, Function Spaces
+and Applications, 5 (Prague, 1994), 177–230, Prometheus, Prague, 1994. 32
+[36] L. Tartar, An introduction to Sobolev spaces and interpolation spaces. Lecture Notes of the Unione Matematica
+Italiana, 3. Springer, Berlin; UMI, Bologna, 2007. 27, 28, 30
+[37] N. N. Trong, B. L. T. Thanh, T. D. Do, Hardy-Lane-Emden inequalities for p−Laplacian on arbitrary domains,
+NoDEA Nonlinear Differential Equations Appl., 29 (2022), Paper No. 59, 30 pp. 15
+[38] A. Wannebo, Hardy inequalities, Proc. Amer. Math. Soc., 109 (1990), 85–95. 4, 22
+(L. Brasco) Dipartimento di Matematica e Informatica
+Universit`a degli Studi di Ferrara
+Via Machiavelli 35, 44121 Ferrara, Italy
+Email address: lorenzo.brasco@unife.it
+(F. Prinari) Dipartimento di Scienze Agrarie, Alimentari e Agro-ambientali
+Universit`a di Pisa
+Via del Borghetto 80, 56124 Pisa, Italy
+Email address: francesca.prinari@unipi.it
+(A. C. Zagati) Dipartimento di Scienze Matematiche, Fisiche e Informatiche
+Universit`a di Parma
+Parco Area delle Scienze 53/a, Campus, 43124 Parma, Italy
+Email address: annachiara.zagati@unipr.it
+
diff --git a/p9FPT4oBgHgl3EQfMjQS/content/tmp_files/load_file.txt b/p9FPT4oBgHgl3EQfMjQS/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e823de735d3b53c04977961f8332a3d3f1d596ee
--- /dev/null
+++ b/p9FPT4oBgHgl3EQfMjQS/content/tmp_files/load_file.txt
@@ -0,0 +1,1411 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf,len=1410
+page_content='SOBOLEV EMBEDDINGS AND DISTANCE FUNCTIONS  LORENZO BRASCO, FRANCESCA PRINARI, AND ANNA CHIARA ZAGATI  Abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' On a general open set of the euclidean space, we study the relation between the  embedding of the homogeneous Sobolev space D1,p  0  into Lq and the summability properties of  the distance function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' We prove that in the superconformal case (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' when p is larger than the  dimension) these two facts are equivalent, while in the subconformal and conformal cases (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  when p is less than or equal to the dimension) we construct counterexamples to this equivalence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' In  turn, our analysis permits to study the asymptotic behaviour of the positive solution of the Lane-  Emden equation for the p−Laplacian with sub-homogeneous right-hand side, as the exponent  p diverges to ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' The case of first eigenfunctions of the p−Laplacian is included, as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' As  particular cases of our analysis, we retrieve some well-known convergence results, under optimal  assumptions on the open sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' We also give some new geometric estimates for generalized principal  frequencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Contents  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Introduction  2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Homogeneous Sobolev spaces  2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Main results  3  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Plan of the paper  6  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Preliminaries  7  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Notation  7  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Sobolev embeddings  9  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  The Lane-Emden equation  11  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  The distance function  15  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  A Morrey–type inequality and its consequences  18  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Embedding theorems  24  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  The case q < p  24  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  The case p = q: continuity  28  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  The case p = q: compactness  29  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  The super-homogeneous case q > p and beyond  31  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Asymptotics  33  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Asymptotics for λp,q(Ω)  33  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Asymptotics for the solution of the Lane-Emden equation  35  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Asymptotics for λp(Ω)  37  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Asymptotics for the first p−eigenfunction  37  Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  An infinite strip with slowly shrinking ends  40  References  41  Date: January 31, 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  2010 Mathematics Subject Classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' 46E35, 35J92, 35P30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Key words and phrases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Sobolev embeddings, p−Laplacian, Lane-Emden equation, inradius, distance function,  capacity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  1  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='13026v1  [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='AP]  30 Jan 2023  2  BRASCO, PRINARI, AND ZAGATI  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Introduction  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Homogeneous Sobolev spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Let 1 < p < ∞ and let Ω ⊆ RN be an open set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' We indicate  by D1,p  0 (Ω) the homogeneous Sobolev space defined by the completion of C∞  0 (Ω), with respect to  the norm  ψ �→ ∥∇ψ∥Lp(Ω),  for every ψ ∈ C∞  0 (Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Our primary goal is to deepen the study of conditions on Ω assuring the validity of the continuous  embedding  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='1)  D1,p  0 (Ω) �→ Lq(Ω),  in the range 1 ≤ q ≤ p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Equivalently, if we introduce the generalized principal frequencies  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='2)  λp,q(Ω) :=  inf  ψ∈C∞  0 (Ω)  �ˆ  Ω  |∇ψ|p dx : ∥ψ∥Lq(Ω) = 1  �  ,  we seek for necessary and sufficient conditions on Ω assuring that λp,q(Ω) > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Indeed, λp,q(Ω) is  nothing but the sharp constant in the following Poincar´e-type inequality  c  �ˆ  Ω  |ψ|q dx  � p  q  ≤  ˆ  Ω  |∇ψ|p dx,  for every ψ ∈ C∞  0 (Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  This is a classical subject, we refer to [32, Chapter 15] for a thorough treatment of the problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' In  particular, before proceeding further, it is important to recall some important facts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  The first one is the following remarkable equivalence  D1,p  0 (Ω) �→ Lq(Ω) is continuous  ⇐⇒  D1,p  0 (Ω) �→ Lq(Ω) is compact,  which holds in the sub-homogeneous case 1 ≤ q < p < ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' We refer to [32, Theorem 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='2] for this  result (see also [11, Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='2], for a different proof).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Such an equivalence ceases to be true at  the threshold q = p, as shown by the simple example of  Ω = RN−1 × (−1, 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  A second important fact is that, for the super-homogeneous case p < q, we have  D1,p  0 (Ω) �→ Lp(Ω) is continuous  ⇐⇒  D1,p  0 (Ω) �→ Lq(Ω) is continuous,  and  D1,p  0 (Ω) �→ Lp(Ω) is compact  ⇐⇒  D1,p  0 (Ω) �→ Lq(Ω) is compact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  More precisely, here q is such that  p < q  �  �  �  �  �  <  N p  N − p,  if 1 < p < N,  < ∞,  if p = N,  ≤ ∞,  if p ≥ N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  We refer to [32, Theorem 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='1] and [32, Theorem 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='1] for these equivalences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' This second fact  explains why we will essentially limit ourselves to treat the case q ≤ p and only briefly discuss the  case q > p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  In particular, in this paper we want to discuss the link between the continuous (and compact)  embedding (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='1) and the summability of the distance function  dΩ(x) := min  y∈∂Ω |x − y|,  for every x ∈ Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  SOBOLEV EMBEDDINGS AND DISTANCE FUNCTIONS  3  At this aim, it is useful to recall that in [11] (see also [13]), a similar study has been done, with the  so-called p−torsion function of Ω in place of dΩ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' The former, denoted by wΩ  p,1, is formally defined  as the positive solution of  −∆pu = 1,  in Ω,  u = 0,  on ∂Ω,  where ∆pu = div(|∇u|p−2∇u) is the p−Laplace operator, see [11, Definitions 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='1 and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='2] for the  precise definition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Then, for the case q < p, in [11, Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='2] the first author and Ruffini proved  that  D1,p  0 (Ω) �→ Lq(Ω) is continuous  ⇐⇒  wΩ  p,1 ∈ L  p−1  p−q q(Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  As for the limit case q = p, by [11, Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='3] we have  D1,p  0 (Ω) �→ Lp(Ω) is continuous  ⇐⇒  wΩ  p,1 ∈ L∞(Ω),  and  D1,p  0 (Ω) �→ Lp(Ω) is compact  ⇐⇒  lim  R→+∞ ∥wΩ  p,1∥L∞(RN\\BR) = 0,  where BR is the N−dimensional ball of center 0 and radius R > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  These characterizations are quite useful: we give an example in Appendix A of an open planar set  with infinite volume, for which one can get the compactness of the embedding D1,2  0 (Ω) �→ L2(Ω) by  appealing to the torsion function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Nevertheless, dealing with the p−torsion function is not always  practical, thus the previous characterizations are a bit implicit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' It would be desirable to have some  characterizations which are more intrinsically geometric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Roughly speaking, in this paper we will study to which extent we can replace wΩ  p,1 with dΩ in  the aforementioned results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' For capacitary reasons, we will see that this is possible only in the  superconformal case p > N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' In the case p ≤ N, we will find that some summability conditions on  dΩ are necessary for the embeddings to hold, but not sufficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Main results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' In this paper, we will show at first that for 1 ≤ q < p  D1,p  0 (Ω) �→ Lq(Ω) is continuous  =⇒  dΩ ∈ L  p q  p−q (Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  In the case q = p, we will prove that  D1,p  0 (Ω) �→ Lp(Ω) is continuous  =⇒  dΩ ∈ L∞(Ω),  and  D1,p  0 (Ω) �→ Lp(Ω) is compact  =⇒  lim  R→+∞ ∥dΩ∥L∞(RN\\BR) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Moreover, when p > N we will show that all these implications actually become equivalences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' We  will also construct suitable counterexamples to show that for 1 < p ≤ N, on the contrary, none of  the converse implications hold true.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  We recall that the condition  lim  R→+∞ ∥dΩ∥L∞(RN\\BR) = 0,  is somehow classical in the theory of Sobolev spaces, when it holds Ω is said to be quasibounded  (see for example [1, 14]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Remark 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='1 (Comparison with previous results, q < p).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' The fact that the continuity of the  embedding implies the stated summability of dΩ can be found in [7, Theorem 3], at least for the  case p = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' However, apart for the generalization to p ̸= 2, our proof is different and exploits a  4  BRASCO, PRINARI, AND ZAGATI  comparison principle for the sub-homogeneous Lane-Emden equation, that we recently proved in  [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' This in turn permits to obtain a geometric estimate on λp,q of the type  λp,q(Ω)  �ˆ  Ω  d  p q  p−q  Ω  dx  � p−q  q  ≤ C,  with a constant C which does not blow-up as q ↗ p, differently from [7] (see Remark 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='2 below).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  The converse implication exploits the same idea of [7], i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' it is based on Hardy’s inequality  CΩ  ˆ  Ω  |u|p  dp  Ω  dx ≤  ˆ  Ω  |∇u|p dx,  for every u ∈ C∞  0 (Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  There is however a difference here: while the result in [7] is proved conditionally on the validity of  such an inequality, we use here the important fact that such an inequality holds for every open set  Ω ⊊ RN, provided p > N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' This is a major result proved independently by Lewis [30] and Wannebo  [38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Remark 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='2 (Comparison with previous results, q = p).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Here our embedding results were already  known and due to Adams.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' However, to prove that on a quasibounded open set the embedding  D1,p  0 (Ω) �→ Lp(Ω) is compact for p > N, we use a different argument.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  As before, the crucial  ingredient is the Hardy inequality recalled above, which permits to give a simpler proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' We believe  this fact to be of independent interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  With these embedding results at hand, we then proceed to study the asymptotic behaviour of  both λp,q(Ω) and their relevant extremals (provided they exist), in the limit as p goes to ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Here  we are going to unify and extend previous results, scattered in the literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' For example, for the  generalized principal frequencies, we will prove that  lim  p→∞  �  λp,q(Ω)  � 1  p =  1  ∥dΩ∥Lq(Ω)  and  lim  p→∞  �  λp(Ω)  � 1  p = 1  rΩ  ,  for every open set Ω ⊊ RN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Here we used the simplified notation λp(Ω) = λp,p(Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' The quantity  rΩ is the inradius of Ω, which coincides with the supremum of the distance function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  As for the relevant extremals, we will prove at first that under the assumption dΩ ∈ Lq(Ω) for  some 1 ≤ q < ∞ and Ω connected, we have  lim  p→∞ ∥wΩ  p,q − dΩ∥Lq(Ω) = 0,  where for q < p the function wΩ  p,q is the unique positive solution of the Lane-Emden equation  −∆pu = uq−1,  in Ω,  with Dirichlet homogeneous boundary conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' By observing that (see equation (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='14) below)  ∥wΩ  p,q∥Lq(Ω) =  �  λp,q(Ω)  �  1  q−p ,  we get that  wΩ  p,q :=  �  λp,q(Ω)  �  1  p−q wΩ  p,q,  is the unique positive extremal in D1,p  0 (Ω) for λp,q(Ω) and we have  lim  p→∞  ����wΩ  p,q −  dΩ  ∥dΩ∥Lq(Ω)  ����  Lq(Ω)  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  SOBOLEV EMBEDDINGS AND DISTANCE FUNCTIONS  5  We remark that this convergence is obtained under the optimal assumption dΩ ∈ Lq(Ω), thus Ω is  not supposed either bounded or with finite volume.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Moreover, by an interpolation argument, we  can upgrade these convergences and infer convergence in Lr(Ω) and C0,β(Ω), for every q < r ≤ ∞  and 0 < β < 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  In the case of λp(Ω), extremals in D1,p  0 (Ω) are usually called first eigenfunctions of the p−Laplacian  with Dirichlet conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' In this case, we will prove that if Ω is connected and quasibounded, then  the family {up} is precompact in L∞(Ω) and every accumulation point u∞ is a solution of  min  u∈W 1,∞(Ω)  �  ∥∇u∥L∞(Ω) : ∥u∥L∞(Ω) = 1, u ≡ 0 on ∂Ω  �  = 1  rΩ  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Here each up is the first positive eigenfunction on Ω, normalized by the requirement to have unit  Lp(Ω) norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Finally, we will also consider the variational problem associated to the endpoint Poincar´e-Sobolev  constant λp,∞(Ω) for p > N, recently studied in [17] and [22] when Ω is a bounded open set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' More  precisely, we will generalize [17, Theorems 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='1 and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='3], by showing that for every open set Ω ⊊ RN,  it holds  lim  q→∞ λp,q(Ω) = λp,∞(Ω),  and by proving that the variational problem defining λp,∞(Ω) has a minimizer under the sole  assumption of quasiboundedness on Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Moreover, inspired by [17, Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='3], we will also study  the asymptotic behaviour of both λp,∞ and its extremals, as p goes to ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  At the level of generalized principal frequencies, we can summarize the previous convergence  results with the following diagram, which holds for every N < p < ∞, every 1 ≤ q ≤ p and every  open set Ω ⊊ RN (see Corollary 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='1, Corollary 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='2 and Corollary 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  �  λp,q(Ω)  � 1  p  �  λp,∞(Ω)  � 1  p  1  ∥dΩ∥Lq(Ω)  1  rΩ  q→∞  p→∞  p=q→∞  p→∞  The elements in the bottom line have to be considered as 0, whenever dΩ ̸∈ Lq(Ω) or rΩ = +∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Moreover, when Ω is such that dΩ ∈ Lq0(Ω) for some q0 < ∞, then we can close the diagram by  1  ∥dΩ∥Lq(Ω)  q→∞  −→  1  rΩ  ,  thus making it commutative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Remark 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='3 (Comparison with previous results).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' These convergence results are not a complete  novelty, of course.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' However, our treatment extends, improves and generalizes some known results  previously obtained by various authors in some particular cases (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' q = 1 or q = p) and under  more restrictive assumptions on Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' The asymptotics for λp(Ω) generalize [26, Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='5] and [18,  Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='1], shown under the restrictive assumption that Ω is a bounded open set (see also [16,  Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='1]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  6  BRASCO, PRINARI, AND ZAGATI  The behaviour of λp,1(Ω) is due to [5, Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='1] and [28, Theorem 1], in the case of an  open bounded set, after getting the uniform convergence of the relevant extremals wΩ  p,1 to dΩ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' This  result is extended to sets with finite volume in [12, Corollary A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' As for the constant λp,∞, the  case of open bounded sets is considered in [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  We point out that the extension of these convergence results to open sets which are unbounded or  with infinite volume is not trivial: we crucially rely on the comparison principle for the Lane-Emden  equation recalled above, as well as on the asymptotic behaviour as p goes to ∞ of the following  Morrey-type constant  µp(B1) :=  inf  u∈W 1,p(B1)  �ˆ  B1  |∇u|p dx : u(0) = 1 and u(z) = 0  �  ,  with z ∈ ∂B1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  The study of this constant is contained in Section 4 below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' The study of the asymptotics for µp(B1)  permits in turn to obtain a couple of collateral results,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' which are interesting in themselves: the  behaviour for large p of the two sharp Hardy constants  hp(Ω) =  inf  u∈C∞  0 (Ω)  �ˆ  Ω  |∇u|p dx :  ����  u  dΩ  ����  Lp(Ω)  = 1  �  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  and  hp,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='∞(Ω) =  inf  u∈C∞  0 (Ω)  �  �  �  �  �  ˆ  Ω  |∇u|p dx :  ������  u  d  1− N  p  Ω  ������  L∞(Ω)  = 1  �  �  �  �  �  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  as well as the asymptotic behaviour of the sharp Morrey constant  mp(Ω) :=  inf  u∈C∞  0 (Ω)  �ˆ  Ω  |∇u|p dx : [u]C0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='αp(Ω) = 1  �  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  where αp := 1 − N  p .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  We observe that the latter is actually independent of the open set Ω, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' it coincides with that of  the whole space (see Corollary 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='3 below, for example).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Some studies on such a constant and its  extremals have been done recently by Hynd and Seuffert in a series of papers (see [23, 24] and [25]),  but the exact value of the sharp constant is still unknown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' We show in Corollary 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='3 that  lim  p→∞  �  mp(Ω)  � 1  p = lim  p→∞  �  mp(RN)  � 1  p = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Plan of the paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' In Section 2 we present the functional analytic setting, give some pre-  liminary embedding results and recall some important properties of the Lane-Emden equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Then in Section 3 we discuss the role of summability assumptions on the distance function  dΩ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' This section also contains a generalized version of the classical Ascoli-Arzel`a Theorem, for  continuous functions on quasibounded open sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  In the subsequent Section 4 we present one of the key ingredients of this work, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' an Hardy’s  inequality which holds for every open set Ω ⊊ RN and p > N (see Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' In particular, we  focus on the asymptotics of the relevant sharp constant, when p goes to ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' For this reason, we  first need to study the asymptotics of a particular sharp Morrey-type constant (see Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Section 5 contains the main embedding theorems for D1,p  0 (Ω) and their relations with the summa-  bility of the distance function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Finally, in Section 6 we investigate the asymptotic behaviour for the  generalized principal frequencies and the positive solutions of Lane-Emden equation when p goes  to ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  SOBOLEV EMBEDDINGS AND DISTANCE FUNCTIONS  7  Acknowledgments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' We thank Ryan Hynd and Erik Lindgren for some discussions on Hardy’s  inequality and the constant λp,∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' This paper has been finalized during the meeting “PDEs in  Cogne: a friendly meeting in the snow ”, held in Cogne in January 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' We wish to thank the  organizers for the kind invitation and the nice working atmosphere provided during the staying.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' are members of the Gruppo Nazionale per l’Analisi Matematica, la Probabilit`a  e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Preliminaries  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Notation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' For x0 ∈ RN and R > 0, we will denote by BR(x0) the N−dimensional open  ball with radius R, centered at x0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' In particular, when the center coincides with the origin, we  will simply write BR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' For an open set Ω ⊊ RN, we denote by dΩ the distance function from the  boundary ∂Ω, defined by  dΩ(x) := min  y∈∂Ω |x − y|,  for every x ∈ Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  We extend dΩ by 0 in RN \\Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' We define the inradius rΩ of Ω as the radius of a largest ball contained  in Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' More precisely, this quantity is given by  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='1)  rΩ = sup  �  r > 0 : there exists x0 ∈ Ω such that Br(x0) ⊂ Ω  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  It is well-known that this coincides with the supremum over Ω of dΩ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  The following simple result will be quite useful.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Let Ω ⊊ RN be an open set, we denote by C0(Ω) the completion of C∞  0 (Ω) with  respect to the sup norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Then we get  C0(Ω) ⊂  �  u ∈ Cbound(Ω) : u = 0 on ∂Ω  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Here Cbound(Ω) is the set of continuous and bounded functions on Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Let {un}n∈N ⊂ C∞  0 (Ω) be a Cauchy sequence, with respect to the sup norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' In particular,  it is Cauchy sequence in Cbound(Ω), which is a Banach space (see for example [21, Theorem 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='9]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Thus, there exists u ∈ Cbound(Ω) such that un converges to u uniformly on Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Moreover, such a  function must vanish at the boundary ∂Ω, as a uniform limit of functions with compact support in  Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  □  For every open set Ω ⊆ RN, 0 < α ≤ 1 and u a continuous function on Ω, we set  [u]C0,α(Ω) =  sup  x̸=y;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' x,y∈Ω  |u(x) − u(y)|  |x − y|α  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  We have the following interpolation–type estimate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Let 0 < β < α ≤ 1, let 1 ≤ γ ≤ ∞ and let Ω ⊊ RN be an open set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' For every  u ∈ C0(Ω) ∩ Lγ(Ω) such that  [u]C0,α(Ω) < +∞,  we have  [u]C0,β(Ω) ≤ C1 ∥u∥θ  Lγ(Ω) [u]1−θ  C0,α(Ω),  with θ = α − β  α + N  γ  ,  8  BRASCO, PRINARI, AND ZAGATI  for some C1 = C1(N, α, β, γ) > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Moreover, if 1 ≤ γ < ∞ we also have  ∥u∥L∞(Ω) ≤ C2 ∥u∥χ  Lγ(Ω) [u]1−χ  C0,α(Ω),  with χ =  α  α + N  γ  ,  for some C2 = C2(N, α, γ) > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' By Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='1, we can extend u to a continuous function on the whole RN, by setting it to  be 0 on RN \\ Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' We first observe that for such an extension it holds  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='2)  [u]C0,α(Ω) = [u]C0,α(RN).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Indeed, we may write  [u]C0,α(RN) = max  �  [u]C0,α(Ω),  sup  x∈Ω,y /∈Ω  |u(x)|  |x − y|α  �  = max  �  [u]C0,α(Ω),  sup  x∈Ω,y /∈Ω  |u(x)|  |x − y|α  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  If x ∈ Ω and y /∈ Ω then the segment x y connecting x and y is such that x y ∩ Ω ̸= ∅ and  x y ∩ (RN \\ Ω) ̸= ∅.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Hence, there exists y0 ∈ x y ∩ ∂Ω satisfying  |x − y| ≥ |x − y0|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  This implies  |u(x)|  |x − y|α ≤ |u(x) − u(y0)|  |x − y0|α  ≤ [u]C0,α(Ω),  that gives  sup  x∈Ω,y /∈Ω  |u(x)|  |x − y|α ≤ [u]C0,α(Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  This concludes the proof of (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  We now come to the proof of the claimed interpolation inequality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' For every x, y ∈ RN such that  x ̸= y, we write  |u(x) − u(y)|  |x − y|β  =  �|u(x) − u(y)|  |x − y|α  � β  α  |u(x) − u(y)|  α−β  α  ≤ [u]  β  α  C0,α(Ω)  �  |u(x)|  α−β  α  + |u(y)|  α−β  α  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='3)  Observe that we used the triangle inequality and the sub-additivity of concave powers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' In order to  estimate the last term, we use that for every z ∈ BR(x) we have  |u(x)| ≤ |u(x) − u(z)| + |u(z)| ≤ [u]C0,α(Ω) |x − z|α + |u(z)|  ≤ Rα [u]C0,α(Ω) + |u(z)|,  where we also used (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' We now take the integral average of this estimate on BR(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' This gives  |u(x)| ≤ Rα [u]C0,α(Ω) +  1  ωN RN  ˆ  BR(x)  |u(z)| dz  ≤ Rα [u]C0,α(Ω) + (ωN RN)− 1  γ  �ˆ  Ω  |u(z)|γ dz  � 1  γ  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='4)  SOBOLEV EMBEDDINGS AND DISTANCE FUNCTIONS  9  With the same argument, we have also  |u(y)| ≤ Rα [u]C0,α(Ω) + (ωN RN)− 1  γ  �ˆ  Ω  |u(z)|γ dz  � 1  γ  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  We insert these estimates in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='3) and use again the subadditivity of concave powers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' We get  |u(x) − u(y)|  |x − y|β  ≤ 2 [u]  β  α  C0,α(Ω)  �  Rα−β [u]  α−β  α  C0,α(Ω) +  �  1  ωN RN  � α−β  α γ  ∥u∥  α−β  α  Lγ(Ω)  �  ,  which is valid for every x ̸= y and every R > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' If we not optimize in R > 0, we finally get the  desired estimate for the C0,β seminorm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' The sup norm can be estimated with a similar optimization  argument, by using (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  □  Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' We remark that the constants C1 and C2 in the previous result are given by  C1 = 2 ω  −  α−β  γ α+N  N  �α γ  N  �  N  α γ+N 1  χ,  and  C2 = ω  − χ  γ  N  �α γ  N  �  N  α γ+N 1  χ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  In particular, we notice that C1 stays uniformly bounded, as α varies in (β, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Similary, the constant  C2 stays bounded, as α varies in (0, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' This observation will be useful in the sequel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Sobolev embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' We recall the following family of Gagliardo-Nirenberg interpolation  inequalities  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='5)  ∥ψ∥Lr(Ω) ≤ GN,p,q,r ∥∇ψ∥ϑ  Lp(Ω) ∥ψ∥1−ϑ  Lq(Ω),  for every ψ ∈ C∞  0 (Ω),  which hold for every 1 < p < ∞, 1 ≤ q ≤ p and r satisfying  �  �  �  �  �  �  �  q < r ≤  Np  N − p,  if 1 < p < N,  q < r < ∞,  if p = N,  q < r ≤ ∞,  if p > N,  with GN,p,q,r > 0 only depending on N, p, q, r and  ϑ =  N (r − q)  N r (p − q) + p q r,  (for a proof, see for example [11, Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='6]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  For 1 < p < ∞ and Ω ⊂ RN open set, we will indicate by W 1,p  0  (Ω) the closure of C∞  0 (Ω) in the  usual Sobolev space W 1,p(Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' We will say that Ω is (p, q)−admissible if λp,q(Ω) > 0, the latter  being defined in (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  By using (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='5), one can prove the following result:  Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Let 1 ≤ q < p < ∞ and let Ω ⊆ RN be an open set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Then  D1,p  0 (Ω) �→ Lq(Ω)  ⇐⇒  W 1,p  0  (Ω) �→ Lq(Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  In particular, if Ω ⊆ RN is a (p, q)−admissible open set, then  W 1,p  0  (Ω) = D1,p  0 (Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  10  BRASCO, PRINARI, AND ZAGATI  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' The implication =⇒ is straightforward.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' For the converse implication, we suppose that there  exists C > 0 such that  ∥ψ∥Lq(Ω) ≤ C ∥ψ∥W 1,p(Ω),  for every ψ ∈ C∞  0 (Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  By applying the Gagliardo-Nirenberg inequality (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='5) with r = p, it holds in particular  ∥ψ∥Lq(Ω) ≤ C ∥ψ∥W 1,p(Ω) ≤ C  �  ∥∇ψ∥Lp(Ω) + GN,p,q,p ∥∇ψ∥ϑ  Lp(Ω)∥ψ∥1−ϑ  Lq(Ω)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  With a standard application of Young’s inequality with exponents 1/ϑ and 1/(1−ϑ), we can absorb  the Lq norm on the right-hand side and get  ∥ψ∥Lq(Ω) ≤ �C ∥∇ψ∥Lp(Ω),  for some �C > 0 independent of ψ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Thus, the embedding D1,p  0 (Ω) �→ Lq(Ω) holds, as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  The last part of the statement follows by [10, Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  □  Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' It is easily seen that the following implication holds  λp(Ω) > 0  =⇒  W 1,p  0  (Ω) = D1,p  0 (Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Indeed, the positivity of λp(Ω) automatically gives that  ∥∇u∥Lp(Ω)  and  ∥u∥W 1,p(Ω),  are equivalent norms on C∞  0 (Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  The following simple result will be useful.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Observe that we do not put any restriction either on  q or on the open set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Let 1 < p < ∞, 1 ≤ q ≤ ∞ and let Ω ⊊ RN be an open set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Then  λp,q(Ω) =  inf  ψ∈C∞  0 (Ω)  �ˆ  Ω  |∇ψ|p dx : ∥ψ∥Lq(Ω) = 1  �  =  inf  ψ∈W 1,p  0  (Ω)  �ˆ  Ω  |∇ψ|p dx : ∥ψ∥Lq(Ω) = 1  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' We first observe that the problem on the right-hand side is actually settled on W 1,p  0  (Ω) ∩  Lq(Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Since we have C∞  0 (Ω) ⊂ W 1,p  0  (Ω) ∩ Lq(Ω), we immediately obtain  inf  ψ∈C∞  0 (Ω)  �ˆ  Ω  |∇ψ|p dx : ∥ψ∥Lq(Ω) = 1  �  ≥  inf  ψ∈W 1,p  0  (Ω)  �ˆ  Ω  |∇ψ|p dx : ∥ψ∥Lq(Ω) = 1  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  In order to prove the reverse inequality, we first observe that if λp,q(Ω) = 0, then from the previous  inequality we would get  0 =  inf  ψ∈C∞  0 (Ω)  �ˆ  Ω  |∇ψ|p dx : ∥ψ∥Lq(Ω) = 1  �  ≥  inf  ψ∈W 1,p  0  (Ω)  �ˆ  Ω  |∇ψ|p dx : ∥ψ∥Lq(Ω) = 1  �  ≥ 0,  and thus the desired identity trivially holds true.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Let us now suppose that λp,q(Ω) > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' For every u ∈ W 1,p  0  (Ω) ∩ Lq(Ω) not identically vanishing,  there exists a sequence {un}n∈N ⊂ C∞  0 (Ω) such that  lim  n→∞ ∥∇un − ∇u∥Lp(Ω) = lim  n→∞ ∥un − u∥Lp(Ω) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  By using the definition of λp,q(Ω) > 0, we have  λp,q(Ω) ∥un − um∥p  Lq(Ω) ≤ ∥∇un − ∇um∥p  Lp(Ω),  for every n, m ∈ N,  SOBOLEV EMBEDDINGS AND DISTANCE FUNCTIONS  11  thus, in particular, {un}n∈N is a Cauchy sequence in Lq(Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' This shows that we have  lim  n→∞ ∥un − u∥Lq(Ω) = 0,  as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Hence, we get  λp,q(Ω) ≤ lim  n→∞  ˆ  Ω  |∇un|p dx  ∥un∥p  Lq(Ω)  =  ˆ  Ω  |∇u|p dx  ∥u∥p  Lq(Ω)  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Finally, by taking the infimum on W 1,p  0  (Ω) ∩ Lq(Ω) on the right-hand side, we obtain that  λp,q(Ω) ≤  inf  ψ∈W 1,p  0  (Ω)  �ˆ  Ω  |∇ψ|p dx : ∥ψ∥Lq(Ω) = 1  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  This concludes the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  □  In the sequel, we will need the following Poincar´e–type inequality, for functions which vanish at  a point of the boundary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Obviously, this may hold only in the superconformal case p > N, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' in  the case where points have positive p−capacity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='7 (A Poincar´e inequality).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Let p > N and u ∈ W 1,p(BR(x0)) be such that u(z) = 0,  with z ∈ ∂BR(x0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Then there exists a constant CN,p > 0 such that  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='6)  ˆ  BR(x0)  |u|p dx ≤ CN,p Rp  ˆ  BR(x0)  |∇u|p dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' It is sufficient to consider the case x0 = 0 and R = 1, then the general case follows by scaling  and translating.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' For the proof of (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='6), we can use a standard contradiction argument, exploiting  compact Sobolev embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' We assume by contradiction that (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='6) fails to hold with a uniform  constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Thus, there exists a sequence {un}n∈N ⊂ W 1,p(B1) such that  ∥un∥Lp(B1) = 1,  lim  n→∞ ∥∇un∥Lp(B1) = 0,  and  un(z) = 0 with z ∈ ∂B1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  In particular, {un}n∈N is bounded in W 1,p(B1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Hence, thanks to compact Sobolev embeddings for  p > N, there exists u ∈ W 1,p(B1) ∩ C(B1) such that un converges to u weakly in W 1,p(B1) and  uniformly in B1, up to a subsequence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' In particular, we get  ∥∇u∥Lp(B1) ≤ lim inf  n→∞ ∥∇un∥Lp(B1) = 0  and  u(z) = lim  n→∞ un(z) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Since B1 is a connected set, the last two facts imply that u ≡ 0 in B1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' However, by the uniform  convergence we also have  ∥u∥Lp(B1) = lim  n→∞ ∥un∥Lp(B1) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  This contradicts the fact that u identically vanishes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  □  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' The Lane-Emden equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Let 1 ≤ q < p < ∞ and let Ω ⊂ RN be a (p, q)−admissible open set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' We say that  a function v ∈ W 1,p  0  (Ω) is a weak solution of the Lane-Emden equation  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='7)  − ∆pu = |u|q−2 u,  in Ω,  if it satisfies  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='8)  ˆ  Ω  ⟨|∇v|p−2 ∇v, ∇ψ⟩ dx =  ˆ  Ω  |v|q−2 v ψ dx,  for every ψ ∈ C∞  0 (Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  12  BRASCO, PRINARI, AND ZAGATI  In the case q = 1, for a non-negative function v, we follow the convention  |v|q−2 v = vq−1 = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  By density, in the weak formulation (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='8) we can admit test functions in W 1,p  0  (Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='9 (Scalings).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Let 1 ≤ q < p < ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Given t > 0, it is easily seen that if u ∈ W 1,p  0  (Ω) is  a weak solution of (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='7), then the rescaled function  ut(x) = t  p  p−q u  �x − x0  t  �  ,  is a weak solution of the same equation, in the new set x0 + t Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' On the other hand, if u ∈ W 1,p  0  (Ω)  weakly solves (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='7), then the function  v = α  1  p−q u  is a weak solution of  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='9)  − ∆pu = α |u|q−2 u,  in Ω,  with α > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  We recall that if Ω ⊆ RN is a (p, q)−admissible connected open set for some 1 ≤ q < p < ∞,  then there exists a unique weak positive solution of the following problem  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='10)  �  �  �  �  �  −∆pu = |u|q−2u,  in Ω,  u ∈ W 1,p  0  (Ω),  u > 0,  in Ω,  see [10, Corollary 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' We will denote this solution by wΩ  p,q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' We recall that the latter also coincides  with the unique positive solution of  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='11)  min  ψ∈W 1,p  0  (Ω)  Fp,q(ψ),  where  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='12)  Fp,q(ψ) := 1  p  ˆ  Ω  |∇ψ|p dx − 1  q  ˆ  Ω  |ψ|q dx,  for every ψ ∈ W 1,p  0  (Ω),  see [10, Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' By optimality and thanks to the relevant normalization condition on the Lq  norm, when Ω is a connected (p, q)−admissible open set, the positive minimizer of (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='2) coincides  with the weak positive solution of (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='9) corresponding to the choice α = λp,q(Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  The next proof is standard, we include it for completeness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Let 1 < p < ∞, 1 ≤ q < p and let Ω ⊆ RN be a (p, q)-admissible connected  open set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Then  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='13)  min  ψ∈W 1,p  0  (Ω)  Fp,q(ψ) = q − p  p q  �  1  λp,q(Ω)  �  q  p−q  and  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='14)  ˆ  Ω  |∇wΩ  p,q|p dx =  ˆ  Ω  |wΩ  p,q|q dx =  �  1  λp,q(Ω)  �  q  p−q  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  SOBOLEV EMBEDDINGS AND DISTANCE FUNCTIONS  13  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Exploiting the different homogeneities of the two integrals and the fact that the minimum  problem is equivalently settled on W 1,p  0  (Ω)\\{0} (since a positive minimizer exists, see [10, Theorem  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='3]), we get that  min  ψ∈W 1,p  0  (Ω)  Fp,q(ψ) = −  max  ψ∈W 1,p  0  (Ω)\\{0},t>0  �tq  q  ˆ  Ω  |ψ|q dx − tp  p  ˆ  Ω  |∇ψ|p dx  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  It is easily seen that, for every ψ ∈ W 1,p  0  (Ω) \\ {0}, the function  t �→ tq  q  ˆ  Ω  |ψ|q dx − tp  p  ˆ  Ω  |∇ψ|p dx  is maximal for  t0 =  �  �  �  �  ˆ  Ω  |ψ|q dx  ˆ  Ω  |∇ψ|p dx  �  �  �  �  1  p−q  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  With such a choice of t, we get  tq  0  q  ˆ  Ω  |ψ|q dx − tp  0  p  ˆ  Ω  |∇ψ|p dx = p − q  p q  �ˆ  Ω  |ψ|q dx  �  p  p−q  �ˆ  Ω  |∇ψ|p dx  �  q  p−q .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Then, by recalling the definition of λp,q(Ω), we get (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='13).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Finally, since wΩ  p,q satifies the Lane-Emden equation (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='7), by using this solution as a test function  in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='8), we get that  ˆ  Ω  |∇wΩ  p,q|p dx =  ˆ  Ω  |wΩ  p,q|q dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  This implies  Fp,q(wΩ  p,q) = q − p  p q  ˆ  Ω  |wΩ  p,q|q dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Thanks to (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='13), equality (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='14) easily follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  □  We now discuss the behavior of the L∞ norm of wΩ  p,q when 1 ≤ q < ∞ is fixed, p goes to ∞ and  Ω is a bounded convex open set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' This result will be useful somewhere in Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Let 1 < p < ∞, 1 ≤ q < p and Ω ⊆ RN be a bounded convex open set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Then  lim  p→∞ ∥wΩ  p,q∥L∞(Ω) = rΩ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  In particular, it holds  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='15)  lim  p→∞ wB1  p,q(0) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' For every η ∈ C∞  0 (Ω) and ε > 0, the function  ψ =  |η|p  (wΩ  p,q + ε)p−1 ∈ W 1,p  0  (Ω),  14  BRASCO, PRINARI, AND ZAGATI  is a feasible test function in the equation (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='8) for wΩ  p,q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Hence, by applying Picone’s inequality for  the p−Laplacian (see [3]), we get that  ˆ  Ω  (wΩ  p,q) q−1  |η|p  (wΩ  p,q + ε)p−1 dx =  ˆ  Ω  �  |∇wΩ  p,q|p−2 ∇wΩ  p,q, ∇  �  |η|p  (wΩ  p,q + ε)p−1  ��  dx  ≤  ˆ  Ω  |∇η|p dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Since wΩ  p,q ∈ W 1,p  0  (Ω) is strictly positive by the minimum principle, by sending ε to 0, we get  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='16)  ˆ  Ω  |η|p  (wΩ  p,q) p−q dx ≤  ˆ  Ω  |∇η|p dx,  for every η ∈ C∞  0 (Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  By recalling the definition of λp(Ω) and that wΩ  p,q is bounded, the latter estimate implies that  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='17)  1 ≤ ∥wΩ  p,q∥p−q  L∞(Ω) λp(Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  By raising to the power 1/p and using that  lim  p→∞  �  λp(Ω)  � 1  p = 1  rΩ  ,  (see [26, Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='5]), from (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='17) we obtain  rΩ ≤ lim inf  p→∞ ∥wΩ  p,q∥L∞(Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  On the other hand, by using [10, Corollary 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='3], we have that  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='18)  ∥wΩ  p,q∥L∞(Ω) ≤  � 2  πp,q  �  p  p−q �q p − q + p  p  � 1  q  r  p−q  p  Ω  ,  where πp,q is the following one-dimensional Sobolev-Poincar´e constant  πp,q :=  �  λp,q((0, 1))  � 1  p .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  We claim that  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='19)  πp,q ≥ 2(1− 1  p)  �  q  �  1 − 1  p  �  + 1  � 1  q  ,  for every 1 < p < ∞ and 1 ≤ q < ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Postponing the proof of this fact for a moment, we see that  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='18) and (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='19) would give  lim sup  p→∞ ∥wΩ  p,q∥L∞(Ω) ≤ rΩ,  as desired.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Then the last part of the statement would follow by using that wB1  p,q is radially symmetric  decreasing, so that wB1  p,q(0) = ∥wB1  p,q∥L∞(B1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  We are left with establishing (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='19).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Let ϕ ∈ C∞  0 ((0, 1)), for every t ∈ (0, 1), we have that  |ϕ(t)| = |ϕ(t) − ϕ(0)| ≤  ˆ t  0  |ϕ′| dt ≤ t1− 1  p ∥ϕ′∥Lp([0,1]),  and  |ϕ(t)| = |ϕ(t) − ϕ(1)| ≤  ˆ 1  t  |ϕ′| dt ≤ (1 − t)1− 1  p ∥ϕ′∥Lp([0,1]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  SOBOLEV EMBEDDINGS AND DISTANCE FUNCTIONS  15  By raising to the power q and integrating the first estimate on (0, 1/2) and the second one on  (1/2, 1), we get  ˆ 1/2  0  |ϕ(t)|q dt ≤  1  q  �  1 − 1  p  �  + 1  �1  2  �q(1− 1  p)+1  ∥ϕ′∥q  Lp([0,1]),  and  ˆ 1  1/2  |ϕ(t)|q dt ≤  1  q  �  1 − 1  p  �  + 1  �1  2  �q(1− 1  p)+1  ∥ϕ′∥q  Lp([0,1]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Then, by summing up, we obtain  ˆ 1  0  |ϕ(t)|q dt ≤  1  q  �  1 − 1  p  �  + 1  �1  2  �q(1− 1  p)  ∥ϕ′∥q  Lp([0,1]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  By raising to the power 1/q on both sides and using the arbitrariness of ϕ, we get (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='19).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  □  Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' We point out that inequality (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='16) holds for general open sets: in this case, if the  open set is not (p, q)−admissible, the function wΩ  p,q has to be carefully defined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' We refer to [11,  Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='5] for the case of the p−torsion function, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' the case q = 1 and 1 < p < ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' The  general case is contained in [9, Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='1] and [37, Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' The distance function  In this section we investigate some consequences of the summability of the distance function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  First of all, we prove that when d α  Ω is summable for some 0 < α < ∞, the set Ω has finite inradius.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  This comes with an explicit (sharp) bound.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Let 0 < α < ∞ and let Ω ⊊ RN be an open set such that dα  Ω ∈ L1(Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Then rΩ < +∞  and it holds  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='1)  rΩ ≤ CN,α  �ˆ  Ω  dα  Ω dx  �  1  N+α  ,  where the constant CN,α is given by  CN,α =  �  N ωN  ˆ 1  0  (1 − ϱ)α ϱN−1 dϱ  �−  1  N+α  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Moreover, inequality (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='1) is sharp, since equality holds for a ball.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Let Br(x0) ⊆ Ω, then we have that  (r − |x − x0|)+ = dBr(x0)(x) ≤ dΩ(x),  for every x ∈ Br(x0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  By raising to the power α and integrating, we get  ˆ  Br(x0)  (r − |x − x0|)α  + dx ≤  ˆ  Ω  dα  Ω dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  16  BRASCO, PRINARI, AND ZAGATI  By using the change of variable y = (x − x0)/r, from the previous estimate we also get  rN+α ≤  ˆ  Ω  dα  Ω dx  ˆ  B1  (1 − |y|)α  + dy  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  If we now take the supremum over the admissible balls, we get the conclusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  □  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Let 0 < α < ∞ and let Ω ⊊ RN be an open set such that rΩ < +∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Then for every  0 < β < 1 we have  [dΩ]C0,β(Ω) ≤ (2 rΩ)1−β.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' We extend dΩ to be 0 outside Ω and consider it as a Lipschitz continuous function defined  on the whole RN, By recalling (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='2), for every 0 < β < 1 we have  [dΩ]C0,β(Ω) = [dΩ]C0,β(RN).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  It is now sufficient to write for t > 0  [dΩ]C0,β(RN) = max  �  sup  x̸=y;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' |x−y|≤t  |dΩ(x) − dΩ(y)|  |x − y|β  ,  sup  |x−y|>t  |dΩ(x) − dΩ(y)|  |x − y|β  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  For the first term on the right-hand side, we can just use the 1−Lipschitz character of dΩ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' For the  second one, it is sufficient to use that dΩ is bounded by rΩ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' This gives  [dΩ]C0,β(RN) = max  �  t1−β, 2 rΩ  tβ  �  ,  for every t > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  By choosing t = 2 rΩ, we get the claimed estimate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  □  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Let Ω ⊊ RN be an open set such that dα  Ω ∈ L1(RN), for some 0 < α < ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Then for  every R ≥ rΩ/2, we have  dΩ(x) ≤ 2  �  1  ωN  ˆ  RN\\BR  dα  Ω dy  �  1  N+α  ,  for every |x| > R + rΩ  2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  In particular, Ω is quasibounded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Let R ≥ rΩ/2 and let x ∈ RN be such that |x| > R + rΩ/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' If x ̸∈ Ω, then dΩ(x) = 0 and  there is nothing to prove.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Let us suppose that x ∈ Ω, so that dΩ(x) > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' We consider the ball  B :=  �  y ∈ RN : |x − y| < dΩ(x)  2  �  ,  and observe that  dΩ(y) ≥ 1  2 dΩ(x),  for every y ∈ B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  We raise to the power α and integrate this inequality over B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' This gives  2−α dΩ(x)α |B| ≤  ˆ  B  dΩ(y)α dy,  that is  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='2)  ωN 2−α−N dΩ(x)α+N ≤  ˆ  B  dΩ(y)α dy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  SOBOLEV EMBEDDINGS AND DISTANCE FUNCTIONS  17  We then observe that  |y| ≥ |x| − |y − x| > |x| − 1  2 dΩ(x) ≥ |x| − rΩ  2 > R,  for every y ∈ B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  This gives that B ⊆ RN \\ BR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' By using the previous inclusion in (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='2), we get  ωN 2−α−N dΩ(x)α+N ≤  ˆ  RN\\BR  dΩ(y)α dy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  This concludes the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  □  Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' The converse implication does not hold true: indeed, there exist quasibounded open  sets for which d α  Ω /∈ L1(RN), for any 0 < α < ∞ (see Example A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  We conclude this section with a generalized version of Ascoli-Arzel`a Theorem, which is valid  when Ω is a quasibounded open set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' This is probably well-known, but we have not been able to  detect it in the literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Thus, we include its proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Let Ω ⊆ RN be a quasibounded open set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Let  {un}n∈N ⊂  �  u ∈ Cbound(Ω) : u = 0 on ∂Ω  �  be a sequence with the following properties:  (a) there exists M > 0 such that ∥un∥L∞(Ω) ≤ M, for every n ∈ N;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  (b) there exist δ0 > 0 and a function ω : (0, δ0] → (0, +∞) such that  lim  δ→0+ ω(δ) = 0,  and  ωn(δ) := sup  �  |un(x) − un(y)| : x, y ∈ Ω, |x − y| ≤ δ  �  ≤ ω(δ),  for every 0 < δ ≤ δ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Then, there exists u ∈ Cbound(Ω) vanishing on ∂Ω such that  lim  n→∞ ∥un − u∥L∞(Ω) = 0,  up to a subsequence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Let us denote by k0 ∈ N the smallest natural number such that Ω∩Bk is not empty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Thanks  to the assumptions, {un}n∈N is a bounded and equicontinuous sequence on the compact set Ω∩Bk,  for every k ≥ k0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' By applying the classical Ascoli-Arzel´a Theorem for compact sets, together with  a diagonal argument, we have that there exists a function u ∈ C(Ω) such that, up to a subsequence,  un converges uniformly to u on Ω ∩ Bk, for every k ≥ k0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  We will show that un converges to u uniformly on the whole Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Let 0 < δ ≤ δ0, since Ω is  quasibounded, there exists Rδ > 0 such that  dΩ(x) ≤ δ,  for x ∈ Ω \\ BRδ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  For every x ∈ Ω \\ BRδ, we take y ∈ ∂Ω such that |x − y| = dΩ(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' By using property (b), the  triangle inequality and the fact that un(y) = 0, we get that for every n ∈ N  |un(x) − u(x)| = lim  m→∞ |un(x) − um(x)|  ≤ |un(x) − un(y)| + lim  m→∞ |um(x) − um(y)| ≤ 2 ω(dΩ(x)) ≤ 2 ω(δ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  18  BRASCO, PRINARI, AND ZAGATI  This implies that  ∥un − u∥L∞(Ω) = max  �  ∥un − u∥L∞(Ω\\BRδ ), ∥un − u∥L∞(Ω∩BRδ )  �  ≤ max  �  2 ω(δ), ∥un − u∥L∞(Ω∩BRδ )  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  By taking the limit as n goes to ∞ and exploiting the uniform convergence of un to u on Ω ∩ BRδ,  we obtain that  lim sup  n→∞ ∥un − u∥L∞(Ω) ≤ 2 ω(δ),  for 0 < δ ≤ δ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  By arbitrariness of δ and using the properties of ω, we get  lim  n→∞ ∥un − u∥L∞(Ω) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  This also shows that u vanishes on ∂Ω, as a uniform limit of functions with the same property.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Moreover, using again that Cbound(Ω) is a Banach space, we finally get that u ∈ Cbound(Ω), as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  This concludes the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  □  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' A Morrey–type inequality and its consequences  We will need the following Morrey–type sharp constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Let x0 ∈ RN and let R > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' For every p > N and every fixed z ∈ ∂BR(x0), we set  µp(BR(x0);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' {z}) :=  min  ϕ∈W 1,p(BR(x0))  �ˆ  BR(x0)  |∇ϕ|p dx : ϕ(x0) = 1 and ϕ(z) = 0  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Then:  (1) the minimum above is independent of the point z ∈ ∂BR(x0);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  (2) we have the scaling  µp(BR(x0);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' {z}) = RN−p µp  �  B1(x0);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  � z  R  ��  ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  (3) the family  �� 1  ωN  µp(BR(x0);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' {z})  � 1  p �  p>N  is non-decreasing;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  (4) we have the following asymptotics  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='1)  lim  p→∞  �  µp(BR(x0);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' {z})  � 1  p = 1  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' We first show that µp (BR(x0);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' {z}) is actually a minimum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' To this aim, we consider a  minimizing sequence {un}n∈N ⊂ W 1,p(BR(x0)) for the problem defined by µp (BR(x0);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' {z}), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  lim  n→∞  ˆ  BR(x0)  |∇un|p dx = µp (BR(x0);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' {z}) ,  un(x0) = 1  and  un(z) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  By Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='7, we also have that  ˆ  BR(x0)  |un|p dx ≤ CN,p Rp  ˆ  BR(x0)  |∇un|p dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  SOBOLEV EMBEDDINGS AND DISTANCE FUNCTIONS  19  This implies that {un}n∈N is a bounded sequence in W 1,p(BR(x0)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Hence, thanks to compact  Sobolev embeddings for p > N, there exists u ∈ W 1,p(BR(x0))∩C(BR(x0)) such that un converges  to u weakly in W 1,p(BR(x0)) and uniformly in BR(x0), up to a subsequence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' This implies that  u(x0) = 1 and u(z) = 0, thus u is an admissible trial function for the problem µp (BR(x0);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' {z}).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Moreover, by lower semicontinuity we have  ˆ  BR(x0)  |∇u|p dx ≤ lim  n→∞  ˆ  BR(x0)  |∇un|p dx = µp (BR(x0);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' {z}) ,  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' u is a minimizer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  The proof of part (1) and part (2) easily follow by standard arguments, while part (3) is a  consequence of H¨older’s inequality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  It remains to prove part (4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' We suppose without loss of generality that x0 = 0 and R = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Thus, we have to show that  lim  p→∞  �  µp (B1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' {z})  � 1  p = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  We observe that dB1 is admissible for the problem µp (B1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' {z}), thus we get that  �  µp (B1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' {z})  � 1  p ≤ ω  1  p  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  This in turn implies that  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='2)  lim sup  p→∞  �  µp (B1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' {z})  � 1  p ≤ lim  p→∞ ω  1  p  N = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  We now prove that  lim inf  p→∞  �  µp (B1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' {z})  � 1  p ≥ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  At this aim, we consider Up ∈ W 1,p(B1) a minimizer for µp (B1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' {z}), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  �ˆ  B1  |∇Up|p dx  � 1  p  =  �  µp (B1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' {z})  � 1  p ,  Up(0) = 1,  and  Up(z) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  By applying Holder’s inequality, we have  �ˆ  B1  |∇Up|p0 dx  � 1  p0  ≤ ω  1  p0 − 1  p  N  �ˆ  B1  |∇Up|p dx  � 1  p  ,  for every p > p0 > N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Moreover, thanks again to Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='7, we have  ˆ  B1  |Up|p0 dx ≤ CN,p  ˆ  B1  |∇Up|p0 dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Taking into account (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='2), the above inequality implies that the sequence {Up}p>N is bounded in  W 1,p0(B1) for every fixed p0 > N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Then, there exists U∞ ∈ W 1,p0(B1) ∩ C(B1) such that {Up}p>N  converges to U∞ weakly in W 1,p0(B1) and uniformly in B1, up to taking a sequence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Thanks  to a standard argument, we have that {Up}p>N converges to U∞ weakly in W 1,q(B1) for every  20  BRASCO, PRINARI, AND ZAGATI  p0 ≤ q < ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Thanks to the claimed convergence, we get that  �ˆ  B1  |∇U∞|q dx  � 1  q  ≤ lim inf  p→∞  �ˆ  B1  |∇Up|q dx  � 1  q  ≤ lim inf  p→∞ ω  1  q − 1  p  N  �ˆ  B1  |∇Up|p dx  � 1  p  = ω  1  q  N lim inf  p→∞  �  µp(B1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' {z})  � 1  p ,  for every q ≥ p0,  and, by sending q to ∞ and recalling (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='2), it holds that  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='3)  1 ≥ lim inf  p→∞  �  µp(B1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' {z})  � 1  p ≥ ∥∇U∞∥L∞(B1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Hence U∞ is a 1−Lipschitz continuous function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Accordingly, we get  ∥∇U∞∥L∞(B1) ≥ |U∞(0)|  dB1(0) = 1,  which, combined with (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='3), gives the conclusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  □  Remark 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Thanks to Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='1 part (1), fixed a point z ∈ ∂B1, we can define  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='4)  µp(B1) :=  min  u∈W 1,p(B1)  �ˆ  B1  |∇u|p dx : u(0) = 1 and u(z) = 0  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Moreover, as an easy consequence of Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='1, when p > N we get the following estimate  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='5)  |u(x0) − u(z)| ≤  R1− N  p  �  µp(B1)  � 1  p ∥∇u∥Lp(BR(x0)),  for u ∈ W 1,p(BR(x0)) and z ∈ ∂BR(x0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Corollary 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='3 (Sharp Morrey constant).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Let N < p < ∞ and let Ω ⊆ RN be an open set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' We  define the sharp Morrey constant  mp(Ω) :=  inf  u∈C∞  0 (Ω)  �ˆ  Ω  |∇u|p dx : [u]C0,αp(Ω) = 1  �  ,  where αp := 1 − N  p .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Then the constant mp(Ω) is independent of Ω, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' we have  mp(Ω) = mp(RN).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Moreover, we have  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='6)  µp(B1) ≤ mp(RN) ≤ N ωN  �p − N  p − 1  �p−1  ,  and  lim  p→∞  �  mp(RN)  � 1  p = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' We first show that mp(Ω) is independent of Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' The fact that mp(RN) ≤ mp(Ω) follows by  monotonicity with respect to sets inclusion and the fact that  [u]C0,αp(Ω) = [u]C0,αp(RN),  for every u ∈ C∞  0 (Ω),  see (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  SOBOLEV EMBEDDINGS AND DISTANCE FUNCTIONS  21  In order to show that mp(Ω) ≤ mp(RN), let u ∈ C∞  0 (RN) and let  ur(x) = u  �x − x0  r  �  ,  with x0 ∈ RN and r > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Since u has compact support, we have ur ∈ C∞  0 (Ω) for some suitable x0 and r small enough.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Then,  by scaling and thanks to (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='2), it holds  mp(Ω) ≤  ˆ  Ω  |∇ur|p dx  [ur]p  C0,αp(Ω)  =  ˆ  RN |∇ur|p dx  [ur]p  C0,αp(RN)  =  ˆ  RN |∇u|p dx  [u]p  C0,αp(RN)  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  By taking the infimum on C∞  0 (RN) on the right-hand side, we get the claimed inequality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  We now come to the proof of (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Let u ∈ C∞  0 (RN), for the lower bound it is sufficient to prove  that  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='7)  |u(x) − u(y)| ≤  1  �  µp(B1)  � 1  p ∥∇u∥Lp(Ω) |x − y|αp,  for every x, y ∈ RN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  If x = y, then (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='7) trivially holds, thus let us assume that x ̸= y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Without loss of generality, we  assume u(x) > u(y) and we define  v(z) := u(z) − u(y)  u(x) − u(y),  for z ∈ RN,  which satisfies v(x) = 1 and v(y) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Since v ∈ W 1,p(BR(x)) with R = |x − y|, we have from (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='5)  that  1 = |v(x)| ≤  |x − y|αp  �  µp(B1)  � 1  p ∥∇v∥Lp(BR(x)) =  |x − y|αp  �  µp(B1)  � 1  p  1  |u(x) − u(y)| ∥∇u∥Lp(BR(x)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  From this estimate, we get  |u(x) − u(y)| ≤  |x − y|αp  �  µp(B1)  � 1  p ∥∇u∥Lp(BR(x)) ≤  |x − y|αp  �  µp(B1)  � 1  p ∥∇u∥Lp(RN),  which is the claimed inequality (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  As for the upper bound, for every u ∈ C∞  0 (B1) \\ {0}, by the first part of the proof and the very  definition of mp, we have  mp(RN) = mp(B1) ≤  ∥∇u∥p  Lp(B1)  [u]p  C0,αp(B1)  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Moreover, by using that u is compactly supported in B1, we have  [u]C0,αp(B1) ≥  sup  x∈B1,y∈∂B1  |u(x)|  |x − y|αp ≥ |u(0)|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Thus, for every u ∈ C∞  0 (B1) such that |u(0)| ̸= 0, we get  mp(RN) ≤  ∥∇u∥p  Lp(B1)  |u(0)|p  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  22  BRASCO, PRINARI, AND ZAGATI  By density, the last estimate is still true for functions u ∈ W 1,p  0  (B1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Now we consider the function  u(x) = (1 − |x|  p−N  p−1 ) ∈ W 1,p  0  (B1),  hence there exists un ∈ C∞  0 (B1) such that un converges to u in W 1,p  0  (B1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Since  [u]C0,αp(B1) =  sup  x̸=y,x,y∈B1  ���|x|  p−N  p−1 − |y|  p−N  p−1  ���  |x − y|αp  ≥ 1,  it holds that  �  mp(RN)  � 1  p ≤ lim inf  n→∞  ∥∇un∥Lp(RN)  [un]C0,αp(RN)  ≤ lim sup  n→∞  (N ωN)  1  p  �p − N  p − 1  � p−1  p  [un]C0,αp(B1)  ≤ (N ωN)  1  p  �p − N  p − 1  � p−1  p  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  This shows the claimed upper bound.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Finally, by taking the p−rooth in (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='6) and using (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='1), we get the desired asymptotics for mp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  □  The following Hardy inequality for general open sets was originally proved for q = p in [30] (see  also [20] and [38]), without determination of an explicit constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' The latter can be found in [4, 15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  We generalize the result to cover the case p ≤ q ≤ ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' We will pay due attention to the asymptotic  behaviour of the sharp constant, as p goes to ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='4 (Hardy’s inequality).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Let N < p ≤ q ≤ ∞ and let Ω ⊊ RN be an open set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' We set  hp,q(Ω) =  inf  u∈C∞  0 (Ω)  �  �  �  �  �  ˆ  Ω  |∇u|p dx :  ������  u  d  N  q + p−N  p  Ω  ������  Lq(Ω)  = 1  �  �  �  �  �  ,  for p < q ≤ ∞,  and  hp(Ω) =  inf  u∈C∞  0 (Ω)  �ˆ  Ω  |∇u|p dx :  ����  u  dΩ  ����  Lp(Ω)  = 1  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  We have that  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='8)  hp,q(Ω) ≥  �  hp(Ω)  � p  q �  hp,∞(Ω)  � q−p  q ,  for p < q < ∞,  and  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='9)  hp(Ω) ≥  �p − N  p  �p  ,  hp,∞(Ω) ≥ µp(B1),  where µp(B1) is the same constant as in (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Moreover, it holds  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='10)  lim  p→∞  �  hp(Ω)  � 1  p = lim  p→∞  �  hp,∞(Ω)  � 1  p = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' We first prove the lower bound in the extremal case, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' for q = ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Let x ∈ Ω and let  x ∈ ∂Ω be such that  |x − x| = dΩ(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  For every u ∈ C∞  0 (Ω) and every p > N, we thus get  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='11)  |u(x)| ≤ dΩ(x)1− N  p  (µp(B1))  1  p  �ˆ  BdΩ(x)(x)  |∇u|p dx  � 1  p  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  SOBOLEV EMBEDDINGS AND DISTANCE FUNCTIONS  23  By taking the supremum over Ω, we get  ������  u  d  1− N  p  Ω  ������  L∞(Ω)  ≤  1  (µp(B1))  1  p  �ˆ  RN |∇u|p dx  � 1  p  ,  for every u ∈ C∞  0 (Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  This gives the desired Hardy inequality result for q = ∞, together with the claimed lower bound  in (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' In the case p = q, the estimate in (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='9) comes from [4, 15], as already recalled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  The case p < q < ∞ now simply follows from interpolation of the two endpoints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Indeed, for  every u ∈ C∞  0 (Ω), we have  �ˆ  Ω  |u|q  dγ q  Ω  dx  � p  q  ≤  �ˆ  Ω  |u|p  dp  Ω  dx  � p  q  ������  u  d  γ q−p  q−p  Ω  ������  (q−p) p  q  L∞(Ω)  where we set for simplicity  γ = N  q + p − N  p  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  We observe that  γ q − p  q − p = 1 − N  p ,  thus by using the definitions of hp(Ω) and hp,∞(Ω), we obtain  �ˆ  Ω  |u|q  dγ q  Ω  dx  � p  q  ≤  �  1  hp(Ω)  � p  q �  1  hp,∞(Ω)  � q−p  q  ˆ  Ω  |∇u|p dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  By taking the infimum over u ∈ C∞  0 (Ω), we get the lower bound (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  In order to prove the last statement, for the case q = ∞, from (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='9) and Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='1 we have  lim inf  p→∞  �  hp,∞(Ω)  � 1  p ≥ lim  p→∞  �  µp(B1)  � 1  p = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  In the case p = q, we directly have  lim inf  p→∞  �  hp(Ω)  � 1  p ≥ lim  p→∞  p − N  p  = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  In order to prove that the lim sup is smaller than or equal to 1, it is sufficient to use a suitable trial  function: for every x0 ∈ Ω, we have that  ϕ(x) =  �  r − |x − x0|  �  + ∈ W 1,p  0  (Ω),  for r = dΩ(x0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Since p > N, we can infer existence of a sequence {ϕn}n∈N ⊂ C∞  0 (Ω) such that  lim  n→∞ ∥∇ϕn − ∇ϕ∥Lp(Ω) = lim  n→∞ ∥ϕn − ϕ∥L∞(Ω) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Thus we get  �  hp,∞(Ω)  � 1  p ≤ lim  n→∞  ∥∇ϕn∥Lp(Ω)  ������  ϕn  d  p−N  p  Ω  ������  L∞(Ω)  =  (ωN rN)  1  p  ������  ϕ  d  p−N  p  Ω  ������  L∞(Ω)  ,  24  BRASCO, PRINARI, AND ZAGATI  and  �  hp(Ω)  � 1  p ≤ lim  n→∞  ∥∇ϕn∥Lp(Ω)  ����  ϕn  dΩ  ����  Lp(Ω)  = (ωN rN)  1  p  ����  ϕ  dΩ  ����  Lp(Ω)  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  By using that  lim  p→∞  (ωN rN)  1  p  ������  ϕ  d  p−N  p  Ω  ������  L∞(Ω)  = lim  p→∞  (ωN rN)  1  p  ����  ϕ  dΩ  ����  Lp(Ω)  =  inf  x∈Br(x0)  dΩ(x)  (r − |x − x0|)+  ≤ dΩ(x0)  r  = 1,  we then obtain the desired conclusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  □  Remark 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' By a standard density argument, for every p > N and p ≤ q ≤ ∞ the Hardy  inequality  hp,q(Ω)  ������  u  d  N  q + p−N  p  Ω  ������  p  Lq(Ω)  ≤  ˆ  Ω  |∇u|p dx,  still holds in both spaces D1,p  0 (Ω) and W 1,p  0  (Ω), for every open set Ω ⊊ RN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Embedding theorems  For the ease of presentation of our main embedding results, we distinguish between three cases:  the case q < p;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  the case q = p with Ω having finite inradius;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  the case q = p with Ω being a quasibounded set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Then, in the final subsection, we will briefly discuss the case q > p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' The case q < p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Let 1 ≤ q < p < ∞ and let Ω ⊊ RN be an open set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' The following facts hold:  (i) we have that  D1,p  0 (Ω) �→ Lq(Ω)  =⇒  dΩ ∈ L  p q  p−q (Ω),  and the following upper bound holds  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='1)  λp,q(Ω)  �ˆ  Ω  d  p q  p−q  Ω  dx  � p−q  q  ≤ λp(B1);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  (ii) moreover, if N < p < ∞, then we also have  dΩ ∈ L  p q  p−q (Ω)  =⇒  D1,p  0 (Ω) �→ Lq(Ω),  and the following lower bound holds  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='2)  hp(Ω) ≤ λp,q(Ω)  �ˆ  Ω  d  p q  p−q  Ω  dx  � p−q  q  ,  where hp(Ω) is the sharp Hardy constant (see Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='4);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  SOBOLEV EMBEDDINGS AND DISTANCE FUNCTIONS  25  (iii) finally, if p ≤ N, there exists an open set T ⊊ RN such that  dT ∈ L1(T ) ∩ L∞(T )  but  D1,p  0 (T ) ̸�→ Lq(T ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' We prove each point separately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  (i) Let x0 ∈ Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Since both wB1  p,q and wΩ  p,q are continuous functions, evaluating the lower bound  in [10, Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='2] at x = x0 and r = dΩ(x0), we get  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='3)  dΩ(x0)  p  p−q wB1  p,q(0) ≤ wΩ  p,q(x0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Then, by raising to the power q both sides of (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='3), integrating on Ω and exploiting (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='14),  we get  ˆ  Ω  d  p q  p−q  Ω  dx ≤  �  wB1  p,q(0)  �−q ˆ  Ω  (wΩ  p,q)q(x) dx =  �  wB1  p,q(0)  �−q  �  1  λp,q(Ω)  �  q  p−q  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  By using (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='17) for the ball B1  �  wB1  p,q(0)  �−q ≤  �  λp(B1)  �  q  p−q ,  we get the claimed summability of dΩ, together with the upper bound in (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  (ii) Let us suppose that dΩ ∈ L  p q  p−q (Ω) and p > N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' For every u ∈ C∞  0 (Ω), a joint application  of H¨older’s and Hardy’s inequalities (see Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='4) leads to  ˆ  Ω  |u|q dx ≤  �ˆ  Ω  |u|p  d p  Ω  dx  � q  p �ˆ  Ω  d  p q  p−q  Ω  dx  � p−q  p  ≤  �  hp(Ω)  �− q  p �ˆ  Ω  |∇u|p dx  � q  p �ˆ  Ω  d  p q  p−q  Ω  dx  � p−q  p  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  This in turn implies that  ˆ  Ω  |∇u|p dx  �ˆ  Ω  |u|q dx  � p  q ≥  hp(Ω)  �ˆ  Ω  d  p q  p−q  Ω  dx  � p−q  q .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  By taking the infimum on C∞  0 (Ω) on the left-hand side, we get the lower bound in (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  This in particular shows that λp,q(Ω) > 0, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' we have the embedding  D1,p  0 (Ω) �→ Lq(Ω),  as desired.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  (iii) We construct an open set T ⊆ RN such that, under the assumption 1 < p ≤ N  dT ∈ L1(T ) ∩ L∞(T ), hence dT ∈ Lα(T ) for every α ∈ [1, +∞];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  D1,p  0 (T ) is not compactly embedded in Lq(T ), for every 1 ≤ q < p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  We consider the (N − 1)−dimensional open hypercube Q = (0, 1)N−1 ⊆ RN−1 and we  define  Ck = Q × (k, k + 1],  for every k ∈ N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  26  BRASCO, PRINARI, AND ZAGATI  Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' The construction of the set T .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' The horizontal dashed lines denote the  separation lines between the cubes Ck.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' The dashed circular line highlights the ball  with maximal radius rT .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Then, for every k ∈ N, we take a dyadic partition of Ck, made of 2k N cubes with side  length 2−k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' We indicate by Ck(j) each of these cubes, with j = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' , 2k N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' We also denote  by xk(j) the center of the cube Ck(j) and by  Sk :=  �  xk(i) : 1 ≤ i ≤ 2k N�  ,  the collection of all these centers, at a given k ∈ N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Finally, we call infinite fragile tower  the open set given by  T =  �  k∈N  (Ck \\ Sk) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  We first show that the condition dT ∈ L1(T ) ∩ L∞(T ) is satisfied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Indeed, we first observe  that  rT = 5  12,  which implies that dT ∈ L∞(T ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Moreover, we have  dT (x) ≤ 2−k−1 √  N,  for x ∈ Ck(j) \\ {xk(j)},  j = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' , 2k N and k ∈ N,  by construction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Then  ˆ  T  dT dx =  �  k∈N  2kN  �  j=1  ˆ  Ck(j)\\{xk(j)}  dT dx  ≤  √  N  2  �  k∈N  � 1  2k  �  |Ck \\ Sk| =  √  N  2  �  k∈N  � 1  2k  �  =  √  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  SOBOLEV EMBEDDINGS AND DISTANCE FUNCTIONS  27  We now show that for every 1 ≤ q < p ≤ N, we have  λp,q(T ) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  This would imply that D1,p  0 (T ) is not continuously embedded in Lq(T ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' At this aim, for  every m ∈ N, we introduce the truncated tower  Tm =  � m  �  k=0  (Ck \\ Sk)  �  \\ (Q × {m + 1}).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  This is a bounded open set contained in T , thus, by monotonicity with respect to set  inclusion, we have  λp,q(T ) ≤ λp,q(Tm).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Therefore, in order to get the desired conclusion, it is sufficient to show that  lim  m→∞ λp,q(Tm) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Since p ≤ N, we know that points have zero p−capacity and thus we have (see [36, Chapter  17])  λp,q(Tm) = λp,q(Q × (0, m + 1)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  By appealing to [8, Main Theorem], the last quantity can be estimated from above by  λp,q(Q × (0, m + 1)) ≤  �πp,q  2  �p  �  HN−1(Q × (0, m + 1))  |Q × (0, m + 1)|1− 1  p + 1  q  �p  ≤  �πp,q  2  �p  �  2 (N − 1) (m + 1) + 2  (m + 1)1− 1  p + 1  q  �p  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  By using that q < p, it is easily seen that the last term converges to 0, as m goes to ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  This gives the desired conclusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  The proof is now over.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  □  Before proceeding further, a couple of comments are in order on the geometric estimates obtained  in the previous result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Remark 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' For p = 2, the lower bound (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='1) has been obtained in [7, Theorem 3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' The proof  there is simpler: up to some technical issues, it is simply based on using the trial function dΩ in  the definition of λ2,q(Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' However, this produces a poorer estimate: observe that the constant  appearing in [7, equation (9)] blows-up as q ↗ p = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' This is not the case for our estimate (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Remark 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Let N < p < ∞, 1 ≤ q < p and let Ω ⊆ RN be an open set, such that |Ω| < ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' If  dΩ ∈ L  p q  p−q (Ω), then, from the lower bound in (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='2), we get  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='4)  λp,q(Ω) |Ω|  p−q  q  ≥ hp(Ω)  rp  Ω  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  This is an extension to general open sets of the geometric estimate contained in [10, Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  The constant hp(Ω) is very likely not to be sharp, it would be interesting to determine the sharp  constant for (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  28  BRASCO, PRINARI, AND ZAGATI  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' The case p = q: continuity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Let 1 < p < ∞ and let Ω ⊊ RN be an open set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' The following facts hold:  (i) we have that  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='5)  D1,p  0 (Ω) �→ Lp(Ω)  =⇒  dΩ ∈ L∞(Ω),  and the following upper bound holds  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='6)  λp(Ω) rp  Ω ≤ λp(B1);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  (ii) moreover, if N < p < ∞, then we also have  dΩ ∈ L∞(Ω)  =⇒  D1,p  0 (Ω) �→ Lp(Ω),  and the following lower bound holds  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='7)  hp(Ω) ≤ λp(Ω) rp  Ω;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  (iii) finally, if p ≤ N, then for the open set P := RN \\ ZN we have  dP ∈ L∞(P)  but  D1,p  0 (P) ̸�→ Lp(P).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  (i) Let λp(Ω) > 0 and let {Brn(xn)}n∈N ⊆ Ω be a sequence of balls such that rn  converges to rΩ as n goes to ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Thanks to the monotonicity with respect to sets inclusion  of λp, we get that  λp(Ω) ≤ λp(Brn(xn)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  In particular, using the scaling properties of λp, we obtain that  r p  n ≤ λp(B1)  λp(Ω) ,  and, by sending n to ∞, we get rΩ < +∞ and the upper bound in (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='6);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  (ii) let us suppose that rΩ < +∞ and N < p < ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' By applying the Hardy inequality of  Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='4, we have that  ˆ  Ω  |u|p dx ≤ r p  Ω  ˆ  Ω  |u|p  dp  Ω  dx ≤  1  hp(Ω) r p  Ω  ˆ  Ω  |∇u|p dx,  for every u ∈ C∞  0 (Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  By taking the infimum on C∞  0 (Ω), we get the lower bound in (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  In particular, if  rΩ < +∞, then λp(Ω) > 0 and thus the continuous embedding D1,p  0 (Ω) �→ Lp(Ω) holds  true;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  (iii) it is sufficient to note that  λp(P) ≤ λp(Bm \\ ZN),  for every m ∈ N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Thanks to the assumption p ≤ N, again by [36, Chapter 17] it holds  λp(Bm \\ ZN) = λp(Bm).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  By using the scale property of λp, we get that  λp(P) ≤ lim  m→∞ λp(Bm) = lim  m→∞  λp(B1)  mp  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  This gives the desired conclusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  The proof is concluded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  □  SOBOLEV EMBEDDINGS AND DISTANCE FUNCTIONS  29  Remark 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' For p > N, the lower bound (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='7) is an extension to general open sets with finite  inradius of the Hersch-Protter-Kajikiya inequality  λp(Ω) ≥  �πp  2  �p 1  rp  Ω  ,  which is valid for every Ω ⊆ RN open convex set and every 1 < p < ∞ (see [19, 33] for the case  p = 2 and [27] for the general case).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Such an extension can be also found in [34, Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='1],  with a different proof and a poorer constant: the result in [34] is stated for bounded open sets,  however a closer inspection of the proof reveals that it still works for open sets with finite inradius.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Here as well, it would be very interesting to determine the sharp constant CN,p such that for  every Ω ⊆ RN open set with finite inradius, we have  λp(Ω) ≥ CN,p  rp  Ω  ,  for every N < p < ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  We observe that by (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='7) and (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='9), we have  CN,p ≥  �p − N  p  �p  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' The case p = q: compactness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Let 1 < p < ∞ and let Ω ⊊ RN be an open set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' The following facts hold:  (i) we have that  D1,p  0 (Ω) �→ Lp(Ω) is compact  =⇒  Ω is quasibounded;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  (ii) moreover, if N < p < ∞, then we also have  Ω is quasibounded  =⇒  D1,p  0 (Ω) �→ Lp(Ω) is compact;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  (iii) finally, if p ≤ N and T ⊊ RN is the same open set of Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='1, then T is quasibounded  and the embedding D1,p  0 (T ) �→ Lp(T ) is continuous, but not compact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  (i) This follows from [1, Example 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' For completeness, we sketch the idea of the  proof: let us suppose that Ω is not quasibounded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Then there exists a sequence of balls  {Br(xn)}n∈N ⊆ Ω, with r > 0 fixed and  lim  n→∞ |xn| = +∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  We consider ψ ∈ C∞  0 (B1) \\ {0} and then we simply set  ψn(x) = ψ  �x − xn  r  �  ,  for x ∈ Br(xn), n ∈ N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  It is easily seen that {ψn}n∈N is bounded in D1,p  0 (Ω), but it can not converge in Lp(Ω);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  (ii) this result can be found in [2, Theorem 2], but here we give an alternative proof, which relies  on the Hardy inequality of Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Let p > N and assume that Ω is quasibounded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' By  Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='4, we already know that D1,p  0 (Ω) is a functional space, continuously embedded  in Lp(Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Let {un}n∈N ⊆ D1,p  0 (Ω) be a bounded sequence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' We can extend these functions  by 0 outside Ω and consider them as elements of W 1,p(RN).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' In order to apply the classical  Riesz–Fr´echet–Kolmogorov Theorem, we first observe that by Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='4 we have that  {un}n∈N is bounded in Lp(RN), as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  30  BRASCO, PRINARI, AND ZAGATI  Moreover, the bound on the Lp norm of the gradients guarantees that translations con-  verge to 0 in Lp(Ω) uniformly in n, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  lim  |h|→0 sup  n∈N  ˆ  RN |un(x + h) − un(x)|p dx = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  The crucial point is to exclude the “loss of mass at infinity”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  For this, we exploit the  assumption that Ω is quasibounded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' The latter entails that for every ε > 0, there exists  R > 0 such that  ∥dΩ∥L∞(Ω\\BR) < ε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Let ηR ∈ C∞(RN) be such that  0 ≤ ηR ≤ 1,  ηR = 1 in RN \\ BR+1,  ηR ≡ 0 in BR,  |∇ηR| ≤ C,  for some universal constant C > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Then  sup  n∈N  ∥∇(unηR)∥Lp(Ω) ≤ sup  n∈N  ∥∇un∥Lp(Ω) + C sup  n∈N  ∥un∥Lp(Ω) =: M < +∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Since the functions un ηR belong to D1,p  0 (Ω), by applying H¨older’s and Hardy’s inequalities  (see Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='4 and Remark 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='5), for every n ∈ N we have that  �ˆ  Ω\\BR+1  |un|p dx  � 1  p  ≤ ∥dΩ∥L∞(Ω\\BR)  �ˆ  Ω  |un ηR|p  dp  Ω  dx  � 1  p  ≤ ε hp(Ω)− 1  p  �ˆ  Ω  |∇(un ηR)|p dx  � 1  p  ≤ ε hp(Ω)− 1  p M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  We can thus appeal to the Riesz–Fr´echet–Kolmogorov Theorem and get that, up to a  subsequence, {un}n∈N strongly converges in Lp(Ω);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  (iii) we consider the set T defined as in the proof of Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='1 part (iii).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Since dT ∈ L1(T ), by  applying Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='3, we have that T is quasibounded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Moreover, the embedding D1,p  0 (T ) �→  Lp(T ) holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Indeed, it is sufficient to notice that T is bounded in one direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Thus, by  Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='5, we can infer  W 1,p  0  (T ) = D1,p  0 (T ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  However, the embedding D1,p  0 (T ) �→ Lp(T ) can not be compact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Indeed, we take v ∈  C∞  0 (Q × (0, 1)) not identically zero and we build a bounded sequence {vk}k∈N by simply  translating v in the vertical direction, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' for every k ∈ N we set  vk(x′, xN) = v(x′, xN − k),  for every (x′, xN) ∈ Q × (k, k + 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  By appealing again to [36, Chapter 17], we have that  vk ∈ C∞  0 (Q × (k, k + 1)) ⊆ W 1,p  0  (Q × (k, k + 1))  = W 1,p  0  ((Q × (k, k + 1)) \\ Sk) ⊆ W 1,p  0  (T ) = D1,p  0 (T ),  for every k ∈ N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Hence, the sequence {vk}k∈N is bounded in D1,p  0 (T ) and ∥vk∥Lp(T ) > 0 is  constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' This shows that {vk}k∈N can not admit a converging subsequence in Lp(T ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  This concludes the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  □  SOBOLEV EMBEDDINGS AND DISTANCE FUNCTIONS  31  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' The super-homogeneous case q > p and beyond.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' In what follows, for an open set Ω ⊆ RN  and for 0 < β ≤ 1, we consider the space  C0,β(Ω) =  �  u ∈ Cbound(Ω) : [u]C0,β(Ω) < +∞  �  ,  endowed with the standard norm  ∥u∥C0,β(Ω) = ∥u∥L∞(Ω) + [u]C0,β(Ω),  for every u ∈ C0,β(Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  As a consequence of the previous embedding results, we can draw the following picture, for the case  N < p < q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' The proof is essentially an exercise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Corollary 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Let p > N and let Ω ⊊ RN be an open set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' The following facts hold:  (i) if dΩ ∈ L∞(Ω), then we have  D1,p  0 (Ω) �→ Lq(Ω),  for every p ≤ q ≤ ∞,  and  D1,p  0 (Ω) �→ C0(Ω) ∩ C0,β(Ω),  for every 0 < β ≤ αp;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  (ii) if Ω is quasibounded, then the above embeddings are compact, for  p ≤ q ≤ ∞  and  0 < β < αp;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  (iii) if dΩ ∈ Lγ(Ω), for some 1 ≤ γ < ∞, then we have  D1,p  0 (Ω) �→ Lq(Ω),  for every  p γ  p + γ ≤ q ≤ ∞,  and such an embedding is compact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  (i) Let dΩ ∈ L∞(Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' The existence of the embedding D1,p  0 (Ω) �→ Lp(Ω) is a consequence  of Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='4 part (ii).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' By using the Gagliardo-Nirenberg interpolation inequality (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='5)  with q = p, it follows that D1,p  0 (Ω) is continuously embedded in every Lq(Ω) with p ≤ q ≤ ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  As for the embedding in H¨older spaces: we observe at first that from the embedding  D1,p  0 (Ω) �→ L∞(Ω), we obtain that each {un}n∈N ⊂ C∞  0 (Ω) which is a Cauchy sequence in  the norm of D1,p  0 (Ω), is a Cauchy sequence in the sup norm, as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Thus, by recalling the  definition of the completion space C0(Ω), we get that D1,p  0 (Ω) �→ C0(Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' By using this fact  and Corollary 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='3, we thus get that D1,p  0 (Ω) is continuously embedded in C0(Ω)∩C0,αp(Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Then Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='2 gives the desired conclusion;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  (ii) we now suppose that Ω is quasibounded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' In order to prove the first statement, it is sufficient  to observe that the embedding D1,p  0 (Ω) �→ Lq(Ω) is compact for q = p thanks to Theorem  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='6 part (ii).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' By applying again the Gagliardo-Nirenberg inequality (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='5) with q = p, we  conclude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  The case of C0(Ω) ∩ C0,β(Ω) follows as above, by combining Morrey’s inequality and  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  (iii) we first recall that the assumption dΩ ∈ Lγ(Ω), for some 1 ≤ γ < ∞, implies that Ω is  a quasibounded set (see Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' The compact embedding D1,p  0 (Ω) �→ Lq(Ω) easily  follows by Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='1 part (ii), when q = p γ/(p+γ), while the case q = ∞ was just proved  in the part (ii) above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' We conclude, by interpolation, that the embedding is compact for  every p γ/(p + γ) ≤ q ≤ ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  The proof is now complete  □  32  BRASCO, PRINARI, AND ZAGATI  Remark 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' It is not difficult to see that the compact embedding of Corollary 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='7 part (ii) does  not extend up to the borderline case β = αp = 1 − N/p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' This can be seen by means of a standard  scaling argument: take Ω = B1 and ψ ∈ C∞  0 (B1) \\ {0}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' We define the sequence  ψn(x) = n  N−p  p  ψ(n x),  for n ∈ N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  It is easily seen that  ∥∇ψn∥Lp(B1) = ∥∇ψ∥Lp(B1)  and  [ψn]C0,αp(B1) = [ψ]C0,αp(B1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  On the other hand, by construction, we have that ψn converges uniformly to 0 as n goes to ∞,  since N − p < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Thus, for this sequence we can not have convergence in the norm of C0,αp(B1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  We complete the previous result by giving some geometric estimates for the generalized principal  frequencies λp,q in the case N < p < q, as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Corollary 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Let N < p < ∞, p ≤ q ≤ ∞ and let Ω ⊊ RN be an open set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' We have that  λp,q(Ω) > 0  ⇐⇒  rΩ < +∞,  and  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='8)  hp,q(Ω)  r  p−N+N p  q  Ω  ≤ λp,q(Ω) ≤ λp,q(B1)  r  p−N+N p  q  Ω  ,  with hp,q(Ω) defined in Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Moreover, if Ω is quasibounded, then there exists up,q ∈  W 1,p  0  (Ω) which solves  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='9)  λp,q(Ω) =  inf  u∈W 1,p  0  (Ω)  �ˆ  Ω  |∇u|p dx : ∥u∥Lq(Ω) = 1  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Let us assume λp,q(Ω) > 0 and let {Brn(xn)}n∈N ⊆ Ω be a sequence of balls such that rn  goes to rΩ, as n goes to ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' As in the proof of Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='4 part (i), it follows that  r  p−N+N p  q  n  ≤ λp,q(B1)  λp,q(Ω) ,  and, by sending n to ∞, we get rΩ < +∞ and the upper bound in (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  In order to prove the reverse implication, we first observe that this has already been proved in  Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='4 for the case q = p part (ii).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' For the case p < q ≤ ∞, it is sufficient to use the same  argument, in conjuction with the general Hardy inequality of Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' This comes with the  lower bound in (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' We leave the details to the reader.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  We now come to the existence part, under the stronger assumption that Ω is quasibounded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  We first observe that the identity (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='9) follows from Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Moreover, the assumption on Ω,  Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='4 and Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='5 guarantee that we have  D1,p  0 (Ω) = W 1,p  0  (Ω),  thanks to Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' The existence of a minimizer is now an easy consequence of the Direct  Method in the Calculus of Variations, once observed that W 1,p  0  (Ω) is weakly closed and that we  have the compact embeddings of Corollary 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='7 at our disposal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  □  Remark 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' We notice that the value of λp,∞(B1) can be made explicit: according to [35,  Theorem 2E] we have  λp,∞(B1) =  �p − N  p − 1  �p−1  N ωN,  for p > N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  SOBOLEV EMBEDDINGS AND DISTANCE FUNCTIONS  33  This implies that the upper bound for the sharp Morrey constant in (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='6) can be rewritten as  mp(RN) ≤ λp,∞(B1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Moreover, such a value is uniquely attained by the functions  u(x) = ±  �  1 − |x|  p−N  p−1  �  + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  We refer to [17, 22] for a thorough study of the variational problem associated to λp,∞, in the case  of bounded sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Asymptotics  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Asymptotics for λp,q(Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Corollary 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Let 1 ≤ q < ∞ and let Ω ⊊ RN be an open set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Then  lim  p→∞  �  λp,q(Ω)  � 1  p =  1  ∥dΩ∥Lq(Ω)  ,  and  lim  p→∞  �  λp,∞(Ω)  � 1  p = 1  rΩ  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  In the previous equations, the right-hand sides have to be considered 0, if dΩ ̸∈ Lq(Ω) or rΩ = +∞,  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' We start with the case q = ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' If rΩ = +∞, thanks to Corollary 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='9, there is nothing to  prove.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Let us assume rΩ < +∞, it is sufficient to take the p−rooth in (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='8) and use that  lim  p→∞  �  λp,∞(B1)  � 1  p = 1,  (see Remark 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='10) and (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' This gives the desired conclusion as p goes to ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  We now consider the case q < ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' We first suppose that dΩ ∈ Lq(Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Observe that for every p > 2 q,  we have  dΩ(x)  p q  p−q ≤ r  q2  p−q  Ω  dΩ(x)q ≤  �  max{1, rΩ}  �q  dΩ(x)q,  for every x ∈ Ω,  thus we can apply the Dominated Convergence Theorem to get that  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='1)  lim  p→∞  �ˆ  Ω  d  p q  p−q  Ω  dx  � p−q  q p  =  �ˆ  Ω  d q  Ω dx  � 1  q  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Moreover, by Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='1, for every p > q and p > N, we have the two-sided estimate  hp(Ω) ≤ λp,q(Ω)  �ˆ  Ω  d  p q  p−q  Ω  dx  � p−q  q  ≤ λp(B1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  By raising this estimate to the power 1/p, using (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='10), (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='1) and the following fact  lim  p→∞  �  λp(B1)  � 1  p = 1,  (see [26, Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='5]), we get the desired conclusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  34  BRASCO, PRINARI, AND ZAGATI  We now suppose that dΩ /∈ Lq(Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Let n0 ∈ N such that Ωn := Ω ∩ Bn ̸= ∅ for every n ≥ n0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  By applying the first part of this proof to the set Ωn with n ≥ n0, we have that  lim  p→∞  �  λp,q(Ωn)  � 1  p =  1  ∥dΩn∥Lq(Ωn)  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Hence, by using the monotonicity of λp,q with respect to the set inclusion, we get that  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='2)  lim sup  p→∞  �  λp,q(Ω)  � 1  p ≤  1  ∥dΩn∥Lq(Ωn)  ,  for every n ≥ n0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' We extend each distance function dΩn equal to 0 in RN \\ Ωn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' We note that the  family {dΩn}n≥n0 is not decreasing with respect to n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Thus, in order to conclude, it is sufficient to  prove that  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='3)  lim  n→∞ dΩn(x) = dΩ(x),  for every x ∈ Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Indeed, by passing to the limit in (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='2) as n goes to ∞ and by using Monotone Convergence  Theorem, we get that  lim sup  p→∞  �  λp,q(Ω)  � 1  p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  In order to show (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='3), we note that, for every x ∈ Ω, there exists nx ≥ n0 such that BdΩ(x)(x) ⊆ Ωn,  for every n ≥ nx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' This implies that  dΩ(x) = dΩn(x),  for every n ≥ nx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  This concludes the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  □  Corollary 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Let N < p < ∞ and let Ω ⊊ RN be an open set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Then  lim  q→∞ λp,q(Ω) = λp,∞(Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Let ψ ∈ C∞  0 (Ω) \\ {0}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' By definition of λp,q(Ω) we have that, for every q ≥ p, it holds  λp,q(Ω) ≤  ˆ  Ω  |∇ψ|p dx  �ˆ  Ω  |ψ|q dx  � p  q .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  If we now take the limit as q goes to ∞, we get  lim sup  q→∞ λp,q(Ω) ≤ lim  q→∞  ˆ  Ω  |∇ψ|p dx  �ˆ  Ω  |ψ|q dx  � p  q =  ˆ  Ω  |∇ψ|p dx  ∥ψ∥ p  L∞(Ω)  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  By arbitrariness of ψ and recalling the definition of λp,∞(Ω), we obtain  lim sup  q→∞ λp,q(Ω) ≤ λp,∞(Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  In order to show the converse inequality, we can assume that λp,∞(Ω) > 0, otherwise from the  previous inequality we already get the desired result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Since p > N, by Corollary 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='9 we have that  SOBOLEV EMBEDDINGS AND DISTANCE FUNCTIONS  35  rΩ < +∞ and thus λp(Ω) > 0, as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Then, for every u ∈ C∞  0 (Ω) \\ {0} and for every p < q < ∞  it holds  ∥u∥Lq(Ω) ≤ ∥u∥  p  q  Lp(Ω) ∥u∥  1− p  q  L∞(Ω) ≤  �  λp(Ω)  �− 1  q ∥∇u∥  p  q  Lp(Ω) ∥u∥  1− p  q  L∞(Ω),  by interpolation in Lebesgue spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Hence, we have the following lower bound  ∥∇u∥Lp(Ω)  ∥u∥Lq(Ω)  ≥  �  λp(Ω)  � 1  q ∥∇u∥  1− p  q  Lp(Ω)  ∥u∥  1− p  q  L∞(Ω)  ≥  �  λp(Ω)  � 1  q �  λp,∞(Ω)  � q−p  p q .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  By raising to the power p on both sides and taking the infimum on C∞  0 (Ω) \\ {0} on the left-hand  side, this yields  λp,q(Ω) ≥  �  λp(Ω)  � p  q �  λp,∞(Ω)  � q−p  q .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  By sending q to ∞ in this inequality, we get  lim inf  q→∞ λp,q(Ω) ≥ λp,∞(Ω),  as desired.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  □  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Asymptotics for the solution of the Lane-Emden equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Let Ω ⊊ RN be an open  connected set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' In this subsection we will assume that 1 ≤ q < ∞ and dΩ ∈ Lq(Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' By Lemma  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='1, the last assumption entails that dΩ ∈ L∞(Ω), as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Thus, by interpolation, we have that  dΩ ∈ L(p q)/(p−q)(Ω) for every q < p < ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Hence, by Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='1, Ω is (p, q)−admissible for every  p > max{N, q} and, by [10, Corollary 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='4], there exists a unique positive solution wΩ  p,q to (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='10) for  every q < p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' In the following theorem, we will study the asymptotic behavior of wΩ  p,q, as p goes to  ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Theorem 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Let 1 ≤ q < ∞ and let Ω ⊊ RN be an open connected set such that dΩ ∈ Lq(Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Then  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='4)  lim  p→∞ ∥wΩ  p,q − dΩ∥Lr(Ω) = 0  and  lim  p→∞ ∥wΩ  p,q − dΩ∥C0,β(Ω) = 0  for every q ≤ r ≤ ∞ and every 0 < β < 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' We will first show that (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='4) holds to r = q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Then, by interpolation, we will obtain all the  other claimed convergences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Part 1: convergence in Lq(Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' We extend each function wΩ  p,q to RN by setting it to be zero in  RN \\ Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' First of all, we note that, by using (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='14) and Corollary 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='1, we have  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='5)  lim  p→∞  ˆ  Ω  |∇wΩ  p,q|p dx = lim  p→∞  ˆ  Ω  |wΩ  p,q|q dx = lim  p→∞  �  �  �  1  �  λp,q(Ω)  � 1  p  �  �  �  p q  p−q  =  ˆ  Ω  d q  Ω dx,  which implies  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='6)  lim  p→∞ ∥∇wΩ  p,q||Lp(Ω) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Moreover, by applying (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='5), we find the upper bound  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='7)  0 < wΩ  p,q(x) ≤  dΩ(x)αp  �  µp(B1)  � 1  p ∥∇wΩ  p,q∥Lp(Ω),  for every x ∈ Ω,  36  BRASCO, PRINARI, AND ZAGATI  where αp = 1 − N/p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' On the other hand, thanks to (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='3), we obtain the lower bound  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='8)  (dΩ(x))  p  p−q wB1  p,q(0) ≤ wΩ  p,q(x),  for every x ∈ Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  By sending p to ∞ in (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='7) and (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='8) and taking into account (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='1), (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='6) and (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='15), we get that  lim  p→∞ wΩ  p,q(x) = dΩ(x),  for every x ∈ Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  The pointwise convergence, combined with the convergence of the Lq norm given by (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='5), implies  that  lim  p→∞ ∥wΩ  p,q − dΩ∥Lq(Ω) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Part 2: convergence in L∞(Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' By Corollary 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='7, we have that wΩ  p,q ∈ C0(Ω)∩C0,αp(Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Moreover,  by applying the estimate on the sharp Morrey constant of Corollary 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='3, we have that wΩ  p,q satisfies  [wΩ  p,q]C0,αp(Ω) ≤  �  1  mp(Ω)  � 1  p  ∥∇wΩ  p,q∥Lp(Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  By using (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='6) and Corollary 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='3, we have  lim sup  p→∞ [wΩ  p,q]C0,αp(Ω) ≤ 1,  and thus in particular the seminorms [wΩ  p,q]C0,αp(Ω) are uniformly bounded, for p large enough.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' We  also observe that by Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='2, we have  [dΩ]C0,αp(Ω) ≤ (2 rΩ)1−αp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  We now apply Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='2 to wΩ  p,q − dΩ, with α = αp and γ = q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Thus, for every 0 < β < 1 and  every p such that αp > β, we have  [wΩ  p,q − dΩ]C0,β(Ω) ≤ C1 ∥wΩ  p,q − dΩ∥θp  Lq(Ω) [wΩ  p,q − dΩ]1−θp  C0,αp(Ω),  with θp = αp − β  αp + N  q  ,  and  ∥wΩ  p,q − dΩ∥L∞(Ω) ≤ C2 ∥wΩ  p,q − dΩ∥χp  Lq(Ω) [wΩ  p,q − dΩ]1−χp  C0,αp(Ω),  with χp =  αp  αp + N  q  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  We observe that, for p diverging to ∞, the exponent αp goes to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Thus, the constants C1 and C2,  which depend on p through αp, stay uniformly bounded as p goes to ∞ (see Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='2 and Remark  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' By using this fact, the bound on the C0,αp seminorms inferred above and the convergence in  Lq proved in Part 1, the previous interpolation estimates give  lim  p→∞  �  ∥wΩ  p,q − dΩ∥L∞(Ω) + [wΩ  p,q − dΩ]C0,β(Ω)  �  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Finally, the convergence in Lr(Ω) for q < r < ∞ can be obtained by interpolation in Lebesgue  spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  □  SOBOLEV EMBEDDINGS AND DISTANCE FUNCTIONS  37  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Asymptotics for λp(Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' The following corollary generalizes the result shown, independently,  in [18, Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='1] and [26, Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' While these treat the case of bounded open sets, we  enlarge the result to cover every open set, without further restrictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Corollary 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Let Ω ⊊ RN be an open set, then  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='9)  lim  p→∞  �  λp(Ω)  � 1  p = 1  rΩ  ,  where the right-hand side has to be considered 0, if rΩ = +∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' First of all, we note that for every 0 < r < rΩ there exists a ball Br(xr) ⊆ Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Hence, by  applying [26, Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='5], it holds  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='10)  lim sup  p→∞  �  λp(Ω)  � 1  p ≤ lim sup  p→∞  �  λp(Br(xr))  � 1  p = 1  r .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  By sending r → rΩ, we get  lim sup  p→∞  �  λp(Ω)  � 1  p ≤ 1  rΩ  ,  where the right-hand side is 0 when rΩ = +∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' In order to obtain the reverse inequality when  rΩ < +∞, it is sufficient to apply (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='7) and (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='10), to get that  lim inf  p→∞  �  λp(Ω)  � 1  p ≥ 1  rΩ  lim  p→∞  �  hp(Ω)  � 1  p = 1  rΩ  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  This concludes the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  □  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Asymptotics for the first p−eigenfunction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' We first recall that for every function u ∈  W 1,∞(Ω) vanishing on the boundary ∂Ω, we have  |u(x)| ≤ dΩ(x) ∥∇u∥L∞(Ω),  for every x ∈ Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  This may be seen as a limit case of Hardy’s inequality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' In particular ± dΩ/rΩ is a solution of the  following minimization problem  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='11)  min  u∈W 1,∞(Ω)  �  ∥∇u∥L∞(Ω) : ∥u∥L∞(Ω) = 1, u ≡ 0 on ∂Ω  �  = 1  rΩ  ,  provided Ω has finite inradius.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Theorem 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Let Ω ⊊ RN be an open connected quasibounded set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Then, for every N < p < ∞,  there exists a unique positive solution up of the problem  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='12)  λp(Ω) =  min  u∈W 1,p  0  (Ω)  �ˆ  Ω  |∇u|p dx :  ˆ  Ω  |u|p dx = 1  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Moreover, the family {up}p>N is precompact in C0,β(Ω) for every 0 < β < 1 and every accumu-  lation point u∞ is a solution of (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='11), possibly different from dΩ/rΩ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' We first observe that λp(Ω) > 0, thanks to the assumption on Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Thus, by Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='5, we  have  W 1,p  0  (Ω) = D1,p  0 (Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  By Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='6, for every p > N the embedding W 1,p  0  (Ω) �→ Lp(Ω) is compact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Hence, by using  also Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='6, it follows that, for every p > N, there exists a positive solution up ∈ W 1,p  0  (Ω) of  the minimization problem (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='12).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Uniqueness can now be inferred by using the Benguria hidden  38  BRASCO, PRINARI, AND ZAGATI  convexity principle of [6, 29], for example, as generalized in [10, Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' See also [3] and [31]  for other proofs of the uniqueness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Without loss of generality, let {pn}n∈N be an increasing sequence diverging at ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' In particular,  there exists n0 ∈ N such that pn > N for every n ≥ n0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' We denote by upn the unique positive  solution of the problem defining λpn(Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' By applying (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='5) and (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='7), we find that  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='13)  |upn(x)| ≤  1  �  µpn(B1)  � 1  pn  �  λpn(Ω)  � 1  pn dΩ(x)αpn ,  for every x ∈ Ω,  and  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='14)  |upn(x) − upn(y)| ≤  1  �  µpn(B1)  � 1  pn  �  λpn(Ω)  � 1  pn |x − y|αpn ,  for every x, y ∈ Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Since Ω is quasibounded, the previous estimates assures that we can apply Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Thus,  we get that {upn}n≥n0 converges uniformly to a function u∞ ∈ C0(Ω), up to a subsequence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' By  passing to the limit in (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='13) and in (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='14) as n goes to ∞, we obtain that  |u∞(x)| ≤ 1  rΩ  dΩ(x),  for every x ∈ Ω,  and  |u∞(x) − u∞(y)| ≤ 1  rΩ  |x − y|,  for every x, y ∈ Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Observe that we also used (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='1) and (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' In particular u∞ ∈ W 1,∞(Ω) and it satisfies  ∥u∞∥L∞(Ω) ≤ 1  and  ∥∇u∞∥L∞(Ω) ≤ 1  rΩ  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  If we also prove that ∥u∞∥L∞(Ω) ≥ 1, we can conclude that u∞ is a minimizer for the problem  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='11).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  In order to show this, for every R > 0, we take ηR ∈ C∞(RN) such that  0 ≤ ηR ≤ 1,  ηR = 1 in RN \\ BR+1,  ηR = 0 in BR,  |∇ηR| ≤ C,  for some universal constant C > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Then  sup  n≥n0  ∥∇(upnηR)∥Lpn(Ω) ≤ sup  n≥n0  ∥∇upn∥Lpn(Ω) + C sup  n>N  ∥upn∥Lpn(Ω)  = sup  n≥n0  �  λpn(Ω)  � 1  pn + C  ≤ 1  rΩ  sup  n≥n0  �  λpn(B1)  � 1  pn + C =: M < +∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  We notice that M > 0 only depends on N and rΩ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Now, thanks to (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='10), there exists p > N such  that  �  hp(Ω)  � 1  p ≥ 1  2,  for every p ≥ p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Since Ω is quasibounded, for every 0 < ε ≤ 1/2, there exists Rε > 0 such that  ∥dΩ∥L∞(Ω\\BRϵ) <  ε  2 M .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  SOBOLEV EMBEDDINGS AND DISTANCE FUNCTIONS  39  By using the properties of η and applying H¨older’s and Hardy’s inequalities to upnηRε ∈ W 1,p  0  (Ω),  for every pn ≥ max{p, pn0}, we have that  ˆ  Ω\\BRε+1  |upn|pn dx =  ˆ  Ω\\BRε+1  |upnηRε|pn dx ≤ ∥dΩ∥ pn  L∞(Ω\\BRε)  ˆ  Ω  |upn ηRϵ|pn  d pn  Ω  dx  ≤ ∥dΩ∥ pn  L∞(Ω\\BRε)  1  hpn(Ω)  ˆ  Ω  |∇(upn ηRε)|pn dx  ≤ ε pn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Hence  1 =  ˆ  Ω\\BRε+1  |upn|pn dx +  ˆ  BRε+1  |upn|pn dx ≤ ε pn +  ˆ  BRε+1  |upn|pn dx,  that is  �  1 − ε pn� 1  pn ≤  �  ωN (Rϵ + 1)N� 1  pn  sup  BRϵ+1  |upn|,  for every pn ≥ max{p, pn0}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  By exploiting the uniform convergence of the family {upn}n≥n0 to u∞ on compact sets, if we take  the limit as n goes to ∞, we get  1 ≤ sup  BRε+1  |u∞| ≤ sup  Ω  |u∞|,  which proves the claim for every Ω quasibounded set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  In order to get the convergence in C0,β(Ω) for 0 < β < 1, we can use the same interpolation  argument as in Part 2 of the proof of Theorem 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' It is sufficient to observe that it holds  [u∞]C0,β(Ω) ≤ 21−β ∥u∞∥1−β  L∞(Ω) ∥∇u∞∥β  L∞(Ω),  an estimate that can be proved by repeating the proof of Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' We leave the details to the  reader.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  □  Remark 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' We underline that, differently from the case 1 ≤ q < p, when p = q it may happen  that the accumulation points of the family {up}p>N do not coincide with dΩ (see [18, Corollary  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='7]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' We refer to [17, Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='14] for a study of the multiplicity of extremals for problem (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='11),  in the case of open bounded sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  With the same arguments as in the previous proof, we can show a similar result for minimizers  of λp,∞(Ω), whose existence is given by Corollary 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='9 when Ω is quasibounded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' This generalizes  [17, Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' We omit the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Theorem 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Let N < p and let Ω ⊊ RN be a quasibounded open set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Let up,∞ ∈ W 1,p  0  (Ω) be a  positive solution of  λp,∞(Ω) =  min  u∈W 1,p  0  (Ω)  �ˆ  Ω  |∇u|p dx : ∥u∥L∞(Ω) = 1  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Then the family {up,∞}p>N is precompact in C0,β(Ω) for every 0 < β < 1 and every accumulation  point u∞ is a solution of (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='11).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  40  BRASCO, PRINARI, AND ZAGATI  Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' An infinite strip with slowly shrinking ends  In the next example, we consider a quasibounded open set for which dγ  Ω /∈ L1(RN), for any  0 < γ < ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Example A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' For every α > 0 and x1 ∈ R, we set  f1(x1) =  1  log (2 + x2  1)  and  fα(x1) = f1  �x1  α  �  =  1  log  �  2 +  �x1  α  �2�.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Then we consider the quasibounded open set  Ωα =  �  x = (x1, x2) ∈ R2 : x1 ∈ R, |x2| < fα(x1)  �  ,  with α2 > (log 2)−3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Observe that for this set we have dγ  Ω ̸∈ L1(Ω), for any 0 < γ < ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Thus, by Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='1 part (i),  we have  D1,2  0 (Ωα) ̸�→ Lq(Ωα),  for every 1 ≤ q < 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  On the other hand, since Ωα is bounded in the x2 direction, we easily get that λ2(Ωα) > 0, that is  D1,2  0 (Ωα) �→ L2(Ωα).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  As for the compactness of this embedding, we observe that this can not be directly inferred from  Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='4, since we are in the critical situation p = 2 = N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Nevertheless, we are going to show  that actually such an embedding is compact, thanks to the particular geometry of the set Ωα.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' In  particular, the Dirichlet-Laplacian on Ωα has a discrete spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  We define  Ωα,R := Ωα ∩  �  (−R, R) × (−R, R)  �  ,  for R ≥ R0 =  1  log 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  We denote by wΩα the torsion function of Ωα, defined as  wΩα := lim  R→∞ wΩα,R,  where wΩα,R ∈ W 1,2  0  (Ωα,R) is the torsion function of Ωα,R, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' it solves  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='1)  − ∆u = 1,  in Ωα,R,  (see [11, Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='2]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' In order to prove the compactness of the embedding of D1,2  0 (Ωα) �→  L2(Ωα), it is sufficient to prove that  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='2)  lim  R→∞ ∥wΩα∥L∞(Ω\\BR) = 0,  thanks to [11, Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' We will achieve (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='2) by exploiting the geometry of Ωα in order to  construct a suitable upper barrier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' For every α > 0 and x1 ∈ R, we set  F1(x1) = (f1(x1))2  and  Fα(x1) := F1  �x1  α  �  = (fα(x1))2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Observe that  ���F ′′  1  �x1  α  ���� ≤ 2 (log 2)−3,  thus, if we take α > 0 such that α2 > (log 2)−3, we obtain  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='3)  |F ′′  α(x1)| = 1  α2  ���F ′′  1  �x1  α  ���� ≤ 2 (1 − C),  for x1 ∈ R,  SOBOLEV EMBEDDINGS AND DISTANCE FUNCTIONS  41  for some C = C(α) ∈ (0, 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' With such a choice of α, we consider the function  Uα(x1, x2) = Fα(x1) − x2  2  2 C  ,  for every (x1, x2) ∈ Ωα.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  We claim that this is the desired upper barrier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Indeed, by construction we have Uα ≥ 0 and,  thanks to (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='3), it holds  −∆Uα(x1, x2) = 1  C − F ′′  α(x1)  2 C  ≥ 1,  for every (x1, x2) ∈ Ωα.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  By applying the Comparison Principle in every Ωα,R we get that  wΩα,R(x) ≤ Uα(x) ≤ Fα(x1)  2 C  ,  for every x = (x1, x2) ∈ Ωα,R,  and such an estimate does not depend on R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Hence, by sending R to ∞, we have that  wΩα(x) ≤ Fα(x1)  2 C  ,  for every x = (x1, x2) ∈ Ωα.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  By using the properties of Fα = (fα)2 and the previous estimate, we eventually get (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  References  [1] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Adams, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Fournier, Sobolev spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Second edition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Pure and Applied Mathematics (Amsterdam),  140.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Elsevier/Academic Press, Amsterdam, 2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' 3, 29  [2] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Adams, Compact Sobolev imbeddings for unbounded domains with discrete boundaries, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Anal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=', 24 (1968), 326–333.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' 29  [3] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Allegretto, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Huang, A Picone’s identity for the p−Laplacian and applications, Nonlinear Anal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=', 32  (1998), 819–830.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' 14, 38  [4] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Avkhadiev, Hardy type inequalities in higher dimensions with explicit estimate of constants, Lobachevskii  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=', 21 (2006), 3–31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' 22, 23  [5] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Bhattacharya, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Di Benedetto, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Manfredi, Limits as p → ∞ of ∆pup = f and related extremal problems,  Some topics in nonlinear PDEs (Turin, 1989).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Rend.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Sem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Mat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Univ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Politec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Torino 1989, Special Issue, 15–68  (1991).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' 6  [6] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Belloni, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Kawohl, A direct uniqueness proof for equations involving the p−Laplace operator, Manuscripta  Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=', 109 (2002), 229–231.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' 38  [7] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' van den Berg, Estimates for the torsion function and Sobolev constants, Potential Anal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=', 36 (2012), 607–616.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  3, 4, 27  [8] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Brasco, On principal frequencies and isoperimetric ratios in convex sets, Ann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Fac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Toulouse Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' (6),  29 (2020), 977–1005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' 27  [9] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Brasco, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Franzina, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Ruffini, Schr¨odinger operators with negative potentials and Lane-Emden densities,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Funct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Anal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=', 274 (2018), 1825–1863.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' 15  [10] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Brasco, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Prinari, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Zagati, A comparison principle for the Lane–Emden equation and applications to  geometric estimates, Nonlinear Analysis, 220 (2022), 112847 4, 10, 12, 13, 14, 25, 27, 35, 38  [11] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Brasco, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Ruffini, Compact Sobolev embeddings and torsion functions, Ann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Inst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Henri Poincar´e, Anal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Non Lin´eaire, 34 (2017), 817–843.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' 2, 3, 9, 15, 40  [12] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Briani, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Buttazzo, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Prinari, Some inequalities involving perimeter and torsional rigidity, Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Optim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=', 84 (2021), 2727–2741.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' 6  [13] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Bucur, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Buttazzo, On the characterization of the compact embedding of Sobolev spaces, Calc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Var.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Partial  Differential Equations, 44 (2012), 455–475.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' 3  [14] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Clark, An embedding theorem for function spaces, Pacific J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=', 19 (1965), 243–251.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' 3  [15] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Chen, Hardy-type inequalities and principal frequency of the p−Laplacian, preprint (2020), available at  arXiv:2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='06782v1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' 22, 23  [16] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Champion, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' De Pascale, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Jimenez, The ∞-eigenvalue problem and a problem of a optimal transportation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Anal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' 13 4 (2009), 547–565.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' 5  [17] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Ercole, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Pereira, Asymptotics for the best Sobolev constants and their extremal functions, Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Nachr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=',  289 (2016), 1433–1449 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' 5, 6, 33, 39  42  BRASCO, PRINARI, AND ZAGATI  [18] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Fukagai, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Ito, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Narukawa, Limit as p → ∞ of p−Laplace eigenvalue problems and L∞−inequality of  the Poincar´e type, Differential Integral Equations, 12 (1999), 183 – 206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' 5, 37, 39  [19] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Hersch, Sur la fr´equence fondamentale d’une membrane vibrante: ´evaluations par d´efaut et principe de  maximum, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Angew.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=', 11 (1960), 387–413.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' 29  [20] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Hajlasz, Pointwise Hardy inequalities, Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Amer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=', 127 (1999), 417– 423.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' 22  [21] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Hewitt, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Stromberg, Real and Abstract Analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' A modern treatment of the theory of functions of one  real variable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Springer-Verlag, New York, 1965.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' 7  [22] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Hynd, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Lindgren, Extremal functions for Morrey’s inequality in convex domains, Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Ann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=', 375 (2019),  1721–1743.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' 5, 33  [23] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Hynd, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Seuffert, Extremal functions for Morrey’s inequality, Arch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Ration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Mech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Anal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=', 241 (2021),  903–945.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' 6  [24] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Hynd, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Seuffert, Asymptotic flatness of Morrey extremals, Calc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Var.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Partial Differential Equations, 59  (2020), Paper No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' 159, 24 pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' 6  [25] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Hynd, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Seuffert, On the symmetry and monotonicity of Morrey extremals, Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Pure Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Anal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=',  19 (2020), 5285–5303.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' 6  [26] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Juutinen, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Lindqvist, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Manfredi, The ∞−eigenvalue problem, Arch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Rational Mech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Anal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=', 148 (1999),  89–105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' 5, 14, 33, 37  [27] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Kajikiya, A priori estimate for the first eigenvalue of the p−Laplacian, Differential Integral Equations, 28  (2015), 1011–1028.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' 29  [28] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Kawohl, On a family of torsional creep problems, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Reine Angew.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=', 410 (1990), 1–22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' 6  [29] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Kawohl, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Lucia, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Prashanth, Simplicity of the principal eigenvalue for indefinite quasilinear problems,  Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Differential Equations, 12 (2007), 407–434.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' 38  [30] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Lewis, Uniformly fat sets, Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Amer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=', 308 (1988), 177–196.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' 4, 22  [31] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Lindqvist, On the equation div(|∇u|p−2 ∇u)+λ |u|p−2 u = 0, Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Amer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=', 109 (1990), 157–164.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='  38  [32] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Maz’ya, Sobolev spaces with applications to elliptic partial differential equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Second, revised and aug-  mented edition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical  Sciences], 342.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Springer, Heidelberg, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' 2  [33] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Protter, A lower bound for the fundamental frequency of a convex region, Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Amer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=', 81  (1981), 65–70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' 29  [34] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Poliquin, Principal frequency of the p−Laplacian and the inradius of Euclidean domains, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Topol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Anal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=', 7  (2015), 505–511.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' 29  [35] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Talenti, Inequalities in rearrangement invariant function spaces, in Nonlinear Analysis, Function Spaces  and Applications, 5 (Prague, 1994), 177–230, Prometheus, Prague, 1994.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' 32  [36] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Tartar, An introduction to Sobolev spaces and interpolation spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Lecture Notes of the Unione Matematica  Italiana, 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Springer, Berlin;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' UMI, Bologna, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' 27, 28, 30  [37] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Trong, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Thanh, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Do, Hardy-Lane-Emden inequalities for p−Laplacian on arbitrary domains,  NoDEA Nonlinear Differential Equations Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=', 29 (2022), Paper No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' 59, 30 pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' 15  [38] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Wannebo, Hardy inequalities, Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Amer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=', 109 (1990), 85–95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' 4, 22  (L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Brasco) Dipartimento di Matematica e Informatica  Universit`a degli Studi di Ferrara  Via Machiavelli 35, 44121 Ferrara, Italy  Email address: lorenzo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='brasco@unife.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='it  (F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Prinari) Dipartimento di Scienze Agrarie, Alimentari e Agro-ambientali  Universit`a di Pisa  Via del Borghetto 80, 56124 Pisa, Italy  Email address: francesca.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='prinari@unipi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='it  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content=' Zagati) Dipartimento di Scienze Matematiche, Fisiche e Informatiche  Universit`a di Parma  Parco Area delle Scienze 53/a, Campus, 43124 Parma, Italy  Email address: annachiara.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='zagati@unipr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
+page_content='it' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9FPT4oBgHgl3EQfMjQS/content/2301.13026v1.pdf'}
diff --git a/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf b/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..926d1c926ca801b3e0821584ff76d0ad979d04b8
--- /dev/null
+++ b/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:0c74400d803d799b7c99831fa3bade73813bac7d2b2d8a727b42de58c3918280
+size 1818314
diff --git a/rtAyT4oBgHgl3EQfz_l6/vector_store/index.faiss b/rtAyT4oBgHgl3EQfz_l6/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..7c21f5f592fc38884a0cd5560d49a4b15666110f
--- /dev/null
+++ b/rtAyT4oBgHgl3EQfz_l6/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:c67a4585724559c526234fdc6af1df4a7008868631ba42f6f8b3d6e2417f6428
+size 17170477
diff --git a/rtAyT4oBgHgl3EQfz_l6/vector_store/index.pkl b/rtAyT4oBgHgl3EQfz_l6/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..b47f43ee8fd6a1207be0550b291ec2dc17efbe48
--- /dev/null
+++ b/rtAyT4oBgHgl3EQfz_l6/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:40e75565060d89bb8cfb092fdc2b9e647718c76e49ed53a119da5af2a756f40f
+size 536903
diff --git a/stE1T4oBgHgl3EQfjgQE/vector_store/index.faiss b/stE1T4oBgHgl3EQfjgQE/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..36be1c40246b6c4da84eedb1efcc8b968b6e33a7
--- /dev/null
+++ b/stE1T4oBgHgl3EQfjgQE/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:fc889428a4864421e735dcc66cf2d80a3340f75eabc11715ced7eb264af78237
+size 1966125
diff --git a/tNE3T4oBgHgl3EQfjwpk/content/tmp_files/2301.04591v1.pdf.txt b/tNE3T4oBgHgl3EQfjwpk/content/tmp_files/2301.04591v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..0bf39911eeed92d602e44341250ba89ea35757bb
--- /dev/null
+++ b/tNE3T4oBgHgl3EQfjwpk/content/tmp_files/2301.04591v1.pdf.txt
@@ -0,0 +1,1364 @@
+arXiv:2301.04591v1  [cs.CR]  11 Jan 2023
+MVAM: Multi-variant Attacks on Memory for IoT Trust Computing
+Arup Kumar Sarker∗, Md Khairul Islam†, Yuan Tian‡
+∗†University of Virginia, Charlottesville, VA 22904, USA, {djy8hg, mi3se}@virginia.edu
+‡University of California, Los Angeles, CA 90095-1405, USA yuant@ucla.edu
+Abstract—With the significant development of the Internet
+of Things and low-cost cloud services, the sensory and data
+processing requirements of IoT systems are continually going
+up. TrustZone is a hardware-protected Trusted Execution En-
+vironment (TEE) for ARM processors specifically designed for
+IoT handheld systems. It provides memory isolation techniques
+to protect the trusted application data from being exploited by
+malicious entities. In this work, we focus on identifying differ-
+ent vulnerabilities of the TrustZone extension of ARM Cortex-
+M processors. Then design and implement a threat model to
+execute those attacks. We have found that the TrustZone is
+vulnerable to buffer overflow based attacks. We have used this
+to create an attack called MOFlow and successfully leaked
+the data of another trusted app. This is done by intentionally
+overflowing the memory of one app to access the encrypted
+memory of other apps inside the secure world. We have also
+found that, by not validating the input parameters in the
+entry function, TrustZone has exposed a security weakness. We
+call this Achilles’ heel and present an attack model showing
+how to exploit this weakness too. Our proposed novel attacks
+are implemented and successfully tested on two recent ARM
+Cortex-M processors available on the market (M23 and M33).
+Index Terms—Trust Computing, IoT, TrustZone, Cortex-M,
+vulnerability, Instruction TCM(ITCM), Data TCM(DTCM)
+1. Introduction
+ARM TrustZone is an embedded security system for
+ARM Cortex processors. Recently, ARM included Trust-
+Zone into IoT computing with cortex-m processors. The
+benefit of TrustZone is its compact and lightweight nature,
+allowing for both worlds (Figure 1) to operate on a single
+processor core. Because of this secure operating system,
+ARM micro-controllers can store all system-essential li-
+braries and applications in a secure area [1]. The defense
+mechanism in TrustZone is to protect memory (physical and
+cache) and process. For example, memory in both worlds is
+isolated with a security attribute Unit (SAU), even the same
+app with different signatures running in two different worlds
+has to go with a robust verification process and execute in
+isolation. Work stretching across different applications, both
+secure and not secure, can do so through a software-based
+Figure 1. TrustZone Core Virtualization
+secure monitor which mediates between the two security
+worlds. This software-based secure monitor is executed on
+the same core as all the other processes, and thus consumes
+less power than the traditional approaches detailed above.
+Even with this, there are malicious attacks by observing
+entry and exit onto the address of cache, compromising the
+messaging channel between a non-secure process and secure
+process [2]. To target this problem, some research papers
+are used isolated cache protection design to narrow down
+the access space.
+Due to limited or not availability of cache, access
+
+in memory inside Trusted Execution Environment(TEE) is
+shared and not bound to specific secure kernel process. So,
+the TEE delineates specific memory addresses in accor-
+dance with their world. There is no tightly coupled memory
+dedicated to a specific app in the secure zone. A trusted
+execution environment can be easily exploited by leaking
+memory within the shared space. Without authorization
+or access to protected enclaves, the attacks can be quite
+effective at collecting the users’ private and secure data.
+This allows sensitive information to be stored out of reach
+for applications operating outside of the secure world.
+With the use of ARM TrustZone in the IoT ecosystem,
+memory access in these devices have a significant research
+focus within single and cloud with multiple connected smart
+devices. The goal of our study is to research and develop
+security exploit encrypted information to gather sensitive
+user information into the normal world. Although the secu-
+rity attribute Unit (SAU) ensures the security, certain input
+parameters might expose the access of secure memory if the
+developer forgets to check memory-bound checking non-
+secure callable zone. The system should have an automatic
+guard to validate the memory-bound checking. Poor imple-
+mentation at the nonsecure callable side might expose the
+potential loophole. This will create multiple openings for
+external attacks. A secure framework should not have APIs
+to get non-accessible data from the user level. TrustZone
+does not have any automatic internal memory management
+like with a high-level programming language. Moreover,
+security design and protection work differently in x86. Most
+of the low-level APIs are primitive and do not have any
+metrics to benchmark the security level. We have not found
+the API security validation from the ARM platform. A
+developer has to perform extensive operations for allocating
+memory and clearing them. Any intentional or unintentional
+memory leakage might expose the sensitive data even from
+the secure TrustZone memory.
+The proposed threat model of MOFlow is based on the
+experimental results and found memory leaks during the
+access to out-of-bound data even in the TrustZone secure
+world. We also find, using invalid parameters in the Entry
+function, it is possible to infiltrate the secure world. We
+call this an Achilles’ heel for the TrustZone security. These
+successful attacks will highlight security vulnerabilities in
+the current ARM Cortex-M processors which need to be
+addressed to ensure the safety of the IoT systems. This
+will also help us understand potential risks associated with
+TrustZone and improve the security of IoT trust computing.
+In short our contributions in this work are:
+•
+We have done a robust exploration of the security
+vulnerabilities during the communication in between
+normal and secure world in the ARM TrustZone
+Cortext-M processor and defined open scopes of
+possible compromise of the system.
+•
+We propose a threat model to exploit memory over-
+flow with intentional or unintentional fraudulent
+communication, encapsulated with security attribute
+unit along with mechanism for creating Achilles’s
+heel.
+•
+We also expose the APIs limitations and the implica-
+tion of a low-level framework that creates a possible
+loophole for the intruder.
+•
+We provide best practices for the defense improve-
+ment inside TrustZone based on the experimental
+results and analysis that includes an additional layer
+of verification.
+•
+Finally, we propose a trust model with TrustZone ex-
+tension APIs and verifier along with communication
+flows.
+Paper Organizations. The rest of the paper is organized
+as follows. Section 2 presents the backgrounds on TrustZone
+and its architecture. Section 3 explains the motivation behind
+the attacks and what was the expected outcome. Section
+3.4 has the design of the threat model. Then Section 3.5
+shows how we planned to apply it to ARM TrustZone.
+Section 4 presents the experimental setup. In Section 5
+we list the different types of attacks we performed on the
+TrustZone and its results. Discussions on the implications
+of our findings, possible mitigation plans against the attacks
+and future works are added in Section 6. Section 7 lists
+the related works. Section 8 contains the limitations of our
+work. And finally, Section 9 has the conclusion.
+2. Background
+There are multi-variety of designs in ARM TrustZone
+to ensure security. ARM Cortex M23 [3] and M33 [4] do
+not have any in-built cache because of the compact design
+and priority on security features. In ARM Cortex-M35P, the
+process cache is the primary element of in-memory design
+to create a bridge between the processor execution and the
+relatively slower memory access. In the TrustZone-M design
+both instruction and data, a memory is expanded with an
+additional feature called an NS flag which helps to identify
+the security domain. This flag bit will be used to isolate
+the memory. These lines are not accessible from the normal
+world directly. But it is common for both worlds, during
+the execution of the processor. So the normal and secure
+world will try to use this memory line to support its running
+application.
+The main reason for this design is to maximize the
+utilization of the memory and improve system performance.
+ARM sets specific hardware to secure the access of memory
+by any world application. But the access pattern is not secure
+in simple designed cortex M33 or M23 where only a single
+memory unit is available. Moreover, M55 [5] has a robust
+memory with instruction and data. These will communi-
+cate with customs-designed newly introduced instruction
+and data Tightly-Coupled Memory (TCM). Access patterns
+between TCM to cache can be easily monitored by an
+attacker process, leaving TrustZone vulnerable for the cache
+access side-channel attacks. From the beginning of trust
+computing, there is a vast number of studies on Intel-based
+SGX secure container [6], [7], but very few studies are done
+on TrustZone [8], running on mobile platforms. A graphic
+overview of the cache-based attack is seen in Figure 2.
+
+Figure 2. A standard communication by using shared resources
+This security probing involved reading literature regard-
+ing the TrustZone-M architecture, control flow, and compo-
+nents. After re-framing the approach, the team began look-
+ing into previous effective cyber-attacks and the fundamental
+principles behind them. Though TrustZone-M provides a lot
+of new obstacles for attackers to overcome, we believed that
+certain attack models could be modified and applied to this
+security architecture. Throughout our literature exploration,
+we came across the MOFlow bug [9].
+The MOFlow bug relies on a TEE/Non-secure commu-
+nication with the standard API of TrustZone. A nonsecure
+app sends a short message to a secure app to check if the
+app is active in the background. When a secure UI/service
+app falls out of responses with another due to inactivity or
+being killed or crashed, it is needed to be able to check
+if they are still alive. There will be data inconsistencies
+due to interaction by the user or server or any connected
+apps in the IoT system. That encrypted piece of data is sent
+from another node to check its status or availability. When
+the crashed or killed secure node receives this request, it
+responds with the same piece of encrypted data to prove
+to the nonsecure app that the secure app is still in place.
+This is where the vulnerability lies. The request message
+also includes information about its length. Below, we will
+draw out a scenario of how communication can be used to
+extract information from a secure app [10].
+A normal world app is a malicious user and wants to
+extract sensitive information from the secure world app.
+So communication from Non-secure will go to secure for
+checking the availability of the service. The request consists
+of an encrypted message (e.g, 16KB lengths), but the normal
+world app intentionally lies about the length of the encrypted
+message and says that it is 128KB long (the maximum
+request length). The secure app receives this request and
+allocates a 128KB memory buffer to contain the encrypted
+message it is supposed to send back to the malicious app
+in Non-secure. The secure world then stores the 16KB
+encrypted message on the 128KB memory buffer and sends
+it back to the Non-secure. This is where the vulnerability
+lies. Security attributes in secure zone do not verify that
+the encrypted message length is equal to the length value
+provided. This tricks the secure world app into sending over
+112KB of possibly sensitive information.
+The lack of this safeguard on secure zone allowed
+malicious users to use the MOFlow vulnerability to extract
+data from unsuspecting secure world apps. In this work, we
+intend to perform the MOFlow attack to target an ARM
+TrustZone-enabled micro-controller. This attack requires an
+important assumption which we will make for this experi-
+ment: the malicious user has planted a buggy application on
+the secure world. This is an important assumption because,
+without a buggy application within the secure world, there
+is no avenue for the attacker to interface with the secure
+world. While this obstacle seems difficult to overcome, we
+believe that it is a plausible scenario. With the onset of
+IoT systems, particularly smart homes, the user is free to
+download and use third-party applications that provide ad-
+ditional features. This app store provides an avenue through
+which a malicious user could plant a seemingly innocuous
+application that contains a bug enabling MOFlow attacks.
+Any user that downloads this malicious application opens
+the door for attackers to execute the MOFlow attack on a
+TrustZone-enabled device. In Section 5.6, we have discussed
+the attack model tailoring MOFlow to TrustZone-enabled
+micro-controllers.
+3. Overview of Approach
+3.1. A Motivating Use Case
+To provide a motivating example, suppose there exists
+an IoT smart home device that is powered by a TrustZone-
+M enabled micro-controller. This smart home device can
+be connected to sensors such as a user’s smartwatch device,
+house lights, front door, and many other miscellaneous smart
+household IoT devices. The smart device can also interact
+with multiple cloud servers for each app that provides users
+the functionality to make purchases, check health statuses,
+and send messages and emails. If the MOFlow attack is
+proven to work within TrustZone-M devices it could lead
+to serious violations in the integrity of TrustZone’s secu-
+rity measures. Specifically for the described TrustZone-M
+powered IoT device, an attacker can publish a malicious
+application with memory leakage to the device’s affiliated
+marketplace and disguise the application as a seemingly
+innocent service that a user could end up downloading
+(similar to utterance checking) into their smart device’s
+
+Normal World
+Secure World
+Trusted
+Application
+Application
+TZ Library
+C3
+SSL
+TZ Daemon
+User
+User
+C3
+Privilege
+Privilege
+Trusted World
+TZ Driver
+SMC Interface
+Kernel
+Normal World Kernel
+Secure Monitor
+DRAMsecure zone. TrustZone applications can retrieve sensitive in-
+formation from the server to get access to a sensor and save
+it to the memory. From there, the malicious application is
+among different other legitimate applications for sensors that
+could have the functionality to retrieve sensitive information
+from a using shared memory space. The attacker could
+then invoke this compromised secure-world application by
+overflowing the secure memory space. If another sensor’s
+data is saved on the device, the attacker could gather the
+user’s device identifiers, device authentication key, and other
+data from the memory.
+3.2. Expected Robustness Properties
+Let’s define communication properties between Non −
+secure and T EE
+with a set of blocks instructions
+X{x1, x2, x3, ..., xn} ⇔ Y {y1, y2, y3, ..., yn}. If △m is the
+leakage memory, then the response of X from the T EE is,
+RX = OY + △m
+where OY , is the the expected allocated memory.
+The model tries to perform the maximum number of
+attacks on T EE and increase the number of successful
+attacks SN. Target is to maximize the amount of leaked
+memory, Fm with the generator function L. So,
+lim
+△m→ Fm f(△m) = L
+So for all instructions X{x1, x2, x3, ..., xn}, output re-
+sponse is generated with multiple equations as follows,
+Rx1 = △mx1 + Ox1
+Rx2 = △mx2 + Ox2
+Rx3 = △mx3 + Ox3
+· · ·
+Rxn = △mxn + Oxn
+To verify the robustness properties of T EE secure com-
+munications, △m should be 0, e.g.,
+△m = △mx1 + △mx2 + △mx3 + ... + △mxn = 0
+(1)
+In this paper, by performing a set of attacks, we will
+invalidate the robustness properties of T EE.
+3.3. Aligning Problems on ARM TrustZone
+We have done a robust study on normal-world user and
+kernel space and have learned of vulnerabilities allowing
+attackers to gain full control of the normal-world kernel
+space. It is possible to discern physical addresses from
+virtual information. Address translations play a vital role in
+allocating memory and are thus a prime area for an attack.
+By design, the whole memory is divided into multiple parts.
+Our first target is to find a path to access the secure memory.
+Moreover, the cycle counter can be used as a precision
+timer that is accessed by only super users. In addition, a
+non-privileged app can access information without super-
+user permissions and with no virtual to physical address
+translation or cycle count.
+This creates an opportunity for prime and probe attacks.
+To do that, there can be multiple scenarios. When a normal
+world app tries to access securely by not following the
+standard protocol, on the framework side, there should be
+some security measures to protect any kind of illegal access.
+Security Attribute Unit(SAU) and Implementation Defined
+Attribution Unit(IDAU) will raise kernel fault in response.
+What if the developer made the mistake of adding memory
+boundary checking in the non-secure callable? A normal
+world app will have access to the whole memory of a secure
+world. Many high-level programming languages have inbuilt
+garbage collectors to free allocated memory and handle
+memory leaks. If a system does not have a built-in garbage
+collector, it should have support at the framework level to
+handle memory leakage internally.
+ARM TrustZone is based on low-level language, As-
+sembly, and C. In these languages, developers have to
+manage every allocated memory checking. One of the major
+limitations in the ARM TrustZone framework is, it does
+not have any in-built memory management support, even
+for secure zones. This opens the door for the overflow
+of the memory in a secure zone and possible leakage of
+valuable data. In Figure 2, communication line C3 is the
+main way between normal world user and kernel space.
+With C3 superuser access, a non-privileged app gets access
+information without cycle count and address translation. C3
+is executed with a TrustZone daemon or library which needs
+an extensive authentication process for the execution in a
+secure world. But C3 has access to a nonsecure callable.
+Intentional memory accessible is possible with bad coding
+and generates Achilles’ heels. An attacker can get overflow
+memory data by using standard TrustZone API. No other
+apps, including TrustZone itself, will have a single idea
+about the theft of the information.
+3.4. Threat Model Design
+Based on the design by ARM, all cryptographic oper-
+ations are executed in an isolated environment [11], [12].
+That means API execution in a process of a cryptographic
+library like SSL is isolated in the secure world. We have
+designed our threat model based on the assumptions that
+there must be a channel of handshaking between the normal
+world and secure world data or instruction transmission.
+If those operations happen either on the SMC interface
+or TZ manager, then the attacker can easily get data by
+using standard protocol from a secure world and extracting
+necessary information to get the AES key. Because Zhang et
+al. [13] demonstrates a way of recovering the full AES128
+key using the application level attack in a shorter time.
+Now the main idea is to get data from the memory
+by overflowing the assigned data structure. All apps in the
+secure world use shared resources. Assigning memory to
+an app is a loosely coupled operation at the processor. If a
+malicious app overflows its memory scope, it can easily get
+
+data that was not assigned. Although the data is encrypted, it
+can be easily decrypted by using a T-table-based decryption
+mechanism. Moreover, input parameters play an important
+part in getting the level of access to a secure world. There
+is no standard system in the TrustZone framework to handle
+any fuzzy attacks. Developers might not check all the corner
+cases of access memory in non-secure callable parts. SAU
+and IDAU do not guarantee parameter level verification at
+non-secure callable regions. Here comes the Achilles heel.
+With that attacker can compromise the non-secure callable
+and get full access to secure world memory.
+The proposed threat model will work from the appli-
+cation level with user privilege, which does not have any
+assumption to break the hardware-enabled trust execution
+environment. So executing the code from normal world
+user space to kernel space does not need any API call or
+permission from the TZ library or TZ manager in kernel
+space. A malicious process in a secure space can run and
+infect any operation and remain intact inside an app. This
+process might have access to memory data with the back-
+door leakage. Based on this analogy, this threat model is
+more resilient in the IoT system and does not need any
+dependencies on the TrustZone specific platform. Based on
+this threat model, suppose, an attacker has both a secure and
+non-secure app, running on an IoT device, and he wants to
+steal information from other vendors’ apps running on the
+same device.
+Figure 3. The Proposed Threat Model
+In Figure 3, A2 is the malicious app that memory leaks.
+In ARM TrustZone, there is no support for handling mali-
+cious memory overflow, inside a secure zone. So, A2 will
+read data from the DRAM which was assigned to any other
+app, and send it back to the normal world by following the
+APIs of non-secure callable. Because in TrustZone memory,
+there is no tightly coupled memory bound to a specific app.
+As a result, even the TrustZone framework and no other app
+will detect the theft of information. For the simplicity of the
+threat model, we have excluded the decryption mechanism
+of secure data from the project scopes.
+Figure 4. ARM Cortext-M micro-controller modes
+3.5. Apply Threat Model to ARM TrustZone
+ARM Cortext-m is designed as a component of IoT
+ecosystem. As it is low power, TrustZone security extension
+is optional. That means, chipset vendor has the flexibity
+to design chip. For example, NXPLPC55S28 is based on
+Cortex-M33, but this board does not have TrustZone security
+extension. As it is low powered micro-controller, proces-
+sor works differently than ARM cortex-A. ARM Cortex-M
+processor works in two different modes in Figure-4. When
+running application software, the CPU is in Thread mode,
+and for handling exceptions, it is in Handler mode. When the
+processor exits reset, it enters Thread mode and exits Thread
+mode when all exceptions have been processed. Execution
+can be privileged or unprivileged in Thread mode. Execution
+is Privileged in Handler mode. Memory maps are used to
+divide the Secure and Normal worlds, and transitions are
+handled automatically in exception handling routines.That’s
+why multiple secure function entry points are supported by
+Armv8-M [14].
+Because of that, all access to different memory might be
+on multiple in parallel. Although SAU and IDAU protect the
+memory access with NS bit, what is transmitting from the
+secure zone does not have any control. Moreover, in both
+thread and handler mode, within the region of secure mem-
+ory, data access is performed based on the programming
+logic of secure memory. Attribute units are independent
+and do not have any influence on application features. This
+design opens research questions about the security flaws
+inside secure and non-secure callable and that’s how our
+proposed thread model has implications on the secure zone.
+4. Experimental Setup
+Multiple vendors develop board based on ARM Cortex-
+M along with development environment. Our primary anal-
+
+Processor Modes
+Non-Secure
+Secure
+Handler Mode
+Handler Mode
+Thread Mode
+Thread ModeA3
+A2
+A2
+A7
+A7
+A3
+A7
+A7
+A4
+A2
+A8
+A8
+A4
+A4
+A8
+A8Normal World
+Secure World
+Trusted
+Application
+Application
+TZ Library
+C3
+SSL
+个
+TZ
+Daemon
+User
+User
+C3
+Privilege
+Privilege
+Trusted
+TZ Driver
+A2
+Interface
+World Kernel
+SMC
+Defect by
+Normal World Kernel
+Overflow!
+Secure
+!!!!!
+Monitor
+DRAM
+A1
+A1
+A5
+A5
+A1
+A5
+A2
+A2
+A6
+A6
+A6-
+A2
+A2
+A6ysis for feasibility test, was started with QEMU emulator
+for RPI3 kernel in linux [15]–[17]. But we were unable
+to replicate the defined problem in target domain. Because,
+it doesn’t have TrustZone framework and the architecture
+is not comply the current state of the arts. NXP and
+Nuvoton released R&D board based on ARM cortex-M
+and we have used NXPLPC55S69 [18] and [19] Nuvoton
+M2351. Nuvoton-M2351 has a single core M23 processor
+and NXPLPC55S69 has a dual-core M33 processor with
+DRAM. Both of them have support for TrustZone instruc-
+tions. Our initial plan was to use the Cortex-M35P and
+M55 processors. Because they have the latest TrustZone
+implementation. Cortex-M55 has additional instruction and
+data tightly coupled memory. These are configurable to the
+specific app for the fixed memory location. Unfortunately,
+we couldn’t get either of them publicly available on the
+market. Or even if they were available, there were substantial
+amount of time delay for the delivery due to chip shortage.
+So, we chose the M23 and M33-based boards. We have
+also received an NXPLPC55S28 board, developed with a
+single ARM cortex M33 processor. But it does not have any
+support of TrustZone, so it couldn’t be used in this work.
+5. Attacks on ARM Cortex-M
+We have performed multiple attacks on Cortex M pro-
+cessors. Some attacks are failed due to security properties
+by ARM. Failed attacks are an Invalid transition from secure
+to the normal world, the invalid entry point from normal to
+secure world, and invalid data access from the normal world.
+We do have some success. Success attacks are Invalid input
+parameters in the entry function, we call it Achilles’ heel and
+steal Memory data inside a secure world, we call it Heart
+Bleed. In the next subsections, we will describe in detail
+all attacks. Source codes for all of the attacks are publicly
+available on https://github.com/arupcsedu/MVAM.
+5.1. Memory Map
+Before going into details about our experiments, let’s
+check the run-time memory attribute map of ARM Cortex-
+M in Figure 5. We have exported this memory snapshot
+from the LPCNXP55S69 board, during running the program.
+We see the NS Program flash base is 0x0001 0000. The
+Secure Program flash base is 0x1000 0000. A Non-secure
+Callable, here with NXP, we call a Veneer Table, the entry
+point to secure area base is 0x1000 FE000. A combination
+of SAU (Secure Attribute unit) and IDAU (Implementation
+Defined Attribution Unit) ensures the separation of each
+memory footprint with security. Here SAU is internal with
+a processor and IDAU is external units, normally designed
+by chipset vendors, for example, NXP has that flexibility to
+design IDAU.
+Figure 5. Memory map of Secure, Non-Secure and Non-Secure Callable
+5.2. Invalid Transition From Secure to Normal
+World
+In this attack, a direct address to non-secure RESET is
+used to jump into the normal world. There are two issues
+related to this approach in Listing-1. First, all core registers
+are not clear so there is a potential data leak. Second, the
+most LSB of address into the normal world has to be cleared.
+We have not performed those and the requirement is not met
+for the transition to the normal world. As a result, a secure
+fault is generated by SAU.
+#define CODE_START_NS 0x00010000
+#define AHB_LAYERS_COUNT 12U
+#define NON_SECURE_START CODE_START_NS
+if (testCaseNumber ==
+FAULT_INV_S_TO_NS_TRANS)
+{
+funcptr_ns ResetHandler_ns;
+/* Non-secure main stack address */
+__TZ_set_MSP_NS(*((uint32_t
+
+SAU+IDAU
+MPC/PPC
+ResultingSecurityLevel
+NS
+NS-User
+NS
+-
+RAMO
+0x20008000
+0x20007FFF
+NS
+S-Priv
+Noaccess
+0x20000000
+0x14007FFF
+SRAMX (alias)
+NS-User
+5
+0x1400_0000
+0x1301_FFFF
+Boot-ROM (alias)
+NS-User
+0x13000000
+0x1009_FFFF
+S
+NS-User
+FLASH (alias)
+0x10010000
+NSC
+S-Priv
+NSC
+0x1000FFFF
+VeneerTable
+0x1000FE00
+0x1000FDFF
+S-Priv
+5
+Secure Code
+0x1000_0000
+0x0400_7FFF
+SRAMX
+NS
+NS-User
+NS
+0x0400_0000
+0x0301_FFFF
+Boot-ROM
+NS
+NS-User
+NS
+0x03000000
+0x0009 FFFF
+NS
+NS-User
+NS
+0x00078000
+0x0007-7FFF
+PROGRAMFLASH
+NS
+NS-User
+NS
+Non-secure Code
+0x00010000
+0x0000FFFF
+NS
+S-Priv
+No.access
+0000000x*)(NON_SECURE_START)));
+/* Initialize the non-secure vector table
+*/
+SCB_NS->VTOR = NON_SECURE_START;
+/* Function pointer for the Non-secure
+reset handler */
+ResetHandler_ns =
+(funcptr_ns)(*((uint32_t
+*)((NON_SECURE_START) + 4U)));
+/* Invalid switch to non secure */
+__asm("BXNS %0" : : "r"(ResetHandler_ns));
+}
+Listing 1. Attack with Invalid Transition From Secure to Normal World
+Both
+issues
+can
+be
+solved
+by
+using
+the
+cmse nonsecure call keyword attribute. If this attribute
+is used for a function call to a normal world, the compiler
+will do three things. First, clear all used registers to avoid
+potential data leak. Second, clear LSB address bit. Third,
+jump to address using BXNS instruction. The BXNS
+instruction causes a branch to an address and instruction
+set specified by a register and causes a transition from
+the Secure to the Non-secure domain. This variant of
+the instruction must only be used when additional steps
+required to make such a transition safe are taken [20].
+5.3. Invalid Entry From Normal to Secure World
+In Listing-2, a function pointer, PRINTF NSE is in-
+tentionally increased by 4. It is defined with a non-secure
+callable function DbgConsole Printf NSE in the veneer ta-
+ble. By this the Secure Gateway(SG) instruction is skipped,
+when a function is called. This causes an illegal entry point
+into a secure world and a secure fault is generated. The
+correct entry point into the secure world is ensured by using
+cmse nonsecure entry keyword attribute for every entry
+function so that it clears the register value and LSB address
+bit. Then the linker creates a veneer table for all entry
+functions with SG instructions.
+#define SEC_ADDRESS 0x10000000
+#define NONSEC_ADDRESS 0x20130000
+typedef void (*funcptr_t)(char const *s);
+#define PRINTF_NSE DbgConsole_Printf_NSE
+if (testCaseNumber == FAULT_INV_S_ENTRY)
+{
+func_ptr =
+(funcptr_t)((uint32_t)&PRINTF_NSE +
+4);
+func_ptr("Invalid Test Case\r\n");
+}
+/* Non-secure callable (entry) function */
+TZM_IS_NOSECURE_ENTRY void
+DbgConsole_Printf_NSE(char const *s)
+{
+size_t string_length;
+/* Access to non-secure memory from
+secure world has to be properly
+validated */
+/* Check whether string is properly
+terminated */
+string_length = strnlen(s,
+MAX_STRING_LENGTH);
+if ((string_length == MAX_STRING_LENGTH)
+&& (s[string_length] != ’\0’))
+{
+PRINTF("Input data error: String too
+long or invalid string
+termination!\r\n");
+abort();
+}
+PRINTF(s);
+}
+Listing 2. Attack with Invalid Transition From REE to TEE
+5.4. Invalid Data Access From Normal World
+In Listing - 3, the pointer is set to the address defined
+by NONSEC ADDRESS. This address has a non-secure
+attribute in SAU but it has a secure attribute in AHB secure
+controller. If data is read from this address, the data bus
+error is generated. Compared to attacks for accessing the
+memory address, SEC ADDRESS where the secure fault
+is generated, this error is caught by AHB secure controller,
+not by SAU. Because in the SAU this address is non-secure.
+So the access from the normal world is correct from SAU’s
+perspective. In the normal world, the application does not
+have access to secure memory.
+#define SEC_ADDRESS 0x10000000
+#define NONSEC_ADDRESS 0x20130000
+typedef void (*funcptr_t)(char const *s);
+#define PRINTF_NSE DbgConsole_Printf_NSE
+if (testCaseNumber ==
+FAULT_INV_NS_DATA_ACCESS)
+{
+test_ptr = (uint32_t *)(SEC_ADDRESS);
+test_value = *test_ptr;
+}
+Listing 3. Attack with Invalid data access to TEE
+5.5. Achilles’ Heel - Invalid Parameters in Entry
+Function
+In this attack, the input parameter is set to address
+0x10000000 in Listing-4. This address has a secure attribute
+(see SAU settings in the memory map picture). This secure
+violation is not detected by secure fault, since the input
+parameter is used by the secure function in a secure mode.
+So this function has access to the whole memory. However,
+every entry function should check the source of all input
+
+data to avoid potential data leaks from secure memory. The
+correctness of input data cannot be checked automatically.
+So, this function is an Achilles’ heel, which can be used to
+enter the secure world by using a valid secure location as an
+input parameter. This has to be checked by software, using
+TT instruction by publisher vendors to protect Achilles’ heel
+if the developer forgot to set a check in the NSC layer.
+#define SEC_ADDRESS 0x10000000
+#define NONSEC_ADDRESS 0x20130000
+typedef void (*funcptr_t)(char const *s);
+#define PRINTF_NSE DbgConsole_Printf_NSE
+if (testCaseNumber == FAULT_INV_S_ENTRY)
+{
+func_ptr =
+(funcptr_t)((uint32_t)&PRINTF_NSE +
+4);
+func_ptr("Invalid Test Case\r\n");
+}
+/* Non-secure callable (entry) function */
+TZM_IS_NOSECURE_ENTRY void
+DbgConsole_Printf_NSE(char const *s)
+{
+size_t string_length;
+/* Access to non-secure memory from
+secure world has to be properly
+validated */
+/* Check whether string is properly
+terminated */
+string_length = strnlen(s,
+MAX_STRING_LENGTH);
+if ((string_length == MAX_STRING_LENGTH)
+&& (s[string_length] != ’\0’))
+{
+PRINTF("Input data error: String too
+long or invalid string
+termination!\r\n");
+abort();
+}
+/* Check whether string is located in
+non-secure memory */
+#if (__GNUC__ != 10)
+if (cmse_check_address_range((void *)s,
+string_length, CMSE_NONSECURE |
+CMSE_MPU_READ) == NULL)
+{
+PRINTF("Achilles’ Heel exception:
+String is not located in normal
+world!\r\n");
+abort();
+}
+#endif
+PRINTF(s);
+}
+Listing 4. Achilles’ Heel Attack during access TEE with invalid input
+parameters
+5.6. MOFlow - Steal Memory Data Inside Secure
+World
+Along with the Achilles’ heel, we have implemented
+our threat model, MOFlow. In the MOFlow attacks, men-
+tioned in Listing-5 a secure attacker app(A2) with memory
+overflow is running on the secure zone. Here, moflow()
+function is implemented in the secure app which memory
+leaks. There are three other test apps(A1/A3/A5) running on
+the TrustZone memory which does not have any leakage.
+Because of memory overflow in A2, it is getting more en-
+crypted unassigned data from the memory which is allocated
+to other apps. A2 returns all data to the normal world by
+following the proper standard of TrustZone. Application,
+A1/A3/A5 and even TrustZone itself does not have a single
+idea about this stealing, as it is happening in a specific
+program space. With a T-table-based mechanism, it can be
+decrypted to actual data. Like in the MOFlow attacks, a
+secure zone is acting as a server and returning sensitive
+information to the normal world.
+#define FAULT_HEART_BLEED 0
+#define FAULT_INV_S_TO_NS_TRANS 1
+#define FAULT_INV_S_ENTRY 2
+#define FAULT_INV_NS_DATA_ACCESS 3
+#define FAULT_INV_INPUT_PARAMS 4
+#define FAULT_INV_NS_DATA2_ACCESS 5
+#define MAX_SMEM_SIZE 4e+9
+TZM_IS_NOSECURE_ENTRY char*
+GetDRAMData_NSE(void)
+{
+char leakData[MAX_SMEM_SIZE];
+char *lDataPtr = GetDRAMData();
+PRINTF("Read from Veneer Table:\n");
+for(int i = 0; i < MAX_SMEM_SIZE; i++)
+{
+leakData[i] = lDataPtr[i];
+printf("%c",leakData[i]);
+}
+leakData[MAX_SMEM_SIZE] = ’\0’;
+//strcpy(leakData, lDataPtr);
+return leakData;
+}
+char* GetDRAMData()
+{
+return leakedData;
+}
+void moflow()
+{
+char str[] = "I am malicious. Check my
+tail";
+testCaseNumber = FAULT_HEART_BLEED;
+int len = strlen(str);
+for(int i = 0; i < len + COM_DRAM_OFFSET;
+
+i++)
+{
+leakedData[i] = str[i];
+PRINTF("%c", leakedData[i]);
+}
+leakedData[len + COM_DRAM_OFFSET] = ’\0’;
+PRINTF("\nDecrypt the above data from my
+tail.\n");
+return ;
+}
+Listing 5. MOFlow Attack on TEE with buffer overflow
+6. Discussions
+6.1. Implications of Our Findings
+The Achilles’ heel attack (Section 5.5) indicates it is
+important to check the memory locations as an input pa-
+rameter. Without properly validating the inputs, they can
+be modified by an attacker and be used to compromise the
+execution of the target function. However, to the best of our
+knowledge, there is no automated tool available to detect
+invalid parameters. So developers would need to ensure their
+methods properly validate input parameters before using
+them for any sensitive process. Also, vendors would have to
+ensure software using their platform can prevent this kind of
+attack. The MOFlow attack ( Section 5.6 ) takes advantage
+of the lack of tight coupling memory with applications that
+are using them. So any trusted application can access the
+memory of another trusted app and read the encrypted data.
+Even though the application data is encrypted, hackers may
+exploit the encryption algorithm used in ARM TrustZone to
+decrypt the extracted data. Lapid et al. [21] showed using
+GPU-based analysis it is possible to crack the TrustZone
+implementation of AES. However, the SAU can be used to
+limit the applications from accessing others’ data and thus
+resolve this vulnerability.
+6.2. Mitigation plan
+By design, TrustZone ensures the security to access the
+secure world. No unauthorized app can access any user
+or kernel service inside a secure world. But ensuring the
+security of data within TEE is challenging. Ron et al. [22]
+showed how an attacker can run arbitrary code in a secure
+world and how to handle those attacks with protection
+measurements. These are designed on top of control-flow
+attacks [23], [24]. We will focus on the mitigation plan
+of protecting memory leakages and vulnerable points in
+non-secure callable so that any bad coding or intentional
+attacks are handled within the TrustZone framework. This
+will ensure the robustness of the system.
+Non-secure callable give the bridge to a normal world
+app for sending any data or instruction to a secure world.
+Without the proper, guard for checking memory boundary in
+the veneer table, a potential Achilles heel will be created and
+compromised the whole system. There should be a mech-
+anism inside the non-secure callable to check the memory
+boundary of a secure world. For example, in the Listing-
+6 below, cmse check address range() provides validity
+of incoming requests address range and blocks inside the
+non-secure callable regions for an Achilles heel.
+/* Check whether string is located in
+non-secure memory */
+#if (__GNUC__ != 10)
+if (cmse_check_address_range((void *)s,
+string_length, CMSE_NONSECURE |
+CMSE_MPU_READ) == NULL)
+{
+PRINTF("Achilles’ Heel exception:
+String is not located in normal
+world!\r\n");
+abort();
+}
+#endif
+Listing 6. Checking for a potential Achilles’ Heel attack
+A commercial application in the robust IoT ecosystems,
+multiple vendors will develop different kinds of services. To
+relay this kind of security checking on 3rd party application
+developers instead of automatic platform support is a risky
+design.
+The primitive APIs for memory management are ex-
+posed by TrustZone. Process and executing the business
+logic of certain services is vital and error prune even for
+ARM platform developers. Furthermore, if the vendor ap-
+plication developer does not have an in-depth understanding
+of the underlying security design, the internal memory map
+can be messed up. As a result, attackers may be able to
+read sensitive data from other memory locations or trigger
+a system crash. When the code reads a variable quantity of
+data and assumes that a sentinel, such as a NULL in a string,
+exists to terminate the read operation, a crash can occur.
+If the expected sentinel isn’t found in the out-of-bounds
+memory, too much data is read, resulting in a segmentation
+fault or a buffer overflow. Any instruction can change an
+index or execute pointer arithmetic on a memory address
+that is outside the buffer’s limits. Following that, a read
+operation yields undefined or unexpected results.
+To handle this, we are proposing an additional layer of
+security in between non-secure callable and secure zone.
+The purpose is to handle the abnormality of bad code inside
+the secure zone. This is expected that a 3rd party developer
+can write vulnerable code. The system should have a defense
+mechanism to find in various stages of development. We
+have not found any extensive tools to detect issues inside the
+secure applications with MCUExpress tools [25] by NXP.
+ARM provides tools for memory profiling for other chipset
+[26], not which has embedded TrustZone framework for 3rd
+party vendors. There are 3rd party C-based memory profilers
+[27]–[29] to analyze memory usage and highlight potential
+memory leak issues. But these are not customized for the
+profiling memory with security constraints. For example,
+root routes of new instances that could cause memory leaks.
+
+The root pathways provide information on why the instance
+is not freed. When determining how a memory leak happens,
+this is the most crucial information.
+To overcome MOFLow attacks, we have proposed
+a communication design flow mentioned in the Figure-6.
+There will be multiple components inside the non-secure
+callable and secure region of TrustZone and will comply
+with the security principle of SAU and IDAU.
+Figure 6. The Proposed Trust Model
+Non-secure callable (NSC) is a shared region (5) for
+both secure and non-secure execution. Boundary Verifier
+will cross-check the request from non-secure instruction
+(e.g. x1) and validate the address range. If it is valid, then
+TZ Interface APIs will be used for accessing the memory.
+Otherwise, an error (e.g. e1) will be generated for the non-
+secure process. Non-secure app might be multi-threaded and
+executes parallel instructions. The purpose of the handling
+error in NSC to isolate defected instructions outside of the
+secure zone with meaningful information in error set (e.g.
+E{e1, e2, e3, ..., en}). This will block all possible Achilles’
+heels in NSC.
+We propose two additional components for the secure
+zone. TZx APIs with leak collector is an extension frame-
+work, consists of an API set, build on top of primitive
+TrustZone APIs. These APIs will have leak collectors in
+related logic and solve the problem of circular dependencies
+on the shared resource. Verifier in the secure zone plays a
+vital role to protect MOFlow attacks. Whenever a non-secure
+process will try to access any information which is held
+by a data structure, the verifier checks the boundary of the
+allocated memory before responding to non-secure process.
+Data security in shared memory with blocked Achilles’s
+heels provides additional attributes for the robustness of the
+TrustZone.
+6.3. Future Works
+It is possible to further extend our attack model by
+reducing the search space inside the TrustZone for the target
+data. This can help to trace the data for a particular trusted
+application inside the secure zone faster. Thus stealing the
+data only for that target application. For example, Chen et
+al. [30] proposed a cache flushing-based side-channel attack
+on the ARM processors to reduce the search space to find
+a specific key value within the cache memory.
+7. Related Works
+Many of the recent TrustZone vulnerabilities are caused
+by cache attacks [31]. Cache-based side-channel attacks
+mainly focus on the execution time and trace of user’s ac-
+cesses during the cache operations to perform these attacks.
+Lipp et al. [32] used the lack of ‘cache flush‘ on old ARM
+cores (before ARMv8) to monitor cache activity within the
+ARM TrustZone from outside. The cache coherence proto-
+col allowed processors to fetch shared cache lines and thus
+exposing them to cache-based attacks. Taking advantage of
+the coherence protocol in a multiprocessor system, Yarom
+et al. [33] was able to examine cache lines of one core from
+another by flush and reload attack. Lapid et al. [21] exploited
+the misaligned T-table of the Keymaster Trustlet of ARM
+TrustZone in Samsung mobile and successfully extracted the
+AES-256 keys.
+Side-channel-based attacks also have been extensively
+studied on the ARM TrustZone. Chen et al. [30] was able to
+exploit a downgrade attack on TAs (Trusted Applications),
+by patching the old version onto the new one. The system’s
+vulnerability would let others replace the current trust with
+an old vulnerable one and use that to run the TA.
+DMA (Direct Memory Access) attacks are also contin-
+uously under research. Yahuda et al. [34] showed that by
+dumping memory frequently using DMA transactions, write
+patterns can be examined. In ARM TrustZone, they were
+able to extract RSA keys. The DAGGER tool [35] can steal
+cryptographic keys using a DMA-based keystroke logger. It
+can also attack the OS-kernel structure and file cache.
+The ARM debugging feature lets a host get read/write
+access to the TrustZone [36] and leak private keys. The
+defective ECDSA signing in Qualcomm’s implementation
+of Android’s hardware-backed Keystore let attackers extract
+a 256-bit private key from the key store [37].
+Current Work’s Limitations: Most of the attacks on
+ARM TrustZone focus on Cortex-A processors. However,
+the ARM Cortex-M processor is increasingly becoming
+more popular in Mobile and IoT applications. Because it
+is optimized specifically for them. Its design structure (fast
+hardware-based transition, no memory management, no-
+cache) is also much different from that of Cortex-A. So it
+is important to properly investigate possible vulnerabilities
+in its security protocols and TrustZone implementation.
+8. Limitations of Our Work
+The proposed attacks are done based on the assumption
+that we can install our vulnerable trusted application on the
+victim’s device. This might not be possible in some cases
+where the attacker doesn’t have access to the victim’s device.
+However, it is possible to modify applications that the victim
+trusts and use that to install the modified vulnerable app.
+
+ecure Callable
+Secure
+Invalid
+Boundary
+Verifier
+Verifier
+Primitive
+Valid
+TZ APIS
+TZx APIs
+with leak
+TZ
+collector
+nterface
+APIsEven though our attack model has successfully extracted
+other applications’ data from the secured zone, they are
+encrypted. So a separate tool will be needed to decrypt the
+data and make meaning out of it. However, some prior works
+have already been successful in cracking the encryption
+implementation of ARM TrustZone [21]. So it is possible to
+overcome this limitation. Our used processor ARM Cortex-
+M33 is not the latest release with the ARM TrustZone
+feature. Despite our best efforts, we were unable to find
+any development boards in the market with the latex ARM
+Cortex-M35P and M55 processors. So the attack models
+might not represent an exact evaluation of the state-of-the-
+art ARM architecture and countermeasures. However, due
+to the short time limit of the project, it was impossible to
+wait for development boards with a very long delivery time.
+9. Conclusion
+After performing a series of different attacks on the
+ARM Cortex-M micro-controller with the proposed threat
+model, the MOFlow and Achilles heel approaches were
+successfully able to access encrypted data from the secure
+world region. However, there are some key limitations and
+controlled factors that make this vulnerability less likely to
+occur organically. The successful MOFlow attack can only
+be performed if the attacker can gain access to the secure
+world of a TrustZone’s secure region. A potential route of
+work to improve the likelihood of a successful MOFlow
+attack in the wild is finding a way to reduce the search space
+in the secure zone region. Secondly, retrieving the victim’s
+sensitive data from the TrustZone-M micro-controller is only
+one step in the process. Since the information is encrypted in
+the secure region, an attacker would need to exploit the cor-
+rect decryption algorithm that TrustZone uses to obtain the
+plain-text information. One future route of work would be to
+investigate the implementation of TrustZone-M’s encryption
+and decryption algorithms and try to exploit them from the
+micro-controller. Doing so would enhance our current work
+significantly. Another opportunity for future work would be
+performing CacheTrack side-channel attacks on the Cortex-
+M35P or Cortex-M55 micro-controllers once their demand
+in the micro-controller market decreases. The Cortex-M35P
+and Cortex- M55 processors are considered state-of-the-art
+chips for TrustZone-M computing with instruction and data
+tightly coupled memory and there is a lack of research
+exploring these specific chips for novel vulnerabilities.
+References
+[1]
+S.
+Thornton,
+“Arm
+trustzone
+explained.”
+[Online].
+Available:
+https://www.microcontrollertips.com/embedded-security-brief-arm-trustzone-explained/
+[2]
+N. Liu, M. Yu, W. Zang, and R. S. Sandhu, “Cost and effectiveness of
+trustzone defense and side-channel attack on arm platform.” J. Wirel.
+Mob. Networks Ubiquitous Comput. Dependable Appl., vol. 11, no. 4,
+pp. 1–15, 2020.
+[3]
+ARM,
+“Cortex-m23.”
+[Online].
+Available:
+https://developer.arm.com/Processors/Cortex-M23
+[4]
+——,
+“Cortex-m33.”
+[Online].
+Available:
+https://developer.arm.com/Processors/Cortex-M33
+[5]
+——,
+“Cortex-m55.”
+[Online].
+Available:
+https://developer.arm.com/Processors/Cortex-M55
+[6]
+Y. X. et al, “Controlled-channel attacks: Deterministic side channels
+for untrusted operating systems,” in IEEE Symposium on Security and
+Privacy.
+IEEE S&P, 2015.
+[7]
+T. K. M.-W. Shih, S. Lee and M. Peinado, “T-sgx: Eradicating
+controlled-channel attacks against enclave programs,” in The Network
+and Distributed System Security Symposium (NDSS).
+NDSS, 2017.
+[8]
+D. G. M. Lipp, C. M. R. Spreitzer, and S. Mangard, “Armageddon:
+Cache attacks on mobile devices,” in 25th USENIX Security Sympo-
+sium 16).
+USENIX, 2016.
+[9]
+C.
+Commons,
+“The
+heartbleed
+bug.”
+[Online].
+Available:
+https://heartbleed.com
+[10] J.
+Fruhlinger,
+“What
+is
+the
+heartbleed
+bug,
+how
+does
+it
+work
+and
+how
+was
+it
+fixed?”
+[Online].
+Available:
+https://www.csoonline.com/article/3223203/what-is-the-heartbleed-bug-how-does-it-work-and-how-was-it-fixed.html
+[11] W. L. N. Zhang, K. Sun and Y. T. Hou, “Case: Cache-assisted secure
+execution on arm processors,” in IEEE Symposium on Security and
+Privacy.
+IEEE S&P, 2016.
+[12] Y. C. Y. Zhou, X. Wang and Z. Wang, “Armlock: Hardware-based
+fault isolation for arm,” in ACM Conference on Computer and Com-
+munications Security.
+ACM CCS, 2014, p. 558–569.
+[13] K. S. Ning Zhang, W. L. Deborah Shands, and Y. T. Hou, “Trusense:
+Information leakage from trustzone,” in International Conference on
+Computer Communications.
+INFOCOM, 2018, p. 19.
+[14] A. Developer, “Arm trustzone technology.” [Online]. Available:
+https://developer.arm.com/documentation/100690/0201/Arm-TrustZone-technology?lang=en
+[15] D. Vyas, “Emuation using qemu’s native raspi2/3 machine.” [Online].
+Available: https://github.com/dhruvvyas90/qemu-rpi-kernel
+[16] R. dev Vyas, “Raspberry pi documentation.” [Online]. Available:
+https://www.raspberrypi.com/documentation/computers/using linux.html
+[17] R.
+Pi,
+“The
+linux
+kernel
+user’s
+and
+administrator’s
+guide.”
+[Online].
+Available:
+https://github.com/raspberrypi/linux/blob/rpi-5.15.y/Documentation/admin-guide/index.rst
+[18] N.
+Developer,
+“Lpcxpresso55s69
+de-
+velopment
+board.”
+[Online].
+Available:
+https://www.nxp.com/design/development-boards/lpcxpresso-boards/lpcxpresso55s69-development-board:LPC55S69-EVK
+[19] ——,
+“Numicro®
+m2351
+series
+–
+a
+trustzone®
+empowered
+microcontroller series focusing on iot security.” [Online]. Available:
+https://www.nuvoton.com/products/microcontrollers/arm-cortex-m23-mcus/m2351-series/?
+locale=en
+[20] ARM,
+“Bx,
+bxns:
+Branch
+and
+exchange
+instruction
+set
+and
+branch
+and
+exchange
+non-secure.”
+[Online].
+Available:
+https://developer.arm.com/documentation/100076/0200/a32-t32-instruction-set-reference/a32-and-t32-instructions/bx--bxns
+[21] B. Lapid and A. Wool, “Cache-attacks on the arm trustzone im-
+plementations of aes-256 and aes-256-gcm via gpu-based analysis,”
+in International Conference on Selected Areas in Cryptography.
+Springer, 2018, pp. 235–256.
+[22] R. Stajnrod, R. Ben Yehuda, and N. J. Zaidenberg, “Attacking trust-
+zone on devices lacking memory protection,” Journal of Computer
+Virology and Hacking Techniques, pp. 1–11, 2021.
+[23] M. Zhang and R. Sekar, “Control flow integrity for {COTS} binaries,”
+in 22nd USENIX Security Symposium (USENIX Security 13), 2013,
+pp. 337–352.
+[24] L. Davi, P. Koeberl, and A.-R. Sadeghi, “Hardware-assisted fine-
+grained
+control-flow
+integrity:
+Towards
+efficient
+protection
+of
+embedded systems against software exploitation,” in 2014 51st
+ACM/EDAC/IEEE Design Automation Conference (DAC).
+IEEE,
+2014, pp. 1–6.
+[25] N. Semiconductors, “Mcuxpresso ide user guide.” [Online]. Available:
+https://www.nxp.com/docs/en/user-guide/MCUXpresso IDE User Guide.pdf
+[26] ARM,
+“Memory
+leak
+detection.”
+[Online].
+Available:
+https://developer.arm.com/documentation/102604/0100/Memory-leak-detection
+
+[27] milostosic, “Mtuner- advanced c/c++ profiler.” [Online]. Available:
+https://github.com/milostosic/MTuner
+[28] V.
+Developers,
+“Valgrind
+documentation.”
+[Online].
+Available:
+https://github.com/milostosic/MTuner
+[29] A.
+Developer,
+“Inspect
+your
+app’s
+memory
+us-
+age
+with
+memory
+profiler.”
+[Online].
+Available:
+https://developer.android.com/studio/profile/memory-profiler
+[30] Y. Chen, Y. Zhang, Z. Wang, and T. Wei, “Downgrade attack on
+trustzone,” arXiv preprint arXiv:1707.05082, 2017.
+[31] M. Mushtaq, M. A. Mukhtar, V. Lapotre, M. K. Bhatti, and G. Gog-
+niat, “Winter is here! a decade of cache-based side-channel attacks,
+detection & mitigation for rsa,” Information Systems, vol. 92, p.
+101524, 2020.
+[32] M. Lipp, D. Gruss, R. Spreitzer, C. Maurice, and S. Mangard,
+“Armageddon: Cache attacks on mobile devices,” in 25th USENIX
+Security Symposium 16, 2016, pp. 549–564.
+[33] Y. Yarom and K. Falkner, “Flush+ reload: A high resolution, low
+noise, l3 cache side-channel attack,” in 23rd USENIX Security Sym-
+posium 14, 2014, pp. 719–732.
+[34] R. B. Yehuda and N. J. Zaidenberg, “Protection against reverse
+engineering in arm,” International Journal of Information Security,
+vol. 19, no. 1, pp. 39–51, 2020.
+[35] G. Irazoqui, T. Eisenbarth, and B. Sunar, “Cross processor cache
+attacks,” in Proceedings of the 11th ACM on Asia conference on
+computer and communications security, 2016, pp. 353–364.
+[36] Z. Ning and F. Zhang, “Understanding the security of arm debugging
+features,” in 2019 IEEE Symposium on Security and Privacy (SP).
+IEEE, 2019, pp. 602–619.
+[37] K. Ryan, “Hardware-backed heist: Extracting ecdsa keys from qual-
+comm’s trustzone,” in Proceedings of the 2019 ACM SIGSAC Confer-
+ence on Computer and Communications Security, 2019, pp. 181–194.
+
diff --git a/tNE3T4oBgHgl3EQfjwpk/content/tmp_files/load_file.txt b/tNE3T4oBgHgl3EQfjwpk/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5704c2dd16c7b74062172b633e21f71669f00200
--- /dev/null
+++ b/tNE3T4oBgHgl3EQfjwpk/content/tmp_files/load_file.txt
@@ -0,0 +1,815 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf,len=814
+page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='04591v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='CR]  11 Jan 2023  MVAM: Multi-variant Attacks on Memory for IoT Trust Computing  Arup Kumar Sarker∗, Md Khairul Islam†, Yuan Tian‡  ∗†University of Virginia, Charlottesville, VA 22904, USA, {djy8hg, mi3se}@virginia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='edu  ‡University of California, Los Angeles, CA 90095-1405, USA yuant@ucla.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='edu  Abstract—With the significant development of the Internet  of Things and low-cost cloud services, the sensory and data  processing requirements of IoT systems are continually going  up.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' TrustZone is a hardware-protected Trusted Execution En-  vironment (TEE) for ARM processors specifically designed for  IoT handheld systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' It provides memory isolation techniques  to protect the trusted application data from being exploited by  malicious entities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' In this work, we focus on identifying differ-  ent vulnerabilities of the TrustZone extension of ARM Cortex-  M processors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Then design and implement a threat model to  execute those attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' We have found that the TrustZone is  vulnerable to buffer overflow based attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' We have used this  to create an attack called MOFlow and successfully leaked  the data of another trusted app.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' This is done by intentionally  overflowing the memory of one app to access the encrypted  memory of other apps inside the secure world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' We have also  found that, by not validating the input parameters in the  entry function, TrustZone has exposed a security weakness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' We  call this Achilles’ heel and present an attack model showing  how to exploit this weakness too.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Our proposed novel attacks  are implemented and successfully tested on two recent ARM  Cortex-M processors available on the market (M23 and M33).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  Index Terms—Trust Computing, IoT, TrustZone, Cortex-M,  vulnerability, Instruction TCM(ITCM), Data TCM(DTCM)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Introduction  ARM TrustZone is an embedded security system for  ARM Cortex processors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Recently, ARM included Trust-  Zone into IoT computing with cortex-m processors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' The  benefit of TrustZone is its compact and lightweight nature,  allowing for both worlds (Figure 1) to operate on a single  processor core.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Because of this secure operating system,  ARM micro-controllers can store all system-essential li-  braries and applications in a secure area [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' The defense  mechanism in TrustZone is to protect memory (physical and  cache) and process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' For example, memory in both worlds is  isolated with a security attribute Unit (SAU), even the same  app with different signatures running in two different worlds  has to go with a robust verification process and execute in  isolation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Work stretching across different applications, both  secure and not secure, can do so through a software-based  Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' TrustZone Core Virtualization  secure monitor which mediates between the two security  worlds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' This software-based secure monitor is executed on  the same core as all the other processes, and thus consumes  less power than the traditional approaches detailed above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  Even with this, there are malicious attacks by observing  entry and exit onto the address of cache, compromising the  messaging channel between a non-secure process and secure  process [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' To target this problem, some research papers  are used isolated cache protection design to narrow down  the access space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  Due to limited or not availability of cache, access  in memory inside Trusted Execution Environment(TEE) is  shared and not bound to specific secure kernel process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' So,  the TEE delineates specific memory addresses in accor-  dance with their world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' There is no tightly coupled memory  dedicated to a specific app in the secure zone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' A trusted  execution environment can be easily exploited by leaking  memory within the shared space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Without authorization  or access to protected enclaves, the attacks can be quite  effective at collecting the users’ private and secure data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  This allows sensitive information to be stored out of reach  for applications operating outside of the secure world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  With the use of ARM TrustZone in the IoT ecosystem,  memory access in these devices have a significant research  focus within single and cloud with multiple connected smart  devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' The goal of our study is to research and develop  security exploit encrypted information to gather sensitive  user information into the normal world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Although the secu-  rity attribute Unit (SAU) ensures the security, certain input  parameters might expose the access of secure memory if the  developer forgets to check memory-bound checking non-  secure callable zone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' The system should have an automatic  guard to validate the memory-bound checking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Poor imple-  mentation at the nonsecure callable side might expose the  potential loophole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' This will create multiple openings for  external attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' A secure framework should not have APIs  to get non-accessible data from the user level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' TrustZone  does not have any automatic internal memory management  like with a high-level programming language.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Moreover,  security design and protection work differently in x86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Most  of the low-level APIs are primitive and do not have any  metrics to benchmark the security level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' We have not found  the API security validation from the ARM platform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' A  developer has to perform extensive operations for allocating  memory and clearing them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Any intentional or unintentional  memory leakage might expose the sensitive data even from  the secure TrustZone memory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  The proposed threat model of MOFlow is based on the  experimental results and found memory leaks during the  access to out-of-bound data even in the TrustZone secure  world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' We also find, using invalid parameters in the Entry  function, it is possible to infiltrate the secure world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' We  call this an Achilles’ heel for the TrustZone security.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' These  successful attacks will highlight security vulnerabilities in  the current ARM Cortex-M processors which need to be  addressed to ensure the safety of the IoT systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' This  will also help us understand potential risks associated with  TrustZone and improve the security of IoT trust computing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  In short our contributions in this work are: We have done a robust exploration of the security  vulnerabilities during the communication in between  normal and secure world in the ARM TrustZone  Cortext-M processor and defined open scopes of  possible compromise of the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' We propose a threat model to exploit memory over-  flow with intentional or unintentional fraudulent  communication, encapsulated with security attribute  unit along with mechanism for creating Achilles’s  heel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' We also expose the APIs limitations and the implica-  tion of a low-level framework that creates a possible  loophole for the intruder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' We provide best practices for the defense improve-  ment inside TrustZone based on the experimental  results and analysis that includes an additional layer  of verification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Finally, we propose a trust model with TrustZone ex-  tension APIs and verifier along with communication  flows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  Paper Organizations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' The rest of the paper is organized  as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Section 2 presents the backgrounds on TrustZone  and its architecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Section 3 explains the motivation behind  the attacks and what was the expected outcome.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Section  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='4 has the design of the threat model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Then Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='5  shows how we planned to apply it to ARM TrustZone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  Section 4 presents the experimental setup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' In Section 5  we list the different types of attacks we performed on the  TrustZone and its results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Discussions on the implications  of our findings, possible mitigation plans against the attacks  and future works are added in Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Section 7 lists  the related works.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Section 8 contains the limitations of our  work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' And finally, Section 9 has the conclusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Background  There are multi-variety of designs in ARM TrustZone  to ensure security.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' ARM Cortex M23 [3] and M33 [4] do  not have any in-built cache because of the compact design  and priority on security features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' In ARM Cortex-M35P, the  process cache is the primary element of in-memory design  to create a bridge between the processor execution and the  relatively slower memory access.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' In the TrustZone-M design  both instruction and data, a memory is expanded with an  additional feature called an NS flag which helps to identify  the security domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' This flag bit will be used to isolate  the memory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' These lines are not accessible from the normal  world directly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' But it is common for both worlds, during  the execution of the processor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' So the normal and secure  world will try to use this memory line to support its running  application.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  The main reason for this design is to maximize the  utilization of the memory and improve system performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  ARM sets specific hardware to secure the access of memory  by any world application.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' But the access pattern is not secure  in simple designed cortex M33 or M23 where only a single  memory unit is available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Moreover, M55 [5] has a robust  memory with instruction and data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' These will communi-  cate with customs-designed newly introduced instruction  and data Tightly-Coupled Memory (TCM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Access patterns  between TCM to cache can be easily monitored by an  attacker process, leaving TrustZone vulnerable for the cache  access side-channel attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' From the beginning of trust  computing, there is a vast number of studies on Intel-based  SGX secure container [6], [7], but very few studies are done  on TrustZone [8], running on mobile platforms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' A graphic  overview of the cache-based attack is seen in Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' A standard communication by using shared resources  This security probing involved reading literature regard-  ing the TrustZone-M architecture, control flow, and compo-  nents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' After re-framing the approach, the team began look-  ing into previous effective cyber-attacks and the fundamental  principles behind them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Though TrustZone-M provides a lot  of new obstacles for attackers to overcome, we believed that  certain attack models could be modified and applied to this  security architecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Throughout our literature exploration,  we came across the MOFlow bug [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  The MOFlow bug relies on a TEE/Non-secure commu-  nication with the standard API of TrustZone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' A nonsecure  app sends a short message to a secure app to check if the  app is active in the background.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' When a secure UI/service  app falls out of responses with another due to inactivity or  being killed or crashed, it is needed to be able to check  if they are still alive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' There will be data inconsistencies  due to interaction by the user or server or any connected  apps in the IoT system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' That encrypted piece of data is sent  from another node to check its status or availability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' When  the crashed or killed secure node receives this request, it  responds with the same piece of encrypted data to prove  to the nonsecure app that the secure app is still in place.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  This is where the vulnerability lies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' The request message  also includes information about its length.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Below, we will  draw out a scenario of how communication can be used to  extract information from a secure app [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  A normal world app is a malicious user and wants to  extract sensitive information from the secure world app.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  So communication from Non-secure will go to secure for  checking the availability of the service.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' The request consists  of an encrypted message (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='g, 16KB lengths), but the normal  world app intentionally lies about the length of the encrypted  message and says that it is 128KB long (the maximum  request length).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' The secure app receives this request and  allocates a 128KB memory buffer to contain the encrypted  message it is supposed to send back to the malicious app  in Non-secure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' The secure world then stores the 16KB  encrypted message on the 128KB memory buffer and sends  it back to the Non-secure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' This is where the vulnerability  lies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Security attributes in secure zone do not verify that  the encrypted message length is equal to the length value  provided.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' This tricks the secure world app into sending over  112KB of possibly sensitive information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  The lack of this safeguard on secure zone allowed  malicious users to use the MOFlow vulnerability to extract  data from unsuspecting secure world apps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' In this work, we  intend to perform the MOFlow attack to target an ARM  TrustZone-enabled micro-controller.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' This attack requires an  important assumption which we will make for this experi-  ment: the malicious user has planted a buggy application on  the secure world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' This is an important assumption because,  without a buggy application within the secure world, there  is no avenue for the attacker to interface with the secure  world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' While this obstacle seems difficult to overcome, we  believe that it is a plausible scenario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' With the onset of  IoT systems, particularly smart homes, the user is free to  download and use third-party applications that provide ad-  ditional features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' This app store provides an avenue through  which a malicious user could plant a seemingly innocuous  application that contains a bug enabling MOFlow attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  Any user that downloads this malicious application opens  the door for attackers to execute the MOFlow attack on a  TrustZone-enabled device.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' In Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='6, we have discussed  the attack model tailoring MOFlow to TrustZone-enabled  micro-controllers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Overview of Approach  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' A Motivating Use Case  To provide a motivating example, suppose there exists  an IoT smart home device that is powered by a TrustZone-  M enabled micro-controller.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' This smart home device can  be connected to sensors such as a user’s smartwatch device,  house lights, front door, and many other miscellaneous smart  household IoT devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' The smart device can also interact  with multiple cloud servers for each app that provides users  the functionality to make purchases, check health statuses,  and send messages and emails.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' If the MOFlow attack is  proven to work within TrustZone-M devices it could lead  to serious violations in the integrity of TrustZone’s secu-  rity measures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Specifically for the described TrustZone-M  powered IoT device,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' an attacker can publish a malicious  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='application with memory leakage to the device’s affiliated  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='marketplace and disguise the application as a seemingly  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='innocent service that a user could end up downloading  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='(similar to utterance checking) into their smart device’s  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='Normal World  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='Secure World  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='Trusted  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='Application  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='Application  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='TZ Library  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='C3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='SSL  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='TZ Daemon  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='User  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='User  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='C3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='Privilege  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='Privilege  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='Trusted World  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='TZ Driver  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='SMC Interface  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='Kernel  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='Normal World Kernel  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='Secure Monitor  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='DRAMsecure zone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' TrustZone applications can retrieve sensitive in-  formation from the server to get access to a sensor and save  it to the memory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' From there, the malicious application is  among different other legitimate applications for sensors that  could have the functionality to retrieve sensitive information  from a using shared memory space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' The attacker could  then invoke this compromised secure-world application by  overflowing the secure memory space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' If another sensor’s  data is saved on the device, the attacker could gather the  user’s device identifiers, device authentication key, and other  data from the memory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Expected Robustness Properties  Let’s define communication properties between Non −  secure and T EE  with a set of blocks instructions  X{x1, x2, x3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=', xn} ⇔ Y {y1, y2, y3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=', yn}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' If △m is the  leakage memory, then the response of X from the T EE is,  RX = OY + △m  where OY , is the the expected allocated memory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  The model tries to perform the maximum number of  attacks on T EE and increase the number of successful  attacks SN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Target is to maximize the amount of leaked  memory, Fm with the generator function L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' So,  lim  △m→ Fm f(△m) = L  So for all instructions X{x1, x2, x3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=', xn}, output re-  sponse is generated with multiple equations as follows,  Rx1 = △mx1 + Ox1  Rx2 = △mx2 + Ox2  Rx3 = △mx3 + Ox3  · ·  Rxn = △mxn + Oxn  To verify the robustness properties of T EE secure com-  munications, △m should be 0, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=',  △m = △mx1 + △mx2 + △mx3 + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' + △mxn = 0  (1)  In this paper, by performing a set of attacks, we will  invalidate the robustness properties of T EE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Aligning Problems on ARM TrustZone  We have done a robust study on normal-world user and  kernel space and have learned of vulnerabilities allowing  attackers to gain full control of the normal-world kernel  space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' It is possible to discern physical addresses from  virtual information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Address translations play a vital role in  allocating memory and are thus a prime area for an attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  By design, the whole memory is divided into multiple parts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  Our first target is to find a path to access the secure memory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  Moreover, the cycle counter can be used as a precision  timer that is accessed by only super users.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' In addition, a  non-privileged app can access information without super-  user permissions and with no virtual to physical address  translation or cycle count.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  This creates an opportunity for prime and probe attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  To do that, there can be multiple scenarios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' When a normal  world app tries to access securely by not following the  standard protocol, on the framework side, there should be  some security measures to protect any kind of illegal access.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  Security Attribute Unit(SAU) and Implementation Defined  Attribution Unit(IDAU) will raise kernel fault in response.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  What if the developer made the mistake of adding memory  boundary checking in the non-secure callable?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' A normal  world app will have access to the whole memory of a secure  world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Many high-level programming languages have inbuilt  garbage collectors to free allocated memory and handle  memory leaks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' If a system does not have a built-in garbage  collector, it should have support at the framework level to  handle memory leakage internally.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  ARM TrustZone is based on low-level language, As-  sembly, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' In these languages, developers have to  manage every allocated memory checking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' One of the major  limitations in the ARM TrustZone framework is, it does  not have any in-built memory management support, even  for secure zones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' This opens the door for the overflow  of the memory in a secure zone and possible leakage of  valuable data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' In Figure 2, communication line C3 is the  main way between normal world user and kernel space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  With C3 superuser access, a non-privileged app gets access  information without cycle count and address translation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' C3  is executed with a TrustZone daemon or library which needs  an extensive authentication process for the execution in a  secure world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' But C3 has access to a nonsecure callable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  Intentional memory accessible is possible with bad coding  and generates Achilles’ heels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' An attacker can get overflow  memory data by using standard TrustZone API.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' No other  apps, including TrustZone itself, will have a single idea  about the theft of the information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Threat Model Design  Based on the design by ARM, all cryptographic oper-  ations are executed in an isolated environment [11], [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  That means API execution in a process of a cryptographic  library like SSL is isolated in the secure world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' We have  designed our threat model based on the assumptions that  there must be a channel of handshaking between the normal  world and secure world data or instruction transmission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  If those operations happen either on the SMC interface  or TZ manager, then the attacker can easily get data by  using standard protocol from a secure world and extracting  necessary information to get the AES key.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Because Zhang et  al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' [13] demonstrates a way of recovering the full AES128  key using the application level attack in a shorter time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  Now the main idea is to get data from the memory  by overflowing the assigned data structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' All apps in the  secure world use shared resources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Assigning memory to  an app is a loosely coupled operation at the processor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' If a  malicious app overflows its memory scope, it can easily get  data that was not assigned.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Although the data is encrypted, it  can be easily decrypted by using a T-table-based decryption  mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Moreover, input parameters play an important  part in getting the level of access to a secure world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' There  is no standard system in the TrustZone framework to handle  any fuzzy attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Developers might not check all the corner  cases of access memory in non-secure callable parts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' SAU  and IDAU do not guarantee parameter level verification at  non-secure callable regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Here comes the Achilles heel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  With that attacker can compromise the non-secure callable  and get full access to secure world memory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  The proposed threat model will work from the appli-  cation level with user privilege, which does not have any  assumption to break the hardware-enabled trust execution  environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' So executing the code from normal world  user space to kernel space does not need any API call or  permission from the TZ library or TZ manager in kernel  space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' A malicious process in a secure space can run and  infect any operation and remain intact inside an app.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' This  process might have access to memory data with the back-  door leakage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Based on this analogy, this threat model is  more resilient in the IoT system and does not need any  dependencies on the TrustZone specific platform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Based on  this threat model, suppose, an attacker has both a secure and  non-secure app, running on an IoT device, and he wants to  steal information from other vendors’ apps running on the  same device.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' The Proposed Threat Model  In Figure 3, A2 is the malicious app that memory leaks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  In ARM TrustZone, there is no support for handling mali-  cious memory overflow, inside a secure zone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' So, A2 will  read data from the DRAM which was assigned to any other  app, and send it back to the normal world by following the  APIs of non-secure callable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Because in TrustZone memory,  there is no tightly coupled memory bound to a specific app.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  As a result, even the TrustZone framework and no other app  will detect the theft of information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' For the simplicity of the  threat model, we have excluded the decryption mechanism  of secure data from the project scopes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' ARM Cortext-M micro-controller modes  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Apply Threat Model to ARM TrustZone  ARM Cortext-m is designed as a component of IoT  ecosystem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' As it is low power, TrustZone security extension  is optional.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' That means, chipset vendor has the flexibity  to design chip.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' For example, NXPLPC55S28 is based on  Cortex-M33, but this board does not have TrustZone security  extension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' As it is low powered micro-controller, proces-  sor works differently than ARM cortex-A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' ARM Cortex-M  processor works in two different modes in Figure-4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' When  running application software, the CPU is in Thread mode,  and for handling exceptions, it is in Handler mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' When the  processor exits reset, it enters Thread mode and exits Thread  mode when all exceptions have been processed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Execution  can be privileged or unprivileged in Thread mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Execution  is Privileged in Handler mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Memory maps are used to  divide the Secure and Normal worlds, and transitions are  handled automatically in exception handling routines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='That’s  why multiple secure function entry points are supported by  Armv8-M [14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  Because of that, all access to different memory might be  on multiple in parallel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Although SAU and IDAU protect the  memory access with NS bit, what is transmitting from the  secure zone does not have any control.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Moreover, in both  thread and handler mode, within the region of secure mem-  ory, data access is performed based on the programming  logic of secure memory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Attribute units are independent  and do not have any influence on application features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' This  design opens research questions about the security flaws  inside secure and non-secure callable and that’s how our  proposed thread model has implications on the secure zone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Experimental Setup  Multiple vendors develop board based on ARM Cortex-  M along with development environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Our primary anal-  Processor Modes  Non-Secure  Secure  Handler Mode  Handler Mode  Thread Mode  Thread ModeA3  A2  A2  A7  A7  A3  A7  A7  A4  A2  A8  A8  A4  A4  A8  A8Normal World  Secure World  Trusted  Application  Application  TZ Library  C3  SSL  个  TZ  Daemon  User  User  C3  Privilege  Privilege  Trusted  TZ Driver  A2  Interface  World Kernel  SMC  Defect by  Normal World Kernel  Overflow!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  Secure  !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='!!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  Monitor  DRAM  A1  A1  A5  A5  A1  A5  A2  A2  A6  A6  A6-  A2  A2  A6ysis for feasibility test, was started with QEMU emulator  for RPI3 kernel in linux [15]–[17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' But we were unable  to replicate the defined problem in target domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Because,  it doesn’t have TrustZone framework and the architecture  is not comply the current state of the arts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' NXP and  Nuvoton released R&D board based on ARM cortex-M  and we have used NXPLPC55S69 [18] and [19] Nuvoton  M2351.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Nuvoton-M2351 has a single core M23 processor  and NXPLPC55S69 has a dual-core M33 processor with  DRAM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Both of them have support for TrustZone instruc-  tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Our initial plan was to use the Cortex-M35P and  M55 processors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Because they have the latest TrustZone  implementation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Cortex-M55 has additional instruction and  data tightly coupled memory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' These are configurable to the  specific app for the fixed memory location.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Unfortunately,  we couldn’t get either of them publicly available on the  market.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Or even if they were available, there were substantial  amount of time delay for the delivery due to chip shortage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  So, we chose the M23 and M33-based boards.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' We have  also received an NXPLPC55S28 board, developed with a  single ARM cortex M33 processor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' But it does not have any  support of TrustZone, so it couldn’t be used in this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Attacks on ARM Cortex-M  We have performed multiple attacks on Cortex M pro-  cessors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Some attacks are failed due to security properties  by ARM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Failed attacks are an Invalid transition from secure  to the normal world, the invalid entry point from normal to  secure world, and invalid data access from the normal world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  We do have some success.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Success attacks are Invalid input  parameters in the entry function, we call it Achilles’ heel and  steal Memory data inside a secure world, we call it Heart  Bleed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' In the next subsections, we will describe in detail  all attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Source codes for all of the attacks are publicly  available on https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='com/arupcsedu/MVAM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Memory Map  Before going into details about our experiments, let’s  check the run-time memory attribute map of ARM Cortex-  M in Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' We have exported this memory snapshot  from the LPCNXP55S69 board, during running the program.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  We see the NS Program flash base is 0x0001 0000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' The  Secure Program flash base is 0x1000 0000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' A Non-secure  Callable, here with NXP, we call a Veneer Table, the entry  point to secure area base is 0x1000 FE000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' A combination  of SAU (Secure Attribute unit) and IDAU (Implementation  Defined Attribution Unit) ensures the separation of each  memory footprint with security.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Here SAU is internal with  a processor and IDAU is external units, normally designed  by chipset vendors, for example, NXP has that flexibility to  design IDAU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Memory map of Secure, Non-Secure and Non-Secure Callable  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Invalid Transition From Secure to Normal  World  In this attack, a direct address to non-secure RESET is  used to jump into the normal world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' There are two issues  related to this approach in Listing-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' First, all core registers  are not clear so there is a potential data leak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Second, the  most LSB of address into the normal world has to be cleared.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  We have not performed those and the requirement is not met  for the transition to the normal world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' As a result, a secure  fault is generated by SAU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  #define CODE_START_NS 0x00010000  #define AHB_LAYERS_COUNT 12U  #define NON_SECURE_START CODE_START_NS  if (testCaseNumber ==  FAULT_INV_S_TO_NS_TRANS)  {  funcptr_ns ResetHandler_ns;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='/* Non-secure main stack address */  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='__TZ_set_MSP_NS(*((uint32_t  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='SAU+IDAU  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='MPC/PPC  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='ResultingSecurityLevel  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='NS  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='NS-User  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='NS RAMO  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='0x20008000  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='0x20007FFF  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='NS  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='S-Priv  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='Noaccess  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='0x20000000  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='0x14007FFF  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='SRAMX (alias)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='NS-User  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='0x1400_0000  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='0x1301_FFFF  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='Boot-ROM (alias)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='NS-User  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='0x13000000  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='0x1009_FFFF  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='S  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='NS-User  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='FLASH (alias)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='0x10010000  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='NSC  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='S-Priv  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='NSC  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='0x1000FFFF  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='VeneerTable  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='0x1000FE00  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='0x1000FDFF  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='S-Priv  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='Secure Code  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='0x1000_0000  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='0x0400_7FFF  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='SRAMX  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='NS  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='NS-User  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='NS  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='0x0400_0000  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='0x0301_FFFF  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='Boot-ROM  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='NS  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='NS-User  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='NS  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='0x03000000  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='0x0009 FFFF  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='NS  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='NS-User  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='NS  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='0x00078000  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='0x0007-7FFF  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='PROGRAMFLASH  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='NS  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='NS-User  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='NS  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='Non-secure Code  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='0x00010000  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='0x0000FFFF  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='NS  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='S-Priv  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='access  0000000x*)(NON_SECURE_START)));' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  /* Initialize the non-secure vector table  /  SCB_NS->VTOR = NON_SECURE_START;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  /* Function pointer for the Non-secure  reset handler */  ResetHandler_ns =  (funcptr_ns)(*((uint32_t  )((NON_SECURE_START) + 4U)));' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  /* Invalid switch to non secure */  __asm("BXNS %0" : : "r"(ResetHandler_ns));' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  }  Listing 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Attack with Invalid Transition From Secure to Normal World  Both  issues  can  be  solved  by  using  the  cmse nonsecure call keyword attribute.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' If this attribute  is used for a function call to a normal world, the compiler  will do three things.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' First, clear all used registers to avoid  potential data leak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Second, clear LSB address bit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Third,  jump to address using BXNS instruction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' The BXNS  instruction causes a branch to an address and instruction  set specified by a register and causes a transition from  the Secure to the Non-secure domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' This variant of  the instruction must only be used when additional steps  required to make such a transition safe are taken [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Invalid Entry From Normal to Secure World  In Listing-2, a function pointer, PRINTF NSE is in-  tentionally increased by 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' It is defined with a non-secure  callable function DbgConsole Printf NSE in the veneer ta-  ble.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' By this the Secure Gateway(SG) instruction is skipped,  when a function is called.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' This causes an illegal entry point  into a secure world and a secure fault is generated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' The  correct entry point into the secure world is ensured by using  cmse nonsecure entry keyword attribute for every entry  function so that it clears the register value and LSB address  bit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Then the linker creates a veneer table for all entry  functions with SG instructions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  #define SEC_ADDRESS 0x10000000  #define NONSEC_ADDRESS 0x20130000  typedef void (*funcptr_t)(char const *s);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  #define PRINTF_NSE DbgConsole_Printf_NSE  if (testCaseNumber == FAULT_INV_S_ENTRY)  {  func_ptr =  (funcptr_t)((uint32_t)&PRINTF_NSE +  4);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  func_ptr("Invalid Test Case\\r\\n");' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  }  /* Non-secure callable (entry) function */  TZM_IS_NOSECURE_ENTRY void  DbgConsole_Printf_NSE(char const *s)  {  size_t string_length;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  /* Access to non-secure memory from  secure world has to be properly  validated */  /* Check whether string is properly  terminated */  string_length = strnlen(s,  MAX_STRING_LENGTH);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  if ((string_length == MAX_STRING_LENGTH)  && (s[string_length] !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='= ’\\0’))  {  PRINTF("Input data error: String too  long or invalid string  termination!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='\\r\\n");' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  abort();' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  }  PRINTF(s);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  }  Listing 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Attack with Invalid Transition From REE to TEE  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Invalid Data Access From Normal World  In Listing - 3, the pointer is set to the address defined  by NONSEC ADDRESS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' This address has a non-secure  attribute in SAU but it has a secure attribute in AHB secure  controller.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' If data is read from this address, the data bus  error is generated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Compared to attacks for accessing the  memory address, SEC ADDRESS where the secure fault  is generated, this error is caught by AHB secure controller,  not by SAU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Because in the SAU this address is non-secure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  So the access from the normal world is correct from SAU’s  perspective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' In the normal world, the application does not  have access to secure memory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  #define SEC_ADDRESS 0x10000000  #define NONSEC_ADDRESS 0x20130000  typedef void (*funcptr_t)(char const *s);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  #define PRINTF_NSE DbgConsole_Printf_NSE  if (testCaseNumber ==  FAULT_INV_NS_DATA_ACCESS)  {  test_ptr = (uint32_t *)(SEC_ADDRESS);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  test_value = *test_ptr;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  }  Listing 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Attack with Invalid data access to TEE  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Achilles’ Heel - Invalid Parameters in Entry  Function  In this attack, the input parameter is set to address  0x10000000 in Listing-4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' This address has a secure attribute  (see SAU settings in the memory map picture).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' This secure  violation is not detected by secure fault, since the input  parameter is used by the secure function in a secure mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  So this function has access to the whole memory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' However,  every entry function should check the source of all input  data to avoid potential data leaks from secure memory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' The  correctness of input data cannot be checked automatically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  So, this function is an Achilles’ heel, which can be used to  enter the secure world by using a valid secure location as an  input parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' This has to be checked by software, using  TT instruction by publisher vendors to protect Achilles’ heel  if the developer forgot to set a check in the NSC layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  #define SEC_ADDRESS 0x10000000  #define NONSEC_ADDRESS 0x20130000  typedef void (*funcptr_t)(char const *s);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  #define PRINTF_NSE DbgConsole_Printf_NSE  if (testCaseNumber == FAULT_INV_S_ENTRY)  {  func_ptr =  (funcptr_t)((uint32_t)&PRINTF_NSE +  4);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  func_ptr("Invalid Test Case\\r\\n");' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  }  /* Non-secure callable (entry) function */  TZM_IS_NOSECURE_ENTRY void  DbgConsole_Printf_NSE(char const *s)  {  size_t string_length;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  /* Access to non-secure memory from  secure world has to be properly  validated */  /* Check whether string is properly  terminated */  string_length = strnlen(s,  MAX_STRING_LENGTH);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  if ((string_length == MAX_STRING_LENGTH)  && (s[string_length] !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='= ’\\0’))  {  PRINTF("Input data error: String too  long or invalid string  termination!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='\\r\\n");' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  abort();' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  }  /* Check whether string is located in  non-secure memory */  #if (__GNUC__ !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='= 10)  if (cmse_check_address_range((void *)s,  string_length, CMSE_NONSECURE |  CMSE_MPU_READ) == NULL)  {  PRINTF("Achilles’ Heel exception:  String is not located in normal  world!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='\\r\\n");' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  abort();' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  }  #endif  PRINTF(s);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  }  Listing 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Achilles’ Heel Attack during access TEE with invalid input  parameters  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' MOFlow - Steal Memory Data Inside Secure  World  Along with the Achilles’ heel, we have implemented  our threat model, MOFlow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' In the MOFlow attacks, men-  tioned in Listing-5 a secure attacker app(A2) with memory  overflow is running on the secure zone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Here, moflow()  function is implemented in the secure app which memory  leaks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' There are three other test apps(A1/A3/A5) running on  the TrustZone memory which does not have any leakage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  Because of memory overflow in A2, it is getting more en-  crypted unassigned data from the memory which is allocated  to other apps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' A2 returns all data to the normal world by  following the proper standard of TrustZone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Application,  A1/A3/A5 and even TrustZone itself does not have a single  idea about this stealing, as it is happening in a specific  program space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' With a T-table-based mechanism, it can be  decrypted to actual data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Like in the MOFlow attacks, a  secure zone is acting as a server and returning sensitive  information to the normal world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  #define FAULT_HEART_BLEED 0  #define FAULT_INV_S_TO_NS_TRANS 1  #define FAULT_INV_S_ENTRY 2  #define FAULT_INV_NS_DATA_ACCESS 3  #define FAULT_INV_INPUT_PARAMS 4  #define FAULT_INV_NS_DATA2_ACCESS 5  #define MAX_SMEM_SIZE 4e+9  TZM_IS_NOSECURE_ENTRY char*  GetDRAMData_NSE(void)  {  char leakData[MAX_SMEM_SIZE];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  char *lDataPtr = GetDRAMData();' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  PRINTF("Read from Veneer Table:\\n");' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  for(int i = 0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' i < MAX_SMEM_SIZE;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' i++)  {  leakData[i] = lDataPtr[i];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  printf("%c",leakData[i]);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  }  leakData[MAX_SMEM_SIZE] = ’\\0’;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  //strcpy(leakData, lDataPtr);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  return leakData;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  }  char* GetDRAMData()  {  return leakedData;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  }  void moflow()  {  char str[] = "I am malicious.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Check my  tail";' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  testCaseNumber = FAULT_HEART_BLEED;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  int len = strlen(str);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  for(int i = 0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' i < len + COM_DRAM_OFFSET;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  i++)  {  leakedData[i] = str[i];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  PRINTF("%c", leakedData[i]);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  }  leakedData[len + COM_DRAM_OFFSET] = ’\\0’;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  PRINTF("\\nDecrypt the above data from my  tail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='\\n");' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  return ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  }  Listing 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' MOFlow Attack on TEE with buffer overflow  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Discussions  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Implications of Our Findings  The Achilles’ heel attack (Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='5) indicates it is  important to check the memory locations as an input pa-  rameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Without properly validating the inputs, they can  be modified by an attacker and be used to compromise the  execution of the target function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' However, to the best of our  knowledge, there is no automated tool available to detect  invalid parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' So developers would need to ensure their  methods properly validate input parameters before using  them for any sensitive process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Also, vendors would have to  ensure software using their platform can prevent this kind of  attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' The MOFlow attack ( Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='6 ) takes advantage  of the lack of tight coupling memory with applications that  are using them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' So any trusted application can access the  memory of another trusted app and read the encrypted data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  Even though the application data is encrypted, hackers may  exploit the encryption algorithm used in ARM TrustZone to  decrypt the extracted data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Lapid et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' [21] showed using  GPU-based analysis it is possible to crack the TrustZone  implementation of AES.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' However, the SAU can be used to  limit the applications from accessing others’ data and thus  resolve this vulnerability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Mitigation plan  By design, TrustZone ensures the security to access the  secure world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' No unauthorized app can access any user  or kernel service inside a secure world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' But ensuring the  security of data within TEE is challenging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Ron et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' [22]  showed how an attacker can run arbitrary code in a secure  world and how to handle those attacks with protection  measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' These are designed on top of control-flow  attacks [23], [24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' We will focus on the mitigation plan  of protecting memory leakages and vulnerable points in  non-secure callable so that any bad coding or intentional  attacks are handled within the TrustZone framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' This  will ensure the robustness of the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  Non-secure callable give the bridge to a normal world  app for sending any data or instruction to a secure world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  Without the proper, guard for checking memory boundary in  the veneer table, a potential Achilles heel will be created and  compromised the whole system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' There should be a mech-  anism inside the non-secure callable to check the memory  boundary of a secure world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' For example, in the Listing-  6 below, cmse check address range() provides validity  of incoming requests address range and blocks inside the  non-secure callable regions for an Achilles heel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  /* Check whether string is located in  non-secure memory */  #if (__GNUC__ !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='= 10)  if (cmse_check_address_range((void *)s,  string_length, CMSE_NONSECURE |  CMSE_MPU_READ) == NULL)  {  PRINTF("Achilles’ Heel exception:  String is not located in normal  world!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='\\r\\n");' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  abort();' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  }  #endif  Listing 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Checking for a potential Achilles’ Heel attack  A commercial application in the robust IoT ecosystems,  multiple vendors will develop different kinds of services.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' To  relay this kind of security checking on 3rd party application  developers instead of automatic platform support is a risky  design.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  The primitive APIs for memory management are ex-  posed by TrustZone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Process and executing the business  logic of certain services is vital and error prune even for  ARM platform developers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Furthermore, if the vendor ap-  plication developer does not have an in-depth understanding  of the underlying security design, the internal memory map  can be messed up.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' As a result, attackers may be able to  read sensitive data from other memory locations or trigger  a system crash.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' When the code reads a variable quantity of  data and assumes that a sentinel, such as a NULL in a string,  exists to terminate the read operation, a crash can occur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  If the expected sentinel isn’t found in the out-of-bounds  memory, too much data is read, resulting in a segmentation  fault or a buffer overflow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Any instruction can change an  index or execute pointer arithmetic on a memory address  that is outside the buffer’s limits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Following that, a read  operation yields undefined or unexpected results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  To handle this, we are proposing an additional layer of  security in between non-secure callable and secure zone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  The purpose is to handle the abnormality of bad code inside  the secure zone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' This is expected that a 3rd party developer  can write vulnerable code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' The system should have a defense  mechanism to find in various stages of development.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' We  have not found any extensive tools to detect issues inside the  secure applications with MCUExpress tools [25] by NXP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  ARM provides tools for memory profiling for other chipset  [26], not which has embedded TrustZone framework for 3rd  party vendors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' There are 3rd party C-based memory profilers  [27]–[29] to analyze memory usage and highlight potential  memory leak issues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' But these are not customized for the  profiling memory with security constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' For example,  root routes of new instances that could cause memory leaks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  The root pathways provide information on why the instance  is not freed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' When determining how a memory leak happens,  this is the most crucial information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  To overcome MOFLow attacks, we have proposed  a communication design flow mentioned in the Figure-6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  There will be multiple components inside the non-secure  callable and secure region of TrustZone and will comply  with the security principle of SAU and IDAU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' The Proposed Trust Model  Non-secure callable (NSC) is a shared region (5) for  both secure and non-secure execution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Boundary Verifier  will cross-check the request from non-secure instruction  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' x1) and validate the address range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' If it is valid, then  TZ Interface APIs will be used for accessing the memory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  Otherwise, an error (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' e1) will be generated for the non-  secure process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Non-secure app might be multi-threaded and  executes parallel instructions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' The purpose of the handling  error in NSC to isolate defected instructions outside of the  secure zone with meaningful information in error set (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  E{e1, e2, e3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=', en}).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' This will block all possible Achilles’  heels in NSC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  We propose two additional components for the secure  zone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' TZx APIs with leak collector is an extension frame-  work, consists of an API set, build on top of primitive  TrustZone APIs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' These APIs will have leak collectors in  related logic and solve the problem of circular dependencies  on the shared resource.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Verifier in the secure zone plays a  vital role to protect MOFlow attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Whenever a non-secure  process will try to access any information which is held  by a data structure, the verifier checks the boundary of the  allocated memory before responding to non-secure process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  Data security in shared memory with blocked Achilles’s  heels provides additional attributes for the robustness of the  TrustZone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Future Works  It is possible to further extend our attack model by  reducing the search space inside the TrustZone for the target  data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' This can help to trace the data for a particular trusted  application inside the secure zone faster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Thus stealing the  data only for that target application.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' For example, Chen et  al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' [30] proposed a cache flushing-based side-channel attack  on the ARM processors to reduce the search space to find  a specific key value within the cache memory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Related Works  Many of the recent TrustZone vulnerabilities are caused  by cache attacks [31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Cache-based side-channel attacks  mainly focus on the execution time and trace of user’s ac-  cesses during the cache operations to perform these attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  Lipp et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' [32] used the lack of ‘cache flush‘ on old ARM  cores (before ARMv8) to monitor cache activity within the  ARM TrustZone from outside.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' The cache coherence proto-  col allowed processors to fetch shared cache lines and thus  exposing them to cache-based attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Taking advantage of  the coherence protocol in a multiprocessor system, Yarom  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' [33] was able to examine cache lines of one core from  another by flush and reload attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Lapid et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' [21] exploited  the misaligned T-table of the Keymaster Trustlet of ARM  TrustZone in Samsung mobile and successfully extracted the  AES-256 keys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  Side-channel-based attacks also have been extensively  studied on the ARM TrustZone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' [30] was able to  exploit a downgrade attack on TAs (Trusted Applications),  by patching the old version onto the new one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' The system’s  vulnerability would let others replace the current trust with  an old vulnerable one and use that to run the TA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  DMA (Direct Memory Access) attacks are also contin-  uously under research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Yahuda et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' [34] showed that by  dumping memory frequently using DMA transactions, write  patterns can be examined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' In ARM TrustZone, they were  able to extract RSA keys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' The DAGGER tool [35] can steal  cryptographic keys using a DMA-based keystroke logger.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' It  can also attack the OS-kernel structure and file cache.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  The ARM debugging feature lets a host get read/write  access to the TrustZone [36] and leak private keys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' The  defective ECDSA signing in Qualcomm’s implementation  of Android’s hardware-backed Keystore let attackers extract  a 256-bit private key from the key store [37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  Current Work’s Limitations: Most of the attacks on  ARM TrustZone focus on Cortex-A processors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' However,  the ARM Cortex-M processor is increasingly becoming  more popular in Mobile and IoT applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Because it  is optimized specifically for them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Its design structure (fast  hardware-based transition, no memory management, no-  cache) is also much different from that of Cortex-A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' So it  is important to properly investigate possible vulnerabilities  in its security protocols and TrustZone implementation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Limitations of Our Work  The proposed attacks are done based on the assumption  that we can install our vulnerable trusted application on the  victim’s device.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' This might not be possible in some cases  where the attacker doesn’t have access to the victim’s device.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  However, it is possible to modify applications that the victim  trusts and use that to install the modified vulnerable app.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  ecure Callable  Secure  Invalid  Boundary  Verifier  Verifier  Primitive  Valid  TZ APIS  TZx APIs  with leak  TZ  collector  nterface  APIsEven though our attack model has successfully extracted  other applications’ data from the secured zone, they are  encrypted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' So a separate tool will be needed to decrypt the  data and make meaning out of it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' However, some prior works  have already been successful in cracking the encryption  implementation of ARM TrustZone [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' So it is possible to  overcome this limitation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Our used processor ARM Cortex-  M33 is not the latest release with the ARM TrustZone  feature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Despite our best efforts, we were unable to find  any development boards in the market with the latex ARM  Cortex-M35P and M55 processors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' So the attack models  might not represent an exact evaluation of the state-of-the-  art ARM architecture and countermeasures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' However, due  to the short time limit of the project, it was impossible to  wait for development boards with a very long delivery time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Conclusion  After performing a series of different attacks on the  ARM Cortex-M micro-controller with the proposed threat  model, the MOFlow and Achilles heel approaches were  successfully able to access encrypted data from the secure  world region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' However, there are some key limitations and  controlled factors that make this vulnerability less likely to  occur organically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' The successful MOFlow attack can only  be performed if the attacker can gain access to the secure  world of a TrustZone’s secure region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' A potential route of  work to improve the likelihood of a successful MOFlow  attack in the wild is finding a way to reduce the search space  in the secure zone region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Secondly, retrieving the victim’s  sensitive data from the TrustZone-M micro-controller is only  one step in the process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Since the information is encrypted in  the secure region, an attacker would need to exploit the cor-  rect decryption algorithm that TrustZone uses to obtain the  plain-text information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' One future route of work would be to  investigate the implementation of TrustZone-M’s encryption  and decryption algorithms and try to exploit them from the  micro-controller.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Doing so would enhance our current work  significantly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Another opportunity for future work would be  performing CacheTrack side-channel attacks on the Cortex-  M35P or Cortex-M55 micro-controllers once their demand  in the micro-controller market decreases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' The Cortex-M35P  and Cortex- M55 processors are considered state-of-the-art  chips for TrustZone-M computing with instruction and data  tightly coupled memory and there is a lack of research  exploring these specific chips for novel vulnerabilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  References  [1]  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  Thornton,  “Arm  trustzone  explained.”  [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  Available:  https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='microcontrollertips.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='com/embedded-security-brief-arm-trustzone-explained/  [2]  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Liu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Yu, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Zang, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Sandhu, “Cost and effectiveness of  trustzone defense and side-channel attack on arm platform.” J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Wirel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  Mob.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Networks Ubiquitous Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Dependable Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' 11, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' 4,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' 1–15, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  [3]  ARM,  “Cortex-m23.”  [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  Available:  https://developer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='arm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='com/Processors/Cortex-M23  [4]  ——,  “Cortex-m33.”  [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  Available:  https://developer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='arm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='com/Processors/Cortex-M33  [5]  ——,  “Cortex-m55.”  [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  Available:  https://developer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='arm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='com/Processors/Cortex-M55  [6]  Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' et al, “Controlled-channel attacks: Deterministic side channels  for untrusted operating systems,” in IEEE Symposium on Security and  Privacy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  IEEE S&P, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  [7]  T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='-W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Shih, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Lee and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Peinado, “T-sgx: Eradicating  controlled-channel attacks against enclave programs,” in The Network  and Distributed System Security Symposium (NDSS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  NDSS, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  [8]  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Lipp, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Spreitzer, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Mangard, “Armageddon:  Cache attacks on mobile devices,” in 25th USENIX Security Sympo-  sium 16).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  USENIX, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  [9]  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  Commons,  “The  heartbleed  bug.”  [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  Available:  https://heartbleed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='com  [10] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  Fruhlinger,  “What  is  the  heartbleed  bug,  how  does  it  work  and  how  was  it  fixed?”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  Available:  https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='csoonline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='com/article/3223203/what-is-the-heartbleed-bug-how-does-it-work-and-how-was-it-fixed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='html  [11] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Zhang, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Sun and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Hou, “Case: Cache-assisted secure  execution on arm processors,” in IEEE Symposium on Security and  Privacy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  IEEE S&P, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  [12] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Zhou, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Wang and Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Wang, “Armlock: Hardware-based  fault isolation for arm,” in ACM Conference on Computer and Com-  munications Security.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  ACM CCS, 2014, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' 558–569.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  [13] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Ning Zhang, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Deborah Shands, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Hou, “Trusense:  Information leakage from trustzone,” in International Conference on  Computer Communications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  INFOCOM, 2018, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  [14] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Developer, “Arm trustzone technology.” [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Available:  https://developer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='arm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='com/documentation/100690/0201/Arm-TrustZone-technology?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='lang=en  [15] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Vyas, “Emuation using qemu’s native raspi2/3 machine.” [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  Available: https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='com/dhruvvyas90/qemu-rpi-kernel  [16] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' dev Vyas, “Raspberry pi documentation.” [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Available:  https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='raspberrypi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='com/documentation/computers/using linux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='html  [17] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  Pi,  “The  linux  kernel  user’s  and  administrator’s  guide.”  [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  Available:  https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='com/raspberrypi/linux/blob/rpi-5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='y/Documentation/admin-guide/index.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='rst  [18] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  Developer,  “Lpcxpresso55s69  de-  velopment  board.”  [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  Available:  https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='nxp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='com/design/development-boards/lpcxpresso-boards/lpcxpresso55s69-development-board:LPC55S69-EVK  [19] ——,  “Numicro®  m2351  series  –  a  trustzone®  empowered  microcontroller series focusing on iot security.” [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Available:  https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='nuvoton.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='com/products/microcontrollers/arm-cortex-m23-mcus/m2351-series/?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  locale=en  [20] ARM,  “Bx,  bxns:  Branch  and  exchange  instruction  set  and  branch  and  exchange  non-secure.”  [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  Available:  https://developer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='arm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='com/documentation/100076/0200/a32-t32-instruction-set-reference/a32-and-t32-instructions/bx--bxns  [21] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Lapid and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Wool, “Cache-attacks on the arm trustzone im-  plementations of aes-256 and aes-256-gcm via gpu-based analysis,”  in International Conference on Selected Areas in Cryptography.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  Springer, 2018, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' 235–256.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  [22] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Stajnrod, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Ben Yehuda, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Zaidenberg, “Attacking trust-  zone on devices lacking memory protection,” Journal of Computer  Virology and Hacking Techniques, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' 1–11, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  [23] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Zhang and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Sekar, “Control flow integrity for {COTS} binaries,”  in 22nd USENIX Security Symposium (USENIX Security 13), 2013,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' 337–352.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  [24] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Davi, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Koeberl, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='-R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Sadeghi, “Hardware-assisted fine-  grained  control-flow  integrity:  Towards  efficient  protection  of  embedded systems against software exploitation,” in 2014 51st  ACM/EDAC/IEEE Design Automation Conference (DAC).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  IEEE,  2014, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' 1–6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  [25] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Semiconductors, “Mcuxpresso ide user guide.” [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Available:  https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='nxp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='com/docs/en/user-guide/MCUXpresso IDE User Guide.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='pdf  [26] ARM,  “Memory  leak  detection.”  [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  Available:  https://developer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='arm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='com/documentation/102604/0100/Memory-leak-detection  [27] milostosic, “Mtuner- advanced c/c++ profiler.” [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Available:  https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='com/milostosic/MTuner  [28] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  Developers,  “Valgrind  documentation.”  [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  Available:  https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='com/milostosic/MTuner  [29] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  Developer,  “Inspect  your  app’s  memory  us-  age  with  memory  profiler.”  [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  Available:  https://developer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='android.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='com/studio/profile/memory-profiler  [30] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Chen, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Zhang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Wang, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Wei, “Downgrade attack on  trustzone,” arXiv preprint arXiv:1707.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='05082, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  [31] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Mushtaq, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Mukhtar, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Lapotre, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Bhatti, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Gog-  niat, “Winter is here!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' a decade of cache-based side-channel attacks,  detection & mitigation for rsa,” Information Systems, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' 92, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  101524, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  [32] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Lipp, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Gruss, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Spreitzer, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Maurice, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Mangard,  “Armageddon: Cache attacks on mobile devices,” in 25th USENIX  Security Symposium 16, 2016, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' 549–564.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  [33] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Yarom and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Falkner, “Flush+ reload: A high resolution, low  noise, l3 cache side-channel attack,” in 23rd USENIX Security Sym-  posium 14, 2014, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' 719–732.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  [34] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Yehuda and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Zaidenberg, “Protection against reverse  engineering in arm,” International Journal of Information Security,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' 19, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' 39–51, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  [35] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Irazoqui, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Eisenbarth, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Sunar, “Cross processor cache  attacks,” in Proceedings of the 11th ACM on Asia conference on  computer and communications security, 2016, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' 353–364.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  [36] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Ning and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Zhang, “Understanding the security of arm debugging  features,” in 2019 IEEE Symposium on Security and Privacy (SP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  IEEE, 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' 602–619.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content='  [37] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' Ryan, “Hardware-backed heist: Extracting ecdsa keys from qual-  comm’s trustzone,” in Proceedings of the 2019 ACM SIGSAC Confer-  ence on Computer and Communications Security, 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
+page_content=' 181–194.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE3T4oBgHgl3EQfjwpk/content/2301.04591v1.pdf'}
diff --git a/tdE4T4oBgHgl3EQfxQ03/content/tmp_files/2301.05256v1.pdf.txt b/tdE4T4oBgHgl3EQfxQ03/content/tmp_files/2301.05256v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a941b1a262b75e5dfb6f808b1496d4ced3422aa4
--- /dev/null
+++ b/tdE4T4oBgHgl3EQfxQ03/content/tmp_files/2301.05256v1.pdf.txt
@@ -0,0 +1,5802 @@
+Prepared for submission to JHEP
+MIT-CTP/5511
+An effective field theory for non-maximal
+quantum chaos
+Ping Gao and Hong Liu
+Center for Theoretical Physics,
+Massachusetts Institute of Technology, Cambridge, MA 02139, USA
+E-mail: pgao@mit.edu, hong liu@mit.edu
+Abstract: In non-maximally quantum chaotic systems, the exponential behavior of
+out-of-time-ordered correlators (OTOCs) results from summing over exchanges of an
+infinite tower of higher “spin” operators. We construct an effective field theory (EFT)
+to capture these exchanges in (0 + 1) dimensions. The EFT generalizes the one for
+maximally chaotic systems, and reduces to it in the limit of maximal chaos. The theory
+predicts the general structure of OTOCs both at leading order in the 1/N expansion
+(N is the number of degrees of freedom), and after resuming over an infinite number
+of higher order 1/N corrections.
+These general results agree with those previously
+explicitly obtained in specific models. We also show that the general structure of the
+EFT can be extracted from the large q SYK model.
+arXiv:2301.05256v1  [hep-th]  12 Jan 2023
+
+Contents
+1
+Introduction
+1
+2
+The structure of EFT
+6
+2.1
+General setup
+6
+2.2
+Two-component effective mode and constraints from KMS symmetries
+8
+2.3
+Diagonalize the KMS conditions
+12
+2.4
+Reformulating the KMS conditions
+14
+2.5
+The quadratic effective action
+17
+2.6
+Shift symmetry and exponential growth in correlation functions
+21
+2.7
+Summary of the effective field theory
+23
+2.8
+TOC and OTOC
+25
+2.9
+General structure of OTOCs for non-maximal chaos
+27
+3
+Comparisons with OTOCs in various theories
+29
+3.1
+The large q SYK model
+29
+3.2
+Stringy scattering in a AdS black hole
+30
+3.3
+Conformal Regge theory
+32
+4
+Relation to the EFT of maximal chaos
+35
+5
+Identifying the effective fields in the large q SYK model
+37
+5.1
+OTOC of the large q SYK model
+38
+5.2
+Identifying the effective fields
+41
+5.3
+Two-point function of φE
+i
+42
+5.4
+Effective action for large q SYK
+44
+6
+Higher order terms and exponentiation
+47
+6.1
+Towards a scattering formula
+47
+6.2
+An example
+52
+7
+Conclusion and discussion
+55
+A A few oversimplified constructions
+56
+A.1 Multiple effective modes with one time argument
+56
+A.2 Two effective modes with one time argument and ordered coupling
+59
+– i –
+
+B Unitary and dynamical KMS conditions
+59
+C Generalization to polynomial-exponential case
+63
+C.1 Wightman functions
+64
+C.2 The effective action
+66
+D Correlation functions of effective modes in the large q SYK model
+68
+D.1 Canonical quantization trick
+68
+D.2 Solve discrete quantum numbers
+70
+D.3 Correlations
+72
+D.4 The effective action
+75
+E Solve m = 1 vertex
+77
+1
+Introduction
+Information injected into a small subsystem of a quantum many-body system eventu-
+ally spreads under time evolution across the entire system. Such scrambling of quantum
+information can be described in terms of growth of operators under Heisenberg evolu-
+tion. More explicitly, consider a quantum mechanical system with N degrees of freedom
+and few-body interactions among them. The growth of operators can be probed by the
+so-called out-of-time-ordered-correlators (OTOC) [1–6]
+F(t) = ⟨W(t)V (0)W(t)V (0)⟩β = ⟨Ψ2(t)|Ψ1(t)⟩,
+(1.1)
+|Ψ1(t)⟩ ≡ W(t)V (0) |Ψβ⟩ ,
+|Ψ2(t)⟩ ≡ V (0)W(t) |Ψβ⟩ .
+(1.2)
+Here V and W are generic few-body operators which we will take to be Hermitian, and
+⟨· · ·⟩β denotes the thermal average at an inverse temperature β. In (1.2), |Ψβ⟩ denotes
+the thermal field double state the expectation values with respect to which give the
+thermal averages.
+In the large N limit, the degrees of freedom involved in generic few-body operators
+V (0) and W(0) do not overlap with each other. For small t, V (0) and W(t) almost
+commute, and |Ψ1,2⟩ are almost identical, which means that F(t) should be O(1). As
+time increases, W(t) grows, and Ψ1,2 become more and more different, which decreases
+F(t). It is expected for chaotic systems [5]
+F(t) ∼ c1 − c2
+N eλt + · · ·
+(1.3)
+– 1 –
+
+where c1,2 are some constants and λ is the quantum Lyapunov exponent. In contrast,
+H1(t) = ⟨Ψ1(t)|Ψ1(t)⟩ = ⟨V (0)W(t)W(t)V (0)⟩β,
+(1.4)
+H2(t) = ⟨Ψ2(t)|Ψ2(t)⟩ = ⟨W(t)V (0)V (0)W(t)⟩β,
+(1.5)
+the so-called time-ordered correlators (TOCs), always remain O(1). The exponential
+behavior in (1.3) says that in a chaotic system, the slight difference in the initial
+preparation of |Ψ1,2⟩ will be quickly magnified during time evolution, which is the
+essence of the butterfly effect.
+Quantum Lyapunov exponent λ is state-dependent, describing operator growths
+“moderated” by the state under consideration. It has an upper bound [7]
+λ ≤ 2π
+β .
+(1.6)
+The bound is saturated by various systems, including holographic systems in the clas-
+sical gravity limit, and SYK-type systems in the low temperature limit. These “max-
+imally” chaotic systems are special: the exponential time dependence in (1.3) can be
+attributed to the exchange of the stress tensor between W and V (see Fig. 1a), and
+can be described by a hydrodynamic effective theory with a single effective field ϕ
+that plays the dual role of ensuring energy conservation and characterizing operator
+growth [8, 9].
+For non-maximal chaotic systems with λ < 2π
+β , the origin of (1.3) is more intricate,
+arising from exchanging an infinite number of operators. For example, in the SYK
+system, exchange of an operator characterized by some quantum number j leads to an
+exponential decrease in F(t) proportional to e
+2π
+β (j−1)t, which violates the bound for any
+j > 2. Summing over exchanges of an infinite tower of such operators with increasingly
+larger values of j leads to an effective λ satisfying the bound. We will loosely refer to
+j as “spin” in analogue with higher dimensional systems even though there is no spin
+for SYK. Another example is four-point correlation functions of a large N CFT in the
+vacuum state in the so-called conformal Regge regime [10–12], which can be interpreted
+as a thermal OTOC in terms of Rindler time (with β = 2π). Here contribution from
+a spin-j operator in the OPE of WW (and V V ) gives a contribution proportional to
+e(j−1)t (t is now the Rindler time) and summing over an infinite number of higher spin
+operator exchanges gives an λ < 1.
+It is natural to ask whether there exists an effective description with a small number
+of degrees of freedom that can capture the sum over exchanges of the infinite tower of
+operators, with jeff = 1 + λ β
+2π interpreted as the effective spin of the effective fields.
+We should stress that such an effective description is conceptually and philosophi-
+cally different from that is usually used in effective field theory (EFT). Usually an EFT
+– 2 –
+
+(a)
+(b)
+Figure 1. (a) The maximal chaos can be described by exchange of the stress tensor between
+W and V . (b) Sum over infinitely many spin j particles exchange between W and V can be
+viewed as the exchange of a Reggeon.
+is used to describe the dynamics of a small number of “low energy” (or “slow”) degrees
+of freedom whose contributions dominate over others in the regime of interests. Their
+effective actions can be formally defined from path integrals by integrating out other
+“high energy” (or “fast”) modes. There is, however, no such decoupling of “high en-
+ergy” (or “fast”) degrees of freedom here. Spin j (with j > 2) exchanges give important
+contributions to F(t); they cannot be integrated out in the usual sense. We are merely
+asking whether there is a way to capture the effect of the infinite sum. The effective
+fields here may not correspond to genuine physical collective degrees of freedom. The
+philosophy is also very different from the EFT for maximal chaos described in [8]; there
+the stress tensor exchange dominates and the EFT is used to capture the most essential
+part of the stress tensor exchange.
+The question of an effective description for non-maximal chaotic system is closely
+related a well-known problem in QCD, the formulation of EFTs for Reggeons (see
+e.g. [13] for a review). Consider a scattering process in some quantum system (say in
+QCD or string theory)
+V + W → V + W
+(1.7)
+where V, W denote different particles. We denote the scattering amplitude by A(s, t),
+with s the standard variable characterizing the total center of mass energy, and t
+characterizing the momentum exchange between V and W particles. In the regime
+s → ∞ with t finite, each spin j particle exchange between V and W gives a contribution
+to A(s, t) proportional to sj−1. When the Sommerfeld-Watson transform is used to
+summing over all the higher spin exchanges, the scattering amplitude can be written
+in a form
+A(s, t) ∝ gWW(t)gV V (t)sα(t)−1
+(1.8)
+which can be interpreted as the exchange of a single effective particle, called reggeon,
+with an effective spin α(t). gWW, gV V can be interpreted as couplings the Reggeon to
+W and V . See Fig. 1b for an illustration.
+– 3 –
+
+For systems with a gravity dual, the OTOC (1.1) maps to the gravity side a scat-
+tering process precisely of the form (1.7) in a black hole geometry [1–4], with V, W the
+corresponding bulk particles dual the boundary operators. The center of mass energy
+square s for the scattering process is related to time separation t in (1.1) by s ∝ e
+2π
+β t. In
+the bulk language, λ arises from summing over exchanges of an infinite number stringy
+modes with increasingly higher spins.
+In the α′ → 0 limit, the contributions of higher spin stringy modes decouple, with
+only graviton exchange remaining, and the system becomes maximally chaotic. In this
+limit, the maximal value λmax = 2π
+β is universal for all holographic systems, independent
+of the details of the black hole geometries [7], and can be argued as a direct consequence
+of existence of a sharp horizon.
+Having an effective description away from the α′ → 0 limit that can capture an
+infinite number of stringy modes exchanges is clearly valuable. Such an effective de-
+scription can also potentially give insights into what becomes of the event horizon in
+the stringy regime.
+In this paper we make a proposal to formulate an EFT for a non-maximal chaotic
+system. For simplicity, we will restrict to a quantum mechanical system with no spatial
+dependence. Generalization to having spatial dependence should be straightforward,
+and will be left elsewhere.
+Lacking at the moment a first-principle understanding
+of the nature of the effective chaos field(s) or their effective action, our approach is
+phenomenological. We try to identify a minimal set of fields and a minimal set of
+conditions on their action, such that the following criteria are met:
+1. With λ being an input parameter, the EFT gives rise to exponential behavior (1.3)
+for OTOCs, but no exponential for TOCs (1.4)–(1.5).
+2. It captures all the KMS properties of thermal 4-point functions.
+We will see that the above conditions are rather constraining, and the resulting EFT
+can be used to make a general prediction on the structure of OTOCs, which is consistent
+with that previously postulated in [14, 15], and agree with the explicit expressions in
+large q SYK model, holographic systems (obtained from stringy scattering), and the
+conformal Regge theory. Furthermore, we show that in this framework it is possible
+to sum higher order terms in equation (1.3) of the form ekλt
+Nk (with k an integer)1 in an
+exponential, which can again be viewed as a general prediction, and agrees with those
+previously obtained in specific systems [4, 16, 17].
+We also show that the structure proposed for the non-maximal chaos EFT can be
+in fact extracted in the large-q SYK model, where it is possible to identify explicitly
+1Such terms are of the same order and dominate in the regime N → ∞ and t ∼ 1
+λ log N.
+– 4 –
+
+Figure 2. Effective description of W(t1)W(t2) in non-maximal chaotic systems. The black
+dots are bare operators W0. There are now two types of dressing: one type dresses each local
+operator separately (yellow “clouds”), and the other type dresses both operators together
+(blue “clouds”). Maximal chaos case contains only the first type of dressing.
+the chaos effective fields, and make much finer comparison between the EFT and the
+microscopic theory than the structure of TOCs and OTOCs.
+It is worth mentioning here a key difference between the non-maximal EFT to be
+discussed in this paper and that for maximal chaotic systems of [8, 9]. For maximal
+chaotic systems, W(t) can be viewed as W(t) = W[W0(t), ϕ(t)] where “bare” operator
+W0(t) describes W(t) in the large N limit (with no overlap with V0). ϕ(t) is an effective
+field “attached” to W0, i.e. W is obtained by dressing W0 with ϕ. ϕ captures effectively
+the overlap between W(t) and V (0) due to scrambling, and its dynamics leads to 1/N
+corrections indicated in (1.3). For non-maximal chaotic systems, the chaos fields involve
+multiple components: (i) one component dresses each bare local operator as in the
+maximal chaotic case (and indeed it reduces to ϕ in the maximal chaos limit). This
+component carries only one time argument. (ii) There are other components which
+dress both W’s in (1.1), i.e. it has two time arguments (see Fig. 2 for an illustration).
+Existence of such components leads to many new elements which are not present in the
+maximal case.
+The paper is organized as follows. In Section 2, we construct the effective field
+theory of non-maximal chaos with two effective fields φ1,2 and show that the TOC
+does not have exponential growth and OTOC has exponential growth. In Section 3
+we compare the general structure of OTOCs obtained in Sec. 2 with various known
+examples. In Section 4, we show that the two effective fields φ1,2 reduce to a single field
+in the maximal chaos limit and the EFT becomes the same as the EFT constructed
+for maximal chaos.
+In Section 5, we show how the general structure of the EFT
+discussed in Sec. 2 arises in the large q SYK model, and obtain the explicit form of the
+EFT action. In Section 6, we include higher order coupling to effective mode φ1,2 and
+show that certain higher-order terms of the four-point function can be resummed and
+exponentiated. We conclude in Section 7 with a summary and a discussion of future
+directions.
+– 5 –
+
+Wo (t1)
+(2) °M
+Wo (t1) Wo (t2)2
+The structure of EFT
+In this section we discuss the general formulation of an EFT for non-maximally chaotic
+systems. For simplicity we will consider quantum mechanical systems with no spatial
+dependence. Generalization to systems with spatial dependence can be readily made,
+although technically more intricate. We will also use the unit such that β = 2π .
+2.1
+General setup
+Consider a generic four-point Wightman function in thermal state
+Fabcd(t1, t2, t3, t4) = Tr
+�
+e−2πHOa(t1)Ob(t2)Oc(t3)Od(t4)
+�
+≡ ⟨Oa(t1)Ob(t2)Oc(t3)Od(t4)⟩
+(2.1)
+where the subscript refers to the ordering of operators and the time argument should
+be understood as corresponding to each subscript in the same order. We will treat time
+variables as complex, and Fabcd(t1, t2, t3, t4) is analytic in the domain
+D :
+ℑt4 − 2π < ℑt1 < ℑt2 < ℑt3 < ℑt4 .
+(2.2)
+Fabcd obeys the KMS condition
+Fabcd(t1, t2, t3, t4) = Fbcda(t2, t3, t4, t1 + 2πi)
+(2.3)
+which can be iterated cyclically to shift other time variables. It is convenient to intro-
+duce a time-ordered function
+ˆFabcd(t1, t2, t3, t4) ≡ ⟨T Oa(t1)Ob(t2)Oc(t3)Od(t4)⟩
+(2.4)
+where T denotes operators should be ordered from left to right according to the as-
+cending order of their corresponding ℑti. Moreover, it should always be understood
+that
+(ℑti)min − (ℑti)max ∈ (−2π, 0), i = 1, 2, 3, 4 .
+(2.5)
+The KMS condition (2.3) can then be written as
+ˆFabcd(t1, t2, t3, t4) = ˆFabcd(t′
+1, t′
+2, t′
+3, t′
+4),
+t′
+i = ti + 2πimi
+(2.6)
+where mi are integers, and should be such that t′
+i’s obey (2.5).
+Now consider
+ˆFWWV V (t1, t2; t3, t4) = ⟨T W(t1)W(t2)V (t3)V (t4)⟩
+(2.7)
+which by definition is symmetric under swapping t1 ↔ t2 and t3 ↔ t4
+ˆFWWV V (t1, t2; t3, t4) = ˆFWWV V (t2, t1; t3, t4) = ˆFWWV V (t1, t2; t4, t3) .
+(2.8)
+– 6 –
+
+Depending on ℑti, ˆFWWV V (t1, t2; t3, t4) can correspond to TOC or OTOC. For example,
+ˆFWWV V (t1, t2; t3, t4) = ⟨V (t3)W(t1)W(t2)V (t4)⟩,
+ℑt3 < ℑt1 < ℑt2 < ℑt4
+(2.9)
+ˆFWWV V (t1, t2; t3, t4) = ⟨W(t1)V (t3)W(t2)V (t4)⟩,
+ℑt1 < ℑt3 < ℑt2 < ℑt4
+(2.10)
+A TOC and OTOC cannot change into each other under cyclic permutations, so KMS
+conditions (2.3) relate functions within each type.
+Our goal is to develop an effective description for obtaining ˆFWWV V for large N.
+To motivate the structure of our proposed EFT for non-maximally chaotic systems, it
+is useful to recall some key elements of that for maximally chaotic systems introduced
+in [8]. One imagines the scrambling of W(t) allows a coarse-grained description in
+terms of building up an “effective cloud,” i.e.
+W(t) = W[W0(t), ϕ(t)] .
+(2.11)
+Here W0(t) is a “bare” operator involving the original degrees of freedom of W, and ϕ(t)
+is an effective chaos mode that describes macroscopically the growth of the operator in
+the space of degrees of freedom. W(t) in (2.11) is taken to be linear in W0 but can in
+principle have any dependence on the effective field ϕ(t). The dynamics of ϕ is governed
+by a chaos effective theory, with two-point function of ϕ scaling with N as 1/N. Thus
+W0 can also be viewed as giving the leading part of W(t) in a 1/N expansion.
+When ϕ(t) is small, it can be expanded to linear order as
+W(t) = W0(t) + Lt[W0(t)]ϕ(t) + O(ϕ2)
+(2.12)
+where Lt[W0] is a W0-dependent differential operator acting on ϕ. More explicitly,
+Lt[W0(t)]ϕ(t) =
+∞
+�
+m,n=0
+cmn∂m
+t W0(t)∂n
+t ϕ(t)
+(2.13)
+Below it should always be understood that Lt acts on the corresponding ϕ(t) even when
+they are not written adjacently. It then follows that
+W(t)W(t′) = W0(t)W0(t′)+Lt[W0(t)]ϕ(t)W0(t′)+W0(t)Lt′[W0(t′)]ϕ(t′)+O(ϕ2), (2.14)
+which for ℑ(t − t′) ∈ [−2π, 0] gives
+⟨T W(t)W(t′)⟩ = gW(t − t′) + O(1/N),
+gW(t − t′) ≡ ⟨T W0(t)W0(t′)⟩,
+(2.15)
+where we have assumed that one-point function of ϕ is zero. The O(1/N) piece in
+the above equation comes from O(ϕ2) term in (2.14), and is proportional to two-point
+function of φ. The KMS condition for gW is
+gW(t) = gW(−t − 2πi),
+ℑt ∈ [−2π, 0]
+(2.16)
+– 7 –
+
+Note that ⟨W(t)V (0)⟩ ∼ O(1/N) with ⟨W0V0⟩ = 0, as for generic few-body operators
+V, W, their two-point function should vanish at the leading order in 1/N expansion.
+Plugging (2.14) and the corresponding expression for V into (2.7), ˆFWWV V reduces
+to the two-point function of effective mode ϕ(t) at leading order
+ˆFWWV V (t1, t2; t3, t4) = gWgV +
+�
+i=1,2,j=3,4
+Lti ˜Ltj[gWgV ⟨T ϕ(ti)ϕ(tj)⟩EFT]
+(2.17)
+where ˜Lt is the differential operator from a similar expansion of V with cmn → ˜cmn,
+and
+gW ≡ gW(t12) = ⟨T W0(t1)W0(t2)⟩ ,
+gV ≡ gV (t34) = ⟨T V0(t3)V0(t4)⟩ .
+(2.18)
+Here the ⟨·⟩EFT means expectation value evaluated in the effective field theory of ϕ;
+T in ⟨T ϕ(ti)ϕ(tj)⟩EFT follows from the relative magnitude of ℑti and ℑtj.
+Equa-
+tion (2.17) has a very restrictive structure: the two-point function of ϕ in each term
+only depends on the locations of two operators. For example, the ϕ correlation function
+⟨T ϕ(t1)ϕ(t3)⟩EFT has no knowledge of t2, t4 at all. In other words, the four-point func-
+tion essentially reduces to pairwise two-point functions of ϕ. This structure leads to
+various features of ˆF that are consistent with a maximally chaotic system [9], including
+the Lyapunov exponent λ = 1 (after imposing a shift symmetry in the EFT of ϕ), but
+are not present in a non-maximally chaotic system. Since (2.17) is a direct consequence
+of (2.12), for non-maximally chaotic systems, we must generalize (2.12).
+2.2
+Two-component effective mode and constraints from KMS symmetries
+We will now propose a formulation for non-maximally chaotic systems which may be
+considered a minimal generalization of the EFT in [8] for maximal chaos. The formula-
+tion is partially motivated from features of the large q SYK theory, and as we will show
+in Sec. 5, fully captures the physics of that theory. The general structure of OTOCs
+resulting from it is also compatible with the conclusions of [4, 10–12, 18], as we will
+describe later.
+In this formulation ˆF still reduces to two-point functions of some effective fields, but
+the main new ingredient we would like to incorporate is that now two-point functions
+of effective field(s) have knowledge of the locations of all four operators, not just two
+of them. For this purpose we consider the following generalization of (2.12)2
+W(t)W(t′) = W0(t)W0(t′) +
+2
+�
+i=1
+D(i)
+W (t, t′)φi(t, t′) + O(φ2),
+(2.19)
+2We should emphasize that (2.19) and (2.14) should not be viewed as OPEs.
+If there are V
+insertion(s) between W’s we cannot do OPE, while these equations are supposed to be valid for any
+configurations of orderings.
+– 8 –
+
+where there are two fields φ1,2 who depend on both t, t′, and D(1,2)
+W
+(t, t′) are some
+W0-dependent differential operators to be specified more explicitly below. Now φ1,2
+depend on both t and t′ of W(t) and W(t′), which means that we cannot view φ1,2
+as the “dressing” of each individual operator, as in the case of (2.12). Rather they
+should be interpreted as an effective description of the sum over an infinite number of
+higher spin operator exchanges that are known to contribute to ˆF at the leading order
+in non-maximal systems [4, 10–12]. There is a parallel equation with W replaced by
+V ’s.
+The effective theory of φi should satisfy the following criteria:
+1. Exponential growth in OTOCs with an arbitrary Lyapunov exponent λ.
+2. No such exponential growth in TOCs.
+3. All the KMS conditions and analytic properties of ˆFWWV V are satisfied.
+We will show that the above goals can be achieved with a minimal generalization
+of (2.14). In this subsection we first present the prescription for (2.19), and work out
+the constraints on two-point functions of φ1,2 from the KMS conditions of ˆFWWV V ,
+which provide the basic inputs for formulating the theory of φ1,2.
+We will take φ1,2 to “mainly” couple to one of the W’s. A definition which respects
+the swap symmetry (2.8) of ˆF is that φ1 (φ2) couples mainly to the W with the
+smaller (larger) ℑt. Denoting tS (tL) with the smaller (larger) value of ℑt, ℑt′, by
+“mainly” we mean:
+1. φ1(t, t′) = φ1(¯t; tS) depends weakly on ¯t = t+t′
+2
+such that it can be expanded in
+terms of ¯t-derivatives. The dependence on ¯t encodes the nonlocal information of
+the theory. Similarly, φ2(t, t′) = φ2(¯t; tL).
+2. The action of D(i)
+W (t, t′) on φi can be expanded similarly as in (2.13)
+D(1)
+W (t, t′)φ1(t, t′) = W0(tL)LtS[W0]φ1(¯t; tS)
+(2.20)
+D(2)
+W (t, t′)φ2(t, t′) = W0(tS)LtL[W0]φ2(¯t; tL)
+(2.21)
+Lt[W0] ≡
+∞
+�
+m,n=0
+cmn∂m
+t W0(t)∂n
+t .
+(2.22)
+In other words, φ1 couples directly only to W(tS), but does feel the presence
+of W(tL) through weak dependence on ¯t. Note that equation (2.20) should be
+understood to be valid within time-ordered correlation functions, thus there is
+no need to worry about orderings between W0(tL) and W0(tS). Equation (2.20)
+– 9 –
+
+Figure 3. The green region is the domain I1 for φ1(¯t; t) and the blue region is the domain I2
+for φ2(¯t; t). The KMS conditions (2.26)–(2.27) relate φ1 with φ2 through identifying points
+between I1 and I2 as indicated by the black arrows. This generates the periodicity (2.29) on
+I1,2 (red arrows).
+contains no derivative with respect to ¯t; it can be viewed as the leading term in
+a derivative expansion of ¯t.
+For notational simplicity we take the coefficients cnm in (2.20) to be the same for
+D(2)
+W (t, t′), but our discussion can be straightforwardly generalized to the cases that
+they are not the same. The vertex for V will be denoted as ˜Lt with cmn → ˜cmn. The
+above prescription is a minimal nontrivial generalization of (2.12) that satisfies the
+aforestated criteria. In Appendix A we show that a few other simpler prescriptions
+cannot work.
+Since in (2.19) |ℑt−ℑt′| < 2π, by definition, φ1(¯t; t) is defined for ℑ¯t−ℑt ∈ (0, π),
+while φ2(¯t; t) is defined for ℑ¯t − ℑt ∈ (−π, 0). We refer to their domains as I1 and
+I2 respectively, see Fig. 3. Due to symmetries in exchanging t1 and t2, we will take
+ℑt1 < ℑt2, and similarly take ℑt3 < ℑt4. Therefore, φ1 always mainly couples to W(t1)
+and V (t3), φ2 always mainly couples to W(t2) and V (t4). Substituting (2.19)–(2.21)
+into ˆFWWV V we find
+ˆFWWV V (t1, t2; t3, t4) = gWgV +
+�
+i,j=1,2
+Lti ˜Ltj+2
+�
+gWgV
+�
+ˆT φi(¯tW; ti)φj(¯tV ; tj+2)
+��
+(2.23)
+where ¯tW = (t1 + t2)/2, ¯tV = (t3 + t4)/2, and the expectation value of φ1,2 should be
+understood as being evaluated in an effective theory. Unlike in (2.17), where the time-
+ordering T follows from that of ˆF, here in (2.23) the effective fields φ1,2(¯t; t) have two
+– 10 –
+
+I1time variables, and time-ordering in ˆF no longer leads to a unique choice of orderings of
+φi and φj. We will specify the precise meaning of
+�
+ˆT φi(¯tW; ti)φj(¯tV ; tj+2)
+�
+in Section
+2.3. Here we will just list some properties they should satisfy:
+1. Since in time ordered correlation function ˆF we can exchange V and W arbitrarily,
+the ordering of φi, φj in the correlation function should not matter, i.e.
+�
+ˆT φi(¯tW; ti)φj(¯tV ; tj+2)
+�
+=
+�
+ˆT φj(¯tV ; tj+2)φi(¯tW; ti)
+�
+.
+(2.24)
+2. From time translation invariance of the system, ˆF is invariant under shifts of
+all ti by the same constant, which implies the following translation invariance of
+two-point functions of φ1,2,
+�
+ˆT φi(¯t; t)φj(¯t′; t′)
+�
+=
+�
+ˆT φi(¯t + c; t + c)φj(¯t′ + c; t′ + c)
+�
+.
+(2.25)
+3. The KMS conditions satisfied by ˆF imply that these two-point functions of φ1,2
+should satisfy the following constraints
+�
+ˆT φ1(¯t; t)φi(¯t′; t′)
+�
+≃
+�
+ˆT φ2(¯t + πi; t + 2πi)φi(¯t′; t′)
+�
+,
+ℑt < ℑt′
+(2.26)
+�
+ˆT φ2(¯t; t)φi(¯t′; t′)
+�
+≃
+�
+ˆT φ1(¯t + πi; t)φi(¯t′; t′)
+�
+,
+(2.27)
+where ≃ means equal up to zero modes, defined as functions nij(t1, t2; t3, t4) sat-
+isfying
+�
+i,j=1,2
+Lti ˜Ltj[gWgV nij(t1, t2; t3, t4)] = 0 .
+(2.28)
+The zero modes can be viewed as field redefinition freedom of effective fields that
+does not cause any difference in the original four-point function ˆF. From now on,
+we will set nij = 0. Combining (2.26)–(2.27), we also get the following periodicity
+�
+ˆT φi(¯t; t)φj(¯t′; t′)
+�
+≃
+�
+ˆT φi(¯t + 2πi; t + 2πi)φj(¯t′; t′)
+�
+,
+ℑt < ℑt′ .
+(2.29)
+See Fig 3 for a diagrammatical depiction of (2.26)–(2.27).
+4. Four-point function ˆFWWV V (t1, t2; t3, t4) can have potential non-smoothness when
+the imaginary parts of two or more time arguments coincide, as these are the
+locations where ordering of operators change. There are two cases:
+– 11 –
+
+(a) ℑt1 = ℑt2, which corresponds to order changes of W’s within themselves. In
+terms of φ1,2(¯t; t), this corresponds to ℑ¯t−ℑt = 0, where the couplings of W’s
+to φ1,2 are switched.3 Similar statements apply to t3, t4. As stated earlier,
+we will restrict to ℑt1 < ℑt2 and ℑt3 < ℑt4 throughout, so such potential
+non-smoothness will not be relevant for our discussion of
+�
+ˆT φi(¯t; t)φj(¯t′; t′)
+�
+.
+(b) One of ℑt1, ℑt2 coinciding with one of ℑt3, ℑt4, which is a boundary be-
+tween the domains of ti corresponding to TOCs and OTOCs; crossing such
+a boundary a pair of W and V will exchange order. In terms of two-point
+function
+�
+ˆT φi(¯t; t)φj(¯t′; t′)
+�
+, this corresponds to potential non-smoothness
+at ℑt = ℑt′. In the domain D, we should not have any other singularities.
+2.3
+Diagonalize the KMS conditions
+We will now proceed to formulate an effective field theory (EFT) that can be used to
+obtain correlation functions of φi in (2.23).
+There is an immediate difficulty in directly formulating an EFT for φ1,2, due to
+that they are defined in different domains (recall Fig. 3). So they cannot appear in the
+same Lagrangian, but they transform to each other under the constraints (2.26)–(2.27)
+from the KMS conditions. To address this difficulty, we introduce two new fields,
+η±(¯t; t) = 1
+√
+2(φ1(¯t; t − iπ) ± φ2(¯t; t))
+(2.30)
+which are both defined in the domain I2 : ℑ(¯t − t) ∈ (−π, 0). Conversely, we have
+φ1(¯t; t) = 1
+√
+2(η+(¯t; t + iπ) + η−(¯t; t + iπ)),
+φ2(¯t; t) = 1
+√
+2(η+(¯t; t) − η−(¯t; t)) . (2.31)
+We will define two-point functions of φ1,2 in (2.23) in terms of those of η± using (2.31).
+For example,
+�
+ˆT φ1(¯t; t)φ2(¯t′; t′)
+�
+≡ 1
+2
+�
+s,s′=±
+s′ �
+ˆT ηs(¯t; t + iπ)ηs′(¯t′; t′)
+�
+,
+(2.32)
+where on the right hand side the time ordering ˆT is defined in terms of that of ℑt, i.e.
+�
+ˆT ηs(¯t; t)ηs′(¯t′; t′)
+�
+≡
+�
+⟨ηs(¯t; t)ηs′(¯t′; t′)⟩ ,
+ℑt < ℑt′
+⟨ηs′(¯t′; t′)ηs(¯t; t)⟩ ,
+ℑt > ℑt′
+,
+s, s′ = ± .
+(2.33)
+3For example, as we cross from ℑt1 − ℑt2 < 0 to ℑt1 − ℑt2 > 0, W(t1) switches from mainly
+coupled to φ1(¯tW ; t1) to mainly coupled to φ2(¯tW ; t1).
+– 12 –
+
+Now ⟨· · ·⟩ is understood as defined in the EFT of η±, and the right hand side of (2.33)
+should be understood as Wightman functions in the EFT. The motivations for choosing
+ˆT ordering in terms of ℑt are as follows. Firstly, as discussed in item 4b at the end of
+last subsection, correlation functions of φ1,2 have potential non-smoothness at ℑt = ℑt′.
+Ordering in ℑt in η-correlators provides a simple way to realize that. Secondly, we
+assumed that the dependence of φ1,2 on ¯t is weak, so should be η±. Making the ordering
+independent of ¯t is natural.
+Now consider the constraints (2.26)–(2.27). It can be checked that they are satisfied
+provided that
+�
+ˆT ηs(¯t; t)ηs′(¯t′; t′)
+�
+= s
+�
+ˆT ηs(¯t + iπ; t + iπ)ηs′(¯t′; t′)
+�
+,
+(2.34)
+which is diagonal in η±. We see that introducing η± not only resolves the domain issue,
+but also diagonalize the constraints from KMS conditions. Equation (2.34) implies
+.
+�
+ˆT ηs(¯t; t)ηs′(¯t′; t′)
+�
+= s′s
+�
+ˆT ηs(¯t + iπ; t + iπ)ηs′(¯t′ + iπ; t′ + iπ)
+�
+.
+(2.35)
+From (2.25), we have
+�
+ˆT ηs(¯t; t)ηs′(¯t′; t′)
+�
+=
+�
+ˆT ηs(¯t + c; t + c)ηs′(¯t′ + c; t′ + c)
+�
+,
+∀c ∈ C .
+(2.36)
+It then follows from (2.35) that
+�
+ˆT η+(¯t; t)η−(¯t′; t′)
+�
+= −
+�
+ˆT η+(¯t; t)η−(¯t′; t′)
+�
+= 0,
+(2.37)
+i.e. time-ordered functions of η± are also diagonal.
+We now proceed to formulate an effective theory of η± with the following consid-
+erations in mind:
+1. With the assumption of weak dependence on ¯t, we assume that the effective action
+can be expanded in derivatives of ¯t. This leads to an immediate simplification:
+with only derivative dependence on ¯t, the EFT becomes translationally invariant
+in ¯t. Now given (2.36), we also have translation invariance in t, i.e.
+�
+ˆT ηs(¯t; t)ηs′(¯t′; t′)
+�
+=
+�
+ˆT ηs(¯t − ¯t′; t − t′)ηs′(0; 0)
+�
+.
+(2.38)
+The domain for function
+GF(¯t; t) ≡
+�
+ˆT ηs(¯t; t)ηs′(0; 0)
+�
+(2.39)
+is then given by the shaded stripe indicated in Fig. 4.
+At quadratic order in η±, the effective action should be translationally invariant
+in both ¯t and t.
+– 13 –
+
+Figure 4. The correlation functions of ηs are defined on the green strip I ∪ (−I), on which
+a fundamental domain is the shaded parallelogram Dη. We analytically continue Dη to the
+yellow rectangular domain D∗, which is bounded by the red dashed lines.
+2. We would like to interpret (2.34) as the KMS conditions for the η±-system at
+a finite temperature. Given the definition of ˆT in terms of t, it is natural to
+interpret the temperature as being associated with t. However, the condition
+(2.34) shifts both ¯t and t simultaneously, which is not of the conventional form.
+In next subsection, we will discuss how to convert it into the standard form.
+3. So far the time variables ¯t, t are complex.
+To write down an effective action
+we need to choose a real section in the complex ¯t, t planes. From Fig. 4 it is
+convenient to choose the section to be that of imaginary ¯t and real t, i.e. we will
+let ¯t = −i¯τ and write down an action for η±(¯τ; t). It can be viewed as a two-
+dimensional field theory with ¯τ being a “spatial” coordinate and (real) t being
+time. Behavior of correlation functions for η± elsewhere are obtained by analytic
+continuations.
+2.4
+Reformulating the KMS conditions
+In this subsection we reformulate (2.34) as the KMS conditions for η± at a finite tem-
+perature (associated with t) with ¯τ = −ℑ¯t as a spatial direction.
+Let us first recall the standard story. For a quantum field χ in a two-dimensional
+spacetime (t, ¯τ) at a nonzero inverse temperature β, the KMS condition for Wightman
+functions are ⟨χ(¯τ1, t1)χ(¯τ2, t2)⟩ = ⟨χ(¯τ2, t2)χ(¯τ1, t1 + iβ)⟩, and the Feyman functions
+GF(¯τ, t) ≡
+�
+ˆT χ(¯τ, t)χ(0, 0)
+�
+= GF(¯τ, t + iβ), with its fundamental domain being
+ℑt ∈ (−β, 0). GF(¯τ, t) may have non-analytic behavior such as branch cuts at ℑt = 0
+and ℑt = −β.
+– 14 –
+
+JU(-I)
+DNow consider GF(¯t; t) defined in (2.39). From (2.34), the fundamental domain of
+GF(¯t; t) can be chosen to be the region Dη in Fig. 4. Equation (2.34) is not quite
+the KMS condition with β = π (note that this is
+1
+2 of the temperature we started
+with) due to the shift in ¯τ.
+We can resolve this issue by extending the region Dη
+to the larger region D∗ in Fig. 4. Region Dη is bounded above and below by lines
+¯τ − ℑt = ±π, which are part of the boundary of the analytic domain of the original
+four-point function ˆF. The behavior of GF at these boundaries are system-dependent
+and depend on UV physics. In other words, in principle for different systems different
+boundary conditions should be imposed there. In the spirit of effective field theories
+we expect that the general structure of the effective action should not depend on the
+specific UV physics, although the coefficients in the effective action will. Since we are
+only interested in the general structure of the effective action, we can choose a most
+convenient boundary condition: we extend the domain to D∗, and identify the values of
+GF(¯t; t) at ¯τ = −π and ¯τ = 2π. In other words, we have periodic boundary conditions
+in ¯τ direction. Note that later we will only need to use the behavior of GF(¯τ; t) in
+region Dη.
+Denote the conjugate momentum for ¯τ as P, then P = 2
+3m with m an integer. We
+can decompose ηs into three part
+ηs(¯τ; t) = ηs,0(¯τ; t) + ηs,+(¯τ; t) + ηs,−(¯τ; t)
+(2.40)
+where ηs,p contains only ¯τ-momenta P = 2
+3(3n + p) with n an integer and p = −1, 0, 1.
+ηs,p has the behavior
+ηs,p(¯τ + π; t) = e2πip/3ηs,p(¯τ; t),
+p = 0, ± .
+(2.41)
+Because of the additional phase e2πip/3, we should regard ηs,± as complex scalar fields.
+Since the original ηs is a real scalar, we need to identify them as hermitian conjugate
+to each other, i.e.
+η†
+s,p(¯τ; t) = ηs,−p(¯τ; t)
+(2.42)
+Given the translation symmetry, the following correlation functions vanish
+�
+ˆT ηs,0(¯τ; t)ηs,±(0; 0)
+�
+=
+�
+ˆT ηs,+(¯τ; t)ηs,+(0; 0)
+�
+=
+�
+ˆT ηs,−(¯τ; t)ηs,−(0; 0)
+�
+= 0 (2.43)
+and only
+�
+ˆT ηs,0(¯τ; t)ηs,0(0; 0)
+�
+and
+�
+ˆT ηs,∓(¯τ; t)ηs,±(0; 0)
+�
+could survive. In terms of
+these three modes, the KMS conditions (2.34) become
+�
+ˆT ηs,p(¯τ; t − iπ)ηs,−p(0; 0)
+�
+= se−2πip/3 �
+ˆT ηs,p(¯τ; t)ηs,−p(0; 0)
+�
+,
+(2.44)
+– 15 –
+
+Up to a phase these conditions are exactly the ordinary KMS conditions for inverse
+temperature β = π.
+Equation (2.44) can also be interpreted as that ηs,p have the
+following periodic conditions in the imaginary t direction
+ηs,p(¯τ; t − iπ) = se−2πip/3ηs,p(¯τ; t) .
+(2.45)
+Below we will also use Wightman functions
+G>
+s,p(¯τ; t) = ⟨ηs,p(¯τ; t)ηs,−p(0; 0)⟩ ,
+ℑt ∈ (−π, 0)
+(2.46)
+G<
+s,p(¯τ; t) = ⟨ηs,−p(0; 0)ηs,p(¯τ; t)⟩ ,
+ℑt ∈ (0, π) .
+(2.47)
+By translation symmetry, we have the relation G<
+s,p(¯τ; t) = G>
+s,−p(−¯τ; −t), and the KMS
+condition (2.44) can be written in terms of Wightman functions as
+G>
+s,p(¯τ; t − iπ) = se−2πip/3G<
+s,p(¯τ; t),
+ℑt ∈ (0, π) .
+(2.48)
+We can now express
+�
+ˆT φi(¯t; t)φj(0; 0)
+�
+in terms of thermal correlation functions
+of ηs,p. From (2.23), the relevant range for t is ℑt ∈ (−2π, 0). As mentioned earlier,
+thermal correlation functions
+�
+ˆT ηs,p(¯τ; t)ηs,p′(0; 0)
+�
+can have discontinuities at ℑt =
+0, ±π, · · · , which can potentially lead to discontinuity in
+�
+ˆT φi(¯t; t)φj(0; 0)
+�
+at ℑt = −π,
+which would be unphysical.4 To make clear the potential discontinuity, it is convenient
+to write the two-point function of φi using Wightman functions of ηs,p,
+�
+ˆT φ1(¯t; t)φ1(0; 0)
+�
+=
+�
+ˆT φ2(¯t; t)φ2(0; 0)
+�
+=
+�
+1
+2
+�
+s,p G>
+s,p(i¯t; t),
+ℑt ∈ [−π, 0]
+1
+2
+�
+s,p se−2πip/3G>
+s,p(i¯t; t + iπ),
+ℑt ∈ [−2π, −π]
+(2.49)
+�
+ˆT φ1(¯t; t)φ2(0; 0)
+�
+=
+�
+1
+2
+�
+s,p e2πip/3G>
+s,p(i¯t; t),
+ℑt ∈ [−π, 0]
+1
+2
+�
+s,p sG>
+s,p(i¯t; t + iπ),
+ℑt ∈ [−2π, −π]
+(2.50)
+�
+ˆT φ2(¯t; t)φ1(0; 0)
+�
+=
+�
+1
+2
+�
+s,p e−2πip/3G>
+s,p(i¯t; t),
+ℑt ∈ [−π, 0]
+1
+2
+�
+s,p se2πip/3G>
+s,p(i¯t; t + iπ),
+ℑt ∈ [−2π, −π]
+(2.51)
+where we have used (2.44) to shift the t argument of G>
+s,p such that it lies in the analytic
+domain of G>
+s,p.
+In (2.49), in order to avoid potential discontinuity at ℑt = −π we need
+�
+s,p
+G>
+s,p(¯τ, t) =
+�
+s,p
+se−2πip/3G>
+s,p(¯τ; t + iπ),
+ℑt = −π,
+¯τ ∈ [0, 2π] .
+(2.52)
+4As mentioned in item 4b, the only physical singularity for φi correlation function is at ℑt = 0.
+– 16 –
+
+Figure 5. The Keldysh contour of t for ηs,p(¯τ, t). The cross means multiplied with se−2πip/3
+to respect KMS condition (2.44).
+It is important to stress that with ℑt = −π, we have ¯τ ∈ [0, 2π] for two-point functions
+of φ1 or φ2 as indicated in the above equation. Now considering (2.50) and keeping in
+mind that for ℑt = −π, we have ¯τ ∈ [−π, π]. In order to compare with (2.52) we can
+shift ¯τ of (2.50) by π using periodicity (2.41), after which we again find equation (2.52).
+Similarly in (2.51), we have ¯τ ∈ [π, 3π], and after shifting ¯τ by −π we obtain the same
+equation. Equation (2.52) should be understood as two equations, one for τ ∈ [0, π],
+and the other for τ ∈ [π, 2π] which can in turn be shifted to the range τ ∈ [0, π] using
+periodicity (2.41). Applying (2.48) to the left hand side of (2.52) we find
+�
+p
+e−2πip/3G+,p(¯τ, t) =
+�
+p
+e−2πip/3G−,p(¯τ, t),
+ℑt = 0, ¯τ ∈ [0, π]
+(2.53)
+�
+p
+G+,p(¯τ, t) =
+�
+p
+G−,p(¯τ, t),
+ℑt = 0, ¯τ ∈ [0, π]
+(2.54)
+where we have defined for ℑt = 0
+Gs,p(¯τ; t) ≡ ⟨[ηs,p(¯τ; t), ηs,−p(0; 0)]⟩ = G>
+s,p(¯τ; t) − G<
+s,p(¯τ; t) = Gs,−p(−¯τ; −t)
+(2.55)
+Equations (2.53) and (2.54) can also be written in a more compact form
+G+,±(¯τ; t) − G−,±(¯τ; t) = −e±πi/3(G+,0(¯τ; t) − G−,0(¯τ; t))
+ℑt = 0, ¯τ ∈ [0, π] .
+(2.56)
+2.5
+The quadratic effective action
+In this section, we will construct an effective action for ηs,p(¯τ; t) defined in last sub-
+section. We treat Euclidean time ¯τ as spatial coordinate in the range ¯τ ∈ [0, π] and t
+as real time. ηs,p(¯τ; t) satisfy the boundary conditions (2.41) in ¯τ direction. Real-time
+action for excitations in a thermal state can be formulated using the Schwinger-Keldysh
+formalism. We will follow the non-equilibrium EFT approach developed in [8, 19–21].
+To write down a real-time action we need to double the degrees of freedom on a
+two-way Keldysh contour for t, where the fields η(1)
+s,p and η(2)
+s,p are on the first and second
+– 17 –
+
+contour respectively (see Fig. 5). For each ηs,p we also have the so-called r-a variables
+ηr
+s,p, ηa
+s,p defined as
+ηa
+s,p(¯τ; t) = η(1)
+s,p(¯τ; t) − η(2)
+s,p(¯t; t),
+ηr
+s,p(¯τ; t) = (η(1)
+s,p(¯τ; t) + η(2)
+s,p(¯τ; t))/2
+(2.57)
+The effective action should satisfy various unitary constraints and the dynamical KMS
+condition (to ensure local thermal equilibrium). We derive these conditions in detail in
+Appendix B, and just briefly present them here.
+1. The action S[ηr
+s,p, ηa
+s,p] should contain terms in the form of
+ˆ
+Kα1···αk
+s1,p1,··· ,sk,pk(∂¯τ, ∂t)ηα1
+s1,p1(¯τ, t) · · · ηαk
+sk,pk(¯τ, t),
+(α1, · · · αk ∈ {a, r})
+(2.58)
+with �k
+i=1 si = 1 and �k
+i=1 pi = 3Z.
+2. Each term in above form must contain at least one ηa
+s,p.
+3. The imaginary part of effective is nonnegative ℑS[ηr
+s,p, ηa
+s,p] ≥ 0.
+4. For the terms with odd numbers of ηa
+s,p, the action needs to be real, which means
+Kα1···αk
+s1,p1,··· ,sk,pk(∂¯τ, ∂t) =
+�
+Kα1···αk
+s1,−p1,··· ,sk,−pk(∂¯τ, ∂t)
+�∗
+(2.59)
+for α1, · · · , αk contain odd numbers of a.
+5. The action needs to obey dynamical KMS condition S[ηr
+s,p, ηa
+s,p] = S[˜ηr
+s,p, ˜ηa
+s,p],
+where ˜ηr,a
+s,p are defined by (B.19) and (B.20).
+At quadratic order, the effective action SEFT can then be written as
+SEFT =
+�
+s,p
+ˆ π
+0
+d¯τ
+ˆ ∞
+−∞
+dt
+�
+ηa
+s,−pKar
+s,p(∂¯τ, ∂t)ηr
+s,p + 1
+2ηa
+s,−pKaa
+s,p(∂¯τ, ∂t)ηa
+s,p
+�
+(2.60)
+where from the above conditions we have
+Kar
+s,p(∂¯τ, ∂t) =
+�
+Kar
+s,−p(∂¯τ, ∂t)
+�∗ ,
+(2.61)
+ℑ
+�
+s,p
+ηa
+s,−pKaa
+s,p(∂¯τ, ∂t)ηa
+s,p ≥ 0 .
+(2.62)
+In Appendix B, we derive the following dynamical KMS condition for the quadratic
+action (2.60)
+Kar
+s,p(∂¯τ, ∂t) − Kar
+s,−p(−∂¯τ, −∂t) = −2is (tan π(p/3 + ∂t/2))s Kaa
+s,p(∂¯τ, ∂t)
+(2.63)
+– 18 –
+
+As shown in [22], setting Kaa
+s,p = 0 means the local entropy current is conserved and the
+system is non-dissipative. In this case, (2.63) reduces to
+Kar
+s,p(∂¯τ, ∂t) = Kar
+s,−p(−∂¯τ, −∂t) =
+�
+Kar
+s,p(−∂¯τ, −∂t)
+�∗ ,
+(2.64)
+and the resulting action can be factorized [9, 21, 22], i.e. SEFT = Sf[η(1)
+s,p]−Sf[η(2)
+s,p] with
+Sf[ηs,p] = 1
+2
+�
+s,p
+ˆ π
+0
+d¯τ
+ˆ ∞
+−∞
+dt ηs,−pKar
+s,p(∂¯τ, ∂t)ηs,p .
+(2.65)
+Taking t → −iτ in the above action we obtain a Euclidean action defined for both
+Euclidean times ¯τ, τ. We stress that the factorization and thus the Euclidean action
+are not possible when dissipations are included. For simplicity, in this paper we will
+only consider the non-dissipative case with constraint (2.64) though the generalization
+to dissipative case should be straightforward.
+As discussed earlier, we assume that the action can be expanded in derivatives of
+¯τ. As in [8, 9], we cannot, however, expand the action in derivatives in t, since we are
+interested in time scales of order 1/λ so as to be able to probe the exponential growth
+eλt. The Lyapunov exponent λ could be comparable to the inverse temperature β, and
+thus there is no scale separation in t.
+Since ηs,p(¯τ; t) have different boundary conditions (2.41), they allow different lowest
+order of ∂¯τ in the action. For ηs,0, which is periodic in ¯τ, the lowest order of ∂¯τ in Kar
+s,0
+is just constant, namely
+Kar
+s,0(∂¯τ, ∂t) = Ks,0(i∂t) + O(∂¯τ) .
+(2.66)
+For ηs,±, which gains a nontrivial phase after shift ¯τ → ¯τ + π, the lowest order of ∂¯τ in
+Kar
+s,± must be nontrivial, and we will keep to the linear order
+Kar
+s,±(∂¯τ, ∂t) = ∂¯τKs,±(i∂t) + O(∂2
+¯τ) .
+(2.67)
+It follows from (2.64) that for all p,
+Ks,p(i∂t) = (−)pKs,−p(−i∂t) = (−)p (Ks,p(−i∂t))∗ .
+(2.68)
+Thus Ks,0(x) is an even function of x with real coefficients (when expanded in power
+series), while Ks,±(x) are functions of pure imaginary coefficients.
+Keeping only leading orders, we can reduce Kar
+s,0 piece to one dimension of t and
+write the leading order quadratic effective action as
+SEFT =
+�
+s=±
+�ˆ ∞
+−∞
+dtηa
+s,0(t)Ks,0(i∂t)ηr
+s,0(t) +
+�
+p=±
+ˆ π
+0
+d¯τ
+ˆ ∞
+−∞
+dtηa
+s,−p(¯τ; t)∂¯τKs,p(i∂t)ηr
+s,p(¯τ; t)
+�
+.
+(2.69)
+– 19 –
+
+With the leading order effective action (2.69), we have
+Ks,0(i∂t)Gra
+s,0(t) = −δ(t)
+(2.70)
+∂¯τKs,±(i∂t)Gra
+s,±(¯τ; t) = −δ(¯τ)δ(t)
+(2.71)
+where Gra
+s,p are retarded functions of ηs,p, i.e.
+Gra
+s,p(¯τ; t) = iθ(t)Gs,p(¯τ; t) .
+(2.72)
+Give the periodic boundary condition (2.41), we can write
+Gs,0(¯τ; t) = ∆s,0(t),
+Gs,±(¯τ; t) = ∆s,±(t)
+�
+e∓2πi/3 + θ(¯τ)(1 − e∓2πi/3)
+�
+(2.73)
+where ∆s,p(t) can be written in Fourier space as
+θ(t)∆s,0(t) = i
+ˆ
+C
+dω
+e−iωt
+2πKs,0(ω)
+(2.74)
+θ(t)∆s,±(t) = i
+ˆ
+C
+dω
+e−iωt
+2πKs,±(ω)(1 − e∓2πi/3)
+(2.75)
+which holds for t > 0. Here the integral contour C must be above all poles of integrand
+on the complex ω plane because Gra
+s,p(¯τ; t) is proportional to θ(t).
+Note that θ(¯τ)
+in (2.73) comes from ∂¯τ in (2.71).
+Equations (2.73) imply that except for certain jumps at ¯τ = 0, correlation functions
+have no dependence on ¯τ. From item 4b, however, such branch cut should not be present
+in the four-point function ˆF, and thus should be cancelled in (2.23), i.e.
+�
+i,j=1,2
+Lti ˜Ltj+2
+�
+gWgV
+�
+ˆT
+�
+φi(iϵ; ti)φj(0; tj+2) − φi(−iϵ; ti)φj(0; tj+2)
+���
+= 0
+(2.76)
+for infinitesimal positive ϵ. Also note that the above condition is relevant only for TOC
+of types ⟨WV V W⟩ and ⟨V WWV ⟩ for which ℑ¯tW − ¯tV could have either sign without
+changing the order of four fields. All other four-point functions have definite sign for
+ℑ¯tW − ¯tV .
+Now recall the smoothness conditions (2.56), which upon using (2.73)-(2.75) leads
+to
+1
+K+,±(ω) −
+1
+K−,±(ω) = ∓
+√
+3i
+�
+1
+K+,0(ω) −
+1
+K−,0(ω)
+�
+(2.77)
+which shows that the terms in (2.69) are not independent. It can also be checked that
+(2.77) is consistent with constraints (2.68).
+– 20 –
+
+2.6
+Shift symmetry and exponential growth in correlation functions
+Similar to the maximal chaos case [8], we will postulate that the action and the ver-
+tices (2.20)–(2.21) possess a shift symmetry. The choice of the shift symmetry is mo-
+tivated from that OTOCs should have exponential growth, but not TOCs.
+It turns out the requirement can be achieved by the following two conditions
+1. The action and the vertices (2.20)–(2.21) are invariant under
+ηr
+− → ηr
+− + α+eλt + α−e−λt
+(2.78)
+where α± are constants.
+2. There is no exponential growth in the symmetric correlation functions of η+, i.e.
+Grr
++ (¯τ; t) =
+�
+p
+Grr
++,p(¯τ; t) = 1
+2
+�
+p
+�
+G>
++,p(¯τ; t) + G<
++,p(¯τ; t)
+�
+= 0eλt + · · · . (2.79)
+Note that the KMS condition (2.48) leads to the fluctuation-dissipation relation
+Grr
+s,p(¯τ; t) = 1
+2
+1 + se2πip/3e−iπ∂t
+1 − se2πip/3e−iπ∂t Gs,p(¯τ; t),
+ℑt ∈ (0, π) .
+(2.80)
+In terms of φ1,2, the shift symmetry (2.78) can be written as
+(φ1, φ2) → (φ1, φ2) + (e±λ(t+iπ), −e±λt) .
+(2.81)
+We also require that the vertices in (2.20)–(2.21) be compatible with the shift symme-
+try (2.78), i.e. Lt satisfies
+Lt1[gW(t12)e±λ(t1+iπ)] = Lt2[gW(t12)e±λt2]
+(2.82)
+Since η− is a sum of η−,0, η−,±, the invariance under (2.78) means that at least one
+of K−,p has a factor of ∂2
+t − λ2. For convenience, we will write
+K−,p(i∂t) = (∂2
+t − λ2)k−,p(i∂t) .
+(2.83)
+The constraint (2.77) implies that K+,p may also contain a factor ∂2
+t − λ2, and we can
+similarly write5
+Ks,p(i∂t) = (∂2
+t − λ2)ks,p(i∂t) .
+(2.84)
+From (2.68) we have ks,p(x) = (−)pks,−p(−x).6 The general structure of our discussion
+will not depend on the specific forms of k+,p and k−,p.
+5Note that having a factor (∂2
+t − λ2) in K+,p does not imply there is a shift symmetry in η+. An
+important part of the shift symmetry is that vertices should also be invariant.
+6Note that it is enough to impose the invariance under a shift proportional to eλt in non-dissipative
+case. The parity property (2.68) will then lead to invariance under a shift proportional to e−λt.
+– 21 –
+
+Figure 6. The contour C on the ω plane for retarded propagator Gra
+s,p(¯τ; t). The two red
+crosses are poles at ω = ±iλ due to shift symmetry.
+Following from (2.74), we have
+θ(t)∆s,0(t) =
+ˆ
+C
+dω
+2πi
+e−iωt
+(ω2 + λ2)ks,0(ω)
+(2.85)
+where the contour C is chosen to be above all poles (see Fig. 6) of the integrand because
+the LHS is proportional to θ(t). We then find7
+∆s,0(t) =
+i
+2λks,0(iλ)(eλt − e−λt) + · · ·
+(2.86)
+where we used the parity of ks,0, and · · · denote possible contributions from other
+singularities.
+From now on we will suppress · · · and only write exponential terms.
+Using (2.80) and
+G>
+s,p(¯τ; t) = Grr
+s,p(¯τ; t) + 1
+2Gs,p(¯τ; t)
+(2.87)
+we find from (2.86)
+G>
+s,0(¯τ; t) =
+i
+2λks,0(iλ)(1 − se−iλπ)(eλt + se−iλπe−λt) ≡ hs,0(t) .
+(2.88)
+Similarly, from (2.75) we have
+θ(t)∆s,±(t) =
+ˆ
+C
+dω
+2πi
+e−iωt
+(ω2 + λ2)ks,±(ω)(1 − e∓2πi/3)
+(2.89)
+which leads to
+∆s,±(t) = ±e±iπ/3
+2
+√
+3λ
+�
+eλt
+ks,±(iλ) +
+e−λt
+ks,∓(iλ)
+�
+(2.90)
+7Note that when ks,0(x) has no zero at x = iλ, the coefficient of the exponential pieces below
+vanishes.
+– 22 –
+
+and
+G>
+s,±(¯τ; t) =
+�
+hs,±(t)
+¯τ ∈ [0, π]
+e∓2πi/3hs,±(t)
+¯τ ∈ [−π, 0]
+(2.91)
+where hs,± are given by
+hs,±(t) = ±e±iπ/3
+2
+√
+3λ
+� (ks,±(iλ))−1eλt
+1 − se−iπλe±2πi/3 + (ks,±(iλ))−1e−λt
+1 − seiπλe±2πi/3
+�
+.
+(2.92)
+The constraint (2.79) implies that, up to non-exponential pieces,
+Grr
++ (¯τ; t) =
+�
+p
+�
+h+,p(t) + e2πip/3h+,−p(−t)
+�
+= 0,
+(2.93)
+which upon using (2.88) and (2.92), further implies
+k+,±(iλ) = ∓ik+,0(iλ)
+√
+3
+tan
+�π
+2 (λ ± 1/3)
+�
+tan πλ
+2 .
+(2.94)
+Note that (2.94) is consistent with (2.68). Notice that the factor tan
+� π
+2(λ − 1/3)
+�
+on
+the right hand side of (2.94) for k+,−(iλ) becomes zero for λ = 1/3, which cannot
+happen as a zero for k+,−(iλ) would lead to divergences in (2.92). This means that
+k+,0 must have a pole at λ = 1
+3, i.e. k+,0(iλ) ∼ (λ − 1/3)−1, which in turn means that
+the prefactor in (2.86) vanishes and that the factor ∂2
+t − λ2 in K+,0 is in fact not there
+(it cancels with a factor hidden in k+,0). For λ = 2/3, the right hand side of (2.94)
+is divergent for k+,+(iλ), which means that the factor ∂2
+t − λ2 should also cancel for
+K+,+(i∂t) at λ = 2/3. The divergence of the factor tan πλ
+2 for λ = 1 will be commented
+on later in Sec. 4.
+2.7
+Summary of the effective field theory
+We have now discussed all elements of the EFT formulation, which we summarize here
+in one place:
+1. The product W(t1)W(t2) is written in terms of an expansion in terms of two
+effective fields φ1(¯tW; tS) and φ2(¯tW; tL) through a vertex.
+Similar expansion
+applies to V (t3)V (t4). At leading nontrivial order in the 1/N expansion, we have
+ˆFWWV V (t1, t2; t3, t4) = gWgV +
+�
+i,j=1,2
+Lti ˜Ltj+2
+�
+gWgV
+�
+ˆT φi(¯tW; ti)φj(¯tV ; tj+2)
+��
+.
+(2.95)
+The domain of φi is given by Ii in Fig. 3.
+– 23 –
+
+2. The KMS conditions of ˆF impose constraints on correlation functions of φi, which
+can in turn be obtained in terms of those a new pair of fields
+η±(¯t; t) = 1
+√
+2(φ1(¯t; t − iπ) ± φ2(¯t; t))
+(2.96)
+defined in the domain I2. ˆT in (2.95) is defined in terms of ordering of ℑt for η±.
+3. The effective action of η± is written for pure imaginary ¯t = −i¯τ and real t.
+Correlation functions of η± for general complex ¯t and t are obtained from analytic
+continuation. We also assume that the effective action can be expanded in terms
+of derivatives of ¯τ, which in turn implies that the action is translation invariant
+for both ¯τ and t. Two-point functions of η± are then defined in the domain Dη
+of Fig. 4.
+The domain Dη is irregular and inconvenient to work with. It is extended to D∗
+of Fig. 4. η± is then further decomposed into
+ηs(¯τ; t) = ηs,0(¯τ; t) + ηs,+(¯τ; t) + ηs,−(¯τ; t),
+(2.97)
+in terms of periodicity conditions in ¯τ-direction
+ηs,p(¯τ + π; t) = e2πip/3ηs,p(¯τ; t),
+s = ±, p = 0, ± .
+(2.98)
+4. With the decomposition (2.97)–(2.98), the KMS conditions of the original four-
+point function ˆF can be formulated in terms of KMS conditions for ηs,p at the
+inverse temperature π (half of the original inverse temperature), and can be writ-
+ten as periodic conditions in the imaginary t direction
+ηs,p(¯τ; t − iπ) = se−2πip/3ηs,p(¯τ; t) .
+(2.99)
+The leading actions in the ¯τ-derivative expansion for ηs,0 contain no ¯τ derivative
+and thus ηs,0 can be thought as ¯τ-independent, while the leading actions for ηs,±
+contains one ¯τ-derivative.
+5. From (2.96), (2.97) and (2.99), we can write φ1,2 as
+φ1(¯t; t) = ϕ(t) + e
+2πi
+3 ϕ+(¯t; t) + e− 2πi
+3 ϕ−(¯t; t),
+(2.100)
+φ2(¯t; t) = ϕ(t) + ϕ+(¯t; t) + ϕ−(¯t; t),
+(2.101)
+ϕ(t) ≡ 1
+√
+2(η+,0(t) − η−,0(t)),
+ϕ±(¯t; t) ≡ 1
+√
+2(η+,±(i¯t; t) − η−,±(i¯t; t)), (2.102)
+– 24 –
+
+(a)
+(b)
+(c)
+Figure 7. (a) The 4-way contour for F4 (b) The 4-way contour for G4 (c) The 4-way contour
+for H4.
+where we have used that η±,0 can be viewed as being independent of ¯τ. Note
+from (2.99)
+ϕ(t − iπ) = ˜ϕ(t) = 1
+√
+2(η+,0(t) + η−,0(t)),
+ϕ(t − 2πi) = ϕ(t) .
+(2.103)
+6. For OTOCs to have exponential dependence on t, we impose the shift symmetry
+ηr
+− → ηr
+− + α+eλt + α−e−λt
+(2.104)
+on both the action and the vertex. We also require no-exponential growth in
+Grr
++ (¯τ; t), which is needed such that TOCs do not have exponential t-dependence.
+This condition requires that various terms in the action should obey (2.94).
+7. The effective action is further constrained by (2.68), and two continuity condi-
+tions (2.76)–(2.77).
+2.8
+TOC and OTOC
+Now consider the following two four-point functions
+F4 = ⟨W(t1)V (t3)W(t2)V (t4)⟩ ,
+G4 = ⟨V (t3)W(t1)W(t2)V (t4)⟩
+(2.105)
+where ℜt1, ℜt2 ≫ ℜt3, ℜt4 or ℜt1, ℜt2 ≪ ℜt3, ℜt4, i.e. F4 is OTOC and G4 is TOC. We
+suppose each ti has a small imaginary part such that the orderings in (2.105) follow that
+defined in (2.4) (see Fig. 7 as an illustration). For F4, the small imaginary part for each
+ti leads to ℑ¯tW < ℑ¯tV , but for G4, depending on the relative value of the imaginary
+part of each ti, we may have either ℑ¯tW < ℑ¯tV or ℑ¯tW > ℑ¯tV . For definiteness, we
+consider the former case ℑ¯tW < ℑ¯tV .From (2.23) and (2.49)-(2.51), we find that
+F4 − G4 = 1
+2
+�
+s,p
+Lt1 ˜Lt3
+�
+gWgV
+�
+G>
+s,p(i(¯tW − ¯tV ), t13) − G<
+s,p(i(¯tW − ¯tV ), t13)
+��
+– 25 –
+
+= 1
+2
+�
+s,p
+Lt1 ˜Lt3 [gWgV ⟨[ηs,p(i¯tW; t1), ηs,−p(i¯tV ; t3)]⟩]
+= Lt1 ˜Lt3 [gWgV ∆(t13)]
+(2.106)
+where we have used (2.54), and
+∆(t) ≡
+�
+p
+∆+,p(t) =
+�
+p
+∆−,p(t)
+=
+3
+4λ(1/2 − cos πλ) sin πλ
+2 k+,0(iλ)(eiπλ/2eλt + e−iπλ/2e−λt) .
+(2.107)
+In the second line of the above equation we have used (2.94). We thus find that the
+difference between OTOC and TOC has exponential growth. Note that there is no
+divergence in (2.107) at λ = 1
+3; as mentioned earlier below (2.94), k+,0(iλ) has a pole
+at λ = 1
+3, which is canceled by 1/2 − cos πλ.
+We will now show that TOC G4 does not have exponential growth. In terms of
+Wightman functions (2.49) to (2.51), G4 can be written as
+G4 − gWgV =1
+2
+�
+s,p
+Lt1 ˜Lt3
+�
+gWgV G>
+s,p(+; t31)
+�
++ e2πip/3Lt2 ˜Lt3
+�
+gWgV G>
+s,p(+; t32)
+�
++ e2πip/3Lt1 ˜Lt4
+�
+gWgV G>
+s,p(−; t14)
+�
++ Lt2 ˜Lt4
+�
+gWgV G>
+s,p(−; t24)
+�
+(2.108)
+where we assume ℑ¯tW < ℑ¯tV and ± sign in the first time argument means ℑ¯t > 0 or
+ℑ¯t < 0. Using (2.88), (2.91), and (2.82) (and the counterpart for ˜Lt), we can simplify
+(2.108) as
+G4 − gWgV = Lt2 ˜Lt4
+�
+gWgV
+�
+C1eλt24 + C2e−λt24��
+(2.109)
+where
+C1 = 1
+2
+�
+s,p
+(1 + e2πip/3e−iπλ)As,p + (e−2πip/3 + eiπλ)Bs,p
+(2.110)
+C2 = 1
+2
+�
+s,p
+(e−2πip/3 + e−iπλ)As,p + (1 + e2πip/3eiπλ)Bs,p
+(2.111)
+and As,p, Bs,p are defined from (2.88) and (2.92) as
+hs,p ≡ As,peλt + Bs,pe−λt .
+(2.112)
+It can be checked using (2.94) that, C1 = C2 = 0.
+We can similarly examine G4 for ℑ¯tW > ℑ¯tV and another type of TOC
+H4 = ⟨W(t1)W(t2)V (t3)V (t4)⟩
+(2.113)
+– 26 –
+
+with ℑ¯tW < ℑ¯tV . We again find their exponential growth pieces vanish due to (2.94). In
+particular, the condition (2.76) is automatically satisfied up to non-exponential pieces.
+Given that TOCs do not have exponential terms, equation (2.107) implies that
+the exponential terms in OTOCs depend only on k+,0(iλ).
+Note that k+,±(iλ) are
+determined from k+,0(iλ) by (2.94), and k−,p are also constrained from k+,p from (2.77).
+In (2.85) and (2.89), we assumed for simplicity that the integrand only has simple
+poles at ±iλ. This assumption can be relaxed to have higher order poles. In fact, it
+can be shown that at most double poles are allowed due to the condition (2.76). These
+double poles lead to linear-exponential terms te±λt in the correlation functions of η±.
+Interestingly, the contributions from the double poles to any four-point function cancel
+out. So what we discussed in fact gives the most general form for four-point functions.
+See Appendix C for details.
+2.9
+General structure of OTOCs for non-maximal chaos
+We have seen that the shift symmetry (2.81) and requirement (2.79) guarantee expo-
+nential growth of OTOC and the absence of exponential growth of TOC. We will now
+examine the general structure of OTOCs as predicted by the theory.
+Using (2.13), we can expand (2.82) explicitly as
+�
+mn
+cmn
+�
+−e±λ(t+iπ) + (−1)m�
+∂m
+t gW(t)(±λ)n = 0
+(2.114)
+Similar to [9], we define
+GW
+even(±λ, t) =
+�
+m even
+cmn∂m
+t gW(t)
+�
+n
+(±λ)n
+(2.115)
+GW
+odd(±λ, t) =
+�
+m odd
+cmn∂m
+t gW(t)
+�
+n
+(±λ)n
+(2.116)
+and (2.114) becomes
+GW
+even(±λ, t)
+GW
+odd(±λ, t) = ∓ coth λ(t + iπ)
+2
+(2.117)
+KMS transformation of gW(t) is t → −t − 2πi that leads to
+GW
+even(∓λ, t) → GW
+even(∓λ, −t − 2πi) = Geven(∓λ, t)
+(2.118)
+GW
+odd(∓λ, t) → GW
+odd(∓λ, −t − 2πi) = −Godd(∓λ, t)
+(2.119)
+where we used invariance of gW under KMS transformation. This is compatible with
+(2.117) without any restriction on λ, unlike the EFT of [8], where the KMS condition
+of gW restricts λ = λmax = 1 [9].
+– 27 –
+
+Using the definition in (2.115) and (2.116), we can write the OTOC F4 in a more
+symmetric way. Since TOC G4 does not have exponential piece, OTOC F4 has the
+same exponential piece as (2.106). Using the shift symmetry of vertex (2.82), we can
+write each exponential in a symmmetric way
+Lt1[gWe±λt1] = 1
+2
+�
+Lt1[gWe±λt1] + Lt2[gWe±λ(t2−iπ)]
+�
+(2.120)
+˜Lt3[gV e±λt3] = 1
+2
+�
+˜Lt3[gWe±λt3] + ˜Lt4[gWe±λ(t4−iπ)]
+�
+(2.121)
+Using (2.115) and (2.116), we can write the connected piece
+F4 =αeλ(t1+t2−t3−t4+iπ)/2
+�
+GW
+even(λ, t12) cosh λ(t12 + iπ)
+2
++ GW
+odd(λ, t12) sinh λ(t12 + iπ)
+2
+�
+×
+�
+GV
+even(−λ, t34) cosh λ(t34 + iπ)
+2
+− GV
+odd(−λ, t34) sinh λ(t34 + iπ)
+2
+�
++ (λ ↔ −λ)
+=αeλ(t1+t2−t3−t4+iπ)/2GW
+even(λ, t12)GV
+even(−λ, t34)
+cosh λ(t12+iπ)
+2
+cosh λ(t34+iπ)
+2
++ (λ ↔ −λ)
+(2.122)
+where we have used α to denote the prefactor of (2.107), i.e. (2.107) becomes
+∆(t) ≡ α(eiπλ/2eλt + e−iπλ/2e−λt),
+(2.123)
+and used (2.117) in the last line. Equation (2.122) has the same structure as that
+assumed in [14, 15], including the phase eiπλ/2. In [14, 15], in the place of GW
+even(λ, t)
+and GV
+even(−λ, t) are certain advanced and retarded vertices, which are invariant under
+KMS transformation t → −t−2πi. For a specific microscopic system, these two vertices
+may obey certain differential equations [14, 15], which in our language translate into
+conditions on the effective vertices. In (2.122), there is a second term, obtained from
+λ → −λ, which exponentially decays for t1, t2 ≫ t3, t4, and was not present in [14, 15].
+Here it is a consequence of shift symmetry for both signs in (2.78), which are needed in
+order for TOCs to not have exponential growth. In the non-dissipative case, this term
+should also exist even if we only assume shift symmetry for just plus sign in (2.78) as
+explained in footnote 6.
+Now consider the double commutator defined as
+Cθ
+4(t1, t2; t3, t4) = ⟨[W(t1 − iθ), V (t3 − iθ)][W(t2), V (t4)]⟩ ,
+θ ∈ [0, 2π]
+(2.124)
+which can be rewritten in terms of four-point functions leads to
+Cθ
+4 = F θ
+4 − Gθ
+4 + ˜F θ
+4 − ˜Gθ
+4
+(2.125)
+– 28 –
+
+where F θ
+4 and Gθ
+4 are the four-point functions in (2.105) with t1 → t1 − iθ and t3 →
+t3 − iθ, and ˜F θ
+4 and ˜Gθ
+4 are respectively F θ
+4 and Gθ
+4 with exchange W ↔ V , t1 ↔ t3 and
+t3 ↔ t4. It follows from (2.122) that
+Cθ
+4 = 2α cos λπ
+2 eλ(t1+t2−t3−t4)/2GW
+even(λ, t12 − iθ)GV
+even(−λ, t34 − iθ)
+cosh λ(t12+i(π−θ))
+2
+cosh λ(t34+i(π−θ))
+2
++ (λ ↔ −λ) .
+(2.126)
+The factor cos λπ
+2 → 0 as λ → 1, consistent with the result of [9] and those of SYK and
+holographic systems in the maximal chaos limit [4, 14, 15, 23].
+3
+Comparisons with OTOCs in various theories
+In this section we compare the general structure of OTOCs obtained in last section
+with various known examples.
+3.1
+The large q SYK model
+We first look at the large q SYK model [24–27]. OTOC F4 of fundamental fermions was
+obtained in [28] and has the form (after analytic continuation to Lorentzian signature)
+F SYK
+4
+= − 2
+N
+gψ(t12)gψ(t34) cosh λ(t1+t2−t3−t4+iπ)
+2
+cos πλ
+2 cosh λ(t12+iπ)
+2
+cosh λ(t34+iπ)
+2
+(3.1)
+where Gψ(t) is the two-point function fundamental Majorana fermions in the large q
+SYK model (see more details in Section 5.1) given by
+gψ(t) ≡ 1
+2
+�
+cos λπ
+2
+cosh λ(t+iπ)
+2
+�2∆
+(3.2)
+where ∆ = 1/q is the conformal weight of the fundamental fermion ψ. The OTOC (3.1)
+has exactly the form of (2.122), with the cosh λ(t1 +t2 −t3 −t4 +iπ)/2 term containing
+exponentially growing and decaying terms that are both present in (2.122), including
+the phases. We can further identify
+GW
+even(λ, t) = GV
+even(λ, t) = C0(λ)gψ(t),
+α = −
+1
+C0(λ)C0(−λ)N cos(πλ/2)
+(3.3)
+where C0(λ) is a constant. From (2.115) we find that C0(λ) = �
+n c0,nλn. From (2.117)
+we find
+Gψ
+odd(±λ, t) = ∂tgψ(t)C1(λ),
+C1(λ) =
+�
+n
+c1,nλn,
+C0(λ) = λ∆C1(λ) .
+(3.4)
+As the simplest possibility we take c1,n = δn,0 and c0,n = ∆δn,1 which gives
+Lt[W]φ = ∂tWφ + ∆W∂tφ,
+α =
+1
+λ2N∆2 cos(πλ/2)
+(3.5)
+– 29 –
+
+3.2
+Stringy scattering in a AdS black hole
+The next example is the scattering in the AdS black hole background with stringy
+correction [4]. Assume the bulk spacetime dimension is d + 1 and the d-dimensional
+boundary coordinate is xµ = (t, ⃗x). When t1, t2 ≫ t3, t4 or t1, t2 ≪ t3, t4, the boundary
+out-of-time-ordered four-point function F4 is dominated by the W + V → W + V
+scattering near the horizon of the AdS black hole. At GN ∼ 1/N order, the OTOC F4
+is given by8
+F string
+4
+=
+ia4
+0
+(2π)4
+ˆ
+δ(s, |⃗z−⃗z′|) [puψ∗
+1(pu,⃗z; xµ
+1)ψ2(pu,⃗z; xµ
+2)] [pvψ∗
+3(pv,⃗z′; xµ
+3)ψ4(pv,⃗z′; xµ
+4)]
+(3.6)
+where a0 is a number depending on the background, s = a0pupv is the total energy
+of the scattering in the unboosted frame, ψ1,2(pu,⃗z; xµ
+1,2) are wavefunctions of W(xµ
+1,2)
+expanded in the null momentum basis pu, ψ3,4(pv,⃗z; xµ
+3,4) are wavefunctions of V (xµ
+3,4)
+expanded in the orthogonal null momentum basis pv, ⃗z and ⃗z′ are d−1 dimensional bulk
+transverse coordinates, and the integral runs over pu, pv,⃗z,⃗z′. With stringy correction,
+the scattering amplitude δ(s, |⃗z|) for t1 + t2 ≪ t3 + t4 is given by
+δ(s, |⃗z|) ∼ GNs
+ˆ
+dd−1k
+(2π)d−1
+ei⃗k·⃗z
+⃗k2 + µ2(e−iπ/2α′s/4)−α′(⃗k2+µ2)/2r2
+0
+(3.7)
+where r0 is the horizon radius, α′ = ℓ2
+s (with ℓs the string length) and µ2 = d(d−1)r2
+0
+2ℓ2
+AdS .
+By translation symmetry of the AdS-Schwarzschild black hole in transverse direc-
+tions, ψi(p, ⃗z; xµ) are functions of ⃗z − ⃗x. By time translation symmetry, one can show
+that the wave function ψi(p, ⃗z; xµ) in the unboosted frame has the following property
+ψ1,2(pu, ⃗z; xµ) = e−2πa/βψ1,2(pue−2πa/β,⃗z; (t + a, ⃗x))
+(3.8)
+ψ3,4(pv, ⃗z; xµ) = e2πa/βψ3,4(pve2πa/β,⃗z; (t + a, ⃗x))
+(3.9)
+which implies that ψ1,2 = e2πt/βf1,2(pue2πt/β) and ψ3,4 = e−2πt/βf3,4(pve−2πt/β) for some
+functions fi. Here β is the inverse temperature of the black hole. Switching to the
+boosted frame by redefining pu → pue−π(t1+t2)/β leads to
+dpupuψ∗
+1(pu, ⃗z; xµ
+1)ψ2(pu, ⃗z; xµ
+2) → dpupuf ∗
+1(pueπ(t1−t2)/β)f2(pueπ(t2−t1)/β)
+(3.10)
+which is a function of t12. Similarly we can redefine pv → pveπ(t3+t4)/β and find the
+wavefunctions for V become a function of t34. Taking this into (3.6), we can derive
+F string
+4
+= i
+ˆ
+δ(s, |⃗z − ⃗z′|)fW(pu,⃗z − ⃗x1,⃗z − ⃗x2; t12)fV (pv,⃗z′ − ⃗x3,⃗z′ − ⃗x4; t34)
+(3.11)
+8The notation here differs from [4] by switching 2 ↔ 3.
+– 30 –
+
+with s = a0pupve−π(t1+t2−t3−t4)/β and two functions
+fW = puf ∗
+1(pueπ(t1−t2)/β)f2(pueπ(t2−t1)/β)
+(3.12)
+fV = pvf ∗
+3(pveπ(t4−t3)/β)f4(pveπ(t3−t4)/β)
+(3.13)
+In the regime that the scattering amplitude δ(s, |⃗z|) is of order one and slowly
+varies with respect to pu and pv, we can assume the integral over pu and pv in (3.11)
+can be approximated by their characteristic values pu
+c and pv
+c, which only depend on
+the wave functions. Moreover, the spatial dependence of wave function ψi should be
+peaked around ⃗z ∼ ⃗x. To compare with our 0+1 dimensional EFT, we should integrate
+over all ⃗x, which basically sets ⃗x ∼ ⃗z. Since wave functions are translational invariant
+along tranverse directions, we can integrate over ⃗z directly in (3.7), which fixes ⃗k = 0
+and leads to
+δ(s, 0) ∼ −iGNcde−λ(t1+t2−t3−t4+iβ/2)/2
+(t3 + t4 ≫ t1 + t2)
+(3.14)
+where cd is a real constant and the Lyapunov exponent λ is
+λ = 2π
+β
+�
+1 − d(d − 1)α′
+ℓ2
+AdS
+�
+(3.15)
+It follows that we can write (3.6) as
+F string
+4
+∼ GNcde−λ(t1+t2−t3−t4+iβ/2)/2f c
+W(t12)f c
+V (t34)
+(3.16)
+where f c
+W,V means fW,V taking value at pu,v = pu,v
+c
+and we have suppressed all transverse
+coordinates. Comparing (3.16) with (2.122), we see that they both have non-maximal
+exponential growth and the phase −iλβ/4 in (3.16) exactly matches with −iλπ/2 (of
+the −λ term) in (2.122) by β = 2π. In the case of t1 + t2 ≫ t3 + t4, we need to flip the
+phase e−iπ/2 to eiπ/2 in (3.7) and will find consistency with (2.122) as well.
+Matching (3.16) with (2.122) also leads to
+f c
+W(t) = GW
+even(λ, t)
+cosh λ(t+iπ)
+2
+,
+f c
+V (t) = GV
+even(−λ, t)
+cosh λ(t+iπ)
+2
+.
+(3.17)
+For example, in AdS3 [4], we have (β = 2π)
+fW(pu, 0, 0; t12) = 4∆W π2c2
+W
+Γ(∆W)2 (pu)2∆W −1e−4ipu sinh(t12/2)
+(3.18)
+where we have set all transverse coordinates as zero due to the integral over these
+directions. For large ∆W, the characteristic pu is at pu
+c =
+2∆W −1
+4i sinh(t12/2), which leads to
+f c
+W(t) ∼ gW(t12)
+cosh t+iπ
+2
+,
+gW(t) ≡
+1
+(cosh t+iπ
+2 )2∆W
+(3.19)
+– 31 –
+
+where gW(t) is the boundary two-point function in a thermal state. Note that the
+wave function (3.18) is computed in the pure gravity background and does not include
+any stringy corrections that should introduce non-maximal λ to the wave function.
+Thus (3.19) should be compared with the right hand side of (3.17) at leading order
+in α′ expansion, i.e. we can identify GW
+even(1, t) = gW(t). It is clearly of interests to
+understand α′ corrections of (3.18). In general dimension, the explicit forms of wave
+functions are not known, but (3.17) gives a constraint on their general structure.
+3.3
+Conformal Regge theory
+The conformal Regge theory was developed in [10, 11] and analyzed for Lyapunov expo-
+nent and butterfly effect in [18]. Consider a four-point function ⟨W(x1)V (x3)V (x4)W(x2)⟩
+in the CFT in d-dimensional Minkowski spacetime. Assume their locations are assigned
+in the (t, y) plane with
+xi = (ti, yi, 0, · · · , 0)
+(3.20)
+On this plane, we can define Rindler coordinate [18]
+t = U sinh T,
+y = U cosh T
+(3.21)
+where U > 0 is for right Rindler wedge and U < 0 is for left Rindler wedge (see
+Fig. 8). These two wedges are related by analytic continuation T → T + iπ and the
+vacuum in Minkowski spacetime is equivalent to the thermal state in one of the Rindler
+wedge with inverse temperature 2π. We can consider each pair of W and V located
+in two different wedges, by which we can construct an OTOC in one Rindler wedge
+with inverse temperature 2π. For example, we can take T1 = −T2 = T, T3 = T4 = 0,
+U1 = −U2 = U > 0 and U3 = −U4 = 1 (see Fig. 8), which leads to
+⟨W(T, U)V (0, 1)V (0, −1)W(−T, −U)⟩M = ⟨WR(T, U)VR(0, 1)WR(T + iπ, U)VR(iπ, 1)⟩R
+(3.22)
+where the LHS is the correlation function in Minkowski vacuum and the RHS is a
+thermal OTOC in right Rindler wedge. The conformal Regge theory studies this four-
+point function under Regge limit with T → ∞ but fixed U. It has been shown [18]
+that it has a non-maximal exponential growth eλT with λ < 1. This non-maximal
+Lyapunov exponent comes from summing over infinitely many higher spin channels in
+the four-point function.
+To compare with our 0+1 dimensional result, we should perform dimensional re-
+duction by restricting to zero momentum mode along all spatial directions, which is a
+bit intricate. Here we will simply take Ui = U for all i and compare the T-dependence
+with (2.122).
+– 32 –
+
+Figure 8. The locations of four operators in Regge limit.
+By conformal symmetry, the four-point function ⟨W(x1)V (x3)V (x4)W(x2)⟩ can be
+written as
+⟨W(x1)V (x3)V (x4)W(x2)⟩ =
+1
+(x2
+12)∆W (x2
+34)∆V A(u, v)
+(3.23)
+where the conformal invariant cross ratios are
+u = x2
+12x2
+34
+x2
+13x2
+24
+= sinh2 T12
+2 sinh2 T34
+2
+sinh2 T13
+2 sinh2 T24
+2
+,
+v = x2
+14x2
+23
+x2
+13x2
+24
+= sinh2 T14
+2 sinh2 T23
+2
+sinh2 T13
+2 sinh2 T24
+2
+(3.24)
+The Regge limit is for T1, T2 ≫ T3, T4 limit, and we have
+u → 16e−T sinh2 T12
+2 sinh2 T34
+2 ,
+v → 1 − 8e−T/2 sinh T12
+2 sinh T34
+2
+(3.25)
+where we define T = T1 + T2 − T3 − T4 ≫ 0. From [10, 11], A(u, v) under this limit is
+given by9
+A ≈ 2π
+ˆ
+dν ˜α(ν)
+�e−iπ/2
+2
+log v
+�1−j(ν)
+Ωiν(0)
+(3.26)
+where Ωiv(ρ) is a harmonic function on (d − 1)-dimensional hyperbolic space (here by
+assuming Ui = U we have ρ = 0), j(ν) is the leading Regge trajectory, and ˜α(ν) is a
+slowly varying function of ν. In large T limit, the ν-integral can be evaluated using
+saddle point approximation with the saddle point given by ν = 0 [18], which gives
+⟨W(x1)V (x3)V (x4)W(x2)⟩ ≈ CR
+gW(T12)gV (T34)
+�
+cosh T12+iπ
+2
+�λ �
+cosh T34+iπ
+2
+�λeλ(T+iπ)/2 .
+(3.27)
+9To get the correct phase e−iπ/2, one needs to be careful about how u and v circle around origin
+after we set infinitesimal imaginary part Ti → Ti + iϵi with ϵ1 < ϵ3 < ϵ2 < ϵ4 for OTOC. Unlike [10],
+both u and v circle around origin clockwise for 2π when T ≫ 0 in our case.
+– 33 –
+
+M
+MHere CR is a constant, λ = j(0) − 1, and gW,V is the conformal correlator in Rindler
+wedge with no spatial separation
+gW,V (T) =
+1
+�
+cosh T+iπ
+2
+�2∆W,V
+(3.28)
+Now comparing (3.27) with (2.122), we see the downstairs of (3.27) is proportional
+to (cosh T12+iπ
+2
+)λ while in (2.122) we have cosh λ(T12+iπ)
+2
+. It is not clear whether this
+difference is due to we are comparing a d-dimensional theory with a (0+1)-dimensional
+system. Assuming not, we can match (3.27) with (2.122) with the identification
+GW,V
+even(±λ, T) = KW,V (±λ)cosh λ(T+iπ)
+2
+�
+cosh T+iπ
+2
+�2∆W,V +λ
+(3.29)
+α =
+CR
+KW(λ)KV (−λ) =
+CR
+KW(−λ)KV (λ)
+(3.30)
+up to arbitrary KW,V (λ). Since this equation is essentially the same for W and V except
+conformal dimensions, we will suppress W, V labels in the following. Using (2.117), we
+have
+Godd(±λ, T) = ∓K(±λ)sinh λ(T+iπ)
+2
+�
+cosh T+iπ
+2
+�2∆+λ
+(3.31)
+which leads to
+G(±λ, T) ≡
+�
+mn
+cmn∂m
+T G(T)(±λ)n
+(3.32)
+=Geven(±λ, T) + Godd(±λ, T) = K(±λ)e∓ λ(T +iπ)
+2
+�
+cosh T+iπ
+2
+�2∆+λ
+(3.33)
+Let us define the Fourier transformation of G(T) as
+I(∆; ω) =
+ˆ ∞
+−∞
+dTeiωTG(T − iϵ)
+(3.34)
+where ϵ is an infinitesimal positive number. It has been shown in [29] that
+I(∆; ω) = 22∆−1π2e−iπ∆+πωΓ(∆ + iω)Γ(∆ − iω)/Γ(2∆)
+(3.35)
+From (3.33), it is clear that the Fourier transformation of G(±λ, T) is K(±λ)e∓iπλ/2I(∆+
+λ/2; ω ± iλ/2), which leads to
+G(±λ, T) = K(±λ)e∓iπλ/2
+2π
+ˆ
+dωe−iωT I(∆ + λ/2; ω ± iλ/2)
+I(∆; ω)
+I(∆; ω)
+– 34 –
+
+= 2λK(±λ)e−iπλ/2Γ(2∆)
+2πΓ(2∆ + λ)
+ˆ
+dωe−iωT Γ(∆ + λ ∓ iω)
+Γ(∆ ∓ iω)
+I(∆; ω)
+= 2λK(±λ)e−iπλ/2Γ(2∆)
+Γ(2∆ + λ)
+Γ(∆ + λ ± ∂T)
+Γ(∆ ± ∂T)
+G(T)
+(3.36)
+From this equation and the definition (3.32), there is no unique solution for the coeffi-
+cient cmn of the differential operator LT. A convenient choice is
+K(±λ) = ±iΓ(2∆ + λ)
+2λΓ(2∆)
+(3.37)
+LT =
+�
+mn
+cmn∂m
+T (∂φ
+T)n = ie−iπλ/2 Γ
+�
+λ + λ−1∂φ
+T(∆λ−1∂φ
+T + ∂T)
+�
+λ−1∂φ
+TΓ
+�
+λ−1∂φ
+T(∆λ−1∂φ
+T + ∂T)
+�
+(3.38)
+where ∂T acts on bare operator and ∂φ
+T acts on the effective mode. Note that this LT
+can be expanded in power series in both ∂T and ∂φ
+T. Moreover, we can expand LT near
+maximal chaos limit λ = 1 and find
+LT = (∂T +∆∂φ
+T)+(1−λ)
+�
+(γ + iπ
+2 )(∂T + ∆∂φ
+T) + (∆ − π2
+6 ∂2
+T)∂φ
+T
+�
++O((1−λ)2, (∂φ
+T)2)
+(3.39)
+where γ is the Euler’s constant. The first term is the same as (3.5) and the subleading
+terms can be regarded as perturbative corrections of higher spins to the vertex.
+4
+Relation to the EFT of maximal chaos
+The effective field theory for maximal chaos was constructed in [8], which contains just
+one effective mode ϕ on a Keldysh contour in the thermal state with inverse temperature
+β = 2π. This effective mode ϕ has correlation function with exponential growth that
+explains the behavior of OTOC. In this section, we will show that our effective field
+theory of non-maximal chaos at maximal chaos λ = 1 can be equivalently connected to
+the theory in [8]. In particular, our two-component effective mode φ1,2 reduces to one
+mode ϕ.
+Taking the maximal chaos limit λ → 1 in (2.94), we see that both k+,±(iλ) diverge.
+This implies that the two operators K+,±(i∂t) do not contain the factor ∂2
+t − λ2 at
+maximal chaos.
+Physically, the two component fields η+,±(¯τ; t) decouple from the
+dynamics of quantum chaos. Now let us examine the behavior of k−,p(iλ) in this limit.
+Consider ω = iλ in (2.77); there are two equations but three parameters k−,±(iλ) and
+k−,0(iλ), whose general solution is
+1
+k−,±(iλ) = ±
+√
+3i
+��
+1 +
+1
+tan
+� π
+2(λ ± 1/3)
+�
+tan πλ
+2
+�
+1
+k+,0(iλ) −
+1
+k−,0(iλ)
+�
+.
+(4.1)
+– 35 –
+
+In the λ → 1 limit, with k+,0(iλ) finite,10 we have
+1
+k−,±(i) = ±
+√
+3i
+�
+1
+k+,0(i) −
+1
+k−,0(i)
+�
+(4.2)
+In the EFT of maximal chaos [8], the effective mode ϕ is local and only depends on
+one time variable. This implies that our two effective modes φ1,2 at λ = 1 should not
+have any nontrivial dependence on ¯t. In other words, consistency requires that η−,±
+must also decouple at maximal chaos, which implies
+k+,0(i) = k−,0(i)
+(4.3)
+From (2.100)–(2.102) we then find that in the λ → 1 limit, ϕ± decouple (i.e. they are
+not relevant for the exponential behavior), and
+φ1(¯t; t) = φ2(¯t; t) = ϕ(t)
+(4.4)
+That is, in this limit, ¯t-dependences drop out and φ1,2 become the same field. Further-
+more, from (2.103), ϕ has periodicity 2π in imaginary t direction, i.e. it satisfies the
+standard KMS condition with inverse temperature 2π. We have thus fully recovered
+the setup of the EFT for maximal chaos.
+The EFT action (i.e. the part relevant for exponential behavior) now becomes
+SEFT =
+�
+s=±
+ˆ ∞
+−∞
+dt ηa
+s,0(t)Ks,0(i∂t)ηr
+s,0(t)
+= 1
+2
+�
+s=±
+ˆ ∞
+−∞
+dt(ϕa + s ˜ϕa)Ks,0(i∂t)(ϕr + s ˜ϕr)
+=
+ˆ ∞
+−∞
+dtϕaK(i∂t)ϕr + ˜ϕaK(i∂t) ˜ϕr + ϕa ˜K(i∂t) ˜ϕr + ˜ϕa ˜K(i∂t)ϕr
+(4.5)
+where ˜ϕ was introduced in (2.103) and
+K(i∂t) = 1
+2(K+,0(i∂t) + K−,0(i∂t)),
+˜K(i∂t) = 1
+2(K+,0(i∂t) − K−,0(i∂t)) .
+(4.6)
+Now recall from (2.23) that only ϕ is relevant for the four-point function (as W and
+V couple to φ1,2 which become ϕ).
+Furthermore, from (4.3), ϕ and ˜ϕ decouple at
+ω = i. Thus for the purpose of understanding the exponential behavior of the four-
+point function, we can just keep the first term in the effective action (4.5), reducing
+back to [8].
+10See Section 5.4 for a different case.
+– 36 –
+
+As discussed in Sec. 2.1 and 2.2, the differential operator Lt in the vertex that
+couples the bare operators and effective fields has the same form in both maximal and
+non-maximal cases. Moreover, in the λ → 1 limit, the shift symmetry (2.81) of φ1,2,
+becomes
+(φ1, φ2) → (φ1, φ2) + (e±t, e±t)
+→
+ϕ(t) → ϕ(t) + e±t .
+(4.7)
+(2.82) implies that the shift symmetry obeyed by vertex Lt is
+Lt1[gW(t12)e±t1] = Lt2[gW(t12)e±t2]
+(4.8)
+which also matches with that in the EFT of maximal chaos [8].
+To close this section, we note that the Wightman function G>
+−,0(¯τ; t) given in (2.88)
+diverges in the limit λ → 1. This divergence reflects that in the limit G>
+−,0 develops a
+teλt term which is not present for λ < 1. More explicitly, from (2.86) and (2.80), we
+find Grr
+−,0(t) should satisfy
+(1 + e−iπ∂t)Grr
+−,0(t) = 1
+2(1 − e−iπ∂t)
+�
+i
+2λ˜k0(iλ)
+(et − e−t)
+�
+(4.9)
+whose general solution is
+Grr
+−,0(t) =
+t
+2π˜k0(i)
+(et − e−t) + c0(et + e−t)
+(4.10)
+where c0 is an arbitrary constant. It then follows from (2.87)
+G>
+−,0(¯τ; t) =
+t
+2π˜k0(i)
+(et − e−t) +
+�
+c0 +
+i
+4˜k0(i)
+�
+et +
+�
+c0 −
+i
+4˜k0(i)
+�
+e−t .
+(4.11)
+The presence of linear-exponential term in Wightman function at maximal chaos was
+already observed in [8].
+5
+Identifying the effective fields in the large q SYK model
+In this section we examine the large q SYK model in some detail. In this model, four-
+point functions of fundamental fermions can be computed analytically in the Euclidean
+signature. We show that in this theory it is possible to identify two Euclidean effective
+fields φE
+1,2 in terms of the microscopic description, which can be identified as φ1,2(¯t; t)
+of Sec. 2 evaluated in the Euclidean section with pure imaginary ¯t and t. It is possible
+to calculate Euclidean two-point functions of φE
+1,2 using the microscopic description.
+We show that the Lorentzian analytic continuation of these two-point functions can
+be fully captured by the EFT of Sec. 2. This provides a stronger check on the EFT
+formulation than just matching the structure of OTOCs done in Sec. 3.
+– 37 –
+
+5.1
+OTOC of the large q SYK model
+We start with a brief review of the essential aspects of the large q SYK model. The
+SYK model [24, 25] is a 0+1 dimensional quantum mechanical system which consists
+of N Majorana fermions with an all-to-all and q-local Hamiltonian
+H = iq/2
+�
+1≤j1<···<jq≤N
+Jj1···jqψj1 · · · ψjq
+�
+Jj1···jq
+�2 = 2q−1J 2(q − 1)!
+qN q−1
+= J2(q − 1)!
+N q−1
+(5.1)
+where Jj1···jq is a random coupling with Gaussian distribution. At an inverse tempera-
+ture β, it is possible to derive a bilocal effective action in Euclidean signature [26]
+SE = N
+2 log det(∂τ − Σ) + N
+2
+¨ β
+0
+dτ1dτ2
+�
+Σ(τ1, τ2)G(τ1, τ2) − J2
+q G(τ1, τ2)q
+�
+(5.2)
+where G(τ1, τ2) =
+1
+N
+�
+j ψj(τ1)ψj(τ2) is a bi-local field, and Σ is an auxiliary bi-local
+field. In the double scaling limit with N, q → ∞ and N 2/q fixed, it is convenient to
+introduce G(τ1, τ2) = 1
+2sgn(τ1 − τ2)eσ(τ1,τ2)/q and Σ can be integrated out, resulting a
+Liouville action for σ(τ1, τ2) [27],
+SE ≈ N
+4q2
+ˆ
+dτ1dτ2
+�1
+4∂1σ(τ1, τ2)∂2σ(τ1, τ2) − J 2eσ(τ1,τ2)
+�
+.
+(5.3)
+The large q SYK model is obtained by further taking N/q2 → ∞, in which limit the
+Euclidean path integral over σ is dominated by saddle-point solution(s) to the equation
+of motion of (5.3), i.e. by solutions to the Liouville equation
+∂1∂2σ(τ1, τ2) = −2J 2eσ(τ1,τ2) .
+(5.4)
+By definition, σ(τ, τ ′) has the following properties
+σ(τ, τ ′) = σ(τ ′, τ),
+σ(τ, τ) = 0,
+(5.5)
+where the second equation can be interpreted as a UV boundary condition. It is also
+periodic in β for both arguments
+σ(τ, τ ′) = σ(τ ′ + β, τ) .
+(5.6)
+The solution σ0 to (5.4) with time translation symmetry can be interpreted as
+describing the equilibrium state, and can be written as
+eσ0(τ12) =
+cos2 λβ/4
+cos2 λ
+2(|τ12| − β/2),
+τ12 = τ1 − τ2,
+(5.7)
+– 38 –
+
+and λ is obtained from the solution to equation
+λ = 2J cos λβ/4 .
+(5.8)
+The equilibrium two-point function is given by
+G0(τ) = ⟨G(τ, 0)⟩β = 1
+2eσ0(τ)/q,
+τ ∈ [0, β] .
+(5.9)
+From now on, for notational simplicity we use the unit such that β = 2π.
+Fluctuations around the thermal equilibrium can be described by expanding σ =
+σ0 + ϵ around σ0. To order ϵ2, (5.3) becomes
+SE ≈ S0 + N
+8q2
+ˆ
+dτ1dτ2
+�1
+2∂1ϵ(τ1, τ2)∂2ϵ(τ1, τ2) − J 2eσ0(τ12)ϵ2(τ1, τ2)
+�
+(5.10)
+where S0 is a constant scaling as N/q2. By definition we have ⟨ϵ(τ1, τ2)⟩ = 0 to this
+order, where ⟨· · ·⟩ denotes correlation functions of ϵ obtained from path integrals with
+Euclidean action (5.10). Now consider the Euclidean four-point function
+Fψ(τ1, τ2, τ3, τ4) ≡ ⟨G(τ1, τ2)G(τ3, τ4)⟩
+≈ G0(τ12)G0(τ34)
+�
+1 + 1
+q2 ⟨ϵ(τ1, τ2)ϵ(τ3, τ4)⟩
+�
+(5.11)
+where in the second line we have indicated that its leading connected part is given by
+two-point function of ϵ.
+It will be convenient to write (5.10) in a different form by introducing [28]
+x = τ − τ ′,
+¯τ = τ + τ ′
+2
+(5.12)
+and redefine the fields σ(¯τ, x) = σ(τ, τ ′) and ϵ(¯τ, x) = ϵ(τ, τ ′). From (5.5)–(5.6), ϵ(¯τ, x)
+satisfy the following conditions
+ϵ(¯τ, x) = ϵ(¯τ, −x) = ϵ(¯τ + π, 2π − x),
+ϵ(¯τ, 0) = ϵ(¯τ, 2π) = 0
+(5.13)
+from which we can define the fundamental domain of ϵ as Dϵ = {(¯τ, x)|¯τ ∈ [0, π], x ∈
+[0, 2π]} (see Fig. 9). On the fundamental domain Dϵ, we can rewrite the Euclidean
+effective action (5.10) as
+SE = N
+8q2
+ˆ π
+0
+d¯τ
+ˆ 2π
+0
+dx
+�
+1
+4(∂¯τϵ)2 − (∂xϵ)2 −
+λ2
+2 cos2 λ
+2(x − π)ϵ2
+�
+≡ N
+8q2
+ˆ
+d¯τdx ϵLϵ
+(5.14)
+– 39 –
+
+Figure 9. The red region is the fundamental domain Dϵ for ϵ(¯τ, x).
+where the irrelevant constant S0 is omitted, and L is the differential operator corre-
+sponds to the quadratic action.
+Two-point functions of ϵ can be obtained summing over the eigenfunctions of L [28]
+as follows. Eigenfunctions of L can be labeled by two quantum numbers n, m, and
+separated into two groups
+ψn,m(τ, x) = ein¯τψm(x),
+(n, m) ∈ (Z±, M±)
+(5.15)
+with
+Lψn,m(¯τ, x) ≡
+�
+−1
+4∂2
+¯τ + ∂2
+x −
+λ2
+2 cos2 λ(x−π)
+2
+�
+ψn,m(¯τ, x) = n2 − m2
+4
+ψn,m(¯τ, x)
+(5.16)
+where Z+/Z− denotes even/odd integers respectively and M± are two infinite discrete
+sets of real numbers with magnitude larger than 1. When n takes values in Z+ (Z−) ,
+m takes value in M+ (M−). The two-point function of ϵ can then be written as
+⟨ϵ(¯τa, xa)ϵ(¯τb, xb)⟩ =
+�
+(n,m)∈(Z±,M±)
+ein(¯τa−¯τb)ψm(xa)ψm(xb)
+(n2 − m2)/4
+= −2π
+�
+m∈M±
+ψm(xa)ψm(xb)
+m sin mπ
+[cos m(π − |¯τa − ¯τb|) ± cos m(¯τa − ¯τb)]
+(5.17)
+where we define the notation
+¯τa = (τ1 + τ2)/2,
+¯τb = (τ3 + τ4)/2,
+xa = τ1 − τ2,
+xb = τ3 − τ4 .
+(5.18)
+The infinite sum of m in (5.17) can be evaluated in a closed form by Sommerfeld-
+Watson transformation [28]. For different ordering assignment for τk, they lead to TOC
+– 40 –
+
+2元or OTOC after analytic continuation τk → itk. TOCs do not have exponential growth,
+while the OTOC with 2π > τ1 > τ3 > τ2 > τ4 ≥ 0 is given by
+FOTOC = − 2
+N
+G0(τ12)G0(τ34) cos λ(τ1+τ2−τ3−τ4−π)
+2
+cos πλ
+2 cos λ(π−τ12)
+2
+cos λ(π−τ34)
+2
+.
+(5.19)
+After analytic continuation τk → itk, it gives (3.1) mentioned earlier. Notice that, with
+τk → itk, the cosine function in (5.17) leads to exponential growth e±m(t1+t2−t3−t4)/2.
+Since every quantum number m ∈ M± has magnitude greater than 1, the exponential
+growth in each individual term in (5.17) violates the chaos bound. This infinite tower of
+quantum numbers m is the analogue of the infinite tower of higher spins to be summed
+over in the higher dimensional Regge theory.
+5.2
+Identifying the effective fields
+We now seek an alternative way to understand two-point function of ϵ, without going
+through the infinite sums over m, n. We are interested only in the exponential part (af-
+ter analytic continuation) of the two-point function, and would like to identify a finite
+number of effective fields that can capture that.
+For this purpose, consider general solutions to the saddle-point equation (5.4),
+which can be written in a form
+eσ(τ1,τ2) =
+f ′(τ1)g′(τ2)
+J 2(f(τ1) − g(τ2))2
+(5.20)
+where f, g are arbitrary functions. The above parameterization of σ is not unique as
+the right hand side is invariant under an arbitrary SL(2, C) transformation
+f → a + bf
+c + df ,
+g → a + bg
+c + dg,
+bc − ad = 1 .
+(5.21)
+Now consider small perturbations ϵon−shell around the equilibrium solution (5.7) in the
+space of solutions (5.20), which can be parameterized as11
+ϵon−shell(τ1, τ2) = λ(χ1(τ1) − χ2(τ2)) tan λ
+2(τ12 − π) + χ′
+1(τ1) + χ′
+2(τ2)
+(5.22)
+where χ1,2 are two arbitrary (infinitesimal) functions, and parameterize the full set of
+solutions to equation of motion of the quadratic action (5.14). The paramterization
+freedom (5.21) translates to χ1,2 as ϵon−shell being invariant under transformations
+(δχ1(τ1), δχ2(τ2)) =
+�
+−e±iλ(τ1−π), e±iλτ2�
+,
+(5.23)
+11To see this, we can write the equilibrium solution (5.7) as f0(τ) = −eiλ(τ−π), g0(τ) = eiλτ and
+parameterize small perturbations around it as f(τ) = −eiλ(τ−π+χ1(τ)), g(τ) = eiλ(τ+χ2(τ)). Equa-
+tion (5.20) results from expanding χ1,2 to linear order.
+– 41 –
+
+or a simultaneous shift by a constant.
+To obtain an effective description of the exponential behavior, we first rewrite (5.22)
+in a more convenient form
+ϵon−shell(τ1, τ2) =
+1
+∆G0(τ12)
+�
+i=1,2
+Lτi[G0(τ12)]χi(τi)
+(5.24)
+Lτ[O(τ)]χ(τ) ≡ ∂τO(τ)χ(τ) + ∆O(τ)∂τχ(τ)
+(5.25)
+where G0 is the equilibrium two-point function of fundamental fermions given earlier
+in (5.9), and ∆ = 1/q is the conformal dimension of fundamental fermionic operator
+ψi. The differential operator Lτ can be interpreted as a vertex that couples ϵon−shell to
+χi(τi), and from (5.23), it obeys the following symmetry
+Lτ1[G0(τ12)e±iλ(τ1−π)] = Lτ2[G0(τ12)e±iλτ2] .
+(5.26)
+Motived from (5.24), we write ϵ(τ1, τ2) as
+ϵ(τ1, τ2) =
+1
+∆G0(τ12)
+�
+LτL[G0(τ12)]φE
+1 (¯τ; τL) + LτS[G0(τ12)]φE
+2 (¯τ; τS)
+�
+,
+(5.27)
+where ¯τ = τ1+τ2
+2
+. τL (τS) is the larger (smaller) of τ1,2, whose usage ensures that (5.27)
+respects the invariance of ϵ under switch of τ1,2. φE
+1,2 are dynamical counterparts of
+χ1,2, with χ1,2 parameterizing their classical solutions.
+Equation (5.27) is exactly the Euclidean version of (2.19)–(2.21) with the bi-
+fermionic field ϵ identified with the second term in (2.19), Lτ is Euclidean version
+of Lt, and φE
+1,2 are φ1,2 evaluated at Euclidean times. By construction, ϵ as defined
+in (5.27) is invariant under transformations of φE
+1,2 of the form (5.23), and thus what-
+ever the action for φE
+1,2 is, it should be invariant under (5.23), which is precisely the
+Euclidean version of the shift symmetry (2.81). And equation (5.26) can be identified
+with the Euclidean version of the shift symmetry (2.82) satisfied by the effective vertex.
+Given that the action for φE
+1,2 must be invariant under the shift symmetry (5.23),
+we can be certain that correlation functions of φE
+1,2 must contain exponential time-
+dependence. This establish φ1,2 as the effective fields which directly captures the expo-
+nential behavior of two-point function of ϵ.12
+5.3
+Two-point function of φE
+i
+In principle we can try to find the (Euclidean) action of φE
+1,2 by plugging (5.27)
+into (5.10) or (5.14), and being careful about the Jacobian in changing variables from
+12Note that two-point function of ϵ has exponential behavior only when the ordering of time argu-
+ments corresponds to OTOC, while two-point functions of φE always have exponential behavior.
+– 42 –
+
+ϵ to φE
+1,2 in the path integral for ϵ. It is, however, difficult to do in practice. In addition
+to having to understand the Jacobian, various complications discussed in Sec. 2.2–2.3,
+including that φE
+1 and φE
+2 are defined on different domains, should also be faced here.
+Here we show that using (5.14) we can nevertheless find their Euclidean two-point
+functions, and confirm their exponential time-dependence. In next subsection, we show
+that these Euclidean two-point functions can be reproduced from the EFT formulation
+of Sec. 2 by a suitable choice of the action there.
+To compute two-point functions of φE
+1,2, instead of considering (5.27) as a change of
+variables in the path integral, we canonically quantize (5.14) by treating ¯τ as “time”,
+and treat (5.27) as an operator equation. Below we will use ϵ, φE
+1,2 to denote the fields in
+the Euclidean path integral defined with (5.14), and ˆϵ, ˆφE
+1,2 the corresponding operators
+in the canonical quantization. By definition, Euclidean correlation functions of φE
+1,2 are
+given by “time-ordered” correlation functions of ˆφE
+1,2, i.e.
+�
+φE
+i (¯τ; τ)φE
+j (¯τ ′; τ ′)
+�
+= −i
+�
+¯T ˆφE
+i (¯τ; τ)ˆφE
+j (¯τ ′; τ ′)
+�
+c.q.
+(5.28)
+where ¯T denotes ordering in ¯τ and the subscript “c.q.” on the RHS is to distinguish
+the expectation value in Euclidean path integral on the LHS. We outline the main steps
+here, leaving technical calculations to Appendix D:
+1. In canonical quantization of (5.14), we can expand ˆϵ in terms of a complete set
+of modes {gm} as
+ˆϵ(¯τ, x) =
+�
+m
+�
+gmˆam + g∗
+mˆa†
+m
+�
+(5.29)
+where gm solve the equation of motion Lgm(¯τ, x) = 0, and obey the conditions
+gm(¯τ, 0) = gm(¯τ, 2π) = 0 (from (5.13)). m takes value in the same sets M±
+discussed below (5.16). {gm} are assumed to be properly normalized under the
+Klein-Gordon inner product,
+(g1, g2) = − i
+2
+ˆ 2π
+0
+dx (g1∂¯τg∗
+2 − g∗
+2∂¯τg1)
+(5.30)
+such that annihilation and creation operators ˆam and ˆa†
+m obey the standard com-
+mutation relation [ˆam, ˆa†
+m′] = δm,m′.
+Due to the nontrivial boundary condition (5.13) in ¯τ direction, the system is not
+in the vacuum state of ˆam, and it can be shown that ˆam, ˆa†
+m have correlation
+functions13
+�
+ˆas
+mˆas†
+m
+�
+c.q. =
+1
+1 − se−imπ ,
+�
+ˆas†
+mˆas
+m
+�
+c.q. =
+se−imπ
+1 − se−imπ .
+(5.31)
+13Two-point function of ˆϵ then follows and can be checked to give the same answer as (5.17).
+– 43 –
+
+where s = ± labels two different sectors of ˆam and ˆa†
+m with m ∈ M± respectively.
+2. Since the mode functions gm solve the equation of motion of ϵ, from (5.24), they
+can be written as
+gm(¯τ, x) =
+1
+∆G0(τ12)
+�
+i=1,2
+Lτi[G0(τ12)]χi,m(τi)
+(5.32)
+where Lτ is defined in (5.25), and {χi,m} is a complete set of basis functions for
+χi in (5.24). Plugging (5.32) into (5.29), then from (5.27), we can write ˆφE
+1,2 as
+ˆφE
+i (¯τ; τi) =
+�
+m
+(χi,m(τi)ˆam + χ∗
+i,m(τi)ˆa†
+m) .
+(5.33)
+Two-point functions of φE
+i can then follow from (5.31). Notice from (5.33) that
+ˆφE
+i (¯τ; τi) does not have any ¯τ dependence. So the only ¯τ-dependence in two-
+point functions of φE
+1,2 comes from θ(¯τ) on the right hand side of (5.28). Such
+¯τ-dependence is precisely what we had in Sec. 2, see e.g. (2.73), except that there
+it came from our assumption of weak ¯τ-dependence and derivative expansion in
+¯τ, but here for the large q SYK model it is exact.
+From the calculation of Appendix D, we have
+�
+φE
+i (¯τ; τ)φE
+j (0; 0)
+�
+= θ(¯τ)Mij(τ) + θ(−¯τ)Mji(−τ)
+(5.34)
+M11(τ) = M22(τ) = M12(2π − τ) = M21(−τ)
+(5.35)
+=
+8
+N∆2 ×
+�
+ˆm+eiλτ + ˆm1τeiλτ + c.c.,
+τ ∈ [0, 2π]
+ˆm−eiλτ + ˆm1τeiλτ + c.c.,
+τ ∈ [−π, 0]
+(5.36)
+where in the last equality we have kept only the exponential part, and ˆm+, ˆm− and ˆm1
+are some constants given by
+ˆm+ = i2πλ − sin 2πλ + 2(πλ + sin πλ)(2πiλ + 3 − e−iπλ)
+32λ2(πλ + sin πλ)2(1 + eiπλ)
+,
+(5.37)
+ˆm− = ˆm+ +
+1
+4λ2(1 + eiπλ),
+ˆm1 =
+1
+8λ(πλ + sin πλ)(1 + eiπλ)
+(5.38)
+5.4
+Effective action for large q SYK
+We now work out the explicit form the EFT action which match with correlation
+functions (5.35)–(5.36). As our EFT is formulated in Lorentzian time, we need to first
+analytically continue the Euclidena correlation fuctions (5.34). The correct analytic
+continuation for large q SYK model is φE
+j (¯τ; τ) → φj(¯t; t) = −iφE
+j (i¯t; it) and Lτ → Lt.
+– 44 –
+
+Note that (5.36) contains linear-exponential terms te±λt after analytic continuation
+τ → it. From discussion of Appendix C, this means that we need to include quadratic
+order of ∂2
+t − λ2 in some Ks,p(i∂t), i.e.
+K+,p(i∂t) = (∂2
+t − λ2)k+,p(i∂t),
+K−,p(i∂t) = (∂2
+t − λ2)2k−,p(i∂t)
+(5.39)
+where K−,p(x) has a double zero at ±iλ. With appropriate choice of k+,0(iλ), k−,0(iλ)
+and k′
+−,0(iλ) (the derivative to k−,0(x) at iλ) that depend on the three parameters ˆm+,
+ˆm− and ˆm1, we find that this effective action completely reproduces the correlation
+functions (5.34)–(5.36).
+More explicitly, we find in Appendix D.4 that
+k+,0(iλ) = 3λN∆2 cot πλ
+2
+2(1 − 2 cos πλ)
+(5.40)
+k−,0(iλ) = 3N∆2(πλ + sin πλ)
+8λ(2 cos πλ − 1)
+(5.41)
+k′
+−,0(iλ) = −3iN∆2 �
+(2π2λ2 − 5) sin πλ + 2 sin 2πλ + 8πλ cos πλ − πλ
+�
+3πλ tan πλ
+2 + 7
+��
+16λ2(1 − 2 cos πλ)2
+(5.42)
+and other parameters ks,±(iλ) and k′
+−,±(iλ) are derived from the constraints (2.79),
+(2.68) and two continuity conditions (2.76)-(2.77) and explicitly given by (C.22)-(C.24),
+which we copy as follows
+k+,±(iλ) = ∓ik+,0(iλ)
+√
+3
+tan
+�π
+2 (λ ± 1/3)
+�
+tan πλ
+2
+(5.43)
+k−,±(iλ) = ±ik−,0(iλ)
+√
+3
+(5.44)
+k′
+−,±(iλ) = ±
+√
+3
+3
+�
+2λk−,0(iλ)2
+k+,0(iλ)
+�
+1 +
+1
+tan
+� π
+2(λ ± 1/3)
+�
+tan πλ
+2
+�
++ ik′
+−,0(iλ)
+�
+(5.45)
+There is a subtlety in this effective action when we take the maximal chaos limit
+λ → 1. Taking λ → 1 in (5.40)-(5.42), we find that
+k+,0(iλ) → 0,
+k−,0(iλ) ∼ O(1),
+k′
+−,0(iλ) → ∞
+(5.46)
+Note that in (5.39) K+,p is linear in ∂2
+t − λ2, which implies that correlation functions
+for s = + in Section 2.6 all hold. It follows that we will have singular ∆+,0(t) by (2.86).
+This singularity implies that the maximal chaos limit in large q SYK model should be
+taken with some care.
+– 45 –
+
+Indeed, there is a scaling limit in SYK model when we take maximal chaos limit.
+The Lyapunov exponent λ is related to the inverse temperature β and coupling J by
+(5.8). The maximal chaos limit corresponds to strong coupling limit J → ∞ (or equiv-
+alently low temperature limit β → ∞), under which we can solve (5.8) perturbatively
+as (β = 2π)
+λ = 1 −
+1
+πJ + O(1/J 2)
+(5.47)
+However, the low temperature limit should still be understood in the regime of validity
+of large N, i.e. N ≫ J ≫ 1. Therefore, in maximal chaos limit, for (5.40)-(5.42) we
+have
+k+,0(iλ) ∼ O(J −1),
+k−,0(iλ) ∼ O(1),
+k′
+−,0(iλ) ∼ O(J )
+(5.48)
+which by (5.43)-(5.45) implies
+k+,±(iλ) ∼ O(1),
+k−,±(iλ) ∼ O(1),
+k′
+−,±(iλ) ∼ O(1)
+(5.49)
+Given the action (5.39), by (2.74) and (2.75) the exponential terms in retarded corre-
+lation functions scale as
+∆+,p(t) ∼
+e±λt
+k+,±p(iλ),
+∆−,p(t) ∼ k′
+−,±p(iλ)e±λt
+k−,±p(iλ)2
++ (c0 + c1t)
+e±λt
+k−,±p(iλ)
+(5.50)
+where c1,2 are two O(1) numbers. From (5.48) and (5.49) in maximal chaos, there is an
+enhancement of J to ∆s,0(t) while ∆s,±(t) are still O(1). This means that ηs,± decouple
+at maximal chaos at leading order of J . Since ¯τ dependence only exists for p = ±,
+this means that at leading order of J two effective modes φ1,2 reduce to a single field
+at maximal chaos following the same argument for (4.4).
+Note that the first term of ∆−,0(t) in (5.50) is O(J ) but the second term is O(1).
+Therefore, at leading order of J , ∆−,0(t) only has pure exponential terms. Using the
+explicit expression for ∆s,p(t) in (C.25)-(C.28), one can show that
+∆+,0(t) = ∆−,0(t) = 2iJ
+N∆2(et − e−t) + O(1/N)
+(5.51)
+It follows that K−,0(i∂t) in the effective action (5.39) can be reduced to be just linear
+in ∂2
+t − λ2 and we can take ansatz
+Kmax
+s,0 (i∂t) = (∂2
+t − 1)kmax
+s,0 (i∂t)
+(5.52)
+where kmax
+s,0 (i∂t) satisfies
+kmax
++,0 (i) = kmax
+−,0 (i) = N∆2
+4J
+(5.53)
+– 46 –
+
+This is the same condition we impose in (4.3) for maximal chaos. Following the dis-
+cussion in Section 4, this EFT reduces back to case in [8]. Note that the overall scal-
+ing N/J in (5.53) reflects the fact that the effective action for SYK model in strong
+coupling/low temperature limit is proportional to N/(βJ ), which is observed in the
+Schwarzian action [26].
+6
+Higher order terms and exponentiation
+Higher order terms in equation (1.3) are suppressed by higher powers of 1/N. Here
+we show that a subset of terms of the form ekλt
+Nk (k an integer) can be rensummed and
+exponentiated. Such terms dominate in the regime N → ∞ and t ∼ 1
+λ log N such that
+eλt
+N is finte. These contributions come from including higher powers of effective fields φi
+in the product (2.19), but in the effective action still keep only quadratic terms.14 The
+full four-point functions of V and W then involve multi-point correlation functions of
+effective fields φi, which factorize to products of two-point functions. We show that the
+shift symmetry on the vertices that couple W(t1)W(t2) to higher powers of φi implies
+that TOCs again do not have exponential growth, and the OTOC (recall (2.105)) has
+the exponentiated form
+F4 =
+ˆ ∞
+0
+d˜y
+ˆ ∞
+0
+dy e−αy˜yeλ(t1+t2−t3−t4+iπ)/2h(t12, y)˜h(t34, ˜y)
+(6.1)
+where various notations will be explained below.
+We now proceed to describe the
+derivation of (6.1).
+6.1
+Towards a scattering formula
+Without derivative on ¯t, all order generalization of the vertex can be written as
+⟨W(t1)W(t2)⟩0 =
+�
+is=1,2
+j,ks,m∈N
+s=1,··· ,m
+Ci1···im
+j;k1···km
+m!
+∂jgW(t12)∂k1
+ti1φi1(¯tW; ti1) · · · ∂km
+timφim(¯tW; tim)
+(6.2)
+≡
+�
+{Is},m
+1
+m!CI1···ImφI1 · · · φIm
+(6.3)
+where in the first line ⟨·⟩0 means taking the expectation value of bare operators, and
+we assume ℑt1 < ℑt2 so that the arguments for φi is ti (i = 1, 2); and in the second
+14Including nonlinear terms in the EFT action leads to higher order terms of the form ek1λt
+N k2 with
+k2 > k1.
+– 47 –
+
+line we defined the notation
+I ≡ (i, k),
+φI ≡ ∂k
+tiφi(¯tW; ti),
+CI1···Im =
+�
+j
+Ci1···im
+j;k1···km∂jgW(t12)
+(6.4)
+where C is a tensor function of t12.
+Note that separate t1,2 derivatives on W0(t1,2)
+in (2.20) and (2.21) are combined to act on the argument of gW(t12) by translation
+symmetry. In (6.2), the range of the sum for m is from 0 to ∞ but the sum for j, ks
+could be either finite or infinite for each m. For simplicity, we will consider their ranges
+to be finite at each m. For each ks, we choose the range of sum to be the same, i.e.
+k1, · · · , km ∈ {0, · · · , dm}. This choice defines φI in (6.4) as a 2dm dimensional vector
+at each m. It follows that CI1···Im can be chosen as a symmetric tensor of order m by the
+permutation symmetry of among all φI in (6.3). For m = 0, we have Cj = δj,0 because
+the leading order of (6.2) is just gW(t12). Similarly expansion applies to ⟨V (t3)V (t4)⟩
+for ℑt34 ∈ (−2π, 0) with notation
+⟨V (t3)V (t4)⟩0 =
+�
+{Is},m
+1
+m!
+˜CI1···Im ˜φI1 · · · ˜φIm
+(6.5)
+˜φI ≡ ∂k
+ti+2φi(¯tV ; ti+2),
+˜CI1···Im =
+�
+j
+˜Ci1···im
+j;k1···km∂jgV (t34)
+(6.6)
+With four time variables (t1, t2, t3, t4) in the analytic domain D, a generic four-point
+function ˆF is
+ˆF(t1, t2; t3, t4) =
+�
+{Is,I′s},m,m′
+CI1···Im ˜CI′
+1···I′
+m′
+m!m′!
+�
+ˆT φI1 · · · φIm ˜φI′
+1 · · · ˜φI′
+m′
+�
+(6.7)
+With the effective action being quadratic, the (m + m′)-point function of φi factorizes
+into products of two-point functions. We will ignore the self-interaction terms (those
+pairs of φi with same ¯t) because they do not grow in OTOC. It follows that m′ = m
+and
+ˆF(t1, t2; t3, t4) ≈
+�
+{Is,I′s},m
+CI1···Im ˜CI′
+1···I′m
+m!
+m
+�
+s=1
+�
+ˆT φIs ˜φI′
+s
+�
+(6.8)
+where the the permutation symmetry in Wick contraction gives m! that cancels one m!
+in the denominator.
+The KMS condition requires ˆF invariant under t1 → t2 − 2πi and t2 → t1 (and
+also t3 → t4 − 2πi and t4 → t3). Using (2.26)-(2.27), we find coefficients C and ˜C must
+satisfy the constraints
+Ci1···im
+j;k1···km = (−)jC
+¯i1···¯im
+j;k1···km,
+˜Ci1···im
+j;k1···km = (−)j ˜C
+¯i1···¯im
+j;k1···km
+(6.9)
+– 48 –
+
+where the map i → ¯i means 1 ↔ 2. This is equivalent to
+CI1···Im(t) = C¯I1···¯Im(−t − 2πi),
+˜CI1···Im(t) = ˜C¯I1···¯Im(−t − 2πi)
+(6.10)
+where ¯I means (i, k) → (¯i, k).
+We further require the right hand side of (6.3) to be invariant under shift symmetry
+(2.81), which lead to
+CI1···Im(∂k1δφi1) · · · φIm = 0,
+δφi ≡ (δφ1, δφ2) = (e±λ(t1+iπ), −e±λt2)
+(6.11)
+for arbitrary φI. This is a quite strong constraint. Let us define the 2dm dimensional
+vector eI = ∂kδφi at each m and (6.11) becomes
+�
+I1
+CI1···ImeI1 = 0
+(6.12)
+At each m, for the symmetric tensor C we can always find a linear independent set of
+vectors {u(m)a} such that
+CI1···Im =
+�
+a∈Dm
+ξ(m)
+a
+u(m)a
+I1
+· · · u(m)a
+Im
+(6.13)
+where Dm is the size of the set, and ξ(m)
+a
+is a Dm dimensional vector function of t12. By
+(6.12), the whole set {u(m)a} must be orthogonal to e, i.e. u(m)a
+I
+eI = 0 for all a ∈ Dm.
+Similar decomposition applies to ˜C.
+From the definition of C, it is a function of t12, and so is u(m)a
+I
+= u(m)a
+I
+(t12). The
+orthogonality to eI for each u(m)a
+I
+leads to
+�
+k
+u(m)a
+1,k (t12)(±λ)ke±λ(t1+iπ) =
+�
+k
+u(m)a
+2,k (t12)(±λ)ke±λt2
+(6.14)
+which implies
+u(m)a
++
+(±λ, t12) = ∓u(m)a
+−
+(±λ, t12) coth λ(t12 + iπ)
+2
+(6.15)
+where we define
+u(m)a
+±
+(λ, t) ≡ 1
+2
+�
+k
+(u(m)a
+1,k (t) ± u(m)a
+2,k (t))λk
+(6.16)
+Take transformation t1 → t2 − 2πi, t2 → t1 and (i, k) ↔ (¯i, k) in (6.15). It follows that
+u(m)a
+¯I
+(−t12 − 2πi) is also an orthogonal vector to eI where ¯I = (¯i, k). Let us choose
+the normalization of u(m)a
+I
+such that ξ(m)
+a
+(t12) is invariant under KMS transformation
+t12 → −t12 − 2πi. By KMS symmetry of C in (6.10), we must have both u(m)a
+I
+(t12) and
+u(m)a
+¯I
+(−t12 − 2πi) summed with the same ξ(m)
+a
+coefficient in (6.13). Sometimes, these
+– 49 –
+
+two are linear dependent or even the same, in which cases we just need to include one
+of them.
+Taking (6.13) to (6.8), we have
+ˆF(t1, t2; t3, t4) =
+�
+m
+1
+m!
+�
+a∈Dm,b∈ ˜Dm
+ξ(m)
+a
+˜ξ(m)
+b
+��
+I,I′
+u(m)a
+I
+�
+ˆT φI ˜φI′�
+˜u(m)b
+I′
+�m
+(6.17)
+Note that the shift symmetry (6.14) is in the same form as (2.82). Therefore, we can
+use the same technique in Section 2.8 to show that all TOC do not have exponential
+growth piece. Indeed, the proof in Section 2.8 does not depend on the explicit form of
+Lt. One can complete a similar proof for each �
+I,I′ u(m)a
+I
+�
+ˆT φI ˜φI′�
+˜u(m)b
+I′
+in (6.17) by
+replacing Lt1gW with �
+k u(m)a
+1,k (t12)∂k
+t1 and Lt2gW = �
+k u(m)a
+2,k (t12)∂k
+t2 (and doing similar
+replacement for Lt3,4) in Section 2.8.
+For OTOC F4 in (2.105), the replacement still holds. Similar to (2.122), we can
+write in a symmetric way that
+�
+I,I′
+u(m)a
+I
+�
+φI ˜φI′�
+˜u(m)b
+I′
+=αeλ(t1+t2−t3−t4+iπ)/2
+�
+u(m)a
++
+(λ, t12) cosh λ(t12 + iπ)
+2
++ u(m)a
+−
+(λ, t12) sinh λ(t12 + iπ)
+2
+�
+×
+�
+˜u(m)a
++
+(−λ, t34) cosh λ(t34 + iπ)
+2
+− ˜u(m)a
+−
+(−λ, t34) sinh λ(t34 + iπ)
+2
+�
++ (λ ↔ −λ)
+=αeλ(t1+t2−t3−t4+iπ)/2u(m)a
++
+(λ, t12)˜u(m)a
++
+(−λ, t34)
+cosh λ(t12+iπ)
+2
+cosh λ(t34+iπ)
+2
++ (λ ↔ −λ)
+(6.18)
+where we defined
+˜u(m)a
+±
+(λ, t) ≡ 1
+2
+�
+k
+(˜u(m)a
+1,k (t) ± ˜u(m)a
+2,k (t))λk
+(6.19)
+and used (6.15) in the last step for both u(m)a
+±
+and ˜u(m)a
+±
+.
+Since we are only interested in large Lorentzian time separation t1, t2 ≫ t3, t4 or
+t1, t2 ≪ t3, t4, we only need to keep the exponentially growth term in (6.18) because the
+other term is exponentially suppressed. Let us take t1, t2 ≫ t3, t4, then (6.17) becomes
+F4 =
+�
+m
+1
+m!
+�
+a∈Dm
+ξ(m)
+a
+�
+u(m)a
++
+(λ, t12)
+cosh λ(t12+iπ)
+2
+�m �
+b∈ ˜Dm
+˜ξ(m)
+b
+�
+˜u(m)b
++
+(−λ, t34)
+cosh λ(t34+iπ)
+2
+�m
+Xm
+(6.20)
+with the exponential growth
+X ≡ αeλ(t1+t2−t3−t4+iπ)/2
+(6.21)
+– 50 –
+
+Assume we can do an inverse Mellin transformation to define h and ˜h as
+�
+a∈Dm
+ξ(m)
+a
+�
+u(m)a
++
+(λ, t12)
+cosh λ(t12+iπ)
+2
+�m
+=
+ˆ ∞
+0
+dyymh(t12, y)
+(6.22)
+�
+b∈ ˜Dm
+˜ξ(m)
+b
+�
+˜u(m)b
++
+(−λ, t34)
+cosh λ(t34+iπ)
+2
+�m
+=
+ˆ ∞
+0
+d˜y(−˜y)m˜h(t34, ˜y)
+(6.23)
+Then we can rewrite (6.20) as
+F4 =
+ˆ ∞
+0
+d˜y
+ˆ ∞
+0
+dy
+�
+m
+1
+m!h(t12, y)(−Xy˜y)m˜h(t34, ˜y)
+=
+ˆ ∞
+0
+d˜y
+ˆ ∞
+0
+dye−Xy˜yh(t12, y)˜h(t34, ˜y)
+(6.24)
+This has exactly the same form as [16, 17], and also matches with the trans-plankian
+string scattering formula near horizon of a AdS black hole [4]. In [16], this scattering
+formula was conjectured by a heuristic argument and the authors of [17] later proved
+it with a specific structure of Feynmann diagrams. In this work, we show that (6.24)
+holds in a more general scenario since it is just a result of a shift symmetry.
+Note that the assumption of inverse Mellin transformation requires analyticity in
+m.
+This is a nontrivial constraint on the vertices because at each level of m one
+could have choosen ξ(m)
+a
+and the sets Dm and ˜Dm quite randomly in a pattern without
+analyticity in m. However, there is a simple and sufficient way to guarantee analyticity,
+which requires three parts:
+1. The total ways of coupling between bare operator and effective mode does not
+change as we increase the number m of effective modes, which picks Dm and ˜Dm
+as some fixed sets for all m, in which the vector dimension 2dm is also fixed.
+2. All these types of couplings exist at any level of m, which releases the m depen-
+dence of u(m)a
++
+.
+3. The coefficient ξ(m)
+a
+is an analytic function of m.
+It is noteworthy that the ordinary ladder diagrams in eikonal scattering obeys these
+three conditions. Therefore, this explains why the exponentiation in (6.24) is also a
+result of eikonal scattering [4], in which e−Xy˜y is the eikonal scattering amplitude, h is
+the wave function of two W’s and ˜h is the wave function of two V ’s.
+– 51 –
+
+6.2
+An example
+In this subsection, we will present a simple example following the general construction
+in the last subsection. We will solve a simple orthogonal vector uI, find the vertices
+leading to this vector uI, compute the exponentiation formula and compare it with the
+known result of large q SYK model [17].
+Let us first solve the orthogonal vectors ua
+I. Define q = e−λ(t12+iπ) and the equation
+ua
+IeI = 0 can be written as
+�
+k
+ua
+1k(q)λk =
+�
+k
+ua
+2k(q)λkq,
+�
+k
+ua
+1k(q)(−λ)kq =
+�
+k
+ua
+2k(q)(−λ)k
+(6.25)
+Without loss of generality, we can assume ua
+I is a polynomial in q
+ua
+I =
+pa
+�
+n=0
+ca
+I,nqn
+(6.26)
+up to normalization where pa could be either a finite number or ∞. Then (6.25) leads
+to
+�
+k
+ca
+1k,nλk =
+�
+k
+ca
+2k,n−1λk,
+�
+k
+ca
+1k,n−1(−λ)k =
+�
+k
+ca
+2k,n(−λ)k
+(6.27)
+for n ≥ 0 with definition ca
+I,−1 = 0. The simplest nontrivial solution is for pa = 1 and
+k = 0, 1
+c10,0 = c20,1 = −λ,
+c20,0 = c10,1 = λc
+(6.28)
+c11,0 = c21,1 = 1,
+c21,0 = c11,1 = c
+(6.29)
+We can choose the normalization of uI such that it is invariant under KMS trans-
+formation q → 1/q and i → ¯i. In this case, by the discussion below (6.16), we can
+construct a KMS invariant C just using this vector. It is easy to see that the appropriate
+normalization is q−1/2 and the orthogonal vector is
+u10 = λ(cq − 1)
+q1/2
+,
+u11 = 1 + cq
+q1/2 ,
+u20 = λ(c − q)
+q1/2
+,
+u21 = c + q
+q1/2
+(6.30)
+Then we will solve the vertices with coefficients Ci1···im
+j;k1···km leading to this vector uI
+for each order m. Let us start with m = 1. We can further impose a simple condition
+that j only takes values 0 and 1 in (6.4). Define n-th order ∂t12 derivative to bare
+correlator gW(t12) = g(q) as gn(q) = (−λq∂q)ng(q) with g0(q) = g(q). For c ̸= 0, ∞,
+comparing (6.4) and (6.13) leads to
+Ci
+0;kg(q) + Ci
+1;kg1(q) = ξ(1)(q)uik(q)
+(6.31)
+– 52 –
+
+Our goal is to solve coefficients Ci
+j;k. However, for arbitrary Ci
+j;k and ξ(1)(q), this is
+also a differential equation for g(q), which will constrain g(q) to a specific form. We
+solve (6.31) in detail in Appendix E and present the result here. The correlation g(q)
+must be in the form
+g(q) = (q1/2 + q−1/2)−2∆
+(6.32)
+up to normalization and with a constant ∆. It is obvious that this g(q) obyes KMS
+symmetry g(q) = g(1/q). With this solution, the coefficients Ci
+j;k are
+C1
+0;0 = ∆λ(c − 1)
+c + 1
+,
+C1
+1;0 = 1,
+C1
+0;1 = ∆,
+C1
+1,1 =
+c − 1
+(c + 1)λ
+(6.33)
+C2
+0;0 = ∆λ(c − 1)
+c + 1
+,
+C2
+1;0 = −1,
+C2
+0;1 = ∆,
+C2
+1;1 = − c − 1
+(c + 1)λ
+(6.34)
+where we choose the normalization such that C1
+1;0 = 1. One can check that this solution
+obeys KMS symmetry (6.9). Taking them into (6.31) and using (6.30), we find
+ξ(1)(q) =
+2∆g(q)
+(1 + c)(q1/2 + q−1/2)
+(6.35)
+which is explicitly KMS invariant as expected.
+In the two component vertex form, we have
+�
+jk
+Ci
+j;k∂jg(t12)∂k
+tiφi(¯t; ti) = (∂gφ1 + ∆g∂φ1, −∂gφ2 + ∆g∂φ2)
++
+�c − 1
+c + 1
+�
+(∆λgφ1 + λ−1∂g∂φ1, ∆λgφ2 − λ−1∂g∂φ2)
+(6.36)
+where on the RHS we have suppressed the notation and the derivatives only act on the
+second argument of φi(¯t; ti). Note that the first line, namely c = 1, exactly matches
+with the vertex (3.5) of large q SYK model.
+To construct the higher order coupling coefficient Ci1···im
+j;k1···km such that (6.13) holds
+for all m is not hard for this example. The point is to note the following feature
+gn(q)
+g(q) =
+Pn(q)
+(1 + q)n
+(6.37)
+where Pn(q) is a n-order polynomial has no factor of (1+q). Therefore, for any n-order
+polynomial Pn(q), we can pick a linear combination such that
+n
+�
+j=0
+wj
+gj(q)
+g(q) =
+1
+(1 + q)n
+n
+�
+j=0
+wj(1 + q)n−jPj(q) =
+Pn(q)
+(1 + q)n
+(6.38)
+– 53 –
+
+Since q1/2uI(q) is a first order polynomial of q, the product qm/2uI1(q) · · · uIm(q) is a
+polynomial of q up to order m for each choice of (I1, · · · , Im). It follows that we can
+choose Ci1,··· ,ik
+j,k1···km such that
+CI1···Im =
+m
+�
+j=1
+Ci1,··· ,ik
+j;k1···km(−λq∂q)jg(q) =
+z(m)g(q)
+(q1/2 + q−1/2)muI1(q) · · · uIm(q)
+(6.39)
+where z(m) is a constant that could depend on m. It clear that (6.39) obeys KMS
+symmetry (6.10).
+If we only include this type of orthogonal vector uI in C, we have
+ξ(m) =
+z(m)g(q)
+(q1/2 + q−1/2)m,
+u±(λ, t) = λc(q ± 1)
+q1/2
+,
+u±(−λ, t) = −λ(1 ± q)
+q1/2
+(6.40)
+which by (6.22) and (6.23) leads to
+ˆ ∞
+0
+dyymh(t12, y) = z(m)gW(t12)(λc)m
+�
+cosh λ(t12+iπ)
+2
+�m
+(6.41)
+ˆ ∞
+0
+d˜y˜ym˜h(t34, ˜y) =
+˜z(m)gV (t34)λm
+�
+cosh λ(t34+iπ)
+2
+�m
+(6.42)
+where we assume the vertex of V consists of the same vector uI but with a possibly
+different coefficient ˜z(m). For analytic functions z(m) and ˜z(m) that decay fast enough
+along ℑm → ±∞, the Mellin inversion theorem guarantees the existence of h(t12, y)
+and ˜h(t34, ˜y). However, to determine the exact form of z(m) and ˜z(m) needs detailed
+knowledge of the dynamics of underlying UV model (for example [17]).
+For large q SYK model, we can choose W = V to be the fundamental Majorana
+fermion ψ, whose conformal weight is ∆ = 1/q. The α parameter in (6.21) is given
+by (3.5). Its exponentiation exactly falls into above case of c = 1 with the following
+choices of z(m) and ˜z(m)
+z(m) = ˜z(m) = Γ(2∆ + m)
+2mΓ(2∆)
+(6.43)
+which leads to
+h(t, y) = ˜h(t, y) = gψ(t)
+�
+2
+λ cosh λ(t+iπ)
+2
+�2∆
+Γ(2∆)
+y2∆−1 exp
+�
+−2y
+λ cosh λ(t + iπ)
+2
+�
+(6.44)
+where gψ(t) is the fermion correlation function (3.2). One can check that this exactly
+matches with the result in [17].
+– 54 –
+
+7
+Conclusion and discussion
+In this paper, we constructed an effective field theory to capture the behavior of OTOCs
+of non-maximal quantum chaotic systems. While the theory is constructed phenomeno-
+logically, we showed that it is constraining enough to predict the general structure of
+OTOCs both at leading order in the 1/N expansion, and after resuming over an infinite
+number of higher order corrections. These general results agree with those preciously
+explicitly obtained in specific models. We also showed that the general structure of the
+EFT can in fact be extracted from the large q SYK model, providing further support
+for its validity. There are many future directions to explore, on which we make some
+brief comments.
+Higher dimensional systems
+A most immediate direction is to generalize the cur-
+rent discussion to higher dimensional systems. Including spatial directions will make it
+possible to consider much wider range of physical issues, for example, operator growths
+and scrambling in spatial directions (such as the behavior of the butterfly velocity),
+connections between quantum chaos and energy as well as charge transports, and so
+on.
+In the case of maximal chaos, a phenomenon that connects chaos and energy
+transport is the so-called pole-skipping [8, 30]. Understanding what happens to this
+phenomenon for non-maximal chaotic systems is of interests. In [31] it was conjectured
+that pole-skipping survives in non-maximal system and the location of pole-skipping is
+given by
+(ω, k) = i(2π/β)(1, 1/u(T)
+B )
+(7.1)
+where u(T)
+B
+is an upper bound of the true butterfly velocity uB. An EFT including
+spatial directions could help check the conjecture and understand connections between
+energy transport and chaos in more general systems.
+Physical nature of the effective fields and the shift symmetry
+Here we in-
+troduced chaos effective fields and shift symmetry on phenomenology ground. In the
+example of the large-q SYK model, we can identify the effective fields and origin of
+shift symmetry from the microscopic system. It is, however, not clear whether the
+understanding obtained in this model can be applied to general systems.
+In maximal chaotic holographic systems, the shift symmetry of the EFT should
+be related to the existence of a sharp horizon. It is an outstanding question regarding
+the nature of the horizon when including stringy corrections on the gravity side, un-
+derstanding the physical nature and origin of the shift symmetry for non-maximal case
+could provide hints for this question.
+– 55 –
+
+Effective field theories for Reggeons
+As mentioned in the Introduction (see
+Fig. 1b), there is a close connection between the exponential behavior in non-maximally
+chaotic systems and scattering amplitudes in the Regge limit.
+Our formulation of
+an EFT for non-maximally chaotic systems could provide new ideas for formulat-
+ing effective field theories for Reggeons. More explicitly, the stringy scattering pro-
+cesses corresponding to OTOCs in holographic systems can be described by the BFKL
+Pomeron [4, 32].
+The effective fields we identified could shed light on an effective
+description of the Pomeron.
+Acknowledgements
+We would like to thank Mark Mezei and Daniel Jafferis for stimulating and helpful
+discussions. PG is supported by the US Department of Defense (DOD) grant KK2014
+and also by the Simons foundation as a member of the It from Qubit collaboration. HL
+is supported by the Office of High Energy Physics of U.S. Department of Energy under
+grant Contract Number DE-SC0012567 and DE-SC0020360 (MIT contract # 578218).
+A
+A few oversimplified constructions
+In this appendix, we list two oversimplified constructions of EFT for non-maximal
+chaos, which are slightly generalized from the EFT for maximal chaos [8, 9] with one
+time argument. It turns out that both constructions are only compatible with maximal
+chaos. The purpose of this section serves as a support for the construction in Section
+2 as a minimal and sufficient generalization to account for non-maximal chaos.
+In
+particular, including two time arguments in the effective modes is necessary.
+A.1
+Multiple effective modes with one time argument
+The simplest generalization of [8, 9] is to include more effective modes but still for-
+mulated with one time argument.
+Let us label these effective modes as ϕµ with
+µ = 1, · · · , D for some finite D. The four-point function ˆFWWV V (t1, t2; t3, t4) is sym-
+metric under exchange of t1 ↔ t2 and t3 ↔ t4 respectively. Therefore, to define the
+coupling between a bare operator W0 and effective modes ϕµ, we must respect this
+symmetry. There are two simple ways: one is that every W0 couples with all ϕµ, the
+other is coupling in an ordered way (just like (2.20) and (2.21) for two effective modes).
+Here we will consider the first choice.
+In this case, the coupling in linear order of ϕµ is
+W(t) = W0(t) + Lµ
+t W0(t)ϕµ(t),
+V (t) = V0(t) + ˜Lµ
+t V0(t)ϕµ(t)
+(A.1)
+– 56 –
+
+where µ is summed from 1 to D and Lµ
+t is a set of differential operators
+Lµ
+t W0(t)ϕµ(t) =
+�
+nm
+cµ
+nm∂n
+t W0(t)∂m
+t ϕµ(t)
+(A.2)
+and ˜Lµ
+t is defined similarly with cµ
+nm → ˜cµ
+nm. To quadratic order of ϕµ, the four-point
+function is
+ˆFWWV V (t1, t2; t3, t4) =
+�
+i,j=1,2
+Lµ
+tigW ˜Lν
+tj+2gV ⟨T ϕµ(ti)ϕν(tj+2)⟩
+(A.3)
+where gW,V are short for gW(t12) and gV (t34) and ⟨T ϕµϕν⟩ is the Euclidean time ordered
+two-point function in the thermal state. Imposing the same shift symmetry [8]
+ϕµ(t) → ϕµ(t) + αe±λt
+(A.4)
+in the effective action, we will have the following exponential terms in the Wightman
+function
+⟨ϕµ(t)ϕν(0)⟩ = dµνeλt + ¯dµνe−λt
+(A.5)
+where cµν and ¯cµν are two nonzero constant matrices.
+Let us consider OTOC F4 and TOC G4 defined as
+F4 = ⟨W(t1)V (t3)W(t2)V (t4)⟩ ,
+H4 = ⟨W(t1)W(t2)V (t3)V (t4)⟩
+(A.6)
+where t1, t2 ≫ t3, t4 or t1, t2 ≪ t3, t4. For TOC, we have
+H4 =dµν
+�
+Lµ
+t1gWeλt1 + Lµ
+t2gWeλt2� �
+˜Lν
+t3gV e−λt3 + ˜Lν
+t4gV e−λt4�
++ b.c.
+(A.7)
+where b.c. means bar-conjugate which replaces cµν with ¯cµν and swaps eλt ↔ e−λt. For
+OTOC, we have
+F4 = H4 +
+�
+dµν
+�
+˜Lµ
+t3gV eλt3Lν
+t2gWe−λt2 − Lµ
+t2gWeλt2 ˜Lν
+t3gV e−λt3�
++ b.c.
+�
+(A.8)
+Let us define two vector functions
+vµ(t1, t2) = Lµ
+t1gWeλt1 + Lµ
+t2gWeλt2,
+uν(t3, t4) = ˜Lν
+t3gV e−λt3 + ˜Lν
+t4gV e−λt4
+(A.9)
+Absence of exponential terms in TOC H4 means
+dµνvµ(t1, t2)uν(t3, t4) = 0
+(A.10)
+and the other equation with bar-conjugate. For (A.10), we can first expand vµ and
+write it as
+Geven(t3, t4; t) = − tanh λt
+2 Godd(t3, t4; t)
+(A.11)
+– 57 –
+
+where we define
+Geven/odd(t3, t4; t) ≡
+�
+n even/odd
+�
+m
+dµνuν(t3, t4)cµ
+nm∂n
+t gW(t)λm
+(A.12)
+Let us consider a few cases.
+1. If both sides of (A.11) are nonzero, we can take a KMS transformation t →
+−t − 2πi in (A.11). Since gW(t) = gW(−t − 2πi) by KMS condition, we have
+Geven → Geven and Godd → −Godd and thus (A.11) yields
+tanh λt
+2 = tanh λ(t + 2πi)
+2
+=⇒ λ = 1
+(A.13)
+2. If both sides of (A.11) are zero, this means
+dµνuν(t3, t4)Lµ
+t1gWeλt1 = 0,
+dµνuν(t3, t4)Lµ
+t2gWeλt2 = 0
+(A.14)
+Then we can expand uν in the second equation and find a similar equation to
+(A.11)
+˜Geven(t1, t2; t) = tanh λt
+2
+˜Godd(t1, t2; t)
+(A.15)
+where we define
+˜Geven/odd(t1, t2; t) ≡
+�
+n even/odd
+�
+m
+dµν(Lµ
+t2gWeλt2)˜cν
+nm∂n
+t gW(t)(−λ)m
+(A.16)
+If both sides of (A.15) are nonzero, the KMS transformation in (A.15) again leads
+to (A.13) and maximal chaos λ = 1.
+3. If both sides of (A.15) are zero, we have
+dµνLµ
+t2gWeλt2 ˜Lν
+tjgV e−λtj = 0,
+j = 3, 4
+(A.17)
+Similarly, using the first equation of (A.14), we will have either λ = 1 or
+dµνLµ
+t1gWeλt1 ˜Lν
+tjgV e−λtj = 0,
+j = 3, 4
+(A.18)
+Then we can consider another TOC H′
+4 = ⟨V (t3)V (t4)W(t1)W(t2)⟩. Following a
+similar analysis for H4 (which simply swaps t1,2 ↔ t3,4 and W ↔ V everywhere),
+we will have either λ = 1 or
+dµν ˜Lµ
+tjgV eλtjLν
+tigWe−λti = 0,
+i = 1, 2,
+j = 3, 4
+(A.19)
+Taking both (A.17) and (A.19) into (A.8), we find that the exponential terms
+proportional to dµν vanish in F4. Similarly, we can show that the bar-conjugate
+terms vanish as well. This means that if we require exponential growth of OTOC
+but no exponential growth in TOC, we must have maximal chaos λ = 1 in this
+model.
+– 58 –
+
+A.2
+Two effective modes with one time argument and ordered coupling
+As we mentioned before, for two effective modes ϕi with i = 1, 2, there is another simple
+way to couple bare operators with them in a symmetric way. This is essentially the
+same as our proposal (2.20) and (2.21) in which W0(tS) couples with ϕ1(τS) and W0(tL)
+couples with ϕ2(tL) where tL,S is the one of t1 and t2 with larger (smaller) imaginary
+part. The only difference is that here we will consider the effective modes with one
+time argument. In other words, there is no ¯t argument.
+For this model, we can simply substitute φi(¯t, t) in Section 2.2 with
+φi(¯t; t) = ϕi(t)
+(A.20)
+In particular, the KMS symmetry (2.26)-(2.27) reduces to
+�
+ˆT ϕ1(t)ϕi(t′)
+�
+=
+�
+ˆT ϕ2(t)ϕi(t′)
+�
+=
+�
+ˆT ϕ1(t + 2πi)ϕi(t′)
+�
+(A.21)
+This means that the two effective modes ϕi(t) are completely degenerate to a single
+effective mode ϕ(t) in a thermal state with inverse temperature 2π. It reduces to the
+case in [8, 9] which is inevitably restricted to the maximal chaos.
+B
+Unitary and dynamical KMS conditions
+The periodicity (2.45) along imaginary time direction can be understood as ηs,p in a
+thermal state with imaginary chemical potential. Let as define the charge carried by
+ηs,p(¯τ; t) as Q = p, namely
+[Q, ηs,p(¯τ; t)] = pηs,p(¯τ; t)
+(B.1)
+It follows that the state consistent with the KMS condition (2.44) is
+ρ = ˆSe−2πiQ/3e−πH
+(B.2)
+where ˆS is the operator that takes the s value of ηs,p, namely
+ˆSηs,p(¯τ; t) ˆS−1 = sηs,p(¯τ; t)
+(B.3)
+For the state given by (B.2), the time reversal transformation T of ρ is given by
+TρT−1 = ˆSe2πiQ/3e−πH/Z∗ = ρ†
+(B.4)
+where we assumed time reversal invariance of ˆS, Q and H (and also hermicity of ˆS
+and Q). The time reversal transformation T of ηs,p(¯τ; t) is defined as flipping t and ¯τ
+simultaneously
+Tηs,p(¯τ; t)T−1 = ηs,p(−¯τ; −t)
+(B.5)
+– 59 –
+
+From this definition, T2 = 1. In this definition, the periodicity of ηs,p(¯τ; t) along ¯τ
+direction is consistent
+Tηs,p(¯τ + π; t)T−1 = Te2πip/3ηs,p(¯τ; t)T−1 = e−2πip/3ηs,p(−¯τ; −t) = ηs,p(−(¯τ + π); −t)
+(B.6)
+Let us consider the generating functional on the Keldysh contour
+eW[J(1)
+s,p,J(2)
+s,p] = Tr
+�
+ρ
+�
+˜Te−i
+´
+J(2)
+s,−pη(2)
+s,p
+� �
+Tei
+´
+J(1)
+s,−pη(1)
+s,p
+��
+(B.7)
+where T is time ordering and ˜T is inverse time ordering. Let us define another gener-
+ating functional with ρ†
+e
+¯
+W[J(1)
+s,p,J(2)
+s,p] = Tr
+�
+ρ† �
+˜Te−i
+´
+J(2)
+s,−pη(2)
+s,p
+� �
+Tei
+´
+J(1)
+s,−pη(1)
+s,p
+��
+(B.8)
+Suppose the generating functional can be represented by the path integral of effective
+field theory
+eW[J(1)
+s,p,J(2)
+s,p] =
+ˆ
+Dη(1)
+s,pDη(2)
+s,peiI[J(1)
+s,p,η(1)
+s,p;J(2)
+s,p,η(2)
+s,p]
+(B.9)
+Similar formula applies to ¯W with I replaced with ¯I. The unitary and dynamical KMS
+conditions are as follows.
+1. Taking two sources J(1) and J(2) identical leads to vanishing W and ¯W. To satisfy
+this condition, we impose
+I[Js,p, ηs,p; Js,p, ηs,p] = ¯I[Js,p, ηs,p; Js,p, ηs,p] = 0
+(B.10)
+Turning off the sources, the effective action for ηa,r
+s,p in Keldysh formalism needs
+to obey
+S[ηr
+s,p, ηa
+s,p = 0] = ¯S[ηr
+s,p, ηa
+s,p = 0] = 0
+(B.11)
+This means that the effective action does not have Kr···rηr · · · ηr term. In other
+words, each term in the action must contain at least one ηa
+s,p.
+2. Taking complex conjugate of (B.7), assuming J∗
+s,p = Js,−p, it is clear that
+W[J(1)
+s,p , J(2)
+s,p ]∗ = ¯W[J(2)
+s,p , J(1)
+s,p ]
+(B.12)
+To guarantee this condition, we need to impose
+I[J(1)
+s,p , η(1)
+s,p; J(2)
+s,p , η(2)
+s,p]∗ = −¯I[J(2)
+s,p , η(2)
+s,p; J(1)
+s,p , η(1)
+s,p]
+(B.13)
+which written in terms of effective action without source is
+S[ηr
+s,p, ηa
+s,p]∗ = − ¯S[ηr
+s,p, −ηa
+s,p]
+(B.14)
+– 60 –
+
+3. Under time reversal transformation, the generating functional W becomes
+eW[J(1)
+s,p(¯τ;t),J(2)
+s,p(¯τ;t)] = Tr
+�
+ρ† �
+Tei
+´
+J(2)∗
+s,−p(¯τ;t)η(2)
+s,p(−¯τ;−t)� �
+˜Te−i
+´
+J(1)∗
+s,−p(¯τ;t)η(1)
+s,p(−¯τ;−t)��∗
+= Tr
+�
+ρ
+�
+Tei
+´
+J(1)
+s,−p(¯τ;t)η(1)
+s,−p(−¯τ;−t)� �
+˜Te−i
+´
+J(2)
+s,−p(¯τ;t)η(2)
+s,−p(−¯τ;−t)��
+= Tr
+��
+Tei
+´
+J(1)
+s,−p(¯τ;t)η(1)
+s,−p(−¯τ;−t−iπ)se2πip/3�
+ρ
+�
+˜Te−i
+´
+J(2)
+s,−p(¯τ;t)η(2)
+s,−p(−¯τ;−t)��
+= Tr
+�
+ρ
+�
+˜Te−i
+´
+J(2)
+s,p(¯τ;t)η(2)
+s,p(−¯τ;−t)� �
+Tei
+´
+J(1)
+s,p(¯τ;t)η(1)
+s,p(−¯τ;−t−iπ)se−2πip/3��
+= eW[se2πip/3J(1)
+s,−p(−¯τ;−t−iπ),J(2)
+s,−p(−¯τ;−t)]
+(B.15)
+where J∗
+s,p(¯τ; t) is the complex conjugate source of Js,p(¯τ; t). Applying (B.15)
+twice maps back to original W[J(1)
+s,p (¯τ; t), J(2)
+s,p (¯τ; t)].
+Define the notation
+˜J(1)
+s,p (¯τ; t) = se2πip/3J(1)
+s,−p(−¯τ; −t − iπ),
+˜J(2)
+s,p (¯τ; t) = J(2)
+s,−p(−¯τ; −t)
+(B.16)
+˜η(1)
+s,p(¯τ; t) = se2πip/3η(1)
+s,−p(−¯τ; −t − iπ),
+˜η(2)
+s,p(¯τ; t) = η(2)
+s,−p(−¯τ; −t)
+(B.17)
+and (B.15) can be written as
+W[J(1)
+s,p , J(2)
+s,p ] = W[ ˜J(1)
+s,p , ˜J(2)
+s,p ]
+(B.18)
+In terms of a-r fields, we can rewrite (B.17) as
+˜ηa
+s,p(¯τ; t) = Dp
++ηa
+s,−p(−¯τ; −t) − 2Dp
+−ηr
+s,−p(−¯τ; −t)
+(B.19)
+˜ηr
+s,p(¯τ; t) = Dp
++ηr
+s,−p(−¯τ; −t) − 1
+2Dp
+−ηa
+s,−p(−¯τ; −t)
+(B.20)
+where we defined two operators
+Dp
+± = 1
+2(1 ± se2πip/3eiπ∂t)
+(B.21)
+Taking (B.18) into (B.9), we can derive the dynamical KMS condition
+I[J(1)
+s,p , η(1)
+s,p; J(2)
+s,p , η(2)
+s,p] = I[ ˜J(1)
+s,p , ˜η(1)
+s,p; ˜J(2)
+s,p , ˜η(2)
+s,p]
+(B.22)
+Turning off the sources, the effective action for ηa,r
+s,p in Keldysh formalism needs
+to obey
+S[ηr
+s,p, ηa
+s,p] = S[˜ηr
+s,p, ˜ηa
+s,p]
+(B.23)
+For ¯W, the time reversal symmetry just changes the factor e2πip/3 to e−2πip/3 in
+(B.15). This leads to a slightly different dynamical KMS condition
+¯I[J(1)
+s,p , η(1)
+s,p; J(2)
+s,p , η(2)
+s,p] = ¯I[ ¯J(1)
+s,p , ¯η(1)
+s,p; ¯J(2)
+s,p , ¯η(2)
+s,p]
+(B.24)
+– 61 –
+
+where ¯Js,p and ¯ηs,p are the same as (B.16) and (B.17) except replacing e2πip/3 with
+e−2πip/3. Turning off the sources, the effective action obeys
+¯S[ηr
+s,p, ηa
+s,p] = ¯S[¯ηr
+s,p, ¯ηa
+s,p]
+(B.25)
+where
+¯ηa
+s,p(¯τ; t) = D−p
++ ηa
+s,−p(−¯τ; −t) − 2D−p
+− ηr
+s,−p(−¯τ; −t)
+(B.26)
+¯ηr
+s,p(¯τ; t) = D−p
++ ηr
+s,−p(−¯τ; −t) − 1
+2D−p
+− ηa
+s,−p(−¯τ; −t)
+(B.27)
+4. The imaginary part of both I and ¯I needs to be nonnegative to guarantee con-
+vergent of path integral. Turning off the sources, the effective actions should
+obey
+ℑS[ηr
+s,p, ηa
+s,p] ≥ 0,
+ℑ ¯S[ηr
+s,p, ηa
+s,p] ≥ 0
+(B.28)
+These four unitary and KMS conditions need to be consistent with each other.
+First, we should check if the dynamical KMS conditions (B.23) and (B.25) are consistent
+with (B.14). Using (B.25) and (B.14), we can write down a new KMS-type symmetry
+for S
+S[ηr
+s,p, −ηa
+s,p] = − ¯S[ηr
+s,p, ηa
+s,p]∗ = − ¯S[¯ηr
+s,p, ¯ηa
+s,p]∗ = S[¯ηr
+s,p, −¯ηa
+s,p]
+(B.29)
+Combine with (B.23), we have one more condition
+S[ηr
+s,p, ηa
+s,p] = S[se2πip/3eiπ∂tηr
+s,p, se2πip/3eiπ∂tηa
+s,p]
+(B.30)
+which holds for any local, time t translational invariant and (both ˆS and Q) charge
+conserved action S. In other words, each term in the action should be in the form of
+ˆ
+Kα1···αk
+s1,p1,··· ,sk,pk(∂¯τ, ∂t)ηα1
+s1,p1(¯τ, t) · · · ηαk
+sk,pk(¯τ, t),
+(α1, · · · αk ∈ {a, r})
+(B.31)
+with �k
+i=1 si = 1 and �k
+i=1 pi = 3Z.
+The second case we need to check is the consistency between (B.14) and (B.28). It
+is easy to see that they together lead to another inequality to S
+ℑS[ηr
+s,p, −ηa
+s,p] = −ℑ ¯S[ηr
+s,p, ηa
+s,p]∗ = ℑ ¯S[ηr
+s,p, ηa
+s,p] ≥ 0
+(B.32)
+Given each term in the effective action in the form of (B.31), this inequality together
+with (B.28) leads to further constraint to the terms with odd numbers of ηa
+s,p, namely
+Kα1···αk
+s1,p1,··· ,sk,pk(∂¯τ, ∂t) =
+�
+Kα1···αk
+s1,−p1,··· ,sk,−pk(∂¯τ, ∂t)
+�∗
+(B.33)
+– 62 –
+
+for α1, · · · , αk contain odd numbers of a.
+Let us focus on the quadratic action, it is given by (2.60), which is copied here
+S[ηr
+s,p, ηa
+s,p] =
+�
+s,p
+ˆ π
+0
+d¯τ
+ˆ ∞
+−∞
+dt
+�
+ηa
+s,−pKar
+s,p(∂¯τ, ∂t)ηr
+s,p + 1
+2ηa
+s,−pKaa
+s,p(∂¯τ, ∂t)ηa
+s,p
+�
+(B.34)
+where no pure ηr term due to (B.11). By definition, we have
+Kaa
+s,p(∂¯τ, ∂t) = Kaa
+s,−p(−∂¯τ, −∂t)
+(B.35)
+By (B.33) and (B.28), we have
+Kar
+s,p(∂¯τ, ∂t) = Kar
+s,−p(∂¯τ, ∂t)∗,
+ℑ
+�
+s,p
+ηa
+s,−pKaa
+s,p(∂¯τ, ∂t)ηa
+s,p ≥ 0
+(B.36)
+To solve the dynamical KMS condition, taking the transformation (B.19) and (B.20)
+into RHS of (B.23), we will generally have all types aa, ar and rr terms. Requiring
+these three terms all match with LHS leads to a single condition
+Kar
+s,p(∂¯τ, ∂t) − Kar
+s,−p(−∂¯τ, −∂t) = −2is (tan π(p/3 + ∂t/2))s Kaa
+s,p(∂¯τ, ∂t)
+(B.37)
+In non-dissipation case, we have Kaa = 0, which implies
+Kar
+s,p(∂¯τ, ∂t) = Kar
+s,−p(−∂¯τ, −∂t) = Ks,p(−∂¯τ, −∂t)∗
+(B.38)
+Taking this back to (B.34), one can easily see that S[ηr
+s,p, ηa
+s,p] factorizes as
+S[ηr
+s,p, ηa
+s,p] = Sf[η(1)
+s,p] − Sf[η(2)
+s,p]
+(B.39)
+where
+Sf[ηs,p] = 1
+2
+�
+s,p
+ˆ π
+0
+d¯τ
+ˆ ∞
+−∞
+dtηs,−pKar
+s,p(∂¯τ, ∂t)ηs,p
+(B.40)
+is a real action.
+C
+Generalization to polynomial-exponential case
+The differential operator Ks,p(i∂t) can be generalized to contain higher powers of ∂2
+t −λ2,
+which would lead to polynomial-exponential behaviors tke±λt in correlation functions.
+However, it turns out that most of these polynomial-exponential terms are excluded by
+the self-consistency condition (2.76): there are two cases ℑ¯tW < ℑ¯tV and ℑ¯tW > ℑ¯tV
+in the TOC G4, which must smoothly match each other at ℑ¯tW = ℑ¯tV .
+– 63 –
+
+If we only have pure exponential terms, it is automatically compatible with this
+condition because G4 does not grow exponentially in both cases due to Grr
++ = 0 (up to
+non-exponential terms) as explained in Section 2.8. However, as we show in this section
+that this matching condition of G4 becomes nontrivial when we include polynomial-
+exponential terms. It turns out that only pure exponential and linear-exponential terms
+are allowed in correlation functions, which implies that Ks,p(i∂t) can at most contain
+quadratic ∂2
+t − λ2. Furthermore, we will solve the most general Wightman functions of
+effective modes that obey all three constraints (2.56), (2.76) and (2.79).
+C.1
+Wightman functions
+It is convenient to work directly with Wightman functions. Let us assume for p = 0, ±
+that
+G>
+s,p(¯τ; t) =
+�
+hs,p(t)
+¯τ ∈ [0, π]
+e−2πip/3hs,p(t)
+¯τ ∈ [−π, 0]
+(C.1)
+where each hs,p(t) contains polynomial-exponential pieces
+hs,p(t) =
+n
+�
+k=0
+γk
+s,ptkeλt + sγk
+s,−p(−t − iπ)ke−λ(t+iπ) = shs,−p(−t − iπ)
+(C.2)
+where n is finite number and the coefficient choice manifests KMS condition (2.48). It
+follows that
+Gra
+s,p(¯τ; t) = θ(t)
+�
+∆s,p(t)
+¯τ ∈ [0, π]
+e−2πip/3∆s,p(t)
+¯τ ∈ [−π, 0]
+(C.3)
+with
+∆s,p(t) = hs,p(t) − e2πip/3hs,−p(−t)
+(C.4)
+The smoothness condition (2.56) can be written in this case as
+∆+,±(t) − ∆−,±(t) = −e±πi/3(∆+,0(t) − ∆−,0(t))
+(C.5)
+Let us explicitly implement the requirement that G4 is smoothly defined at ℑ¯tW =
+ℑ¯tV . For ℑ¯tW < ℑ¯tV , G4 is given by (2.108). For ℑ¯tW > ℑ¯tV , G4 is given by flipping
+the sign of the first argument of G>
+s,p, namely
+G4 − gWgV =1
+2
+�
+s,p
+Lt1 ˜Lt3
+�
+gWgV G>
+s,p(−; t31)
+�
++ e2πip/3Lt2 ˜Lt3
+�
+gWgV G>
+s,p(−; t32)
+�
++ e2πip/3Lt1 ˜Lt4
+�
+gWgV G>
+s,p(+; t14)
+�
++ Lt2 ˜Lt4
+�
+gWgV G>
+s,p(+; t24)
+�
+(C.6)
+– 64 –
+
+The reason that Grr
++ = 0 leads to G4 = 0 in (2.108) is that the shift symmetry
+of vertex (2.82) transforms the four pure exponential terms in (2.108) to just one
+exponential function of t2 and t4 in (2.109). However, for polynomial-exponential terms,
+we do not have an extended symmetry transforming, say, tk
+1eλt1 to tk
+2eλt2. Therefore,
+to make sure (2.108) matches with (C.6) at ℑ¯tW = ℑ¯tV for the quadratic and higher
+polynomial-exponential pieces, we must require the four terms in both (2.108) and
+(C.6) match with each other separately
+�
+s,p
+hs,p(t) ≃
+�
+s,p
+e−2πip/3hs,p(t) ≃
+�
+s,p
+e2πip/3hs,p(t)
+(C.7)
+where “≃” means that the equation hold for tke±λt terms with k > 1. The k = 1 case
+is a little bit different and will be discussed later. It follows that
+�
+s
+hs,p(t) ≃ 0,
+p = ±
+(C.8)
+where there is no constraint to p = 0 piece simply because G>
+s,0(t) is independent on ¯τ.
+Using ansatz (C.2), we can easily show order by order from (C.8) for p = ± that
+γk
+s,± = 0,
+k = 2, · · · , n
+(C.9)
+Then by Grr
++ = 0 (2.93), we have
+h+,0(t) + h+,0(−t) ≃ 0 =⇒ γk
++,0 = 0,
+k = 2, · · · , n
+(C.10)
+On the other hand, using (C.1), (C.4), (C.5) and (C.10) that
+h−,0(t) − h−,0(−t) ≃ 0 =⇒ γk
+−,0 = 0,
+k = 2, · · · , n
+(C.11)
+In this way, the consistency conditions and shift symmetry kill all quadratic and higher
+polynomial-exponential terms.
+For the linear-exponential term, the shift symmetry of vertex (2.82) does help a
+bit because, for example,
+Lt1[gW(t1 − t2)e±λ(t1+iπ)] = Lt1[gWt1e±λ(t1+iπ)] − t2Lt2[gWe±λt2]
+(C.12)
+However, this is still not enough to save nontrivial linear-exponential term in hs,±(t).
+After some algebra, matching the linear-exponential pieces in (2.108) and (C.6) leads
+to
+γ1
++,+ = γ1
++,− = 0,
+γ1
+−,+ = cos(π(λ/2 + 1/3))
+cos(π(λ/2 − 1/3))γ1
+−,−
+(C.13)
+– 65 –
+
+Taking this into (2.93) leads to γ1
++,0 = 0. Using (C.5), we can solve
+γ1
+−,± = −
+cos(πλ/2)
+cos π(λ/2 ∓ 1/3)γ1
+−,0
+(C.14)
+In particular, we should have γ1
+−,0 = γ1
+−,+ = 0 and γ1
+−,− ̸= 0 when λ = 1/3. Taking
+these solutions to G4, one can see that no linear-exponential term survives.
+With the existence of linear-exponential growth term, the constraint to the pure
+exponential term is slightly different. Comparing the pure exponential piece in (C.2)
+and (2.112), we should identify
+As,p = γ0
+s,p,
+Bs,p = s(γ0
+s,−p − iπγ1
+s,−p)e−iλπ
+(C.15)
+Taking this into (2.93) and (C.5) leads to
+γ0
++,± = −
+cos (πλ/2)
+cos π(λ/2 ∓ 1/3)γ0
++,0
+(C.16)
+γ0
+−,± = −
+cos (πλ/2)
+cos π(λ/2 ∓ 1/3)γ0
+−,0 ±
+√
+3(2iγ0
++,0 + πγ1
+−,0)
+4 cos2 π(λ/2 ∓ 1/3)
+(C.17)
+Taking these solutions into (2.110) and (2.111), we will find both C1 and C2 vanish.
+One can also check (C.6) vanishes as well. This confirms the result in Section 2.8 that
+Grr
++ = 0 and smoothness condition (C.5) imply vanishing pure exponential terms in
+TOC for both ordering of ℑ¯tW,V .
+In conclusion, the consistency conditions require h+,p(t) only contain pure exponen-
+tial terms and h−,p(t) only contain up to linear-exponential terms. With the expression
+(C.2), there are only three independent parameters γ0
++,0, γ0
+−,0 and γ1
+−,0. Other parame-
+ters are determined by the following relation
+γ0
++,p = (−)p
+cos (πλ/2)
+cos π(λ/2 − p/3)γ0
++,0
+(C.18)
+γ0
+−,p = (−)p
+cos (πλ/2)
+cos π(λ/2 − p/3)γ0
+−,0 + p
+√
+3(2iγ0
++,0 + πγ1
+−,0)
+4 cos2 π(λ/2 − p/3)
+(C.19)
+γ1
+−,p = (−)p
+cos(πλ/2)
+cos π(λ/2 − p/3)γ1
+−,0
+(C.20)
+C.2
+The effective action
+The above most general consistent Wightman functions correspond to the effective
+actions in the form of (2.69) with
+K+,p(i∂t) = (∂2
+t − λ2)k+,p(i∂t),
+K−,p(i∂t) = (∂2
+t − λ2)2k−,p(i∂t)
+(C.21)
+– 66 –
+
+where one should note that K−,p(x) has a double zero at ±iλ. By symmetry (2.68), we
+have ks,p(x) = (−)pks,−p(−x). Since K+,p is linear in ∂2
+t − λ2, the computation (2.93)
+for Grr
++ = 0 up to non-exponential terms still hold and leads to the same condition
+(2.94):
+k+,±(iλ) = ∓ik+,0(iλ)
+√
+3
+tan
+�π
+2 (λ ± 1/3)
+�
+tan πλ
+2
+(C.22)
+The smoothness condition (2.77) at ω = iλ leads to
+k−,±(iλ) = ±ik−,0(iλ)
+√
+3
+(C.23)
+k′
+−,±(iλ) = ±
+√
+3
+3
+�
+2λk−,0(iλ)2
+k+,0(iλ)
+�
+1 +
+1
+tan
+� π
+2(λ ± 1/3)
+�
+tan πλ
+2
+�
++ ik′
+−,0(iλ)
+�
+(C.24)
+which allows three undetermined parameters k+,0(iλ), k−,0(iλ) and k′
+−,0(iλ).
+From
+(2.74) and (2.75), we have
+∆+,0(t) =
+i
+2λk+,0(iλ)(eλt − e−λt)
+(C.25)
+∆+,±(t) = ± e±iπ/3
+2
+√
+3λ
+�
+eλt
+k+,±(iλ) +
+e−λt
+k+,∓(iλ)
+�
+(C.26)
+∆−,0(t) =λk′
+−,0(iλ) − ik−,0(iλ)
+4λ3k−,0(iλ)2
+(eλt − e−λt) +
+i
+4λ2k−,0(iλ)t(eλt + e−λt)
+(C.27)
+∆−,±(t) = ± e±iπ/3
+4
+√
+3λ2
+�λk′
+−,±(iλ) − ik−,±(iλ)
+iλk−,±(iλ)2
+eλt + λk′
+−,∓(iλ) − ik−,∓(iλ)
+iλk−,∓(iλ)2
+e−λt
++t
+�
+eλt
+k−,±(iλ) −
+e−λt
+k−,∓(iλ)
+��
+(C.28)
+where we see linear-exponential terms appear because of the double poles in 1/K−,p(ω)
+at ω = ±iλ.
+Take ansatz (C.2) with n = 0 for s = + and n = 1 for s = −. Using (C.4) and
+comparing with (C.25)-(C.28), we find
+γ0
++,0 =
+1
+2iλ(e−iπλ − 1)k+,0(iλ)
+(C.29)
+γ1
+−,0 =
+i
+4λ2(e−iπλ + 1)k−,0(iλ)
+(C.30)
+γ0
+−,0 =
+�
+1 + eiπλ�
+λk′
+−,0(iλ) − i
+�
+1 + eiπλ − iπλ
+�
+k−,0(iλ)
+16λ3 cos2 πλ
+2 k−,0(iλ)2
+(C.31)
+– 67 –
+
+and other γk
+s,p are given by (C.18)-(C.20). By the conclusion from last subsection, this
+implies that the action with (C.21) and three constraints (C.22)-(C.24) lead to absence
+of exponential terms in TOC.
+Using (C.25)-(C.28) and the first line of (2.107), we find that
+∆(t) =
+3
+4λ(1/2 − cos πλ) sin πλ
+2 k+,0(iλ)(eiπλ/2eλt + e−iπλ/2e−λt)
+(C.32)
+which exactly matches with (2.107). This means that for any four-point functions,
+k−,0(iλ) and k′
+−,0(iλ) are irrelevant parameters in the action. What we discussed in
+Section 2.8 with pure exponential case is indeed the most general situation for four-
+point functions.
+D
+Correlation functions of effective modes in the large q SYK
+model
+In this appendix, we first ignore the prefector N/(8q2) in the action (5.14). In the end,
+this prefactor simply adds a 8/(N∆2) factor to any two-point function.
+D.1
+Canonical quantization trick
+As explained in Section 5.3, we will take the mathematical trick of canonical quan-
+tization to solve the Euclidean two-point function of ϵ(¯τ, x). First, we need to solve
+the equations of motion Lgm(¯τ, x) = 0 for wave function gm(¯τ, x) with UV condition
+gm(¯τ, 0) = gm(¯τ, 2π) = 0 from (5.13) and expand the quantized field ˆϵ(¯τ, x) in terms of
+ˆϵ(¯τ, x) =
+�
+m
+gmˆam + g∗
+mˆa†
+m
+(D.1)
+where ˆam and ˆa†
+m are annihilation and creation operators obeying canonical commu-
+tation relation [ˆam, ˆa†
+m′] = δm,m′, and gm is well-normalized under Klein-Gordon inner
+product, which is defined in (5.30). Note that the quantum number m must be discrete
+because the spatial direction x is finite. Due to translation symmetry in ¯τ, we can
+choose the positive energy wave function
+gm(¯τ, x) ∝ e−im¯τ,
+m ≥ 0
+(D.2)
+for which the Hamiltonian H has eigen value m and
+[H, ˆa†
+m] = mˆa†
+m,
+[H, ˆam] = −mˆam
+(D.3)
+– 68 –
+
+Since gm(¯τ, x) is on-shell, following from (5.22) it can be expanded as
+gm(¯τ, x) =
+1
+∆G0(τ12)
+�
+i=1,2
+LτiG0(τ12)χi,m(¯τ; τi)
+(D.4)
+where ¯τ in χi,m(¯τ; τi) is just a dummy argument whose dependence is trivial. It follows
+that we can rewrite (D.1) as
+ˆϵ(¯τ, x) =
+1
+∆G0(x)
+�
+i=1,2
+LτiG0(x)ˆχi(¯τ; τi)
+(D.5)
+ˆχi(¯τ; τi) ≡
+�
+m
+χi,m(¯τ; τi)ˆam + χ∗
+i,m(¯τ; τi)ˆa†
+m
+(D.6)
+where Lτ is defined in (5.25). By the fundamental domain Dϵ, the defining domain for
+ˆχ1(¯τ; τ) is {¯τ ∈ [0, π], τ − ¯τ ∈ [0, π]} and that for ˆχ2(¯τ; τ) is {¯τ ∈ [0, π], τ − ¯τ ∈ [−π, 0]}.
+Note that the path integral is defined on the finite spacetime Dϵ. To compute any
+correlation function of quantized field ˆϵ on Dϵ, we must first specify the states on time
+slice ¯τ = 0, π respectively. This is dictated by the boundary condition of ϵ(¯τ, x) in
+the Euclidean path integral on Dϵ at ¯τ = 0, π. From the first equation of (5.13), we
+see that any configurations of ϵ(0, x) is identified with ϵ(π, 2π − x). For our canonical
+quantization trick, this implies that we need to trace over all states at ¯τ = 0, π with a
+reflection x → 2π − x. More explicitly, we consider the following Wightman function
+W(¯τ, x; ¯τ ′, x′) ≡ 1
+Z Tr
+�
+Pe−iπHˆϵ(¯τ, x)ˆϵ(¯τ ′, x′)
+�
+,
+Z ≡ Tr
+�
+Pe−iπH�
+(D.7)
+where the time evolution for ¯τ = π is present and P is the reflection operator
+Pˆϵ(¯τ, x)P −1 = ˆϵ(¯τ, 2π − x)
+(D.8)
+Therefore, we will define the expectation ⟨· · · ⟩c.q. as
+⟨· · · ⟩c.q. ≡ 1
+Z Tr
+�
+Pe−iπH · · ·
+�
+(D.9)
+Expanding in ˆam and ˆa†
+m, we have
+W(¯τ, x; ¯τ ′, x′) =
+�
+m
+1
+Nm
+�
+gm(¯τ, x)g∗
+m(¯τ ′, x′)
+�
+ˆamˆa†
+m
+�
+c.q.
++g∗
+m(¯τ, x)gm(¯τ ′, x′)
+�
+ˆa†
+mˆam
+�
+c.q.
+�
+(D.10)
+Since the Euclidean two-point function ⟨ϵ(¯τ, x)ϵ(¯τ ′, x′)⟩ is symmetric under exchange
+of ¯τ, x with ¯τ ′, x′, this corresponds to the Feynman propagator of ˆϵ(¯τ, x), i.e.
+⟨ϵ(¯τ, x)ϵ(¯τ ′, x′)⟩ = −i
+� ¯T ˆϵ(¯τ, x)ˆϵ(¯τ ′, x′)
+�
+c.q.
+(D.11)
+– 69 –
+
+= −i[θ(¯τ − ¯τ ′)W(¯τ, x; ¯τ ′, x′) + θ(¯τ ′ − ¯τ)W(¯τ ′, x′; ¯τ, x)]
+(D.12)
+where ¯T is the time ordering of ¯τ and ¯τ − ¯τ ′ is restricted to [−π, π]. We emphasize that
+the LHS of (D.11) is a Euclidean two-point function and the RHS of (D.11) is just a
+mathematical trick to compute it in terms of a Feynman propagator of quantized field
+ˆϵ by regarding ¯τ as “time”. The quantized field ˆϵ and the corresponding Hilbert space
+are part of the trick and have no physical meaning.
+On the domain Dϵ, taking above equations into (5.11) leads to
+Fψ(τ1,τ2, τ3, τ4) = G0(τ12)G0(τ34)
++
+�
+i,j=1,2
+LτiLτj+2
+�
+G0(τ12)G0(τ34)
+�
+−i
+� ¯T ˆχi(¯τa; τi)ˆχj(¯τb; τj+2)
+�
+c.q.
+��
+(D.13)
+where one should note that the dummy argument ¯τ plays a role in the time ordering
+¯T though its explicit dependence in (D.4) is trivial. Given (D.5), it is noteworthy that
+the reflection (D.8) acts nontrivially on ˆχi. The transformation (¯τ, x) → (¯τ, 2π − x) is
+equivalent to (τ1, τ2) → (τ2 + π, τ1 − π), which implies
+P ˆχ1(¯τ, τ)P −1 = ˆχ2(¯τ, τ − π),
+P ˆχ2(¯τ, τ)P −1 = ˆχ1(¯τ, τ + π)
+(D.14)
+Taking this back to (D.13) and using definition (D.9), we have the following KMS
+conditions
+� ¯T ˆχ1(0; τ)ˆχj(¯τ ′; τ ′)
+�
+c.q. =
+� ¯T ˆχ2(π; τ)ˆχj(¯τ ′; τ ′)
+�
+c.q.
+(D.15)
+� ¯T ˆχ2(0; −τ)ˆχj(¯τ ′; τ ′)
+�
+c.q. =
+� ¯T ˆχ1(π; 2π − τ)ˆχj(¯τ ′; τ ′)
+�
+c.q.
+(D.16)
+where τ ∈ [0, π] by the defining domain of ˆχi.
+It is very interesting that the Euclidean four-point function (D.13) now has the
+same structure as (2.23). Therefore, we would like to define the Euclidean two-point
+function of two effective fields φE
+1,2(¯τ; τ) such that
+�
+φE
+i (¯τ; τ)φE
+j (¯τ ′; τ ′)
+�
+≡ −i
+� ¯T ˆχi(¯τ; τ)ˆχj(¯τ ′; τ ′)
+�
+c.q.
+(D.17)
+Take this definition into (D.13) and analytically continue ¯τk → itk. Comparing with
+(2.23), we will identify the Euclidean fields φE
+i as φi after analytic continuation. In
+particular, the two KMS conditions (D.15) and (D.16) in terms of φE
+i are equivalent to
+the KMS conditions of φi (2.26)-(2.27).
+D.2
+Solve discrete quantum numbers
+From the general solution (5.22) to Lϵ = 0, let us expand χi in Fourier modes
+χ1(τ) =
+�
+m
+Ame−imτ,
+χ2(τ) =
+�
+m
+Bme−imτ
+(D.18)
+– 70 –
+
+The UV condition (5.13) for τ1 = τ2 (x = 0) leads to
+− λ(Am − Bm) tan λπ
+2 − im(Am + Bm) = 0
+(D.19)
+and for τ1 = τ2 + 2π (x = 2π) leads to
+λ(Ame−2miπ − Bm) tan λπ
+2 − im(Ame−2miπ + Bm) = 0
+(D.20)
+Combining these two equations, we have
+Am
+Bm
+= λ tan λπ
+2 − im
+λ tan λπ
+2 + im = λ tan λπ
+2 + im
+λ tan λπ
+2 − ime2miπ
+(D.21)
+which leads to
+λ tan λπ
+2 + im = ±e−πim(λ tan λπ
+2 − im),
+Am = ±Bmeimπ
+(D.22)
+These two cases can be solved as two sets of positive quantum numbers m
+M+ = {m > 0|λ tan λπ
+2 + m cot mπ
+2
+= 0}
+(D.23)
+M− = {m > λ|λ tan λπ
+2 − m tan mπ
+2
+= 0}
+(D.24)
+where m = λ is excluded in M− because it leads to trivial ϵ. This is exactly the shift
+symmetry (5.23) of the ϵon−shell in (5.22). Note that here we only choose positive m
+because it is indeed the positive frequency of the canonical quantization in (5.29).
+It follows that in (D.4) we can take
+χ1,m(¯τ; τ) = Ame−imτ,
+χ2,m(¯τ; τ) = Bme−imτ,
+m ∈ M±
+(D.25)
+For convenience, we will add a superscipt “±” to distinguish the two types of solutions
+with m ∈ M± respectively. Let us take
+A+
+m = B+
+meimπ = i eimπ/2
+2λ
+�
+N +
+m
+,
+A−
+m = −B−
+meimπ =
+eimπ/2
+2λ
+�
+N −
+m
+(D.26)
+which leads to wave functions
+g+
+m(¯τ, x) = e−im¯τ
+�
+N +
+m
+�m
+λ cos m
+2 (π − x) + sin m
+2 (π − x) tan λ
+2(π − x)
+�
+(D.27)
+g−
+m(¯τ, x) = e−im¯τ
+�
+N −
+m
+�m
+λ sin m
+2 (π − x) − cos m
+2 (π − x) tan λ
+2(π − x)
+�
+(D.28)
+– 71 –
+
+where g±
+m is even/odd under x → 2π − x. Taking these solutions into Klein-Gordon
+inner product (5.30) leads to
+N ±
+m = (m − λ)(m + λ)(mπ ∓ sin mπ)/λ2
+(D.29)
+It follows from (D.6) that
+ˆχ1(¯τ; τ) =
+�
+s=±
+�
+m∈Ms
+As
+me−imτˆas
+m + As∗
+meimτˆas†
+m
+(D.30)
+ˆχ2(¯τ; τ) =
+�
+s=±
+�
+m∈Ms
+Bs
+me−imτˆas
+m + Bs∗
+meimτˆas†
+m
+(D.31)
+D.3
+Correlations
+To compute the correlation functions, we need to first evaluate the expectation value
+of ˆas
+mˆas†
+m. Taking (D.30) and (D.31) into the conditions (D.15) and (D.16) leads to
+�
+ˆas
+mˆas†
+m
+�
+c.q. = seimπ �
+ˆas†
+mˆas
+m
+�
+c.q.
+(D.32)
+By canonical quantization, we have [ˆas
+m, ˆas†
+m] = 1, which yields15
+�
+ˆas
+mˆas†
+m
+�
+c.q. =
+1
+1 − se−imπ ,
+�
+ˆas†
+mˆas
+m
+�
+c.q. =
+se−imπ
+1 − se−imπ
+(D.33)
+In the following, we will compute the correlations by summing over Matsubara
+frequencies m. The method is the Sommerfeld-Watson transformation used in [28] and
+we will only restrict ourselves to exponential pieces. Since the ¯τ dependence is only
+through time ordering, in the following we will suppress the argument ¯τ in ˆχi(¯τ; τ) in
+the computation of Wightman functions with specified ordering of fields, e.g.
+⟨ˆχ1(τ1)ˆχ1(τ2)⟩c.q. ≡ ⟨ˆχ1(¯τ; τ1)ˆχ1(0; τ2)⟩c.q.
+(¯τ > 0)
+=
+�
+s=±
+�
+m∈Ms
+As
+mAs∗
+m
+�
+e−imτ12 �
+as
+mas†
+m
+�
+c.q. + eimτ12 �
+as†
+mas
+m
+�
+c.q.
+�
+= 1
+4
+�
+s=±
+�
+m∈±Ms
+e−imτ12
+(1 ∓ e−imπ)(m − λ)(m + λ)(mπ ∓ sin πm)
+(D.34)
+where in the second line, we extend the sum over m to both positive and negative M±
+due to the two terms in the first line.
+Let us compute s = ± separately. For s = +, we insert
+1
+2πi
+(πm − sin mπ)/(cos mπ − 1)
+m cot mπ/2 + λ tan λπ/2
+(D.35)
+15We can also derive these equations by the definition of these operators in the Fock space generated
+by ˆas†
+m if we add an infinitesimal negative imaginary part to all m.
+– 72 –
+
+(a)
+(b)
+Figure 10. (a) The contour of C+ that circles around all ±M+ (black dots) anticlockwise.
+The three poles (red dots) at 0, ±λ are not circled. (b) We can deform the contour C+ through
+infinity to just three clockwise circles around 0, ±λ.
+into the sum and change the sum over m to anticlockwise contour integral along small
+circles of m around all ±M+, which we denoted as C+ (see Fig. 10). The denominator
+of (D.35) pickes out the residue at these points and the numerator is the reciprocal of
+residues. Our purpose is to deform the contour to small circles around 0, ±λ. However,
+the extra 1/(cos mπ − 1) gives additional unwanted poles at even integers. To replace
+it with an equivalent expression, we use (D.22) to write
+1
+cos mπ − 1 = (λ tan λπ/2)2 + m2
+−2m2
+(D.36)
+at all m ∈ ±M+. Putting them all together, we have
+⟨ˆχ1(τ1)ˆχ1(τ2)⟩+
+c.q. = −1
+4
+‰
+C+
+dm
+2πi
+e−imτ12((λ tan λπ/2)2 + m2)
+2m2(1 − e−imπ)(m − λ)(m + λ)(m cot mπ/2 + λ tan λπ/2)
+(D.37)
+Note that though 1 − e−imπ = 0 for even m, they are not poles because m cot mπ/2 is
+also divergent for even m and cancels it out. For τ12 ∈ (0, π), the integral over infinite
+arc on upper and lower half planes are both zero. Then the integral reduces to residues
+at 0, ±λ
+⟨ˆχ1(τ1)ˆχ1(τ2)⟩+
+c.q. = 1
+4Res0,±λ
+�
+e−imτ12((λ tan λπ/2)2 + m2)
+2m2(1 − e−imπ)(m − λ)(m + λ)(m cot mπ/2 + λ tan λπ/2)
+�
+(D.38)
+If τ12 ∈ (−π, 0), we need simply multiply both numerator and denominator of (D.37)
+by e−imπ and replace the e−imπ in denominator by (λ tan λπ/2+im)/(λ tan λπ/2−im)
+due to (D.22). This leads to
+⟨ˆχ1(τ1)ˆχ1(τ2)⟩+
+c.q. = −1
+4
+‰
+C+
+dm
+2πi
+e−im(τ12+π)(λ tan λπ/2 − im)2
+2m2(1 − e−imπ)(m − λ)(m + λ)(m cot mπ/2 + λ tan λπ/2)
+– 73 –
+
+= 1
+4Res0,±λ
+�
+e−im(τ12+π)(λ tan λπ/2 − im)2
+2m2(1 − e−imπ)(m − λ)(m + λ)(m cot mπ/2 + λ tan λπ/2)
+�
+(D.39)
+If τ12 ∈ (π, 2π), we will multiply both numerator and denominator of (D.37) by eimπ
+and replace the eimπ in denominator by (λ tan λπ/2 − im)/(λ tan λπ/2 + im) instead.
+This leads to
+⟨ˆχ1(τ1)ˆχ1(τ2)⟩+
+c.q. = 1
+4Res0,±λ
+�
+e−im(τ12−π)(λ tan λπ/2 + im)2
+2m2(1 − e−imπ)(m − λ)(m + λ)(m cot mπ/2 + λ tan λπ/2)
+�
+(D.40)
+Similarly, for s = −, we need to consider the contour C− that circles around all
+points in M−, and insert
+1
+2πi
+(πm + sin mπ)/(cos mπ + 1)
+m tan mπ/2 − λ tan λπ/2
+≃
+1
+2πi
+(πm + sin mπ)((λ tan λπ/2)2 + m2)/(2m2)
+m tan mπ/2 − λ tan λπ/2
+(D.41)
+where “≃” means equal at the poles M− by (D.36). Following a similar computation,
+this leads to
+⟨ˆχ1(τ1)ˆχ1(τ2)⟩−
+c.q. = −1
+4Res0,±λ
+�
+e−imτ12((λ tan λπ/2)2 + m2)
+2m2(1 + e−imπ)(m − λ)(m + λ)(m tan mπ/2 − λ tan λπ/2)
+�
+(D.42)
+for τ12 ∈ (0, π), and
+⟨ˆχ1(τ1)ˆχ1(τ2)⟩−
+c.q. = 1
+4Res0,±λ
+�
+e−im(τ12+π)(λ tan λπ/2 − im)2
+2m2(1 + e−imπ)(m − λ)(m + λ)(m tan mπ/2 − λ tan λπ/2)
+�
+(D.43)
+for τ12 ∈ (−π, 0), and
+⟨ˆχ1(τ1)ˆχ1(τ2)⟩−
+c.q. = 1
+4Res0,±λ
+�
+e−im(τ12−π)(λ tan λπ/2 + im)2
+2m2(1 + e−imπ)(m − λ)(m + λ)(m tan mπ/2 − λ tan λπ/2)
+�
+(D.44)
+for τ12 ∈ (π, 2π).
+Note that ˆχ2 is not completely independent from ˆχ1 due to (D.26), above formula
+indeed covers all correlations between ˆχ1 and ˆχ2. Explicitly, with translation symmetry
+we have
+⟨ˆχ1(τ)ˆχ1(0)⟩c.q. = ⟨ˆχ2(τ)ˆχ2(0)⟩c.q. = ⟨ˆχ1(τ)ˆχ1(0)⟩+
+c.q. + ⟨ˆχ1(τ)ˆχ1(0)⟩−
+c.q.
+(D.45)
+⟨ˆχ1(τ)ˆχ2(0)⟩c.q. = ⟨ˆχ1(τ − π)ˆχ1(0)⟩+
+c.q. − ⟨ˆχ1(τ − π)ˆχ1(0)⟩−
+c.q.
+(D.46)
+⟨ˆχ2(τ)ˆχ1(0)⟩c.q. = ⟨ˆχ1(τ + π)ˆχ1(0)⟩+
+c.q. − ⟨ˆχ1(τ + π)ˆχ1(0)⟩−
+c.q.
+(D.47)
+– 74 –
+
+Evaluation of residues is straightforward and leads to
+⟨ˆχ1(τ)ˆχ1(0)⟩c.q. = ⟨ˆχ2(τ)ˆχ2(0)⟩c.q. = ⟨ˆχ1(2π − τ)ˆχ2(0)⟩c.q. = ⟨ˆχ2(−τ)ˆχ1(0)⟩c.q. (D.48)
+=i ×
+�
+ˆm+eiλτ + ˆm1τeiλτ + c.c.,
+τ ∈ [0, 2π]
+ˆm−eiλτ + ˆm1τeiλτ + c.c.,
+τ ∈ [−π, 0]
+(D.49)
+where star means complex conjugate and
+ˆm+ = i2πλ − sin 2πλ + 2(πλ + sin πλ)(2πiλ + 3 − e−iπλ)
+32λ2(πλ + sin πλ)2(1 + eiπλ)
+,
+(D.50)
+ˆm− = ˆm+ +
+1
+4λ2(1 + eiπλ),
+ˆm1 =
+1
+8λ(πλ + sin πλ)(1 + eiπλ)
+(D.51)
+As a consistent check, one can show that the correlator (D.48) obeys the KMS condition
+(D.15) and (D.16). It is noteworthy that even if the computations for even and odd
+modes are different for the ranges τ ∈ [0, π] and τ ∈ [π, 2π], we still have smoothness
+of ⟨ˆχ1(τ)ˆχ1(0)⟩ at τ = π in (D.49), which is consistent with item 4b of our effective
+theory.
+Using (D.17) and restoring the 8/(N∆2) factor in (D.48), we can derive the two-
+point function of φE
+i as
+�
+φE
+i (¯τ; τ)φE
+j (0; 0)
+�
+= θ(¯τ)Mij(τ) + θ(−¯τ)Mji(−τ)
+(D.52)
+M11(τ) = M22(τ) = M12(2π − τ) = M21(−τ)
+(D.53)
+=
+8
+N∆2 ×
+�
+ˆm+eiλτ + ˆm1τeiλτ + c.c.,
+τ ∈ [0, 2π]
+ˆm−eiλτ + ˆm1τeiλτ + c.c.,
+τ ∈ [−π, 0]
+(D.54)
+where the argument ranges in (D.52) are
+i = j : {(¯τ, τ)|¯τ ∈ [−π, π], ¯τ − τ ∈ [−π, π]}
+(D.55)
+i = 1, j = 2 : {(¯τ, τ)|¯τ ∈ [−π, π], ¯τ − τ ∈ [−2π, 0]}
+(D.56)
+i = 2, j = 1 : {(¯τ, τ)|¯τ ∈ [−π, π], ¯τ − τ ∈ [0, 2π]}
+(D.57)
+D.4
+The effective action
+The effective action will be still formulated in ηs,p(¯τ; t) variables and the correlation
+functions of φi will be given by (2.49) to (2.51). Since the correlation function (D.54)
+contains linear-exponential terms, the effective action needs to contain quadratic factor
+of ∂2
+t − λ2. It turns out that we need to take the action (2.69) with
+K+,p(i∂t) = (∂2
+t − λ2)k+,p(i∂t),
+K−,p(i∂t) = (∂2
+t − λ2)2k−,p(i∂t)
+(D.58)
+– 75 –
+
+where K−,p(x) has a double zero at ±iλ.
+By symmetry (2.68), we have ks,p(x) =
+(−)pks,−p(−x). This effective action has been thoroughly discussed in Appendix C.2.
+To match the correlation functions (D.52) with this EFT action, let us first com-
+pute
+�
+ˆT φi(¯t; t)φj(0; 0)
+�
+correlation functions by (2.49)-(2.51) with the most general
+consistent Wightman functions solved in Appendix C.1, which are also results of the
+action (D.58) by the analysis in Appendix C.2. Then we compare
+�
+ˆT φi(¯t; t)φj(0; 0)
+�
+with (D.52) after analytic continuation.
+Since these correlation functions obey the
+same KMS conditions, matching one of them is sufficient. In the following, we will take
+i = j = 1 and assume ℑt ∈ [−2π, 0].
+The most general consistent Wightman function in Appendix C.1 takes the form
+(C.1) and (C.2) where h+,p only contains pure exponential terms and h−,p only contains
+up to linear-exponential terms. The coefficients γk
+s,p are constrained by (C.18)-(C.20).
+Using these solutions in (2.49) we have
+�
+ˆT φ1(¯t; t)φ1(0; 0)
+�
+=
+�
+(m+ + m1t)e−λt + ( ¯m+ + ¯m1t)eλt,
+ℑ¯t ∈ [−π, 0]
+(m− − ¯m1t)e−λt + ( ¯m− − m1t)eλt,
+ℑ¯t ∈ [0, π]
+(D.59)
+where ℑ¯t − ℑt ∈ [0, π] and
+¯m+ = 3((γ0
+−,0 + γ0
++,0)(1 − 2 cos πλ) − 2(πγ1
+−,0 + 2iγ0
++,0) sin πλ)
+2(1 − 2 cos πλ)2
+(D.60)
+m+ = 3e−iπλ(2γ0
++,0 + iπγ1
+−,0)
+2(1 − 2 cos πλ)
+− e−iπλ ¯m+
+(D.61)
+m− = ¯m+ −
+6γ0
++,0
+1 − 2 cos πλ
+(D.62)
+¯m− = m+ − 6e−iπλγ0
++,0
+1 − 2 cos πλ
+(D.63)
+¯m1 = eiπλm1 =
+3γ1
+−,0
+2(1 − 2 cos πλ)
+(D.64)
+Comparing with (D.52)-(D.54) with analytic continuation φE
+j (¯τ; τ) → φj(¯t; t) = −iφE
+j (i¯t; it),
+in which θ(¯τ) → θ(−ℑ¯t) and τ → it, we should identify
+γ1
+−,0 =
+2i(2 cos πλ − 1)
+3λN∆2(πλ + sin πλ)(1 + e−iπλ)
+(D.65)
+γ0
++,0 =
+1 − 2 cos πλ
+3λ2N∆2(1 + e−iπλ)
+(D.66)
+γ0
+−,0 = −(πλ + 4i) sin 2πλ − (πλ + 7i)(πλ + sin πλ) + πλ(2πλ + 9i) cos πλ + iπλ cos 2πλ
+3λ2N∆2 (1 + e−iπλ) (πλ + sin πλ)2
+(D.67)
+– 76 –
+
+Moreover, in Appendix C.2 we show that the most general consistent Wightman
+functions in Appendix C.1 can also be reproduced by the effective action (C.21). Given
+the parameter relations (C.29)-(C.31), we can derive
+k+,0(iλ) = 3λN∆2 cot πλ
+2
+2(1 − 2 cos πλ)
+(D.68)
+k−,0(iλ) = 3N∆2(πλ + sin πλ)
+8λ(2 cos πλ − 1)
+(D.69)
+k′
+−,0(iλ) = −3iN∆2 �
+(2π2λ2 − 5) sin πλ + 2 sin 2πλ + 8πλ cos πλ − πλ
+�
+3πλ tan πλ
+2 + 7
+��
+16λ2(1 − 2 cos πλ)2
+(D.70)
+In conclusion, the action (2.69) with (D.58) and (D.68)-(D.70) fully captures the cor-
+relation of the effective modes φE
+i after analytic continuation.
+E
+Solve m = 1 vertex
+In matrix form the equation (6.31) is
+�C1
+0;0g(q) + C1
+1;0g1(q) C1
+0;1g(q) + C1
+1;1g1(q)
+C2
+0;0g(q) + C2
+1;0g1(q) C2
+0;1g(q) + C2
+1;1g1(q)
+�
+= ξ(1)(q)
+q1/2
+�−λ(1 − cq) 1 + cq
+λ(c − q)
+c + q
+�
+(E.1)
+Note that each entry on RHS has zero at ±c or ±1/c respectively. Taking q = ±c, ±1/c
+on LHS, we can immediately derive
+C1
+1;0 = −C1
+0;0g(1/c)
+g1(1/c) ,
+C1
+1;1 = −C1
+0;1g(−1/c)
+g1(−1/c) ,
+C2
+1;0 = −C2
+0;0g(c)
+g1(c) ,
+C2
+1;1 = −C2
+0,1g(−c)
+g1(−c)
+(E.2)
+Taking this back to (E.1), we have
+−C1
+0;0
+g1(1/c)g(q) − g(1/c)g1(q)
+g1(1/c)λ(1 − cq)
+= C1
+0;1
+g1(−1/c)g(q) − g(−1/c)g1(q)
+g1(−1/c)(1 + cq)
+= C2
+0;0
+g1(c)g(q) − g(c)g1(q)
+g1(c)λ(c − q)
+= C2
+0;1
+g1(−c)g(q) − g(−c)g1(q)
+g1(−c)(c + q)
+= ξ(1)(q)
+q1/2
+(E.3)
+Using KMS symmetry gn(q) = (−)ngn(1/q), comparing the first line and the second
+line of above equations lead to
+ξ(1)(q)/C1
+0;0 = ξ(1)(1/q)/C2
+0;0,
+ξ(1)(q)/C2
+0;1 = ξ(1)(1/q)/C1
+0;1
+(E.4)
+– 77 –
+
+Then we just need to solve the first line of (E.3), which is a first order differential
+equation
+(C1
+0;0 + λC1
+0;1) + (C1
+0;0 − λC1
+0;1)cq
+(C1
+0;0A + λC1
+0;1B) + (C1
+0;0A − λC1
+0;1B)cq = g1(q)
+g(q) ,
+A = g(1/c)
+g1(1/c),
+B = g(−1/c)
+g1(−1/c)
+(E.5)
+The solution of above type equation is
+α + βq
+γ + θq = g1(q)
+g(q)
+=⇒ g(q) = q−α/(γλ)(γ + θq)(αθ−βγ)/(γθλ)
+(E.6)
+Requiring KMS symmetry g(q) = g(1/q) leads to
+γ = θ,
+β = −α,
+g(q) = (q1/2 + q−1/2)−2∆,
+∆ = β/(γλ)
+(E.7)
+Using this solution of g(q), we have
+g(q)
+g1(q) = −
+1 + q
+∆λ(1 − q) =⇒ A =
+1 + c
+∆λ(1 − c),
+B =
+1 − c
+∆λ(1 + c)
+(E.8)
+Plugging this back to (E.5) and using (E.7), we only find one independent relation
+(1 + c)C1
+0;0 + λ(1 − c)C1
+0;1 = 0. Taking this back to (E.2) leads to
+C1
+0;0 = ∆λ(c − 1)
+c + 1
+,
+C1
+1;0 = 1,
+C1
+0;1 = ∆,
+C1
+1,1 =
+c − 1
+(c + 1)λ
+(E.9)
+where we have chosen the normalization C1
+1;0 = 1. Taking them back to (E.1), we can
+solve
+ξ(1)(q) =
+2∆g(q)
+(1 + c)(q1/2 + q−1/2)
+(E.10)
+which is explicitly KMS invariant as expected. Taking this to (E.4) and (E.2), we have
+C2
+0;0 = ∆λ(c − 1)
+c + 1
+,
+C2
+1;0 = −1,
+C2
+0;1 = ∆,
+C2
+1;1 = − c − 1
+(c + 1)λ
+(E.11)
+One can check that this solution also obeys KMS symmetry (6.9).
+References
+[1] S.H. Shenker and D. Stanford, Black holes and the butterfly effect, JHEP 03 (2014)
+067 [1306.0622].
+[2] S.H. Shenker and D. Stanford, Multiple Shocks, JHEP 12 (2014) 046 [1312.3296].
+– 78 –
+
+[3] D.A. Roberts, D. Stanford and L. Susskind, Localized shocks, JHEP 03 (2015) 051
+[1409.8180].
+[4] S.H. Shenker and D. Stanford, Stringy effects in scrambling, JHEP 05 (2015) 132
+[1412.6087].
+[5] A. Kitaev, Hidden correlations in the Hawking radiation and thermal noise, talk at
+KITP (2015) .
+[6] D.A. Roberts and D. Stanford, Two-dimensional conformal field theory and the
+butterfly effect, Phys. Rev. Lett. 115 (2015) 131603 [1412.5123].
+[7] J. Maldacena, S.H. Shenker and D. Stanford, A bound on chaos, JHEP 08 (2016) 106
+[1503.01409].
+[8] M. Blake, H. Lee and H. Liu, A quantum hydrodynamical description for scrambling
+and many-body chaos, JHEP 10 (2018) 127 [1801.00010].
+[9] M. Blake and H. Liu, On systems of maximal quantum chaos, JHEP 05 (2021) 229
+[2102.11294].
+[10] M.S. Costa, V. Goncalves and J. Penedones, Conformal Regge theory, JHEP 12 (2012)
+091 [1209.4355].
+[11] L. Cornalba, Eikonal methods in AdS/CFT: Regge theory and multi-reggeon exchange,
+0710.5480.
+[12] P. Kravchuk and D. Simmons-Duffin, Light-ray operators in conformal field theory,
+JHEP 11 (2018) 102 [1805.00098].
+[13] J.R. Forshaw and D.A. Ross, Quantum Chromodynamics and the Pomeron, Cambridge
+Lecture Notes in Physics, Cambridge University Press (1997),
+10.1017/CBO9780511524387.
+[14] A. Kitaev and S.J. Suh, The soft mode in the Sachdev-Ye-Kitaev model and its gravity
+dual, JHEP 05 (2018) 183 [1711.08467].
+[15] Y. Gu and A. Kitaev, On the relation between the magnitude and exponent of OTOCs,
+JHEP 02 (2019) 075 [1812.00120].
+[16] D. Stanford, Z. Yang and S. Yao, Subleading Weingartens, JHEP 02 (2022) 200
+[2107.10252].
+[17] Y. Gu, A. Kitaev and P. Zhang, A two-way approach to out-of-time-order correlators,
+JHEP 03 (2022) 133 [2111.12007].
+[18] M. Mezei and G. S´arosi, Chaos in the butterfly cone, JHEP 01 (2020) 186
+[1908.03574].
+[19] M. Crossley, P. Glorioso and H. Liu, Effective field theory of dissipative fluids, JHEP
+09 (2017) 095 [1511.03646].
+– 79 –
+
+[20] P. Glorioso, M. Crossley and H. Liu, Effective field theory of dissipative fluids (II):
+classical limit, dynamical KMS symmetry and entropy current, JHEP 09 (2017) 096
+[1701.07817].
+[21] H. Liu and P. Glorioso, Lectures on non-equilibrium effective field theories and
+fluctuating hydrodynamics, PoS TASI2017 (2018) 008 [1805.09331].
+[22] P. Glorioso and H. Liu, The second law of thermodynamics from symmetry and
+unitarity, 1612.07705.
+[23] A. Kitaev, Near-coherent scrambling, talk at IAS (2017) .
+[24] S. Sachdev and J. Ye, Gapless spin-fluid ground state in a random quantum heisenberg
+magnet, Physical Review Letters 70 (1993) 3339.
+[25] A. Kitaev, A simple model of quantum holography, in KITP strings seminar and
+Entanglement, vol. 12, 2015.
+[26] J. Maldacena and D. Stanford, Remarks on the Sachdev-Ye-Kitaev model, Phys. Rev.
+D 94 (2016) 106002 [1604.07818].
+[27] J.S. Cotler, G. Gur-Ari, M. Hanada, J. Polchinski, P. Saad, S.H. Shenker et al., Black
+Holes and Random Matrices, JHEP 05 (2017) 118 [1611.04650].
+[28] C. Choi, M. Mezei and G. S´arosi, Exact four point function for large q SYK from
+Regge theory, JHEP 05 (2021) 166 [1912.00004].
+[29] K. Papadodimas and S. Raju, An Infalling Observer in AdS/CFT, JHEP 10 (2013)
+212 [1211.6767].
+[30] S. Grozdanov, K. Schalm and V. Scopelliti, Black hole scrambling from hydrodynamics,
+Phys. Rev. Lett. 120 (2018) 231601 [1710.00921].
+[31] C. Choi, M. Mezei and G. S´arosi, Pole skipping away from maximal chaos, 2010.08558.
+[32] R.C. Brower, J. Polchinski, M.J. Strassler and C.-I. Tan, The Pomeron and
+gauge/string duality, JHEP 12 (2007) 005 [hep-th/0603115].
+– 80 –
+
diff --git a/tdE4T4oBgHgl3EQfxQ03/content/tmp_files/load_file.txt b/tdE4T4oBgHgl3EQfxQ03/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..44e344a34e70cad614088d1c620d300dd18672c3
--- /dev/null
+++ b/tdE4T4oBgHgl3EQfxQ03/content/tmp_files/load_file.txt
@@ -0,0 +1,2826 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf,len=2825
+page_content='Prepared for submission to JHEP  MIT-CTP/5511  An effective field theory for non-maximal  quantum chaos  Ping Gao and Hong Liu  Center for Theoretical Physics,  Massachusetts Institute of Technology, Cambridge, MA 02139, USA  E-mail: pgao@mit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='edu, hong liu@mit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='edu  Abstract: In non-maximally quantum chaotic systems, the exponential behavior of  out-of-time-ordered correlators (OTOCs) results from summing over exchanges of an  infinite tower of higher “spin” operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' We construct an effective field theory (EFT)  to capture these exchanges in (0 + 1) dimensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The EFT generalizes the one for  maximally chaotic systems, and reduces to it in the limit of maximal chaos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The theory  predicts the general structure of OTOCs both at leading order in the 1/N expansion  (N is the number of degrees of freedom), and after resuming over an infinite number  of higher order 1/N corrections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  These general results agree with those previously  explicitly obtained in specific models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' We also show that the general structure of the  EFT can be extracted from the large q SYK model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='05256v1  [hep-th]  12 Jan 2023  Contents  1  Introduction  1  2  The structure of EFT  6  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1  General setup  6  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='2  Two-component effective mode and constraints from KMS symmetries  8  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='3  Diagonalize the KMS conditions  12  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='4  Reformulating the KMS conditions  14  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='5  The quadratic effective action  17  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='6  Shift symmetry and exponential growth in correlation functions  21  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='7  Summary of the effective field theory  23  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='8  TOC and OTOC  25  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='9  General structure of OTOCs for non-maximal chaos  27  3  Comparisons with OTOCs in various theories  29  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1  The large q SYK model  29  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='2  Stringy scattering in a AdS black hole  30  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='3  Conformal Regge theory  32  4  Relation to the EFT of maximal chaos  35  5  Identifying the effective fields in the large q SYK model  37  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1  OTOC of the large q SYK model  38  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='2  Identifying the effective fields  41  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='3  Two-point function of φE  i  42  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='4  Effective action for large q SYK  44  6  Higher order terms and exponentiation  47  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1  Towards a scattering formula  47  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='2  An example  52  7  Conclusion and discussion  55  A A few oversimplified constructions  56  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1 Multiple effective modes with one time argument  56  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='2 Two effective modes with one time argument and ordered coupling  59  – i –  B Unitary and dynamical KMS conditions  59  C Generalization to polynomial-exponential case  63  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1 Wightman functions  64  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='2 The effective action  66  D Correlation functions of effective modes in the large q SYK model  68  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1 Canonical quantization trick  68  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='2 Solve discrete quantum numbers  70  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='3 Correlations  72  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='4 The effective action  75  E Solve m = 1 vertex  77  1  Introduction  Information injected into a small subsystem of a quantum many-body system eventu-  ally spreads under time evolution across the entire system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Such scrambling of quantum  information can be described in terms of growth of operators under Heisenberg evolu-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' More explicitly, consider a quantum mechanical system with N degrees of freedom  and few-body interactions among them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The growth of operators can be probed by the  so-called out-of-time-ordered-correlators (OTOC) [1–6]  F(t) = ⟨W(t)V (0)W(t)V (0)⟩β = ⟨Ψ2(t)|Ψ1(t)⟩,  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1)  |Ψ1(t)⟩ ≡ W(t)V (0) |Ψβ⟩ ,  |Ψ2(t)⟩ ≡ V (0)W(t) |Ψβ⟩ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='2)  Here V and W are generic few-body operators which we will take to be Hermitian, and  ⟨· · ·⟩β denotes the thermal average at an inverse temperature β.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' In (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='2), |Ψβ⟩ denotes  the thermal field double state the expectation values with respect to which give the  thermal averages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  In the large N limit, the degrees of freedom involved in generic few-body operators  V (0) and W(0) do not overlap with each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' For small t, V (0) and W(t) almost  commute, and |Ψ1,2⟩ are almost identical, which means that F(t) should be O(1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' As  time increases, W(t) grows, and Ψ1,2 become more and more different, which decreases  F(t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' It is expected for chaotic systems [5]  F(t) ∼ c1 − c2  N eλt + · · ·  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='3)  – 1 –  where c1,2 are some constants and λ is the quantum Lyapunov exponent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' In contrast,  H1(t) = ⟨Ψ1(t)|Ψ1(t)⟩ = ⟨V (0)W(t)W(t)V (0)⟩β,  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='4)  H2(t) = ⟨Ψ2(t)|Ψ2(t)⟩ = ⟨W(t)V (0)V (0)W(t)⟩β,  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='5)  the so-called time-ordered correlators (TOCs), always remain O(1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The exponential  behavior in (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='3) says that in a chaotic system, the slight difference in the initial  preparation of |Ψ1,2⟩ will be quickly magnified during time evolution, which is the  essence of the butterfly effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Quantum Lyapunov exponent λ is state-dependent, describing operator growths  “moderated” by the state under consideration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' It has an upper bound [7]  λ ≤ 2π  β .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='6)  The bound is saturated by various systems, including holographic systems in the clas-  sical gravity limit, and SYK-type systems in the low temperature limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' These “max-  imally” chaotic systems are special: the exponential time dependence in (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='3) can be  attributed to the exchange of the stress tensor between W and V (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' 1a), and  can be described by a hydrodynamic effective theory with a single effective field ϕ  that plays the dual role of ensuring energy conservation and characterizing operator  growth [8, 9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  For non-maximal chaotic systems with λ < 2π  β , the origin of (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='3) is more intricate,  arising from exchanging an infinite number of operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' For example, in the SYK  system, exchange of an operator characterized by some quantum number j leads to an  exponential decrease in F(t) proportional to e  2π  β (j−1)t, which violates the bound for any  j > 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Summing over exchanges of an infinite tower of such operators with increasingly  larger values of j leads to an effective λ satisfying the bound.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' We will loosely refer to  j as “spin” in analogue with higher dimensional systems even though there is no spin  for SYK.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Another example is four-point correlation functions of a large N CFT in the  vacuum state in the so-called conformal Regge regime [10–12], which can be interpreted  as a thermal OTOC in terms of Rindler time (with β = 2π).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Here contribution from  a spin-j operator in the OPE of WW (and V V ) gives a contribution proportional to  e(j−1)t (t is now the Rindler time) and summing over an infinite number of higher spin  operator exchanges gives an λ < 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  It is natural to ask whether there exists an effective description with a small number  of degrees of freedom that can capture the sum over exchanges of the infinite tower of  operators, with jeff = 1 + λ β  2π interpreted as the effective spin of the effective fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  We should stress that such an effective description is conceptually and philosophi-  cally different from that is usually used in effective field theory (EFT).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Usually an EFT  – 2 –  (a)  (b)  Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' (a) The maximal chaos can be described by exchange of the stress tensor between  W and V .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' (b) Sum over infinitely many spin j particles exchange between W and V can be  viewed as the exchange of a Reggeon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  is used to describe the dynamics of a small number of “low energy” (or “slow”) degrees  of freedom whose contributions dominate over others in the regime of interests.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Their  effective actions can be formally defined from path integrals by integrating out other  “high energy” (or “fast”) modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' There is, however, no such decoupling of “high en-  ergy” (or “fast”) degrees of freedom here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Spin j (with j > 2) exchanges give important  contributions to F(t);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' they cannot be integrated out in the usual sense.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' We are merely  asking whether there is a way to capture the effect of the infinite sum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The effective  fields here may not correspond to genuine physical collective degrees of freedom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The  philosophy is also very different from the EFT for maximal chaos described in [8];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' there  the stress tensor exchange dominates and the EFT is used to capture the most essential  part of the stress tensor exchange.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  The question of an effective description for non-maximal chaotic system is closely  related a well-known problem in QCD, the formulation of EFTs for Reggeons (see  e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' [13] for a review).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Consider a scattering process in some quantum system (say in  QCD or string theory)  V + W → V + W  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='7)  where V, W denote different particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' We denote the scattering amplitude by A(s, t),  with s the standard variable characterizing the total center of mass energy, and t  characterizing the momentum exchange between V and W particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' In the regime  s → ∞ with t finite, each spin j particle exchange between V and W gives a contribution  to A(s, t) proportional to sj−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' When the Sommerfeld-Watson transform is used to  summing over all the higher spin exchanges, the scattering amplitude can be written  in a form  A(s, t) ∝ gWW(t)gV V (t)sα(t)−1  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='8)  which can be interpreted as the exchange of a single effective particle, called reggeon,  with an effective spin α(t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' gWW, gV V can be interpreted as couplings the Reggeon to  W and V .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' See Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' 1b for an illustration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  – 3 –  For systems with a gravity dual, the OTOC (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1) maps to the gravity side a scat-  tering process precisely of the form (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='7) in a black hole geometry [1–4], with V, W the  corresponding bulk particles dual the boundary operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The center of mass energy  square s for the scattering process is related to time separation t in (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1) by s ∝ e  2π  β t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' In  the bulk language, λ arises from summing over exchanges of an infinite number stringy  modes with increasingly higher spins.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  In the α′ → 0 limit, the contributions of higher spin stringy modes decouple, with  only graviton exchange remaining, and the system becomes maximally chaotic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' In this  limit, the maximal value λmax = 2π  β is universal for all holographic systems, independent  of the details of the black hole geometries [7], and can be argued as a direct consequence  of existence of a sharp horizon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Having an effective description away from the α′ → 0 limit that can capture an  infinite number of stringy modes exchanges is clearly valuable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Such an effective de-  scription can also potentially give insights into what becomes of the event horizon in  the stringy regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  In this paper we make a proposal to formulate an EFT for a non-maximal chaotic  system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' For simplicity, we will restrict to a quantum mechanical system with no spatial  dependence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Generalization to having spatial dependence should be straightforward,  and will be left elsewhere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Lacking at the moment a first-principle understanding  of the nature of the effective chaos field(s) or their effective action, our approach is  phenomenological.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' We try to identify a minimal set of fields and a minimal set of  conditions on their action, such that the following criteria are met:  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' With λ being an input parameter, the EFT gives rise to exponential behavior (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='3)  for OTOCs, but no exponential for TOCs (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='4)–(1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' It captures all the KMS properties of thermal 4-point functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  We will see that the above conditions are rather constraining, and the resulting EFT  can be used to make a general prediction on the structure of OTOCs, which is consistent  with that previously postulated in [14, 15], and agree with the explicit expressions in  large q SYK model, holographic systems (obtained from stringy scattering), and the  conformal Regge theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Furthermore, we show that in this framework it is possible  to sum higher order terms in equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='3) of the form ekλt  Nk (with k an integer)1 in an  exponential, which can again be viewed as a general prediction, and agrees with those  previously obtained in specific systems [4, 16, 17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  We also show that the structure proposed for the non-maximal chaos EFT can be  in fact extracted in the large-q SYK model, where it is possible to identify explicitly  1Such terms are of the same order and dominate in the regime N → ∞ and t ∼ 1  λ log N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  – 4 –  Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Effective description of W(t1)W(t2) in non-maximal chaotic systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The black  dots are bare operators W0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' There are now two types of dressing: one type dresses each local  operator separately (yellow “clouds”), and the other type dresses both operators together  (blue “clouds”).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Maximal chaos case contains only the first type of dressing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  the chaos effective fields, and make much finer comparison between the EFT and the  microscopic theory than the structure of TOCs and OTOCs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  It is worth mentioning here a key difference between the non-maximal EFT to be  discussed in this paper and that for maximal chaotic systems of [8, 9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' For maximal  chaotic systems, W(t) can be viewed as W(t) = W[W0(t), ϕ(t)] where “bare” operator  W0(t) describes W(t) in the large N limit (with no overlap with V0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' ϕ(t) is an effective  field “attached” to W0, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' W is obtained by dressing W0 with ϕ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' ϕ captures effectively  the overlap between W(t) and V (0) due to scrambling, and its dynamics leads to 1/N  corrections indicated in (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' For non-maximal chaotic systems, the chaos fields involve  multiple components: (i) one component dresses each bare local operator as in the  maximal chaotic case (and indeed it reduces to ϕ in the maximal chaos limit).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' This  component carries only one time argument.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' (ii) There are other components which  dress both W’s in (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' it has two time arguments (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' 2 for an illustration).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Existence of such components leads to many new elements which are not present in the  maximal case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  The paper is organized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' In Section 2, we construct the effective field  theory of non-maximal chaos with two effective fields φ1,2 and show that the TOC  does not have exponential growth and OTOC has exponential growth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' In Section 3  we compare the general structure of OTOCs obtained in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' 2 with various known  examples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' In Section 4, we show that the two effective fields φ1,2 reduce to a single field  in the maximal chaos limit and the EFT becomes the same as the EFT constructed  for maximal chaos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  In Section 5, we show how the general structure of the EFT  discussed in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' 2 arises in the large q SYK model, and obtain the explicit form of the  EFT action.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' In Section 6, we include higher order coupling to effective mode φ1,2 and  show that certain higher-order terms of the four-point function can be resummed and  exponentiated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' We conclude in Section 7 with a summary and a discussion of future  directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  – 5 –  Wo (t1)  (2) °M  Wo (t1) Wo (t2)2  The structure of EFT  In this section we discuss the general formulation of an EFT for non-maximally chaotic  systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' For simplicity we will consider quantum mechanical systems with no spatial  dependence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Generalization to systems with spatial dependence can be readily made,  although technically more intricate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' We will also use the unit such that β = 2π .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1  General setup  Consider a generic four-point Wightman function in thermal state  Fabcd(t1, t2, t3, t4) = Tr  �  e−2πHOa(t1)Ob(t2)Oc(t3)Od(t4)  �  ≡ ⟨Oa(t1)Ob(t2)Oc(t3)Od(t4)⟩  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1)  where the subscript refers to the ordering of operators and the time argument should  be understood as corresponding to each subscript in the same order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' We will treat time  variables as complex, and Fabcd(t1, t2, t3, t4) is analytic in the domain  D :  ℑt4 − 2π < ℑt1 < ℑt2 < ℑt3 < ℑt4 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='2)  Fabcd obeys the KMS condition  Fabcd(t1, t2, t3, t4) = Fbcda(t2, t3, t4, t1 + 2πi)  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='3)  which can be iterated cyclically to shift other time variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' It is convenient to intro-  duce a time-ordered function  ˆFabcd(t1, t2, t3, t4) ≡ ⟨T Oa(t1)Ob(t2)Oc(t3)Od(t4)⟩  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='4)  where T denotes operators should be ordered from left to right according to the as-  cending order of their corresponding ℑti.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Moreover, it should always be understood  that  (ℑti)min − (ℑti)max ∈ (−2π, 0), i = 1, 2, 3, 4 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='5)  The KMS condition (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='3) can then be written as  ˆFabcd(t1, t2, t3, t4) = ˆFabcd(t′  1, t′  2, t′  3, t′  4),  t′  i = ti + 2πimi  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='6)  where mi are integers, and should be such that t′  i’s obey (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Now consider  ˆFWWV V (t1, t2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t3, t4) = ⟨T W(t1)W(t2)V (t3)V (t4)⟩  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='7)  which by definition is symmetric under swapping t1 ↔ t2 and t3 ↔ t4  ˆFWWV V (t1, t2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t3, t4) = ˆFWWV V (t2, t1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t3, t4) = ˆFWWV V (t1, t2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t4, t3) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='8)  – 6 –  Depending on ℑti, ˆFWWV V (t1, t2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t3, t4) can correspond to TOC or OTOC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' For example,  ˆFWWV V (t1, t2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t3, t4) = ⟨V (t3)W(t1)W(t2)V (t4)⟩,  ℑt3 < ℑt1 < ℑt2 < ℑt4  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='9)  ˆFWWV V (t1, t2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t3, t4) = ⟨W(t1)V (t3)W(t2)V (t4)⟩,  ℑt1 < ℑt3 < ℑt2 < ℑt4  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='10)  A TOC and OTOC cannot change into each other under cyclic permutations, so KMS  conditions (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='3) relate functions within each type.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Our goal is to develop an effective description for obtaining ˆFWWV V for large N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  To motivate the structure of our proposed EFT for non-maximally chaotic systems, it  is useful to recall some key elements of that for maximally chaotic systems introduced  in [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' One imagines the scrambling of W(t) allows a coarse-grained description in  terms of building up an “effective cloud,” i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  W(t) = W[W0(t), ϕ(t)] .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='11)  Here W0(t) is a “bare” operator involving the original degrees of freedom of W, and ϕ(t)  is an effective chaos mode that describes macroscopically the growth of the operator in  the space of degrees of freedom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' W(t) in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='11) is taken to be linear in W0 but can in  principle have any dependence on the effective field ϕ(t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The dynamics of ϕ is governed  by a chaos effective theory, with two-point function of ϕ scaling with N as 1/N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Thus  W0 can also be viewed as giving the leading part of W(t) in a 1/N expansion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  When ϕ(t) is small, it can be expanded to linear order as  W(t) = W0(t) + Lt[W0(t)]ϕ(t) + O(ϕ2)  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='12)  where Lt[W0] is a W0-dependent differential operator acting on ϕ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' More explicitly,  Lt[W0(t)]ϕ(t) =  ∞  �  m,n=0  cmn∂m  t W0(t)∂n  t ϕ(t)  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='13)  Below it should always be understood that Lt acts on the corresponding ϕ(t) even when  they are not written adjacently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' It then follows that  W(t)W(t′) = W0(t)W0(t′)+Lt[W0(t)]ϕ(t)W0(t′)+W0(t)Lt′[W0(t′)]ϕ(t′)+O(ϕ2), (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='14)  which for ℑ(t − t′) ∈ [−2π, 0] gives  ⟨T W(t)W(t′)⟩ = gW(t − t′) + O(1/N),  gW(t − t′) ≡ ⟨T W0(t)W0(t′)⟩,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='15)  where we have assumed that one-point function of ϕ is zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The O(1/N) piece in  the above equation comes from O(ϕ2) term in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='14), and is proportional to two-point  function of φ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The KMS condition for gW is  gW(t) = gW(−t − 2πi),  ℑt ∈ [−2π, 0]  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='16)  – 7 –  Note that ⟨W(t)V (0)⟩ ∼ O(1/N) with ⟨W0V0⟩ = 0, as for generic few-body operators  V, W, their two-point function should vanish at the leading order in 1/N expansion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Plugging (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='14) and the corresponding expression for V into (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='7), ˆFWWV V reduces  to the two-point function of effective mode ϕ(t) at leading order  ˆFWWV V (t1, t2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t3, t4) = gWgV +  �  i=1,2,j=3,4  Lti ˜Ltj[gWgV ⟨T ϕ(ti)ϕ(tj)⟩EFT]  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='17)  where ˜Lt is the differential operator from a similar expansion of V with cmn → ˜cmn,  and  gW ≡ gW(t12) = ⟨T W0(t1)W0(t2)⟩ ,  gV ≡ gV (t34) = ⟨T V0(t3)V0(t4)⟩ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='18)  Here the ⟨·⟩EFT means expectation value evaluated in the effective field theory of ϕ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  T in ⟨T ϕ(ti)ϕ(tj)⟩EFT follows from the relative magnitude of ℑti and ℑtj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Equa-  tion (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='17) has a very restrictive structure: the two-point function of ϕ in each term  only depends on the locations of two operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' For example, the ϕ correlation function  ⟨T ϕ(t1)ϕ(t3)⟩EFT has no knowledge of t2, t4 at all.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' In other words, the four-point func-  tion essentially reduces to pairwise two-point functions of ϕ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' This structure leads to  various features of ˆF that are consistent with a maximally chaotic system [9], including  the Lyapunov exponent λ = 1 (after imposing a shift symmetry in the EFT of ϕ), but  are not present in a non-maximally chaotic system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Since (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='17) is a direct consequence  of (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='12), for non-maximally chaotic systems, we must generalize (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='12).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='2  Two-component effective mode and constraints from KMS symmetries  We will now propose a formulation for non-maximally chaotic systems which may be  considered a minimal generalization of the EFT in [8] for maximal chaos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The formula-  tion is partially motivated from features of the large q SYK theory, and as we will show  in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' 5, fully captures the physics of that theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The general structure of OTOCs  resulting from it is also compatible with the conclusions of [4, 10–12, 18], as we will  describe later.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  In this formulation ˆF still reduces to two-point functions of some effective fields, but  the main new ingredient we would like to incorporate is that now two-point functions  of effective field(s) have knowledge of the locations of all four operators, not just two  of them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' For this purpose we consider the following generalization of (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='12)2  W(t)W(t′) = W0(t)W0(t′) +  2  �  i=1  D(i)  W (t, t′)φi(t, t′) + O(φ2),  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='19)  2We should emphasize that (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='19) and (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='14) should not be viewed as OPEs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  If there are V  insertion(s) between W’s we cannot do OPE, while these equations are supposed to be valid for any  configurations of orderings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  – 8 –  where there are two fields φ1,2 who depend on both t, t′, and D(1,2)  W  (t, t′) are some  W0-dependent differential operators to be specified more explicitly below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Now φ1,2  depend on both t and t′ of W(t) and W(t′), which means that we cannot view φ1,2  as the “dressing” of each individual operator, as in the case of (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='12).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Rather they  should be interpreted as an effective description of the sum over an infinite number of  higher spin operator exchanges that are known to contribute to ˆF at the leading order  in non-maximal systems [4, 10–12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' There is a parallel equation with W replaced by  V ’s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  The effective theory of φi should satisfy the following criteria:  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Exponential growth in OTOCs with an arbitrary Lyapunov exponent λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' No such exponential growth in TOCs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' All the KMS conditions and analytic properties of ˆFWWV V are satisfied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  We will show that the above goals can be achieved with a minimal generalization  of (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='14).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' In this subsection we first present the prescription for (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='19), and work out  the constraints on two-point functions of φ1,2 from the KMS conditions of ˆFWWV V ,  which provide the basic inputs for formulating the theory of φ1,2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  We will take φ1,2 to “mainly” couple to one of the W’s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' A definition which respects  the swap symmetry (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='8) of ˆF is that φ1 (φ2) couples mainly to the W with the  smaller (larger) ℑt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Denoting tS (tL) with the smaller (larger) value of ℑt, ℑt′, by  “mainly” we mean:  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' φ1(t, t′) = φ1(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' tS) depends weakly on ¯t = t+t′  2  such that it can be expanded in  terms of ¯t-derivatives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The dependence on ¯t encodes the nonlocal information of  the theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Similarly, φ2(t, t′) = φ2(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' tL).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The action of D(i)  W (t, t′) on φi can be expanded similarly as in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='13)  D(1)  W (t, t′)φ1(t, t′) = W0(tL)LtS[W0]φ1(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' tS)  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='20)  D(2)  W (t, t′)φ2(t, t′) = W0(tS)LtL[W0]φ2(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' tL)  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='21)  Lt[W0] ≡  ∞  �  m,n=0  cmn∂m  t W0(t)∂n  t .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='22)  In other words, φ1 couples directly only to W(tS), but does feel the presence  of W(tL) through weak dependence on ¯t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Note that equation (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='20) should be  understood to be valid within time-ordered correlation functions, thus there is  no need to worry about orderings between W0(tL) and W0(tS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Equation (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='20)  – 9 –  Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The green region is the domain I1 for φ1(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) and the blue region is the domain I2  for φ2(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The KMS conditions (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='26)–(2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='27) relate φ1 with φ2 through identifying points  between I1 and I2 as indicated by the black arrows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' This generates the periodicity (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='29) on  I1,2 (red arrows).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  contains no derivative with respect to ¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' it can be viewed as the leading term in  a derivative expansion of ¯t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  For notational simplicity we take the coefficients cnm in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='20) to be the same for  D(2)  W (t, t′), but our discussion can be straightforwardly generalized to the cases that  they are not the same.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The vertex for V will be denoted as ˜Lt with cmn → ˜cmn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The  above prescription is a minimal nontrivial generalization of (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='12) that satisfies the  aforestated criteria.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' In Appendix A we show that a few other simpler prescriptions  cannot work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Since in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='19) |ℑt−ℑt′| < 2π, by definition, φ1(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) is defined for ℑ¯t−ℑt ∈ (0, π),  while φ2(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) is defined for ℑ¯t − ℑt ∈ (−π, 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' We refer to their domains as I1 and  I2 respectively, see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Due to symmetries in exchanging t1 and t2, we will take  ℑt1 < ℑt2, and similarly take ℑt3 < ℑt4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Therefore, φ1 always mainly couples to W(t1)  and V (t3), φ2 always mainly couples to W(t2) and V (t4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Substituting (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='19)–(2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='21)  into ˆFWWV V we find  ˆFWWV V (t1, t2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t3, t4) = gWgV +  �  i,j=1,2  Lti ˜Ltj+2  �  gWgV  �  ˆT φi(¯tW;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' ti)φj(¯tV ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' tj+2)  ��  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='23)  where ¯tW = (t1 + t2)/2, ¯tV = (t3 + t4)/2, and the expectation value of φ1,2 should be  understood as being evaluated in an effective theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Unlike in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='17), where the time-  ordering T follows from that of ˆF, here in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='23) the effective fields φ1,2(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) have two  – 10 –  I1time variables, and time-ordering in ˆF no longer leads to a unique choice of orderings of  φi and φj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' We will specify the precise meaning of  �  ˆT φi(¯tW;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' ti)φj(¯tV ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' tj+2)  �  in Section  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Here we will just list some properties they should satisfy:  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Since in time ordered correlation function ˆF we can exchange V and W arbitrarily,  the ordering of φi, φj in the correlation function should not matter, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  �  ˆT φi(¯tW;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' ti)φj(¯tV ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' tj+2)  �  =  �  ˆT φj(¯tV ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' tj+2)φi(¯tW;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' ti)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='24)  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' From time translation invariance of the system, ˆF is invariant under shifts of  all ti by the same constant, which implies the following translation invariance of  two-point functions of φ1,2,  �  ˆT φi(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t)φj(¯t′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t′)  �  =  �  ˆT φi(¯t + c;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t + c)φj(¯t′ + c;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t′ + c)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='25)  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The KMS conditions satisfied by ˆF imply that these two-point functions of φ1,2  should satisfy the following constraints  �  ˆT φ1(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t)φi(¯t′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t′)  �  ≃  �  ˆT φ2(¯t + πi;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t + 2πi)φi(¯t′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t′)  �  ,  ℑt < ℑt′  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='26)  �  ˆT φ2(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t)φi(¯t′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t′)  �  ≃  �  ˆT φ1(¯t + πi;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t)φi(¯t′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t′)  �  ,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='27)  where ≃ means equal up to zero modes, defined as functions nij(t1, t2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t3, t4) sat-  isfying  �  i,j=1,2  Lti ˜Ltj[gWgV nij(t1, t2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t3, t4)] = 0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='28)  The zero modes can be viewed as field redefinition freedom of effective fields that  does not cause any difference in the original four-point function ˆF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' From now on,  we will set nij = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Combining (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='26)–(2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='27), we also get the following periodicity  �  ˆT φi(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t)φj(¯t′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t′)  �  ≃  �  ˆT φi(¯t + 2πi;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t + 2πi)φj(¯t′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t′)  �  ,  ℑt < ℑt′ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='29)  See Fig 3 for a diagrammatical depiction of (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='26)–(2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='27).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Four-point function ˆFWWV V (t1, t2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t3, t4) can have potential non-smoothness when  the imaginary parts of two or more time arguments coincide, as these are the  locations where ordering of operators change.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' There are two cases:  – 11 –  (a) ℑt1 = ℑt2, which corresponds to order changes of W’s within themselves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' In  terms of φ1,2(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t), this corresponds to ℑ¯t−ℑt = 0, where the couplings of W’s  to φ1,2 are switched.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='3 Similar statements apply to t3, t4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' As stated earlier,  we will restrict to ℑt1 < ℑt2 and ℑt3 < ℑt4 throughout, so such potential  non-smoothness will not be relevant for our discussion of  �  ˆT φi(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t)φj(¯t′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t′)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (b) One of ℑt1, ℑt2 coinciding with one of ℑt3, ℑt4, which is a boundary be-  tween the domains of ti corresponding to TOCs and OTOCs;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' crossing such  a boundary a pair of W and V will exchange order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' In terms of two-point  function  �  ˆT φi(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t)φj(¯t′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t′)  �  , this corresponds to potential non-smoothness  at ℑt = ℑt′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' In the domain D, we should not have any other singularities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='3  Diagonalize the KMS conditions  We will now proceed to formulate an effective field theory (EFT) that can be used to  obtain correlation functions of φi in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='23).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  There is an immediate difficulty in directly formulating an EFT for φ1,2, due to  that they are defined in different domains (recall Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' So they cannot appear in the  same Lagrangian, but they transform to each other under the constraints (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='26)–(2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='27)  from the KMS conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' To address this difficulty, we introduce two new fields,  η±(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) = 1  √  2(φ1(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t − iπ) ± φ2(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t))  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='30)  which are both defined in the domain I2 : ℑ(¯t − t) ∈ (−π, 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Conversely, we have  φ1(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) = 1  √  2(η+(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t + iπ) + η−(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t + iπ)),  φ2(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) = 1  √  2(η+(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) − η−(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t)) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='31)  We will define two-point functions of φ1,2 in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='23) in terms of those of η± using (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='31).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  For example,  �  ˆT φ1(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t)φ2(¯t′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t′)  �  ≡ 1  2  �  s,s′=±  s′ �  ˆT ηs(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t + iπ)ηs′(¯t′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t′)  �  ,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='32)  where on the right hand side the time ordering ˆT is defined in terms of that of ℑt, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  �  ˆT ηs(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t)ηs′(¯t′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t′)  �  ≡  �  ⟨ηs(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t)ηs′(¯t′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t′)⟩ ,  ℑt < ℑt′  ⟨ηs′(¯t′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t′)ηs(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t)⟩ ,  ℑt > ℑt′  ,  s, s′ = ± .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='33)  3For example, as we cross from ℑt1 − ℑt2 < 0 to ℑt1 − ℑt2 > 0, W(t1) switches from mainly  coupled to φ1(¯tW ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t1) to mainly coupled to φ2(¯tW ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  – 12 –  Now ⟨· · ·⟩ is understood as defined in the EFT of η±, and the right hand side of (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='33)  should be understood as Wightman functions in the EFT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The motivations for choosing  ˆT ordering in terms of ℑt are as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Firstly, as discussed in item 4b at the end of  last subsection, correlation functions of φ1,2 have potential non-smoothness at ℑt = ℑt′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Ordering in ℑt in η-correlators provides a simple way to realize that.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Secondly, we  assumed that the dependence of φ1,2 on ¯t is weak, so should be η±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Making the ordering  independent of ¯t is natural.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Now consider the constraints (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='26)–(2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='27).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' It can be checked that they are satisfied  provided that  �  ˆT ηs(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t)ηs′(¯t′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t′)  �  = s  �  ˆT ηs(¯t + iπ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t + iπ)ηs′(¯t′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t′)  �  ,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='34)  which is diagonal in η±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' We see that introducing η± not only resolves the domain issue,  but also diagonalize the constraints from KMS conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Equation (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='34) implies  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  �  ˆT ηs(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t)ηs′(¯t′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t′)  �  = s′s  �  ˆT ηs(¯t + iπ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t + iπ)ηs′(¯t′ + iπ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t′ + iπ)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='35)  From (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='25), we have  �  ˆT ηs(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t)ηs′(¯t′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t′)  �  =  �  ˆT ηs(¯t + c;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t + c)ηs′(¯t′ + c;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t′ + c)  �  ,  ∀c ∈ C .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='36)  It then follows from (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='35) that  �  ˆT η+(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t)η−(¯t′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t′)  �  = −  �  ˆT η+(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t)η−(¯t′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t′)  �  = 0,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='37)  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' time-ordered functions of η± are also diagonal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  We now proceed to formulate an effective theory of η± with the following consid-  erations in mind:  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' With the assumption of weak dependence on ¯t, we assume that the effective action  can be expanded in derivatives of ¯t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' This leads to an immediate simplification:  with only derivative dependence on ¯t, the EFT becomes translationally invariant  in ¯t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Now given (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='36), we also have translation invariance in t, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  �  ˆT ηs(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t)ηs′(¯t′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t′)  �  =  �  ˆT ηs(¯t − ¯t′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t − t′)ηs′(0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' 0)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='38)  The domain for function  GF(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) ≡  �  ˆT ηs(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t)ηs′(0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' 0)  �  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='39)  is then given by the shaded stripe indicated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  At quadratic order in η±, the effective action should be translationally invariant  in both ¯t and t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  – 13 –  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The correlation functions of ηs are defined on the green strip I ∪ (−I), on which  a fundamental domain is the shaded parallelogram Dη.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' We analytically continue Dη to the  yellow rectangular domain D∗, which is bounded by the red dashed lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' We would like to interpret (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='34) as the KMS conditions for the η±-system at  a finite temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Given the definition of ˆT in terms of t, it is natural to  interpret the temperature as being associated with t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' However, the condition  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='34) shifts both ¯t and t simultaneously, which is not of the conventional form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  In next subsection, we will discuss how to convert it into the standard form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' So far the time variables ¯t, t are complex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  To write down an effective action  we need to choose a real section in the complex ¯t, t planes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' From Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' 4 it is  convenient to choose the section to be that of imaginary ¯t and real t, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' we will  let ¯t = −i¯τ and write down an action for η±(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' It can be viewed as a two-  dimensional field theory with ¯τ being a “spatial” coordinate and (real) t being  time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Behavior of correlation functions for η± elsewhere are obtained by analytic  continuations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='4  Reformulating the KMS conditions  In this subsection we reformulate (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='34) as the KMS conditions for η± at a finite tem-  perature (associated with t) with ¯τ = −ℑ¯t as a spatial direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Let us first recall the standard story.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' For a quantum field χ in a two-dimensional  spacetime (t, ¯τ) at a nonzero inverse temperature β, the KMS condition for Wightman  functions are ⟨χ(¯τ1, t1)χ(¯τ2, t2)⟩ = ⟨χ(¯τ2, t2)χ(¯τ1, t1 + iβ)⟩, and the Feyman functions  GF(¯τ, t) ≡  �  ˆT χ(¯τ, t)χ(0, 0)  �  = GF(¯τ, t + iβ), with its fundamental domain being  ℑt ∈ (−β, 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' GF(¯τ, t) may have non-analytic behavior such as branch cuts at ℑt = 0  and ℑt = −β.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  – 14 –  JU(-I)  DNow consider GF(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) defined in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='39).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' From (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='34), the fundamental domain of  GF(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) can be chosen to be the region Dη in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Equation (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='34) is not quite  the KMS condition with β = π (note that this is  1  2 of the temperature we started  with) due to the shift in ¯τ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  We can resolve this issue by extending the region Dη  to the larger region D∗ in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Region Dη is bounded above and below by lines  ¯τ − ℑt = ±π, which are part of the boundary of the analytic domain of the original  four-point function ˆF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The behavior of GF at these boundaries are system-dependent  and depend on UV physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' In other words, in principle for different systems different  boundary conditions should be imposed there.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' In the spirit of effective field theories  we expect that the general structure of the effective action should not depend on the  specific UV physics, although the coefficients in the effective action will.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Since we are  only interested in the general structure of the effective action, we can choose a most  convenient boundary condition: we extend the domain to D∗, and identify the values of  GF(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) at ¯τ = −π and ¯τ = 2π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' In other words, we have periodic boundary conditions  in ¯τ direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Note that later we will only need to use the behavior of GF(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) in  region Dη.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Denote the conjugate momentum for ¯τ as P, then P = 2  3m with m an integer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' We  can decompose ηs into three part  ηs(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) = ηs,0(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) + ηs,+(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) + ηs,−(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t)  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='40)  where ηs,p contains only ¯τ-momenta P = 2  3(3n + p) with n an integer and p = −1, 0, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  ηs,p has the behavior  ηs,p(¯τ + π;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) = e2πip/3ηs,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t),  p = 0, ± .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='41)  Because of the additional phase e2πip/3, we should regard ηs,± as complex scalar fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Since the original ηs is a real scalar, we need to identify them as hermitian conjugate  to each other, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  η†  s,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) = ηs,−p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t)  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='42)  Given the translation symmetry, the following correlation functions vanish  �  ˆT ηs,0(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t)ηs,±(0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' 0)  �  =  �  ˆT ηs,+(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t)ηs,+(0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' 0)  �  =  �  ˆT ηs,−(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t)ηs,−(0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' 0)  �  = 0 (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='43)  and only  �  ˆT ηs,0(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t)ηs,0(0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' 0)  �  and  �  ˆT ηs,∓(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t)ηs,±(0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' 0)  �  could survive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' In terms of  these three modes, the KMS conditions (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='34) become  �  ˆT ηs,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t − iπ)ηs,−p(0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' 0)  �  = se−2πip/3 �  ˆT ηs,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t)ηs,−p(0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' 0)  �  ,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='44)  – 15 –  Up to a phase these conditions are exactly the ordinary KMS conditions for inverse  temperature β = π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Equation (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='44) can also be interpreted as that ηs,p have the  following periodic conditions in the imaginary t direction  ηs,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t − iπ) = se−2πip/3ηs,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='45)  Below we will also use Wightman functions  G>  s,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) = ⟨ηs,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t)ηs,−p(0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' 0)⟩ ,  ℑt ∈ (−π, 0)  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='46)  G<  s,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) = ⟨ηs,−p(0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' 0)ηs,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t)⟩ ,  ℑt ∈ (0, π) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='47)  By translation symmetry, we have the relation G<  s,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) = G>  s,−p(−¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' −t), and the KMS  condition (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='44) can be written in terms of Wightman functions as  G>  s,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t − iπ) = se−2πip/3G<  s,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t),  ℑt ∈ (0, π) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='48)  We can now express  �  ˆT φi(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t)φj(0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' 0)  �  in terms of thermal correlation functions  of ηs,p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' From (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='23), the relevant range for t is ℑt ∈ (−2π, 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' As mentioned earlier,  thermal correlation functions  �  ˆT ηs,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t)ηs,p′(0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' 0)  �  can have discontinuities at ℑt =  0, ±π, · · · , which can potentially lead to discontinuity in  �  ˆT φi(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t)φj(0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' 0)  �  at ℑt = −π,  which would be unphysical.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='4 To make clear the potential discontinuity, it is convenient  to write the two-point function of φi using Wightman functions of ηs,p,  �  ˆT φ1(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t)φ1(0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' 0)  �  =  �  ˆT φ2(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t)φ2(0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' 0)  �  =  �  1  2  �  s,p G>  s,p(i¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t),  ℑt ∈ [−π, 0]  1  2  �  s,p se−2πip/3G>  s,p(i¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t + iπ),  ℑt ∈ [−2π, −π]  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='49)  �  ˆT φ1(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t)φ2(0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' 0)  �  =  �  1  2  �  s,p e2πip/3G>  s,p(i¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t),  ℑt ∈ [−π, 0]  1  2  �  s,p sG>  s,p(i¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t + iπ),  ℑt ∈ [−2π, −π]  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='50)  �  ˆT φ2(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t)φ1(0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' 0)  �  =  �  1  2  �  s,p e−2πip/3G>  s,p(i¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t),  ℑt ∈ [−π, 0]  1  2  �  s,p se2πip/3G>  s,p(i¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t + iπ),  ℑt ∈ [−2π, −π]  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='51)  where we have used (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='44) to shift the t argument of G>  s,p such that it lies in the analytic  domain of G>  s,p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  In (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='49), in order to avoid potential discontinuity at ℑt = −π we need  �  s,p  G>  s,p(¯τ, t) =  �  s,p  se−2πip/3G>  s,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t + iπ),  ℑt = −π,  ¯τ ∈ [0, 2π] .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='52)  4As mentioned in item 4b, the only physical singularity for φi correlation function is at ℑt = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  – 16 –  Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The Keldysh contour of t for ηs,p(¯τ, t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The cross means multiplied with se−2πip/3  to respect KMS condition (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='44).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  It is important to stress that with ℑt = −π, we have ¯τ ∈ [0, 2π] for two-point functions  of φ1 or φ2 as indicated in the above equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Now considering (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='50) and keeping in  mind that for ℑt = −π, we have ¯τ ∈ [−π, π].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' In order to compare with (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='52) we can  shift ¯τ of (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='50) by π using periodicity (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='41), after which we again find equation (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='52).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Similarly in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='51), we have ¯τ ∈ [π, 3π], and after shifting ¯τ by −π we obtain the same  equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Equation (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='52) should be understood as two equations, one for τ ∈ [0, π],  and the other for τ ∈ [π, 2π] which can in turn be shifted to the range τ ∈ [0, π] using  periodicity (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='41).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Applying (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='48) to the left hand side of (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='52) we find  �  p  e−2πip/3G+,p(¯τ, t) =  �  p  e−2πip/3G−,p(¯τ, t),  ℑt = 0, ¯τ ∈ [0, π]  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='53)  �  p  G+,p(¯τ, t) =  �  p  G−,p(¯τ, t),  ℑt = 0, ¯τ ∈ [0, π]  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='54)  where we have defined for ℑt = 0  Gs,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) ≡ ⟨[ηs,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t), ηs,−p(0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' 0)]⟩ = G>  s,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) − G<  s,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) = Gs,−p(−¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' −t)  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='55)  Equations (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='53) and (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='54) can also be written in a more compact form  G+,±(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) − G−,±(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) = −e±πi/3(G+,0(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) − G−,0(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t))  ℑt = 0, ¯τ ∈ [0, π] .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='56)  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='5  The quadratic effective action  In this section, we will construct an effective action for ηs,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) defined in last sub-  section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' We treat Euclidean time ¯τ as spatial coordinate in the range ¯τ ∈ [0, π] and t  as real time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' ηs,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) satisfy the boundary conditions (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='41) in ¯τ direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Real-time  action for excitations in a thermal state can be formulated using the Schwinger-Keldysh  formalism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' We will follow the non-equilibrium EFT approach developed in [8, 19–21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  To write down a real-time action we need to double the degrees of freedom on a  two-way Keldysh contour for t, where the fields η(1)  s,p and η(2)  s,p are on the first and second  – 17 –  contour respectively (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' 5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' For each ηs,p we also have the so-called r-a variables  ηr  s,p, ηa  s,p defined as  ηa  s,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) = η(1)  s,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) − η(2)  s,p(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t),  ηr  s,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) = (η(1)  s,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) + η(2)  s,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t))/2  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='57)  The effective action should satisfy various unitary constraints and the dynamical KMS  condition (to ensure local thermal equilibrium).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' We derive these conditions in detail in  Appendix B, and just briefly present them here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The action S[ηr  s,p, ηa  s,p] should contain terms in the form of  ˆ  Kα1···αk  s1,p1,··· ,sk,pk(∂¯τ, ∂t)ηα1  s1,p1(¯τ, t) · · · ηαk  sk,pk(¯τ, t),  (α1, · · · αk ∈ {a, r})  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='58)  with �k  i=1 si = 1 and �k  i=1 pi = 3Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Each term in above form must contain at least one ηa  s,p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The imaginary part of effective is nonnegative ℑS[ηr  s,p, ηa  s,p] ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' For the terms with odd numbers of ηa  s,p, the action needs to be real, which means  Kα1···αk  s1,p1,··· ,sk,pk(∂¯τ, ∂t) =  �  Kα1···αk  s1,−p1,··· ,sk,−pk(∂¯τ, ∂t)  �∗  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='59)  for α1, · · · , αk contain odd numbers of a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The action needs to obey dynamical KMS condition S[ηr  s,p, ηa  s,p] = S[˜ηr  s,p, ˜ηa  s,p],  where ˜ηr,a  s,p are defined by (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='19) and (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='20).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  At quadratic order, the effective action SEFT can then be written as  SEFT =  �  s,p  ˆ π  0  d¯τ  ˆ ∞  −∞  dt  �  ηa  s,−pKar  s,p(∂¯τ, ∂t)ηr  s,p + 1  2ηa  s,−pKaa  s,p(∂¯τ, ∂t)ηa  s,p  �  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='60)  where from the above conditions we have  Kar  s,p(∂¯τ, ∂t) =  �  Kar  s,−p(∂¯τ, ∂t)  �∗ ,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='61)  ℑ  �  s,p  ηa  s,−pKaa  s,p(∂¯τ, ∂t)ηa  s,p ≥ 0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='62)  In Appendix B, we derive the following dynamical KMS condition for the quadratic  action (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='60)  Kar  s,p(∂¯τ, ∂t) − Kar  s,−p(−∂¯τ, −∂t) = −2is (tan π(p/3 + ∂t/2))s Kaa  s,p(∂¯τ, ∂t)  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='63)  – 18 –  As shown in [22], setting Kaa  s,p = 0 means the local entropy current is conserved and the  system is non-dissipative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' In this case, (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='63) reduces to  Kar  s,p(∂¯τ, ∂t) = Kar  s,−p(−∂¯τ, −∂t) =  �  Kar  s,p(−∂¯τ, −∂t)  �∗ ,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='64)  and the resulting action can be factorized [9, 21, 22], i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' SEFT = Sf[η(1)  s,p]−Sf[η(2)  s,p] with  Sf[ηs,p] = 1  2  �  s,p  ˆ π  0  d¯τ  ˆ ∞  −∞  dt ηs,−pKar  s,p(∂¯τ, ∂t)ηs,p .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='65)  Taking t → −iτ in the above action we obtain a Euclidean action defined for both  Euclidean times ¯τ, τ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' We stress that the factorization and thus the Euclidean action  are not possible when dissipations are included.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' For simplicity, in this paper we will  only consider the non-dissipative case with constraint (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='64) though the generalization  to dissipative case should be straightforward.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  As discussed earlier, we assume that the action can be expanded in derivatives of  ¯τ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' As in [8, 9], we cannot, however, expand the action in derivatives in t, since we are  interested in time scales of order 1/λ so as to be able to probe the exponential growth  eλt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The Lyapunov exponent λ could be comparable to the inverse temperature β, and  thus there is no scale separation in t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Since ηs,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) have different boundary conditions (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='41), they allow different lowest  order of ∂¯τ in the action.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' For ηs,0, which is periodic in ¯τ, the lowest order of ∂¯τ in Kar  s,0  is just constant, namely  Kar  s,0(∂¯τ, ∂t) = Ks,0(i∂t) + O(∂¯τ) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='66)  For ηs,±, which gains a nontrivial phase after shift ¯τ → ¯τ + π, the lowest order of ∂¯τ in  Kar  s,± must be nontrivial, and we will keep to the linear order  Kar  s,±(∂¯τ, ∂t) = ∂¯τKs,±(i∂t) + O(∂2  ¯τ) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='67)  It follows from (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='64) that for all p,  Ks,p(i∂t) = (−)pKs,−p(−i∂t) = (−)p (Ks,p(−i∂t))∗ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='68)  Thus Ks,0(x) is an even function of x with real coefficients (when expanded in power  series), while Ks,±(x) are functions of pure imaginary coefficients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Keeping only leading orders, we can reduce Kar  s,0 piece to one dimension of t and  write the leading order quadratic effective action as  SEFT =  �  s=±  �ˆ ∞  −∞  dtηa  s,0(t)Ks,0(i∂t)ηr  s,0(t) +  �  p=±  ˆ π  0  d¯τ  ˆ ∞  −∞  dtηa  s,−p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t)∂¯τKs,p(i∂t)ηr  s,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='69)  – 19 –  With the leading order effective action (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='69), we have  Ks,0(i∂t)Gra  s,0(t) = −δ(t)  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='70)  ∂¯τKs,±(i∂t)Gra  s,±(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) = −δ(¯τ)δ(t)  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='71)  where Gra  s,p are retarded functions of ηs,p, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Gra  s,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) = iθ(t)Gs,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='72)  Give the periodic boundary condition (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='41), we can write  Gs,0(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) = ∆s,0(t),  Gs,±(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) = ∆s,±(t)  �  e∓2πi/3 + θ(¯τ)(1 − e∓2πi/3)  �  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='73)  where ∆s,p(t) can be written in Fourier space as  θ(t)∆s,0(t) = i  ˆ  C  dω  e−iωt  2πKs,0(ω)  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='74)  θ(t)∆s,±(t) = i  ˆ  C  dω  e−iωt  2πKs,±(ω)(1 − e∓2πi/3)  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='75)  which holds for t > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Here the integral contour C must be above all poles of integrand  on the complex ω plane because Gra  s,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) is proportional to θ(t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Note that θ(¯τ)  in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='73) comes from ∂¯τ in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='71).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Equations (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='73) imply that except for certain jumps at ¯τ = 0, correlation functions  have no dependence on ¯τ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' From item 4b, however, such branch cut should not be present  in the four-point function ˆF, and thus should be cancelled in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='23), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  �  i,j=1,2  Lti ˜Ltj+2  �  gWgV  �  ˆT  �  φi(iϵ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' ti)φj(0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' tj+2) − φi(−iϵ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' ti)φj(0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' tj+2)  ���  = 0  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='76)  for infinitesimal positive ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Also note that the above condition is relevant only for TOC  of types ⟨WV V W⟩ and ⟨V WWV ⟩ for which ℑ¯tW − ¯tV could have either sign without  changing the order of four fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' All other four-point functions have definite sign for  ℑ¯tW − ¯tV .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Now recall the smoothness conditions (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='56), which upon using (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='73)-(2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='75) leads  to  1  K+,±(ω) −  1  K−,±(ω) = ∓  √  3i  �  1  K+,0(ω) −  1  K−,0(ω)  �  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='77)  which shows that the terms in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='69) are not independent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' It can also be checked that  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='77) is consistent with constraints (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='68).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  – 20 –  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='6  Shift symmetry and exponential growth in correlation functions  Similar to the maximal chaos case [8], we will postulate that the action and the ver-  tices (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='20)–(2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='21) possess a shift symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The choice of the shift symmetry is mo-  tivated from that OTOCs should have exponential growth, but not TOCs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  It turns out the requirement can be achieved by the following two conditions  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The action and the vertices (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='20)–(2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='21) are invariant under  ηr  − → ηr  − + α+eλt + α−e−λt  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='78)  where α± are constants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' There is no exponential growth in the symmetric correlation functions of η+, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Grr  + (¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) =  �  p  Grr  +,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) = 1  2  �  p  �  G>  +,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) + G<  +,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t)  �  = 0eλt + · · · .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='79)  Note that the KMS condition (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='48) leads to the fluctuation-dissipation relation  Grr  s,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) = 1  2  1 + se2πip/3e−iπ∂t  1 − se2πip/3e−iπ∂t Gs,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t),  ℑt ∈ (0, π) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='80)  In terms of φ1,2, the shift symmetry (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='78) can be written as  (φ1, φ2) → (φ1, φ2) + (e±λ(t+iπ), −e±λt) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='81)  We also require that the vertices in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='20)–(2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='21) be compatible with the shift symme-  try (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='78), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Lt satisfies  Lt1[gW(t12)e±λ(t1+iπ)] = Lt2[gW(t12)e±λt2]  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='82)  Since η− is a sum of η−,0, η−,±, the invariance under (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='78) means that at least one  of K−,p has a factor of ∂2  t − λ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' For convenience, we will write  K−,p(i∂t) = (∂2  t − λ2)k−,p(i∂t) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='83)  The constraint (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='77) implies that K+,p may also contain a factor ∂2  t − λ2, and we can  similarly write5  Ks,p(i∂t) = (∂2  t − λ2)ks,p(i∂t) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='84)  From (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='68) we have ks,p(x) = (−)pks,−p(−x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='6 The general structure of our discussion  will not depend on the specific forms of k+,p and k−,p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  5Note that having a factor (∂2  t − λ2) in K+,p does not imply there is a shift symmetry in η+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' An  important part of the shift symmetry is that vertices should also be invariant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  6Note that it is enough to impose the invariance under a shift proportional to eλt in non-dissipative  case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The parity property (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='68) will then lead to invariance under a shift proportional to e−λt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  – 21 –  Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The contour C on the ω plane for retarded propagator Gra  s,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The two red  crosses are poles at ω = ±iλ due to shift symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Following from (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='74), we have  θ(t)∆s,0(t) =  ˆ  C  dω  2πi  e−iωt  (ω2 + λ2)ks,0(ω)  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='85)  where the contour C is chosen to be above all poles (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' 6) of the integrand because  the LHS is proportional to θ(t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' We then find7  ∆s,0(t) =  i  2λks,0(iλ)(eλt − e−λt) + · · ·  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='86)  where we used the parity of ks,0, and · · · denote possible contributions from other  singularities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  From now on we will suppress · · · and only write exponential terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Using (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='80) and  G>  s,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) = Grr  s,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) + 1  2Gs,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t)  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='87)  we find from (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='86)  G>  s,0(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) =  i  2λks,0(iλ)(1 − se−iλπ)(eλt + se−iλπe−λt) ≡ hs,0(t) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='88)  Similarly, from (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='75) we have  θ(t)∆s,±(t) =  ˆ  C  dω  2πi  e−iωt  (ω2 + λ2)ks,±(ω)(1 − e∓2πi/3)  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='89)  which leads to  ∆s,±(t) = ±e±iπ/3  2  √  3λ  �  eλt  ks,±(iλ) +  e−λt  ks,∓(iλ)  �  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='90)  7Note that when ks,0(x) has no zero at x = iλ, the coefficient of the exponential pieces below  vanishes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  – 22 –  and  G>  s,±(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) =  �  hs,±(t)  ¯τ ∈ [0, π]  e∓2πi/3hs,±(t)  ¯τ ∈ [−π, 0]  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='91)  where hs,± are given by  hs,±(t) = ±e±iπ/3  2  √  3λ  � (ks,±(iλ))−1eλt  1 − se−iπλe±2πi/3 + (ks,±(iλ))−1e−λt  1 − seiπλe±2πi/3  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='92)  The constraint (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='79) implies that, up to non-exponential pieces,  Grr  + (¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) =  �  p  �  h+,p(t) + e2πip/3h+,−p(−t)  �  = 0,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='93)  which upon using (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='88) and (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='92), further implies  k+,±(iλ) = ∓ik+,0(iλ)  √  3  tan  �π  2 (λ ± 1/3)  �  tan πλ  2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='94)  Note that (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='94) is consistent with (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='68).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Notice that the factor tan  � π  2(λ − 1/3)  �  on  the right hand side of (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='94) for k+,−(iλ) becomes zero for λ = 1/3, which cannot  happen as a zero for k+,−(iλ) would lead to divergences in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='92).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' This means that  k+,0 must have a pole at λ = 1  3, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' k+,0(iλ) ∼ (λ − 1/3)−1, which in turn means that  the prefactor in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='86) vanishes and that the factor ∂2  t − λ2 in K+,0 is in fact not there  (it cancels with a factor hidden in k+,0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' For λ = 2/3, the right hand side of (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='94)  is divergent for k+,+(iλ), which means that the factor ∂2  t − λ2 should also cancel for  K+,+(i∂t) at λ = 2/3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The divergence of the factor tan πλ  2 for λ = 1 will be commented  on later in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='7  Summary of the effective field theory  We have now discussed all elements of the EFT formulation, which we summarize here  in one place:  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The product W(t1)W(t2) is written in terms of an expansion in terms of two  effective fields φ1(¯tW;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' tS) and φ2(¯tW;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' tL) through a vertex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Similar expansion  applies to V (t3)V (t4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' At leading nontrivial order in the 1/N expansion, we have  ˆFWWV V (t1, t2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t3, t4) = gWgV +  �  i,j=1,2  Lti ˜Ltj+2  �  gWgV  �  ˆT φi(¯tW;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' ti)φj(¯tV ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' tj+2)  ��  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='95)  The domain of φi is given by Ii in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  – 23 –  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The KMS conditions of ˆF impose constraints on correlation functions of φi, which  can in turn be obtained in terms of those a new pair of fields  η±(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) = 1  √  2(φ1(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t − iπ) ± φ2(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t))  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='96)  defined in the domain I2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' ˆT in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='95) is defined in terms of ordering of ℑt for η±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The effective action of η± is written for pure imaginary ¯t = −i¯τ and real t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Correlation functions of η± for general complex ¯t and t are obtained from analytic  continuation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' We also assume that the effective action can be expanded in terms  of derivatives of ¯τ, which in turn implies that the action is translation invariant  for both ¯τ and t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Two-point functions of η± are then defined in the domain Dη  of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  The domain Dη is irregular and inconvenient to work with.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' It is extended to D∗  of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' η± is then further decomposed into  ηs(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) = ηs,0(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) + ηs,+(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) + ηs,−(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t),  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='97)  in terms of periodicity conditions in ¯τ-direction  ηs,p(¯τ + π;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) = e2πip/3ηs,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t),  s = ±, p = 0, ± .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='98)  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' With the decomposition (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='97)–(2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='98), the KMS conditions of the original four-  point function ˆF can be formulated in terms of KMS conditions for ηs,p at the  inverse temperature π (half of the original inverse temperature), and can be writ-  ten as periodic conditions in the imaginary t direction  ηs,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t − iπ) = se−2πip/3ηs,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='99)  The leading actions in the ¯τ-derivative expansion for ηs,0 contain no ¯τ derivative  and thus ηs,0 can be thought as ¯τ-independent, while the leading actions for ηs,±  contains one ¯τ-derivative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' From (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='96), (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='97) and (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='99), we can write φ1,2 as  φ1(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) = ϕ(t) + e  2πi  3 ϕ+(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) + e− 2πi  3 ϕ−(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t),  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='100)  φ2(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) = ϕ(t) + ϕ+(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) + ϕ−(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t),  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='101)  ϕ(t) ≡ 1  √  2(η+,0(t) − η−,0(t)),  ϕ±(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) ≡ 1  √  2(η+,±(i¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) − η−,±(i¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t)), (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='102)  – 24 –  (a)  (b)  (c)  Figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' (a) The 4-way contour for F4 (b) The 4-way contour for G4 (c) The 4-way contour  for H4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  where we have used that η±,0 can be viewed as being independent of ¯τ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Note  from (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='99)  ϕ(t − iπ) = ˜ϕ(t) = 1  √  2(η+,0(t) + η−,0(t)),  ϕ(t − 2πi) = ϕ(t) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='103)  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' For OTOCs to have exponential dependence on t, we impose the shift symmetry  ηr  − → ηr  − + α+eλt + α−e−λt  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='104)  on both the action and the vertex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' We also require no-exponential growth in  Grr  + (¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t), which is needed such that TOCs do not have exponential t-dependence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  This condition requires that various terms in the action should obey (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='94).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The effective action is further constrained by (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='68), and two continuity condi-  tions (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='76)–(2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='77).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='8  TOC and OTOC  Now consider the following two four-point functions  F4 = ⟨W(t1)V (t3)W(t2)V (t4)⟩ ,  G4 = ⟨V (t3)W(t1)W(t2)V (t4)⟩  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='105)  where ℜt1, ℜt2 ≫ ℜt3, ℜt4 or ℜt1, ℜt2 ≪ ℜt3, ℜt4, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' F4 is OTOC and G4 is TOC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' We  suppose each ti has a small imaginary part such that the orderings in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='105) follow that  defined in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='4) (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' 7 as an illustration).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' For F4, the small imaginary part for each  ti leads to ℑ¯tW < ℑ¯tV , but for G4, depending on the relative value of the imaginary  part of each ti, we may have either ℑ¯tW < ℑ¯tV or ℑ¯tW > ℑ¯tV .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' For definiteness, we  consider the former case ℑ¯tW < ℑ¯tV .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='From (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='23) and (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='49)-(2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='51), we find that  F4 − G4 = 1  2  �  s,p  Lt1 ˜Lt3  �  gWgV  �  G>  s,p(i(¯tW − ¯tV ), t13) − G<  s,p(i(¯tW − ¯tV ), t13)  ��  – 25 –  = 1  2  �  s,p  Lt1 ˜Lt3 [gWgV ⟨[ηs,p(i¯tW;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t1), ηs,−p(i¯tV ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t3)]⟩]  = Lt1 ˜Lt3 [gWgV ∆(t13)]  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='106)  where we have used (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='54), and  ∆(t) ≡  �  p  ∆+,p(t) =  �  p  ∆−,p(t)  =  3  4λ(1/2 − cos πλ) sin πλ  2 k+,0(iλ)(eiπλ/2eλt + e−iπλ/2e−λt) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='107)  In the second line of the above equation we have used (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='94).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' We thus find that the  difference between OTOC and TOC has exponential growth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Note that there is no  divergence in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='107) at λ = 1  3;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' as mentioned earlier below (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='94), k+,0(iλ) has a pole  at λ = 1  3, which is canceled by 1/2 − cos πλ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  We will now show that TOC G4 does not have exponential growth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' In terms of  Wightman functions (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='49) to (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='51), G4 can be written as  G4 − gWgV =1  2  �  s,p  Lt1 ˜Lt3  �  gWgV G>  s,p(+;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t31)  �  + e2πip/3Lt2 ˜Lt3  �  gWgV G>  s,p(+;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t32)  �  + e2πip/3Lt1 ˜Lt4  �  gWgV G>  s,p(−;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t14)  �  + Lt2 ˜Lt4  �  gWgV G>  s,p(−;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t24)  �  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='108)  where we assume ℑ¯tW < ℑ¯tV and ± sign in the first time argument means ℑ¯t > 0 or  ℑ¯t < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Using (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='88), (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='91), and (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='82) (and the counterpart for ˜Lt), we can simplify  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='108) as  G4 − gWgV = Lt2 ˜Lt4  �  gWgV  �  C1eλt24 + C2e−λt24��  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='109)  where  C1 = 1  2  �  s,p  (1 + e2πip/3e−iπλ)As,p + (e−2πip/3 + eiπλ)Bs,p  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='110)  C2 = 1  2  �  s,p  (e−2πip/3 + e−iπλ)As,p + (1 + e2πip/3eiπλ)Bs,p  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='111)  and As,p, Bs,p are defined from (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='88) and (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='92) as  hs,p ≡ As,peλt + Bs,pe−λt .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='112)  It can be checked using (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='94) that, C1 = C2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  We can similarly examine G4 for ℑ¯tW > ℑ¯tV and another type of TOC  H4 = ⟨W(t1)W(t2)V (t3)V (t4)⟩  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='113)  – 26 –  with ℑ¯tW < ℑ¯tV .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' We again find their exponential growth pieces vanish due to (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='94).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' In  particular, the condition (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='76) is automatically satisfied up to non-exponential pieces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Given that TOCs do not have exponential terms, equation (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='107) implies that  the exponential terms in OTOCs depend only on k+,0(iλ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Note that k+,±(iλ) are  determined from k+,0(iλ) by (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='94), and k−,p are also constrained from k+,p from (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='77).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  In (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='85) and (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='89), we assumed for simplicity that the integrand only has simple  poles at ±iλ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' This assumption can be relaxed to have higher order poles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' In fact, it  can be shown that at most double poles are allowed due to the condition (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='76).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' These  double poles lead to linear-exponential terms te±λt in the correlation functions of η±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Interestingly, the contributions from the double poles to any four-point function cancel  out.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' So what we discussed in fact gives the most general form for four-point functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  See Appendix C for details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='9  General structure of OTOCs for non-maximal chaos  We have seen that the shift symmetry (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='81) and requirement (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='79) guarantee expo-  nential growth of OTOC and the absence of exponential growth of TOC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' We will now  examine the general structure of OTOCs as predicted by the theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Using (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='13), we can expand (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='82) explicitly as  �  mn  cmn  �  −e±λ(t+iπ) + (−1)m�  ∂m  t gW(t)(±λ)n = 0  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='114)  Similar to [9], we define  GW  even(±λ, t) =  �  m even  cmn∂m  t gW(t)  �  n  (±λ)n  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='115)  GW  odd(±λ, t) =  �  m odd  cmn∂m  t gW(t)  �  n  (±λ)n  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='116)  and (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='114) becomes  GW  even(±λ, t)  GW  odd(±λ, t) = ∓ coth λ(t + iπ)  2  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='117)  KMS transformation of gW(t) is t → −t − 2πi that leads to  GW  even(∓λ, t) → GW  even(∓λ, −t − 2πi) = Geven(∓λ, t)  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='118)  GW  odd(∓λ, t) → GW  odd(∓λ, −t − 2πi) = −Godd(∓λ, t)  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='119)  where we used invariance of gW under KMS transformation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' This is compatible with  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='117) without any restriction on λ, unlike the EFT of [8], where the KMS condition  of gW restricts λ = λmax = 1 [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  – 27 –  Using the definition in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='115) and (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='116), we can write the OTOC F4 in a more  symmetric way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Since TOC G4 does not have exponential piece, OTOC F4 has the  same exponential piece as (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='106).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Using the shift symmetry of vertex (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='82), we can  write each exponential in a symmmetric way  Lt1[gWe±λt1] = 1  2  �  Lt1[gWe±λt1] + Lt2[gWe±λ(t2−iπ)]  �  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='120)  ˜Lt3[gV e±λt3] = 1  2  �  ˜Lt3[gWe±λt3] + ˜Lt4[gWe±λ(t4−iπ)]  �  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='121)  Using (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='115) and (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='116), we can write the connected piece  F4 =αeλ(t1+t2−t3−t4+iπ)/2  �  GW  even(λ, t12) cosh λ(t12 + iπ)  2  + GW  odd(λ, t12) sinh λ(t12 + iπ)  2  �  ×  �  GV  even(−λ, t34) cosh λ(t34 + iπ)  2  − GV  odd(−λ, t34) sinh λ(t34 + iπ)  2  �  + (λ ↔ −λ)  =αeλ(t1+t2−t3−t4+iπ)/2GW  even(λ, t12)GV  even(−λ, t34)  cosh λ(t12+iπ)  2  cosh λ(t34+iπ)  2  + (λ ↔ −λ)  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='122)  where we have used α to denote the prefactor of (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='107), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='107) becomes  ∆(t) ≡ α(eiπλ/2eλt + e−iπλ/2e−λt),  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='123)  and used (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='117) in the last line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Equation (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='122) has the same structure as that  assumed in [14, 15], including the phase eiπλ/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' In [14, 15], in the place of GW  even(λ, t)  and GV  even(−λ, t) are certain advanced and retarded vertices, which are invariant under  KMS transformation t → −t−2πi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' For a specific microscopic system, these two vertices  may obey certain differential equations [14, 15], which in our language translate into  conditions on the effective vertices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' In (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='122), there is a second term, obtained from  λ → −λ, which exponentially decays for t1, t2 ≫ t3, t4, and was not present in [14, 15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Here it is a consequence of shift symmetry for both signs in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='78), which are needed in  order for TOCs to not have exponential growth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' In the non-dissipative case, this term  should also exist even if we only assume shift symmetry for just plus sign in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='78) as  explained in footnote 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Now consider the double commutator defined as  Cθ  4(t1, t2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t3, t4) = ⟨[W(t1 − iθ), V (t3 − iθ)][W(t2), V (t4)]⟩ ,  θ ∈ [0, 2π]  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='124)  which can be rewritten in terms of four-point functions leads to  Cθ  4 = F θ  4 − Gθ  4 + ˜F θ  4 − ˜Gθ  4  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='125)  – 28 –  where F θ  4 and Gθ  4 are the four-point functions in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='105) with t1 → t1 − iθ and t3 →  t3 − iθ, and ˜F θ  4 and ˜Gθ  4 are respectively F θ  4 and Gθ  4 with exchange W ↔ V , t1 ↔ t3 and  t3 ↔ t4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' It follows from (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='122) that  Cθ  4 = 2α cos λπ  2 eλ(t1+t2−t3−t4)/2GW  even(λ, t12 − iθ)GV  even(−λ, t34 − iθ)  cosh λ(t12+i(π−θ))  2  cosh λ(t34+i(π−θ))  2  + (λ ↔ −λ) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='126)  The factor cos λπ  2 → 0 as λ → 1, consistent with the result of [9] and those of SYK and  holographic systems in the maximal chaos limit [4, 14, 15, 23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  3  Comparisons with OTOCs in various theories  In this section we compare the general structure of OTOCs obtained in last section  with various known examples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1  The large q SYK model  We first look at the large q SYK model [24–27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' OTOC F4 of fundamental fermions was  obtained in [28] and has the form (after analytic continuation to Lorentzian signature)  F SYK  4  = − 2  N  gψ(t12)gψ(t34) cosh λ(t1+t2−t3−t4+iπ)  2  cos πλ  2 cosh λ(t12+iπ)  2  cosh λ(t34+iπ)  2  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1)  where Gψ(t) is the two-point function fundamental Majorana fermions in the large q  SYK model (see more details in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1) given by  gψ(t) ≡ 1  2  �  cos λπ  2  cosh λ(t+iπ)  2  �2∆  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='2)  where ∆ = 1/q is the conformal weight of the fundamental fermion ψ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The OTOC (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1)  has exactly the form of (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='122), with the cosh λ(t1 +t2 −t3 −t4 +iπ)/2 term containing  exponentially growing and decaying terms that are both present in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='122), including  the phases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' We can further identify  GW  even(λ, t) = GV  even(λ, t) = C0(λ)gψ(t),  α = −  1  C0(λ)C0(−λ)N cos(πλ/2)  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='3)  where C0(λ) is a constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' From (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='115) we find that C0(λ) = �  n c0,nλn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' From (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='117)  we find  Gψ  odd(±λ, t) = ∂tgψ(t)C1(λ),  C1(λ) =  �  n  c1,nλn,  C0(λ) = λ∆C1(λ) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='4)  As the simplest possibility we take c1,n = δn,0 and c0,n = ∆δn,1 which gives  Lt[W]φ = ∂tWφ + ∆W∂tφ,  α =  1  λ2N∆2 cos(πλ/2)  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='5)  – 29 –  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='2  Stringy scattering in a AdS black hole  The next example is the scattering in the AdS black hole background with stringy  correction [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Assume the bulk spacetime dimension is d + 1 and the d-dimensional  boundary coordinate is xµ = (t, ⃗x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' When t1, t2 ≫ t3, t4 or t1, t2 ≪ t3, t4, the boundary  out-of-time-ordered four-point function F4 is dominated by the W + V → W + V  scattering near the horizon of the AdS black hole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' At GN ∼ 1/N order, the OTOC F4  is given by8  F string  4  =  ia4  0  (2π)4  ˆ  δ(s, |⃗z−⃗z′|) [puψ∗  1(pu,⃗z;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' xµ  1)ψ2(pu,⃗z;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' xµ  2)] [pvψ∗  3(pv,⃗z′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' xµ  3)ψ4(pv,⃗z′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' xµ  4)]  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='6)  where a0 is a number depending on the background, s = a0pupv is the total energy  of the scattering in the unboosted frame, ψ1,2(pu,⃗z;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' xµ  1,2) are wavefunctions of W(xµ  1,2)  expanded in the null momentum basis pu, ψ3,4(pv,⃗z;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' xµ  3,4) are wavefunctions of V (xµ  3,4)  expanded in the orthogonal null momentum basis pv, ⃗z and ⃗z′ are d−1 dimensional bulk  transverse coordinates, and the integral runs over pu, pv,⃗z,⃗z′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' With stringy correction,  the scattering amplitude δ(s, |⃗z|) for t1 + t2 ≪ t3 + t4 is given by  δ(s, |⃗z|) ∼ GNs  ˆ  dd−1k  (2π)d−1  ei⃗k·⃗z  ⃗k2 + µ2(e−iπ/2α′s/4)−α′(⃗k2+µ2)/2r2  0  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='7)  where r0 is the horizon radius, α′ = ℓ2  s (with ℓs the string length) and µ2 = d(d−1)r2  0  2ℓ2  AdS .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  By translation symmetry of the AdS-Schwarzschild black hole in transverse direc-  tions, ψi(p, ⃗z;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' xµ) are functions of ⃗z − ⃗x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' By time translation symmetry, one can show  that the wave function ψi(p, ⃗z;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' xµ) in the unboosted frame has the following property  ψ1,2(pu, ⃗z;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' xµ) = e−2πa/βψ1,2(pue−2πa/β,⃗z;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' (t + a, ⃗x))  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='8)  ψ3,4(pv, ⃗z;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' xµ) = e2πa/βψ3,4(pve2πa/β,⃗z;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' (t + a, ⃗x))  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='9)  which implies that ψ1,2 = e2πt/βf1,2(pue2πt/β) and ψ3,4 = e−2πt/βf3,4(pve−2πt/β) for some  functions fi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Here β is the inverse temperature of the black hole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Switching to the  boosted frame by redefining pu → pue−π(t1+t2)/β leads to  dpupuψ∗  1(pu, ⃗z;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' xµ  1)ψ2(pu, ⃗z;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' xµ  2) → dpupuf ∗  1(pueπ(t1−t2)/β)f2(pueπ(t2−t1)/β)  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='10)  which is a function of t12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Similarly we can redefine pv → pveπ(t3+t4)/β and find the  wavefunctions for V become a function of t34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Taking this into (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='6), we can derive  F string  4  = i  ˆ  δ(s, |⃗z − ⃗z′|)fW(pu,⃗z − ⃗x1,⃗z − ⃗x2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t12)fV (pv,⃗z′ − ⃗x3,⃗z′ − ⃗x4;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t34)  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='11)  8The notation here differs from [4] by switching 2 ↔ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  – 30 –  with s = a0pupve−π(t1+t2−t3−t4)/β and two functions  fW = puf ∗  1(pueπ(t1−t2)/β)f2(pueπ(t2−t1)/β)  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='12)  fV = pvf ∗  3(pveπ(t4−t3)/β)f4(pveπ(t3−t4)/β)  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='13)  In the regime that the scattering amplitude δ(s, |⃗z|) is of order one and slowly  varies with respect to pu and pv, we can assume the integral over pu and pv in (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='11)  can be approximated by their characteristic values pu  c and pv  c, which only depend on  the wave functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Moreover, the spatial dependence of wave function ψi should be  peaked around ⃗z ∼ ⃗x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' To compare with our 0+1 dimensional EFT, we should integrate  over all ⃗x, which basically sets ⃗x ∼ ⃗z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Since wave functions are translational invariant  along tranverse directions, we can integrate over ⃗z directly in (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='7), which fixes ⃗k = 0  and leads to  δ(s, 0) ∼ −iGNcde−λ(t1+t2−t3−t4+iβ/2)/2  (t3 + t4 ≫ t1 + t2)  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='14)  where cd is a real constant and the Lyapunov exponent λ is  λ = 2π  β  �  1 − d(d − 1)α′  ℓ2  AdS  �  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='15)  It follows that we can write (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='6) as  F string  4  ∼ GNcde−λ(t1+t2−t3−t4+iβ/2)/2f c  W(t12)f c  V (t34)  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='16)  where f c  W,V means fW,V taking value at pu,v = pu,v  c  and we have suppressed all transverse  coordinates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Comparing (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='16) with (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='122), we see that they both have non-maximal  exponential growth and the phase −iλβ/4 in (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='16) exactly matches with −iλπ/2 (of  the −λ term) in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='122) by β = 2π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' In the case of t1 + t2 ≫ t3 + t4, we need to flip the  phase e−iπ/2 to eiπ/2 in (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='7) and will find consistency with (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='122) as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Matching (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='16) with (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='122) also leads to  f c  W(t) = GW  even(λ, t)  cosh λ(t+iπ)  2  ,  f c  V (t) = GV  even(−λ, t)  cosh λ(t+iπ)  2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='17)  For example, in AdS3 [4], we have (β = 2π)  fW(pu, 0, 0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t12) = 4∆W π2c2  W  Γ(∆W)2 (pu)2∆W −1e−4ipu sinh(t12/2)  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='18)  where we have set all transverse coordinates as zero due to the integral over these  directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' For large ∆W, the characteristic pu is at pu  c =  2∆W −1  4i sinh(t12/2), which leads to  f c  W(t) ∼ gW(t12)  cosh t+iπ  2  ,  gW(t) ≡  1  (cosh t+iπ  2 )2∆W  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='19)  – 31 –  where gW(t) is the boundary two-point function in a thermal state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Note that the  wave function (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='18) is computed in the pure gravity background and does not include  any stringy corrections that should introduce non-maximal λ to the wave function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Thus (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='19) should be compared with the right hand side of (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='17) at leading order  in α′ expansion, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' we can identify GW  even(1, t) = gW(t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' It is clearly of interests to  understand α′ corrections of (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='18).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' In general dimension, the explicit forms of wave  functions are not known, but (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='17) gives a constraint on their general structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='3  Conformal Regge theory  The conformal Regge theory was developed in [10, 11] and analyzed for Lyapunov expo-  nent and butterfly effect in [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Consider a four-point function ⟨W(x1)V (x3)V (x4)W(x2)⟩  in the CFT in d-dimensional Minkowski spacetime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Assume their locations are assigned  in the (t, y) plane with  xi = (ti, yi, 0, · · · , 0)  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='20)  On this plane, we can define Rindler coordinate [18]  t = U sinh T,  y = U cosh T  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='21)  where U > 0 is for right Rindler wedge and U < 0 is for left Rindler wedge (see  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' 8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' These two wedges are related by analytic continuation T → T + iπ and the  vacuum in Minkowski spacetime is equivalent to the thermal state in one of the Rindler  wedge with inverse temperature 2π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' We can consider each pair of W and V located  in two different wedges, by which we can construct an OTOC in one Rindler wedge  with inverse temperature 2π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' For example, we can take T1 = −T2 = T, T3 = T4 = 0,  U1 = −U2 = U > 0 and U3 = −U4 = 1 (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' 8), which leads to  ⟨W(T, U)V (0, 1)V (0, −1)W(−T, −U)⟩M = ⟨WR(T, U)VR(0, 1)WR(T + iπ, U)VR(iπ, 1)⟩R  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='22)  where the LHS is the correlation function in Minkowski vacuum and the RHS is a  thermal OTOC in right Rindler wedge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The conformal Regge theory studies this four-  point function under Regge limit with T → ∞ but fixed U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' It has been shown [18]  that it has a non-maximal exponential growth eλT with λ < 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' This non-maximal  Lyapunov exponent comes from summing over infinitely many higher spin channels in  the four-point function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  To compare with our 0+1 dimensional result, we should perform dimensional re-  duction by restricting to zero momentum mode along all spatial directions, which is a  bit intricate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Here we will simply take Ui = U for all i and compare the T-dependence  with (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='122).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  – 32 –  Figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The locations of four operators in Regge limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  By conformal symmetry, the four-point function ⟨W(x1)V (x3)V (x4)W(x2)⟩ can be  written as  ⟨W(x1)V (x3)V (x4)W(x2)⟩ =  1  (x2  12)∆W (x2  34)∆V A(u, v)  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='23)  where the conformal invariant cross ratios are  u = x2  12x2  34  x2  13x2  24  = sinh2 T12  2 sinh2 T34  2  sinh2 T13  2 sinh2 T24  2  ,  v = x2  14x2  23  x2  13x2  24  = sinh2 T14  2 sinh2 T23  2  sinh2 T13  2 sinh2 T24  2  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='24)  The Regge limit is for T1, T2 ≫ T3, T4 limit, and we have  u → 16e−T sinh2 T12  2 sinh2 T34  2 ,  v → 1 − 8e−T/2 sinh T12  2 sinh T34  2  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='25)  where we define T = T1 + T2 − T3 − T4 ≫ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' From [10, 11], A(u, v) under this limit is  given by9  A ≈ 2π  ˆ  dν ˜α(ν)  �e−iπ/2  2  log v  �1−j(ν)  Ωiν(0)  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='26)  where Ωiv(ρ) is a harmonic function on (d − 1)-dimensional hyperbolic space (here by  assuming Ui = U we have ρ = 0), j(ν) is the leading Regge trajectory, and ˜α(ν) is a  slowly varying function of ν.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' In large T limit, the ν-integral can be evaluated using  saddle point approximation with the saddle point given by ν = 0 [18], which gives  ⟨W(x1)V (x3)V (x4)W(x2)⟩ ≈ CR  gW(T12)gV (T34)  �  cosh T12+iπ  2  �λ �  cosh T34+iπ  2  �λeλ(T+iπ)/2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='27)  9To get the correct phase e−iπ/2, one needs to be careful about how u and v circle around origin  after we set infinitesimal imaginary part Ti → Ti + iϵi with ϵ1 < ϵ3 < ϵ2 < ϵ4 for OTOC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Unlike [10],  both u and v circle around origin clockwise for 2π when T ≫ 0 in our case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  – 33 –  M  MHere CR is a constant, λ = j(0) − 1, and gW,V is the conformal correlator in Rindler  wedge with no spatial separation  gW,V (T) =  1  �  cosh T+iπ  2  �2∆W,V  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='28)  Now comparing (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='27) with (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='122), we see the downstairs of (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='27) is proportional  to (cosh T12+iπ  2  )λ while in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='122) we have cosh λ(T12+iπ)  2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' It is not clear whether this  difference is due to we are comparing a d-dimensional theory with a (0+1)-dimensional  system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Assuming not, we can match (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='27) with (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='122) with the identification  GW,V  even(±λ, T) = KW,V (±λ)cosh λ(T+iπ)  2  �  cosh T+iπ  2  �2∆W,V +λ  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='29)  α =  CR  KW(λ)KV (−λ) =  CR  KW(−λ)KV (λ)  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='30)  up to arbitrary KW,V (λ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Since this equation is essentially the same for W and V except  conformal dimensions, we will suppress W, V labels in the following.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Using (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='117), we  have  Godd(±λ, T) = ∓K(±λ)sinh λ(T+iπ)  2  �  cosh T+iπ  2  �2∆+λ  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='31)  which leads to  G(±λ, T) ≡  �  mn  cmn∂m  T G(T)(±λ)n  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='32)  =Geven(±λ, T) + Godd(±λ, T) = K(±λ)e∓ λ(T +iπ)  2  �  cosh T+iπ  2  �2∆+λ  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='33)  Let us define the Fourier transformation of G(T) as  I(∆;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' ω) =  ˆ ∞  −∞  dTeiωTG(T − iϵ)  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='34)  where ϵ is an infinitesimal positive number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' It has been shown in [29] that  I(∆;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' ω) = 22∆−1π2e−iπ∆+πωΓ(∆ + iω)Γ(∆ − iω)/Γ(2∆)  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='35)  From (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='33), it is clear that the Fourier transformation of G(±λ, T) is K(±λ)e∓iπλ/2I(∆+  λ/2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' ω ± iλ/2), which leads to  G(±λ, T) = K(±λ)e∓iπλ/2  2π  ˆ  dωe−iωT I(∆ + λ/2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' ω ± iλ/2)  I(∆;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' ω)  I(∆;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' ω)  – 34 –  = 2λK(±λ)e−iπλ/2Γ(2∆)  2πΓ(2∆ + λ)  ˆ  dωe−iωT Γ(∆ + λ ∓ iω)  Γ(∆ ∓ iω)  I(∆;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' ω)  = 2λK(±λ)e−iπλ/2Γ(2∆)  Γ(2∆ + λ)  Γ(∆ + λ ± ∂T)  Γ(∆ ± ∂T)  G(T)  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='36)  From this equation and the definition (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='32), there is no unique solution for the coeffi-  cient cmn of the differential operator LT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' A convenient choice is  K(±λ) = ±iΓ(2∆ + λ)  2λΓ(2∆)  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='37)  LT =  �  mn  cmn∂m  T (∂φ  T)n = ie−iπλ/2 Γ  �  λ + λ−1∂φ  T(∆λ−1∂φ  T + ∂T)  �  λ−1∂φ  TΓ  �  λ−1∂φ  T(∆λ−1∂φ  T + ∂T)  �  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='38)  where ∂T acts on bare operator and ∂φ  T acts on the effective mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Note that this LT  can be expanded in power series in both ∂T and ∂φ  T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Moreover, we can expand LT near  maximal chaos limit λ = 1 and find  LT = (∂T +∆∂φ  T)+(1−λ)  �  (γ + iπ  2 )(∂T + ∆∂φ  T) + (∆ − π2  6 ∂2  T)∂φ  T  �  +O((1−λ)2, (∂φ  T)2)  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='39)  where γ is the Euler’s constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The first term is the same as (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='5) and the subleading  terms can be regarded as perturbative corrections of higher spins to the vertex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  4  Relation to the EFT of maximal chaos  The effective field theory for maximal chaos was constructed in [8], which contains just  one effective mode ϕ on a Keldysh contour in the thermal state with inverse temperature  β = 2π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' This effective mode ϕ has correlation function with exponential growth that  explains the behavior of OTOC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' In this section, we will show that our effective field  theory of non-maximal chaos at maximal chaos λ = 1 can be equivalently connected to  the theory in [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' In particular, our two-component effective mode φ1,2 reduces to one  mode ϕ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Taking the maximal chaos limit λ → 1 in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='94), we see that both k+,±(iλ) diverge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  This implies that the two operators K+,±(i∂t) do not contain the factor ∂2  t − λ2 at  maximal chaos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Physically, the two component fields η+,±(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) decouple from the  dynamics of quantum chaos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Now let us examine the behavior of k−,p(iλ) in this limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Consider ω = iλ in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='77);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' there are two equations but three parameters k−,±(iλ) and  k−,0(iλ), whose general solution is  1  k−,±(iλ) = ±  √  3i  ��  1 +  1  tan  � π  2(λ ± 1/3)  �  tan πλ  2  �  1  k+,0(iλ) −  1  k−,0(iλ)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1)  – 35 –  In the λ → 1 limit, with k+,0(iλ) finite,10 we have  1  k−,±(i) = ±  √  3i  �  1  k+,0(i) −  1  k−,0(i)  �  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='2)  In the EFT of maximal chaos [8], the effective mode ϕ is local and only depends on  one time variable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' This implies that our two effective modes φ1,2 at λ = 1 should not  have any nontrivial dependence on ¯t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' In other words, consistency requires that η−,±  must also decouple at maximal chaos, which implies  k+,0(i) = k−,0(i)  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='3)  From (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='100)–(2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='102) we then find that in the λ → 1 limit, ϕ± decouple (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' they are  not relevant for the exponential behavior), and  φ1(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) = φ2(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) = ϕ(t)  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='4)  That is, in this limit, ¯t-dependences drop out and φ1,2 become the same field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Further-  more, from (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='103), ϕ has periodicity 2π in imaginary t direction, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' it satisfies the  standard KMS condition with inverse temperature 2π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' We have thus fully recovered  the setup of the EFT for maximal chaos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  The EFT action (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' the part relevant for exponential behavior) now becomes  SEFT =  �  s=±  ˆ ∞  −∞  dt ηa  s,0(t)Ks,0(i∂t)ηr  s,0(t)  = 1  2  �  s=±  ˆ ∞  −∞  dt(ϕa + s ˜ϕa)Ks,0(i∂t)(ϕr + s ˜ϕr)  =  ˆ ∞  −∞  dtϕaK(i∂t)ϕr + ˜ϕaK(i∂t) ˜ϕr + ϕa ˜K(i∂t) ˜ϕr + ˜ϕa ˜K(i∂t)ϕr  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='5)  where ˜ϕ was introduced in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='103) and  K(i∂t) = 1  2(K+,0(i∂t) + K−,0(i∂t)),  ˜K(i∂t) = 1  2(K+,0(i∂t) − K−,0(i∂t)) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='6)  Now recall from (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='23) that only ϕ is relevant for the four-point function (as W and  V couple to φ1,2 which become ϕ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Furthermore, from (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='3), ϕ and ˜ϕ decouple at  ω = i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Thus for the purpose of understanding the exponential behavior of the four-  point function, we can just keep the first term in the effective action (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='5), reducing  back to [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  10See Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='4 for a different case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  – 36 –  As discussed in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1 and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='2, the differential operator Lt in the vertex that  couples the bare operators and effective fields has the same form in both maximal and  non-maximal cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Moreover, in the λ → 1 limit, the shift symmetry (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='81) of φ1,2,  becomes  (φ1, φ2) → (φ1, φ2) + (e±t, e±t)  →  ϕ(t) → ϕ(t) + e±t .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='7)  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='82) implies that the shift symmetry obeyed by vertex Lt is  Lt1[gW(t12)e±t1] = Lt2[gW(t12)e±t2]  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='8)  which also matches with that in the EFT of maximal chaos [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  To close this section, we note that the Wightman function G>  −,0(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) given in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='88)  diverges in the limit λ → 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' This divergence reflects that in the limit G>  −,0 develops a  teλt term which is not present for λ < 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' More explicitly, from (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='86) and (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='80), we  find Grr  −,0(t) should satisfy  (1 + e−iπ∂t)Grr  −,0(t) = 1  2(1 − e−iπ∂t)  �  i  2λ˜k0(iλ)  (et − e−t)  �  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='9)  whose general solution is  Grr  −,0(t) =  t  2π˜k0(i)  (et − e−t) + c0(et + e−t)  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='10)  where c0 is an arbitrary constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' It then follows from (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='87)  G>  −,0(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) =  t  2π˜k0(i)  (et − e−t) +  �  c0 +  i  4˜k0(i)  �  et +  �  c0 −  i  4˜k0(i)  �  e−t .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='11)  The presence of linear-exponential term in Wightman function at maximal chaos was  already observed in [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  5  Identifying the effective fields in the large q SYK model  In this section we examine the large q SYK model in some detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' In this model, four-  point functions of fundamental fermions can be computed analytically in the Euclidean  signature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' We show that in this theory it is possible to identify two Euclidean effective  fields φE  1,2 in terms of the microscopic description, which can be identified as φ1,2(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t)  of Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' 2 evaluated in the Euclidean section with pure imaginary ¯t and t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' It is possible  to calculate Euclidean two-point functions of φE  1,2 using the microscopic description.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  We show that the Lorentzian analytic continuation of these two-point functions can  be fully captured by the EFT of Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' This provides a stronger check on the EFT  formulation than just matching the structure of OTOCs done in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  – 37 –  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1  OTOC of the large q SYK model  We start with a brief review of the essential aspects of the large q SYK model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The  SYK model [24, 25] is a 0+1 dimensional quantum mechanical system which consists  of N Majorana fermions with an all-to-all and q-local Hamiltonian  H = iq/2  �  1≤j1<···<jq≤N  Jj1···jqψj1 · · · ψjq  �  Jj1···jq  �2 = 2q−1J 2(q − 1)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  qN q−1  = J2(q − 1)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  N q−1  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1)  where Jj1···jq is a random coupling with Gaussian distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' At an inverse tempera-  ture β, it is possible to derive a bilocal effective action in Euclidean signature [26]  SE = N  2 log det(∂τ − Σ) + N  2  ¨ β  0  dτ1dτ2  �  Σ(τ1, τ2)G(τ1, τ2) − J2  q G(τ1, τ2)q  �  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='2)  where G(τ1, τ2) =  1  N  �  j ψj(τ1)ψj(τ2) is a bi-local field, and Σ is an auxiliary bi-local  field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' In the double scaling limit with N, q → ∞ and N 2/q fixed, it is convenient to  introduce G(τ1, τ2) = 1  2sgn(τ1 − τ2)eσ(τ1,τ2)/q and Σ can be integrated out, resulting a  Liouville action for σ(τ1, τ2) [27],  SE ≈ N  4q2  ˆ  dτ1dτ2  �1  4∂1σ(τ1, τ2)∂2σ(τ1, τ2) − J 2eσ(τ1,τ2)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='3)  The large q SYK model is obtained by further taking N/q2 → ∞, in which limit the  Euclidean path integral over σ is dominated by saddle-point solution(s) to the equation  of motion of (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='3), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' by solutions to the Liouville equation  ∂1∂2σ(τ1, τ2) = −2J 2eσ(τ1,τ2) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='4)  By definition, σ(τ, τ ′) has the following properties  σ(τ, τ ′) = σ(τ ′, τ),  σ(τ, τ) = 0,  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='5)  where the second equation can be interpreted as a UV boundary condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' It is also  periodic in β for both arguments  σ(τ, τ ′) = σ(τ ′ + β, τ) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='6)  The solution σ0 to (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='4) with time translation symmetry can be interpreted as  describing the equilibrium state, and can be written as  eσ0(τ12) =  cos2 λβ/4  cos2 λ  2(|τ12| − β/2),  τ12 = τ1 − τ2,  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='7)  – 38 –  and λ is obtained from the solution to equation  λ = 2J cos λβ/4 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='8)  The equilibrium two-point function is given by  G0(τ) = ⟨G(τ, 0)⟩β = 1  2eσ0(τ)/q,  τ ∈ [0, β] .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='9)  From now on, for notational simplicity we use the unit such that β = 2π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Fluctuations around the thermal equilibrium can be described by expanding σ =  σ0 + ϵ around σ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' To order ϵ2, (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='3) becomes  SE ≈ S0 + N  8q2  ˆ  dτ1dτ2  �1  2∂1ϵ(τ1, τ2)∂2ϵ(τ1, τ2) − J 2eσ0(τ12)ϵ2(τ1, τ2)  �  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='10)  where S0 is a constant scaling as N/q2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' By definition we have ⟨ϵ(τ1, τ2)⟩ = 0 to this  order, where ⟨· · ·⟩ denotes correlation functions of ϵ obtained from path integrals with  Euclidean action (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Now consider the Euclidean four-point function  Fψ(τ1, τ2, τ3, τ4) ≡ ⟨G(τ1, τ2)G(τ3, τ4)⟩  ≈ G0(τ12)G0(τ34)  �  1 + 1  q2 ⟨ϵ(τ1, τ2)ϵ(τ3, τ4)⟩  �  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='11)  where in the second line we have indicated that its leading connected part is given by  two-point function of ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  It will be convenient to write (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='10) in a different form by introducing [28]  x = τ − τ ′,  ¯τ = τ + τ ′  2  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='12)  and redefine the fields σ(¯τ, x) = σ(τ, τ ′) and ϵ(¯τ, x) = ϵ(τ, τ ′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' From (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='5)–(5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='6), ϵ(¯τ, x)  satisfy the following conditions  ϵ(¯τ, x) = ϵ(¯τ, −x) = ϵ(¯τ + π, 2π − x),  ϵ(¯τ, 0) = ϵ(¯τ, 2π) = 0  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='13)  from which we can define the fundamental domain of ϵ as Dϵ = {(¯τ, x)|¯τ ∈ [0, π], x ∈  [0, 2π]} (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' 9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' On the fundamental domain Dϵ, we can rewrite the Euclidean  effective action (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='10) as  SE = N  8q2  ˆ π  0  d¯τ  ˆ 2π  0  dx  �  1  4(∂¯τϵ)2 − (∂xϵ)2 −  λ2  2 cos2 λ  2(x − π)ϵ2  �  ≡ N  8q2  ˆ  d¯τdx ϵLϵ  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='14)  – 39 –  Figure 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The red region is the fundamental domain Dϵ for ϵ(¯τ, x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  where the irrelevant constant S0 is omitted, and L is the differential operator corre-  sponds to the quadratic action.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Two-point functions of ϵ can be obtained summing over the eigenfunctions of L [28]  as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Eigenfunctions of L can be labeled by two quantum numbers n, m, and  separated into two groups  ψn,m(τ, x) = ein¯τψm(x),  (n, m) ∈ (Z±, M±)  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='15)  with  Lψn,m(¯τ, x) ≡  �  −1  4∂2  ¯τ + ∂2  x −  λ2  2 cos2 λ(x−π)  2  �  ψn,m(¯τ, x) = n2 − m2  4  ψn,m(¯τ, x)  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='16)  where Z+/Z− denotes even/odd integers respectively and M± are two infinite discrete  sets of real numbers with magnitude larger than 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' When n takes values in Z+ (Z−) ,  m takes value in M+ (M−).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The two-point function of ϵ can then be written as  ⟨ϵ(¯τa, xa)ϵ(¯τb, xb)⟩ =  �  (n,m)∈(Z±,M±)  ein(¯τa−¯τb)ψm(xa)ψm(xb)  (n2 − m2)/4  = −2π  �  m∈M±  ψm(xa)ψm(xb)  m sin mπ  [cos m(π − |¯τa − ¯τb|) ± cos m(¯τa − ¯τb)]  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='17)  where we define the notation  ¯τa = (τ1 + τ2)/2,  ¯τb = (τ3 + τ4)/2,  xa = τ1 − τ2,  xb = τ3 − τ4 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='18)  The infinite sum of m in (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='17) can be evaluated in a closed form by Sommerfeld-  Watson transformation [28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' For different ordering assignment for τk, they lead to TOC  – 40 –  2元or OTOC after analytic continuation τk → itk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' TOCs do not have exponential growth,  while the OTOC with 2π > τ1 > τ3 > τ2 > τ4 ≥ 0 is given by  FOTOC = − 2  N  G0(τ12)G0(τ34) cos λ(τ1+τ2−τ3−τ4−π)  2  cos πλ  2 cos λ(π−τ12)  2  cos λ(π−τ34)  2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='19)  After analytic continuation τk → itk, it gives (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1) mentioned earlier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Notice that, with  τk → itk, the cosine function in (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='17) leads to exponential growth e±m(t1+t2−t3−t4)/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Since every quantum number m ∈ M± has magnitude greater than 1, the exponential  growth in each individual term in (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='17) violates the chaos bound.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' This infinite tower of  quantum numbers m is the analogue of the infinite tower of higher spins to be summed  over in the higher dimensional Regge theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='2  Identifying the effective fields  We now seek an alternative way to understand two-point function of ϵ, without going  through the infinite sums over m, n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' We are interested only in the exponential part (af-  ter analytic continuation) of the two-point function, and would like to identify a finite  number of effective fields that can capture that.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  For this purpose, consider general solutions to the saddle-point equation (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='4),  which can be written in a form  eσ(τ1,τ2) =  f ′(τ1)g′(τ2)  J 2(f(τ1) − g(τ2))2  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='20)  where f, g are arbitrary functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The above parameterization of σ is not unique as  the right hand side is invariant under an arbitrary SL(2, C) transformation  f → a + bf  c + df ,  g → a + bg  c + dg,  bc − ad = 1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='21)  Now consider small perturbations ϵon−shell around the equilibrium solution (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='7) in the  space of solutions (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='20), which can be parameterized as11  ϵon−shell(τ1, τ2) = λ(χ1(τ1) − χ2(τ2)) tan λ  2(τ12 − π) + χ′  1(τ1) + χ′  2(τ2)  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='22)  where χ1,2 are two arbitrary (infinitesimal) functions, and parameterize the full set of  solutions to equation of motion of the quadratic action (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='14).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The paramterization  freedom (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='21) translates to χ1,2 as ϵon−shell being invariant under transformations  (δχ1(τ1), δχ2(τ2)) =  �  −e±iλ(τ1−π), e±iλτ2�  ,  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='23)  11To see this, we can write the equilibrium solution (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='7) as f0(τ) = −eiλ(τ−π), g0(τ) = eiλτ and  parameterize small perturbations around it as f(τ) = −eiλ(τ−π+χ1(τ)), g(τ) = eiλ(τ+χ2(τ)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Equa-  tion (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='20) results from expanding χ1,2 to linear order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  – 41 –  or a simultaneous shift by a constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  To obtain an effective description of the exponential behavior, we first rewrite (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='22)  in a more convenient form  ϵon−shell(τ1, τ2) =  1  ∆G0(τ12)  �  i=1,2  Lτi[G0(τ12)]χi(τi)  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='24)  Lτ[O(τ)]χ(τ) ≡ ∂τO(τ)χ(τ) + ∆O(τ)∂τχ(τ)  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='25)  where G0 is the equilibrium two-point function of fundamental fermions given earlier  in (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='9), and ∆ = 1/q is the conformal dimension of fundamental fermionic operator  ψi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The differential operator Lτ can be interpreted as a vertex that couples ϵon−shell to  χi(τi), and from (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='23), it obeys the following symmetry  Lτ1[G0(τ12)e±iλ(τ1−π)] = Lτ2[G0(τ12)e±iλτ2] .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='26)  Motived from (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='24), we write ϵ(τ1, τ2) as  ϵ(τ1, τ2) =  1  ∆G0(τ12)  �  LτL[G0(τ12)]φE  1 (¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' τL) + LτS[G0(τ12)]φE  2 (¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' τS)  �  ,  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='27)  where ¯τ = τ1+τ2  2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' τL (τS) is the larger (smaller) of τ1,2, whose usage ensures that (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='27)  respects the invariance of ϵ under switch of τ1,2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' φE  1,2 are dynamical counterparts of  χ1,2, with χ1,2 parameterizing their classical solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Equation (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='27) is exactly the Euclidean version of (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='19)–(2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='21) with the bi-  fermionic field ϵ identified with the second term in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='19), Lτ is Euclidean version  of Lt, and φE  1,2 are φ1,2 evaluated at Euclidean times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' By construction, ϵ as defined  in (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='27) is invariant under transformations of φE  1,2 of the form (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='23), and thus what-  ever the action for φE  1,2 is, it should be invariant under (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='23), which is precisely the  Euclidean version of the shift symmetry (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='81).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' And equation (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='26) can be identified  with the Euclidean version of the shift symmetry (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='82) satisfied by the effective vertex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Given that the action for φE  1,2 must be invariant under the shift symmetry (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='23),  we can be certain that correlation functions of φE  1,2 must contain exponential time-  dependence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' This establish φ1,2 as the effective fields which directly captures the expo-  nential behavior of two-point function of ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='12  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='3  Two-point function of φE  i  In principle we can try to find the (Euclidean) action of φE  1,2 by plugging (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='27)  into (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='10) or (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='14), and being careful about the Jacobian in changing variables from  12Note that two-point function of ϵ has exponential behavior only when the ordering of time argu-  ments corresponds to OTOC, while two-point functions of φE always have exponential behavior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  – 42 –  ϵ to φE  1,2 in the path integral for ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' It is, however, difficult to do in practice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' In addition  to having to understand the Jacobian, various complications discussed in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='2–2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='3,  including that φE  1 and φE  2 are defined on different domains, should also be faced here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Here we show that using (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='14) we can nevertheless find their Euclidean two-point  functions, and confirm their exponential time-dependence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' In next subsection, we show  that these Euclidean two-point functions can be reproduced from the EFT formulation  of Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' 2 by a suitable choice of the action there.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  To compute two-point functions of φE  1,2, instead of considering (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='27) as a change of  variables in the path integral, we canonically quantize (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='14) by treating ¯τ as “time”,  and treat (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='27) as an operator equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Below we will use ϵ, φE  1,2 to denote the fields in  the Euclidean path integral defined with (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='14), and ˆϵ, ˆφE  1,2 the corresponding operators  in the canonical quantization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' By definition, Euclidean correlation functions of φE  1,2 are  given by “time-ordered” correlation functions of ˆφE  1,2, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  �  φE  i (¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' τ)φE  j (¯τ ′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' τ ′)  �  = −i  �  ¯T ˆφE  i (¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' τ)ˆφE  j (¯τ ′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' τ ′)  �  c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='28)  where ¯T denotes ordering in ¯τ and the subscript “c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='q.” on the RHS is to distinguish  the expectation value in Euclidean path integral on the LHS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' We outline the main steps  here, leaving technical calculations to Appendix D:  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' In canonical quantization of (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='14), we can expand ˆϵ in terms of a complete set  of modes {gm} as  ˆϵ(¯τ, x) =  �  m  �  gmˆam + g∗  mˆa†  m  �  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='29)  where gm solve the equation of motion Lgm(¯τ, x) = 0, and obey the conditions  gm(¯τ, 0) = gm(¯τ, 2π) = 0 (from (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='13)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' m takes value in the same sets M±  discussed below (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='16).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' {gm} are assumed to be properly normalized under the  Klein-Gordon inner product,  (g1, g2) = − i  2  ˆ 2π  0  dx (g1∂¯τg∗  2 − g∗  2∂¯τg1)  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='30)  such that annihilation and creation operators ˆam and ˆa†  m obey the standard com-  mutation relation [ˆam, ˆa†  m′] = δm,m′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Due to the nontrivial boundary condition (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='13) in ¯τ direction, the system is not  in the vacuum state of ˆam, and it can be shown that ˆam, ˆa†  m have correlation  functions13  �  ˆas  mˆas†  m  �  c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' =  1  1 − se−imπ ,  �  ˆas†  mˆas  m  �  c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' =  se−imπ  1 − se−imπ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='31)  13Two-point function of ˆϵ then follows and can be checked to give the same answer as (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='17).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  – 43 –  where s = ± labels two different sectors of ˆam and ˆa†  m with m ∈ M± respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Since the mode functions gm solve the equation of motion of ϵ, from (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='24), they  can be written as  gm(¯τ, x) =  1  ∆G0(τ12)  �  i=1,2  Lτi[G0(τ12)]χi,m(τi)  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='32)  where Lτ is defined in (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='25), and {χi,m} is a complete set of basis functions for  χi in (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='24).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Plugging (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='32) into (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='29), then from (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='27), we can write ˆφE  1,2 as  ˆφE  i (¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' τi) =  �  m  (χi,m(τi)ˆam + χ∗  i,m(τi)ˆa†  m) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='33)  Two-point functions of φE  i can then follow from (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='31).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Notice from (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='33) that  ˆφE  i (¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' τi) does not have any ¯τ dependence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' So the only ¯τ-dependence in two-  point functions of φE  1,2 comes from θ(¯τ) on the right hand side of (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='28).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Such  ¯τ-dependence is precisely what we had in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' 2, see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='73), except that there  it came from our assumption of weak ¯τ-dependence and derivative expansion in  ¯τ, but here for the large q SYK model it is exact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  From the calculation of Appendix D, we have  �  φE  i (¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' τ)φE  j (0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' 0)  �  = θ(¯τ)Mij(τ) + θ(−¯τ)Mji(−τ)  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='34)  M11(τ) = M22(τ) = M12(2π − τ) = M21(−τ)  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='35)  =  8  N∆2 ×  �  ˆm+eiλτ + ˆm1τeiλτ + c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=',  τ ∈ [0, 2π]  ˆm−eiλτ + ˆm1τeiλτ + c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=',  τ ∈ [−π, 0]  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='36)  where in the last equality we have kept only the exponential part, and ˆm+, ˆm− and ˆm1  are some constants given by  ˆm+ = i2πλ − sin 2πλ + 2(πλ + sin πλ)(2πiλ + 3 − e−iπλ)  32λ2(πλ + sin πλ)2(1 + eiπλ)  ,  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='37)  ˆm− = ˆm+ +  1  4λ2(1 + eiπλ),  ˆm1 =  1  8λ(πλ + sin πλ)(1 + eiπλ)  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='38)  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='4  Effective action for large q SYK  We now work out the explicit form the EFT action which match with correlation  functions (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='35)–(5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='36).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' As our EFT is formulated in Lorentzian time, we need to first  analytically continue the Euclidena correlation fuctions (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='34).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The correct analytic  continuation for large q SYK model is φE  j (¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' τ) → φj(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) = −iφE  j (i¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' it) and Lτ → Lt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  – 44 –  Note that (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='36) contains linear-exponential terms te±λt after analytic continuation  τ → it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' From discussion of Appendix C, this means that we need to include quadratic  order of ∂2  t − λ2 in some Ks,p(i∂t), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  K+,p(i∂t) = (∂2  t − λ2)k+,p(i∂t),  K−,p(i∂t) = (∂2  t − λ2)2k−,p(i∂t)  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='39)  where K−,p(x) has a double zero at ±iλ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' With appropriate choice of k+,0(iλ), k−,0(iλ)  and k′  −,0(iλ) (the derivative to k−,0(x) at iλ) that depend on the three parameters ˆm+,  ˆm− and ˆm1, we find that this effective action completely reproduces the correlation  functions (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='34)–(5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='36).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  More explicitly, we find in Appendix D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='4 that  k+,0(iλ) = 3λN∆2 cot πλ  2  2(1 − 2 cos πλ)  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='40)  k−,0(iλ) = 3N∆2(πλ + sin πλ)  8λ(2 cos πλ − 1)  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='41)  k′  −,0(iλ) = −3iN∆2 �  (2π2λ2 − 5) sin πλ + 2 sin 2πλ + 8πλ cos πλ − πλ  �  3πλ tan πλ  2 + 7  ��  16λ2(1 − 2 cos πλ)2  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='42)  and other parameters ks,±(iλ) and k′  −,±(iλ) are derived from the constraints (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='79),  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='68) and two continuity conditions (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='76)-(2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='77) and explicitly given by (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='22)-(C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='24),  which we copy as follows  k+,±(iλ) = ∓ik+,0(iλ)  √  3  tan  �π  2 (λ ± 1/3)  �  tan πλ  2  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='43)  k−,±(iλ) = ±ik−,0(iλ)  √  3  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='44)  k′  −,±(iλ) = ±  √  3  3  �  2λk−,0(iλ)2  k+,0(iλ)  �  1 +  1  tan  � π  2(λ ± 1/3)  �  tan πλ  2  �  + ik′  −,0(iλ)  �  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='45)  There is a subtlety in this effective action when we take the maximal chaos limit  λ → 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Taking λ → 1 in (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='40)-(5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='42), we find that  k+,0(iλ) → 0,  k−,0(iλ) ∼ O(1),  k′  −,0(iλ) → ∞  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='46)  Note that in (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='39) K+,p is linear in ∂2  t − λ2, which implies that correlation functions  for s = + in Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='6 all hold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' It follows that we will have singular ∆+,0(t) by (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='86).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  This singularity implies that the maximal chaos limit in large q SYK model should be  taken with some care.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  – 45 –  Indeed, there is a scaling limit in SYK model when we take maximal chaos limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  The Lyapunov exponent λ is related to the inverse temperature β and coupling J by  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The maximal chaos limit corresponds to strong coupling limit J → ∞ (or equiv-  alently low temperature limit β → ∞), under which we can solve (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='8) perturbatively  as (β = 2π)  λ = 1 −  1  πJ + O(1/J 2)  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='47)  However, the low temperature limit should still be understood in the regime of validity  of large N, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' N ≫ J ≫ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Therefore, in maximal chaos limit, for (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='40)-(5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='42) we  have  k+,0(iλ) ∼ O(J −1),  k−,0(iλ) ∼ O(1),  k′  −,0(iλ) ∼ O(J )  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='48)  which by (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='43)-(5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='45) implies  k+,±(iλ) ∼ O(1),  k−,±(iλ) ∼ O(1),  k′  −,±(iλ) ∼ O(1)  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='49)  Given the action (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='39), by (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='74) and (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='75) the exponential terms in retarded corre-  lation functions scale as  ∆+,p(t) ∼  e±λt  k+,±p(iλ),  ∆−,p(t) ∼ k′  −,±p(iλ)e±λt  k−,±p(iλ)2  + (c0 + c1t)  e±λt  k−,±p(iλ)  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='50)  where c1,2 are two O(1) numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' From (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='48) and (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='49) in maximal chaos, there is an  enhancement of J to ∆s,0(t) while ∆s,±(t) are still O(1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' This means that ηs,± decouple  at maximal chaos at leading order of J .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Since ¯τ dependence only exists for p = ±,  this means that at leading order of J two effective modes φ1,2 reduce to a single field  at maximal chaos following the same argument for (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Note that the first term of ∆−,0(t) in (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='50) is O(J ) but the second term is O(1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Therefore, at leading order of J , ∆−,0(t) only has pure exponential terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Using the  explicit expression for ∆s,p(t) in (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='25)-(C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='28), one can show that  ∆+,0(t) = ∆−,0(t) = 2iJ  N∆2(et − e−t) + O(1/N)  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='51)  It follows that K−,0(i∂t) in the effective action (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='39) can be reduced to be just linear  in ∂2  t − λ2 and we can take ansatz  Kmax  s,0 (i∂t) = (∂2  t − 1)kmax  s,0 (i∂t)  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='52)  where kmax  s,0 (i∂t) satisfies  kmax  +,0 (i) = kmax  −,0 (i) = N∆2  4J  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='53)  – 46 –  This is the same condition we impose in (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='3) for maximal chaos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Following the dis-  cussion in Section 4, this EFT reduces back to case in [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Note that the overall scal-  ing N/J in (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='53) reflects the fact that the effective action for SYK model in strong  coupling/low temperature limit is proportional to N/(βJ ), which is observed in the  Schwarzian action [26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  6  Higher order terms and exponentiation  Higher order terms in equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='3) are suppressed by higher powers of 1/N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Here  we show that a subset of terms of the form ekλt  Nk (k an integer) can be rensummed and  exponentiated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Such terms dominate in the regime N → ∞ and t ∼ 1  λ log N such that  eλt  N is finte.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' These contributions come from including higher powers of effective fields φi  in the product (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='19), but in the effective action still keep only quadratic terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='14 The  full four-point functions of V and W then involve multi-point correlation functions of  effective fields φi, which factorize to products of two-point functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' We show that the  shift symmetry on the vertices that couple W(t1)W(t2) to higher powers of φi implies  that TOCs again do not have exponential growth, and the OTOC (recall (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='105)) has  the exponentiated form  F4 =  ˆ ∞  0  d˜y  ˆ ∞  0  dy e−αy˜yeλ(t1+t2−t3−t4+iπ)/2h(t12, y)˜h(t34, ˜y)  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1)  where various notations will be explained below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  We now proceed to describe the  derivation of (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1  Towards a scattering formula  Without derivative on ¯t, all order generalization of the vertex can be written as  ⟨W(t1)W(t2)⟩0 =  �  is=1,2  j,ks,m∈N  s=1,··· ,m  Ci1···im  j;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='k1···km  m!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  ∂jgW(t12)∂k1  ti1φi1(¯tW;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' ti1) · · · ∂km  timφim(¯tW;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' tim)  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='2)  ≡  �  {Is},m  1  m!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='CI1···ImφI1 · · · φIm  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='3)  where in the first line ⟨·⟩0 means taking the expectation value of bare operators, and  we assume ℑt1 < ℑt2 so that the arguments for φi is ti (i = 1, 2);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' and in the second  14Including nonlinear terms in the EFT action leads to higher order terms of the form ek1λt  N k2 with  k2 > k1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  – 47 –  line we defined the notation  I ≡ (i, k),  φI ≡ ∂k  tiφi(¯tW;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' ti),  CI1···Im =  �  j  Ci1···im  j;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='k1···km∂jgW(t12)  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='4)  where C is a tensor function of t12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Note that separate t1,2 derivatives on W0(t1,2)  in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='20) and (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='21) are combined to act on the argument of gW(t12) by translation  symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' In (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='2), the range of the sum for m is from 0 to ∞ but the sum for j, ks  could be either finite or infinite for each m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' For simplicity, we will consider their ranges  to be finite at each m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' For each ks, we choose the range of sum to be the same, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  k1, · · · , km ∈ {0, · · · , dm}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' This choice defines φI in (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='4) as a 2dm dimensional vector  at each m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' It follows that CI1···Im can be chosen as a symmetric tensor of order m by the  permutation symmetry of among all φI in (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' For m = 0, we have Cj = δj,0 because  the leading order of (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='2) is just gW(t12).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Similarly expansion applies to ⟨V (t3)V (t4)⟩  for ℑt34 ∈ (−2π, 0) with notation  ⟨V (t3)V (t4)⟩0 =  �  {Is},m  1  m!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  ˜CI1···Im ˜φI1 · · · ˜φIm  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='5)  ˜φI ≡ ∂k  ti+2φi(¯tV ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' ti+2),  ˜CI1···Im =  �  j  ˜Ci1···im  j;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='k1···km∂jgV (t34)  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='6)  With four time variables (t1, t2, t3, t4) in the analytic domain D, a generic four-point  function ˆF is  ˆF(t1, t2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t3, t4) =  �  {Is,I′s},m,m′  CI1···Im ˜CI′  1···I′  m′  m!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='m′!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  �  ˆT φI1 · · · φIm ˜φI′  1 · · · ˜φI′  m′  �  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='7)  With the effective action being quadratic, the (m + m′)-point function of φi factorizes  into products of two-point functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' We will ignore the self-interaction terms (those  pairs of φi with same ¯t) because they do not grow in OTOC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' It follows that m′ = m  and  ˆF(t1, t2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t3, t4) ≈  �  {Is,I′s},m  CI1···Im ˜CI′  1···I′m  m!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  m  �  s=1  �  ˆT φIs ˜φI′  s  �  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='8)  where the the permutation symmetry in Wick contraction gives m!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' that cancels one m!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  in the denominator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  The KMS condition requires ˆF invariant under t1 → t2 − 2πi and t2 → t1 (and  also t3 → t4 − 2πi and t4 → t3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Using (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='26)-(2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='27), we find coefficients C and ˜C must  satisfy the constraints  Ci1···im  j;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='k1···km = (−)jC  ¯i1···¯im  j;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='k1···km,  ˜Ci1···im  j;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='k1···km = (−)j ˜C  ¯i1···¯im  j;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='k1···km  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='9)  – 48 –  where the map i → ¯i means 1 ↔ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' This is equivalent to  CI1···Im(t) = C¯I1···¯Im(−t − 2πi),  ˜CI1···Im(t) = ˜C¯I1···¯Im(−t − 2πi)  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='10)  where ¯I means (i, k) → (¯i, k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  We further require the right hand side of (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='3) to be invariant under shift symmetry  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='81), which lead to  CI1···Im(∂k1δφi1) · · · φIm = 0,  δφi ≡ (δφ1, δφ2) = (e±λ(t1+iπ), −e±λt2)  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='11)  for arbitrary φI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' This is a quite strong constraint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Let us define the 2dm dimensional  vector eI = ∂kδφi at each m and (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='11) becomes  �  I1  CI1···ImeI1 = 0  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='12)  At each m, for the symmetric tensor C we can always find a linear independent set of  vectors {u(m)a} such that  CI1···Im =  �  a∈Dm  ξ(m)  a  u(m)a  I1  · · u(m)a  Im  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='13)  where Dm is the size of the set, and ξ(m)  a  is a Dm dimensional vector function of t12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' By  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='12), the whole set {u(m)a} must be orthogonal to e, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' u(m)a  I  eI = 0 for all a ∈ Dm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Similar decomposition applies to ˜C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  From the definition of C, it is a function of t12, and so is u(m)a  I  = u(m)a  I  (t12).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The  orthogonality to eI for each u(m)a  I  leads to  �  k  u(m)a  1,k (t12)(±λ)ke±λ(t1+iπ) =  �  k  u(m)a  2,k (t12)(±λ)ke±λt2  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='14)  which implies  u(m)a  +  (±λ, t12) = ∓u(m)a  −  (±λ, t12) coth λ(t12 + iπ)  2  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='15)  where we define  u(m)a  ±  (λ, t) ≡ 1  2  �  k  (u(m)a  1,k (t) ± u(m)a  2,k (t))λk  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='16)  Take transformation t1 → t2 − 2πi, t2 → t1 and (i, k) ↔ (¯i, k) in (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='15).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' It follows that  u(m)a  ¯I  (−t12 − 2πi) is also an orthogonal vector to eI where ¯I = (¯i, k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Let us choose  the normalization of u(m)a  I  such that ξ(m)  a  (t12) is invariant under KMS transformation  t12 → −t12 − 2πi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' By KMS symmetry of C in (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='10), we must have both u(m)a  I  (t12) and  u(m)a  ¯I  (−t12 − 2πi) summed with the same ξ(m)  a  coefficient in (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='13).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Sometimes, these  – 49 –  two are linear dependent or even the same, in which cases we just need to include one  of them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Taking (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='13) to (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='8), we have  ˆF(t1, t2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t3, t4) =  �  m  1  m!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  �  a∈Dm,b∈ ˜Dm  ξ(m)  a  ˜ξ(m)  b  ��  I,I′  u(m)a  I  �  ˆT φI ˜φI′�  ˜u(m)b  I′  �m  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='17)  Note that the shift symmetry (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='14) is in the same form as (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='82).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Therefore, we can  use the same technique in Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='8 to show that all TOC do not have exponential  growth piece.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Indeed, the proof in Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='8 does not depend on the explicit form of  Lt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' One can complete a similar proof for each �  I,I′ u(m)a  I  �  ˆT φI ˜φI′�  ˜u(m)b  I′  in (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='17) by  replacing Lt1gW with �  k u(m)a  1,k (t12)∂k  t1 and Lt2gW = �  k u(m)a  2,k (t12)∂k  t2 (and doing similar  replacement for Lt3,4) in Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  For OTOC F4 in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='105), the replacement still holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Similar to (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='122), we can  write in a symmetric way that  �  I,I′  u(m)a  I  �  φI ˜φI′�  ˜u(m)b  I′  =αeλ(t1+t2−t3−t4+iπ)/2  �  u(m)a  +  (λ, t12) cosh λ(t12 + iπ)  2  + u(m)a  −  (λ, t12) sinh λ(t12 + iπ)  2  �  ×  �  ˜u(m)a  +  (−λ, t34) cosh λ(t34 + iπ)  2  − ˜u(m)a  −  (−λ, t34) sinh λ(t34 + iπ)  2  �  + (λ ↔ −λ)  =αeλ(t1+t2−t3−t4+iπ)/2u(m)a  +  (λ, t12)˜u(m)a  +  (−λ, t34)  cosh λ(t12+iπ)  2  cosh λ(t34+iπ)  2  + (λ ↔ −λ)  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='18)  where we defined  ˜u(m)a  ±  (λ, t) ≡ 1  2  �  k  (˜u(m)a  1,k (t) ± ˜u(m)a  2,k (t))λk  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='19)  and used (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='15) in the last step for both u(m)a  ±  and ˜u(m)a  ±  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Since we are only interested in large Lorentzian time separation t1, t2 ≫ t3, t4 or  t1, t2 ≪ t3, t4, we only need to keep the exponentially growth term in (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='18) because the  other term is exponentially suppressed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Let us take t1, t2 ≫ t3, t4, then (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='17) becomes  F4 =  �  m  1  m!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  �  a∈Dm  ξ(m)  a  �  u(m)a  +  (λ, t12)  cosh λ(t12+iπ)  2  �m �  b∈ ˜Dm  ˜ξ(m)  b  �  ˜u(m)b  +  (−λ, t34)  cosh λ(t34+iπ)  2  �m  Xm  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='20)  with the exponential growth  X ≡ αeλ(t1+t2−t3−t4+iπ)/2  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='21)  – 50 –  Assume we can do an inverse Mellin transformation to define h and ˜h as  �  a∈Dm  ξ(m)  a  �  u(m)a  +  (λ, t12)  cosh λ(t12+iπ)  2  �m  =  ˆ ∞  0  dyymh(t12, y)  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='22)  �  b∈ ˜Dm  ˜ξ(m)  b  �  ˜u(m)b  +  (−λ, t34)  cosh λ(t34+iπ)  2  �m  =  ˆ ∞  0  d˜y(−˜y)m˜h(t34, ˜y)  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='23)  Then we can rewrite (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='20) as  F4 =  ˆ ∞  0  d˜y  ˆ ∞  0  dy  �  m  1  m!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='h(t12, y)(−Xy˜y)m˜h(t34, ˜y)  =  ˆ ∞  0  d˜y  ˆ ∞  0  dye−Xy˜yh(t12, y)˜h(t34, ˜y)  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='24)  This has exactly the same form as [16, 17], and also matches with the trans-plankian  string scattering formula near horizon of a AdS black hole [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' In [16], this scattering  formula was conjectured by a heuristic argument and the authors of [17] later proved  it with a specific structure of Feynmann diagrams.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' In this work, we show that (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='24)  holds in a more general scenario since it is just a result of a shift symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Note that the assumption of inverse Mellin transformation requires analyticity in  m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  This is a nontrivial constraint on the vertices because at each level of m one  could have choosen ξ(m)  a  and the sets Dm and ˜Dm quite randomly in a pattern without  analyticity in m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' However, there is a simple and sufficient way to guarantee analyticity,  which requires three parts:  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The total ways of coupling between bare operator and effective mode does not  change as we increase the number m of effective modes, which picks Dm and ˜Dm  as some fixed sets for all m, in which the vector dimension 2dm is also fixed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' All these types of couplings exist at any level of m, which releases the m depen-  dence of u(m)a  +  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The coefficient ξ(m)  a  is an analytic function of m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  It is noteworthy that the ordinary ladder diagrams in eikonal scattering obeys these  three conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Therefore, this explains why the exponentiation in (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='24) is also a  result of eikonal scattering [4], in which e−Xy˜y is the eikonal scattering amplitude, h is  the wave function of two W’s and ˜h is the wave function of two V ’s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  – 51 –  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='2  An example  In this subsection, we will present a simple example following the general construction  in the last subsection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' We will solve a simple orthogonal vector uI, find the vertices  leading to this vector uI, compute the exponentiation formula and compare it with the  known result of large q SYK model [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Let us first solve the orthogonal vectors ua  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Define q = e−λ(t12+iπ) and the equation  ua  IeI = 0 can be written as  �  k  ua  1k(q)λk =  �  k  ua  2k(q)λkq,  �  k  ua  1k(q)(−λ)kq =  �  k  ua  2k(q)(−λ)k  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='25)  Without loss of generality, we can assume ua  I is a polynomial in q  ua  I =  pa  �  n=0  ca  I,nqn  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='26)  up to normalization where pa could be either a finite number or ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Then (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='25) leads  to  �  k  ca  1k,nλk =  �  k  ca  2k,n−1λk,  �  k  ca  1k,n−1(−λ)k =  �  k  ca  2k,n(−λ)k  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='27)  for n ≥ 0 with definition ca  I,−1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The simplest nontrivial solution is for pa = 1 and  k = 0, 1  c10,0 = c20,1 = −λ,  c20,0 = c10,1 = λc  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='28)  c11,0 = c21,1 = 1,  c21,0 = c11,1 = c  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='29)  We can choose the normalization of uI such that it is invariant under KMS trans-  formation q → 1/q and i → ¯i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' In this case, by the discussion below (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='16), we can  construct a KMS invariant C just using this vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' It is easy to see that the appropriate  normalization is q−1/2 and the orthogonal vector is  u10 = λ(cq − 1)  q1/2  ,  u11 = 1 + cq  q1/2 ,  u20 = λ(c − q)  q1/2  ,  u21 = c + q  q1/2  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='30)  Then we will solve the vertices with coefficients Ci1···im  j;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='k1···km leading to this vector uI  for each order m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Let us start with m = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' We can further impose a simple condition  that j only takes values 0 and 1 in (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Define n-th order ∂t12 derivative to bare  correlator gW(t12) = g(q) as gn(q) = (−λq∂q)ng(q) with g0(q) = g(q).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' For c ̸= 0, ∞,  comparing (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='4) and (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='13) leads to  Ci  0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='kg(q) + Ci  1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='kg1(q) = ξ(1)(q)uik(q)  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='31)  – 52 –  Our goal is to solve coefficients Ci  j;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' However, for arbitrary Ci  j;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='k and ξ(1)(q), this is  also a differential equation for g(q), which will constrain g(q) to a specific form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' We  solve (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='31) in detail in Appendix E and present the result here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The correlation g(q)  must be in the form  g(q) = (q1/2 + q−1/2)−2∆  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='32)  up to normalization and with a constant ∆.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' It is obvious that this g(q) obyes KMS  symmetry g(q) = g(1/q).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' With this solution, the coefficients Ci  j;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='k are  C1  0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='0 = ∆λ(c − 1)  c + 1  ,  C1  1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='0 = 1,  C1  0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1 = ∆,  C1  1,1 =  c − 1  (c + 1)λ  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='33)  C2  0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='0 = ∆λ(c − 1)  c + 1  ,  C2  1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='0 = −1,  C2  0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1 = ∆,  C2  1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1 = − c − 1  (c + 1)λ  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='34)  where we choose the normalization such that C1  1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='0 = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' One can check that this solution  obeys KMS symmetry (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Taking them into (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='31) and using (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='30), we find  ξ(1)(q) =  2∆g(q)  (1 + c)(q1/2 + q−1/2)  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='35)  which is explicitly KMS invariant as expected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  In the two component vertex form, we have  �  jk  Ci  j;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='k∂jg(t12)∂k  tiφi(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' ti) = (∂gφ1 + ∆g∂φ1, −∂gφ2 + ∆g∂φ2)  +  �c − 1  c + 1  �  (∆λgφ1 + λ−1∂g∂φ1, ∆λgφ2 − λ−1∂g∂φ2)  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='36)  where on the RHS we have suppressed the notation and the derivatives only act on the  second argument of φi(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' ti).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Note that the first line, namely c = 1, exactly matches  with the vertex (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='5) of large q SYK model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  To construct the higher order coupling coefficient Ci1···im  j;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='k1···km such that (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='13) holds  for all m is not hard for this example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The point is to note the following feature  gn(q)  g(q) =  Pn(q)  (1 + q)n  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='37)  where Pn(q) is a n-order polynomial has no factor of (1+q).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Therefore, for any n-order  polynomial Pn(q), we can pick a linear combination such that  n  �  j=0  wj  gj(q)  g(q) =  1  (1 + q)n  n  �  j=0  wj(1 + q)n−jPj(q) =  Pn(q)  (1 + q)n  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='38)  – 53 –  Since q1/2uI(q) is a first order polynomial of q, the product qm/2uI1(q) · · · uIm(q) is a  polynomial of q up to order m for each choice of (I1, · · · , Im).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' It follows that we can  choose Ci1,··· ,ik  j,k1···km such that  CI1···Im =  m  �  j=1  Ci1,··· ,ik  j;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='k1···km(−λq∂q)jg(q) =  z(m)g(q)  (q1/2 + q−1/2)muI1(q) · · · uIm(q)  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='39)  where z(m) is a constant that could depend on m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' It clear that (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='39) obeys KMS  symmetry (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  If we only include this type of orthogonal vector uI in C, we have  ξ(m) =  z(m)g(q)  (q1/2 + q−1/2)m,  u±(λ, t) = λc(q ± 1)  q1/2  ,  u±(−λ, t) = −λ(1 ± q)  q1/2  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='40)  which by (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='22) and (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='23) leads to  ˆ ∞  0  dyymh(t12, y) = z(m)gW(t12)(λc)m  �  cosh λ(t12+iπ)  2  �m  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='41)  ˆ ∞  0  d˜y˜ym˜h(t34, ˜y) =  ˜z(m)gV (t34)λm  �  cosh λ(t34+iπ)  2  �m  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='42)  where we assume the vertex of V consists of the same vector uI but with a possibly  different coefficient ˜z(m).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' For analytic functions z(m) and ˜z(m) that decay fast enough  along ℑm → ±∞, the Mellin inversion theorem guarantees the existence of h(t12, y)  and ˜h(t34, ˜y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' However, to determine the exact form of z(m) and ˜z(m) needs detailed  knowledge of the dynamics of underlying UV model (for example [17]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  For large q SYK model, we can choose W = V to be the fundamental Majorana  fermion ψ, whose conformal weight is ∆ = 1/q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The α parameter in (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='21) is given  by (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Its exponentiation exactly falls into above case of c = 1 with the following  choices of z(m) and ˜z(m)  z(m) = ˜z(m) = Γ(2∆ + m)  2mΓ(2∆)  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='43)  which leads to  h(t, y) = ˜h(t, y) = gψ(t)  �  2  λ cosh λ(t+iπ)  2  �2∆  Γ(2∆)  y2∆−1 exp  �  −2y  λ cosh λ(t + iπ)  2  �  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='44)  where gψ(t) is the fermion correlation function (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' One can check that this exactly  matches with the result in [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  – 54 –  7  Conclusion and discussion  In this paper, we constructed an effective field theory to capture the behavior of OTOCs  of non-maximal quantum chaotic systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' While the theory is constructed phenomeno-  logically, we showed that it is constraining enough to predict the general structure of  OTOCs both at leading order in the 1/N expansion, and after resuming over an infinite  number of higher order corrections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' These general results agree with those preciously  explicitly obtained in specific models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' We also showed that the general structure of the  EFT can in fact be extracted from the large q SYK model, providing further support  for its validity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' There are many future directions to explore, on which we make some  brief comments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Higher dimensional systems  A most immediate direction is to generalize the cur-  rent discussion to higher dimensional systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Including spatial directions will make it  possible to consider much wider range of physical issues, for example, operator growths  and scrambling in spatial directions (such as the behavior of the butterfly velocity),  connections between quantum chaos and energy as well as charge transports, and so  on.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  In the case of maximal chaos, a phenomenon that connects chaos and energy  transport is the so-called pole-skipping [8, 30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Understanding what happens to this  phenomenon for non-maximal chaotic systems is of interests.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' In [31] it was conjectured  that pole-skipping survives in non-maximal system and the location of pole-skipping is  given by  (ω, k) = i(2π/β)(1, 1/u(T)  B )  (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1)  where u(T)  B  is an upper bound of the true butterfly velocity uB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' An EFT including  spatial directions could help check the conjecture and understand connections between  energy transport and chaos in more general systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Physical nature of the effective fields and the shift symmetry  Here we in-  troduced chaos effective fields and shift symmetry on phenomenology ground.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' In the  example of the large-q SYK model, we can identify the effective fields and origin of  shift symmetry from the microscopic system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' It is, however, not clear whether the  understanding obtained in this model can be applied to general systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  In maximal chaotic holographic systems, the shift symmetry of the EFT should  be related to the existence of a sharp horizon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' It is an outstanding question regarding  the nature of the horizon when including stringy corrections on the gravity side, un-  derstanding the physical nature and origin of the shift symmetry for non-maximal case  could provide hints for this question.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  – 55 –  Effective field theories for Reggeons  As mentioned in the Introduction (see  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' 1b), there is a close connection between the exponential behavior in non-maximally  chaotic systems and scattering amplitudes in the Regge limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Our formulation of  an EFT for non-maximally chaotic systems could provide new ideas for formulat-  ing effective field theories for Reggeons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' More explicitly, the stringy scattering pro-  cesses corresponding to OTOCs in holographic systems can be described by the BFKL  Pomeron [4, 32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  The effective fields we identified could shed light on an effective  description of the Pomeron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Acknowledgements  We would like to thank Mark Mezei and Daniel Jafferis for stimulating and helpful  discussions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' PG is supported by the US Department of Defense (DOD) grant KK2014  and also by the Simons foundation as a member of the It from Qubit collaboration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' HL  is supported by the Office of High Energy Physics of U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Department of Energy under  grant Contract Number DE-SC0012567 and DE-SC0020360 (MIT contract # 578218).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  A  A few oversimplified constructions  In this appendix, we list two oversimplified constructions of EFT for non-maximal  chaos, which are slightly generalized from the EFT for maximal chaos [8, 9] with one  time argument.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' It turns out that both constructions are only compatible with maximal  chaos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The purpose of this section serves as a support for the construction in Section  2 as a minimal and sufficient generalization to account for non-maximal chaos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  In  particular, including two time arguments in the effective modes is necessary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1  Multiple effective modes with one time argument  The simplest generalization of [8, 9] is to include more effective modes but still for-  mulated with one time argument.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Let us label these effective modes as ϕµ with  µ = 1, · · · , D for some finite D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The four-point function ˆFWWV V (t1, t2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t3, t4) is sym-  metric under exchange of t1 ↔ t2 and t3 ↔ t4 respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Therefore, to define the  coupling between a bare operator W0 and effective modes ϕµ, we must respect this  symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' There are two simple ways: one is that every W0 couples with all ϕµ, the  other is coupling in an ordered way (just like (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='20) and (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='21) for two effective modes).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Here we will consider the first choice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  In this case, the coupling in linear order of ϕµ is  W(t) = W0(t) + Lµ  t W0(t)ϕµ(t),  V (t) = V0(t) + ˜Lµ  t V0(t)ϕµ(t)  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1)  – 56 –  where µ is summed from 1 to D and Lµ  t is a set of differential operators  Lµ  t W0(t)ϕµ(t) =  �  nm  cµ  nm∂n  t W0(t)∂m  t ϕµ(t)  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='2)  and ˜Lµ  t is defined similarly with cµ  nm → ˜cµ  nm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' To quadratic order of ϕµ, the four-point  function is  ˆFWWV V (t1, t2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t3, t4) =  �  i,j=1,2  Lµ  tigW ˜Lν  tj+2gV ⟨T ϕµ(ti)ϕν(tj+2)⟩  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='3)  where gW,V are short for gW(t12) and gV (t34) and ⟨T ϕµϕν⟩ is the Euclidean time ordered  two-point function in the thermal state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Imposing the same shift symmetry [8]  ϕµ(t) → ϕµ(t) + αe±λt  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='4)  in the effective action, we will have the following exponential terms in the Wightman  function  ⟨ϕµ(t)ϕν(0)⟩ = dµνeλt + ¯dµνe−λt  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='5)  where cµν and ¯cµν are two nonzero constant matrices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Let us consider OTOC F4 and TOC G4 defined as  F4 = ⟨W(t1)V (t3)W(t2)V (t4)⟩ ,  H4 = ⟨W(t1)W(t2)V (t3)V (t4)⟩  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='6)  where t1, t2 ≫ t3, t4 or t1, t2 ≪ t3, t4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' For TOC, we have  H4 =dµν  �  Lµ  t1gWeλt1 + Lµ  t2gWeλt2� �  ˜Lν  t3gV e−λt3 + ˜Lν  t4gV e−λt4�  + b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='7)  where b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' means bar-conjugate which replaces cµν with ¯cµν and swaps eλt ↔ e−λt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' For  OTOC, we have  F4 = H4 +  �  dµν  �  ˜Lµ  t3gV eλt3Lν  t2gWe−λt2 − Lµ  t2gWeλt2 ˜Lν  t3gV e−λt3�  + b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  �  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='8)  Let us define two vector functions  vµ(t1, t2) = Lµ  t1gWeλt1 + Lµ  t2gWeλt2,  uν(t3, t4) = ˜Lν  t3gV e−λt3 + ˜Lν  t4gV e−λt4  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='9)  Absence of exponential terms in TOC H4 means  dµνvµ(t1, t2)uν(t3, t4) = 0  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='10)  and the other equation with bar-conjugate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' For (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='10), we can first expand vµ and  write it as  Geven(t3, t4;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) = − tanh λt  2 Godd(t3, t4;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t)  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='11)  – 57 –  where we define  Geven/odd(t3, t4;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) ≡  �  n even/odd  �  m  dµνuν(t3, t4)cµ  nm∂n  t gW(t)λm  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='12)  Let us consider a few cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' If both sides of (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='11) are nonzero, we can take a KMS transformation t →  −t − 2πi in (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='11).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Since gW(t) = gW(−t − 2πi) by KMS condition, we have  Geven → Geven and Godd → −Godd and thus (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='11) yields  tanh λt  2 = tanh λ(t + 2πi)  2  =⇒ λ = 1  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='13)  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' If both sides of (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='11) are zero, this means  dµνuν(t3, t4)Lµ  t1gWeλt1 = 0,  dµνuν(t3, t4)Lµ  t2gWeλt2 = 0  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='14)  Then we can expand uν in the second equation and find a similar equation to  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='11)  ˜Geven(t1, t2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) = tanh λt  2  ˜Godd(t1, t2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t)  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='15)  where we define  ˜Geven/odd(t1, t2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) ≡  �  n even/odd  �  m  dµν(Lµ  t2gWeλt2)˜cν  nm∂n  t gW(t)(−λ)m  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='16)  If both sides of (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='15) are nonzero, the KMS transformation in (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='15) again leads  to (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='13) and maximal chaos λ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' If both sides of (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='15) are zero, we have  dµνLµ  t2gWeλt2 ˜Lν  tjgV e−λtj = 0,  j = 3, 4  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='17)  Similarly, using the first equation of (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='14), we will have either λ = 1 or  dµνLµ  t1gWeλt1 ˜Lν  tjgV e−λtj = 0,  j = 3, 4  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='18)  Then we can consider another TOC H′  4 = ⟨V (t3)V (t4)W(t1)W(t2)⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Following a  similar analysis for H4 (which simply swaps t1,2 ↔ t3,4 and W ↔ V everywhere),  we will have either λ = 1 or  dµν ˜Lµ  tjgV eλtjLν  tigWe−λti = 0,  i = 1, 2,  j = 3, 4  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='19)  Taking both (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='17) and (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='19) into (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='8), we find that the exponential terms  proportional to dµν vanish in F4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Similarly, we can show that the bar-conjugate  terms vanish as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' This means that if we require exponential growth of OTOC  but no exponential growth in TOC, we must have maximal chaos λ = 1 in this  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  – 58 –  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='2  Two effective modes with one time argument and ordered coupling  As we mentioned before, for two effective modes ϕi with i = 1, 2, there is another simple  way to couple bare operators with them in a symmetric way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' This is essentially the  same as our proposal (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='20) and (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='21) in which W0(tS) couples with ϕ1(τS) and W0(tL)  couples with ϕ2(tL) where tL,S is the one of t1 and t2 with larger (smaller) imaginary  part.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The only difference is that here we will consider the effective modes with one  time argument.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' In other words, there is no ¯t argument.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  For this model, we can simply substitute φi(¯t, t) in Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='2 with  φi(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) = ϕi(t)  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='20)  In particular, the KMS symmetry (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='26)-(2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='27) reduces to  �  ˆT ϕ1(t)ϕi(t′)  �  =  �  ˆT ϕ2(t)ϕi(t′)  �  =  �  ˆT ϕ1(t + 2πi)ϕi(t′)  �  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='21)  This means that the two effective modes ϕi(t) are completely degenerate to a single  effective mode ϕ(t) in a thermal state with inverse temperature 2π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' It reduces to the  case in [8, 9] which is inevitably restricted to the maximal chaos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  B  Unitary and dynamical KMS conditions  The periodicity (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='45) along imaginary time direction can be understood as ηs,p in a  thermal state with imaginary chemical potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Let as define the charge carried by  ηs,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) as Q = p, namely  [Q, ηs,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t)] = pηs,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t)  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1)  It follows that the state consistent with the KMS condition (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='44) is  ρ = ˆSe−2πiQ/3e−πH  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='2)  where ˆS is the operator that takes the s value of ηs,p, namely  ˆSηs,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) ˆS−1 = sηs,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t)  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='3)  For the state given by (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='2), the time reversal transformation T of ρ is given by  TρT−1 = ˆSe2πiQ/3e−πH/Z∗ = ρ†  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='4)  where we assumed time reversal invariance of ˆS, Q and H (and also hermicity of ˆS  and Q).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The time reversal transformation T of ηs,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) is defined as flipping t and ¯τ  simultaneously  Tηs,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t)T−1 = ηs,p(−¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' −t)  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='5)  – 59 –  From this definition, T2 = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' In this definition, the periodicity of ηs,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) along ¯τ  direction is consistent  Tηs,p(¯τ + π;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t)T−1 = Te2πip/3ηs,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t)T−1 = e−2πip/3ηs,p(−¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' −t) = ηs,p(−(¯τ + π);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' −t)  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='6)  Let us consider the generating functional on the Keldysh contour  eW[J(1)  s,p,J(2)  s,p] = Tr  �  ρ  �  ˜Te−i  ´  J(2)  s,−pη(2)  s,p  � �  Tei  ´  J(1)  s,−pη(1)  s,p  ��  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='7)  where T is time ordering and ˜T is inverse time ordering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Let us define another gener-  ating functional with ρ†  e  ¯  W[J(1)  s,p,J(2)  s,p] = Tr  �  ρ† �  ˜Te−i  ´  J(2)  s,−pη(2)  s,p  � �  Tei  ´  J(1)  s,−pη(1)  s,p  ��  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='8)  Suppose the generating functional can be represented by the path integral of effective  field theory  eW[J(1)  s,p,J(2)  s,p] =  ˆ  Dη(1)  s,pDη(2)  s,peiI[J(1)  s,p,η(1)  s,p;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='J(2)  s,p,η(2)  s,p]  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='9)  Similar formula applies to ¯W with I replaced with ¯I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The unitary and dynamical KMS  conditions are as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Taking two sources J(1) and J(2) identical leads to vanishing W and ¯W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' To satisfy  this condition, we impose  I[Js,p, ηs,p;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Js,p, ηs,p] = ¯I[Js,p, ηs,p;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Js,p, ηs,p] = 0  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='10)  Turning off the sources, the effective action for ηa,r  s,p in Keldysh formalism needs  to obey  S[ηr  s,p, ηa  s,p = 0] = ¯S[ηr  s,p, ηa  s,p = 0] = 0  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='11)  This means that the effective action does not have Kr···rηr · · · ηr term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' In other  words, each term in the action must contain at least one ηa  s,p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Taking complex conjugate of (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='7), assuming J∗  s,p = Js,−p, it is clear that  W[J(1)  s,p , J(2)  s,p ]∗ = ¯W[J(2)  s,p , J(1)  s,p ]  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='12)  To guarantee this condition, we need to impose  I[J(1)  s,p , η(1)  s,p;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' J(2)  s,p , η(2)  s,p]∗ = −¯I[J(2)  s,p , η(2)  s,p;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' J(1)  s,p , η(1)  s,p]  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='13)  which written in terms of effective action without source is  S[ηr  s,p, ηa  s,p]∗ = − ¯S[ηr  s,p, −ηa  s,p]  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='14)  – 60 –  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Under time reversal transformation, the generating functional W becomes  eW[J(1)  s,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='t),J(2)  s,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='t)] = Tr  �  ρ† �  Tei  ´  J(2)∗  s,−p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='t)η(2)  s,p(−¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='−t)� �  ˜Te−i  ´  J(1)∗  s,−p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='t)η(1)  s,p(−¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='−t)��∗  = Tr  �  ρ  �  Tei  ´  J(1)  s,−p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='t)η(1)  s,−p(−¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='−t)� �  ˜Te−i  ´  J(2)  s,−p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='t)η(2)  s,−p(−¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='−t)��  = Tr  ��  Tei  ´  J(1)  s,−p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='t)η(1)  s,−p(−¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='−t−iπ)se2πip/3�  ρ  �  ˜Te−i  ´  J(2)  s,−p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='t)η(2)  s,−p(−¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='−t)��  = Tr  �  ρ  �  ˜Te−i  ´  J(2)  s,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='t)η(2)  s,p(−¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='−t)� �  Tei  ´  J(1)  s,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='t)η(1)  s,p(−¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='−t−iπ)se−2πip/3��  = eW[se2πip/3J(1)  s,−p(−¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='−t−iπ),J(2)  s,−p(−¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='−t)]  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='15)  where J∗  s,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) is the complex conjugate source of Js,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Applying (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='15)  twice maps back to original W[J(1)  s,p (¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t), J(2)  s,p (¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Define the notation  ˜J(1)  s,p (¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) = se2πip/3J(1)  s,−p(−¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' −t − iπ),  ˜J(2)  s,p (¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) = J(2)  s,−p(−¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' −t)  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='16)  ˜η(1)  s,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) = se2πip/3η(1)  s,−p(−¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' −t − iπ),  ˜η(2)  s,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) = η(2)  s,−p(−¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' −t)  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='17)  and (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='15) can be written as  W[J(1)  s,p , J(2)  s,p ] = W[ ˜J(1)  s,p , ˜J(2)  s,p ]  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='18)  In terms of a-r fields, we can rewrite (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='17) as  ˜ηa  s,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) = Dp  +ηa  s,−p(−¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' −t) − 2Dp  −ηr  s,−p(−¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' −t)  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='19)  ˜ηr  s,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) = Dp  +ηr  s,−p(−¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' −t) − 1  2Dp  −ηa  s,−p(−¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' −t)  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='20)  where we defined two operators  Dp  ± = 1  2(1 ± se2πip/3eiπ∂t)  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='21)  Taking (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='18) into (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='9), we can derive the dynamical KMS condition  I[J(1)  s,p , η(1)  s,p;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' J(2)  s,p , η(2)  s,p] = I[ ˜J(1)  s,p , ˜η(1)  s,p;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' ˜J(2)  s,p , ˜η(2)  s,p]  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='22)  Turning off the sources, the effective action for ηa,r  s,p in Keldysh formalism needs  to obey  S[ηr  s,p, ηa  s,p] = S[˜ηr  s,p, ˜ηa  s,p]  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='23)  For ¯W, the time reversal symmetry just changes the factor e2πip/3 to e−2πip/3 in  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='15).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' This leads to a slightly different dynamical KMS condition  ¯I[J(1)  s,p , η(1)  s,p;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' J(2)  s,p , η(2)  s,p] = ¯I[ ¯J(1)  s,p , ¯η(1)  s,p;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' ¯J(2)  s,p , ¯η(2)  s,p]  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='24)  – 61 –  where ¯Js,p and ¯ηs,p are the same as (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='16) and (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='17) except replacing e2πip/3 with  e−2πip/3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Turning off the sources, the effective action obeys  ¯S[ηr  s,p, ηa  s,p] = ¯S[¯ηr  s,p, ¯ηa  s,p]  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='25)  where  ¯ηa  s,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) = D−p  + ηa  s,−p(−¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' −t) − 2D−p  − ηr  s,−p(−¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' −t)  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='26)  ¯ηr  s,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) = D−p  + ηr  s,−p(−¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' −t) − 1  2D−p  − ηa  s,−p(−¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' −t)  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='27)  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The imaginary part of both I and ¯I needs to be nonnegative to guarantee con-  vergent of path integral.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Turning off the sources, the effective actions should  obey  ℑS[ηr  s,p, ηa  s,p] ≥ 0,  ℑ ¯S[ηr  s,p, ηa  s,p] ≥ 0  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='28)  These four unitary and KMS conditions need to be consistent with each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  First, we should check if the dynamical KMS conditions (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='23) and (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='25) are consistent  with (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='14).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Using (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='25) and (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='14), we can write down a new KMS-type symmetry  for S  S[ηr  s,p, −ηa  s,p] = − ¯S[ηr  s,p, ηa  s,p]∗ = − ¯S[¯ηr  s,p, ¯ηa  s,p]∗ = S[¯ηr  s,p, −¯ηa  s,p]  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='29)  Combine with (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='23), we have one more condition  S[ηr  s,p, ηa  s,p] = S[se2πip/3eiπ∂tηr  s,p, se2πip/3eiπ∂tηa  s,p]  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='30)  which holds for any local, time t translational invariant and (both ˆS and Q) charge  conserved action S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' In other words, each term in the action should be in the form of  ˆ  Kα1···αk  s1,p1,··· ,sk,pk(∂¯τ, ∂t)ηα1  s1,p1(¯τ, t) · · · ηαk  sk,pk(¯τ, t),  (α1, · · · αk ∈ {a, r})  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='31)  with �k  i=1 si = 1 and �k  i=1 pi = 3Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  The second case we need to check is the consistency between (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='14) and (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='28).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' It  is easy to see that they together lead to another inequality to S  ℑS[ηr  s,p, −ηa  s,p] = −ℑ ¯S[ηr  s,p, ηa  s,p]∗ = ℑ ¯S[ηr  s,p, ηa  s,p] ≥ 0  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='32)  Given each term in the effective action in the form of (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='31), this inequality together  with (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='28) leads to further constraint to the terms with odd numbers of ηa  s,p, namely  Kα1···αk  s1,p1,··· ,sk,pk(∂¯τ, ∂t) =  �  Kα1···αk  s1,−p1,··· ,sk,−pk(∂¯τ, ∂t)  �∗  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='33)  – 62 –  for α1, · · · , αk contain odd numbers of a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Let us focus on the quadratic action, it is given by (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='60), which is copied here  S[ηr  s,p, ηa  s,p] =  �  s,p  ˆ π  0  d¯τ  ˆ ∞  −∞  dt  �  ηa  s,−pKar  s,p(∂¯τ, ∂t)ηr  s,p + 1  2ηa  s,−pKaa  s,p(∂¯τ, ∂t)ηa  s,p  �  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='34)  where no pure ηr term due to (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='11).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' By definition, we have  Kaa  s,p(∂¯τ, ∂t) = Kaa  s,−p(−∂¯τ, −∂t)  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='35)  By (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='33) and (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='28), we have  Kar  s,p(∂¯τ, ∂t) = Kar  s,−p(∂¯τ, ∂t)∗,  ℑ  �  s,p  ηa  s,−pKaa  s,p(∂¯τ, ∂t)ηa  s,p ≥ 0  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='36)  To solve the dynamical KMS condition, taking the transformation (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='19) and (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='20)  into RHS of (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='23), we will generally have all types aa, ar and rr terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Requiring  these three terms all match with LHS leads to a single condition  Kar  s,p(∂¯τ, ∂t) − Kar  s,−p(−∂¯τ, −∂t) = −2is (tan π(p/3 + ∂t/2))s Kaa  s,p(∂¯τ, ∂t)  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='37)  In non-dissipation case, we have Kaa = 0, which implies  Kar  s,p(∂¯τ, ∂t) = Kar  s,−p(−∂¯τ, −∂t) = Ks,p(−∂¯τ, −∂t)∗  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='38)  Taking this back to (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='34), one can easily see that S[ηr  s,p, ηa  s,p] factorizes as  S[ηr  s,p, ηa  s,p] = Sf[η(1)  s,p] − Sf[η(2)  s,p]  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='39)  where  Sf[ηs,p] = 1  2  �  s,p  ˆ π  0  d¯τ  ˆ ∞  −∞  dtηs,−pKar  s,p(∂¯τ, ∂t)ηs,p  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='40)  is a real action.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  C  Generalization to polynomial-exponential case  The differential operator Ks,p(i∂t) can be generalized to contain higher powers of ∂2  t −λ2,  which would lead to polynomial-exponential behaviors tke±λt in correlation functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  However, it turns out that most of these polynomial-exponential terms are excluded by  the self-consistency condition (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='76): there are two cases ℑ¯tW < ℑ¯tV and ℑ¯tW > ℑ¯tV  in the TOC G4, which must smoothly match each other at ℑ¯tW = ℑ¯tV .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  – 63 –  If we only have pure exponential terms, it is automatically compatible with this  condition because G4 does not grow exponentially in both cases due to Grr  + = 0 (up to  non-exponential terms) as explained in Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' However, as we show in this section  that this matching condition of G4 becomes nontrivial when we include polynomial-  exponential terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' It turns out that only pure exponential and linear-exponential terms  are allowed in correlation functions, which implies that Ks,p(i∂t) can at most contain  quadratic ∂2  t − λ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Furthermore, we will solve the most general Wightman functions of  effective modes that obey all three constraints (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='56), (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='76) and (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='79).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1  Wightman functions  It is convenient to work directly with Wightman functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Let us assume for p = 0, ±  that  G>  s,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) =  �  hs,p(t)  ¯τ ∈ [0, π]  e−2πip/3hs,p(t)  ¯τ ∈ [−π, 0]  (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1)  where each hs,p(t) contains polynomial-exponential pieces  hs,p(t) =  n  �  k=0  γk  s,ptkeλt + sγk  s,−p(−t − iπ)ke−λ(t+iπ) = shs,−p(−t − iπ)  (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='2)  where n is finite number and the coefficient choice manifests KMS condition (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='48).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' It  follows that  Gra  s,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) = θ(t)  �  ∆s,p(t)  ¯τ ∈ [0, π]  e−2πip/3∆s,p(t)  ¯τ ∈ [−π, 0]  (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='3)  with  ∆s,p(t) = hs,p(t) − e2πip/3hs,−p(−t)  (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='4)  The smoothness condition (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='56) can be written in this case as  ∆+,±(t) − ∆−,±(t) = −e±πi/3(∆+,0(t) − ∆−,0(t))  (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='5)  Let us explicitly implement the requirement that G4 is smoothly defined at ℑ¯tW =  ℑ¯tV .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' For ℑ¯tW < ℑ¯tV , G4 is given by (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='108).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' For ℑ¯tW > ℑ¯tV , G4 is given by flipping  the sign of the first argument of G>  s,p, namely  G4 − gWgV =1  2  �  s,p  Lt1 ˜Lt3  �  gWgV G>  s,p(−;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t31)  �  + e2πip/3Lt2 ˜Lt3  �  gWgV G>  s,p(−;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t32)  �  + e2πip/3Lt1 ˜Lt4  �  gWgV G>  s,p(+;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t14)  �  + Lt2 ˜Lt4  �  gWgV G>  s,p(+;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t24)  �  (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='6)  – 64 –  The reason that Grr  + = 0 leads to G4 = 0 in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='108) is that the shift symmetry  of vertex (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='82) transforms the four pure exponential terms in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='108) to just one  exponential function of t2 and t4 in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='109).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' However, for polynomial-exponential terms,  we do not have an extended symmetry transforming, say, tk  1eλt1 to tk  2eλt2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Therefore,  to make sure (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='108) matches with (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='6) at ℑ¯tW = ℑ¯tV for the quadratic and higher  polynomial-exponential pieces, we must require the four terms in both (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='108) and  (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='6) match with each other separately  �  s,p  hs,p(t) ≃  �  s,p  e−2πip/3hs,p(t) ≃  �  s,p  e2πip/3hs,p(t)  (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='7)  where “≃” means that the equation hold for tke±λt terms with k > 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The k = 1 case  is a little bit different and will be discussed later.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' It follows that  �  s  hs,p(t) ≃ 0,  p = ±  (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='8)  where there is no constraint to p = 0 piece simply because G>  s,0(t) is independent on ¯τ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Using ansatz (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='2), we can easily show order by order from (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='8) for p = ± that  γk  s,± = 0,  k = 2, · · · , n  (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='9)  Then by Grr  + = 0 (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='93), we have  h+,0(t) + h+,0(−t) ≃ 0 =⇒ γk  +,0 = 0,  k = 2, · · · , n  (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='10)  On the other hand, using (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1), (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='4), (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='5) and (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='10) that  h−,0(t) − h−,0(−t) ≃ 0 =⇒ γk  −,0 = 0,  k = 2, · · · , n  (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='11)  In this way, the consistency conditions and shift symmetry kill all quadratic and higher  polynomial-exponential terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  For the linear-exponential term, the shift symmetry of vertex (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='82) does help a  bit because, for example,  Lt1[gW(t1 − t2)e±λ(t1+iπ)] = Lt1[gWt1e±λ(t1+iπ)] − t2Lt2[gWe±λt2]  (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='12)  However, this is still not enough to save nontrivial linear-exponential term in hs,±(t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  After some algebra, matching the linear-exponential pieces in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='108) and (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='6) leads  to  γ1  +,+ = γ1  +,− = 0,  γ1  −,+ = cos(π(λ/2 + 1/3))  cos(π(λ/2 − 1/3))γ1  −,−  (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='13)  – 65 –  Taking this into (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='93) leads to γ1  +,0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Using (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='5), we can solve  γ1  −,± = −  cos(πλ/2)  cos π(λ/2 ∓ 1/3)γ1  −,0  (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='14)  In particular, we should have γ1  −,0 = γ1  −,+ = 0 and γ1  −,− ̸= 0 when λ = 1/3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Taking  these solutions to G4, one can see that no linear-exponential term survives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  With the existence of linear-exponential growth term, the constraint to the pure  exponential term is slightly different.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Comparing the pure exponential piece in (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='2)  and (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='112), we should identify  As,p = γ0  s,p,  Bs,p = s(γ0  s,−p − iπγ1  s,−p)e−iλπ  (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='15)  Taking this into (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='93) and (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='5) leads to  γ0  +,± = −  cos (πλ/2)  cos π(λ/2 ∓ 1/3)γ0  +,0  (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='16)  γ0  −,± = −  cos (πλ/2)  cos π(λ/2 ∓ 1/3)γ0  −,0 ±  √  3(2iγ0  +,0 + πγ1  −,0)  4 cos2 π(λ/2 ∓ 1/3)  (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='17)  Taking these solutions into (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='110) and (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='111), we will find both C1 and C2 vanish.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  One can also check (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='6) vanishes as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' This confirms the result in Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='8 that  Grr  + = 0 and smoothness condition (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='5) imply vanishing pure exponential terms in  TOC for both ordering of ℑ¯tW,V .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  In conclusion, the consistency conditions require h+,p(t) only contain pure exponen-  tial terms and h−,p(t) only contain up to linear-exponential terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' With the expression  (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='2), there are only three independent parameters γ0  +,0, γ0  −,0 and γ1  −,0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Other parame-  ters are determined by the following relation  γ0  +,p = (−)p  cos (πλ/2)  cos π(λ/2 − p/3)γ0  +,0  (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='18)  γ0  −,p = (−)p  cos (πλ/2)  cos π(λ/2 − p/3)γ0  −,0 + p  √  3(2iγ0  +,0 + πγ1  −,0)  4 cos2 π(λ/2 − p/3)  (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='19)  γ1  −,p = (−)p  cos(πλ/2)  cos π(λ/2 − p/3)γ1  −,0  (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='20)  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='2  The effective action  The above most general consistent Wightman functions correspond to the effective  actions in the form of (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='69) with  K+,p(i∂t) = (∂2  t − λ2)k+,p(i∂t),  K−,p(i∂t) = (∂2  t − λ2)2k−,p(i∂t)  (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='21)  – 66 –  where one should note that K−,p(x) has a double zero at ±iλ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' By symmetry (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='68), we  have ks,p(x) = (−)pks,−p(−x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Since K+,p is linear in ∂2  t − λ2, the computation (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='93)  for Grr  + = 0 up to non-exponential terms still hold and leads to the same condition  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='94):  k+,±(iλ) = ∓ik+,0(iλ)  √  3  tan  �π  2 (λ ± 1/3)  �  tan πλ  2  (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='22)  The smoothness condition (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='77) at ω = iλ leads to  k−,±(iλ) = ±ik−,0(iλ)  √  3  (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='23)  k′  −,±(iλ) = ±  √  3  3  �  2λk−,0(iλ)2  k+,0(iλ)  �  1 +  1  tan  � π  2(λ ± 1/3)  �  tan πλ  2  �  + ik′  −,0(iλ)  �  (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='24)  which allows three undetermined parameters k+,0(iλ), k−,0(iλ) and k′  −,0(iλ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  From  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='74) and (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='75), we have  ∆+,0(t) =  i  2λk+,0(iλ)(eλt − e−λt)  (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='25)  ∆+,±(t) = ± e±iπ/3  2  √  3λ  �  eλt  k+,±(iλ) +  e−λt  k+,∓(iλ)  �  (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='26)  ∆−,0(t) =λk′  −,0(iλ) − ik−,0(iλ)  4λ3k−,0(iλ)2  (eλt − e−λt) +  i  4λ2k−,0(iλ)t(eλt + e−λt)  (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='27)  ∆−,±(t) = ± e±iπ/3  4  √  3λ2  �λk′  −,±(iλ) − ik−,±(iλ)  iλk−,±(iλ)2  eλt + λk′  −,∓(iλ) − ik−,∓(iλ)  iλk−,∓(iλ)2  e−λt  +t  �  eλt  k−,±(iλ) −  e−λt  k−,∓(iλ)  ��  (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='28)  where we see linear-exponential terms appear because of the double poles in 1/K−,p(ω)  at ω = ±iλ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Take ansatz (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='2) with n = 0 for s = + and n = 1 for s = −.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Using (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='4) and  comparing with (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='25)-(C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='28), we find  γ0  +,0 =  1  2iλ(e−iπλ − 1)k+,0(iλ)  (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='29)  γ1  −,0 =  i  4λ2(e−iπλ + 1)k−,0(iλ)  (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='30)  γ0  −,0 =  �  1 + eiπλ�  λk′  −,0(iλ) − i  �  1 + eiπλ − iπλ  �  k−,0(iλ)  16λ3 cos2 πλ  2 k−,0(iλ)2  (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='31)  – 67 –  and other γk  s,p are given by (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='18)-(C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='20).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' By the conclusion from last subsection, this  implies that the action with (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='21) and three constraints (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='22)-(C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='24) lead to absence  of exponential terms in TOC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Using (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='25)-(C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='28) and the first line of (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='107), we find that  ∆(t) =  3  4λ(1/2 − cos πλ) sin πλ  2 k+,0(iλ)(eiπλ/2eλt + e−iπλ/2e−λt)  (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='32)  which exactly matches with (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='107).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' This means that for any four-point functions,  k−,0(iλ) and k′  −,0(iλ) are irrelevant parameters in the action.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' What we discussed in  Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='8 with pure exponential case is indeed the most general situation for four-  point functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  D  Correlation functions of effective modes in the large q SYK  model  In this appendix, we first ignore the prefector N/(8q2) in the action (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='14).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' In the end,  this prefactor simply adds a 8/(N∆2) factor to any two-point function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1  Canonical quantization trick  As explained in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='3, we will take the mathematical trick of canonical quan-  tization to solve the Euclidean two-point function of ϵ(¯τ, x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' First, we need to solve  the equations of motion Lgm(¯τ, x) = 0 for wave function gm(¯τ, x) with UV condition  gm(¯τ, 0) = gm(¯τ, 2π) = 0 from (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='13) and expand the quantized field ˆϵ(¯τ, x) in terms of  ˆϵ(¯τ, x) =  �  m  gmˆam + g∗  mˆa†  m  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1)  where ˆam and ˆa†  m are annihilation and creation operators obeying canonical commu-  tation relation [ˆam, ˆa†  m′] = δm,m′, and gm is well-normalized under Klein-Gordon inner  product, which is defined in (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='30).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Note that the quantum number m must be discrete  because the spatial direction x is finite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Due to translation symmetry in ¯τ, we can  choose the positive energy wave function  gm(¯τ, x) ∝ e−im¯τ,  m ≥ 0  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='2)  for which the Hamiltonian H has eigen value m and  [H, ˆa†  m] = mˆa†  m,  [H, ˆam] = −mˆam  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='3)  – 68 –  Since gm(¯τ, x) is on-shell, following from (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='22) it can be expanded as  gm(¯τ, x) =  1  ∆G0(τ12)  �  i=1,2  LτiG0(τ12)χi,m(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' τi)  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='4)  where ¯τ in χi,m(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' τi) is just a dummy argument whose dependence is trivial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' It follows  that we can rewrite (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1) as  ˆϵ(¯τ, x) =  1  ∆G0(x)  �  i=1,2  LτiG0(x)ˆχi(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' τi)  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='5)  ˆχi(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' τi) ≡  �  m  χi,m(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' τi)ˆam + χ∗  i,m(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' τi)ˆa†  m  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='6)  where Lτ is defined in (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='25).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' By the fundamental domain Dϵ, the defining domain for  ˆχ1(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' τ) is {¯τ ∈ [0, π], τ − ¯τ ∈ [0, π]} and that for ˆχ2(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' τ) is {¯τ ∈ [0, π], τ − ¯τ ∈ [−π, 0]}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Note that the path integral is defined on the finite spacetime Dϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' To compute any  correlation function of quantized field ˆϵ on Dϵ, we must first specify the states on time  slice ¯τ = 0, π respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' This is dictated by the boundary condition of ϵ(¯τ, x) in  the Euclidean path integral on Dϵ at ¯τ = 0, π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' From the first equation of (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='13), we  see that any configurations of ϵ(0, x) is identified with ϵ(π, 2π − x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' For our canonical  quantization trick, this implies that we need to trace over all states at ¯τ = 0, π with a  reflection x → 2π − x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' More explicitly, we consider the following Wightman function  W(¯τ, x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' ¯τ ′, x′) ≡ 1  Z Tr  �  Pe−iπHˆϵ(¯τ, x)ˆϵ(¯τ ′, x′)  �  ,  Z ≡ Tr  �  Pe−iπH�  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='7)  where the time evolution for ¯τ = π is present and P is the reflection operator  Pˆϵ(¯τ, x)P −1 = ˆϵ(¯τ, 2π − x)  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='8)  Therefore, we will define the expectation ⟨· · · ⟩c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' as  ⟨· · · ⟩c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' ≡ 1  Z Tr  �  Pe−iπH · · ·  �  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='9)  Expanding in ˆam and ˆa†  m, we have  W(¯τ, x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' ¯τ ′, x′) =  �  m  1  Nm  �  gm(¯τ, x)g∗  m(¯τ ′, x′)  �  ˆamˆa†  m  �  c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  +g∗  m(¯τ, x)gm(¯τ ′, x′)  �  ˆa†  mˆam  �  c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  �  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='10)  Since the Euclidean two-point function ⟨ϵ(¯τ, x)ϵ(¯τ ′, x′)⟩ is symmetric under exchange  of ¯τ, x with ¯τ ′, x′, this corresponds to the Feynman propagator of ˆϵ(¯τ, x), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  ⟨ϵ(¯τ, x)ϵ(¯τ ′, x′)⟩ = −i  � ¯T ˆϵ(¯τ, x)ˆϵ(¯τ ′, x′)  �  c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='11)  – 69 –  = −i[θ(¯τ − ¯τ ′)W(¯τ, x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' ¯τ ′, x′) + θ(¯τ ′ − ¯τ)W(¯τ ′, x′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' ¯τ, x)]  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='12)  where ¯T is the time ordering of ¯τ and ¯τ − ¯τ ′ is restricted to [−π, π].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' We emphasize that  the LHS of (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='11) is a Euclidean two-point function and the RHS of (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='11) is just a  mathematical trick to compute it in terms of a Feynman propagator of quantized field  ˆϵ by regarding ¯τ as “time”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The quantized field ˆϵ and the corresponding Hilbert space  are part of the trick and have no physical meaning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  On the domain Dϵ, taking above equations into (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='11) leads to  Fψ(τ1,τ2, τ3, τ4) = G0(τ12)G0(τ34)  +  �  i,j=1,2  LτiLτj+2  �  G0(τ12)G0(τ34)  �  −i  � ¯T ˆχi(¯τa;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' τi)ˆχj(¯τb;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' τj+2)  �  c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  ��  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='13)  where one should note that the dummy argument ¯τ plays a role in the time ordering  ¯T though its explicit dependence in (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='4) is trivial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Given (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='5), it is noteworthy that  the reflection (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='8) acts nontrivially on ˆχi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The transformation (¯τ, x) → (¯τ, 2π − x) is  equivalent to (τ1, τ2) → (τ2 + π, τ1 − π), which implies  P ˆχ1(¯τ, τ)P −1 = ˆχ2(¯τ, τ − π),  P ˆχ2(¯τ, τ)P −1 = ˆχ1(¯τ, τ + π)  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='14)  Taking this back to (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='13) and using definition (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='9), we have the following KMS  conditions  � ¯T ˆχ1(0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' τ)ˆχj(¯τ ′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' τ ′)  �  c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' =  � ¯T ˆχ2(π;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' τ)ˆχj(¯τ ′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' τ ′)  �  c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='15)  � ¯T ˆχ2(0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' −τ)ˆχj(¯τ ′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' τ ′)  �  c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' =  � ¯T ˆχ1(π;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' 2π − τ)ˆχj(¯τ ′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' τ ′)  �  c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='16)  where τ ∈ [0, π] by the defining domain of ˆχi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  It is very interesting that the Euclidean four-point function (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='13) now has the  same structure as (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='23).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Therefore, we would like to define the Euclidean two-point  function of two effective fields φE  1,2(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' τ) such that  �  φE  i (¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' τ)φE  j (¯τ ′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' τ ′)  �  ≡ −i  � ¯T ˆχi(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' τ)ˆχj(¯τ ′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' τ ′)  �  c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='17)  Take this definition into (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='13) and analytically continue ¯τk → itk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Comparing with  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='23), we will identify the Euclidean fields φE  i as φi after analytic continuation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' In  particular, the two KMS conditions (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='15) and (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='16) in terms of φE  i are equivalent to  the KMS conditions of φi (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='26)-(2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='27).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='2  Solve discrete quantum numbers  From the general solution (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='22) to Lϵ = 0, let us expand χi in Fourier modes  χ1(τ) =  �  m  Ame−imτ,  χ2(τ) =  �  m  Bme−imτ  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='18)  – 70 –  The UV condition (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='13) for τ1 = τ2 (x = 0) leads to  − λ(Am − Bm) tan λπ  2 − im(Am + Bm) = 0  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='19)  and for τ1 = τ2 + 2π (x = 2π) leads to  λ(Ame−2miπ − Bm) tan λπ  2 − im(Ame−2miπ + Bm) = 0  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='20)  Combining these two equations, we have  Am  Bm  = λ tan λπ  2 − im  λ tan λπ  2 + im = λ tan λπ  2 + im  λ tan λπ  2 − ime2miπ  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='21)  which leads to  λ tan λπ  2 + im = ±e−πim(λ tan λπ  2 − im),  Am = ±Bmeimπ  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='22)  These two cases can be solved as two sets of positive quantum numbers m  M+ = {m > 0|λ tan λπ  2 + m cot mπ  2  = 0}  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='23)  M− = {m > λ|λ tan λπ  2 − m tan mπ  2  = 0}  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='24)  where m = λ is excluded in M− because it leads to trivial ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' This is exactly the shift  symmetry (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='23) of the ϵon−shell in (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='22).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Note that here we only choose positive m  because it is indeed the positive frequency of the canonical quantization in (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='29).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  It follows that in (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='4) we can take  χ1,m(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' τ) = Ame−imτ,  χ2,m(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' τ) = Bme−imτ,  m ∈ M±  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='25)  For convenience, we will add a superscipt “±” to distinguish the two types of solutions  with m ∈ M± respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Let us take  A+  m = B+  meimπ = i eimπ/2  2λ  �  N +  m  ,  A−  m = −B−  meimπ =  eimπ/2  2λ  �  N −  m  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='26)  which leads to wave functions  g+  m(¯τ, x) = e−im¯τ  �  N +  m  �m  λ cos m  2 (π − x) + sin m  2 (π − x) tan λ  2(π − x)  �  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='27)  g−  m(¯τ, x) = e−im¯τ  �  N −  m  �m  λ sin m  2 (π − x) − cos m  2 (π − x) tan λ  2(π − x)  �  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='28)  – 71 –  where g±  m is even/odd under x → 2π − x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Taking these solutions into Klein-Gordon  inner product (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='30) leads to  N ±  m = (m − λ)(m + λ)(mπ ∓ sin mπ)/λ2  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='29)  It follows from (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='6) that  ˆχ1(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' τ) =  �  s=±  �  m∈Ms  As  me−imτˆas  m + As∗  meimτˆas†  m  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='30)  ˆχ2(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' τ) =  �  s=±  �  m∈Ms  Bs  me−imτˆas  m + Bs∗  meimτˆas†  m  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='31)  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='3  Correlations  To compute the correlation functions, we need to first evaluate the expectation value  of ˆas  mˆas†  m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Taking (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='30) and (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='31) into the conditions (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='15) and (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='16) leads to  �  ˆas  mˆas†  m  �  c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' = seimπ �  ˆas†  mˆas  m  �  c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='32)  By canonical quantization, we have [ˆas  m, ˆas†  m] = 1, which yields15  �  ˆas  mˆas†  m  �  c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' =  1  1 − se−imπ ,  �  ˆas†  mˆas  m  �  c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' =  se−imπ  1 − se−imπ  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='33)  In the following, we will compute the correlations by summing over Matsubara  frequencies m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The method is the Sommerfeld-Watson transformation used in [28] and  we will only restrict ourselves to exponential pieces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Since the ¯τ dependence is only  through time ordering, in the following we will suppress the argument ¯τ in ˆχi(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' τ) in  the computation of Wightman functions with specified ordering of fields, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  ⟨ˆχ1(τ1)ˆχ1(τ2)⟩c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' ≡ ⟨ˆχ1(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' τ1)ˆχ1(0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' τ2)⟩c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (¯τ > 0)  =  �  s=±  �  m∈Ms  As  mAs∗  m  �  e−imτ12 �  as  mas†  m  �  c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' + eimτ12 �  as†  mas  m  �  c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  �  = 1  4  �  s=±  �  m∈±Ms  e−imτ12  (1 ∓ e−imπ)(m − λ)(m + λ)(mπ ∓ sin πm)  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='34)  where in the second line, we extend the sum over m to both positive and negative M±  due to the two terms in the first line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Let us compute s = ± separately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' For s = +, we insert  1  2πi  (πm − sin mπ)/(cos mπ − 1)  m cot mπ/2 + λ tan λπ/2  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='35)  15We can also derive these equations by the definition of these operators in the Fock space generated  by ˆas†  m if we add an infinitesimal negative imaginary part to all m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  – 72 –  (a)  (b)  Figure 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' (a) The contour of C+ that circles around all ±M+ (black dots) anticlockwise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  The three poles (red dots) at 0, ±λ are not circled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' (b) We can deform the contour C+ through  infinity to just three clockwise circles around 0, ±λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  into the sum and change the sum over m to anticlockwise contour integral along small  circles of m around all ±M+, which we denoted as C+ (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' 10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The denominator  of (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='35) pickes out the residue at these points and the numerator is the reciprocal of  residues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Our purpose is to deform the contour to small circles around 0, ±λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' However,  the extra 1/(cos mπ − 1) gives additional unwanted poles at even integers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' To replace  it with an equivalent expression, we use (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='22) to write  1  cos mπ − 1 = (λ tan λπ/2)2 + m2  −2m2  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='36)  at all m ∈ ±M+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Putting them all together, we have  ⟨ˆχ1(τ1)ˆχ1(τ2)⟩+  c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' = −1  4  ‰  C+  dm  2πi  e−imτ12((λ tan λπ/2)2 + m2)  2m2(1 − e−imπ)(m − λ)(m + λ)(m cot mπ/2 + λ tan λπ/2)  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='37)  Note that though 1 − e−imπ = 0 for even m, they are not poles because m cot mπ/2 is  also divergent for even m and cancels it out.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' For τ12 ∈ (0, π), the integral over infinite  arc on upper and lower half planes are both zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Then the integral reduces to residues  at 0, ±λ  ⟨ˆχ1(τ1)ˆχ1(τ2)⟩+  c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' = 1  4Res0,±λ  �  e−imτ12((λ tan λπ/2)2 + m2)  2m2(1 − e−imπ)(m − λ)(m + λ)(m cot mπ/2 + λ tan λπ/2)  �  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='38)  If τ12 ∈ (−π, 0), we need simply multiply both numerator and denominator of (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='37)  by e−imπ and replace the e−imπ in denominator by (λ tan λπ/2+im)/(λ tan λπ/2−im)  due to (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='22).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' This leads to  ⟨ˆχ1(τ1)ˆχ1(τ2)⟩+  c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' = −1  4  ‰  C+  dm  2πi  e−im(τ12+π)(λ tan λπ/2 − im)2  2m2(1 − e−imπ)(m − λ)(m + λ)(m cot mπ/2 + λ tan λπ/2)  – 73 –  = 1  4Res0,±λ  �  e−im(τ12+π)(λ tan λπ/2 − im)2  2m2(1 − e−imπ)(m − λ)(m + λ)(m cot mπ/2 + λ tan λπ/2)  �  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='39)  If τ12 ∈ (π, 2π), we will multiply both numerator and denominator of (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='37) by eimπ  and replace the eimπ in denominator by (λ tan λπ/2 − im)/(λ tan λπ/2 + im) instead.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  This leads to  ⟨ˆχ1(τ1)ˆχ1(τ2)⟩+  c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' = 1  4Res0,±λ  �  e−im(τ12−π)(λ tan λπ/2 + im)2  2m2(1 − e−imπ)(m − λ)(m + λ)(m cot mπ/2 + λ tan λπ/2)  �  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='40)  Similarly, for s = −, we need to consider the contour C− that circles around all  points in M−, and insert  1  2πi  (πm + sin mπ)/(cos mπ + 1)  m tan mπ/2 − λ tan λπ/2  ≃  1  2πi  (πm + sin mπ)((λ tan λπ/2)2 + m2)/(2m2)  m tan mπ/2 − λ tan λπ/2  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='41)  where “≃” means equal at the poles M− by (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='36).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Following a similar computation,  this leads to  ⟨ˆχ1(τ1)ˆχ1(τ2)⟩−  c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' = −1  4Res0,±λ  �  e−imτ12((λ tan λπ/2)2 + m2)  2m2(1 + e−imπ)(m − λ)(m + λ)(m tan mπ/2 − λ tan λπ/2)  �  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='42)  for τ12 ∈ (0, π), and  ⟨ˆχ1(τ1)ˆχ1(τ2)⟩−  c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' = 1  4Res0,±λ  �  e−im(τ12+π)(λ tan λπ/2 − im)2  2m2(1 + e−imπ)(m − λ)(m + λ)(m tan mπ/2 − λ tan λπ/2)  �  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='43)  for τ12 ∈ (−π, 0), and  ⟨ˆχ1(τ1)ˆχ1(τ2)⟩−  c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' = 1  4Res0,±λ  �  e−im(τ12−π)(λ tan λπ/2 + im)2  2m2(1 + e−imπ)(m − λ)(m + λ)(m tan mπ/2 − λ tan λπ/2)  �  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='44)  for τ12 ∈ (π, 2π).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Note that ˆχ2 is not completely independent from ˆχ1 due to (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='26), above formula  indeed covers all correlations between ˆχ1 and ˆχ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Explicitly, with translation symmetry  we have  ⟨ˆχ1(τ)ˆχ1(0)⟩c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' = ⟨ˆχ2(τ)ˆχ2(0)⟩c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' = ⟨ˆχ1(τ)ˆχ1(0)⟩+  c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' + ⟨ˆχ1(τ)ˆχ1(0)⟩−  c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='45)  ⟨ˆχ1(τ)ˆχ2(0)⟩c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' = ⟨ˆχ1(τ − π)ˆχ1(0)⟩+  c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' − ⟨ˆχ1(τ − π)ˆχ1(0)⟩−  c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='46)  ⟨ˆχ2(τ)ˆχ1(0)⟩c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' = ⟨ˆχ1(τ + π)ˆχ1(0)⟩+  c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' − ⟨ˆχ1(τ + π)ˆχ1(0)⟩−  c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='47)  – 74 –  Evaluation of residues is straightforward and leads to  ⟨ˆχ1(τ)ˆχ1(0)⟩c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' = ⟨ˆχ2(τ)ˆχ2(0)⟩c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' = ⟨ˆχ1(2π − τ)ˆχ2(0)⟩c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' = ⟨ˆχ2(−τ)ˆχ1(0)⟩c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='48)  =i ×  �  ˆm+eiλτ + ˆm1τeiλτ + c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=',  τ ∈ [0, 2π]  ˆm−eiλτ + ˆm1τeiλτ + c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=',  τ ∈ [−π, 0]  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='49)  where star means complex conjugate and  ˆm+ = i2πλ − sin 2πλ + 2(πλ + sin πλ)(2πiλ + 3 − e−iπλ)  32λ2(πλ + sin πλ)2(1 + eiπλ)  ,  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='50)  ˆm− = ˆm+ +  1  4λ2(1 + eiπλ),  ˆm1 =  1  8λ(πλ + sin πλ)(1 + eiπλ)  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='51)  As a consistent check, one can show that the correlator (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='48) obeys the KMS condition  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='15) and (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='16).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' It is noteworthy that even if the computations for even and odd  modes are different for the ranges τ ∈ [0, π] and τ ∈ [π, 2π], we still have smoothness  of ⟨ˆχ1(τ)ˆχ1(0)⟩ at τ = π in (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='49), which is consistent with item 4b of our effective  theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Using (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='17) and restoring the 8/(N∆2) factor in (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='48), we can derive the two-  point function of φE  i as  �  φE  i (¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' τ)φE  j (0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' 0)  �  = θ(¯τ)Mij(τ) + θ(−¯τ)Mji(−τ)  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='52)  M11(τ) = M22(τ) = M12(2π − τ) = M21(−τ)  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='53)  =  8  N∆2 ×  �  ˆm+eiλτ + ˆm1τeiλτ + c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=',  τ ∈ [0, 2π]  ˆm−eiλτ + ˆm1τeiλτ + c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=',  τ ∈ [−π, 0]  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='54)  where the argument ranges in (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='52) are  i = j : {(¯τ, τ)|¯τ ∈ [−π, π], ¯τ − τ ∈ [−π, π]}  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='55)  i = 1, j = 2 : {(¯τ, τ)|¯τ ∈ [−π, π], ¯τ − τ ∈ [−2π, 0]}  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='56)  i = 2, j = 1 : {(¯τ, τ)|¯τ ∈ [−π, π], ¯τ − τ ∈ [0, 2π]}  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='57)  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='4  The effective action  The effective action will be still formulated in ηs,p(¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) variables and the correlation  functions of φi will be given by (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='49) to (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='51).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Since the correlation function (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='54)  contains linear-exponential terms, the effective action needs to contain quadratic factor  of ∂2  t − λ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' It turns out that we need to take the action (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='69) with  K+,p(i∂t) = (∂2  t − λ2)k+,p(i∂t),  K−,p(i∂t) = (∂2  t − λ2)2k−,p(i∂t)  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='58)  – 75 –  where K−,p(x) has a double zero at ±iλ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  By symmetry (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='68), we have ks,p(x) =  (−)pks,−p(−x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' This effective action has been thoroughly discussed in Appendix C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  To match the correlation functions (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='52) with this EFT action, let us first com-  pute  �  ˆT φi(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t)φj(0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' 0)  �  correlation functions by (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='49)-(2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='51) with the most general  consistent Wightman functions solved in Appendix C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1, which are also results of the  action (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='58) by the analysis in Appendix C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Then we compare  �  ˆT φi(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t)φj(0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' 0)  �  with (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='52) after analytic continuation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Since these correlation functions obey the  same KMS conditions, matching one of them is sufficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' In the following, we will take  i = j = 1 and assume ℑt ∈ [−2π, 0].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  The most general consistent Wightman function in Appendix C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1 takes the form  (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1) and (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='2) where h+,p only contains pure exponential terms and h−,p only contains  up to linear-exponential terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' The coefficients γk  s,p are constrained by (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='18)-(C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='20).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  Using these solutions in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='49) we have  �  ˆT φ1(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t)φ1(0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' 0)  �  =  �  (m+ + m1t)e−λt + ( ¯m+ + ¯m1t)eλt,  ℑ¯t ∈ [−π, 0]  (m− − ¯m1t)e−λt + ( ¯m− − m1t)eλt,  ℑ¯t ∈ [0, π]  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='59)  where ℑ¯t − ℑt ∈ [0, π] and  ¯m+ = 3((γ0  −,0 + γ0  +,0)(1 − 2 cos πλ) − 2(πγ1  −,0 + 2iγ0  +,0) sin πλ)  2(1 − 2 cos πλ)2  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='60)  m+ = 3e−iπλ(2γ0  +,0 + iπγ1  −,0)  2(1 − 2 cos πλ)  − e−iπλ ¯m+  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='61)  m− = ¯m+ −  6γ0  +,0  1 − 2 cos πλ  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='62)  ¯m− = m+ − 6e−iπλγ0  +,0  1 − 2 cos πλ  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='63)  ¯m1 = eiπλm1 =  3γ1  −,0  2(1 − 2 cos πλ)  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='64)  Comparing with (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='52)-(D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='54) with analytic continuation φE  j (¯τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' τ) → φj(¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' t) = −iφE  j (i¯t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' it),  in which θ(¯τ) → θ(−ℑ¯t) and τ → it, we should identify  γ1  −,0 =  2i(2 cos πλ − 1)  3λN∆2(πλ + sin πλ)(1 + e−iπλ)  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='65)  γ0  +,0 =  1 − 2 cos πλ  3λ2N∆2(1 + e−iπλ)  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='66)  γ0  −,0 = −(πλ + 4i) sin 2πλ − (πλ + 7i)(πλ + sin πλ) + πλ(2πλ + 9i) cos πλ + iπλ cos 2πλ  3λ2N∆2 (1 + e−iπλ) (πλ + sin πλ)2  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='67)  – 76 –  Moreover, in Appendix C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='2 we show that the most general consistent Wightman  functions in Appendix C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1 can also be reproduced by the effective action (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='21).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Given  the parameter relations (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='29)-(C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='31), we can derive  k+,0(iλ) = 3λN∆2 cot πλ  2  2(1 − 2 cos πλ)  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='68)  k−,0(iλ) = 3N∆2(πλ + sin πλ)  8λ(2 cos πλ − 1)  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='69)  k′  −,0(iλ) = −3iN∆2 �  (2π2λ2 − 5) sin πλ + 2 sin 2πλ + 8πλ cos πλ − πλ  �  3πλ tan πλ  2 + 7  ��  16λ2(1 − 2 cos πλ)2  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='70)  In conclusion, the action (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='69) with (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='58) and (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='68)-(D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='70) fully captures the cor-  relation of the effective modes φE  i after analytic continuation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  E  Solve m = 1 vertex  In matrix form the equation (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='31) is  �C1  0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='0g(q) + C1  1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='0g1(q) C1  0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1g(q) + C1  1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1g1(q)  C2  0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='0g(q) + C2  1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='0g1(q) C2  0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1g(q) + C2  1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1g1(q)  �  = ξ(1)(q)  q1/2  �−λ(1 − cq) 1 + cq  λ(c − q)  c + q  �  (E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1)  Note that each entry on RHS has zero at ±c or ±1/c respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Taking q = ±c, ±1/c  on LHS, we can immediately derive  C1  1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='0 = −C1  0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='0g(1/c)  g1(1/c) ,  C1  1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1 = −C1  0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1g(−1/c)  g1(−1/c) ,  C2  1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='0 = −C2  0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='0g(c)  g1(c) ,  C2  1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1 = −C2  0,1g(−c)  g1(−c)  (E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='2)  Taking this back to (E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1), we have  −C1  0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='0  g1(1/c)g(q) − g(1/c)g1(q)  g1(1/c)λ(1 − cq)  = C1  0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1  g1(−1/c)g(q) − g(−1/c)g1(q)  g1(−1/c)(1 + cq)  = C2  0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='0  g1(c)g(q) − g(c)g1(q)  g1(c)λ(c − q)  = C2  0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1  g1(−c)g(q) − g(−c)g1(q)  g1(−c)(c + q)  = ξ(1)(q)  q1/2  (E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='3)  Using KMS symmetry gn(q) = (−)ngn(1/q), comparing the first line and the second  line of above equations lead to  ξ(1)(q)/C1  0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='0 = ξ(1)(1/q)/C2  0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='0,  ξ(1)(q)/C2  0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1 = ξ(1)(1/q)/C1  0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1  (E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='4)  – 77 –  Then we just need to solve the first line of (E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='3), which is a first order differential  equation  (C1  0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='0 + λC1  0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1) + (C1  0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='0 − λC1  0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1)cq  (C1  0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='0A + λC1  0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1B) + (C1  0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='0A − λC1  0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1B)cq = g1(q)  g(q) ,  A = g(1/c)  g1(1/c),  B = g(−1/c)  g1(−1/c)  (E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='5)  The solution of above type equation is  α + βq  γ + θq = g1(q)  g(q)  =⇒ g(q) = q−α/(γλ)(γ + θq)(αθ−βγ)/(γθλ)  (E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='6)  Requiring KMS symmetry g(q) = g(1/q) leads to  γ = θ,  β = −α,  g(q) = (q1/2 + q−1/2)−2∆,  ∆ = β/(γλ)  (E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='7)  Using this solution of g(q), we have  g(q)  g1(q) = −  1 + q  ∆λ(1 − q) =⇒ A =  1 + c  ∆λ(1 − c),  B =  1 − c  ∆λ(1 + c)  (E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='8)  Plugging this back to (E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='5) and using (E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='7), we only find one independent relation  (1 + c)C1  0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='0 + λ(1 − c)C1  0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Taking this back to (E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='2) leads to  C1  0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='0 = ∆λ(c − 1)  c + 1  ,  C1  1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='0 = 1,  C1  0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1 = ∆,  C1  1,1 =  c − 1  (c + 1)λ  (E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='9)  where we have chosen the normalization C1  1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='0 = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Taking them back to (E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1), we can  solve  ξ(1)(q) =  2∆g(q)  (1 + c)(q1/2 + q−1/2)  (E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='10)  which is explicitly KMS invariant as expected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Taking this to (E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='4) and (E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='2), we have  C2  0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='0 = ∆λ(c − 1)  c + 1  ,  C2  1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='0 = −1,  C2  0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1 = ∆,  C2  1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1 = − c − 1  (c + 1)λ  (E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='11)  One can check that this solution also obeys KMS symmetry (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  References  [1] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Shenker and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Stanford, Black holes and the butterfly effect, JHEP 03 (2014)  067 [1306.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='0622].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  [2] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Shenker and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Stanford, Multiple Shocks, JHEP 12 (2014) 046 [1312.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='3296].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  – 78 –  [3] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Roberts, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Stanford and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Susskind, Localized shocks, JHEP 03 (2015) 051  [1409.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='8180].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  [4] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Shenker and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Stanford, Stringy effects in scrambling, JHEP 05 (2015) 132  [1412.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='6087].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  [5] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Kitaev, Hidden correlations in the Hawking radiation and thermal noise, talk at  KITP (2015) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  [6] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Roberts and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Stanford, Two-dimensional conformal field theory and the  butterfly effect, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' 115 (2015) 131603 [1412.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='5123].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  [7] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Maldacena, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Shenker and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Stanford, A bound on chaos, JHEP 08 (2016) 106  [1503.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='01409].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  [8] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Blake, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Lee and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Liu, A quantum hydrodynamical description for scrambling  and many-body chaos, JHEP 10 (2018) 127 [1801.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='00010].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  [9] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Blake and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Liu, On systems of maximal quantum chaos, JHEP 05 (2021) 229  [2102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='11294].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  [10] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Costa, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Goncalves and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Penedones, Conformal Regge theory, JHEP 12 (2012)  091 [1209.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='4355].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  [11] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Cornalba, Eikonal methods in AdS/CFT: Regge theory and multi-reggeon exchange,  0710.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='5480.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  [12] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Kravchuk and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Simmons-Duffin, Light-ray operators in conformal field theory,  JHEP 11 (2018) 102 [1805.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='00098].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  [13] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Forshaw and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Ross, Quantum Chromodynamics and the Pomeron, Cambridge  Lecture Notes in Physics, Cambridge University Press (1997),  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='1017/CBO9780511524387.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  [14] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Kitaev and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Suh, The soft mode in the Sachdev-Ye-Kitaev model and its gravity  dual, JHEP 05 (2018) 183 [1711.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='08467].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  [15] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Gu and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Kitaev, On the relation between the magnitude and exponent of OTOCs,  JHEP 02 (2019) 075 [1812.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='00120].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  [16] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Stanford, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Yang and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Yao, Subleading Weingartens, JHEP 02 (2022) 200  [2107.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='10252].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  [17] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Gu, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Kitaev and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Zhang, A two-way approach to out-of-time-order correlators,  JHEP 03 (2022) 133 [2111.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='12007].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  [18] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Mezei and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' S´arosi, Chaos in the butterfly cone, JHEP 01 (2020) 186  [1908.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='03574].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  [19] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Crossley, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Glorioso and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Liu, Effective field theory of dissipative fluids, JHEP  09 (2017) 095 [1511.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='03646].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  – 79 –  [20] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Glorioso, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Crossley and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Liu, Effective field theory of dissipative fluids (II):  classical limit, dynamical KMS symmetry and entropy current, JHEP 09 (2017) 096  [1701.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='07817].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  [21] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Liu and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Glorioso, Lectures on non-equilibrium effective field theories and  fluctuating hydrodynamics, PoS TASI2017 (2018) 008 [1805.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='09331].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  [22] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Glorioso and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Liu, The second law of thermodynamics from symmetry and  unitarity, 1612.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='07705.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  [23] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Kitaev, Near-coherent scrambling, talk at IAS (2017) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  [24] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Sachdev and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Ye, Gapless spin-fluid ground state in a random quantum heisenberg  magnet, Physical Review Letters 70 (1993) 3339.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  [25] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Kitaev, A simple model of quantum holography, in KITP strings seminar and  Entanglement, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' 12, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  [26] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Maldacena and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Stanford, Remarks on the Sachdev-Ye-Kitaev model, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  D 94 (2016) 106002 [1604.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='07818].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  [27] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Cotler, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Gur-Ari, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Hanada, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Polchinski, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Saad, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Shenker et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=', Black  Holes and Random Matrices, JHEP 05 (2017) 118 [1611.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='04650].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  [28] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Choi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Mezei and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' S´arosi, Exact four point function for large q SYK from  Regge theory, JHEP 05 (2021) 166 [1912.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='00004].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  [29] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Papadodimas and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Raju, An Infalling Observer in AdS/CFT, JHEP 10 (2013)  212 [1211.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='6767].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  [30] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Grozdanov, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Schalm and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Scopelliti, Black hole scrambling from hydrodynamics,  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' 120 (2018) 231601 [1710.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='00921].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  [31] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Choi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Mezei and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' S´arosi, Pole skipping away from maximal chaos, 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='08558.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  [32] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Brower, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Polchinski, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Strassler and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='-I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content=' Tan, The Pomeron and  gauge/string duality, JHEP 12 (2007) 005 [hep-th/0603115].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
+page_content='  – 80 –' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tdE4T4oBgHgl3EQfxQ03/content/2301.05256v1.pdf'}
diff --git a/u9E0T4oBgHgl3EQfsQGm/vector_store/index.pkl b/u9E0T4oBgHgl3EQfsQGm/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..8130a6728bddb9eedbd9733b37f8eee6b8c8100a
--- /dev/null
+++ b/u9E0T4oBgHgl3EQfsQGm/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:9a3b5358025f96843bae6c73d94a4bf3f6f53208f8109449f6775f08adbf7143
+size 268647
diff --git a/uNE5T4oBgHgl3EQfLQ6L/content/2301.05472v1.pdf b/uNE5T4oBgHgl3EQfLQ6L/content/2301.05472v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..bae41bd849ad6056bc78bfdc0933124f5d4ffeac
--- /dev/null
+++ b/uNE5T4oBgHgl3EQfLQ6L/content/2301.05472v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:8cc6e12c61e586f7546e816449cdfeed78473732504db7feb2d0e87d3eb6917e
+size 386295
diff --git a/uNE5T4oBgHgl3EQfLQ6L/vector_store/index.faiss b/uNE5T4oBgHgl3EQfLQ6L/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..11007adb7fa5d3a2604884af36561ef4b8e8fcbb
--- /dev/null
+++ b/uNE5T4oBgHgl3EQfLQ6L/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:d5e45b5d41e0a49cdfcff794d7179cbb05879fd9fa06c82e43902daa82a158dd
+size 4980781
diff --git a/uNE5T4oBgHgl3EQfLQ6L/vector_store/index.pkl b/uNE5T4oBgHgl3EQfLQ6L/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..301e362e56b42b587f65ce1dfa9af4ea1f1d702c
--- /dev/null
+++ b/uNE5T4oBgHgl3EQfLQ6L/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:034c5c33fb9b824c0445474ff8e3a5df823767e808d93352143459ce28bff27b
+size 179607
diff --git a/utAzT4oBgHgl3EQfsP2h/content/tmp_files/2301.01657v1.pdf.txt b/utAzT4oBgHgl3EQfsP2h/content/tmp_files/2301.01657v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5b9b44a14b7c028bd5d17f1eb87a5f6e2b6fcd9b
--- /dev/null
+++ b/utAzT4oBgHgl3EQfsP2h/content/tmp_files/2301.01657v1.pdf.txt
@@ -0,0 +1,663 @@
+arXiv:2301.01657v1  [cs.CR]  4 Jan 2023
+CRYPTOGRAPHIC GROUP AND SEMIGROUP ACTIONS
+OLIVER W. GNILKE AND JENS ZUMBR¨AGEL
+Dedicated to Joachim Rosenthal on the occasion of his 60th birthday
+Abstract. We consider actions of a group or a semigroup on a set,
+which generalize the setup of discrete logarithm based cryptosystems.
+Such cryptographic group actions have gained increasing attention re-
+cently in the context of isogeny-based cryptography.
+We introduce
+generic algorithms for the semigroup action problem and discuss lower
+and upper bounds. Also, we investigate Pohlig-Hellman type attacks
+in a general sense. In particular, we consider reductions provided by
+non-invertible elements in a semigroup, and we deal with subgroups in
+the case of group actions.
+Keywords: Discrete logarithm problem; cryptographic group action;
+semigroup action problem.
+1. Introduction
+The discrete logarithm problem has a long and profound history (see [8]
+for a recent survey). In cryptography it has been playing a key role ever
+since Diffie and Hellman have based the security of their famous protocol [6]
+on the hardness of computing discrete logarithms modulo a large prime p.
+The underlying group F∗
+p has then been generalized, most notably to the
+Fq-rational points on an elliptic curve, due to Miller [18] and Koblitz [12].
+In fact, while the discrete logarithm problem in the unit group F∗
+q of a finite
+field can be solved in subexponential time by index calculus algorithms (for
+an overview, see [9]), the fastest known algorithm in a general elliptic curve
+is basically a generic one that requires exponential time.
+However, Shor’s quantum algorithm [24] constitutes a polynomial time at-
+tack on the discrete logarithm problem in any group (as well as on the integer
+factorization problem). These observations, and reports on the progress in
+building quantum computers now achieving a “quantum supremacy” [2],
+underline the need for new concepts to build cryptosystems resistant to
+quantum attacks. An interesting approach is based on isogenies of super-
+singular elliptic curves (SIDH, [10]), which however is broken due to the
+Castryck-Decru attack [4].
+More recently, a commutative supersingular isogeny-based Diffie-Hellman
+scheme (CSIDH, [3]) has been proposed as a more efficient variant, which
+is based on the action of the class group of an endomorphism ring on iso-
+morphism classes of elliptic curves.
+This is an example for an action of
+2010 Mathematics Subject Classification. 94A60.
+The material in this paper was presented in part at the Workshop on Coding and
+Cryptography (WCC 2022) in Rostock, Germany.
+1
+
+2
+OLIVER W. GNILKE AND JENS ZUMBR¨AGEL
+an abelian group on a set, which as a framework suffices to build a Diffie-
+Hellman protocol, as has been observed by Couveignes [5] and independently
+by Rostovtsev and Stolbunov [22, 26].
+With a somewhat different background, Maze, Monico and Rosenthal
+have introduced actions of commutative semigroups on sets [19, 17] in or-
+der to generalize the discrete logarithm problem, one motivation being to
+find examples that do not allow even an (exponential) square-root attack.
+The setup was further investigated by the theses of the present authors, in
+which Zumbr¨agel [27] considered a generalization to non-commutative semi-
+groups and Gnilke [7] showed how a Pohlig-Hellman like reduction applies
+to semigroups with non-invertible elements.
+In this work, we revisit the concept of semigroup actions for discrete log-
+arithm based cryptosystems and connect it to recent proposals of isogeny-
+based cryptography. In the case of abelian group actions, with a view to-
+wards isogenies, this has been considered by Couveignes [5] and, more re-
+cently, by Smith [25] and Alamati et al. [1]. Here we aim to take a slightly
+more abstract viewpoint and introduce generic algorithms for the semigroup
+action problem. We also investigate Pohlig-Hellman type reductions and
+consider those provided by non-units in a semigroup and by subgroups in
+the context of a group action.
+2. Cryptographic semigroup actions
+In this section we briefly recall the notion of a semigroup action and its
+application to cryptography [19, 17].
+By a semigroup we mean a set S with an associative binary operation
+(written multiplicatively). It is called a monoid if a neutral element exists.
+A semigroup action with respect to a semigroup S and a set X is a map
+S × X → X ,
+(s, x) �→ s.x
+such that st.x = s.(t.x) for all s, t ∈ S and x ∈ X. Considering for s ∈ S
+the transformation Φs : X → X, x �→ s.x, this means that Φst = Φs ◦ Φt for
+s, t ∈ S. When there is a semigroup action, then X is also called S-set.
+Definition 2.1. Consider a semigroup S acting on a set X. The semigroup
+action problem is the problem, for given x, y ∈ X to find some s ∈ S such
+that y = s.x.
+So the above problem asks to find preimages of the “orbit map”
+Ψx : S → X ,
+s �→ s.x .
+Suppose that S is a group and let Sx = {s ∈ S | s.x = x} be the stabilizer
+subgroup of x ∈ X. Then the orbit map induces a bijection S/ℓ Sx ∼
+−→ S.x of
+the left cosets and the orbit. Thus solutions to the semigroup action problem
+(which we also call group action problem) are unique up to left congruence
+modulo the stabilizer.
+Since we deal with cryptographic applications, we assume all structures
+to be finite and that the semigroup action is efficiently computable. This
+means that elements of the semigroup S and the set X are encoded by bit
+strings, and both the semigroup operation and the action are computable in
+polynomial time.
+
+CRYPTOGRAPHIC GROUP AND SEMIGROUP ACTIONS
+3
+Example 2.2. Consider a finite cyclic group (G, ·) of order n, which may
+be seen as a Zn-module. If we “forget” its additive structure, we have
+(Zn, ·) × G → G ,
+(s, g) �→ gs ,
+and the semigroup action problem is just the discrete logarithm problem in
+the group G. Note that the action is efficiently computable by a square-
+and-multiply method, provided the group operation is efficient.
+In order to set up a Diffie-Hellman like key agreement, we need some
+way to generate commuting elements of the semigroup S. For simplicity we
+assume here the semigroup to be commutative and have the following key
+agreement scheme:
+Alice
+public
+Bob
+x ∈ X
+a ∈ S
+→
+a.x ∈ X
+b.x ∈ X
+←
+b ∈ S
+kA = a.(b.x)
+kB = b.(a.x)
+Observe that both parties compute the same key ab.x = ba.x. Also notice
+that in the case of Example 2.2 the scheme amounts to classical Diffie-
+Hellman.
+Definition 2.3. Consider a commutative semigroup S acting on a set X.
+The semigroup Diffie-Hellman problem is the problem, for given x, y, z ∈ X
+to find some k ∈ X such that y = a.x, z = b.x and k = ab.x = ba.x for some
+a, b ∈ S.
+It is clear that if one can solve the semigroup action problem, then one
+can break the Diffie-Hellman protocol, while the converse direction is not ob-
+vious. There have been results on subexponential reductions in the classical
+case of group exponentiation [13, 15], and recently on polynomial quantum
+reduction for abelian group actions [11, 20].
+Example 2.4. In isogeny-based cryptography and CSIDH, a particular case
+of interest is the action of an abelian group (the class group in an en-
+domorphism ring) on a set X (of isomorphism classes of elliptic curves),
+cf. [5, 3, 25]. In Couveignes’ work [5] the group action is also assumed to
+be simply transitive, and the semigroup action problem and the semigroup
+Diffie-Hellman problem are called vectorization problem and parallelization
+problem, respectively; if those are intractable, the set X is referred to as a
+hard homogeneous space.
+It would be interesting to view SIDH also in the framework of a group
+action, but this seems not to be obvious, cf. [25, Sec. 15].
+3. Generic algorithms
+We use Maurer’s abstract model of computation [14] to describe generic
+algorithms for a semigroup action. Recall that in this model one specifies
+• a ground set M,
+• a set Π of certain operations f : Mt → M of arity t ∈ {0, 1, 2, . . . },
+• a set Σ of certain relations ρ ⊆ Mt of arity t ∈ {1, 2, . . . }.
+
+4
+OLIVER W. GNILKE AND JENS ZUMBR¨AGEL
+There are internal state variables V1, V2, . . . storing elements in M, which
+cannot be read directly. A generic algorithm A(M, Π, Σ) is then allowed to
+perform computation operations and relation queries for f ∈ Π and ρ ∈ Σ,
+using the internal state variables as input (and operation output). In the
+analysis we usually discard the relation queries and only count the number
+of operations performed.
+Example 3.1. Generic algorithms in a cyclic group of order n can be mod-
+eled using M = Zn, Π = {+} and Σ = {=}. For the discrete logarithm
+problem the state variables are initialized with V1 = 1 and V2 = s ∈ Zn
+random, and the goal is to solve the extraction problem for the value s ∈ V2.
+Now let S × X → X be a semigroup action and fix x ∈ X. In order to
+address the semigroup action problem, we define the ground set as
+M := S/∼x ,
+where
+s ∼x t :⇔ s.x = t.x ,
+and denote the class of s ∈ S by [s]. We allow for any a ∈ S to perform
+the unary operation Φa : M → M, [s] �→ a.[s] := [as]. The state variables
+are initialized with V1 = [1] (assuming that 1 ∈ S, otherwise we adjoin it)
+and V2 = [s] ∈ M, which describes the solutions s to a semigroup action
+problem y = s.x. The goal is to solve the extraction problem for V2, i.e., to
+find some s′ ∈ S such that [s] = [s′].
+If we are dealing with a group action, the set S/∼x = S/ℓ Sx consists of
+the left cosets [s] = sSx of the stabilizer subgroup of x. In this case, we can
+show the following result, which provides a generic lower bound of Ω(√n)
+for the group action problem in a set X of size n.
+Theorem 3.2. Let S × X → X be a transitive group action, which is
+abelian or free.
+Fix x ∈ X and let M := S/ℓ Sx, Π = {Φa | a ∈ S},
+Σ = {=} as above. If s ∈ S is uniformly random, the success probability
+of a generic algorithm A(M, Π, Σ) for the group action problem y = s.x
+using m operation queries is at most 1
+4m2/|X|.
+Proof. Following the proof of [14, Thm. 1] it suffices to upper bound the
+probability that a collision in the state variables occurs. These entries are
+either of the form a.[1] = [a] or of the form b.[s], for known a, b ∈ S. A col-
+lision of type [a] = [a′] is independent of s and can be discarded. Moreover,
+a collision of type b.[s] = b′.[s] means that b−1b′ ∈ Ss.x = sSxs−1, but since
+the action is abelian or free we have sSxs−1 = Sx, again independent of s.
+This means that the only collisions related to s are of the form
+a.[1] = b.[s]
+for some a, b ∈ S. Such an event is equivalent to [s] = [b−1a], and since
+[s] ∈ M is uniformly random it occurs with probability 1/n, where n :=
+|M| = |X|. So if the algorithm computes u and v values of the form a.[1]
+and b.[s] respectively, the probability for a collision is at most uv/n. But
+since u+v ≤ m we have uv ≤ 1
+4m2, from which the result follows.
+□
+The following example shows that there may be much faster generic al-
+gorithms in case the group action is neither abelian nor free.
+
+CRYPTOGRAPHIC GROUP AND SEMIGROUP ACTIONS
+5
+Example 3.3. Let X be a set of size n and let the symmetric group S :=
+Sym X act on X. Fix x ∈ X and let s ∈ S be random. A generic algorithm
+to find the coset [s] ∈ S/ℓ Sx can employ either “usual” collisions [a] = b.[s],
+from which a solution s′ := b−1a can be obtained, or collisions of the form
+b.[s] = b′.[s],
+i.e., c.[s] = [s] for c := b−1b′. If we choose c ∈ S having k fixed points, then
+the event probability is k/n, and thus we may apply a divide-and-conquer
+strategy to obtain [s] in O(log n) steps.
+Furthermore, for proper semigroup actions the difficulty of the generic
+semigroup action problem very much depends on the structure of the semi-
+group, and ranges from efficient algorithms in O(log n) to lower bounds of
+Ω(n), see the examples below. From a cryptography perspective there are
+however issues with applying those actions, as discussed in Section 5.
+Example 3.4. Let S be a semigroup, X a set and ϕ: S → X a bijection.
+Then we can make X an S-set by letting
+s.ϕ(t) = ϕ(st)
+for s, t ∈ S. We assume this action to be efficiently computable and think of
+the inverse map ϕ−1 as “hidden”. For example, if G is a cyclic group with
+generator g, we use the bijection ϕ: (Zn, ·) → G, s �→ gs. Let us look at two
+further cases.
+(1) Suppose that (S, ·) = ({1, . . . , n}, min) and we are given a semigroup
+action problem instance x, y ∈ X where y = s.x. Let a = ϕ−1(x)
+which we suppose is known, e.g., a = n if x = ϕ(n). Since y = s.x =
+s.ϕ(a) = ϕ(sa) = ϕ(saa) = sa.ϕ(a) = sa.x, we may assume that
+s = sa, i.e., s ≤ a. Then for any t ∈ S, t ≤ a, there holds
+t ≤ s ⇔ t = ts ⇔ ta = tsa ⇔ ϕ(ta) = ϕ(tsa)
+⇔ t.ϕ(a) = t.(s.ϕ(a)) ⇔ t.x = t.y .
+Hence, we can find s using binary search in O(log n) steps.
+(2) On the other hand, define (S, ·) = ({0, s1, . . . , sm, 1}, ∧), where ∧ is
+a semilattice operation such that
+0 ∧ si = 0 ,
+1 ∧ si = si ,
+and
+si ∧ sj = 0 whenever i ̸= j ,
+and let o = ϕ(0) and e = ϕ(1) in X. Consider a semigroup action
+problem instance e, y ∈ X where y = s.e. As s.e = s.ϕ(1) = ϕ(s1) =
+ϕ(s) and ϕ is bijective, there is a unique solution s. When using a
+generic algorithm we may for t ∈ S compute t.e = ϕ(t) and t.y =
+t.(s.e) = ts.e = ϕ(ts), where a collision occurs only if t = ts, which
+if s = si means that t ∈ {0, si}. So it requires Ω(n) steps to find any
+collision and thus information about s.
+Note that this example is not interesting for a Diffie-Hellman type
+key agreement, because the key k = a.(b.e) = b.(a.e) will usually
+be o.
+
+6
+OLIVER W. GNILKE AND JENS ZUMBR¨AGEL
+We should mention here that Shoup’s model for generic algorithms [23]
+is also widely used, which is based on representations of algebraic objects
+as random bitstrings. In the case of a cyclic group of order n one has an
+injective “encoding function” σ: Zn → {0, 1}∗, and the algorithm maintains
+a list of encodings (σ(x1), . . . , σ(xk)) to which entries σ(xi +xj) may be
+appended by performing oracle queries. The bitstring representation allows
+a generic algorithm to perform additional operations, like sorting or hashing
+of algebraic objects, and thus enables algorithms based on pseudorandom
+functions such as Pollard’s rho method. It is possible to show a square-root
+lower bound for the group action problem in Shoup’s model by adapting the
+proof of Theorem 3.2.
+Regarding upper bounds for the complexity of the semigroup action prob-
+lem, generic algorithms often aim at finding a collision in square-root time.
+However, in order to deduce a solution from it one needs the ability to in-
+vert some elements in the semigroup. Below we present a version of Shanks’
+baby-step-giant-step method as well as a Pollard-rho type attack for the case
+of group actions.
+Note that in the quantum world generic attacks on group actions may be
+faster than square-root time. Indeed, there are subexponential algorithms
+solving the group action problem for (free) abelian group actions based on
+Kuperberg’s quantum algorithm, cf. [20, Sec. 7].
+4. Collision attacks
+Let X be an S-set of size n and let x ∈ X, y ∈ S.x. We now discuss
+generic upper bounds for the corresponding semigroup action problem, i.e.,
+to find s ∈ S such that y = s.x. An important class of generic algorithms
+relies on finding a collision a.x = b.y for some a, b ∈ S, from which we can
+deduce a solution s := b−1a, provided that b is invertible.
+For analyzing such algorithms, the following combinatorial result on the
+probability that two random subsets are disjoint is useful (cf. [7, Lem. 68]).
+Lemma 4.1. Let X be a set of size n and let A, B ⊆ X be uniformly chosen
+random subsets of size k, ℓ respectively. Then
+1 − kℓ
+n ≤ Pr(A ∩ B = ∅) ≤ exp(− kℓ
+n ) .
+Proof. Let us assume w. l. o. g. that B is fixed. For the lower bound we have
+Pr(A ∩ B ̸= ∅) = Pr(�
+x∈B{x ∈ A}) ≤ �
+x∈B Pr(x ∈ A) = ℓ· k
+n
+by the union bound. For the upper bound we may assume that A consists
+of k randomly chosen elements of X, possibly with repetition, by which the
+probability of being disjoint to B only can increase. Let Ti be the event that
+the i-th element of A does not lie in B, for 1 ≤ i ≤ k. Then these events
+are independent of probability 1− ℓ
+n, whence
+Pr(A ∩ B = ∅) ≤ Pr(�
+i Ti) = (1− ℓ
+n)k ≤ exp(− ℓk
+n ) ,
+since 1+x ≤ exp x holds for all x ∈ R.
+□
+
+CRYPTOGRAPHIC GROUP AND SEMIGROUP ACTIONS
+7
+A time-memory trade-off. We first present a simple time-memory trade-
+off attack adopting Shanks’ baby-step-giant-step method (cf. [7, Sec. 4.2]).
+Let the semigroup S be a monoid with group of invertible elements S∗. The
+algorithm is described as follows.
+(1) precompute a table of entries (bj.y, bj) for bj ∈ S∗ random
+(2) for a ∈ S random, check if a.x = bj.y for some j, if yes output
+s := b−1
+j a
+For the analysis, according to the proof of Lemma 4.1 we may bound
+the collision probability even if the set B := {b1.y, b2.y, . . . } is of a special
+nature (as the bj have to be invertible). It is enough to require that the set
+A := {a1.x, a2.x, . . . } generated by the algorithm behaves as random, which
+holds if the orbit map Ψx: S → X, s �→ s.x has (nearly) constant-sized
+preimages.
+Suppose the algorithm generates k := |A| elements ai.x with ai ∈ S and
+ℓ := |B| elements bj.y with bj ∈ S∗, which is upper bounded by |S∗|. Then
+we infer from Lemma 4.1 that the success probability of the algorithm is at
+least 1
+2 provided that exp(− kℓ
+n ) ≤ 1
+2, or equivalently,
+kℓ ≥ n ln 2 .
+Therefore, an optimal choice of parameters is k, ℓ ∈ Θ(√n), which is
+possible if a sufficient amount of invertible elements is available and there is
+enough memory. In such a case the complexity of this algorithm is seen to
+be O(√n). Next we show an approach how to drastically reduce the memory
+requirement.
+A Pollard-rho attack for group actions. Suppose now that a group G
+acts transitively on a set X of size n. Given x, y ∈ X the group action
+problem asks to find g ∈ G such that y = g.x. We describe a Pollard-rho
+type birthday attack for solving this problem, which is a slight adaption and
+simplification of an algorithm given by Monico [19, Sec. 4.2].
+As before, the idea is to generate elements ai.x, bj.y ∈ X in a pseudo-
+random way and to provoke a collision ai.x = bj.y from which a solution
+g := b−1
+j ai to the group action problem is deduced. But here, this is to be
+done using very little memory while still maintaining a heuristic square-root
+complexity O(√n).
+The algorithm depends on a pseudorandom function f : X → G. Define
+a recursive sequence (a1, a2, a3, . . . ) in G by
+a1 := a ∈ G random ,
+ai+1 := f(ai.x) ai
+for i ≥ 1 ,
+hence a2 = f(a.x) a, a3 = f(f(a.x) a.x) f(a.x) a, etc. Observe that if ai.x =
+aj.x for some i, j then ai+r.x = aj+r.x for all r. Similarly, define a recursive
+sequence (b1, b2, b3, . . . ) in G by
+b1 := b ∈ G random ,
+bj+1 := f(bj.y) bj
+for j ≥ 1 ,
+and note that if ai.x = bj.y then ai+r.x = bj+r.y for all r. The algorithm
+now consists of two steps:
+(1) construct a-loop, i.e., find smallest k such that ak.x = a2k.x
+construct b-loop, i.e., find smallest ℓ such that bℓ.y = b2ℓ.y
+
+8
+OLIVER W. GNILKE AND JENS ZUMBR¨AGEL
+(2) find a collision in the sets
+A := {ak+i.x | 0 ≤ i < k}
+and
+B := {bℓ+j.y | 0 ≤ j < ℓ}
+by checking ak.x = bℓ+s.y for s = 0, 1, 2, . . . ; if successful output
+g := b−1
+ℓ+sak
+Notice here that if ak+i.x = bℓ+j.y for some i, j, then ak.x = a2k.x = bℓ+s.y
+for s := j+k−i.
+We sketch a heuristic analysis of this algorithm. With good probability
+we have |A| = k and |B| = ℓ (if the preperiod does not exceed the period)
+and we expect k, ℓ ∈ O(√n) by the birthday paradox. Assuming that A, B
+behave as random subsets of X we can estimate the probability of a collision
+using Lemma 4.1 by
+Pr(A ∩ B ̸= ∅) ≥ 1−exp
+�
+− kℓ
+n
+�
+∈ Ω(1) ,
+provided that k, ℓ ∈ Ω(√n).
+These arguments show that the algorithm
+has an expected running time of O(√n) and succeeds with non-negligible
+probability.
+This algorithm may be adapted to work also for proper semigroup actions,
+in case the semigroup S has sufficiently many invertible elements S∗ and we
+are able to define a sequence (b1, b2, b3, . . . ) in S∗. Alternatively, as pointed
+out by Maze [16], semigroups with a large subgroup can be attacked by
+excluding all non-units first and then employing the above algorithm on the
+unit subgroup.
+5. Pohlig-Hellman type reductions
+In this section we examine how the hardness of the semigroup action
+problem is affected by exploiting certain substructures. We recollect the
+framework of Pohlig-Hellman type reductions from [7, Sec. 4.3] and discuss
+a few special cases for cryptographic group actions.
+Recall that the classical Pohlig-Hellman algorithm [21] essentially reduces
+the difficulty of the discrete logarithm problem in a cyclic group G of order n
+to that in a group of order the largest prime factor of n. The algorithm can
+be viewed as applying multiplication-by-m maps
+λm : Zn → Zn ,
+s �→ ms
+in order to reduce the problem to the action of the (smaller) ideal mZn. The
+following general concept captures this scenario and many others.
+Definition 5.1. Let S and T be semigroups, let X be an S-set and Y be a
+T-set. A reduction (f, F, G) consists of maps f : S → T and F, G: X → Y
+such that
+f(s).G(x) = F(s.x)
+for all s ∈ S and x ∈ X, see the diagram below.
+S
+Ψx
+�
+f
+�
+X
+F
+�
+T
+ΨG(x)
+� Y
+G
+�
+
+CRYPTOGRAPHIC GROUP AND SEMIGROUP ACTIONS
+9
+For a general reduction (f, F, G) the map f : S → T is not required
+to be a semigroup homomorphism.
+However, if F = G it is reasonable
+to assume this, since f(st).F(x) = F(st.x) = F(s.t.x) = f(s).F(t.x) =
+f(s).f(t).F(x) = f(s)f(t).F(x) for all s, t ∈ S and x ∈ X.
+Example 5.2. Let G be a cyclic group with generator α of composite order
+n = km.
+In the Pohlig-Hellman setup above we may apply the isomor-
+phism mZn ∼= Zk after the multiplication-by-m map λm, which results in
+the natural map π: Zn → Zk. Then one has a reduction (π, Φm, Φm), where
+Φm : ⟨α⟩ → ⟨αm⟩, g �→ gm. Indeed, there holds (gm)π(s) = (gs)m for any
+s ∈ Zn and g ∈ G, see below.
+Zn
+Ψg
+�
+π
+�
+⟨α⟩
+Φm
+�
+Zk
+Ψgm
+� ⟨αm⟩
+Φm
+�
+Given any reduction (f, F, G), an adversary who can solve the semigroup
+action problem in T can restrict the search in S to preimages of the solutions
+in T under the map f. Indeed, given a semigroup action problem instance
+x, y ∈ X where y = s.x, one reduces it to the instance G(x), F(y) ∈ Y where
+F(y) = f(s).G(x). Nevertheless one should note the following caveats:
+(1) In general, for a single solution t ∈ im f ⊆ T of F(y) = t.G(x) it is
+not clear whether there always exists s ∈ f −1(t) such that y = s.x.
+(2) If the above solution t ∈ im f is unique, then t = f(s) and we can
+deduce that s ∈ f −1(t), which may be a much smaller set than S.
+However, the preimage under f could be hard to obtain, and often
+it does not admit a useful semigroup action structure itself.
+Similarly to the Pohlig-Hellman algorithm we may apply several reduc-
+tions (f1, F1, G1), . . . , (fr, Fr, Gr) in parallel to further narrow down the
+search space to s ∈ f −1
+1 (t1) ∩ · · · ∩ f −1
+r (tr) if suitable solutions t1, . . . , tr
+of the reduced semigroup action problems are found.
+Examples based on non-units. We call a reduction effective if the maps
+f, F, G are efficiently computable and there holds 1 < |T| < |S|. The next
+result describes a very general class of reductions.
+Proposition 5.3. Let S be a monoid, X an S-set and m ∈ S. Then the
+triple (λm, Φm, id) forms a reduction, which is effective iff m is not left-
+absorbing and not invertible, provided the semigroup operation and action
+are efficient.
+Proof. For all x ∈ X and s ∈ S there holds that
+λm(s).x = ms.x = m.(s.x) = Φm(s.x) .
+The reduction maps the semigroup S onto its right ideal mS, which is a non-
+trivial proper subsemigroup of S iff λm is not constant or surjective.
+□
+Akin to the Pohlig-Hellman approach for groups of prime power order,
+we may apply this reduction recursively. The idea for solving the semigroup
+
+10
+OLIVER W. GNILKE AND JENS ZUMBR¨AGEL
+action problem y = s.x is to find t1 := m1s from m1.y = t1.x (bearing in
+mind the caveats above), and for obtaining t1 to find t2 := m2m1s from
+m2m1.y = t2.x etc., for suitable non-units m1, m2, . . . of S.
+Hence, the result constitutes a considerable threat to the security of
+a cryptosystem based on proper semigroup actions.
+On the other hand,
+the rather degenerate semigroup S of Example 3.4 (2) contains many non-
+absorbing non-units and yet has a generic complexity of Ω(n) for the semi-
+group action problem. In this case, one has |mS| = 2 for all non-absorbing
+non-units m and the corresponding preimage sets are not useful (see also [7,
+Ex. 79]).
+In conclusion, while it is conceivable that certain semigroup actions avoid
+the attacks outlined in this section and are in fact interesting for cryptogra-
+phy, possible candidates have to be chosen very carefully.
+Examples based on automorphisms. Now we consider a second fam-
+ily of reductions, which also applies to group actions. Let us start with a
+general semigroup S and an S-set X. Its automorphisms are the bijective
+maps ϕ: X → X such that ϕ(s.x) = s.ϕ(x) for all s ∈ S, x ∈ X. We use
+automorphism groups to construct equivalence relations on X compatible
+with the action as follows. Suppose that a group H acts on X by automor-
+phisms, i.e., we have H × X → X, (h, x) �→ h.x, such that h.s.x = s.h.x for
+h ∈ H, s ∈ S, x ∈ X. Let X/∼ be the set of its orbits [x] = {h.x | h ∈ H}.
+This induces an action
+S × X/∼ → X/∼ ,
+(s, [x]) �→ [s.x] .
+Suppose next that the semigroup S is a commutative monoid with unit
+group S∗.
+Then each h ∈ S∗ defines an S-automorphism Ψh : X → X
+by x �→ h.x, so we may consider any subgroup H of S∗ as a group of
+automorphisms of X.
+The relation s ≈ t iff sH = tH then provides a
+semigroup congruence on S, and we denote by S/H := {sH | s ∈ S} its
+classes. Moreover, s ≈ t implies s.x ∼ t.x, for any s, t ∈ S and x ∈ X, so we
+can define an action
+S/H × X/∼ → X/∼ ,
+([s]≈, [x]∼) �→ [s.x]∼ .
+We hence obtain a reduction (f, F, F) with f : S → S/≈ and F : X → X/∼
+being the natural maps, see below.
+S
+Ψx
+�
+f
+�
+X
+F
+�
+S/H
+Ψ[x]
+� X/∼
+F
+�
+In particular, if S = G is an abelian group, so that S∗ = G, we can employ
+any subgroup H of G and thus X/∼ becomes a G/H-set. Regarding the
+practical implications however, the reduced action may not be efficiently
+computable, because the equality of orbits could be difficult to check. In
+any case, an effective reduction attack cannot be of generic type, since we
+are guaranteed a lower square-root complexity for such algorithms due to
+Theorem 3.2.
+
+CRYPTOGRAPHIC GROUP AND SEMIGROUP ACTIONS
+11
+This approach was also described in the context of CSIDH, cf. [25, Sec. 12].
+Remark 5.4. As in Example 2.2 consider the discrete logarithm setup of
+an abelian group X of order n, i.e., we have the action of (Zn, ·) on X by
+exponentiation. Every group automorphism is also an automorphism of X
+as an Zn-set, thus any subgroup H of the automorphism group of X induces
+an action
+(Zn, ·)/H × X/∼ → X/∼,
+([s], [x]) �→ [xs] .
+In the special case of H = {±1} we have the orbits [x] = {x, x−1}, reflecting
+the practice in elliptic curve cryptography to identify the points ±P and
+thus use only the x-coordinate [18].
+Such reductions could potentially weaken the security of the discrete log-
+arithm problem in groups for which the automorphism group has several
+subgroups, e.g., in cyclic groups of order n where ϕ(n) = |Z∗
+n| is smooth.
+However, as mentioned above these reductions appear to be not effective in
+general.
+Let us state a concrete example illustrating this phenomenon.
+Example 5.5. Consider the discrete logarithm problem in a group X of
+prime order n = 29 (e.g., a subgroup of Z∗
+59). Then we have S = (Z29, ·)
+and hence
+S∗ = Z∗
+29 ∼= Z28 ∼= Z4×Z7 .
+Therefore, one could try to exploit the subgroups H1 = ⟨α1⟩, H2 = ⟨α2⟩
+of order 4 and 7 respectively, say α1 = 12 ∈ Z∗
+29 and α2 = 7 ∈ Z∗
+29,
+to attack to problem.
+But the reduced group actions seem to be more
+difficult to compute, e.g., we have Z∗
+29/⟨7⟩ × X/∼ → X/∼ where [x] =
+{x, x7, x20, x24, x23, x16, x25} ∈ X/∼.
+6. Conclusion
+Cryptographic group actions or semigroup actions provide a framework
+that encompasses both the classical discrete logarithm problem as well as
+interesting proposals for post-quantum cryptography. In this article we have
+examined this framework from a theoretical viewpoint and studied the semi-
+group action problem as an analog of the discrete logarithm problem.
+In the case of group actions, the generic complexity can be considered well
+understood, as there is both a square-root lower bound and a square-root
+upper bound for the group action problem. On the other hand, for proper
+semigroup actions the situation appears to be less clear. The generic lower
+bound may exceed the square-root barrier, however such instances tend to
+be degenerate and not interesting for cryptography applications.
+We also have discussed the potential of certain substructures to weaken
+the hardness of the semigroup action problem, in particular in the presence of
+non-units. While such substructures do not guarantee to practically break
+the semigroup action problem, they should be taken into account when
+designing cryptosystems based on semigroup or group actions.
+
+12
+OLIVER W. GNILKE AND JENS ZUMBR¨AGEL
+References
+[1] N. Alamati, L. De Feo, H. Montgomery, S. Patranabis, “Cryptographic group actions and
+applications,” in: Advances in Cryptology—ASIACRYPT 2020, pp. 411–439, LNCS 12492,
+Springer, 2020
+[2] F. Arute, et al., “Quantum supremacy using a programmable superconducting processor,”
+Nature 574 (2019), 505–510
+[3] W. Castryck, T. Lange, C. Martindale, L. Panny, J. Renes, “CSIDH: an efficient post-
+quantum commutative group action,” in:
+Advances in Cryptology—ASIACRYPT 2018,
+pp. 395–427, LNCS 11274, Springer, 2018
+[4] W. Castryck, T. Decru, “An efficient key recovery attack on SIDH,” 15 pages, IACR eprint
+2022/975
+[5] J. M. Couveignes, “Hard homogenous spaces,” 15 pages, IACR eprint 2006/291 (1997, pub-
+lished 2006)
+[6] W. Diffie, M. E. Hellman, “New directions in cryptography,” IEEE Trans. Inform. Theory 22
+(1976) 644–654
+[7] O. W. Gnilke, “The semigroup action problem in cryptography,” Ph. D. dissertation, Univer-
+sity College Dublin (2014)
+[8] R. Granger, A. Joux, “Computing discrete logarithms,” in: Computational Cryptography—
+Algorithmic Aspects of Cryptology, pp. 106–139, Cambridge Univ. Press, 2021
+[9] R. Granger, T. Kleinjung, J. Zumbr¨agel, “Indiscreet logarithms in finite fields of small char-
+acteristic,” Adv. Math. Commun. 12 (2018) 263–286
+[10] L. De Feo, D. Jao, J. Plˆut, “Towards quantum-resistant cryptosystems from supersingular
+elliptic curve isogenies,” J. Math. Cryptol. 8 (2014) 209–247
+[11] S. Galbraith, L. Panny, B. Smith, F. Vercauteren, “Quantum equivalence of the DLP and
+CDHP for group actions,” Math. Cryptol. 1 (2021) 40–44
+[12] N. Koblitz, “Elliptic curve cryptosystems,” Math. Comp. 48 (1987) 203–209
+[13] U. M. Maurer, “Towards the equivalence of breaking the Diffie-Hellman protocol and com-
+puting discrete logarithms,” in: Advances in Cryptology—CRYPTO ’94, pp. 271–281, LNCS
+839, Springer, 1994
+[14] U. M. Maurer, “Abstract models of computation in cryptography,” in: Cryptography and
+Coding 2005, pp. 1–12, LNCS 3796, Springer, 2005
+[15] U. M. Maurer, S. Wolf, “The relationship between breaking the Diffie-Hellman protocol and
+computing discrete logarithms,” SIAM J. Comput. 28 (1999) 1689–1721
+[16] G. Maze, “Algebraic methods for constructing one-way trapdoor functions,” Ph. D. disserta-
+tion, University of Notre Dame (2003)
+[17] G. Maze, C. Monico, J. Rosenthal, “Public-key cryptography based on semigroup actions,”
+Adv. Math. Commun. 1 (2007) 489–507
+[18] V. S. Miller, “Use of elliptic curves in cryptography,” in: Advances in Cryptology—CRYPTO
+’85, pp. 417–426, LNCS 218, Springer, 1986
+[19] C. Monico, “Semirings and semigroup actions in public-key cryptography,” Ph. D. disserta-
+tion, University of Notre Dame (2002)
+[20] H. Montgomery, M. Zhandry, “Full quantum equivalence of group action DLog and CDH,
+and more,” in: Advances in Cryptology—ASIACRYPT 2022 (to appear), Springer, 2022
+[21] S. C. Pohlig, M. E. Hellman, “An improved algorithm for computing logarithms over GF(p)
+and its cryptographic significance,” IEEE Trans. Inform. Theory 24 (1978) 106–110
+[22] A. Rostovtsev, A. Stolbunov, “Public-key cryptosystem based on isogenies,” 19 pages, IACR
+eprint 2006/145
+[23] V. Shoup, “Lower bounds for discrete logarithms and related problems,” in: Advances in
+Cryptology—EUROCRYPT ’97, pp. 256–266, LNCS 1233, Springer, 1997
+[24] P. W. Shor, “Polynomial-time algorithms for prime factorization and discrete logarithms on
+a quantum computer,” SIAM J. Computing 26 (1997) 1484–1509
+[25] B. Smith, “Pre- and post-quantum Diffie-Hellman from groups, actions, and isogenies,” in:
+Workshop on the Arithmetic of Finite Fields 2018, pp. 3–40, LNCS 11321, Springer, 2018
+[26] A. Stolbunov, “Constructing public-key cryptographic schemes based on class group action
+on a set of isogenous elliptic curves,” Adv. Math. Commun. 4 (2010) 215–235
+[27] J. Zumbr¨agel, “Public-key cryptography based on simple semirings,” Ph. D. dissertation,
+University of Zurich (2008)
+Department of Mathematical Sciences, Aalborg University, Denmark
+Email address: owg@math.aau.dk
+Faculty of Comp. Science and Mathematics, University of Passau, Germany
+Email address: jens.zumbraegel@uni-passau.de
+
diff --git a/utAzT4oBgHgl3EQfsP2h/content/tmp_files/load_file.txt b/utAzT4oBgHgl3EQfsP2h/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d705aca44f6f5ab85b6534d10d3f1f8dbc0cd09e
--- /dev/null
+++ b/utAzT4oBgHgl3EQfsP2h/content/tmp_files/load_file.txt
@@ -0,0 +1,619 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf,len=618
+page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='01657v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='CR]  4 Jan 2023  CRYPTOGRAPHIC GROUP AND SEMIGROUP ACTIONS  OLIVER W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' GNILKE AND JENS ZUMBR¨AGEL  Dedicated to Joachim Rosenthal on the occasion of his 60th birthday  Abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' We consider actions of a group or a semigroup on a set,  which generalize the setup of discrete logarithm based cryptosystems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  Such cryptographic group actions have gained increasing attention re-  cently in the context of isogeny-based cryptography.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  We introduce  generic algorithms for the semigroup action problem and discuss lower  and upper bounds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Also, we investigate Pohlig-Hellman type attacks  in a general sense.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' In particular, we consider reductions provided by  non-invertible elements in a semigroup, and we deal with subgroups in  the case of group actions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  Keywords: Discrete logarithm problem;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' cryptographic group action;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  semigroup action problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Introduction  The discrete logarithm problem has a long and profound history (see [8]  for a recent survey).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' In cryptography it has been playing a key role ever  since Diffie and Hellman have based the security of their famous protocol [6]  on the hardness of computing discrete logarithms modulo a large prime p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  The underlying group F∗  p has then been generalized, most notably to the  Fq-rational points on an elliptic curve, due to Miller [18] and Koblitz [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  In fact, while the discrete logarithm problem in the unit group F∗  q of a finite  field can be solved in subexponential time by index calculus algorithms (for  an overview, see [9]), the fastest known algorithm in a general elliptic curve  is basically a generic one that requires exponential time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  However, Shor’s quantum algorithm [24] constitutes a polynomial time at-  tack on the discrete logarithm problem in any group (as well as on the integer  factorization problem).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' These observations, and reports on the progress in  building quantum computers now achieving a “quantum supremacy” [2],  underline the need for new concepts to build cryptosystems resistant to  quantum attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' An interesting approach is based on isogenies of super-  singular elliptic curves (SIDH, [10]), which however is broken due to the  Castryck-Decru attack [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  More recently, a commutative supersingular isogeny-based Diffie-Hellman  scheme (CSIDH, [3]) has been proposed as a more efficient variant, which  is based on the action of the class group of an endomorphism ring on iso-  morphism classes of elliptic curves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  This is an example for an action of  2010 Mathematics Subject Classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' 94A60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  The material in this paper was presented in part at the Workshop on Coding and  Cryptography (WCC 2022) in Rostock, Germany.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  1  2  OLIVER W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' GNILKE AND JENS ZUMBR¨AGEL  an abelian group on a set, which as a framework suffices to build a Diffie-  Hellman protocol, as has been observed by Couveignes [5] and independently  by Rostovtsev and Stolbunov [22, 26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  With a somewhat different background, Maze, Monico and Rosenthal  have introduced actions of commutative semigroups on sets [19, 17] in or-  der to generalize the discrete logarithm problem, one motivation being to  find examples that do not allow even an (exponential) square-root attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  The setup was further investigated by the theses of the present authors, in  which Zumbr¨agel [27] considered a generalization to non-commutative semi-  groups and Gnilke [7] showed how a Pohlig-Hellman like reduction applies  to semigroups with non-invertible elements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  In this work, we revisit the concept of semigroup actions for discrete log-  arithm based cryptosystems and connect it to recent proposals of isogeny-  based cryptography.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' In the case of abelian group actions, with a view to-  wards isogenies, this has been considered by Couveignes [5] and, more re-  cently, by Smith [25] and Alamati et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Here we aim to take a slightly  more abstract viewpoint and introduce generic algorithms for the semigroup  action problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' We also investigate Pohlig-Hellman type reductions and  consider those provided by non-units in a semigroup and by subgroups in  the context of a group action.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Cryptographic semigroup actions  In this section we briefly recall the notion of a semigroup action and its  application to cryptography [19, 17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  By a semigroup we mean a set S with an associative binary operation  (written multiplicatively).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' It is called a monoid if a neutral element exists.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  A semigroup action with respect to a semigroup S and a set X is a map  S × X → X ,  (s, x) �→ s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x  such that st.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x = s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='(t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x) for all s, t ∈ S and x ∈ X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Considering for s ∈ S  the transformation Φs : X → X, x �→ s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x, this means that Φst = Φs ◦ Φt for  s, t ∈ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' When there is a semigroup action, then X is also called S-set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Consider a semigroup S acting on a set X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' The semigroup  action problem is the problem, for given x, y ∈ X to find some s ∈ S such  that y = s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  So the above problem asks to find preimages of the “orbit map”  Ψx : S → X ,  s �→ s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  Suppose that S is a group and let Sx = {s ∈ S | s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x = x} be the stabilizer  subgroup of x ∈ X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Then the orbit map induces a bijection S/ℓ Sx ∼  −→ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x of  the left cosets and the orbit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Thus solutions to the semigroup action problem  (which we also call group action problem) are unique up to left congruence  modulo the stabilizer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  Since we deal with cryptographic applications, we assume all structures  to be finite and that the semigroup action is efficiently computable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' This  means that elements of the semigroup S and the set X are encoded by bit  strings, and both the semigroup operation and the action are computable in  polynomial time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  CRYPTOGRAPHIC GROUP AND SEMIGROUP ACTIONS  3  Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Consider a finite cyclic group (G, ·) of order n, which may  be seen as a Zn-module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' If we “forget” its additive structure, we have  (Zn, ·) × G → G ,  (s, g) �→ gs ,  and the semigroup action problem is just the discrete logarithm problem in  the group G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Note that the action is efficiently computable by a square-  and-multiply method, provided the group operation is efficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  In order to set up a Diffie-Hellman like key agreement, we need some  way to generate commuting elements of the semigroup S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' For simplicity we  assume here the semigroup to be commutative and have the following key  agreement scheme:  Alice  public  Bob  x ∈ X  a ∈ S  →  a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x ∈ X  b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x ∈ X  ←  b ∈ S  kA = a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' (b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x)  kB = b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x)  Observe that both parties compute the same key ab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x = ba.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Also notice  that in the case of Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='2 the scheme amounts to classical Diffie-  Hellman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Consider a commutative semigroup S acting on a set X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  The semigroup Diffie-Hellman problem is the problem, for given x, y, z ∈ X  to find some k ∈ X such that y = a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x, z = b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x and k = ab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x = ba.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x for some  a, b ∈ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  It is clear that if one can solve the semigroup action problem, then one  can break the Diffie-Hellman protocol, while the converse direction is not ob-  vious.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' There have been results on subexponential reductions in the classical  case of group exponentiation [13, 15], and recently on polynomial quantum  reduction for abelian group actions [11, 20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' In isogeny-based cryptography and CSIDH, a particular case  of interest is the action of an abelian group (the class group in an en-  domorphism ring) on a set X (of isomorphism classes of elliptic curves),  cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' [5, 3, 25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' In Couveignes’ work [5] the group action is also assumed to  be simply transitive, and the semigroup action problem and the semigroup  Diffie-Hellman problem are called vectorization problem and parallelization  problem, respectively;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' if those are intractable, the set X is referred to as a  hard homogeneous space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  It would be interesting to view SIDH also in the framework of a group  action, but this seems not to be obvious, cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' [25, Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' 15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Generic algorithms  We use Maurer’s abstract model of computation [14] to describe generic  algorithms for a semigroup action.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Recall that in this model one specifies  a ground set M,  a set Π of certain operations f : Mt → M of arity t ∈ {0, 1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' },  a set Σ of certain relations ρ ⊆ Mt of arity t ∈ {1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' }.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  4  OLIVER W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' GNILKE AND JENS ZUMBR¨AGEL  There are internal state variables V1, V2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' storing elements in M, which  cannot be read directly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' A generic algorithm A(M, Π, Σ) is then allowed to  perform computation operations and relation queries for f ∈ Π and ρ ∈ Σ,  using the internal state variables as input (and operation output).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' In the  analysis we usually discard the relation queries and only count the number  of operations performed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Generic algorithms in a cyclic group of order n can be mod-  eled using M = Zn, Π = {+} and Σ = {=}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' For the discrete logarithm  problem the state variables are initialized with V1 = 1 and V2 = s ∈ Zn  random, and the goal is to solve the extraction problem for the value s ∈ V2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  Now let S × X → X be a semigroup action and fix x ∈ X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' In order to  address the semigroup action problem, we define the ground set as  M := S/∼x ,  where  s ∼x t :⇔ s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x = t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x ,  and denote the class of s ∈ S by [s].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' We allow for any a ∈ S to perform  the unary operation Φa : M → M, [s] �→ a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' [s] := [as].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' The state variables  are initialized with V1 = [1] (assuming that 1 ∈ S, otherwise we adjoin it)  and V2 = [s] ∈ M, which describes the solutions s to a semigroup action  problem y = s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' The goal is to solve the extraction problem for V2, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=', to  find some s′ ∈ S such that [s] = [s′].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  If we are dealing with a group action, the set S/∼x = S/ℓ Sx consists of  the left cosets [s] = sSx of the stabilizer subgroup of x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' In this case, we can  show the following result, which provides a generic lower bound of Ω(√n)  for the group action problem in a set X of size n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Let S × X → X be a transitive group action, which is  abelian or free.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  Fix x ∈ X and let M := S/ℓ Sx, Π = {Φa | a ∈ S},  Σ = {=} as above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' If s ∈ S is uniformly random, the success probability  of a generic algorithm A(M, Π, Σ) for the group action problem y = s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x  using m operation queries is at most 1  4m2/|X|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Following the proof of [14, Thm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' 1] it suffices to upper bound the  probability that a collision in the state variables occurs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' These entries are  either of the form a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' [1] = [a] or of the form b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' [s], for known a, b ∈ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' A col-  lision of type [a] = [a′] is independent of s and can be discarded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Moreover,  a collision of type b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' [s] = b′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' [s] means that b−1b′ ∈ Ss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x = sSxs−1, but since  the action is abelian or free we have sSxs−1 = Sx, again independent of s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  This means that the only collisions related to s are of the form  a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' [1] = b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' [s]  for some a, b ∈ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Such an event is equivalent to [s] = [b−1a], and since  [s] ∈ M is uniformly random it occurs with probability 1/n, where n :=  |M| = |X|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' So if the algorithm computes u and v values of the form a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' [1]  and b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' [s] respectively, the probability for a collision is at most uv/n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' But  since u+v ≤ m we have uv ≤ 1  4m2, from which the result follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  □  The following example shows that there may be much faster generic al-  gorithms in case the group action is neither abelian nor free.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  CRYPTOGRAPHIC GROUP AND SEMIGROUP ACTIONS  5  Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Let X be a set of size n and let the symmetric group S :=  Sym X act on X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Fix x ∈ X and let s ∈ S be random.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' A generic algorithm  to find the coset [s] ∈ S/ℓ Sx can employ either “usual” collisions [a] = b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' [s],  from which a solution s′ := b−1a can be obtained, or collisions of the form  b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' [s] = b′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' [s],  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=', c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='[s] = [s] for c := b−1b′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' If we choose c ∈ S having k fixed points, then  the event probability is k/n, and thus we may apply a divide-and-conquer  strategy to obtain [s] in O(log n) steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  Furthermore, for proper semigroup actions the difficulty of the generic  semigroup action problem very much depends on the structure of the semi-  group, and ranges from efficient algorithms in O(log n) to lower bounds of  Ω(n), see the examples below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' From a cryptography perspective there are  however issues with applying those actions, as discussed in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Let S be a semigroup, X a set and ϕ: S → X a bijection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  Then we can make X an S-set by letting  s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='ϕ(t) = ϕ(st)  for s, t ∈ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' We assume this action to be efficiently computable and think of  the inverse map ϕ−1 as “hidden”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' For example, if G is a cyclic group with  generator g, we use the bijection ϕ: (Zn, ·) → G, s �→ gs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Let us look at two  further cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  (1) Suppose that (S, ·) = ({1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' , n}, min) and we are given a semigroup  action problem instance x, y ∈ X where y = s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Let a = ϕ−1(x)  which we suppose is known, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=', a = n if x = ϕ(n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Since y = s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x =  s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='ϕ(a) = ϕ(sa) = ϕ(saa) = sa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='ϕ(a) = sa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x, we may assume that  s = sa, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=', s ≤ a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Then for any t ∈ S, t ≤ a, there holds  t ≤ s ⇔ t = ts ⇔ ta = tsa ⇔ ϕ(ta) = ϕ(tsa)  ⇔ t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='ϕ(a) = t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='(s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='ϕ(a)) ⇔ t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x = t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='y .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  Hence, we can find s using binary search in O(log n) steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  (2) On the other hand, define (S, ·) = ({0, s1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' , sm, 1}, ∧), where ∧ is  a semilattice operation such that  0 ∧ si = 0 ,  1 ∧ si = si ,  and  si ∧ sj = 0 whenever i ̸= j ,  and let o = ϕ(0) and e = ϕ(1) in X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Consider a semigroup action  problem instance e, y ∈ X where y = s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' As s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='e = s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='ϕ(1) = ϕ(s1) =  ϕ(s) and ϕ is bijective, there is a unique solution s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' When using a  generic algorithm we may for t ∈ S compute t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='e = ϕ(t) and t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='y =  t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='(s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='e) = ts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='e = ϕ(ts), where a collision occurs only if t = ts, which  if s = si means that t ∈ {0, si}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' So it requires Ω(n) steps to find any  collision and thus information about s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  Note that this example is not interesting for a Diffie-Hellman type  key agreement, because the key k = a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' (b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='e) = b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='e) will usually  be o.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  6  OLIVER W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' GNILKE AND JENS ZUMBR¨AGEL  We should mention here that Shoup’s model for generic algorithms [23]  is also widely used, which is based on representations of algebraic objects  as random bitstrings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' In the case of a cyclic group of order n one has an  injective “encoding function” σ: Zn → {0, 1}∗, and the algorithm maintains  a list of encodings (σ(x1), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' , σ(xk)) to which entries σ(xi +xj) may be  appended by performing oracle queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' The bitstring representation allows  a generic algorithm to perform additional operations, like sorting or hashing  of algebraic objects, and thus enables algorithms based on pseudorandom  functions such as Pollard’s rho method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' It is possible to show a square-root  lower bound for the group action problem in Shoup’s model by adapting the  proof of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  Regarding upper bounds for the complexity of the semigroup action prob-  lem, generic algorithms often aim at finding a collision in square-root time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  However, in order to deduce a solution from it one needs the ability to in-  vert some elements in the semigroup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Below we present a version of Shanks’  baby-step-giant-step method as well as a Pollard-rho type attack for the case  of group actions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  Note that in the quantum world generic attacks on group actions may be  faster than square-root time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Indeed, there are subexponential algorithms  solving the group action problem for (free) abelian group actions based on  Kuperberg’s quantum algorithm, cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' [20, Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' 7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Collision attacks  Let X be an S-set of size n and let x ∈ X, y ∈ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' We now discuss  generic upper bounds for the corresponding semigroup action problem, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=',  to find s ∈ S such that y = s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' An important class of generic algorithms  relies on finding a collision a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x = b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='y for some a, b ∈ S, from which we can  deduce a solution s := b−1a, provided that b is invertible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  For analyzing such algorithms, the following combinatorial result on the  probability that two random subsets are disjoint is useful (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' [7, Lem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' 68]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Let X be a set of size n and let A, B ⊆ X be uniformly chosen  random subsets of size k, ℓ respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Then  1 − kℓ  n ≤ Pr(A ∩ B = ∅) ≤ exp(− kℓ  n ) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Let us assume w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' l.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' o.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' that B is fixed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' For the lower bound we have  Pr(A ∩ B ̸= ∅) = Pr(�  x∈B{x ∈ A}) ≤ �  x∈B Pr(x ∈ A) = ℓ· k  n  by the union bound.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' For the upper bound we may assume that A consists  of k randomly chosen elements of X, possibly with repetition, by which the  probability of being disjoint to B only can increase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Let Ti be the event that  the i-th element of A does not lie in B, for 1 ≤ i ≤ k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Then these events  are independent of probability 1− ℓ  n, whence  Pr(A ∩ B = ∅) ≤ Pr(�  i Ti) = (1− ℓ  n)k ≤ exp(− ℓk  n ) ,  since 1+x ≤ exp x holds for all x ∈ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  □  CRYPTOGRAPHIC GROUP AND SEMIGROUP ACTIONS  7  A time-memory trade-off.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' We first present a simple time-memory trade-  off attack adopting Shanks’ baby-step-giant-step method (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' [7, Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='2]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  Let the semigroup S be a monoid with group of invertible elements S∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' The  algorithm is described as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  (1) precompute a table of entries (bj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='y, bj) for bj ∈ S∗ random  (2) for a ∈ S random, check if a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x = bj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='y for some j, if yes output  s := b−1  j a  For the analysis, according to the proof of Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='1 we may bound  the collision probability even if the set B := {b1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='y, b2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='y, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' } is of a special  nature (as the bj have to be invertible).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' It is enough to require that the set  A := {a1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x, a2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' } generated by the algorithm behaves as random, which  holds if the orbit map Ψx: S → X, s �→ s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x has (nearly) constant-sized  preimages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  Suppose the algorithm generates k := |A| elements ai.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x with ai ∈ S and  ℓ := |B| elements bj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='y with bj ∈ S∗, which is upper bounded by |S∗|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Then  we infer from Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='1 that the success probability of the algorithm is at  least 1  2 provided that exp(− kℓ  n ) ≤ 1  2, or equivalently,  kℓ ≥ n ln 2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  Therefore, an optimal choice of parameters is k, ℓ ∈ Θ(√n), which is  possible if a sufficient amount of invertible elements is available and there is  enough memory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' In such a case the complexity of this algorithm is seen to  be O(√n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Next we show an approach how to drastically reduce the memory  requirement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  A Pollard-rho attack for group actions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Suppose now that a group G  acts transitively on a set X of size n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Given x, y ∈ X the group action  problem asks to find g ∈ G such that y = g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' We describe a Pollard-rho  type birthday attack for solving this problem, which is a slight adaption and  simplification of an algorithm given by Monico [19, Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  As before, the idea is to generate elements ai.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x, bj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='y ∈ X in a pseudo-  random way and to provoke a collision ai.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x = bj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='y from which a solution  g := b−1  j ai to the group action problem is deduced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' But here, this is to be  done using very little memory while still maintaining a heuristic square-root  complexity O(√n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  The algorithm depends on a pseudorandom function f : X → G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Define  a recursive sequence (a1, a2, a3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' ) in G by  a1 := a ∈ G random ,  ai+1 := f(ai.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x) ai  for i ≥ 1 ,  hence a2 = f(a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x) a, a3 = f(f(a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x) a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x) f(a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x) a, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Observe that if ai.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x =  aj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x for some i, j then ai+r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x = aj+r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x for all r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Similarly, define a recursive  sequence (b1, b2, b3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' ) in G by  b1 := b ∈ G random ,  bj+1 := f(bj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='y) bj  for j ≥ 1 ,  and note that if ai.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x = bj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='y then ai+r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x = bj+r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='y for all r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' The algorithm  now consists of two steps:  (1) construct a-loop, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=', find smallest k such that ak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x = a2k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x  construct b-loop, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=', find smallest ℓ such that bℓ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='y = b2ℓ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='y  8  OLIVER W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' GNILKE AND JENS ZUMBR¨AGEL  (2) find a collision in the sets  A := {ak+i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x | 0 ≤ i < k}  and  B := {bℓ+j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='y | 0 ≤ j < ℓ}  by checking ak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x = bℓ+s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='y for s = 0, 1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' if successful output  g := b−1  ℓ+sak  Notice here that if ak+i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x = bℓ+j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='y for some i, j, then ak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x = a2k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x = bℓ+s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='y  for s := j+k−i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  We sketch a heuristic analysis of this algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' With good probability  we have |A| = k and |B| = ℓ (if the preperiod does not exceed the period)  and we expect k, ℓ ∈ O(√n) by the birthday paradox.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Assuming that A, B  behave as random subsets of X we can estimate the probability of a collision  using Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='1 by  Pr(A ∩ B ̸= ∅) ≥ 1−exp  �  − kℓ  n  �  ∈ Ω(1) ,  provided that k, ℓ ∈ Ω(√n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  These arguments show that the algorithm  has an expected running time of O(√n) and succeeds with non-negligible  probability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  This algorithm may be adapted to work also for proper semigroup actions,  in case the semigroup S has sufficiently many invertible elements S∗ and we  are able to define a sequence (b1, b2, b3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' ) in S∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Alternatively, as pointed  out by Maze [16], semigroups with a large subgroup can be attacked by  excluding all non-units first and then employing the above algorithm on the  unit subgroup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Pohlig-Hellman type reductions  In this section we examine how the hardness of the semigroup action  problem is affected by exploiting certain substructures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' We recollect the  framework of Pohlig-Hellman type reductions from [7, Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='3] and discuss  a few special cases for cryptographic group actions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  Recall that the classical Pohlig-Hellman algorithm [21] essentially reduces  the difficulty of the discrete logarithm problem in a cyclic group G of order n  to that in a group of order the largest prime factor of n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' The algorithm can  be viewed as applying multiplication-by-m maps  λm : Zn → Zn ,  s �→ ms  in order to reduce the problem to the action of the (smaller) ideal mZn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' The  following general concept captures this scenario and many others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  Definition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Let S and T be semigroups, let X be an S-set and Y be a  T-set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' A reduction (f, F, G) consists of maps f : S → T and F, G: X → Y  such that  f(s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='G(x) = F(s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x)  for all s ∈ S and x ∈ X, see the diagram below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  S  Ψx  �  f  �  X  F  �  T  ΨG(x)  � Y  G  �  CRYPTOGRAPHIC GROUP AND SEMIGROUP ACTIONS  9  For a general reduction (f, F, G) the map f : S → T is not required  to be a semigroup homomorphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  However, if F = G it is reasonable  to assume this, since f(st).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='F(x) = F(st.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x) = F(s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x) = f(s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='F(t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x) =  f(s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='f(t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='F(x) = f(s)f(t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='F(x) for all s, t ∈ S and x ∈ X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  Example 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Let G be a cyclic group with generator α of composite order  n = km.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  In the Pohlig-Hellman setup above we may apply the isomor-  phism mZn ∼= Zk after the multiplication-by-m map λm, which results in  the natural map π: Zn → Zk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Then one has a reduction (π, Φm, Φm), where  Φm : ⟨α⟩ → ⟨αm⟩, g �→ gm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Indeed, there holds (gm)π(s) = (gs)m for any  s ∈ Zn and g ∈ G, see below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  Zn  Ψg  �  π  �  ⟨α⟩  Φm  �  Zk  Ψgm  � ⟨αm⟩  Φm  �  Given any reduction (f, F, G), an adversary who can solve the semigroup  action problem in T can restrict the search in S to preimages of the solutions  in T under the map f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Indeed, given a semigroup action problem instance  x, y ∈ X where y = s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x, one reduces it to the instance G(x), F(y) ∈ Y where  F(y) = f(s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='G(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Nevertheless one should note the following caveats:  (1) In general, for a single solution t ∈ im f ⊆ T of F(y) = t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='G(x) it is  not clear whether there always exists s ∈ f −1(t) such that y = s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  (2) If the above solution t ∈ im f is unique, then t = f(s) and we can  deduce that s ∈ f −1(t), which may be a much smaller set than S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  However, the preimage under f could be hard to obtain, and often  it does not admit a useful semigroup action structure itself.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  Similarly to the Pohlig-Hellman algorithm we may apply several reduc-  tions (f1, F1, G1), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' , (fr, Fr, Gr) in parallel to further narrow down the  search space to s ∈ f −1  1 (t1) ∩ · · · ∩ f −1  r (tr) if suitable solutions t1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' , tr  of the reduced semigroup action problems are found.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  Examples based on non-units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' We call a reduction effective if the maps  f, F, G are efficiently computable and there holds 1 < |T| < |S|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' The next  result describes a very general class of reductions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  Proposition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Let S be a monoid, X an S-set and m ∈ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Then the  triple (λm, Φm, id) forms a reduction, which is effective iff m is not left-  absorbing and not invertible, provided the semigroup operation and action  are efficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' For all x ∈ X and s ∈ S there holds that  λm(s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x = ms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x = m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='(s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x) = Φm(s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  The reduction maps the semigroup S onto its right ideal mS, which is a non-  trivial proper subsemigroup of S iff λm is not constant or surjective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  □  Akin to the Pohlig-Hellman approach for groups of prime power order,  we may apply this reduction recursively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' The idea for solving the semigroup  10  OLIVER W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' GNILKE AND JENS ZUMBR¨AGEL  action problem y = s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x is to find t1 := m1s from m1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='y = t1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x (bearing in  mind the caveats above), and for obtaining t1 to find t2 := m2m1s from  m2m1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='y = t2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=', for suitable non-units m1, m2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' of S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  Hence, the result constitutes a considerable threat to the security of  a cryptosystem based on proper semigroup actions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  On the other hand,  the rather degenerate semigroup S of Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='4 (2) contains many non-  absorbing non-units and yet has a generic complexity of Ω(n) for the semi-  group action problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' In this case, one has |mS| = 2 for all non-absorbing  non-units m and the corresponding preimage sets are not useful (see also [7,  Ex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' 79]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  In conclusion, while it is conceivable that certain semigroup actions avoid  the attacks outlined in this section and are in fact interesting for cryptogra-  phy, possible candidates have to be chosen very carefully.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  Examples based on automorphisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Now we consider a second fam-  ily of reductions, which also applies to group actions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Let us start with a  general semigroup S and an S-set X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Its automorphisms are the bijective  maps ϕ: X → X such that ϕ(s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x) = s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='ϕ(x) for all s ∈ S, x ∈ X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' We use  automorphism groups to construct equivalence relations on X compatible  with the action as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Suppose that a group H acts on X by automor-  phisms, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=', we have H × X → X, (h, x) �→ h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x, such that h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x = s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x for  h ∈ H, s ∈ S, x ∈ X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Let X/∼ be the set of its orbits [x] = {h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x | h ∈ H}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  This induces an action  S × X/∼ → X/∼ ,  (s, [x]) �→ [s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x] .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  Suppose next that the semigroup S is a commutative monoid with unit  group S∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  Then each h ∈ S∗ defines an S-automorphism Ψh : X → X  by x �→ h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x, so we may consider any subgroup H of S∗ as a group of  automorphisms of X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  The relation s ≈ t iff sH = tH then provides a  semigroup congruence on S, and we denote by S/H := {sH | s ∈ S} its  classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Moreover, s ≈ t implies s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x ∼ t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x, for any s, t ∈ S and x ∈ X, so we  can define an action  S/H × X/∼ → X/∼ ,  ([s]≈, [x]∼) �→ [s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='x]∼ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  We hence obtain a reduction (f, F, F) with f : S → S/≈ and F : X → X/∼  being the natural maps, see below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  S  Ψx  �  f  �  X  F  �  S/H  Ψ[x]  � X/∼  F  �  In particular, if S = G is an abelian group, so that S∗ = G, we can employ  any subgroup H of G and thus X/∼ becomes a G/H-set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Regarding the  practical implications however, the reduced action may not be efficiently  computable, because the equality of orbits could be difficult to check.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' In  any case, an effective reduction attack cannot be of generic type, since we  are guaranteed a lower square-root complexity for such algorithms due to  Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  CRYPTOGRAPHIC GROUP AND SEMIGROUP ACTIONS  11  This approach was also described in the context of CSIDH, cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' [25, Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' 12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  Remark 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' As in Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='2 consider the discrete logarithm setup of  an abelian group X of order n, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=', we have the action of (Zn, ·) on X by  exponentiation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Every group automorphism is also an automorphism of X  as an Zn-set, thus any subgroup H of the automorphism group of X induces  an action  (Zn, ·)/H × X/∼ → X/∼,  ([s], [x]) �→ [xs] .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  In the special case of H = {±1} we have the orbits [x] = {x, x−1}, reflecting  the practice in elliptic curve cryptography to identify the points ±P and  thus use only the x-coordinate [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  Such reductions could potentially weaken the security of the discrete log-  arithm problem in groups for which the automorphism group has several  subgroups, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=', in cyclic groups of order n where ϕ(n) = |Z∗  n| is smooth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  However, as mentioned above these reductions appear to be not effective in  general.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  Let us state a concrete example illustrating this phenomenon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  Example 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Consider the discrete logarithm problem in a group X of  prime order n = 29 (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=', a subgroup of Z∗  59).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Then we have S = (Z29, ·)  and hence  S∗ = Z∗  29 ∼= Z28 ∼= Z4×Z7 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  Therefore, one could try to exploit the subgroups H1 = ⟨α1⟩, H2 = ⟨α2⟩  of order 4 and 7 respectively, say α1 = 12 ∈ Z∗  29 and α2 = 7 ∈ Z∗  29,  to attack to problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  But the reduced group actions seem to be more  difficult to compute, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=', we have Z∗  29/⟨7⟩ × X/∼ → X/∼ where [x] =  {x, x7, x20, x24, x23, x16, x25} ∈ X/∼.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Conclusion  Cryptographic group actions or semigroup actions provide a framework  that encompasses both the classical discrete logarithm problem as well as  interesting proposals for post-quantum cryptography.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' In this article we have  examined this framework from a theoretical viewpoint and studied the semi-  group action problem as an analog of the discrete logarithm problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  In the case of group actions, the generic complexity can be considered well  understood, as there is both a square-root lower bound and a square-root  upper bound for the group action problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' On the other hand, for proper  semigroup actions the situation appears to be less clear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' The generic lower  bound may exceed the square-root barrier, however such instances tend to  be degenerate and not interesting for cryptography applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  We also have discussed the potential of certain substructures to weaken  the hardness of the semigroup action problem, in particular in the presence of  non-units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' While such substructures do not guarantee to practically break  the semigroup action problem, they should be taken into account when  designing cryptosystems based on semigroup or group actions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='  12  OLIVER W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' GNILKE AND JENS ZUMBR¨AGEL  References  [1] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Alamati, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' De Feo, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Montgomery, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Patranabis, “Cryptographic group actions and  applications,” in: Advances in Cryptology—ASIACRYPT 2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' 411–439, LNCS 12492,  Springer, 2020  [2] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Arute, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=', “Quantum supremacy using a programmable superconducting processor,”  Nature 574 (2019), 505–510  [3] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Castryck, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Lange, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Martindale, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Panny, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Renes, “CSIDH: an efficient post-  quantum commutative group action,” in:  Advances in Cryptology—ASIACRYPT 2018,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' 395–427, LNCS 11274, Springer, 2018  [4] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Castryck, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Decru, “An efficient key recovery attack on SIDH,” 15 pages, IACR eprint  2022/975  [5] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Couveignes, “Hard homogenous spaces,” 15 pages, IACR eprint 2006/291 (1997, pub-  lished 2006)  [6] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Diffie, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Hellman, “New directions in cryptography,” IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Inform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Theory 22  (1976) 644–654  [7] O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Gnilke, “The semigroup action problem in cryptography,” Ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' dissertation, Univer-  sity College Dublin (2014)  [8] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Granger, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Joux, “Computing discrete logarithms,” in: Computational Cryptography—  Algorithmic Aspects of Cryptology, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' 106–139, Cambridge Univ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Press, 2021  [9] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Granger, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Kleinjung, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Zumbr¨agel, “Indiscreet logarithms in finite fields of small char-  acteristic,” Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' 12 (2018) 263–286  [10] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' De Feo, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Jao, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Plˆut, “Towards quantum-resistant cryptosystems from supersingular  elliptic curve isogenies,” J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Cryptol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' 8 (2014) 209–247  [11] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Galbraith, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Panny, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Smith, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Vercauteren, “Quantum equivalence of the DLP and  CDHP for group actions,” Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Cryptol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' 1 (2021) 40–44  [12] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Koblitz, “Elliptic curve cryptosystems,” Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Comp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' 48 (1987) 203–209  [13] U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Maurer, “Towards the equivalence of breaking the Diffie-Hellman protocol and com-  puting discrete logarithms,” in: Advances in Cryptology—CRYPTO ’94, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' 271–281, LNCS  839, Springer, 1994  [14] U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Maurer, “Abstract models of computation in cryptography,” in: Cryptography and  Coding 2005, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' 1–12, LNCS 3796, Springer, 2005  [15] U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Maurer, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Wolf, “The relationship between breaking the Diffie-Hellman protocol and  computing discrete logarithms,” SIAM J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' 28 (1999) 1689–1721  [16] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Maze, “Algebraic methods for constructing one-way trapdoor functions,” Ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' disserta-  tion, University of Notre Dame (2003)  [17] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Maze, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Monico, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Rosenthal, “Public-key cryptography based on semigroup actions,”  Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' 1 (2007) 489–507  [18] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Miller, “Use of elliptic curves in cryptography,” in: Advances in Cryptology—CRYPTO  ’85, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' 417–426, LNCS 218, Springer, 1986  [19] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Monico, “Semirings and semigroup actions in public-key cryptography,” Ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' disserta-  tion, University of Notre Dame (2002)  [20] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Montgomery, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Zhandry, “Full quantum equivalence of group action DLog and CDH,  and more,” in: Advances in Cryptology—ASIACRYPT 2022 (to appear), Springer, 2022  [21] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Pohlig, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Hellman, “An improved algorithm for computing logarithms over GF(p)  and its cryptographic significance,” IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Inform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Theory 24 (1978) 106–110  [22] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Rostovtsev, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Stolbunov, “Public-key cryptosystem based on isogenies,” 19 pages, IACR  eprint 2006/145  [23] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Shoup, “Lower bounds for discrete logarithms and related problems,” in: Advances in  Cryptology—EUROCRYPT ’97, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' 256–266, LNCS 1233, Springer, 1997  [24] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Shor, “Polynomial-time algorithms for prime factorization and discrete logarithms on  a quantum computer,” SIAM J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Computing 26 (1997) 1484–1509  [25] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Smith, “Pre- and post-quantum Diffie-Hellman from groups, actions, and isogenies,” in:  Workshop on the Arithmetic of Finite Fields 2018, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' 3–40, LNCS 11321, Springer, 2018  [26] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Stolbunov, “Constructing public-key cryptographic schemes based on class group action  on a set of isogenous elliptic curves,” Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' 4 (2010) 215–235  [27] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Zumbr¨agel, “Public-key cryptography based on simple semirings,” Ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' dissertation,  University of Zurich (2008)  Department of Mathematical Sciences, Aalborg University, Denmark  Email address: owg@math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='aau.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='dk  Faculty of Comp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content=' Science and Mathematics, University of Passau, Germany  Email address: jens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='zumbraegel@uni-passau.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
+page_content='de' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utAzT4oBgHgl3EQfsP2h/content/2301.01657v1.pdf'}
diff --git a/xdE5T4oBgHgl3EQfMw71/vector_store/index.faiss b/xdE5T4oBgHgl3EQfMw71/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..9f882037a36b93be90ace747a80d37cefcf5e9e1
--- /dev/null
+++ b/xdE5T4oBgHgl3EQfMw71/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:37828a400045b28fb542a2e1aeee197958d9429c4342a09431acd1c69c66bd8c
+size 2883629
diff --git a/xtFRT4oBgHgl3EQfiDco/content/tmp_files/2301.13585v1.pdf.txt b/xtFRT4oBgHgl3EQfiDco/content/tmp_files/2301.13585v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5a6a146a22fa0c4fdf9fed450536a2cc90d46230
--- /dev/null
+++ b/xtFRT4oBgHgl3EQfiDco/content/tmp_files/2301.13585v1.pdf.txt
@@ -0,0 +1,2167 @@
+Naive imputation implicitly regularizes high-dimensional linear
+models.
+Alexis Ayme, Claire Boyer, Aymeric Dieuleveut
+& Erwan Scornet
+Abstract
+Two different approaches exist to handle missing values for prediction: either impu-
+tation, prior to fitting any predictive algorithms, or dedicated methods able to natively
+incorporate missing values. While imputation is widely (and easily) use, it is unfortu-
+nately biased when low-capacity predictors (such as linear models) are applied afterward.
+However, in practice, naive imputation exhibits good predictive performance. In this
+paper, we study the impact of imputation in a high-dimensional linear model with
+MCAR missing data. We prove that zero imputation performs an implicit regularization
+closely related to the ridge method, often used in high-dimensional problems. Leveraging
+on this connection, we establish that the imputation bias is controlled by a ridge bias,
+which vanishes in high dimension. As a predictor, we argue in favor of the averaged SGD
+strategy, applied to zero-imputed data. We establish an upper bound on its generaliza-
+tion error, highlighting that imputation is benign in the d ≫ √n regime. Experiments
+illustrate our findings.
+1
+Introduction
+Missing data has become an inherent problem in modern data science. Indeed, most real-
+world data sets contain missing entries due to a variety of reasons: merging different data
+sources, sensor failures, difficulty to collect/access data in sensitive fields (e.g., health), just
+to name a few. The simple, yet quite extreme, solution of throwing partial observations
+away can drastically reduce the data set size and thereby hinder further statistical analysis.
+Specific methods should be therefore developed to handle missing values. Most of them are
+dedicated to model estimation, aiming at inferring the underlying model parameters despite
+missing values (see, e.g., Rubin, 1976). In this paper, we take a different route and consider
+a supervised machine learning (ML) problem with missing values in the training and test
+inputs, for which our aim is to build a prediction function (and not to estimate accurately
+the true model parameters).
+Prediction with NA
+A common practice to perform supervised learning with missing
+data is to simply impute the data set first, and then train any predictor on the com-
+pleted/imputed data set.
+The imputation technique can be simple (e.g., using mean
+1
+arXiv:2301.13585v1  [math.ST]  31 Jan 2023
+
+imputation) or more elaborate (Van Buuren and Groothuis-Oudshoorn, 2011; Yoon et al.,
+2018; Muzellec et al., 2020; Ipsen et al., 2022). While such widely-used two-step strategies
+lack deep theoretical foundations, they have been shown to be consistent, provided that
+the approximation capacity of the chosen predictor is large enough (see Josse et al., 2019;
+Le Morvan et al., 2021). When considering low-capacity predictors, such as linear models,
+other theoretically sound strategies consist of decomposing the prediction task with respect
+to all possible missing patterns (see Le Morvan et al., 2020b; Ayme et al., 2022) or by
+automatically detecting relevant patterns to predict, thus breaking the combinatorics of such
+pattern-by-pattern predictors (see the specific NeuMiss architecture in Le Morvan et al.,
+2020a). Proved to be nearly optimal (Ayme et al., 2022), such approaches are likely to
+be robust to very pessimistic missing data scenarios. Inherently, they do not scale with
+high-dimensional data sets, as the variety of missing patterns explodes. Another direction
+is advocated in (Agarwal et al., 2019) relying on principal component regression (PCR) in
+order to train linear models with missing inputs. However, out-of-sample prediction in such
+a case requires to retrain the predictor on the training and test sets (to perform a global PC
+analysis), which strongly departs from classical ML algorithms massively used in practice.
+In this paper, we focus on the high-dimensional regime of linear predictors, which will
+appear to be more favorable to handling missing values via simple and cheap imputation
+methods, in particular in the missing completely at random (MCAR) case.
+High-dimensional linear models
+In supervised learning with complete inputs, when
+training a parametric method (such as a linear model) in a high-dimensional framework, one
+often resorts to an ℓ2 or ridge regularization technique. On the one hand, such regularization
+fastens the optimization procedure (via its convergence rate) (Dieuleveut et al., 2017); on
+the other hand, it also improves the generalization capabilities of the trained predictor
+(Caponnetto and De Vito, 2007; Hsu et al., 2012). In general, this second point holds
+for explicit ℓ2-regularization, but some works also emphasize the ability of optimization
+algorithms to induce an implicit regularization, e.g., via early stopping (Yao et al., 2007) and
+more recently via gradient strategies in interpolation regimes (Bartlett et al., 2020; Chizat
+and Bach, 2020; Pesme et al., 2021).
+Contributions
+For supervised learning purposes, we consider a zero-imputation strategy
+consisting in replacing input missing entries by zero, and we formalize the induced bias on a
+regression task (Section 2). When the missing values are said Missing Completely At Random
+(MCAR), we prove that zero imputation, used prior to training a linear model, introduces
+an implicit regularization closely related to that of ridge regression (Section 3). This bias is
+exemplified to be negligible in settings commonly encountered in high-dimensional regimes,
+e.g., when the inputs admit a low-rank covariance matrix. We then advocate for the choice of
+an averaged stochastic gradient algorithm (SGD) applied on zero-imputed data (Section 4).
+Indeed, such a predictor, being computationally efficient, remains particularly relevant for
+high-dimensional learning. For such a strategy, we establish a generalization bound valid
+for all d, n, in which the impact of imputation on MCAR data is soothed when d ≫ √n.
+2
+
+These theoretical results legitimate the widespread imputation approach, adopted by most
+practitioners, and are corroborated by numerical experiments in Section 5. All proofs are to
+be found in the Appendix.
+2
+Background and motivation
+2.1
+General setting and notations
+In the context of supervised learning, consider n ∈ N input/output observations ((Xi, Yi))i∈[n],
+i.i.d. copies of a generic pair (X, Y ) ∈ Rd × R. By some abuse of notation, we always use
+Xi with i ∈ [n] to denote the i-th observation living in Rd, and Xj (or Xk) with j ∈ [d] (or
+k ∈ [d]) to denote the j-th (or k-th) coordinate of the generic input X (see Section A for
+notations).
+Missing values
+In real data sets, the input covariates (Xi)i∈[n] are often only partially
+observed. To code for this missing information, we introduce the random vector P ∈ {0, 1}d,
+referred to as mask or missing pattern, and such that Pj = 0 if the j-th coordinate of X,
+Xj, is missing and Pj = 1 otherwise. The random vectors P1, . . . , Pn are assumed to be
+i.i.d. copies of a generic random variable P ∈ {0, 1}d and the missing patterns of X1, . . . , Xn.
+Note that we assume that the output is always observed and only entries of the input vectors
+can be missing. Missing data are usually classified into 3 types, initially introduced by
+(Rubin, 1976). In this paper, we focus on the MCAR assumption where missing patterns
+and (underlying) inputs are independent.
+Assumption 1 (Missing Completely At Random - MCAR). The pair (X, Y ) and the
+missing pattern P associated to X are independent.
+For j ∈ [d], we define ρj := P(Pj = 1), i.e., 1 − ρj is the expected proportion of
+missing values on the j-th feature. A particular case of MCAR data requires, not only
+the independence of the mask and the data, but also the independence between all mask
+components, as follows.
+Assumption 1’ (Ho-MCAR: MCAR pattern with independent homogeneous components).
+The pair (X, Y ) and the missing pattern P associated to X are independent, and the
+distribution of P satisfies P ∼ B(ρ)⊗d for 0 < ρ ≤ 1, with 1 − ρ the expected proportion of
+missing values, and B the Bernoulli distribution.
+Naive imputation of covariates
+A common way to handle missing values for any
+learning task is to first impute missing data, to obtain a complete dataset, to which standard
+ML algorithms can then be applied. In particular, constant imputation (using the empirical
+mean or an oracle constant provided by experts) is very common among practitioners. In
+this paper, we consider, even for noncentered distributions, the naive imputation by zero, so
+that the imputed-by-0 observation (Ximp)i, for i ∈ [n], is given by
+(Ximp)i = Pi ⊙ Xi.
+(1)
+3
+
+Risk
+Let f : Rd → R be a measurable prediction function, based on a complete d-
+dimensional input. Its predictive performance can be measured through its quadratic risk,
+R(f) := E
+�
+(Y − f (X))2�
+.
+(2)
+Accordingly, we let f⋆(X) = E[Y |X] be the Bayes predictor for the complete case and R⋆
+the associated risk.
+In the presence of missing data, one can still use the predictor function f, applied to the
+imputed-by-0 input Ximp, resulting in the prediction f(Ximp). In such a setting, the risk of
+f, acting on the imputed data, is defined by
+Rimp(f) := E
+�
+(Y − f(Ximp))2�
+.
+(3)
+For the class F of linear prediction functions from Rd to R, we respectively define
+R⋆(F) = inf
+f∈F R(f),
+(4)
+and
+R⋆
+imp(F) = inf
+f∈F Rimp(f),
+(5)
+as the infimum over the class F with respectively complete and imputed-by-0 input data.
+For any linear prediction function defined by fθ(x) = θ⊤x for any x ∈ Rd and a fixed
+θ ∈ Rd, as fθ is completely determined by the parameter θ, we make the abuse of notation
+of R(θ) to designate R(fθ) (and Rimp(θ) for Rimp(fθ)). We also let θ⋆ ∈ Rd (resp. θ⋆
+imp)
+be a parameter achieving the best risk on the class of linear functions, i.e., such that
+R⋆(F) = R(θ⋆) (resp. R⋆
+imp(F) = Rimp(θ⋆
+imp)).
+Imputation bias
+Even if the prepocessing step consisting of imputing the missing data by
+0 is often used in practice, this imputation technique can introduce a bias in the prediction.
+We formalize this imputation bias as
+Bimp(F) := R⋆
+imp(F) − R⋆(F).
+(6)
+This quantity represents the difference in predictive performance between the best predictor
+on complete data and that on imputed-by-0 inputs. In particular, if this quantity is small,
+the risk of the best predictor on imputed data is close to that of the best predictor when all
+data are available. Note that, in presence of missing values, one might be interested in the
+Bayes predictor
+f⋆
+mis(Ximp, P) = E[Y |Ximp, P].
+(7)
+and its associated risk R⋆
+mis.
+Lemma 2.1. Assume that regression model Y = f⋆(X) + ϵ is such that ϵ and P are
+independent, then R⋆ ≤ R⋆
+mis.
+4
+
+Intuitively, under the classical assumption ε ⊥⊥ P (see Josse et al., 2019), which is a
+verified under Assumption 1, missing data ineluctably deteriorates the original prediction
+problem. As a direct consequence, for a well-specified linear model on the complete case
+f⋆ ∈ F,
+Rimp(F) − R⋆
+mis ≤ Bimp(F).
+(8)
+Consequently, in this paper, we focus our analysis on the bias (and excess risk) associated
+to impute-then-regress strategies with respect to the complete-case problem (right-hand side
+term of (8)) thus controlling the excess risk of imputation with respect to the missing data
+scenario (left-hand side term of (8)).
+In a nutshell, the quantity Bimp(F) thus represents how missing values, handled with
+zero imputation, increase the difficulty of the learning problem. This effect can be tempered
+in a high-dimensional regime, as rigorously studied in Section 3. To give some intuition, let
+us now study the following toy example.
+Example 2.2. Assume an extremely redundant setting in which all covariates are equal,
+that is, for all j ∈ [d], Xj = X1 with E
+�
+X2
+1
+�
+= 1. Also assume that the output is such
+that Y = X1 and that Assumption 1’ holds with ρ = 1/2. In this scenario, due to the
+input redundancy, all θ satisfying �d
+j=1 θj = 1 minimize θ �→ R(θ). Letting, for example,
+θ1 = (1, 0, ..., 0)⊤, we have R⋆ = R(θ1) = 0 but
+Rimp(θ1) = E
+�
+(X1 − P1X1)2�
+= 1
+2.
+This choice of θ1 introduces an irreducible discrepancy between the risk computed on the
+imputed data and the Bayes risk R⋆ = 0. Another choice of parameter could actually
+help to close this gap. Indeed, by exploiting the redundancy in covariates, the parameter
+θ2 = (2/d, 2/d, ..., 2/d)⊤ (which is not a minimizer of the initial risk anymore) gives
+Rimp(θ2) = E
+��
+X1 − 2
+d
+d
+�
+j=1
+PjXj
+�2�
+= 1
+d,
+so that the imputation bias Bimp(F) is bounded by 1/d, tending to zero as the dimension
+increases. Two other important observations on this example follow. First, this bound is
+still valid if EX1 ̸= 0, thus the imputation by 0 is still relevant even for non-centered data.
+Second, we remark that ∥θ2∥2
+2 = 4/d, thus good candidates to predict with imputation seem
+to be of small norm in high dimension. This will be proved for more general settings, in
+Section 4.
+The purpose of this paper is to generalize the phenomenon described in Example 2.2 to
+less stringent settings. In light of this example, we focus our analysis on scenarios for which
+some information is shared across input variables: for linear models, correlation plays such a
+role.
+5
+
+Covariance matrix
+For a generic complete input X ∈ Rd, call Σ := E
+�
+XX⊤�
+the
+associated covariance matrix, admitting the following singular value decomposition
+Σ =
+d
+�
+j=1
+λjvjv⊤
+j ,
+(9)
+where λj (resp. vj) are singular values (resp. singular vectors) of Σ and such that λ1 ≥ ... ≥ λd.
+The associated pseudo-norm is given by, for all θ ∈ Rd,
+∥θ∥2
+Σ := θ⊤Σθ =
+d
+�
+j=1
+λj(v⊤
+j θ)2.
+For the best linear prediction, Y = X⊤θ⋆ + ϵ, and the noise satisfies E[ϵX] = 0 (first order
+condition). Denoting E[ϵ2] = σ2, we have
+EY 2 = ∥θ⋆∥2
+Σ + σ2 =
+d
+�
+j=1
+λj(v⊤
+j θ⋆)2 + σ2.
+(10)
+The quantity λj(v⊤
+j θ⋆)2 can be therefore interpreted as the part of the variance explained
+by the singular direction vj.
+Remark 2.3. Note that, in the setting of Example 2.2, Σ has a unique positive singular
+values λ1 = d, that is to say, all of the variance is concentrated on the first singular direction.
+Actually, our analysis will stress out that a proper decay of singular values leads to low
+imputation biases.
+Furthermore, for the rest of our analysis, we need the following assumptions on the
+second-order moments of X.
+Assumption 2. ∃L < ∞ such that, ∀j ∈ [d], E[X2
+j ] ≤ L2.
+Assumption 3. ∃ℓ > 0 such that, ∀j ∈ [d], E[X2
+j ] ≥ ℓ2.
+For example, Assumption 2 and 3 hold with L2 = ℓ2 = 1 with normalized data.
+3
+Imputation bias for linear models
+3.1
+Implicit regularization of imputation
+Ridge regression, widely used in high-dimensional settings, and notably for its computational
+purposes, amounts to form an ℓ2-penalized version of the least square estimator:
+ˆθλ ∈ arg min
+θ∈Rd
+�
+1
+n
+n
+�
+i=1
+(Yi − fθ(Xi))2 + λ ∥θ∥2
+2
+�
+,
+6
+
+where λ > 0 is the penalization parameter. The associated generalization risk can be written
+as
+Rλ(θ) := R(θ) + λ ∥θ∥2
+2 .
+Proposition 3.1 establishes a link between imputation and ridge penalization.
+Proposition 3.1. Under Assumption 1, let V be the covariance matrix of P (Vij =
+Cov(Pi, Pj)) and H = diag(ρ1, . . . , ρd), with ρj = P(Pj = 1). Then, for all θ,
+Rimp(θ) = R (Hθ) + ∥θ∥2
+V ⊙Σ .
+In particular, under Assumptions 1’, 2 and 3 when L2 = ℓ2,
+Rimp(θ) = R (ρθ) + L2ρ(1 − ρ) ∥θ∥2
+2 .
+(11)
+This result highlights the implicit ℓ2-regularization at work: performing standard re-
+gression on zero-imputed ho-MCAR data can be seen as performing a ridge regression on
+complete data, whose strength λ depends on the missing values proportion. More precisely,
+using Equation (11), the optimal predictor θ⋆
+imp working with imputed samples verifies
+θ⋆
+imp =
+1
+L2ρ arg min
+θ∈Rd
+�
+R (θ) + λimp ∥θ∥2
+2
+�
+,
+with λimp := L2 �
+1−ρ
+ρ
+�
+. We exploit this correspondence in Section 3.2 and 3.3 to control the
+imputation bias.
+3.2
+Imputation bias for linear models with ho-MCAR missing inputs
+When the inputs admit ho-MCAR missing patterns (Assumption 1’), the zero-imputation
+bias Bimp(F) induced in the linear model is controlled by a particular instance of the ridge
+regression bias (see, e.g., Hsu et al., 2012; Dieuleveut et al., 2017; Mourtada, 2019), defined
+in general by
+Bridge,λ(F) := inf
+θ∈Rd {Rλ(θ) − R⋆(F)}
+(12)
+= λ ∥θ⋆∥2
+Σ(Σ+λI)−1 .
+(13)
+Theorem 3.2. Under Assumption 1’, 2, and 3, one has
+Bridge,λ′
+imp(F) ≤ Bimp(F) ≤ Bridge,λimp(F),
+with λ′
+imp := ℓ2 �
+1−ρ
+ρ
+�
+and λimp = L2 �
+1−ρ
+ρ
+�
+.
+7
+
+As could be expected from Proposition 3.1, the zero-imputation bias is lower and upper-
+bounded by the ridge bias, with a penalization constant depending on the fraction of missing
+values. In the specific case where ℓ2 = L2 (same second-order moment), the imputation bias
+exactly equals a ridge bias with a constant L2(1 − ρ)/ρ. Besides, in the extreme case where
+there is no missing data (ρ = 1) then λimp = 0, and the bias vanishes. On the contrary, if
+there is a large percentage of missing values (ρ → 0) then λ′
+imp → +∞ and the imputation
+bias amounts to the excess risk of the naive predictor, i.e., Bimp(F) = R(0Rd) − R⋆(F). For
+the intermediate case where half of the data is likely to be missing (ρ = 1/2), we obtain
+λimp = L2.
+Thus, in terms of statistical guarantees, performing linear regression on imputed inputs
+suffers from a bias comparable to that of a ridge penalization, but with a fixed hyperparameter
+λimp. Note that, when performing standard ridge regression in a high-dimensional setting,
+the best theoretical choice of the penalization parameter usually scales as d/n (see Sridharan
+et al., 2008; Hsu et al., 2012; Mourtada and Rosasco, 2022, for details). If ρ ≳ L2
+n
+d+n
+(which is equivalent to λimp ≲ d
+n), the imputation bias remains smaller than that of the
+ridge regression with the optimal hyperparameter λ = d/n (which is commonly accepted
+in applications). In this context, performing zero-imputation prior to applying a ridge
+regression allows handling easily missing data without drastically increasing the overall bias.
+In turns out that the bias of the ridge regression in random designs, and thus the
+imputation bias, can be controlled, under classical assumptions about low-rank covariance
+structures (Caponnetto and De Vito, 2007; Hsu et al., 2012; Dieuleveut et al., 2017). In all
+following examples, we consider that Tr(Σ) = d, which holds in particular for normalized
+data.
+Example 3.3 (Low-rank covariance matrix with equal singular values). Consider a covariance
+matrix with a low rank r ≪ d and constant eigenvalues (λ1 = · · · = λr =
+d
+r). Then
+Σ(Σ + λimpI)−1 ⪯ λ−1
+r Σ = r
+dΣ and Theorem 3.2 leads to
+Bimp(F) ≤ λimp
+r
+d ∥θ⋆∥2
+Σ .
+Hence, the imputation bias is small when r ≪ d (low-rank setting). Indeed, for a fixed
+dimension, when the covariance is low-rank, there is a lot of redundancy across variables,
+which helps counterbalancing missing information in the input variables, thereby reducing
+the prediction bias.
+Note that Example 3.3 (r ≪ d) is a generalization of Example 2.2 (in which r = 1), and
+is rotation-invariant contrary to the latter.
+Remark 3.4. A first order condition (see equation (29)) implies that ∥θ⋆∥2
+Σ + σ2 = EY 2 =
+R (0Rd), which is independent of the dimension d. Thus, in all our upper bounds, ∥θ⋆∥2
+Σ can
+be replaced by EY 2, which is dimension-free. Consequently, we can interpret Example 3.3
+(and the following examples) upper bound as follows: if r ≪ d, then the risk of the naive
+predictor is divided by d/r ≫ 1. As a consequence, Bimp tends to zero when the dimension
+increases and the rank is fixed.
+8
+
+Example 3.5 (Low-rank covariance matrix compatible with θ⋆ ). Consider a covariance
+matrix with a low rank r ≪ d and assume that ⟨θ⋆, v1⟩2 ≥ · · · ≥ ⟨θ⋆, vd⟩2 (meaning that θ⋆
+is well represented with the first eigendirections of Σ), Theorem 3.2 leads to
+Bimp(F) ≲ λimp
+r(log(r) + 1)
+d
+∥θ⋆∥2
+Σ .
+This result is similar to Example 3.3 (up to a log factor), except that assumptions on
+the eigenvalues of Σ have been replaced by a condition on the compatibility between the
+covariance structure and θ⋆. If θ⋆ is well explained by the largest eigenvalues then the
+imputation bias remains low. This underlines that imputation bias does not only depend on
+the spectral structure of Σ but also on θ⋆.
+Example 3.6 (Spiked model, Johnstone (2001)). In this model, the covariance matrix can be
+decomposed as Σ = Σ≤r + Σ>r where Σ≤r corresponds to the low-rank part of the data with
+large eigenvalues and Σ>r to the residual high-dimensional data. Suppose that Σ>r ⪯ ηI
+(small operator norm) and that all non-zero eigenvalues of Σ≤r are equal, then Theorem 3.2
+gives
+Bimp(F) ≤ λimp
+1 − η
+r
+d ∥θ⋆∥2
+Σ + η ∥θ⋆
+>r∥2
+2 ,
+where θ⋆
+>r is the projection of θ⋆ on the range of Σ>r. Contrary to Example 3.3, Σ is only
+approximately low rank, and one can refer to r as the “effective rank” of Σ (see Bartlett
+et al., 2020). The above upper bound admits a term in O(r/d) (as in Example 3.3), but also
+suffers from a non-compressible part η ∥θ⋆
+>r∥2
+2, due to the presence of residual (potentially
+noisy) high-dimensional data. Note that, if θ⋆
+>r = 0 (only the low-dimensional part of the
+data is informative) then we retrieve the same rate as in Example 3.3.
+3.3
+Imputation bias for linear models and general MCAR settings
+Theorem 3.2 holds only for Ho-MCAR settings, which excludes the case of dependence
+between mask components. To cover the case of dependent variables P1, . . . , Pd under
+Assumption 1, recall ρj := P(Pj = 1) the probability that the component j is not missing,
+and define the matrix C ∈ Rd×d associated to P, given by:
+Ckj := Vk,j
+ρkρj
+,
+(k, j) ∈ [d] × [d].
+(14)
+Furthermore, under Assumption 2, define
+Λimp := L2λmax(C).
+(15)
+The following result establishes an upper bound on the imputation bias for general MCAR
+settings.
+Proposition 3.7. Under Assumption 1 and 2, we have
+Bimp(F) ≤ Bridge,Λimp(F).
+9
+
+The bound on the bias is similar to the one of Theorem 3.2 but appeals to λ = Λimp which
+takes into account the correlations between the components of missing patterns. Remark
+that, under Assumption 1’, there are no correlation and Λimp = L2 1−ρ
+ρ , thus matching
+the result in Theorem 3.2. The following examples highlight generic scenarios in which an
+explicit control on Λimp is obtained.
+Example 3.8 (Limited number of correlations). If each missing pattern component is corre-
+lated with at most k − 1 other components then Λimp ≤ L2k maxj∈[d]
+� 1−ρj
+ρj
+�
+.
+Example 3.9 (Sampling without replacement). Missing pattern components are sampled as
+k components without replacement in [d], then Λimp = L2 k+1
+d−k. In particular, if one half of
+data is missing (k = d
+2) then Λimp ≤ 3L2.
+In conclusion, we proved that the imputation bias is controlled by the ridge bias, with a
+penalization constant Λimp, under any MCAR settings. More precisely, all examples of the
+previous section (Examples 3.3, 3.5 and 3.6), relying on a specific structure of the covariance
+matrix Σ and the best predictor θ⋆, are still valid, replacing λimp by Λimp. Additionally,
+specifying the missing data generation (as in Examples 3.8 and 3.9) allows us to control
+the imputation bias, which is then proved to be small in high dimension, for all the above
+examples.
+4
+SGD on zero-imputed data
+Since the imputation bias is only a part of the story, we need to propose a proper estimation
+strategy for θ⋆
+imp. To this aim, we choose to train a linear predictor on imputed samples,
+using an averaged stochastic gradient algorithm (Polyak and Juditsky, 1992), described
+below. We then establish generalization bounds on the excess risk of this estimation strategy.
+4.1
+Algorithm
+Given an initialization θ0 ∈ Rd and a constant learning rate γ > 0, the iterates of the
+averaged SGD algorithm are given at iteration t by
+θimp,t =
+�
+I − γXimp,tX⊤
+imp,t
+�
+θimp,t−1 + γYtXimp,t,
+(16)
+so that after one pass over the data (early stopping), the final estimator ¯θimp,n is given by
+the Polyak-Ruppert average ¯θimp,n =
+1
+n+1
+�n
+t=1 θimp,t. Such recursive procedures are suitable
+for high-dimensional settings, and indicated for model miss-specification (induced here by
+missing entries), as studied in Bach and Moulines (2013). Besides, they are very competitive
+for large-scale datasets, since one pass over the data requires O(dn) operations.
+4.2
+Generalization bound
+Our aim is to derive a generalization bound on the predictive performance of the above algo-
+rithm, trained on zero-imputed data. To do this, we require the following extra assumptions
+on the complete data.
+10
+
+Assumption 4. There exist σ > 0 and κ > 0 such that E[XX⊤ ∥X∥2
+2] ⪯ κTr(Σ)Σ and
+E[ϵ2 ∥X∥2
+2] ≤ σ2κTr(Σ), where ϵ = Y − X⊤θ⋆.
+Assumption 4 is a classical fourth-moment assumption in stochastic optimization (see
+Bach and Moulines, 2013; Dieuleveut et al., 2017, for details). Indeed, the first statement in
+Assumption 4 holds, for example, if X is a Gaussian vector (with κ = 3) or when X satisfies
+∥X∥2 ≤ κTr(Σ) almost surely. The second statement in Assumption 4 holds, for example, if
+the model is well specified or when the noise ε is almost surely bounded. Note that if the
+first part holds then the second part holds with σ2 ≤ 2E[Y 2] + 2E[Y 4]1/2.
+Our main result, establishing an upper bound on the risk of SGD applied to zero-imputed
+data, follows.
+Theorem 4.1. Under Assumption 4, choosing a constant learning rate γ =
+1
+κTr(Σ)√n leads
+to
+E
+�
+Rimp
+�¯θimp,n
+��
+− R⋆(F) ≲ κTr(Σ)
+√n
+��θ⋆
+imp − θ0
+��2
+2 + σ2 + ∥θ⋆∥2
+Σ
+√n
++ Bimp(F),
+where θ⋆ (resp. θ⋆
+imp) is the best linear predictor for complete (resp. with imputed missing
+values) case.
+Theorem 4.1 gives an upper bound on the difference between the averaged risk E[Rimp
+�¯θimp,n
+�
+]
+of the estimated linear predictor with imputed missing values (in both train and test
+samples) and R⋆(F), the risk of the best linear predictor on the complete case. Inter-
+estingly, by Lemma 2.1 and under a well-specified linear model, the latter also holds for
+E
+�
+Rimp
+�¯θimp,n
+��
+− R⋆
+mis. The generalization bound in Theorem 4.1 takes into account the
+statistical error of the method as well as the optimization error. More precisely, the upper
+bound can be decomposed into (i) a bias associated to the initial condition, (ii) a variance
+term of the considered method, and (iii) the aforementioned imputation bias.
+The variance term (ii) depends on the second moment of Y (as ∥θ⋆∥2
+Σ ≤ EY 2) and
+decreases with a slow rate 1/√n. As seen in Section 3, the imputation bias is upper-bounded
+by the ridge bias with penalization parameter λimp, which is controlled in high dimension
+for low-rank data (see examples in Section 3.2).
+The bias (i) due to the initial condition is the most critical. Indeed, Tr(Σ) = E[∥X∥2
+2] is
+likely to increase with d, e.g., under Assumption 2, Tr(Σ) ≤ dL2. Besides, the starting point
+θ0 may be far from θ⋆
+imp. Fortunately, Lemma 4.2 establishes some properties of θ⋆
+imp.
+Lemma 4.2. Under Assumptions 1 and 3, let V be the covariance matrix of P defined in
+Proposition 3.1. If V is invertible, then
+��θ⋆
+imp
+��2
+2 ≤ Bimp(F)
+ℓ2λmin(V ).
+(17)
+In particular, under Assumption 1’,
+��θ⋆
+imp
+��2
+2 ≤ Bimp(F)
+ℓ2ρ(1 − ρ).
+(18)
+11
+
+Lemma 4.2 controls the norm of the optimal predictor θ⋆
+imp by the imputation bias: if
+the imputation bias is small, then the optimal predictor on zero-imputed data is of low
+norm. According to Section 3, this holds in particular for high-dimensional settings. Thus,
+choosing θ0 = 0 permits us to exploit the upper bound provided by Lemma 4.2 in Theorem
+4.1. With such an initialization, the bias due to this initial condition is upper bounded by
+κTr(Σ)
+√n ∥θ⋆
+imp∥2
+2. Intuitively, as θ⋆
+imp is in an ℓ2-ball of small radius, choosing θ0 within that
+ball, e.g. θ0 = 0 is a good choice.
+Taking into account Lemma 4.2, Proposition 4.3 establishes our final upper bound on
+SGD on zero-imputed data.
+Proposition 4.3. Under Assumptions 1’, 2, 3 and 4, the predictor ¯θimp,n resulting from the
+SGD strategy, defined in Section 4.1, with starting point θ0 = 0 and learning rate γ =
+1
+dκL2√n,
+satisfies
+E
+�
+Rimp
+�¯θimp,n
+��
+− R⋆(F) ≲
+�L2
+ℓ2
+κd
+ρ(1 − ρ)√n + 1
+�
+Bimp(F) + σ2 + ∥θ⋆∥2
+Σ
+√n
+.
+In this upper bound, the first term encapsulates the imputation bias and the one due
+to the initial condition, whilst the second one corresponds to the variance of the training
+procedure. As soon as d ≫ ℓ2
+L2
+ρ(1−ρ)√n
+κ
+then the imputation bias is negligible compared to
+that of the initial condition.
+4.3
+Examples
+According to Examples 3.3 and 3.6, Bimp(F) decreases with the dimension, provided that
+Σ or β are structured. Strikingly, Corollary 4.4 highlights cases where the upper bound of
+Proposition 4.3 is actually dimension-free.
+Corollary 4.4. Suppose that assumptions of Proposition 4.3 hold. Recall that λ1 ≥ . . . ≥ λd
+are the eigenvalues of Σ associated with the eigenvectors v1, . . . , vd.
+(i) (Example 3.3 - Low-rank Σ). If Σ has a low rank r ≪ d and equal non-zero singular
+values, then
+E
+�
+Rimp
+�¯θimp,n
+��
+− R⋆(F) ≲ L2
+ℓ2
+�L2
+ℓ2
+κ
+ρ√n + 1 − ρ
+d
+� r ∥θ⋆∥2
+Σ
+ρ
++ σ2
+√n.
+(ii) (Example 3.6 - Spiked model). If Σ = Σ≤r + Σ>r with Σ>r ⪯ ℓ2ηI, Σ≤r has a low rank
+r ≪ d with equal non-zero singular values, and the projection of θ⋆ on the range of Σ>r
+satisfies θ⋆
+>r = 0, then
+E
+�
+Rimp
+�¯θimp,n
+��
+− R⋆(F) ≲ L2
+ℓ2
+�L2
+ℓ2
+κ
+ρ√n + 1 − ρ
+d
+� r ∥θ⋆∥2
+Σ
+ρ(1 − η) + σ2
+√n.
+12
+
+Corollary 4.4 establishes upper bounds on the risk of SGD applied on zero-imputed data,
+for some particular structures on Σ and θ⋆. These bounds take into account the statistical
+error as well as the optimization one, and are expressed as function of d and n. Since ∥θ⋆∥2
+Σ
+is upper bounded by EY 2 (a dimension-free term), the risks in Corollary 4.4 can also be
+upper bounded by dimension-free quantities, provided d > ℓ2
+L2
+ρ(1−ρ)√n
+κ
+.
+Besides, Corollary 4.4 shows that, for d ≫ ℓ2
+L2
+ρ(1−ρ)√n
+κ
+, the imputation bias is negligible
+with respect to the stochastic error of SGD. Therefore, for structured problems in high-
+dimensional settings for which d ≫ ℓ2
+L2
+ρ(1−ρ)√n
+κ
+, the zero-imputation strategy is consistent,
+with a slow rate of order 1/√n.
+Remark 4.5 (Discussion about slow rates). An important limitation of coupling naive
+imputation with SGD is that fast convergence rates cannot be reached. Indeed, in large
+dimensions, the classical fast rate is given by Tr(Σ(Σ + λI)−1)/n with λ the penalization
+hyper-parameter. The quantity Tr(Σ(Σ + λI)−1), often called degrees of freedom, can
+be negligible w.r.t. d (for instance when Σ has a fast eigenvalue decay). However, when
+working with an imputed dataset, the covariance matrix of the data is not Σ anymore, but
+Σimp = EXimpX⊤
+imp. Therefore, in the case of Assumption 1’ (Ho-MCAR), all the eigenvalues
+of Σimp are larger than ρ(1 − ρ) (preventing the eigenvalues decay obtained when working
+with complete inputs). By concavity of the degrees of freedom (on positive semi-definite
+matrix), we can show that Tr(Σimp(Σimp + λI)−1) ≥ dρ(1−ρ)
+1+λ , hindering traditional fast rates.
+Link with dropout
+Dropout is a classical regularization technique used in deep learning,
+consisting in randomly discarding some neurons at each SGD iteration (Srivastava et al.,
+2014). Regularization properties of dropout have attracted a lot of attention (e.g., Gal and
+Ghahramani, 2016). Interestingly, setting a neuron to 0 on the input layer is equivalent
+to masking the corresponding feature. Running SGD (as in Section 4) on a stream of
+zero-imputed data is thus equivalent to training a neural network with no hidden layer, a
+single output neuron, and dropout on the input layer. Our theoretical analysis describes the
+implicit regularization impact of dropout in that very particular case. Interestingly, this can
+also be applied to the fine-tuning of the last layer of any regression network structure.
+5
+Numerical experiments
+Data simulation
+We generate n = 500 complete input data according to a normal
+distribution with two different covariance structures. First, in the low-rank setting (Ex. 3.3
+and 3.5), the output is formed as Y = β⊤Z + ϵ, with β ∈ Rr, Z ∼ N(0, Ir) and ϵ ∼ N(0, 2),
+and the inputs are given by X = AZ + µ, with a full rank matrix A ∈ Rd×r and a mean
+vector µ ∈ Rd. Note that the dimension d varies in the experiments, while r = 5 is kept
+fixed. Besides, the full model can be rewritten as Y = X⊤θ⋆ + ϵ with θ⋆ = (A†)⊤β where A†
+is the Moore-Penrose inverse of A. Secondly, in the spiked model (Ex. 3.6), the input and
+the output are decomposed as X = (X1, X2) ∈ Rd/2 × Rd/2 and Y = Y1 + Y2, where (X1, Y1)
+13
+
+is generated according to the low-rank model above and (X2, Y2) is given by a linear model
+Y2 = θ⊤
+2 X2 and X2 ∼ N(0, Id/2), choosing ∥θ2∥ = 0.2.
+Two missing data scenarios, with a proportion ρ of observed entries equal to 50%, are
+simulated according to (i) the Ho-MCAR setting (Assumption 1’); and to (ii) the self-masking
+MNAR setting, which departs significantly from the MCAR case as the presence of missing
+data depends on the underlying value itself. More precisely, set α ∈ Rd such that, for all
+j ∈ [d], P(Pj = 1|X) = (1 + e−αjXj)−1 and E[Pj] = 0.5 (50% of missing data on average per
+components).
+Regressors
+For two-step strategies, different imputers are combined with different regres-
+sors. The considered imputers are: the zero imputation method (0-imp) complying with
+the theoretical analysis developed in this paper, the optimal imputation by a constant for
+each input variable (Opti-imp), obtained by training a linear model on the augmented
+data (P ⊙ X, P) (see Le Morvan et al., 2020b, Proposition 3.1), and single imputation by
+chained equations (ICE, (Van Buuren and Groothuis-Oudshoorn, 2011))1. The subsequent
+regressors, implemented in scikit-learn (Pedregosa et al., 2011), are either the averaged
+SGD (SGD, package SGDRegressor) with θ0 = 0 and γ = (d√n)−1 (see Proposition 4.3,
+or the ridge regressor (with a leave-one-out cross-validation, package ridge). Two specific
+methods that do not resort to prior imputation are also assessed: a pattern-by-pattern
+regressor (Le Morvan et al., 2020b; Ayme et al., 2022) (Pat-by-Pat) and a neural network
+architecture (NeuMiss) (Le Morvan et al., 2020a) specifically designed to handle missing
+data in linear prediction.
+Numerical results
+In Figure 1 (a) and (b), we consider Ho-MCAR patterns with Gaussian
+inputs with resp. a low-rank and spiked covariance matrix. The 2-step strategies perform
+remarkably well, with the ICE imputer on the top of the podium, highly appropriate to
+the type of data (MCAR Gaussian) in play. Nonetheless, the naive imputation by zero
+remains competitive in terms of predictive performance and is computationally efficient,
+with a complexity of O(nd), especially compared to ICE, whose complexity is of order n2d3.
+Regarding Figure 1 (b), we note that ridge regression outperforms SGD for large d. Note
+that, in the regime where d ≥ √n, the imputation bias is negligible w.r.t. to the method
+bias, the latter being lower in the case of ridge regression. This highlights the benefit of
+explicit ridge regularization (with a tuned hyperparameter) over the implicit regularization
+induced by the imputation.
+In practice, missing data are not always of the Ho-MCAR type, we compare therefore
+the different algorithms on self-masked data. In Figure 1 (c), we note that specific methods
+remain competitive for larger d compared to MCAR settings. This was to be expected
+since those methods were designed to handle complex missing not at random (MNAR) data.
+However, they still suffer from the curse of dimensionality and turns out to be inefficient in
+large dimension, compared to all two-step strategies.
+1IterativeImputer in scikit-learn (Pedregosa et al., 2011).
+14
+
+Regressor
+0-imp+SGD
+0-imp+Ridge
+Opti-imp+Ridge
+Pat-by-Pat
+ICE+Ridge
+NeuMiss
+Method
+Imputation
+Specific
+10
+1
+10
+2
+10
+3
+10
+4
+Number of features d
+10
+2
+10
+1
+10
+0
+10
+1
+10
+2
+d =
+n
+d = n
+10
+1
+10
+2
+10
+3
+10
+4
+Number of features d
+10
+2
+10
+1
+10
+0
+10
+1
+10
+2
+d =
+n
+d = n
+10
+1
+10
+2
+10
+3
+10
+4
+Number of features d
+10
+2
+10
+1
+10
+0
+10
+1
+10
+2
+d =
+n
+d = n
+(a) Ho-MCAR
+(b) Ho-MCAR
+(c) Self-Masked
++ Low-rank model
++ Spiked model
++ Low-rank model
+Figure 1:
+Risk w.r.t. the input dimension (evaluated on 104 test samples) when 50% of the
+input data is missing. The y-axis corresponds to Rmis(f)−R⋆ = E
+�
+(Y − f(Ximp, P))2�
+−σ2.
+The averaged risk is depicted over 10 repetitions within a 95% confidence interval.
+6
+Discussion and conclusion
+In this paper, we study the impact of zero imputation in high-dimensional linear models.
+We demystify this widespread technique, by exposing its implicit regularization mechanism
+when dealing with MCAR data. We prove that, in high-dimensional regimes, the induced
+bias is similar to that of ridge regression, commonly accepted by practitioners. By providing
+generalization bounds on SGD trained on zero-imputed data, we establish that such two-step
+procedures are statistically sound, while being computationally appealing.
+Theoretical results remain to be established beyond the MCAR case, to properly analyze
+and compare the different strategies for dealing with missing data in MNAR settings (see
+Figure 1 (c)). Extending our results to a broader class of functions (escaping linear functions)
+or even in a classification framework, would be valuable to fully understand the properties
+of imputation.
+References
+Anish Agarwal, Devavrat Shah, Dennis Shen, and Dogyoon Song. On robustness of principal
+component regression. Advances in Neural Information Processing Systems, 32, 2019.
+Alexis Ayme, Claire Boyer, Aymeric Dieuleveut, and Erwan Scornet. Near-optimal rate of
+consistency for linear models with missing values. In International Conference on Machine
+Learning, pages 1211–1243. PMLR, 2022.
+Francis Bach and Eric Moulines. Non-strongly-convex smooth stochastic approximation
+with convergence rate o (1/n). Advances in neural information processing systems, 26,
+2013.
+15
+
+Peter L Bartlett, Philip M Long, G´abor Lugosi, and Alexander Tsigler. Benign overfitting in
+linear regression. Proceedings of the National Academy of Sciences, 117(48):30063–30070,
+2020.
+Andrea Caponnetto and Ernesto De Vito. Optimal rates for the regularized least-squares
+algorithm. Foundations of Computational Mathematics, 7(3):331–368, 2007.
+Lenaic Chizat and Francis Bach. Implicit bias of gradient descent for wide two-layer neural
+networks trained with the logistic loss. In Conference on Learning Theory, pages 1305–1338.
+PMLR, 2020.
+Aymeric Dieuleveut, Nicolas Flammarion, and Francis Bach. Harder, better, faster, stronger
+convergence rates for least-squares regression. The Journal of Machine Learning Research,
+18(1):3520–3570, 2017.
+Yarin Gal and Zoubin Ghahramani. A theoretically grounded application of dropout in
+recurrent neural networks. Advances in neural information processing systems, 29, 2016.
+Daniel Hsu, Sham M Kakade, and Tong Zhang. Random design analysis of ridge regression.
+In Conference on learning theory, pages 9–1. JMLR Workshop and Conference Proceedings,
+2012.
+Niels Bruun Ipsen, Pierre-Alexandre Mattei, and Jes Frellsen. How to deal with missing data
+in supervised deep learning? In ICLR 2022-10th International Conference on Learning
+Representations, 2022.
+Iain M. Johnstone. On the distribution of the largest eigenvalue in principal components
+analysis. The Annals of Statistics, 29(2):295 – 327, 2001. doi: 10.1214/aos/1009210544.
+URL https://doi.org/10.1214/aos/1009210544.
+Julie Josse, Nicolas Prost, Erwan Scornet, and Ga¨el Varoquaux. On the consistency of
+supervised learning with missing values. arXiv preprint arXiv:1902.06931, 2019.
+Marine Le Morvan, Julie Josse, Thomas Moreau, Erwan Scornet, and Ga¨el Varoquaux.
+NeuMiss networks: differentiable programming for supervised learning with missing
+values. In NeurIPS 2020 - 34th Conference on Neural Information Processing Systems,
+Vancouver / Virtual, Canada, December 2020a. URL https://hal.archives-ouvertes.
+fr/hal-02888867.
+Marine Le Morvan, Nicolas Prost, Julie Josse, Erwan Scornet, and Ga¨el Varoquaux. Linear
+predictor on linearly-generated data with missing values: non consistency and solutions.
+In International Conference on Artificial Intelligence and Statistics, pages 3165–3174.
+PMLR, 2020b.
+Marine Le Morvan, Julie Josse, Erwan Scornet, and Ga¨el Varoquaux.
+What’sa good
+imputation to predict with missing values? Advances in Neural Information Processing
+Systems, 34:11530–11540, 2021.
+16
+
+Jaouad Mourtada. Exact minimax risk for linear least squares, and the lower tail of sample
+covariance matrices. arXiv preprint arXiv:1912.10754, 2019.
+Jaouad Mourtada and Lorenzo Rosasco. An elementary analysis of ridge regression with
+random design. arXiv preprint arXiv:2203.08564, 2022.
+Boris Muzellec, Julie Josse, Claire Boyer, and Marco Cuturi. Missing data imputation using
+optimal transport. In International Conference on Machine Learning, pages 7130–7140.
+PMLR, 2020.
+F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blon-
+del, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau,
+M. Brucher, M. Perrot, and E. Duchesnay. Scikit-learn: Machine learning in Python.
+Journal of Machine Learning Research, 12:2825–2830, 2011.
+Scott Pesme, Loucas Pillaud-Vivien, and Nicolas Flammarion. Implicit bias of sgd for diagonal
+linear networks: a provable benefit of stochasticity. Advances in Neural Information
+Processing Systems, 34:29218–29230, 2021.
+Boris T Polyak and Anatoli B Juditsky.
+Acceleration of stochastic approximation by
+averaging. SIAM journal on control and optimization, 30(4):838–855, 1992.
+DONALD B. Rubin. Inference and missing data. Biometrika, 63(3):581–592, 12 1976. ISSN
+0006-3444. doi: 10.1093/biomet/63.3.581. URL https://doi.org/10.1093/biomet/63.
+3.581.
+Karthik Sridharan, Shai Shalev-Shwartz, and Nathan Srebro. Fast rates for regularized
+objectives. Advances in neural information processing systems, 21, 2008.
+Nitish Srivastava, Geoffrey Hinton, Alex Krizhevsky, Ilya Sutskever, and Ruslan Salakhutdi-
+nov. Dropout: a simple way to prevent neural networks from overfitting. The journal of
+machine learning research, 15(1):1929–1958, 2014.
+Stef Van Buuren and Karin Groothuis-Oudshoorn. mice: Multivariate imputation by chained
+equations in r. Journal of statistical software, 45:1–67, 2011.
+Yuan Yao, Lorenzo Rosasco, and Andrea Caponnetto. On early stopping in gradient descent
+learning. Constructive Approximation, 26(2):289–315, 2007.
+Jinsung Yoon, James Jordon, and Mihaela Schaar. Gain: Missing data imputation using
+generative adversarial nets.
+In International conference on machine learning, pages
+5689–5698. PMLR, 2018.
+17
+
+A
+Notations
+For two vectors (or matrices) a, b, we denote by a ⊙ b the Hadamard product (or component-
+wise product). [n] = {1, 2, ..., n}. For two symmetric matrices A and B, A ⪯ B means that
+B − A is positive semi-definite. The symbol ≲ denotes the inequality up to a universal
+constant. Table 1 summarizes the notations used throughout the paper.
+Table 1: Notations
+P
+Mask
+F
+Set of linear functions
+Bimp
+Imputation bias
+Σ
+EXX⊤
+λj
+eigenvalues of Σ
+vj
+eigendirections of Σ
+ΣP
+EPP ⊤
+L2
+the largest second moments maxjEX2
+j (Assumption 2)
+ℓ2
+the smallest second moments minjEX2
+j (Assumption 3)
+θ⋆
+Best linear predictor on complete data
+θ⋆
+imp
+Best linear predictor on imputed data
+r
+Rank of Σ
+ρj
+Theoretical proportion of observed entries
+for the j-th variable in a MCAR setting
+V
+Covariance matrix associated to the missing patterns
+C
+Covariance matrix V renormalized by (ρj)j defined in (14)
+κ
+Kurtosis of the input X
+B
+Proof of the main results
+B.1
+Proof of Lemma 2.1
+The proof is based on the definition of the conditional expectation, and given that
+R⋆ = E
+�
+(Y − E [Y |X])2�
+.
+18
+
+Note that E [Y |X, P] = E [f⋆(X) + ϵ|X, P] = E [f⋆(X)|X, P] = f⋆(X) (by independence of
+ϵ and P). Therefore,
+R⋆ = E
+�
+(Y − f⋆(X))2�
+≤ E
+�
+(Y − E [Y |X, P])2�
+≤ E
+�
+(Y − E [Y |Ximp, P])2�
+≤ R⋆
+mis,
+using that E [Y |Ximp, P] is a measurable function of (X, P).
+B.2
+Preliminary lemmas
+Notation
+Let Xa be a random variable of law La (a modified version of the law of the
+underlying input X) on Rd, and for f ∈ F define
+Ra(f) = E
+�
+(Y − f(Xa))2�
+,
+the associate risk. The Bayes risk is given by
+R⋆
+a(F) = inf
+f∈F E
+�
+(Y − f(Xa))2�
+,
+if the infimum is reached, we denote by f⋆
+a ∈ arg minf∈F Ra(f). The discrepancy between
+both risks, involving either the modified input Xa or the initial input X, can be measured
+through the following bias:
+Ba = R⋆
+a(F) − R⋆(F).
+General decomposition
+The idea of the next lemma is to compare Ra(f) with the true
+risk R(f).
+Lemma B.1. If (Xa ⊥⊥ Y )|X, then, for all θ ∈ Rd,
+Ra (fθ) = R (gθ) + ∥θ∥2
+Γ ,
+where gθ(X) = θ⊤E [Xa|X] and Γ = E
+�
+(Xa − E [Xa|X])(Xa − E [Xa|X])⊤�
+the integrated
+conditional covariance matrix. In consequence, if there exists an invertible linear application
+H such that, E [Xa|X] = H−1X, then
+• For all θ ∈ Rd, gθ is a linear function and
+R⋆
+a(F) = inf
+θ∈Rd
+�
+R (fθ) + ∥θ∥2
+H⊤ΓH
+�
+.
+(19)
+19
+
+• If λmax(HΓH⊤) ≤ Λ, then
+Ba(F) ≤ inf
+θ∈Rd
+�
+R(fθ) + Λ ∥θ∥2
+2
+�
+= Bridge,Λ.
+(20)
+• If λmin(Γ) ≥ µ > 0, then
+∥θ⋆
+a∥2
+2 ≤ Ba(F)
+µ
+.
+(21)
+Remark B.2. Equation (21) is crucial because a bound on the bias Ba(F) actually gives a
+bound for ∥θ⋆
+a∥2
+2 too. This will be of particular interest for Theorem 4.1.
+Proof.
+Ra (fθ) = E
+��
+Y − θ⊤Xa
+�2�
+= E
+�
+E
+��
+Y − E
+�
+θ⊤Xa|X
+�
++ E
+�
+θ⊤Xa|X
+�
+− θ⊤Xa
+�2 ���X
+��
+= E
+��
+Y − E
+�
+θ⊤Xa|X
+��2�
++ E
+�
+E
+��
+E
+�
+θ⊤Xa|X
+�
+− θ⊤Xa
+�2 ���X
+��
+= E
+�
+(Y − gθ(X))2�
++ E
+�
+E
+��
+E
+�
+θ⊤Xa|X
+�
+− θ⊤Xa
+�2 ���X
+��
+= R(gθ) + E
+�
+E
+��
+E
+�
+θ⊤Xa|X
+�
+− θ⊤Xa
+�2 ���X
+��
+.
+since E
+�
+E
+�
+θ⊤Xa|X
+�
+− θ⊤Xa|X
+�
+= 0. Furthermore,
+E
+�
+E
+��
+E
+�
+θ⊤Xa|Z
+�
+− θ⊤Xa
+�2
+|X
+��
+= θ⊤E
+�
+(E [Xa|X] − Xa) (E [Xa|X] − Xa)⊤�
+θ
+= E
+�
+θ⊤E
+�
+(E [Xa|X] − Xa) (E [Xa|X] − Xa)⊤ |X
+�
+θ
+�
+= E
+�
+∥θ∥2
+E[(E[Xa|X]−Xa)(E[Xa|X]−Xa)⊤|X]
+�
+= E
+�
+∥θ∥2
+Γ
+�
+.
+Finally,
+Ra (fθ) = R(gθ) + ∥θ∥2
+Γ.
+Assume that an invertible matrix H exists such that gθ(X) = θ⊤H−1X, thus gθ is a linear
+function. Equation (19) is then obtained by using a change of variable: θ′ = (H−1)⊤θ =
+(H⊤)−1θ and θ = H⊤θ′. Thus, we have gθ′(X) = θ⊤X = fθ(X) and
+Ra (fθ′) = R(fθ) + ∥H⊤θ′∥2
+Γ
+= R(fθ) + ∥θ′∥2
+HΓH⊤.
+20
+
+Then using HΓH⊤ ⪯ ΛI proves (20). Note that, without resorting to the previous
+change of variable, the bias can be written as
+Ba(F) = R
+�
+gθ⋆a
+�
+− R (fθ⋆) + ∥θ⋆
+a∥2
+Γ .
+(22)
+By linearity of gθ⋆a, R
+�
+gθ⋆a
+�
+≥ R (fθ⋆) = R⋆(F) (because gθ⋆a ∈ F).
+Thus, ∥θ⋆
+a∥2
+Γ ≤ Ba(F). Assuming µI ⪯ Γ gives (21), as
+µ ∥θ⋆
+a∥2 ≤ ∥θ⋆
+a∥2
+Γ ≤ Ba(F).
+B.3
+Proof of Section 3
+We consider the case of imputed-by-0 data, i.e.,
+Ximp = P ⊙ X.
+Under the MCAR setting (Assumption 1),
+E [Ximp|X] = H−1X,
+with H = diag(ρ−1
+1 , ..., ρ−1
+d ) (variables always missing are discarded) and (ρj)j∈[d] the
+observation rates associated to each input variable.
+Proof of Proposition 3.1. For i, j ∈ [d],
+Γij = E
+��
+(Ximp)i − E
+�
+(Ximp)i |X
+�� �
+(Ximp)j − E
+�
+(Ximp)j |X
+���
+= E [XiXj(Pi − EPi)(Pj − EPj)]
+= E [XiXj] Cov(Pi, Pj),
+= ΣijVij
+(23)
+since P and X are independent and with V defined in Proposition 3.1. Therefore, applying
+Lemma B.1 with Γ = Σ ⊙ V proves the first part of Proposition 3.1. Regarding the second
+part, under the Ho-MCAR assumption, one has V = ρ(1 − ρ)I, thus Γ = ρ(1 − ρ)diag(Σ).
+Furthermore, if L2 = ℓ2, then diag(Σ) = L2I which gives Γ = L2ρ(1 − ρ)I.
+Proof of Theorem 3.2 and Proposition 3.7. Under Assumption 1, since H is a diagonal ma-
+trix,
+H⊤ΓH = Σ ⊙ C,
+where C is defined in Equation (14).
+21
+
+• Under Assumption 1’, the matrix C satisfies C = 1−ρ
+ρ I. Moreover, under Assumption 2
+(resp. Assumption 3), one has Σ ⊙ C ⪯ 1−ρ
+ρ L2I = λimp (resp. Σ ⊙ C ⪰ 1−ρ
+ρ ℓ2I = λ′
+imp)
+using (19), we obtain
+inf
+θ∈Rd
+�
+R (θ) + λ′
+imp ∥θ∥2
+2
+�
+≤ R⋆
+imp ≤ inf
+θ∈Rd
+�
+R (θ) + λimp ∥θ∥2
+2
+�
+.
+Subtracting R⋆(F), one has
+Bridge,λ′
+imp ≤ Bimp ≤ Bridge,λimp,
+which concludes the proof of Theorem 3.2.
+• Under Assumption 1, we have HΓH⊤ = Σ ⊙ C. Using Lemma E.2, we obtain for all θ,
+∥θ∥2
+HΓH⊤ = ∥θ∥2
+Σ⊙C ≤ λmax(C) ∥θ∥2
+diag(Σ) .
+Under Assumption 2, we have diag(Σ) ⪯ L2I, thus
+∥θ∥2
+HΓH⊤ ≤ L2λmax(C) ∥θ∥2
+2 .
+This shows that λmax(HΓH⊤) ≤ L2λmax(C) = Λimp We conclude on Proposition 3.7
+using Equation (19).
+B.4
+Proof of Lemma 4.2
+Proof. Using (23), we have Γ = V ⊙ Σ. Using that λmin(V )I ⪯ V , by Lemma E.1, we obtain
+λmin(V )I ⊙ Σ ⪯ Γ,
+and equivalently λmin(V ) ⊙ diag(Σ) ⪯ Γ. Under Assumption 3, we have ℓ2I ⪯ diag(Σ), thus
+ℓ2λmin(V )I ⪯ Γ.
+Therefore, λmin(Γ) ≥ ℓ2λmin(V ). Thus, using (21), we obtain the first part of Lemma 4.2:
+ℓ2λmin(V )
+��θ⋆
+imp
+��2
+2 ≤ Bimp(F).
+(24)
+Under Assumption 1’, λmin(V ) = ρ(1 − ρ), so that
+ℓ2ρ(1 − ρ)
+��θ⋆
+imp
+��2
+2 ≤ Bimp(F),
+(25)
+which proves the second part of Lemma 4.2.
+22
+
+C
+Stochastic gradient descent
+C.1
+Proof of Theorem 4.1
+Lemma C.1. Assume (xn, ξn) ∈ H × H are Fn-measurable for a sequence of increas-
+ing σ-fields (Fn), n ⩾ 1. Assume that E [ξn | Fn−1] = 0, E
+�
+∥ξn∥2 | Fn−1
+�
+is finite and
+E
+��
+∥xn∥2 xn ⊗ xn
+�
+| Fn−1
+�
+≼ R2H, with E [xn ⊗ xn | Fn−1] = H for all n ⩾ 1, for some
+R > 0 and invertible operator H. Consider the recursion αn = (I − γxn ⊗ xn) αn−1 + γξn,
+with γR2 ⩽ 1. Then:
+�
+1 − γR2�
+E [⟨¯αn−1, H ¯αn−1⟩] +
+1
+2nγ E ∥αn∥2 ⩽
+1
+2nγ ∥α0∥2 + γ
+n
+n
+�
+k=1
+E ∥ξk∥2 .
+Proof. The idea is to use Lemma C.1 with
+• xk = Ximp,k, yk = Yk
+• H = Σimp = E
+�
+Ximp,kX⊤
+imp,k
+�
+= ΣP ⊙ Σ where ΣP = E
+�
+PP ⊤�
+• αk = θimp,k − θ⋆
+imp
+• ξk = Ximp,k(Yk − X⊤
+imp,kθ⋆
+imp)
+• γ =
+1
+2R2√n
+• R2 = κTr(Σ)
+We can show, with these notations, that recursion (16) leads to recursion αn = (I − γxn ⊗ xn) αn−1+
+γξn with α0 = θ0 − θ⋆
+imp. Now, let’s check the assumption of Lemma C.1.
+• Let show that E
+�
+XimpX⊤
+imp ∥Ximp∥2
+2
+�
+⪯ R2Σimp. Indeed,
+E
+�
+XimpX⊤
+imp ∥Ximp∥2
+2
+�
+⪯ E
+�
+XimpX⊤
+imp ∥X∥2
+2
+�
+,
+using that ∥Ximp∥2
+2 ≤ ∥X∥2
+2, and 0 ≼ XimpX⊤
+imp. Then,
+E
+�
+XimpX⊤
+imp ∥X∥2
+2
+�
+= EE
+�
+XimpX⊤
+imp ∥X∥2
+2 |P
+�
+= EE
+�
+PP ⊤ ⊙ XX⊤ ∥X∥2
+2 |P
+�
+= E
+�
+ΣP ⊙ XX⊤ ∥X∥2
+2
+�
+= ΣP ⊙
+�
+E
+�
+XX⊤ ∥X∥2
+2
+��
+.
+23
+
+According to Assumption 4, E
+�
+XX⊤ ∥X∥2
+2
+�
+⪯ R2Σ, and Lemma E.1 lead to
+E
+�
+XimpX⊤
+imp ∥Ximp∥2
+2
+�
+⪯ R2ΣP ⊙ Σ = R2Σimp.
+• Define ϵimp = Y − X⊤
+impθ⋆
+imp = X⊤θ⋆ + ϵ − X⊤
+impθ⋆
+imp .
+First, we have ϵ2
+imp ≤
+3
+��
+X⊤θ⋆�2 + ϵ2 +
+�
+X⊤
+impθ⋆
+imp
+�2�
+, then
+E
+�
+∥ξ∥2
+2
+�
+= E
+�
+ϵ2
+imp ∥Ximp∥2
+2
+�
+≤ 3E
+���
+X⊤θ⋆�2
++ ϵ2 +
+�
+X⊤
+impθ⋆
+imp
+�2�
+∥Ximp∥2
+2
+�
+≤ 3
+�
+E
+��
+X⊤θ⋆�2
+∥X∥2
+2
+�
++ E
+�
+ϵ2 ∥X∥2
+2
+�
++E
+��
+X⊤
+impθ⋆
+imp
+�2
+∥Ximp∥2
+2
+��
+.
+Let remark that, using Assumption 4
+E
+��
+X⊤θ⋆�2
+∥X∥2
+2
+�
+= E
+�
+θ⋆⊤ �
+XX⊤ ∥X∥2
+2
+�
+θ⋆�
+∥θ⋆∥2
+Σ
+≤ R2θ⋆⊤Σθ
+= R2 ∥θ⋆∥2
+Σ .
+Using the first point, by the same way, E
+��
+X⊤
+impθ⋆
+imp
+�2
+∥Ximp∥2
+2
+�
+≤
+���θ⋆
+imp
+���
+2
+Σimp
+. By
+Assumption 4, we have also than E
+�
+ϵ2 ∥X∥2
+2
+�
+≤ σ2R2. Thus,
+E
+�
+∥ξ∥2
+2
+�
+≤ 3R2 �
+σ2 + ∥θ⋆∥2
+Σ +
+��θ⋆
+imp
+��2
+Σimp
+�
+≤ 3R2 �
+σ2 + 2 ∥θ⋆∥2
+Σ
+�
+,
+because ∥θ⋆∥2
+Σ = R (θ⋆) ≤ Rimp
+�
+θ⋆
+imp
+�
+=
+���θ⋆
+imp
+���
+2
+Σimp
+.
+Consequently we can apply Lemma C.1, to obtain
+�
+1 −
+1
+2√n
+�
+E
+��¯θimp,n − θ⋆
+imp, Σimp(¯θimp,n − θ⋆
+imp)
+��
++
+1
+2nγ E
+��θimp,n − θ⋆
+imp
+��2
+⩽
+1
+2nγ
+��θ⋆
+imp − θ0
+��2 + γ
+n
+n
+�
+k=1
+E ∥ξk∥2 .
+24
+
+The choice γ =
+1
+2R2√n leads to
+E
+��¯θimp,n − θ⋆
+imp
+��2
+Σimp ⩽ 2R2
+√n
+��θ⋆
+imp − θ0
+��2 + 4σ2 + 2 ∥θ⋆∥2
+Σ
+√n
+.
+We conclude on Theorem 4.1 using that,
+E
+�
+Rimp
+�¯θimp
+��
+− R⋆ = E
+�
+Rimp
+�¯θimp
+��
+− R⋆
+imp + R⋆
+imp − R⋆
+= E
+��¯θimp,n − θ⋆
+imp
+��2
+Σimp + Bimp.
+C.2
+Proof of Proposition 4.3 and Corollary 4.4
+Proof of Proposition 4.3. First, under Assumption 2, Tr(Σ) ≤ dL2. Then, initial conditions
+term with θ0 = 0,
+κTr(Σ)
+√n
+��θ⋆
+imp
+��2
+2 ≤
+κL2d
+√nℓ2ρ(1 − ρ)Bimp(F),
+(26)
+using Lemma 4.2. We obtain Proposition 4.3 using inequality above in Theorem 4.1.
+proof of Corollary 4.4. We obtain the upper bounds considered that: according to Theo-
+rem 3.2, Bimp ≤ Bridge,λimp; under Assumption 3, Tr(Σ) ≥ dℓ2. Then, we put together
+Proposition 4.3 and ridge bias bound (see Appendix D).
+C.3
+Miscellaneous
+Proposition C.2. If X statisfies E
+�
+XX⊤ ∥X∥2
+2
+�
+⪯ κTr(Σ)Σ, then E
+�
+ϵ2 ∥X∥2
+2
+�
+≤ σ2κTr(Σ)
+with σ2 ≤ 2E[Y 2] + 2E[Y 4]1/2.
+Proof.
+E
+�
+ϵ2 ∥X∥2
+2
+�
+= E
+��
+Y − X⊤θ⋆�2
+∥X∥2
+2
+�
+≤ 2E
+���
+X⊤θ⋆�2
++ Y 2
+�
+∥X∥2
+2
+�
+≤ 2E
+�
+Y 2 ∥X∥2
+2
+�
++ 2E
+��
+X⊤θ⋆�2
+∥X∥2
+2
+�
+.
+Regarding the first term, by Cauchy Schwarz,
+E
+�
+Y 2 ∥X∥2
+2
+�2
+≤ E
+�
+Y 4�
+E
+�
+∥X∥4
+2
+�
+≤ E
+�
+Y 4�
+E
+�
+Tr
+�
+XX⊤ ∥X∥2
+2
+��
+≤ E
+�
+Y 4�
+κTr(Σ)2.
+25
+
+As for the second term,
+E
+��
+X⊤θ⋆�2
+∥X∥2
+2
+�
+= E
+�
+(θ⋆)⊤XX⊤ ∥X∥2
+2 θ⋆�
+≤ κTr(Σ)E
+�
+(θ⋆)⊤Σθ⋆�
+≤ κTr(Σ) ∥θ⋆∥2
+2 .
+E
+�
+ϵ2 ∥X∥2
+2
+�
+≤ E
+�
+Y 4� 1
+2 κTr(Σ) + κTr(Σ) ∥θ⋆∥2
+Σ ≤ σ2κTr(Σ) ∥θ⋆∥2
+Σ .
+D
+Details on examples
+Recall that
+Bridge,λ(F) = λ ∥θ⋆∥2
+Σ(Σ+λI)−1
+(27)
+= λ
+d
+�
+j=1
+λj
+λj + λ(v⊤
+j θ⋆)2.
+(28)
+D.1
+Low-rank covariance matrix (Example 3.3)
+Proposition D.1 (Low-rank covariance matrix with equal singular values). Consider a
+covariance matrix with a low rank r ≪ d and constant eigenvalues (λ1 = λ2 = ... = λr).
+Then,
+Bridge,λ(F) = λ
+r
+Tr(Σ) ∥θ⋆∥2
+Σ .
+Proof. Using that λ1 = · · · = λr and �r
+j=1 λj = Tr(Σ), we have λ1 = · · · = λr = Tr(Σ)
+r
+.
+Then Σ(Σ + λI)−1 ⪯ λ−1
+r Σ =
+r
+Tr(Σ)Σ. Thus,
+Bridge,λ(F) = λ ∥θ⋆∥2
+Σ(Σ+λI)−1 = λ
+r
+Tr(Σ) ∥θ⋆∥2
+Σ .
+D.2
+Low-rank covariance matrix compatible with θ⋆ (Example 3.5)
+Proposition D.2 (Low-rank covariance matrix compatible with θ⋆). Consider a covariance
+matrix with a low rank r ≪ d and assume that ⟨θ⋆, v1⟩2 ≥ · · · ≥ ⟨θ⋆, vd⟩2, then
+Bridge,λ(F) ≲ λr(log(r) + 1)
+Tr(Σ)
+∥θ⋆∥2
+Σ .
+26
+
+Proof. Recall that
+∥θ⋆∥2
+Σ =
+d
+�
+j=1
+λj(v⊤
+j θ⋆)2.
+(29)
+Under the assumptions of Example 3.5, using that (λj)j and
+�
+(v⊤
+j θ⋆)2�
+j are decreasing,
+then for all k ∈ [r],
+k
+�
+j=1
+λj(v⊤
+k θ⋆)2 ≤ ∥θ⋆∥2
+Σ.
+Thus, for all k ∈ [r],
+(v⊤
+k θ⋆)2 ≤
+∥θ⋆∥2
+Σ
+�k
+j=1 λj
+.
+Using that �r
+j=1 λj = Tr(Σ) and that eigenvalues are decreasing, we have �k
+j=1 λj ≥ k
+r Tr(Σ)
+using Lemma E.3. Then
+Bridge,λ(F) = λ
+r
+�
+k=1
+λk
+λk + λ(v⊤
+k θ⋆)2
+≤ λ
+r
+�
+k=1
+(v⊤
+k θ⋆)2
+≤ λ∥θ⋆∥2
+Σ
+r
+�
+k=1
+1
+�k
+j=1 λj
+≤ λ
+r
+�
+k=1
+r
+kTr(Σ)
+≤ λ
+r
+Tr(Σ)
+r
+�
+k=1
+1
+k
+≲ λ
+r
+Tr(Σ)(log(r) + 1),
+by upper-bounding the Euler-Maclaurin formula.
+D.3
+Spiked covariance matrix (Example 3.6)
+Proposition D.3 (Spiked model). Assume that the covariance matrix is decomposed as
+Σ = Σ≤r + Σ>r. Suppose that Σ>r ⪯ ηI (small operator norm) and that all non-zero
+eigenvalues of Σ≤r are equal, then
+Bridge,λ(F) ≤
+r
+Tr(Σ) − dη ∥θ⋆∥2
+Σ + η ∥θ⋆
+>∥2
+2 .
+where θ⋆
+>r is the projection of θ⋆ on the range of Σ>r.
+27
+
+Proof. One has
+Σ(Σ + λI)−1 = Σ≤(Σ + λI)−1 + Σ>(Σ + λI)−1
+⪯ Σ≤(Σ≤ + λI)−1 + Σ>(Σ> + λI)−1
+⪯ 1
+µΣ≤ + 1
+λΣ>
+where µ is the non-zero eigenvalue of Σ≤. Thus,
+Bridge,λ(F) = ∥θ⋆∥2
+λΣ(Σ+λI)−1
+≤ ∥θ⋆∥2
+λ
+µ Σ≤+Σ>
+≤ λ
+µ ∥θ⋆∥2
+Σ + ∥θ⋆∥2
+Σ> .
+Using that λmax(Σ>) ≤ η, we have
+Bridge,λ(F) ≤ λ
+µ ∥θ⋆∥2
+Σ + η ∥θ⋆
+>∥2
+2 .
+Using Weyl’s inequality, for all j ∈ [d], λj(Σ≤+Σ>) ≤ λj(Σ≤)+η. Summing the previous
+inequalities, we get
+Tr(Σ) ≤ rµ + dη.
+Thus,
+µ ≥ Tr(Σ) − dη
+r
+.
+In consequence,
+Bridge,λ(F) ≤
+r
+Tr(Σ) − dη ∥θ⋆∥2
+Σ + η ∥θ⋆
+>∥2
+2 .
+E
+Technical lemmas
+Lemma E.1. Let A, B, V be three symmetric non-negative matrix, if A ⪯ B then A ⊙ V ⪯
+B ⊙ V .
+Proof. Let X ∼ N(0, V ) and θ ∈ Rd,
+28
+
+∥θ∥2
+A⊙V = θ⊤A ⊙ V θ
+= θ⊤ ��
+EXX⊤�
+⊙ A
+�
+θ
+= E
+�
+θ⊤ ��
+XX⊤�
+⊙ A
+�
+θ
+�
+= E
+�
+��
+i,j
+θi
+��
+XX⊤�
+⊙ A
+�
+ij θj
+�
+�
+= E
+�
+��
+i,j
+θiXiXjAijθj
+�
+�
+= E
+�
+��
+i,j
+(θiXi) (θjXj) Aij
+�
+�
+= E
+�
+∥X ⊙ θ∥2
+A
+�
+≤ E
+�
+∥X ⊙ θ∥2
+B
+�
+= ∥θ∥2
+B⊙V
+Lemma E.2. Let A, B be two non-negative symmetric matrices, then A⊙ B is non-negative
+symmetric and, for all θ ∈ Rd:
+∥θ∥2
+A⊙B ≤ λmax(B) ∥θ∥2
+diag(A) ,
+where diag(A) is the diagonal matrix containing the diagonal terms of A.
+Proof. Let X ∼ N(0, A), thus A = E
+�
+XX⊤�
+, then for θ ∈ Rd
+29
+
+∥θ∥2
+A⊙B = θ⊤A ⊙ Bθ
+= θ⊤ ��
+EXX⊤�
+⊙ B
+�
+θ
+= E
+�
+θ⊤ ��
+XX⊤�
+⊙ B
+�
+θ
+�
+= E
+�
+��
+i,j
+θi
+��
+XX⊤�
+⊙ B
+�
+ij θj
+�
+�
+= E
+�
+��
+i,j
+θiXiXjBijθj
+�
+�
+= E
+�
+��
+i,j
+(θiXi) (θjXj) Bij
+�
+�
+= E
+�
+(X ⊙ θ)⊤ B (X ⊙ θ)
+�
+≥ 0,
+using that B is positive. Thus A ⊙ B is positive. Furthermore,
+∥θ∥2
+A⊙B = E
+�
+(X ⊙ θ)⊤ B (X ⊙ θ)
+�
+≤ λmax(B)E
+�
+(X ⊙ θ)⊤ (X ⊙ θ)
+�
+= λmax(B)E
+��
+i
+θ2
+i X2
+i
+�
+= λmax(B)
+�
+i
+θ2
+i E
+�
+X2
+i
+�
+= λmax(B)
+�
+i
+θ2
+i Aii
+= λmax(B) ∥θ∥2
+diag(A) .
+Lemma E.3. Let (vj)j∈[d]a non-decreasing sequence of positive number, and S = �d
+j=1 vj,
+for all k ∈ [d],
+k
+�
+j=1
+vj ≥ k
+dS.
+Proof. We use a absurd m, if �k
+j=1 vj < k
+dS. Then, using that (vj)j∈[d]are non-decreasing,
+kvk < k
+dS.
+30
+
+Thus vk+1 < 1
+dS, summing last elements,
+d
+�
+j=r+1
+vj < d − r
+d
+S.
+Then,
+S =
+k
+�
+j=1
+vj =
+r
+�
+j=1
+vj +
+d
+�
+j=r+1
+vj < k
+dS + d − r
+d
+S = S.
+Thus, this is absurd.
+31
+
diff --git a/xtFRT4oBgHgl3EQfiDco/content/tmp_files/load_file.txt b/xtFRT4oBgHgl3EQfiDco/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f9313cbbd400618c07dd0930ef740603b79e56d6
--- /dev/null
+++ b/xtFRT4oBgHgl3EQfiDco/content/tmp_files/load_file.txt
@@ -0,0 +1,920 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf,len=919
+page_content='Naive imputation implicitly regularizes high-dimensional linear  models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Alexis Ayme, Claire Boyer, Aymeric Dieuleveut  & Erwan Scornet  Abstract  Two different approaches exist to handle missing values for prediction: either impu-  tation, prior to fitting any predictive algorithms, or dedicated methods able to natively  incorporate missing values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' While imputation is widely (and easily) use, it is unfortu-  nately biased when low-capacity predictors (such as linear models) are applied afterward.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  However, in practice, naive imputation exhibits good predictive performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' In this  paper, we study the impact of imputation in a high-dimensional linear model with  MCAR missing data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' We prove that zero imputation performs an implicit regularization  closely related to the ridge method, often used in high-dimensional problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Leveraging  on this connection, we establish that the imputation bias is controlled by a ridge bias,  which vanishes in high dimension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' As a predictor, we argue in favor of the averaged SGD  strategy, applied to zero-imputed data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' We establish an upper bound on its generaliza-  tion error, highlighting that imputation is benign in the d ≫ √n regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Experiments  illustrate our findings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  1  Introduction  Missing data has become an inherent problem in modern data science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Indeed, most real-  world data sets contain missing entries due to a variety of reasons: merging different data  sources, sensor failures, difficulty to collect/access data in sensitive fields (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=', health), just  to name a few.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' The simple, yet quite extreme, solution of throwing partial observations  away can drastically reduce the data set size and thereby hinder further statistical analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Specific methods should be therefore developed to handle missing values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Most of them are  dedicated to model estimation, aiming at inferring the underlying model parameters despite  missing values (see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=', Rubin, 1976).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' In this paper, we take a different route and consider  a supervised machine learning (ML) problem with missing values in the training and test  inputs, for which our aim is to build a prediction function (and not to estimate accurately  the true model parameters).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Prediction with NA  A common practice to perform supervised learning with missing  data is to simply impute the data set first, and then train any predictor on the com-  pleted/imputed data set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  The imputation technique can be simple (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=', using mean  1  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='13585v1  [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='ST]  31 Jan 2023  imputation) or more elaborate (Van Buuren and Groothuis-Oudshoorn, 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Yoon et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=',  2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Muzellec et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Ipsen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' While such widely-used two-step strategies  lack deep theoretical foundations, they have been shown to be consistent, provided that  the approximation capacity of the chosen predictor is large enough (see Josse et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=', 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Le Morvan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' When considering low-capacity predictors, such as linear models,  other theoretically sound strategies consist of decomposing the prediction task with respect  to all possible missing patterns (see Le Morvan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=', 2020b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Ayme et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=', 2022) or by  automatically detecting relevant patterns to predict, thus breaking the combinatorics of such  pattern-by-pattern predictors (see the specific NeuMiss architecture in Le Morvan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=',  2020a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Proved to be nearly optimal (Ayme et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=', 2022), such approaches are likely to  be robust to very pessimistic missing data scenarios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Inherently, they do not scale with  high-dimensional data sets, as the variety of missing patterns explodes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Another direction  is advocated in (Agarwal et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=', 2019) relying on principal component regression (PCR) in  order to train linear models with missing inputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' However, out-of-sample prediction in such  a case requires to retrain the predictor on the training and test sets (to perform a global PC  analysis), which strongly departs from classical ML algorithms massively used in practice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  In this paper, we focus on the high-dimensional regime of linear predictors, which will  appear to be more favorable to handling missing values via simple and cheap imputation  methods, in particular in the missing completely at random (MCAR) case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  High-dimensional linear models  In supervised learning with complete inputs, when  training a parametric method (such as a linear model) in a high-dimensional framework, one  often resorts to an ℓ2 or ridge regularization technique.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' On the one hand, such regularization  fastens the optimization procedure (via its convergence rate) (Dieuleveut et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=', 2017);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' on  the other hand, it also improves the generalization capabilities of the trained predictor  (Caponnetto and De Vito, 2007;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Hsu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=', 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' In general, this second point holds  for explicit ℓ2-regularization, but some works also emphasize the ability of optimization  algorithms to induce an implicit regularization, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=', via early stopping (Yao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=', 2007) and  more recently via gradient strategies in interpolation regimes (Bartlett et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Chizat  and Bach, 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Pesme et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Contributions  For supervised learning purposes, we consider a zero-imputation strategy  consisting in replacing input missing entries by zero, and we formalize the induced bias on a  regression task (Section 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' When the missing values are said Missing Completely At Random  (MCAR), we prove that zero imputation, used prior to training a linear model, introduces  an implicit regularization closely related to that of ridge regression (Section 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' This bias is  exemplified to be negligible in settings commonly encountered in high-dimensional regimes,  e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=', when the inputs admit a low-rank covariance matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' We then advocate for the choice of  an averaged stochastic gradient algorithm (SGD) applied on zero-imputed data (Section 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Indeed, such a predictor, being computationally efficient, remains particularly relevant for  high-dimensional learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' For such a strategy, we establish a generalization bound valid  for all d, n, in which the impact of imputation on MCAR data is soothed when d ≫ √n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  2  These theoretical results legitimate the widespread imputation approach, adopted by most  practitioners, and are corroborated by numerical experiments in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' All proofs are to  be found in the Appendix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  2  Background and motivation  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='1  General setting and notations  In the context of supervised learning, consider n ∈ N input/output observations ((Xi, Yi))i∈[n],  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' copies of a generic pair (X, Y ) ∈ Rd × R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' By some abuse of notation, we always use  Xi with i ∈ [n] to denote the i-th observation living in Rd, and Xj (or Xk) with j ∈ [d] (or  k ∈ [d]) to denote the j-th (or k-th) coordinate of the generic input X (see Section A for  notations).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Missing values  In real data sets, the input covariates (Xi)i∈[n] are often only partially  observed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' To code for this missing information, we introduce the random vector P ∈ {0, 1}d,  referred to as mask or missing pattern, and such that Pj = 0 if the j-th coordinate of X,  Xj, is missing and Pj = 1 otherwise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' The random vectors P1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' , Pn are assumed to be  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' copies of a generic random variable P ∈ {0, 1}d and the missing patterns of X1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' , Xn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Note that we assume that the output is always observed and only entries of the input vectors  can be missing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Missing data are usually classified into 3 types, initially introduced by  (Rubin, 1976).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' In this paper, we focus on the MCAR assumption where missing patterns  and (underlying) inputs are independent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Assumption 1 (Missing Completely At Random - MCAR).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' The pair (X, Y ) and the  missing pattern P associated to X are independent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  For j ∈ [d], we define ρj := P(Pj = 1), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=', 1 − ρj is the expected proportion of  missing values on the j-th feature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' A particular case of MCAR data requires, not only  the independence of the mask and the data, but also the independence between all mask  components, as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Assumption 1’ (Ho-MCAR: MCAR pattern with independent homogeneous components).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  The pair (X, Y ) and the missing pattern P associated to X are independent, and the  distribution of P satisfies P ∼ B(ρ)⊗d for 0 < ρ ≤ 1, with 1 − ρ the expected proportion of  missing values, and B the Bernoulli distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Naive imputation of covariates  A common way to handle missing values for any  learning task is to first impute missing data, to obtain a complete dataset, to which standard  ML algorithms can then be applied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' In particular, constant imputation (using the empirical  mean or an oracle constant provided by experts) is very common among practitioners.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' In  this paper, we consider, even for noncentered distributions, the naive imputation by zero, so  that the imputed-by-0 observation (Ximp)i, for i ∈ [n], is given by  (Ximp)i = Pi ⊙ Xi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  (1)  3  Risk  Let f : Rd → R be a measurable prediction function, based on a complete d-  dimensional input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Its predictive performance can be measured through its quadratic risk,  R(f) := E  �  (Y − f (X))2�  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  (2)  Accordingly, we let f⋆(X) = E[Y |X] be the Bayes predictor for the complete case and R⋆  the associated risk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  In the presence of missing data, one can still use the predictor function f, applied to the  imputed-by-0 input Ximp, resulting in the prediction f(Ximp).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' In such a setting, the risk of  f, acting on the imputed data, is defined by  Rimp(f) := E  �  (Y − f(Ximp))2�  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  (3)  For the class F of linear prediction functions from Rd to R, we respectively define  R⋆(F) = inf  f∈F R(f),  (4)  and  R⋆  imp(F) = inf  f∈F Rimp(f),  (5)  as the infimum over the class F with respectively complete and imputed-by-0 input data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  For any linear prediction function defined by fθ(x) = θ⊤x for any x ∈ Rd and a fixed  θ ∈ Rd, as fθ is completely determined by the parameter θ, we make the abuse of notation  of R(θ) to designate R(fθ) (and Rimp(θ) for Rimp(fθ)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' We also let θ⋆ ∈ Rd (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' θ⋆  imp)  be a parameter achieving the best risk on the class of linear functions, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=', such that  R⋆(F) = R(θ⋆) (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' R⋆  imp(F) = Rimp(θ⋆  imp)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Imputation bias  Even if the prepocessing step consisting of imputing the missing data by  0 is often used in practice, this imputation technique can introduce a bias in the prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  We formalize this imputation bias as  Bimp(F) := R⋆  imp(F) − R⋆(F).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  (6)  This quantity represents the difference in predictive performance between the best predictor  on complete data and that on imputed-by-0 inputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' In particular, if this quantity is small,  the risk of the best predictor on imputed data is close to that of the best predictor when all  data are available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Note that, in presence of missing values, one might be interested in the  Bayes predictor  f⋆  mis(Ximp, P) = E[Y |Ximp, P].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  (7)  and its associated risk R⋆  mis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Assume that regression model Y = f⋆(X) + ϵ is such that ϵ and P are  independent, then R⋆ ≤ R⋆  mis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  4  Intuitively, under the classical assumption ε ⊥⊥ P (see Josse et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=', 2019), which is a  verified under Assumption 1, missing data ineluctably deteriorates the original prediction  problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' As a direct consequence, for a well-specified linear model on the complete case  f⋆ ∈ F,  Rimp(F) − R⋆  mis ≤ Bimp(F).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  (8)  Consequently, in this paper, we focus our analysis on the bias (and excess risk) associated  to impute-then-regress strategies with respect to the complete-case problem (right-hand side  term of (8)) thus controlling the excess risk of imputation with respect to the missing data  scenario (left-hand side term of (8)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  In a nutshell, the quantity Bimp(F) thus represents how missing values, handled with  zero imputation, increase the difficulty of the learning problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' This effect can be tempered  in a high-dimensional regime, as rigorously studied in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' To give some intuition, let  us now study the following toy example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Assume an extremely redundant setting in which all covariates are equal,  that is, for all j ∈ [d], Xj = X1 with E  �  X2  1  �  = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Also assume that the output is such  that Y = X1 and that Assumption 1’ holds with ρ = 1/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' In this scenario, due to the  input redundancy, all θ satisfying �d  j=1 θj = 1 minimize θ �→ R(θ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Letting, for example,  θ1 = (1, 0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=', 0)⊤, we have R⋆ = R(θ1) = 0 but  Rimp(θ1) = E  �  (X1 − P1X1)2�  = 1  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  This choice of θ1 introduces an irreducible discrepancy between the risk computed on the  imputed data and the Bayes risk R⋆ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Another choice of parameter could actually  help to close this gap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Indeed, by exploiting the redundancy in covariates, the parameter  θ2 = (2/d, 2/d, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=', 2/d)⊤ (which is not a minimizer of the initial risk anymore) gives  Rimp(θ2) = E  ��  X1 − 2  d  d  �  j=1  PjXj  �2�  = 1  d,  so that the imputation bias Bimp(F) is bounded by 1/d, tending to zero as the dimension  increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Two other important observations on this example follow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' First, this bound is  still valid if EX1 ̸= 0, thus the imputation by 0 is still relevant even for non-centered data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Second, we remark that ∥θ2∥2  2 = 4/d, thus good candidates to predict with imputation seem  to be of small norm in high dimension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' This will be proved for more general settings, in  Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  The purpose of this paper is to generalize the phenomenon described in Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='2 to  less stringent settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' In light of this example, we focus our analysis on scenarios for which  some information is shared across input variables: for linear models, correlation plays such a  role.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  5  Covariance matrix  For a generic complete input X ∈ Rd, call Σ := E  �  XX⊤�  the  associated covariance matrix, admitting the following singular value decomposition  Σ =  d  �  j=1  λjvjv⊤  j ,  (9)  where λj (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' vj) are singular values (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' singular vectors) of Σ and such that λ1 ≥ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' ≥ λd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  The associated pseudo-norm is given by, for all θ ∈ Rd,  ∥θ∥2  Σ := θ⊤Σθ =  d  �  j=1  λj(v⊤  j θ)2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  For the best linear prediction, Y = X⊤θ⋆ + ϵ, and the noise satisfies E[ϵX] = 0 (first order  condition).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Denoting E[ϵ2] = σ2, we have  EY 2 = ∥θ⋆∥2  Σ + σ2 =  d  �  j=1  λj(v⊤  j θ⋆)2 + σ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  (10)  The quantity λj(v⊤  j θ⋆)2 can be therefore interpreted as the part of the variance explained  by the singular direction vj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Note that, in the setting of Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='2, Σ has a unique positive singular  values λ1 = d, that is to say, all of the variance is concentrated on the first singular direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Actually, our analysis will stress out that a proper decay of singular values leads to low  imputation biases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Furthermore, for the rest of our analysis, we need the following assumptions on the  second-order moments of X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Assumption 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' ∃L < ∞ such that, ∀j ∈ [d], E[X2  j ] ≤ L2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Assumption 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' ∃ℓ > 0 such that, ∀j ∈ [d], E[X2  j ] ≥ ℓ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  For example, Assumption 2 and 3 hold with L2 = ℓ2 = 1 with normalized data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  3  Imputation bias for linear models  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='1  Implicit regularization of imputation  Ridge regression, widely used in high-dimensional settings, and notably for its computational  purposes, amounts to form an ℓ2-penalized version of the least square estimator:  ˆθλ ∈ arg min  θ∈Rd  �  1  n  n  �  i=1  (Yi − fθ(Xi))2 + λ ∥θ∥2  2  �  ,  6  where λ > 0 is the penalization parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' The associated generalization risk can be written  as  Rλ(θ) := R(θ) + λ ∥θ∥2  2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='1 establishes a link between imputation and ridge penalization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Under Assumption 1, let V be the covariance matrix of P (Vij =  Cov(Pi, Pj)) and H = diag(ρ1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' , ρd), with ρj = P(Pj = 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Then, for all θ,  Rimp(θ) = R (Hθ) + ∥θ∥2  V ⊙Σ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  In particular, under Assumptions 1’, 2 and 3 when L2 = ℓ2,  Rimp(θ) = R (ρθ) + L2ρ(1 − ρ) ∥θ∥2  2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  (11)  This result highlights the implicit ℓ2-regularization at work: performing standard re-  gression on zero-imputed ho-MCAR data can be seen as performing a ridge regression on  complete data, whose strength λ depends on the missing values proportion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' More precisely,  using Equation (11), the optimal predictor θ⋆  imp working with imputed samples verifies  θ⋆  imp =  1  L2ρ arg min  θ∈Rd  �  R (θ) + λimp ∥θ∥2  2  �  ,  with λimp := L2 �  1−ρ  ρ  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' We exploit this correspondence in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='2 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='3 to control the  imputation bias.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='2  Imputation bias for linear models with ho-MCAR missing inputs  When the inputs admit ho-MCAR missing patterns (Assumption 1’), the zero-imputation  bias Bimp(F) induced in the linear model is controlled by a particular instance of the ridge  regression bias (see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=', Hsu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=', 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Dieuleveut et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=', 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Mourtada, 2019), defined  in general by  Bridge,λ(F) := inf  θ∈Rd {Rλ(θ) − R⋆(F)}  (12)  = λ ∥θ⋆∥2  Σ(Σ+λI)−1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  (13)  Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Under Assumption 1’, 2, and 3, one has  Bridge,λ′  imp(F) ≤ Bimp(F) ≤ Bridge,λimp(F),  with λ′  imp := ℓ2 �  1−ρ  ρ  �  and λimp = L2 �  1−ρ  ρ  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  7  As could be expected from Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='1, the zero-imputation bias is lower and upper-  bounded by the ridge bias, with a penalization constant depending on the fraction of missing  values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' In the specific case where ℓ2 = L2 (same second-order moment), the imputation bias  exactly equals a ridge bias with a constant L2(1 − ρ)/ρ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Besides, in the extreme case where  there is no missing data (ρ = 1) then λimp = 0, and the bias vanishes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' On the contrary, if  there is a large percentage of missing values (ρ → 0) then λ′  imp → +∞ and the imputation  bias amounts to the excess risk of the naive predictor, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=', Bimp(F) = R(0Rd) − R⋆(F).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' For  the intermediate case where half of the data is likely to be missing (ρ = 1/2), we obtain  λimp = L2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Thus, in terms of statistical guarantees, performing linear regression on imputed inputs  suffers from a bias comparable to that of a ridge penalization, but with a fixed hyperparameter  λimp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Note that, when performing standard ridge regression in a high-dimensional setting,  the best theoretical choice of the penalization parameter usually scales as d/n (see Sridharan  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=', 2008;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Hsu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=', 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Mourtada and Rosasco, 2022, for details).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' If ρ ≳ L2  n  d+n  (which is equivalent to λimp ≲ d  n), the imputation bias remains smaller than that of the  ridge regression with the optimal hyperparameter λ = d/n (which is commonly accepted  in applications).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' In this context, performing zero-imputation prior to applying a ridge  regression allows handling easily missing data without drastically increasing the overall bias.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  In turns out that the bias of the ridge regression in random designs, and thus the  imputation bias, can be controlled, under classical assumptions about low-rank covariance  structures (Caponnetto and De Vito, 2007;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Hsu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=', 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Dieuleveut et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=', 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' In all  following examples, we consider that Tr(Σ) = d, which holds in particular for normalized  data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='3 (Low-rank covariance matrix with equal singular values).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Consider a covariance  matrix with a low rank r ≪ d and constant eigenvalues (λ1 = · · · = λr =  d  r).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Then  Σ(Σ + λimpI)−1 ⪯ λ−1  r Σ = r  dΣ and Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='2 leads to  Bimp(F) ≤ λimp  r  d ∥θ⋆∥2  Σ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Hence, the imputation bias is small when r ≪ d (low-rank setting).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Indeed, for a fixed  dimension, when the covariance is low-rank, there is a lot of redundancy across variables,  which helps counterbalancing missing information in the input variables, thereby reducing  the prediction bias.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Note that Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='3 (r ≪ d) is a generalization of Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='2 (in which r = 1), and  is rotation-invariant contrary to the latter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' A first order condition (see equation (29)) implies that ∥θ⋆∥2  Σ + σ2 = EY 2 =  R (0Rd), which is independent of the dimension d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Thus, in all our upper bounds, ∥θ⋆∥2  Σ can  be replaced by EY 2, which is dimension-free.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Consequently, we can interpret Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='3  (and the following examples) upper bound as follows: if r ≪ d, then the risk of the naive  predictor is divided by d/r ≫ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' As a consequence, Bimp tends to zero when the dimension  increases and the rank is fixed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  8  Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='5 (Low-rank covariance matrix compatible with θ⋆ ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Consider a covariance  matrix with a low rank r ≪ d and assume that ⟨θ⋆, v1⟩2 ≥ · · · ≥ ⟨θ⋆, vd⟩2 (meaning that θ⋆  is well represented with the first eigendirections of Σ), Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='2 leads to  Bimp(F) ≲ λimp  r(log(r) + 1)  d  ∥θ⋆∥2  Σ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  This result is similar to Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='3 (up to a log factor), except that assumptions on  the eigenvalues of Σ have been replaced by a condition on the compatibility between the  covariance structure and θ⋆.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' If θ⋆ is well explained by the largest eigenvalues then the  imputation bias remains low.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' This underlines that imputation bias does not only depend on  the spectral structure of Σ but also on θ⋆.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='6 (Spiked model, Johnstone (2001)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' In this model, the covariance matrix can be  decomposed as Σ = Σ≤r + Σ>r where Σ≤r corresponds to the low-rank part of the data with  large eigenvalues and Σ>r to the residual high-dimensional data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Suppose that Σ>r ⪯ ηI  (small operator norm) and that all non-zero eigenvalues of Σ≤r are equal, then Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='2  gives  Bimp(F) ≤ λimp  1 − η  r  d ∥θ⋆∥2  Σ + η ∥θ⋆  >r∥2  2 ,  where θ⋆  >r is the projection of θ⋆ on the range of Σ>r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Contrary to Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='3, Σ is only  approximately low rank, and one can refer to r as the “effective rank” of Σ (see Bartlett  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' The above upper bound admits a term in O(r/d) (as in Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='3), but also  suffers from a non-compressible part η ∥θ⋆  >r∥2  2, due to the presence of residual (potentially  noisy) high-dimensional data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Note that, if θ⋆  >r = 0 (only the low-dimensional part of the  data is informative) then we retrieve the same rate as in Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='3  Imputation bias for linear models and general MCAR settings  Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='2 holds only for Ho-MCAR settings, which excludes the case of dependence  between mask components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' To cover the case of dependent variables P1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' , Pd under  Assumption 1, recall ρj := P(Pj = 1) the probability that the component j is not missing,  and define the matrix C ∈ Rd×d associated to P, given by:  Ckj := Vk,j  ρkρj  ,  (k, j) ∈ [d] × [d].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  (14)  Furthermore, under Assumption 2, define  Λimp := L2λmax(C).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  (15)  The following result establishes an upper bound on the imputation bias for general MCAR  settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Under Assumption 1 and 2, we have  Bimp(F) ≤ Bridge,Λimp(F).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  9  The bound on the bias is similar to the one of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='2 but appeals to λ = Λimp which  takes into account the correlations between the components of missing patterns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Remark  that, under Assumption 1’, there are no correlation and Λimp = L2 1−ρ  ρ , thus matching  the result in Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' The following examples highlight generic scenarios in which an  explicit control on Λimp is obtained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='8 (Limited number of correlations).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' If each missing pattern component is corre-  lated with at most k − 1 other components then Λimp ≤ L2k maxj∈[d]  � 1−ρj  ρj  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='9 (Sampling without replacement).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Missing pattern components are sampled as  k components without replacement in [d], then Λimp = L2 k+1  d−k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' In particular, if one half of  data is missing (k = d  2) then Λimp ≤ 3L2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  In conclusion, we proved that the imputation bias is controlled by the ridge bias, with a  penalization constant Λimp, under any MCAR settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' More precisely, all examples of the  previous section (Examples 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='3, 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='5 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='6), relying on a specific structure of the covariance  matrix Σ and the best predictor θ⋆, are still valid, replacing λimp by Λimp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Additionally,  specifying the missing data generation (as in Examples 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='8 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='9) allows us to control  the imputation bias, which is then proved to be small in high dimension, for all the above  examples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  4  SGD on zero-imputed data  Since the imputation bias is only a part of the story, we need to propose a proper estimation  strategy for θ⋆  imp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' To this aim, we choose to train a linear predictor on imputed samples,  using an averaged stochastic gradient algorithm (Polyak and Juditsky, 1992), described  below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' We then establish generalization bounds on the excess risk of this estimation strategy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='1  Algorithm  Given an initialization θ0 ∈ Rd and a constant learning rate γ > 0, the iterates of the  averaged SGD algorithm are given at iteration t by  θimp,t =  �  I − γXimp,tX⊤  imp,t  �  θimp,t−1 + γYtXimp,t,  (16)  so that after one pass over the data (early stopping), the final estimator ¯θimp,n is given by  the Polyak-Ruppert average ¯θimp,n =  1  n+1  �n  t=1 θimp,t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Such recursive procedures are suitable  for high-dimensional settings, and indicated for model miss-specification (induced here by  missing entries), as studied in Bach and Moulines (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Besides, they are very competitive  for large-scale datasets, since one pass over the data requires O(dn) operations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='2  Generalization bound  Our aim is to derive a generalization bound on the predictive performance of the above algo-  rithm, trained on zero-imputed data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' To do this, we require the following extra assumptions  on the complete data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  10  Assumption 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' There exist σ > 0 and κ > 0 such that E[XX⊤ ∥X∥2  2] ⪯ κTr(Σ)Σ and  E[ϵ2 ∥X∥2  2] ≤ σ2κTr(Σ), where ϵ = Y − X⊤θ⋆.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Assumption 4 is a classical fourth-moment assumption in stochastic optimization (see  Bach and Moulines, 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Dieuleveut et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=', 2017, for details).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Indeed, the first statement in  Assumption 4 holds, for example, if X is a Gaussian vector (with κ = 3) or when X satisfies  ∥X∥2 ≤ κTr(Σ) almost surely.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' The second statement in Assumption 4 holds, for example, if  the model is well specified or when the noise ε is almost surely bounded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Note that if the  first part holds then the second part holds with σ2 ≤ 2E[Y 2] + 2E[Y 4]1/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Our main result, establishing an upper bound on the risk of SGD applied to zero-imputed  data, follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Under Assumption 4, choosing a constant learning rate γ =  1  κTr(Σ)√n leads  to  E  �  Rimp  �¯θimp,n  ��  − R⋆(F) ≲ κTr(Σ)  √n  ��θ⋆  imp − θ0  ��2  2 + σ2 + ∥θ⋆∥2  Σ  √n  + Bimp(F),  where θ⋆ (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' θ⋆  imp) is the best linear predictor for complete (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' with imputed missing  values) case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='1 gives an upper bound on the difference between the averaged risk E[Rimp  �¯θimp,n  �  ]  of the estimated linear predictor with imputed missing values (in both train and test  samples) and R⋆(F), the risk of the best linear predictor on the complete case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Inter-  estingly, by Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='1 and under a well-specified linear model, the latter also holds for  E  �  Rimp  �¯θimp,n  ��  − R⋆  mis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' The generalization bound in Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='1 takes into account the  statistical error of the method as well as the optimization error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' More precisely, the upper  bound can be decomposed into (i) a bias associated to the initial condition, (ii) a variance  term of the considered method, and (iii) the aforementioned imputation bias.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  The variance term (ii) depends on the second moment of Y (as ∥θ⋆∥2  Σ ≤ EY 2) and  decreases with a slow rate 1/√n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' As seen in Section 3, the imputation bias is upper-bounded  by the ridge bias with penalization parameter λimp, which is controlled in high dimension  for low-rank data (see examples in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  The bias (i) due to the initial condition is the most critical.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Indeed, Tr(Σ) = E[∥X∥2  2] is  likely to increase with d, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=', under Assumption 2, Tr(Σ) ≤ dL2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Besides, the starting point  θ0 may be far from θ⋆  imp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Fortunately, Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='2 establishes some properties of θ⋆  imp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Under Assumptions 1 and 3, let V be the covariance matrix of P defined in  Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' If V is invertible, then  ��θ⋆  imp  ��2  2 ≤ Bimp(F)  ℓ2λmin(V ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  (17)  In particular, under Assumption 1’,  ��θ⋆  imp  ��2  2 ≤ Bimp(F)  ℓ2ρ(1 − ρ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  (18)  11  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='2 controls the norm of the optimal predictor θ⋆  imp by the imputation bias: if  the imputation bias is small, then the optimal predictor on zero-imputed data is of low  norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' According to Section 3, this holds in particular for high-dimensional settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Thus,  choosing θ0 = 0 permits us to exploit the upper bound provided by Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='2 in Theorem  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' With such an initialization, the bias due to this initial condition is upper bounded by  κTr(Σ)  √n ∥θ⋆  imp∥2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Intuitively, as θ⋆  imp is in an ℓ2-ball of small radius, choosing θ0 within that  ball, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' θ0 = 0 is a good choice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Taking into account Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='2, Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='3 establishes our final upper bound on  SGD on zero-imputed data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Under Assumptions 1’, 2, 3 and 4, the predictor ¯θimp,n resulting from the  SGD strategy, defined in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='1, with starting point θ0 = 0 and learning rate γ =  1  dκL2√n,  satisfies  E  �  Rimp  �¯θimp,n  ��  − R⋆(F) ≲  �L2  ℓ2  κd  ρ(1 − ρ)√n + 1  �  Bimp(F) + σ2 + ∥θ⋆∥2  Σ  √n  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  In this upper bound, the first term encapsulates the imputation bias and the one due  to the initial condition, whilst the second one corresponds to the variance of the training  procedure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' As soon as d ≫ ℓ2  L2  ρ(1−ρ)√n  κ  then the imputation bias is negligible compared to  that of the initial condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='3  Examples  According to Examples 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='3 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='6, Bimp(F) decreases with the dimension, provided that  Σ or β are structured.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Strikingly, Corollary 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='4 highlights cases where the upper bound of  Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='3 is actually dimension-free.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Corollary 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Suppose that assumptions of Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='3 hold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Recall that λ1 ≥ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' ≥ λd  are the eigenvalues of Σ associated with the eigenvectors v1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' , vd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  (i) (Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='3 - Low-rank Σ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' If Σ has a low rank r ≪ d and equal non-zero singular  values, then  E  �  Rimp  �¯θimp,n  ��  − R⋆(F) ≲ L2  ℓ2  �L2  ℓ2  κ  ρ√n + 1 − ρ  d  � r ∥θ⋆∥2  Σ  ρ  + σ2  √n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  (ii) (Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='6 - Spiked model).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' If Σ = Σ≤r + Σ>r with Σ>r ⪯ ℓ2ηI, Σ≤r has a low rank  r ≪ d with equal non-zero singular values, and the projection of θ⋆ on the range of Σ>r  satisfies θ⋆  >r = 0, then  E  �  Rimp  �¯θimp,n  ��  − R⋆(F) ≲ L2  ℓ2  �L2  ℓ2  κ  ρ√n + 1 − ρ  d  � r ∥θ⋆∥2  Σ  ρ(1 − η) + σ2  √n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  12  Corollary 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='4 establishes upper bounds on the risk of SGD applied on zero-imputed data,  for some particular structures on Σ and θ⋆.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' These bounds take into account the statistical  error as well as the optimization one, and are expressed as function of d and n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Since ∥θ⋆∥2  Σ  is upper bounded by EY 2 (a dimension-free term), the risks in Corollary 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='4 can also be  upper bounded by dimension-free quantities, provided d > ℓ2  L2  ρ(1−ρ)√n  κ  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Besides, Corollary 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='4 shows that, for d ≫ ℓ2  L2  ρ(1−ρ)√n  κ  , the imputation bias is negligible  with respect to the stochastic error of SGD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Therefore, for structured problems in high-  dimensional settings for which d ≫ ℓ2  L2  ρ(1−ρ)√n  κ  , the zero-imputation strategy is consistent,  with a slow rate of order 1/√n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Remark 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='5 (Discussion about slow rates).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' An important limitation of coupling naive  imputation with SGD is that fast convergence rates cannot be reached.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Indeed, in large  dimensions, the classical fast rate is given by Tr(Σ(Σ + λI)−1)/n with λ the penalization  hyper-parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' The quantity Tr(Σ(Σ + λI)−1), often called degrees of freedom, can  be negligible w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' d (for instance when Σ has a fast eigenvalue decay).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' However, when  working with an imputed dataset, the covariance matrix of the data is not Σ anymore, but  Σimp = EXimpX⊤  imp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Therefore, in the case of Assumption 1’ (Ho-MCAR), all the eigenvalues  of Σimp are larger than ρ(1 − ρ) (preventing the eigenvalues decay obtained when working  with complete inputs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' By concavity of the degrees of freedom (on positive semi-definite  matrix), we can show that Tr(Σimp(Σimp + λI)−1) ≥ dρ(1−ρ)  1+λ , hindering traditional fast rates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Link with dropout  Dropout is a classical regularization technique used in deep learning,  consisting in randomly discarding some neurons at each SGD iteration (Srivastava et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=',  2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Regularization properties of dropout have attracted a lot of attention (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=', Gal and  Ghahramani, 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Interestingly, setting a neuron to 0 on the input layer is equivalent  to masking the corresponding feature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Running SGD (as in Section 4) on a stream of  zero-imputed data is thus equivalent to training a neural network with no hidden layer, a  single output neuron, and dropout on the input layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Our theoretical analysis describes the  implicit regularization impact of dropout in that very particular case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Interestingly, this can  also be applied to the fine-tuning of the last layer of any regression network structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  5  Numerical experiments  Data simulation  We generate n = 500 complete input data according to a normal  distribution with two different covariance structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' First, in the low-rank setting (Ex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='3  and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='5), the output is formed as Y = β⊤Z + ϵ, with β ∈ Rr, Z ∼ N(0, Ir) and ϵ ∼ N(0, 2),  and the inputs are given by X = AZ + µ, with a full rank matrix A ∈ Rd×r and a mean  vector µ ∈ Rd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Note that the dimension d varies in the experiments, while r = 5 is kept  fixed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Besides, the full model can be rewritten as Y = X⊤θ⋆ + ϵ with θ⋆ = (A†)⊤β where A†  is the Moore-Penrose inverse of A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Secondly, in the spiked model (Ex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='6), the input and  the output are decomposed as X = (X1, X2) ∈ Rd/2 × Rd/2 and Y = Y1 + Y2, where (X1, Y1)  13  is generated according to the low-rank model above and (X2, Y2) is given by a linear model  Y2 = θ⊤  2 X2 and X2 ∼ N(0, Id/2), choosing ∥θ2∥ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Two missing data scenarios, with a proportion ρ of observed entries equal to 50%, are  simulated according to (i) the Ho-MCAR setting (Assumption 1’);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' and to (ii) the self-masking  MNAR setting, which departs significantly from the MCAR case as the presence of missing  data depends on the underlying value itself.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' More precisely, set α ∈ Rd such that, for all  j ∈ [d], P(Pj = 1|X) = (1 + e−αjXj)−1 and E[Pj] = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='5 (50% of missing data on average per  components).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Regressors  For two-step strategies, different imputers are combined with different regres-  sors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' The considered imputers are: the zero imputation method (0-imp) complying with  the theoretical analysis developed in this paper, the optimal imputation by a constant for  each input variable (Opti-imp), obtained by training a linear model on the augmented  data (P ⊙ X, P) (see Le Morvan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=', 2020b, Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='1), and single imputation by  chained equations (ICE, (Van Buuren and Groothuis-Oudshoorn, 2011))1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' The subsequent  regressors, implemented in scikit-learn (Pedregosa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=', 2011), are either the averaged  SGD (SGD, package SGDRegressor) with θ0 = 0 and γ = (d√n)−1 (see Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='3,  or the ridge regressor (with a leave-one-out cross-validation, package ridge).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Two specific  methods that do not resort to prior imputation are also assessed: a pattern-by-pattern  regressor (Le Morvan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=', 2020b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Ayme et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=', 2022) (Pat-by-Pat) and a neural network  architecture (NeuMiss) (Le Morvan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=', 2020a) specifically designed to handle missing  data in linear prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Numerical results  In Figure 1 (a) and (b), we consider Ho-MCAR patterns with Gaussian  inputs with resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' a low-rank and spiked covariance matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' The 2-step strategies perform  remarkably well, with the ICE imputer on the top of the podium, highly appropriate to  the type of data (MCAR Gaussian) in play.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Nonetheless, the naive imputation by zero  remains competitive in terms of predictive performance and is computationally efficient,  with a complexity of O(nd), especially compared to ICE, whose complexity is of order n2d3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Regarding Figure 1 (b), we note that ridge regression outperforms SGD for large d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Note  that, in the regime where d ≥ √n, the imputation bias is negligible w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' to the method  bias, the latter being lower in the case of ridge regression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' This highlights the benefit of  explicit ridge regularization (with a tuned hyperparameter) over the implicit regularization  induced by the imputation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  In practice, missing data are not always of the Ho-MCAR type, we compare therefore  the different algorithms on self-masked data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' In Figure 1 (c), we note that specific methods  remain competitive for larger d compared to MCAR settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' This was to be expected  since those methods were designed to handle complex missing not at random (MNAR) data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  However, they still suffer from the curse of dimensionality and turns out to be inefficient in  large dimension, compared to all two-step strategies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  1IterativeImputer in scikit-learn (Pedregosa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=', 2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='Regressor  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='0-imp+SGD  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='0-imp+Ridge  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='Opti-imp+Ridge  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='Pat-by-Pat  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='ICE+Ridge  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='NeuMiss  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='Method  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='Imputation  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='Specific  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='Number of features d  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='d =  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='n  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='d = n  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='Number of features d  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='d =  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='n  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='d = n  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='Number of features d  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='d =  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='n  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='d = n  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='(a) Ho-MCAR  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='(b) Ho-MCAR  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='(c) Self-Masked  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='+ Low-rank model  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='+ Spiked model  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='+ Low-rank model  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='Figure 1:  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='Risk w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' the input dimension (evaluated on 104 test samples) when 50% of the  input data is missing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' The y-axis corresponds to Rmis(f)−R⋆ = E  �  (Y − f(Ximp, P))2�  −σ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  The averaged risk is depicted over 10 repetitions within a 95% confidence interval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  6  Discussion and conclusion  In this paper, we study the impact of zero imputation in high-dimensional linear models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  We demystify this widespread technique, by exposing its implicit regularization mechanism  when dealing with MCAR data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' We prove that, in high-dimensional regimes, the induced  bias is similar to that of ridge regression, commonly accepted by practitioners.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' By providing  generalization bounds on SGD trained on zero-imputed data, we establish that such two-step  procedures are statistically sound, while being computationally appealing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Theoretical results remain to be established beyond the MCAR case, to properly analyze  and compare the different strategies for dealing with missing data in MNAR settings (see  Figure 1 (c)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Extending our results to a broader class of functions (escaping linear functions)  or even in a classification framework, would be valuable to fully understand the properties  of imputation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  References  Anish Agarwal, Devavrat Shah, Dennis Shen, and Dogyoon Song.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' On robustness of principal  component regression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Advances in Neural Information Processing Systems, 32, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Alexis Ayme, Claire Boyer, Aymeric Dieuleveut, and Erwan Scornet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Near-optimal rate of  consistency for linear models with missing values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' In International Conference on Machine  Learning, pages 1211–1243.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' PMLR, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Francis Bach and Eric Moulines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Non-strongly-convex smooth stochastic approximation  with convergence rate o (1/n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Advances in neural information processing systems, 26,  2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  15  Peter L Bartlett, Philip M Long, G´abor Lugosi, and Alexander Tsigler.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Benign overfitting in  linear regression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Proceedings of the National Academy of Sciences, 117(48):30063–30070,  2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Andrea Caponnetto and Ernesto De Vito.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Optimal rates for the regularized least-squares  algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Foundations of Computational Mathematics, 7(3):331–368, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Lenaic Chizat and Francis Bach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Implicit bias of gradient descent for wide two-layer neural  networks trained with the logistic loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' In Conference on Learning Theory, pages 1305–1338.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  PMLR, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Aymeric Dieuleveut, Nicolas Flammarion, and Francis Bach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Harder, better, faster, stronger  convergence rates for least-squares regression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' The Journal of Machine Learning Research,  18(1):3520–3570, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Yarin Gal and Zoubin Ghahramani.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' A theoretically grounded application of dropout in  recurrent neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Advances in neural information processing systems, 29, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Daniel Hsu, Sham M Kakade, and Tong Zhang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Random design analysis of ridge regression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  In Conference on learning theory, pages 9–1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' JMLR Workshop and Conference Proceedings,  2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Niels Bruun Ipsen, Pierre-Alexandre Mattei, and Jes Frellsen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' How to deal with missing data  in supervised deep learning?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' In ICLR 2022-10th International Conference on Learning  Representations, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Iain M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Johnstone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' On the distribution of the largest eigenvalue in principal components  analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' The Annals of Statistics, 29(2):295 – 327, 2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='1214/aos/1009210544.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  URL https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='1214/aos/1009210544.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Julie Josse, Nicolas Prost, Erwan Scornet, and Ga¨el Varoquaux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' On the consistency of  supervised learning with missing values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' arXiv preprint arXiv:1902.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='06931, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Marine Le Morvan, Julie Josse, Thomas Moreau, Erwan Scornet, and Ga¨el Varoquaux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  NeuMiss networks: differentiable programming for supervised learning with missing  values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' In NeurIPS 2020 - 34th Conference on Neural Information Processing Systems,  Vancouver / Virtual, Canada, December 2020a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' URL https://hal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='archives-ouvertes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  fr/hal-02888867.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Marine Le Morvan, Nicolas Prost, Julie Josse, Erwan Scornet, and Ga¨el Varoquaux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Linear  predictor on linearly-generated data with missing values: non consistency and solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  In International Conference on Artificial Intelligence and Statistics, pages 3165–3174.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  PMLR, 2020b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Marine Le Morvan, Julie Josse, Erwan Scornet, and Ga¨el Varoquaux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  What’sa good  imputation to predict with missing values?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Advances in Neural Information Processing  Systems, 34:11530–11540, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  16  Jaouad Mourtada.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Exact minimax risk for linear least squares, and the lower tail of sample  covariance matrices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' arXiv preprint arXiv:1912.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='10754, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Jaouad Mourtada and Lorenzo Rosasco.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' An elementary analysis of ridge regression with  random design.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' arXiv preprint arXiv:2203.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='08564, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Boris Muzellec, Julie Josse, Claire Boyer, and Marco Cuturi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Missing data imputation using  optimal transport.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' In International Conference on Machine Learning, pages 7130–7140.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  PMLR, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Pedregosa, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Varoquaux, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Gramfort, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Michel, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Thirion, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Grisel, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Blon-  del, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Prettenhofer, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Weiss, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Dubourg, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Vanderplas, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Passos, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Cournapeau,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Brucher, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Perrot, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Duchesnay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Scikit-learn: Machine learning in Python.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Journal of Machine Learning Research, 12:2825–2830, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Scott Pesme, Loucas Pillaud-Vivien, and Nicolas Flammarion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Implicit bias of sgd for diagonal  linear networks: a provable benefit of stochasticity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Advances in Neural Information  Processing Systems, 34:29218–29230, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Boris T Polyak and Anatoli B Juditsky.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Acceleration of stochastic approximation by  averaging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' SIAM journal on control and optimization, 30(4):838–855, 1992.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  DONALD B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Rubin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Inference and missing data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Biometrika, 63(3):581–592, 12 1976.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' ISSN  0006-3444.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='1093/biomet/63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='581.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' URL https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='1093/biomet/63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='581.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Karthik Sridharan, Shai Shalev-Shwartz, and Nathan Srebro.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Fast rates for regularized  objectives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Advances in neural information processing systems, 21, 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Nitish Srivastava, Geoffrey Hinton, Alex Krizhevsky, Ilya Sutskever, and Ruslan Salakhutdi-  nov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Dropout: a simple way to prevent neural networks from overfitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' The journal of  machine learning research, 15(1):1929–1958, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Stef Van Buuren and Karin Groothuis-Oudshoorn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' mice: Multivariate imputation by chained  equations in r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Journal of statistical software, 45:1–67, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Yuan Yao, Lorenzo Rosasco, and Andrea Caponnetto.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' On early stopping in gradient descent  learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Constructive Approximation, 26(2):289–315, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Jinsung Yoon, James Jordon, and Mihaela Schaar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Gain: Missing data imputation using  generative adversarial nets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  In International conference on machine learning, pages  5689–5698.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' PMLR, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  17  A  Notations  For two vectors (or matrices) a, b, we denote by a ⊙ b the Hadamard product (or component-  wise product).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' [n] = {1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=', n}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' For two symmetric matrices A and B, A ⪯ B means that  B − A is positive semi-definite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' The symbol ≲ denotes the inequality up to a universal  constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Table 1 summarizes the notations used throughout the paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='Table 1: Notations  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='P  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='Mask  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='F  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='Set of linear functions  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='Bimp  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='Imputation bias  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='Σ  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='EXX⊤  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='λj  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='eigenvalues of Σ  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='vj  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='eigendirections of Σ  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='ΣP  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='EPP ⊤  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='L2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='the largest second moments maxjEX2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='j (Assumption 2)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='ℓ2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='the smallest second moments minjEX2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='j (Assumption 3)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='θ⋆  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='Best linear predictor on complete data  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='θ⋆  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='imp  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='Best linear predictor on imputed data  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='r  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='Rank of Σ  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='ρj  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='Theoretical proportion of observed entries  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='for the j-th variable in a MCAR setting  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='V  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='Covariance matrix associated to the missing patterns  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='C  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='Covariance matrix V renormalized by (ρj)j defined in (14)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='κ  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='Kurtosis of the input X  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='B  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='Proof of the main results  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='1  Proof of Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='1  The proof is based on the definition of the conditional expectation, and given that  R⋆ = E  �  (Y − E [Y |X])2�  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  18  Note that E [Y |X, P] = E [f⋆(X) + ϵ|X, P] = E [f⋆(X)|X, P] = f⋆(X) (by independence of  ϵ and P).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Therefore,  R⋆ = E  �  (Y − f⋆(X))2�  ≤ E  �  (Y − E [Y |X, P])2�  ≤ E  �  (Y − E [Y |Ximp, P])2�  ≤ R⋆  mis,  using that E [Y |Ximp, P] is a measurable function of (X, P).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='2  Preliminary lemmas  Notation  Let Xa be a random variable of law La (a modified version of the law of the  underlying input X) on Rd, and for f ∈ F define  Ra(f) = E  �  (Y − f(Xa))2�  ,  the associate risk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' The Bayes risk is given by  R⋆  a(F) = inf  f∈F E  �  (Y − f(Xa))2�  ,  if the infimum is reached, we denote by f⋆  a ∈ arg minf∈F Ra(f).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' The discrepancy between  both risks, involving either the modified input Xa or the initial input X, can be measured  through the following bias:  Ba = R⋆  a(F) − R⋆(F).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  General decomposition  The idea of the next lemma is to compare Ra(f) with the true  risk R(f).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Lemma B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' If (Xa ⊥⊥ Y )|X, then, for all θ ∈ Rd,  Ra (fθ) = R (gθ) + ∥θ∥2  Γ ,  where gθ(X) = θ⊤E [Xa|X] and Γ = E  �  (Xa − E [Xa|X])(Xa − E [Xa|X])⊤�  the integrated  conditional covariance matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' In consequence, if there exists an invertible linear application  H such that, E [Xa|X] = H−1X, then  For all θ ∈ Rd, gθ is a linear function and  R⋆  a(F) = inf  θ∈Rd  �  R (fθ) + ∥θ∥2  H⊤ΓH  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  (19)  19  If λmax(HΓH⊤) ≤ Λ, then  Ba(F) ≤ inf  θ∈Rd  �  R(fθ) + Λ ∥θ∥2  2  �  = Bridge,Λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  (20)  If λmin(Γ) ≥ µ > 0, then  ∥θ⋆  a∥2  2 ≤ Ba(F)  µ  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  (21)  Remark B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Equation (21) is crucial because a bound on the bias Ba(F) actually gives a  bound for ∥θ⋆  a∥2  2 too.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' This will be of particular interest for Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Ra (fθ) = E  ��  Y − θ⊤Xa  �2�  = E  �  E  ��  Y − E  �  θ⊤Xa|X  �  + E  �  θ⊤Xa|X  �  − θ⊤Xa  �2 ���X  ��  = E  ��  Y − E  �  θ⊤Xa|X  ��2�  + E  �  E  ��  E  �  θ⊤Xa|X  �  − θ⊤Xa  �2 ���X  ��  = E  �  (Y − gθ(X))2�  + E  �  E  ��  E  �  θ⊤Xa|X  �  − θ⊤Xa  �2 ���X  ��  = R(gθ) + E  �  E  ��  E  �  θ⊤Xa|X  �  − θ⊤Xa  �2 ���X  ��  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  since E  �  E  �  θ⊤Xa|X  �  − θ⊤Xa|X  �  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Furthermore,  E  �  E  ��  E  �  θ⊤Xa|Z  �  − θ⊤Xa  �2  |X  ��  = θ⊤E  �  (E [Xa|X] − Xa) (E [Xa|X] − Xa)⊤�  θ  = E  �  θ⊤E  �  (E [Xa|X] − Xa) (E [Xa|X] − Xa)⊤ |X  �  θ  �  = E  �  ∥θ∥2  E[(E[Xa|X]−Xa)(E[Xa|X]−Xa)⊤|X]  �  = E  �  ∥θ∥2  Γ  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Finally,  Ra (fθ) = R(gθ) + ∥θ∥2  Γ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Assume that an invertible matrix H exists such that gθ(X) = θ⊤H−1X, thus gθ is a linear  function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Equation (19) is then obtained by using a change of variable: θ′ = (H−1)⊤θ =  (H⊤)−1θ and θ = H⊤θ′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Thus, we have gθ′(X) = θ⊤X = fθ(X) and  Ra (fθ′) = R(fθ) + ∥H⊤θ′∥2  Γ  = R(fθ) + ∥θ′∥2  HΓH⊤.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  20  Then using HΓH⊤ ⪯ ΛI proves (20).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Note that, without resorting to the previous  change of variable, the bias can be written as  Ba(F) = R  �  gθ⋆a  �  − R (fθ⋆) + ∥θ⋆  a∥2  Γ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  (22)  By linearity of gθ⋆a, R  �  gθ⋆a  �  ≥ R (fθ⋆) = R⋆(F) (because gθ⋆a ∈ F).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Thus, ∥θ⋆  a∥2  Γ ≤ Ba(F).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Assuming µI ⪯ Γ gives (21), as  µ ∥θ⋆  a∥2 ≤ ∥θ⋆  a∥2  Γ ≤ Ba(F).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='3  Proof of Section 3  We consider the case of imputed-by-0 data, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=',  Ximp = P ⊙ X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Under the MCAR setting (Assumption 1),  E [Ximp|X] = H−1X,  with H = diag(ρ−1  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=', ρ−1  d ) (variables always missing are discarded) and (ρj)j∈[d] the  observation rates associated to each input variable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Proof of Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' For i, j ∈ [d],  Γij = E  ��  (Ximp)i − E  �  (Ximp)i |X  �� �  (Ximp)j − E  �  (Ximp)j |X  ���  = E [XiXj(Pi − EPi)(Pj − EPj)]  = E [XiXj] Cov(Pi, Pj),  = ΣijVij  (23)  since P and X are independent and with V defined in Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Therefore, applying  Lemma B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='1 with Γ = Σ ⊙ V proves the first part of Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Regarding the second  part, under the Ho-MCAR assumption, one has V = ρ(1 − ρ)I, thus Γ = ρ(1 − ρ)diag(Σ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Furthermore, if L2 = ℓ2, then diag(Σ) = L2I which gives Γ = L2ρ(1 − ρ)I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Proof of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='2 and Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Under Assumption 1, since H is a diagonal ma-  trix,  H⊤ΓH = Σ ⊙ C,  where C is defined in Equation (14).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  21  Under Assumption 1’, the matrix C satisfies C = 1−ρ  ρ I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Moreover, under Assumption 2  (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Assumption 3), one has Σ ⊙ C ⪯ 1−ρ  ρ L2I = λimp (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Σ ⊙ C ⪰ 1−ρ  ρ ℓ2I = λ′  imp)  using (19), we obtain  inf  θ∈Rd  �  R (θ) + λ′  imp ∥θ∥2  2  �  ≤ R⋆  imp ≤ inf  θ∈Rd  �  R (θ) + λimp ∥θ∥2  2  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Subtracting R⋆(F), one has  Bridge,λ′  imp ≤ Bimp ≤ Bridge,λimp,  which concludes the proof of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Under Assumption 1, we have HΓH⊤ = Σ ⊙ C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Using Lemma E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='2, we obtain for all θ,  ∥θ∥2  HΓH⊤ = ∥θ∥2  Σ⊙C ≤ λmax(C) ∥θ∥2  diag(Σ) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Under Assumption 2, we have diag(Σ) ⪯ L2I, thus  ∥θ∥2  HΓH⊤ ≤ L2λmax(C) ∥θ∥2  2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  This shows that λmax(HΓH⊤) ≤ L2λmax(C) = Λimp We conclude on Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='7  using Equation (19).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='4  Proof of Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='2  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Using (23), we have Γ = V ⊙ Σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Using that λmin(V )I ⪯ V , by Lemma E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='1, we obtain  λmin(V )I ⊙ Σ ⪯ Γ,  and equivalently λmin(V ) ⊙ diag(Σ) ⪯ Γ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Under Assumption 3, we have ℓ2I ⪯ diag(Σ), thus  ℓ2λmin(V )I ⪯ Γ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Therefore, λmin(Γ) ≥ ℓ2λmin(V ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Thus, using (21), we obtain the first part of Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='2:  ℓ2λmin(V )  ��θ⋆  imp  ��2  2 ≤ Bimp(F).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  (24)  Under Assumption 1’, λmin(V ) = ρ(1 − ρ), so that  ℓ2ρ(1 − ρ)  ��θ⋆  imp  ��2  2 ≤ Bimp(F),  (25)  which proves the second part of Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  22  C  Stochastic gradient descent  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='1  Proof of Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='1  Lemma C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Assume (xn, ξn) ∈ H × H are Fn-measurable for a sequence of increas-  ing σ-fields (Fn), n ⩾ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Assume that E [ξn | Fn−1] = 0, E  �  ∥ξn∥2 | Fn−1  �  is finite and  E  ��  ∥xn∥2 xn ⊗ xn  �  | Fn−1  �  ≼ R2H, with E [xn ⊗ xn | Fn−1] = H for all n ⩾ 1, for some  R > 0 and invertible operator H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Consider the recursion αn = (I − γxn ⊗ xn) αn−1 + γξn,  with γR2 ⩽ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Then:  �  1 − γR2�  E [⟨¯αn−1, H ¯αn−1⟩] +  1  2nγ E ∥αn∥2 ⩽  1  2nγ ∥α0∥2 + γ  n  n  �  k=1  E ∥ξk∥2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' The idea is to use Lemma C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='1 with  xk = Ximp,k, yk = Yk  H = Σimp = E  �  Ximp,kX⊤  imp,k  �  = ΣP ⊙ Σ where ΣP = E  �  PP ⊤�  αk = θimp,k − θ⋆  imp  ξk = Ximp,k(Yk − X⊤  imp,kθ⋆  imp)  γ =  1  2R2√n  R2 = κTr(Σ)  We can show, with these notations, that recursion (16) leads to recursion αn = (I − γxn ⊗ xn) αn−1+  γξn with α0 = θ0 − θ⋆  imp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Now, let’s check the assumption of Lemma C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Let show that E  �  XimpX⊤  imp ∥Ximp∥2  2  �  ⪯ R2Σimp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Indeed,  E  �  XimpX⊤  imp ∥Ximp∥2  2  �  ⪯ E  �  XimpX⊤  imp ∥X∥2  2  �  ,  using that ∥Ximp∥2  2 ≤ ∥X∥2  2, and 0 ≼ XimpX⊤  imp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Then,  E  �  XimpX⊤  imp ∥X∥2  2  �  = EE  �  XimpX⊤  imp ∥X∥2  2 |P  �  = EE  �  PP ⊤ ⊙ XX⊤ ∥X∥2  2 |P  �  = E  �  ΣP ⊙ XX⊤ ∥X∥2  2  �  = ΣP ⊙  �  E  �  XX⊤ ∥X∥2  2  ��  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  23  According to Assumption 4, E  �  XX⊤ ∥X∥2  2  �  ⪯ R2Σ, and Lemma E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='1 lead to  E  �  XimpX⊤  imp ∥Ximp∥2  2  �  ⪯ R2ΣP ⊙ Σ = R2Σimp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Define ϵimp = Y − X⊤  impθ⋆  imp = X⊤θ⋆ + ϵ − X⊤  impθ⋆  imp .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  First, we have ϵ2  imp ≤  3  ��  X⊤θ⋆�2 + ϵ2 +  �  X⊤  impθ⋆  imp  �2�  , then  E  �  ∥ξ∥2  2  �  = E  �  ϵ2  imp ∥Ximp∥2  2  �  ≤ 3E  ���  X⊤θ⋆�2  + ϵ2 +  �  X⊤  impθ⋆  imp  �2�  ∥Ximp∥2  2  �  ≤ 3  �  E  ��  X⊤θ⋆�2  ∥X∥2  2  �  + E  �  ϵ2 ∥X∥2  2  �  +E  ��  X⊤  impθ⋆  imp  �2  ∥Ximp∥2  2  ��  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Let remark that, using Assumption 4  E  ��  X⊤θ⋆�2  ∥X∥2  2  �  = E  �  θ⋆⊤ �  XX⊤ ∥X∥2  2  �  θ⋆�  ∥θ⋆∥2  Σ  ≤ R2θ⋆⊤Σθ  = R2 ∥θ⋆∥2  Σ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Using the first point, by the same way, E  ��  X⊤  impθ⋆  imp  �2  ∥Ximp∥2  2  �  ≤  ���θ⋆  imp  ���  2  Σimp  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' By  Assumption 4, we have also than E  �  ϵ2 ∥X∥2  2  �  ≤ σ2R2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Thus,  E  �  ∥ξ∥2  2  �  ≤ 3R2 �  σ2 + ∥θ⋆∥2  Σ +  ��θ⋆  imp  ��2  Σimp  �  ≤ 3R2 �  σ2 + 2 ∥θ⋆∥2  Σ  �  ,  because ∥θ⋆∥2  Σ = R (θ⋆) ≤ Rimp  �  θ⋆  imp  �  =  ���θ⋆  imp  ���  2  Σimp  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Consequently we can apply Lemma C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='1, to obtain  �  1 −  1  2√n  �  E  ��¯θimp,n − θ⋆  imp, Σimp(¯θimp,n − θ⋆  imp)  ��  +  1  2nγ E  ��θimp,n − θ⋆  imp  ��2  ⩽  1  2nγ  ��θ⋆  imp − θ0  ��2 + γ  n  n  �  k=1  E ∥ξk∥2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  24  The choice γ =  1  2R2√n leads to  E  ��¯θimp,n − θ⋆  imp  ��2  Σimp ⩽ 2R2  √n  ��θ⋆  imp − θ0  ��2 + 4σ2 + 2 ∥θ⋆∥2  Σ  √n  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  We conclude on Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='1 using that,  E  �  Rimp  �¯θimp  ��  − R⋆ = E  �  Rimp  �¯θimp  ��  − R⋆  imp + R⋆  imp − R⋆  = E  ��¯θimp,n − θ⋆  imp  ��2  Σimp + Bimp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='2  Proof of Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='3 and Corollary 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='4  Proof of Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' First, under Assumption 2, Tr(Σ) ≤ dL2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Then, initial conditions  term with θ0 = 0,  κTr(Σ)  √n  ��θ⋆  imp  ��2  2 ≤  κL2d  √nℓ2ρ(1 − ρ)Bimp(F),  (26)  using Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' We obtain Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='3 using inequality above in Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  proof of Corollary 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' We obtain the upper bounds considered that: according to Theo-  rem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='2, Bimp ≤ Bridge,λimp;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' under Assumption 3, Tr(Σ) ≥ dℓ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Then, we put together  Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='3 and ridge bias bound (see Appendix D).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='3  Miscellaneous  Proposition C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' If X statisfies E  �  XX⊤ ∥X∥2  2  �  ⪯ κTr(Σ)Σ, then E  �  ϵ2 ∥X∥2  2  �  ≤ σ2κTr(Σ)  with σ2 ≤ 2E[Y 2] + 2E[Y 4]1/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  E  �  ϵ2 ∥X∥2  2  �  = E  ��  Y − X⊤θ⋆�2  ∥X∥2  2  �  ≤ 2E  ���  X⊤θ⋆�2  + Y 2  �  ∥X∥2  2  �  ≤ 2E  �  Y 2 ∥X∥2  2  �  + 2E  ��  X⊤θ⋆�2  ∥X∥2  2  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Regarding the first term, by Cauchy Schwarz,  E  �  Y 2 ∥X∥2  2  �2  ≤ E  �  Y 4�  E  �  ∥X∥4  2  �  ≤ E  �  Y 4�  E  �  Tr  �  XX⊤ ∥X∥2  2  ��  ≤ E  �  Y 4�  κTr(Σ)2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  25  As for the second term,  E  ��  X⊤θ⋆�2  ∥X∥2  2  �  = E  �  (θ⋆)⊤XX⊤ ∥X∥2  2 θ⋆�  ≤ κTr(Σ)E  �  (θ⋆)⊤Σθ⋆�  ≤ κTr(Σ) ∥θ⋆∥2  2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  E  �  ϵ2 ∥X∥2  2  �  ≤ E  �  Y 4� 1  2 κTr(Σ) + κTr(Σ) ∥θ⋆∥2  Σ ≤ σ2κTr(Σ) ∥θ⋆∥2  Σ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  D  Details on examples  Recall that  Bridge,λ(F) = λ ∥θ⋆∥2  Σ(Σ+λI)−1  (27)  = λ  d  �  j=1  λj  λj + λ(v⊤  j θ⋆)2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  (28)  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='1  Low-rank covariance matrix (Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='3)  Proposition D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='1 (Low-rank covariance matrix with equal singular values).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Consider a  covariance matrix with a low rank r ≪ d and constant eigenvalues (λ1 = λ2 = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' = λr).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Then,  Bridge,λ(F) = λ  r  Tr(Σ) ∥θ⋆∥2  Σ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Using that λ1 = · · · = λr and �r  j=1 λj = Tr(Σ), we have λ1 = · · · = λr = Tr(Σ)  r  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Then Σ(Σ + λI)−1 ⪯ λ−1  r Σ =  r  Tr(Σ)Σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Thus,  Bridge,λ(F) = λ ∥θ⋆∥2  Σ(Σ+λI)−1 = λ  r  Tr(Σ) ∥θ⋆∥2  Σ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='2  Low-rank covariance matrix compatible with θ⋆ (Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='5)  Proposition D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='2 (Low-rank covariance matrix compatible with θ⋆).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Consider a covariance  matrix with a low rank r ≪ d and assume that ⟨θ⋆, v1⟩2 ≥ · · · ≥ ⟨θ⋆, vd⟩2, then  Bridge,λ(F) ≲ λr(log(r) + 1)  Tr(Σ)  ∥θ⋆∥2  Σ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  26  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Recall that  ∥θ⋆∥2  Σ =  d  �  j=1  λj(v⊤  j θ⋆)2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  (29)  Under the assumptions of Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='5, using that (λj)j and  �  (v⊤  j θ⋆)2�  j are decreasing,  then for all k ∈ [r],  k  �  j=1  λj(v⊤  k θ⋆)2 ≤ ∥θ⋆∥2  Σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Thus, for all k ∈ [r],  (v⊤  k θ⋆)2 ≤  ∥θ⋆∥2  Σ  �k  j=1 λj  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Using that �r  j=1 λj = Tr(Σ) and that eigenvalues are decreasing, we have �k  j=1 λj ≥ k  r Tr(Σ)  using Lemma E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Then  Bridge,λ(F) = λ  r  �  k=1  λk  λk + λ(v⊤  k θ⋆)2  ≤ λ  r  �  k=1  (v⊤  k θ⋆)2  ≤ λ∥θ⋆∥2  Σ  r  �  k=1  1  �k  j=1 λj  ≤ λ  r  �  k=1  r  kTr(Σ)  ≤ λ  r  Tr(Σ)  r  �  k=1  1  k  ≲ λ  r  Tr(Σ)(log(r) + 1),  by upper-bounding the Euler-Maclaurin formula.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='3  Spiked covariance matrix (Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='6)  Proposition D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='3 (Spiked model).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Assume that the covariance matrix is decomposed as  Σ = Σ≤r + Σ>r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Suppose that Σ>r ⪯ ηI (small operator norm) and that all non-zero  eigenvalues of Σ≤r are equal, then  Bridge,λ(F) ≤  r  Tr(Σ) − dη ∥θ⋆∥2  Σ + η ∥θ⋆  >∥2  2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  where θ⋆  >r is the projection of θ⋆ on the range of Σ>r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  27  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' One has  Σ(Σ + λI)−1 = Σ≤(Σ + λI)−1 + Σ>(Σ + λI)−1  ⪯ Σ≤(Σ≤ + λI)−1 + Σ>(Σ> + λI)−1  ⪯ 1  µΣ≤ + 1  λΣ>  where µ is the non-zero eigenvalue of Σ≤.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Thus,  Bridge,λ(F) = ∥θ⋆∥2  λΣ(Σ+λI)−1  ≤ ∥θ⋆∥2  λ  µ Σ≤+Σ>  ≤ λ  µ ∥θ⋆∥2  Σ + ∥θ⋆∥2  Σ> .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Using that λmax(Σ>) ≤ η, we have  Bridge,λ(F) ≤ λ  µ ∥θ⋆∥2  Σ + η ∥θ⋆  >∥2  2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Using Weyl’s inequality, for all j ∈ [d], λj(Σ≤+Σ>) ≤ λj(Σ≤)+η.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Summing the previous  inequalities, we get  Tr(Σ) ≤ rµ + dη.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Thus,  µ ≥ Tr(Σ) − dη  r  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  In consequence,  Bridge,λ(F) ≤  r  Tr(Σ) − dη ∥θ⋆∥2  Σ + η ∥θ⋆  >∥2  2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  E  Technical lemmas  Lemma E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Let A, B, V be three symmetric non-negative matrix, if A ⪯ B then A ⊙ V ⪯  B ⊙ V .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Let X ∼ N(0, V ) and θ ∈ Rd,  28  ∥θ∥2  A⊙V = θ⊤A ⊙ V θ  = θ⊤ ��  EXX⊤�  ⊙ A  �  θ  = E  �  θ⊤ ��  XX⊤�  ⊙ A  �  θ  �  = E  �  ��  i,j  θi  ��  XX⊤�  ⊙ A  �  ij θj  �  �  = E  �  ��  i,j  θiXiXjAijθj  �  �  = E  �  ��  i,j  (θiXi) (θjXj) Aij  �  �  = E  �  ∥X ⊙ θ∥2  A  �  ≤ E  �  ∥X ⊙ θ∥2  B  �  = ∥θ∥2  B⊙V  Lemma E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Let A, B be two non-negative symmetric matrices, then A⊙ B is non-negative  symmetric and, for all θ ∈ Rd:  ∥θ∥2  A⊙B ≤ λmax(B) ∥θ∥2  diag(A) ,  where diag(A) is the diagonal matrix containing the diagonal terms of A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Let X ∼ N(0, A), thus A = E  �  XX⊤�  , then for θ ∈ Rd  29  ∥θ∥2  A⊙B = θ⊤A ⊙ Bθ  = θ⊤ ��  EXX⊤�  ⊙ B  �  θ  = E  �  θ⊤ ��  XX⊤�  ⊙ B  �  θ  �  = E  �  ��  i,j  θi  ��  XX⊤�  ⊙ B  �  ij θj  �  �  = E  �  ��  i,j  θiXiXjBijθj  �  �  = E  �  ��  i,j  (θiXi) (θjXj) Bij  �  �  = E  �  (X ⊙ θ)⊤ B (X ⊙ θ)  �  ≥ 0,  using that B is positive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Thus A ⊙ B is positive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Furthermore,  ∥θ∥2  A⊙B = E  �  (X ⊙ θ)⊤ B (X ⊙ θ)  �  ≤ λmax(B)E  �  (X ⊙ θ)⊤ (X ⊙ θ)  �  = λmax(B)E  ��  i  θ2  i X2  i  �  = λmax(B)  �  i  θ2  i E  �  X2  i  �  = λmax(B)  �  i  θ2  i Aii  = λmax(B) ∥θ∥2  diag(A) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Lemma E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Let (vj)j∈[d]a non-decreasing sequence of positive number, and S = �d  j=1 vj,  for all k ∈ [d],  k  �  j=1  vj ≥ k  dS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' We use a absurd m, if �k  j=1 vj < k  dS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content=' Then, using that (vj)j∈[d]are non-decreasing,  kvk < k  dS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  30  Thus vk+1 < 1  dS, summing last elements,  d  �  j=r+1  vj < d − r  d  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Then,  S =  k  �  j=1  vj =  r  �  j=1  vj +  d  �  j=r+1  vj < k  dS + d − r  d  S = S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  Thus, this is absurd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
+page_content='  31' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtFRT4oBgHgl3EQfiDco/content/2301.13585v1.pdf'}
diff --git a/zNAyT4oBgHgl3EQf0vni/vector_store/index.faiss b/zNAyT4oBgHgl3EQf0vni/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..cd59268aaed2faac8c7069b0486bc8af10d84aca
--- /dev/null
+++ b/zNAyT4oBgHgl3EQf0vni/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:165bd219325e73326939f5e0cb5ee357820366757d5762e595f0d6385d030783
+size 7536685
diff --git a/zjlab/vector_store/index.faiss b/zjlab/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..0e4a5877dfd03ebcaddde31716c6fe0a50797a89
--- /dev/null
+++ b/zjlab/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:47d38c518f4a64f4cde84f747919886e662db1e8cdbca5be97e38e92981db4cb
+size 393261
diff --git a/zjlab/vector_store/index.pkl b/zjlab/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..527c2ade33ba49f08f7b09ef8ba8d28c35e200e6
--- /dev/null
+++ b/zjlab/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:a4a3125717d46f6599078f359fabe6a750fd1e663b1de0cb2c0141abfcc2f77b
+size 23166
diff --git a/zjlab/vector_store/index_kw.faiss b/zjlab/vector_store/index_kw.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..8a7617448682f0ad6b856e58af44cc9992a1e332
--- /dev/null
+++ b/zjlab/vector_store/index_kw.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:1431ab242c8c3599c408c67d17dd1913be8ba16f501156b8576f67784db734c8
+size 671789
diff --git a/zjlab/vector_store/index_kw.pkl b/zjlab/vector_store/index_kw.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..555cb0fcfa36bdbb4de38da62d7a7514093750bd
--- /dev/null
+++ b/zjlab/vector_store/index_kw.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:21e38ae2396504d8af0ddd86e552b280f17be5238104667bacfacc3f45ae9c40
+size 5742